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| // 初始事实：定义数字 1 和 2 存在 | ||
| Exist(Literal(1) :: Int) | ||
| Exist(Literal(2) :: Int) | ||
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| // 规则：如果 X 存在，Y 存在，且 X + Y = W，则 W 也存在 | ||
| Exist(Literal(`X) :: Int), Exist(Literal(`Y) :: Int), Literal(`X) :: Int + Literal(`Y) :: Int == Literal(`W) :: Int => Exist(Literal(`W) :: Int) | ||
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| // 查询：数字 5 是否存在？ | ||
| Exist(Literal(5) :: Int) => Query() |
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| // 初始事实 | ||
| Collinear(F, A, C) | ||
| Collinear(F, E, B) | ||
| Collinear(D, B, G) | ||
| Collinear(A, G, C) | ||
| Collinear(D, B, H) | ||
| Collinear(I, A, D) | ||
| Collinear(E, I, C) | ||
| Collinear(E, J, B) | ||
| Length(K, A) == Length(K, F) | ||
| Length(K, F) == Length(K, J) | ||
| Length(L, F) == Length(L, G) | ||
| Length(L, B) == Length(L, F) | ||
| Length(M, G) == Length(M, H) | ||
| Length(M, C) == Length(M, G) | ||
| Length(N, D) == Length(N, H) | ||
| Length(N, H) == Length(N, I) | ||
| Length(O, E) == Length(O, I) | ||
| Length(O, I) == Length(O, J) | ||
| Length(K, P) == Length(K, F) | ||
| Length(L, P) == Length(L, F) | ||
| Length(M, Q) == Length(M, G) | ||
| Length(L, Q) == Length(L, G) | ||
| Length(N, R) == Length(N, H) | ||
| Length(M, R) == Length(M, H) | ||
| Length(K, T) == Length(K, J) | ||
| Length(O, T) == Length(O, J) | ||
| Length(O, S) == Length(O, I) | ||
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| // R1: KA=KF & KF=KJ & KT=KJ => F,A,J,T 共圆 | ||
| Length(`P1, `P2) == Length(`P1, `P3), Length(`P1, `P3) == Length(`P1, `P4), Length(`P1, `P5) == Length(`P1, `P4) => Cyclic(`P3, `P2, `P4, `P5) | ||
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| // R2: F,A,J,T 共圆 & KA=KF & KP=KF & KF=KJ => A,F,P,T 共圆 | ||
| Cyclic(`P1, `P2, `P3, `P4), Length(`P5, `P2) == Length(`P5, `P1), Length(`P5, `P6) == Length(`P5, `P1), Length(`P5, `P1) == Length(`P5, `P3) => Cyclic(`P2, `P1, `P6, `P4) | ||
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| // R3: ND=NH & NR=NH & NH=NI => D,I,R,H 共圆 | ||
| Length(`P1, `P2) == Length(`P1, `P3), Length(`P1, `P4) == Length(`P1, `P3), Length(`P1, `P3) == Length(`P1, `P5) => Cyclic(`P2, `P5, `P4, `P3) | ||
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| // R4: D,I,R,H 共圆 => ∠DHR=∠DIR | ||
| Cyclic(`P1, `P2, `P3, `P4) => Degree(`P1, `P4, `P3) == Degree(`P1, `P2, `P3) | ||
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| // R5: MG=MH & MR=MH & MC=MG => H,C,R,G 共圆 | ||
| Length(`P1, `P2) == Length(`P1, `P3), Length(`P1, `P4) == Length(`P1, `P3), Length(`P1, `P5) == Length(`P1, `P2) => Cyclic(`P3, `P5, `P4, `P2) | ||
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| // R6: H,C,R,G 共圆 => ∠HGC=∠HRC | ||
