%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP013-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n011.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Sat Jul 16 10:51:50 EDT 2022 % Result : Unsatisfiable 7.34s 7.38s % Output : Proof 7.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : GRP013-1 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.13 % Command : moca.sh %s % 0.13/0.35 % Computer : n011.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Mon Jun 13 11:14:48 EDT 2022 % 0.13/0.35 % CPUTime : % 7.34/7.38 % SZS status Unsatisfiable % 7.34/7.38 % SZS output start Proof % 7.34/7.38 The input problem is unsatisfiable because % 7.34/7.38 % 7.34/7.38 [1] the following set of Horn clauses is unsatisfiable: % 7.34/7.38 % 7.34/7.38 product(identity, X, X) % 7.34/7.38 product(X, identity, X) % 7.34/7.38 product(inverse(X), X, identity) % 7.34/7.38 product(X, inverse(X), identity) % 7.34/7.38 product(X, Y, multiply(X, Y)) % 7.34/7.38 product(X, Y, Z) & product(X, Y, W) ==> Z = W % 7.34/7.38 product(X, Y, U) & product(Y, Z, V) & product(U, Z, W) ==> product(X, V, W) % 7.34/7.38 product(X, Y, U) & product(Y, Z, V) & product(X, V, W) ==> product(U, Z, W) % 7.34/7.38 product(A, A, identity) % 7.34/7.38 product(a, b, c) % 7.34/7.38 product(inverse(a), inverse(b), d) % 7.34/7.38 product(inverse(A), inverse(B), C) ==> product(A, C, B) % 7.34/7.38 product(c, d, identity) ==> \bottom % 7.34/7.38 % 7.34/7.38 This holds because % 7.34/7.38 % 7.34/7.38 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 7.34/7.38 % 7.34/7.38 E: % 7.34/7.38 f1(true__, Z, W) = Z % 7.34/7.38 f10(product(c, d, identity)) = true__ % 7.34/7.38 f10(true__) = false__ % 7.34/7.38 f2(product(X, Y, W), X, Y, Z, W) = W % 7.34/7.38 f2(true__, X, Y, Z, W) = f1(product(X, Y, Z), Z, W) % 7.34/7.38 f3(true__, X, V, W) = product(X, V, W) % 7.34/7.38 f4(true__, X, Y, U, V, W) = f3(product(X, Y, U), X, V, W) % 7.34/7.39 f5(product(U, Z, W), Y, Z, V, X, U, W) = true__ % 7.34/7.39 f5(true__, Y, Z, V, X, U, W) = f4(product(Y, Z, V), X, Y, U, V, W) % 7.34/7.39 f6(true__, U, Z, W) = product(U, Z, W) % 7.34/7.39 f7(true__, X, Y, U, Z, W) = f6(product(X, Y, U), U, Z, W) % 7.34/7.39 f8(product(X, V, W), Y, Z, V, X, U, W) = true__ % 7.34/7.39 f8(true__, Y, Z, V, X, U, W) = f7(product(Y, Z, V), X, Y, U, Z, W) % 7.34/7.39 f9(product(inverse(A), inverse(B), C), A, C, B) = true__ % 7.34/7.39 f9(true__, A, C, B) = product(A, C, B) % 7.34/7.39 product(A, A, identity) = true__ % 7.34/7.39 product(X, Y, multiply(X, Y)) = true__ % 7.34/7.39 product(X, identity, X) = true__ % 7.34/7.39 product(X, inverse(X), identity) = true__ % 7.34/7.39 product(a, b, c) = true__ % 7.34/7.39 product(identity, X, X) = true__ % 7.34/7.39 product(inverse(X), X, identity) = true__ % 7.34/7.39 product(inverse(a), inverse(b), d) = true__ % 7.34/7.39 G: % 7.34/7.39 true__ = false__ % 7.34/7.39 % 7.34/7.39 This holds because % 7.34/7.39 % 7.34/7.39 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 7.34/7.39 % 7.34/7.39 % 7.34/7.39 d -> c % 7.34/7.39 