| Cyclic(`P1, `P2, `P3, `P4) => Degree(`P1, `P4, `P2) == Degree(`P1, `P3, `P2) | ||
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| // R7: I,A,D共线 & ∠DHR=∠DIR & D,B,H共线 & ∠HGC=∠HRC & D,B,G共线 & A,G,C共线 => ∠ACR=∠AIR | ||
| Collinear(`P1, `P2, `P3), Degree(`P3, `P4, `P5) == Degree(`P3, `P1, `P5), Collinear(`P3, `P6, `P4), Degree(`P4, `P7, `P8) == Degree(`P4, `P5, `P8), Collinear(`P3, `P6, `P7), Collinear(`P2, `P7, `P8) => Degree(`P2, `P8, `P5) == Degree(`P2, `P1, `P5) | ||
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| // R8: ∠ACR=∠AIR => A,I,R,C 共圆 | ||
| Degree(`P1, `P2, `P3) == Degree(`P1, `P4, `P3) => Cyclic(`P1, `P4, `P3, `P2) | ||
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| // R9: OE=OI & OI=OJ & OT=OJ & OS=OI => E,I,J,T 共圆 | ||
| Length(`P1, `P2) == Length(`P1, `P3), Length(`P1, `P3) == Length(`P1, `P4), Length(`P1, `P5) == Length(`P1, `P4), Length(`P1, `P6) == Length(`P1, `P3) => Cyclic(`P2, `P3, `P5, `P5) | ||
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| // R11: E,I,J,T 共圆 => ∠JTI=∠JEI | ||
| Cyclic(`P1, `P2, `P3, `P4) => Degree(`P3, `P2, `P4) == Degree(`P3, `P1, `P2) | ||
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| // R12: F,A,J,T 共圆 => ∠AFJ=∠ATJ | ||
| Cyclic(`P1, `P2, `P3, `P4) => Degree(`P2, `P1, `P3) == Degree(`P2, `P4, `P3) | ||
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| // R13: E,I,C共线 & ∠JTI=∠JEI & E,J,B共线 & ∠AFJ=∠ATJ & F,A,C共线 & F,E,B共线 => ∠CAT=∠CIT | ||
| Collinear(`P1, `P2, `P3), Degree(`P4, `P2, `P8) == Degree(`P4, `P1, `P2), Collinear(`P1, `P4, `P6), Degree(`P7, `P5, `P4) == Degree(`P7, `P8, `P4), Collinear(`P5, `P7, `P3), Collinear(`P5, `P1, `P6) => Degree(`P3, `P7, `P8) == Degree(`P3, `P2, `P8) | ||
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| // R14: ∠CAT=∠CIT => A,I,T,C 共圆 | ||
| Degree(`P1, `P2, `P3) == Degree(`P1, `P4, `P3) => Cyclic(`P2, `P4, `P3, `P1) | ||
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| // R15: A,I,R,C 共圆 & A,I,T,C 共圆 => A,C,T,R 共圆 | ||
| Cyclic(`P1, `P2, `P3, `P4), Cyclic(`P1, `P2, `P5, `P4) => Cyclic(`P1, `P4, `P5, `P3) | ||
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| // R16: ∠AFP=∠ATP & F,A,C共线 & ∠CAT=∠CRT => ∠CRT=∠FPT | ||
| Degree(`P1, `P2, `P3) == Degree(`P1, `P4, `P3), Collinear(`P2, `P1, `P5), Degree(`P5, `P1, `P4) == Degree(`P5, `P6, `P4) => Degree(`P5, `P6, `P4) == Degree(`P2, `P3, `P4) | ||
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| // R17: H,C,R,G 共圆 & MG=MH & MQ=MG & MC=MG => C,R,G,Q 共圆 | ||
| Cyclic(`P1, `P2, `P3, `P4), Length(`P5, `P4) == Length(`P5, `P1), Length(`P5, `P6) == Length(`P5, `P4), Length(`P5, `P2) == Length(`P5, `P4) => Cyclic(`P2, `P3, `P4, `P6) | ||
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| // R18: Q,G,C,R 共圆 => ∠QGC=∠QRC | ||
| Cyclic(`P1, `P2, `P3, `P4) => Degree(`P1, `P2, `P3) == Degree(`P1, `P4, `P3) | ||
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| // R19: LP=LF & LF=LG & LQ=LG & LB=LF => F,Q,P,G 共圆 | ||
| Length(`P1, `P2) == Length(`P1, `P3), Length(`P1, `P3) == Length(`P1, `P4), Length(`P1, `P5) == Length(`P1, `P4), Length(`P1, `P6) == Length(`P1, `P3) => Cyclic(`P3, `P5, `P2, `P4) | ||
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| // R20: F,Q,P,G 共圆 => ∠FPQ=∠FGQ | ||
| Cyclic(`P1, `P2, `P3, `P4) => Degree(`P1, `P3, `P2) == Degree(`P1, `P4, `P2) | ||
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| // R21: ∠QGC=∠QRC & A,G,C共线 & ∠FPQ=∠FGQ & F,A,C共线 => ∠FPQ=∠CRQ | ||
| Degree(`P1, `P2, `P3) == Degree(`P1, `P4, `P3), Collinear(`P6, `P2, `P3), Degree(`P5, `P7, `P1) == Degree(`P5, `P2, `P1), Collinear(`P5, `P6, `P3) => Degree(`P5, `P7, `P1) == Degree(`P3, `P4, `P1) | ||
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| // R22: ∠CRT=∠FPT & ∠FPQ=∠CRQ => ∠TPQ=∠TRQ | ||
| Degree(`P1, `P2, `P3) == Degree(`P4, `P5, `P3), Degree(`P4, `P5, `P6) == Degree(`P1, `P2, `P6) => Degree(`P3, `P5, `P6) == Degree(`P3, `P2, `P6) | ||
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| // R23: ∠TPQ=∠TRQ => Q,P,R,T 共圆 | ||
| Degree(`P3, `P5, `P6) == Degree(`P3, `P2, `P6) => Cyclic(`P6, `P5, `P2, `P3) | ||
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| // 查询：A,I,T,C 是否共圆？ | ||
| Cyclic(A, I, T, C) => Query() | ||
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| // 初始事实 | ||
| Collinear(B, A, C) | ||
| Collinear(G, I, E) | ||
| Length(B, A) == Length(B, C) | ||
| Length(D, A) == Length(D, B) | ||
| Length(D, E) == Length(D, B) | ||
| Length(F, B) == Length(F, C) | ||
| Length(F, E) == Length(F, B) | ||
| Length(F, G) == Length(F, B) | ||
| Length(D, I) == Length(D, B) | ||
| Perp(A, G, A, D) | ||
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| // R1: FB = FC & FG = FB & FE = FB ⇒ F 是 △CGE 的外心 | ||
| Length(`P1, `P5) == Length(`P1, `P2), Length(`P1, `P3) == Length(`P1, `P5), Length(`P1, `P4) == Length(`P1, `P5) => Circumcenter(`P1, `P2, `P3, `P4) | ||
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| // R2: FB = FC & FG = FB & FE = FB ⇒ G,B,E,C 共圆 | ||
| Length(`P1, `P3) == Length(`P1, `P5), Length(`P1, `P2) == Length(`P1, `P3), Length(`P1, `P4) == Length(`P1, `P3) => Cyclic(`P2, `P3, `P4, `P5) | ||
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| // R3: G,B,E,C 共圆 ⇒ ∠ECB = ∠EGB | ||
| Cyclic(`P1, `P2, `P3, `P4) => Degree(`P3, `P4, `P2) == Degree(`P3, `P1, `P2) | ||
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| // R4: G,B,E,C 共圆 ⇒ ∠EBC = ∠EGC | ||
| Cyclic(`P1, `P2, `P3, `P4) => Degree(`P3, `P2, `P4) == Degree(`P3, `P1, `P4) | ||
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| // R5: DA = DB & DI = DB & DE = DB ⇒ I,B,E,A 共圆 | ||
| Length(`P1, `P5) == Length(`P1, `P3), Length(`P1, `P2) == Length(`P1, `P3), Length(`P1, `P4) == Length(`P1, `P3) => Cyclic(`P2, `P3, `P4, `P5) | ||
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| // R6: I,B,E,A 共圆 ⇒ ∠IEB = ∠IAB | ||
| Cyclic(`P1, `P2, `P3, `P4) => Degree(`P1, `P3, `P2) == Degree(`P1, `P4, `P2) | ||
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| // R7: B,A,C共线 & ∠EBC = ∠EGC & ∠IEB = ∠IAB & G,I,E共线 ⇒ ∠BAI = ∠ACG | ||
| Collinear(`P1, `P2, `P3), Degree(`P4, `P1, `P3) == Degree(`P4, `P5, `P3), Degree(`P6, `P4, `P1) == Degree(`P6, `P2, `P1), Collinear(`P5, `P6, `P4) => Degree(`P1, `P2, `P6) == Degree(`P2, `P3, `P5) | ||
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| // R8: DA = DB & DI = DB ⇒ D 是 △ABI 的外心 | ||
| Length(`P1, `P2) == Length(`P1, `P3), Length(`P1, `P4) == Length(`P1, `P3) => Circumcenter(`P1, `P2, `P3, `P4) | ||
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| // R9: D是△ABI的外心 & AG ⟂ AD ⇒ ∠BAG = ∠BIA | ||
| Circumcenter(`P1, `P2, `P3, `P4), Perp(`P2, `P5, `P2, `P1) => Degree(`P3, `P2, `P5) == Degree(`P3, `P4, `P2) | ||
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| // R10: B,A,C 共线 & ∠BIA = ∠BAG ⇒ ∠BIA = ∠CAG | ||
| Collinear(`P1, `P2, `P3), Degree(`P1, `P4, `P2) == Degree(`P1, `P2, `P5) => Degree(`P1, `P4, `P2) == Degree(`P3, `P2, `P5) | ||
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| // R11: ∠BAI = ∠ACG & ∠BIA = ∠CAG => AB:CG = AI:CA | ||
| Degree(`P1, `P2, `P4) == Degree(`P2, `P3, `P5), Degree(`P1, `P4, `P2) == Degree(`P3, `P2, `P5) => Ratio(`P2, `P1, `P3, `P5) == Ratio(`P2, `P4, `P3, `P2) | ||
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| // R12: AB:CG = AI:CA & BA = BC => BC:GC = IA:CA | ||
| Ratio(`P2, `P1, `P3, `P5) == Ratio(`P2, `P4, `P3, `P2), Length(`P1, `P2) == Length(`P1, `P3) => Ratio(`P1, `P3, `P5, `P3) == Ratio(`P4, `P2, `P3, `P2) | ||
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| // R13: B,A,C 共线 & ∠EBC = ∠EGC & ∠IEB = ∠IAB & G,I,E 共线 => ∠BCG = ∠CAI | ||
| Collinear(`P1, `P2, `P3), Degree(`P6, `P1, `P3) == Degree(`P6, `P5, `P3), Degree(`P4, `P6, `P1) == Degree(`P4, `P2, `P1), Collinear(`P5, `P4, `P6) => Degree(`P1, `P3, `P5) == Degree(`P3, `P2, `P4) | ||
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| // R14: BC:GC = IA:CA & ∠BCG = ∠CAI => ∠CBG = ∠CIA | ||
| Ratio(`P1, `P3, `P5, `P3) == Ratio(`P4, `P2, `P3, `P2), Degree(`P1, `P3, `P5) == Degree(`P3, `P2, `P4) => Degree(`P3, `P1, `P5) == Degree(`P3, `P4, `P2) | ||
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| // R15: B,A,C 共线 & ∠EBC = ∠EGC & ∠IEB = ∠IAB & G,I,E 共线 => ∠(IA-BC) = ∠GCB | ||
| Collinear(`P1, `P2, `P3), Degree(`P6, `P1, `P3) == Degree(`P6, `P5, `P3), Degree(`P4, `P6, `P1) == Degree(`P4, `P2, `P1), Collinear(`P5, `P4, `P6) => Angle(`P4, `P2, `P1, `P3) == Degree(`P5, `P3, `P1) | ||
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| // R16: ∠(IA-BC) = ∠GCB => IA ∥ GC | ||
| Angle(`P4, `P2, `P1, `P3) == Degree(`P5, `P3, `P1) => Para(`P4, `P2, `P5, `P3) | ||
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| // R17: ∠ECB = ∠EGB & B,A,C 共线 & ∠CBG = ∠CIA & IA ∥ CG => ∠ICG = ∠CEG | ||
| Degree(`P6, `P3, `P1) == Degree(`P6, `P5, `P1), Collinear(`P1, `P2, `P3), Degree(`P3, `P1, `P5) == Degree(`P3, `P4, `P2), Para(`P4, `P2, `P5, `P3) => Degree(`P4, `P3, `P5) == Degree(`P3, `P6, `P5) | ||
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| // R18: F is the circumcenter of CGE & ∠ICG = ∠CEG ⇒ CF ⟂ CI | ||
| Circumcenter(`P1, `P2, `P3, `P4), Degree(`P5, `P2, `P3) == Degree(`P2, `P4, `P3) => Perp(`P2, `P1, `P2, `P5) | ||
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| // 查询：CF ⟂ CI？ | ||
| Perp(C, F, C, I) => Query() |
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| // 初始事实 | ||
| Collinear(B, C, A) | ||
| Collinear(B, D, F) | ||
| Collinear(E, A, G) | ||
| Collinear(C, G, F) | ||
| Collinear(B, E, H) | ||
| Collinear(C, H, F) | ||
| Collinear(C, I, F) | ||
| Collinear(D, I, A) | ||
| Para(A, E, B, D) | ||
| Para(B, E, A, D) | ||
| Length(C, A) == Length(C, B) | ||
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| // R1: B,D,F 共线 & E,A,G 共线 & AE ∥ BD => DF ∥ AG | ||
| Collinear(`P1, `P2, `P3), Collinear(`P4, `P5, `P6), Para(`P5, `P4, `P1, `P2) => Para(`P2, `P3, `P5, `P6) | ||
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| // R2: C,I,F 共线 & C,G,F 共线 => I,F,G 共线 | ||
| Collinear(`P1, `P2, `P3), Collinear(`P1, `P4, `P3) => Collinear(`P2, `P3, `P4) | ||
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| // R3: DF ∥ AG & I,F,G 共线 & D,I,A 共线 => IF/IG = FD/GA | ||
| Para(`P1, `P2, `P3, `P4), Collinear(`P5, `P2, `P4), Collinear(`P1, `P5, `P3) => Ratio(`P5, `P2, `P5, `P4) == Ratio(`P2, `P1, `P4, `P3) | ||
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| // R4: B,D,F 共线 & E,A,G 共线 & AE ∥ BD => BF ∥ AG | ||
| Collinear(`P1, `P2, `P3), Collinear(`P4, `P5, `P6), Para(`P5, `P4, `P1, `P2) => Para(`P1, `P3, `P5, `P6) | ||
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| // R5: BF ∥ AG & B,C,A 共线 & C,G,F 共线 => CB/CA = BF/AG | ||
| Para(`P1, `P2, `P3, `P4), Collinear(`P1, `P5, `P3), Collinear(`P5, `P4, `P2) => Ratio(`P5, `P1, `P5, `P3) == Ratio(`P1, `P2, `P3, `P4) | ||
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| // R6: B,E,H 共线 & D,I,A 共线 & BE ∥ AD => BH ∥ DI | ||
| Collinear(`P1, `P2, `P3), Collinear(`P4, `P5, `P6), Para(`P1, `P2, `P6, `P4) => Para(`P1, `P3, `P4, `P5) | ||
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| // R7: C,I,F 共线 & C,H,F 共线 => F,H,I 共线 | ||
| Collinear(`P1, `P2, `P3), Collinear(`P1, `P4, `P3) => Collinear(`P3, `P4, `P2) | ||
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| // R8: BH ∥ DI & B,D,F 共线 & F,H,I 共线 => BF/DF = HF/IF | ||
| Para(`P1, `P2, `P3, `P4), Collinear(`P1, `P3, `P5), Collinear(`P5, `P2, `P4) => Ratio(`P1, `P5, `P3, `P5) == Ratio(`P2, `P5, `P4, `P5) | ||
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| // R9: IF:IG=FD:GA & CB:CA=BF:AG & CA=CB & BF:DF=HF:IF => HF:IF=IG:IF | ||
| Ratio(`P1, `P2, `P1, `P3) == Ratio(`P2, `P4, `P3, `P5), Ratio(`P6, `P7, `P6, `P5) == Ratio(`P7, `P2, `P5, `P3), Length(`P6, `P5) == Length(`P6, `P7), Ratio(`P7, `P2, `P4, `P2) == Ratio(`P8, `P2, `P1, `P2) => Ratio(`P8, `P2, `P1, `P2) == Ratio(`P1, `P3, `P1, `P2) | ||
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||
| // R10: HF:IF = IG:IF => HF = IG | ||
| Ratio(`P1, `P2, `P3, `P2) == Ratio(`P3, `P4, `P3, `P2) => Length(`P1, `P2) == Length(`P3, `P4) | ||
|
|
||
| // 查询：HF 是否等于 IG？ | ||
| Length(H, F) == Length(I, G) => Query() |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,78 @@ | ||
| // 初始事实 | ||
| Collinear(B, E, C) | ||
| Collinear(A, D, E) | ||
| Collinear(A, F, C) | ||
| Collinear(B, D, F) | ||
| Collinear(B, I, C) | ||
| Collinear(A, G, B) | ||
| Collinear(G, D, C) | ||
| Collinear(A, H, C) | ||
| Collinear(D, I, C) | ||
| Collinear(B, J, F) | ||
| Para(B, H, E, F) | ||
| Para(E, I, A, B) | ||
| Para(J, E, A, C) | ||
| Intro(A) | ||
| Intro(B) | ||
| Intro(C) | ||
| Intro(D) | ||
| Intro(E) | ||
| Intro(F) | ||
| Intro(G) | ||
| Intro(H) | ||
| Intro(I) | ||
| Intro(J) | ||
|
|
||
| // R1: A,B,G 共线 & EI ∥ AB => BG ∥ EI | ||
| Collinear(`P1, `P3, `P2), Para(`P4, `P5, `P1, `P2) => Para(`P2, `P3, `P4, `P5) | ||
|
|
||
| // R2: D,I,C 共线 & G,D,C 共线 => C,G,I 共线 | ||
| Collinear(`P1, `P2, `P3), Collinear(`P4, `P1, `P3) => Collinear(`P3, `P4, `P2) | ||
|
|
||
| // R3: D,I,C 共线 & G,D,C 共线 => D,G,I 共线 | ||
| Collinear(`P1, `P2, `P3), Collinear(`P4, `P1, `P3) => Collinear(`P1, `P4, `P2) | ||
|
|
||
| // R4: BG ∥ EI & B,E,C 共线 & C,G,I 共线 => BC:EC = BG:IE | ||
| Para(`P1, `P2, `P3, `P4), Collinear(`P1, `P3, `P5), Collinear(`P5, `P2, `P4) => Ratio(`P1, `P5, `P3, `P5) == Ratio(`P1, `P2, `P4, `P3) | ||
|
|
||
| // R5: A,H,C 共线 & A,F,C 共线 => C,H,F 共线 | ||
| Collinear(`P1, `P2, `P3), Collinear(`P1, `P4, `P3) => Collinear(`P3, `P2, `P4) | ||
|
|
||
| // R6: BH ∥ EF & B,E,C 共线 & C,H,F 共线 => BC:EC = BH:EF | ||
| Para(`P1, `P2, `P3, `P4), Collinear(`P1, `P3, `P5), Collinear(`P5, `P2, `P4) => Ratio(`P1, `P5, `P3, `P5) == Ratio(`P1, `P2, `P3, `P4) | ||
|
|
||
| // R7: A,H,C 共线 & A,F,C 共线 & BH ∥ EF & AC ∥ EJ => ∠BHF = ∠FEJ | ||
| Collinear(`P1, `P2, `P3), Collinear(`P1, `P4, `P3), Para(`P5, `P2, `P6, `P4), Para(`P7, `P6, `P1, `P3) => Degree(`P5, `P2, `P4) == Degree(`P4, `P6, `P7) | ||
|
|
||
| // R8: B,D,F 共线 & A,H,C 共线 & A,F,C 共线 & B,J,F 共线 & AC ∥ EJ => ∠BFH = ∠FJE | ||
| Collinear(`P1, `P2, `P3), Collinear(`P4, `P5, `P6), Collinear(`P4, `P3, `P6), Collinear(`P1, `P7, `P3), Para(`P7, `P8, `P4, `P6) => Degree(`P1, `P3, `P5) == Degree(`P3, `P7, `P8) | ||
|
|
||
| // R9: ∠BHF = ∠FEJ & ∠BFH = ∠FJE => BH:EF = HF:JE | ||
| Degree(`P1, `P2, `P3) == Degree(`P3, `P4, `P5), Degree(`P1, `P3, `P2) == Degree(`P3, `P5, `P4) => Ratio(`P1, `P2, `P4, `P3) == Ratio(`P2, `P3, `P5, `P4) | ||
|
|
||
| // R10: 传递性推导 | ||
| Ratio(`P1, `P2, `P3, `P2) == Ratio(`P1, `P4, `P5, `P3), Ratio(`P1, `P2, `P3, `P2) == Ratio(`P1, `P6, `P3, `P7), Ratio(`P1, `P6, `P3, `P7) == Ratio(`P6, `P7, `P8, `P3) => Ratio(`P6, `P7, `P8, `P3) == Ratio(`P1, `P4, `P5, `P3) | ||
|
|
||
| // R11: A,G,B 共线 & EI ∥ AB => AG ∥ EI | ||
| Collinear(`P1, `P2, `P3), Para(`P4, `P5, `P1, `P3) => Para(`P1, `P2, `P4, `P5) | ||
|
|
||
| // R12: AG ∥ EI & A,D,E 共线 & G,D,I 共线 => DE:AD = IE:AG | ||
| Para(`P1, `P2, `P3, `P4), Collinear(`P1, `P5, `P3), Collinear(`P2, `P5, `P4) => Ratio(`P5, `P3, `P1, `P5) == Ratio(`P4, `P3, `P1, `P2) | ||
|
|
||
| // R13: A,C,F 共线 & EJ ∥ AC => JE ∥ FA | ||
| Collinear(`P1, `P3, `P2), Para(`P4, `P5, `P1, `P2) => Para(`P4, `P5, `P3, `P1) | ||
|
|
||
| // R14: B,J,F 共线 & B,D,F 共线 => D,J,F 共线 | ||
| Collinear(`P1, `P2, `P3), Collinear(`P1, `P4, `P3) => Collinear(`P4, `P2, `P3) | ||
|
|
||
| // R15: JE ∥ FA & A,D,E 共线 & D,J,F 共线 => DE:AD = JE:AF | ||
| Para(`P1, `P2, `P3, `P4), Collinear(`P4, `P5, `P2), Collinear(`P5, `P1, `P3) => Ratio(`P5, `P2, `P4, `P5) == Ratio(`P1, `P2, `P4, `P3) | ||
|
|
||
| // R16: 传递性推导 | ||
| Ratio(`P1, `P2, `P3, `P1) == Ratio(`P4, `P2, `P3, `P5), Ratio(`P1, `P2, `P3, `P1) == Ratio(`P6, `P2, `P3, `P7) => Ratio(`P6, `P2, `P3, `P7) == Ratio(`P4, `P2, `P3, `P5) | ||
|
|
||
| // R17: 传递性推导 | ||
| Ratio(`P1, `P2, `P3, `P4) == Ratio(`P5, `P6, `P7, `P4), Ratio(`P3, `P4, `P8, `P2) == Ratio(`P7, `P4, `P8, `P6) => Ratio(`P1, `P2, `P8, `P2) == Ratio(`P5, `P6, `P8, `P6) | ||
|
|
||
| // 查询：HF/AF = BG/AG ? | ||
| Ratio(H, F, A, F) == Ratio(B, G, A, G) => Query() |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,37 @@ | ||
| // 初始事实 | ||
| Collinear(A, B, E) | ||
| Collinear(G, C, E) | ||
| Collinear(G, A, D) | ||
| Collinear(H, C, E) | ||
| Perp(B, C, A, D) | ||
| Perp(C, E, A, B) | ||
| Length(F, A) == Length(F, C) | ||
| Length(F, A) == Length(F, B) | ||
| Length(F, H) == Length(F, C) | ||
|
|
||
| // R1: G,C,E 共线 & A,B,E 共线 & H,C,E 共线 & CE ⟂ AB ⇒ ∠GEA = ∠AEH | ||
| Collinear(`P1, `P2, `P3), Collinear(`P4, `P5, `P3), Collinear(`P6, `P2, `P3), Perp(`P2, `P3, `P4, `P5) => Degree(`P1, `P3, `P4) == Degree(`P4, `P3, `P6) | ||
|
|
||
| // R2: FA = FC & FH = FC & FA = FB ⇒ H,A,B,C 共圆 | ||
| Length(`P1, `P2) == Length(`P1, `P3), Length(`P1, `P4) == Length(`P1, `P3), Length(`P1, `P2) == Length(`P1, `P5) => Cyclic(`P4, `P2, `P5, `P3) | ||
|
|
||
| // R3: H,A,B,C 共圆 ⇒ ∠HAB = ∠HCB | ||
| Cyclic(`P1, `P2, `P3, `P4) => Degree(`P1, `P2, `P3) == Degree(`P1, `P4, `P3) | ||
|
|
||
| // R4: G,A,D 共线 & BC ⟂ AD ⇒ CB ⟂ GA | ||
| Collinear(`P1, `P2, `P3), Perp(`P4, `P5, `P2, `P3) => Perp(`P5, `P4, `P1, `P2) | ||
|
|
||
| // R5: H,C,E 共线 & G,C,E 共线 & CE ⟂ AB ⇒ AB ⟂ GH | ||
| Collinear(`P1, `P2, `P3), Collinear(`P4, `P2, `P3), Perp(`P2, `P3, `P5, `P6) => Perp(`P5, `P6, `P4, `P1) | ||
|
|
||
| // R6: CB ⟂ GA & AB ⟂ GH ⇒ ∠(CB-GH) = ∠GAB | ||
| Perp(`P1, `P2, `P3, `P4), Perp(`P4, `P2, `P3, `P5) => Angle(`P1, `P2, `P3, `P5) == Degree(`P3, `P4, `P2) | ||
|
|
||
| // R7: G,A,D共线 & A,B,E共线 & ∠HAB=∠HCB & H,C,E共线 & ∠(CB-GH)=∠GAB & G,C,E共线 ⇒ ∠GAE=∠EAH | ||
| Collinear(`P1, `P2, `P3), Collinear(`P2, `P4, `P5), Degree(`P6, `P2, `P4) == Degree(`P6, `P7, `P4), Collinear(`P6, `P7, `P5), Angle(`P7, `P4, `P1, `P6) == Degree(`P1, `P2, `P4), Collinear(`P1, `P7, `P5) => Degree(`P1, `P2, `P5) == Degree(`P6, `P2, `P5) | ||
|
|
||
| // R8: ∠GEA = ∠AEH & ∠GAE = ∠EAH ⇒ EG = EH | ||
| Degree(`P1, `P2, `P3) == Degree(`P4, `P2, `P3), Degree(`P1, `P3, `P2) == Degree(`P4, `P3, `P2) => Length(`P2, `P1) == Length(`P2, `P4) | ||
|
|
||
| // 查询：EG 是否等于 EH？ | ||
| Length(E, G) == Length(E, H) => Query() |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,30 @@ | ||
| // 初始事实 | ||
| Collinear(D, F, C) | ||
| Collinear(F, B, E) | ||
| Perp(F, H, F, G) | ||
| Length(A, C) == Length(A, B) | ||
| Length(A, D) == Length(A, B) | ||
| Length(A, E) == Length(A, B) | ||
| Length(G, F) == Length(G, B) | ||
| Length(G, D) == Length(G, F) | ||
|
|
||
| // 规则 R1: AD=AB, AE=AB, AC=AB => D,B,E,C 共圆 | ||
| Length(`P1, `P2) == Length(`P1, `P3), Length(`P1, `P4) == Length(`P1, `P3), Length(`P1, `P5) == Length(`P1, `P3) => Cyclic(`P2, `P3, `P4, `P5) | ||
|
|
||
| // 规则 R2: 四点共圆 => 圆周角相等 ∠EBD = ∠ECD | ||
| Cyclic(`P1, `P2, `P3, `P4) => Degree(`P3, `P2, `P1) == Degree(`P3, `P4, `P1) | ||
|
|
||
| // 规则 R3: GF=GB, GD=GF => G 是 △FBD 的外心 | ||
| Length(`P1, `P2) == Length(`P1, `P3), Length(`P1, `P4) == Length(`P1, `P2) => Circumcenter(`P1, `P2, `P3, `P4) | ||
|
|
||
| // 规则 R4: 外心 + 垂直关系 => 弦切角性质 ∠HFB = ∠FDB | ||
| Circumcenter(`P1, `P2, `P3, `P4), Perp(`P2, `P5, `P2, `P1) => Degree(`P5, `P2, `P3) == Degree(`P2, `P4, `P3) | ||
|
|
||
| // 规则 R5: 综合共线与角度相等推导角度关系 ∠HFD = Angle(EC, DF) | ||
| Collinear(`P1, `P2, `P3), Degree(`P4, `P5, `P1) == Degree(`P4, `P3, `P1), Degree(`P6, `P2, `P5) == Degree(`P2, `P1, `P5), Collinear(`P2, `P5, `P4) => Degree(`P6, `P2, `P1) == Angle(`P4, `P3, `P1, `P2) | ||
|
|
||
| // 规则 R6: 角度相等 => FH ∥ EC | ||
| Degree(`P1, `P2, `P3) == Angle(`P4, `P5, `P3, `P2) => Para(`P2, `P1, `P4, `P5) | ||
|
|
||
| // 查询：FH 是否平行于 EC？ | ||
| Para(F, H, E, C) => Query() |
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The conclusion has a duplicate variable
P5 in Cyclic(P2,P3,P5,P5). Based on the premise conditions and comparison with similar rules (R1 at line 31), this should likely be Cyclic(P2,P3,P5,P4) or another appropriate variable representing the fourth point. The duplicateP5will cause incorrect cyclic inference.