f1(f3(true__, Y0, Y1, Y3), Y3, multiply(Y0, Y1)) -> multiply(Y0, Y1) % 7.34/7.39 f1(f3(true__, Y0, inverse(Y0), Y3), Y3, identity) -> identity % 7.34/7.39 f1(f3(true__, Y1, Y1, Y3), Y3, identity) -> identity % 7.34/7.39 f1(f3(true__, a, b, Y0), Y0, d) -> c % 7.34/7.39 f1(f3(true__, inverse(Y1), Y1, Y3), Y3, identity) -> identity % 7.34/7.39 f1(f3(true__, inverse(a), inverse(b), Y3), Y3, d) -> c % 7.34/7.39 f1(f6(true__, Y0, Y1, Y3), Y3, multiply(Y0, Y1)) -> multiply(Y0, Y1) % 7.34/7.39 f1(f6(true__, Y2, identity, Y3), Y3, Y2) -> Y2 % 7.34/7.39 f1(f6(true__, a, b, Y0), Y0, c) -> c % 7.34/7.39 f1(f6(true__, identity, Y2, Y3), Y3, Y2) -> Y2 % 7.34/7.39 f1(true__, Z, W) -> Z % 7.34/7.39 f10(f3(true__, c, d, identity)) -> true__ % 7.34/7.39 f10(product(c, d, identity)) -> true__ % 7.34/7.39 f10(true__) -> false__ % 7.34/7.39 f2(product(X, Y, W), X, Y, Z, W) -> W % 7.34/7.39 f2(true__, X, Y, Z, W) -> f1(f6(true__, X, Y, Z), Z, W) % 7.34/7.39 f3(f3(true__, Y0, identity, Y1), Y0, Y1, identity) -> true__ % 7.34/7.39 f3(f3(true__, Y3, Y2, identity), Y3, Y2, identity) -> true__ % 7.34/7.39 f3(f3(true__, Y3, a, b), Y3, d, identity) -> true__ % 7.34/7.39 f3(f3(true__, Y3, identity, inverse(Y2)), Y3, Y2, identity) -> true__ % 7.34/7.39 f3(f6(true__, Y0, a, b), Y0, c, identity) -> true__ % 7.34/7.39 f3(true__, X, V, W) -> f6(true__, X, V, W) % 7.34/7.39 f3(true__, Y0, Y1, multiply(Y0, Y1)) -> true__ % 7.34/7.39 f3(true__, a, c, b) -> true__ % 7.34/7.39 f3(true__, a, d, b) -> true__ % 7.34/7.39 f4(f3(true__, Y0, Y1, Y2), Y3, Y0, Y1, Y2, identity) -> true__ % 7.34/7.39 f4(f3(true__, Y3, Y1, Y4), Y5, Y3, inverse(Y1), Y4, identity) -> true__ % 7.34/7.39 f4(true__, X, Y, U, V, W) -> f3(f6(true__, X, Y, U), X, V, W) % 7.34/7.39 f5(product(U, Z, W), Y, Z, V, X, U, W) -> true__ % 7.34/7.39 f5(true__, Y, Z, V, X, U, W) -> f4(f6(true__, Y, Z, V), X, Y, U, V, W) % 7.34/7.39 f6(true__, Y0, Y1, multiply(Y0, Y1)) -> true__ % 7.34/7.39 f6(true__, Y1, Y1, identity) -> true__ % 7.34/7.39 f6(true__, Y2, identity, Y2) -> true__ % 7.34/7.39 f6(true__, a, b, c) -> true__ % 7.34/7.39 f6(true__, a, c, b) -> true__ % 7.34/7.39 f6(true__, identity, Y2, Y2) -> true__ % 7.34/7.39 f7(true__, X, Y, U, Z, W) -> f6(f6(true__, X, Y, U), U, Z, W) % 7.34/7.39 f8(product(X, V, W), Y, Z, V, X, U, W) -> true__ % 7.34/7.39 f8(true__, Y, Z, V, X, U, W) -> f7(f6(true__, Y, Z, V), X, Y, U, Z, W) % 7.34/7.39 f9(f3(true__, Y0, Y1, Y2), Y0, Y2, Y1) -> true__ % 7.34/7.39 f9(f6(true__, Y0, Y1, Y2), Y0, Y2, Y1) -> true__ % 7.34/7.39 f9(product(inverse(A), inverse(B), C), A, C, B) -> true__ % 7.34/7.39 f9(true__, A, C, B) -> f6(true__, A, C, B) % 7.34/7.39 false__ -> true__ % 7.34/7.39 inverse(Y1) -> Y1 % 7.34/7.39 multiply(Y0, Y0) -> identity % 7.34/7.39 multiply(Y0, identity) -> Y0 % 7.34/7.39 multiply(a, b) -> c % 7.34/7.39 multiply(identity, Y0) -> Y0 % 7.34/7.39 product(U, Z, W) -> f6(true__, U, Z, W) % 7.34/7.39 product(X, Y, multiply(X, Y)) -> true__ % 7.34/7.39 with the LPO induced by % 7.34/7.39 f9 > f5 > f4 > f3 > f8 > f7 > f2 > product > f6 > f1 > f10 > a > d > c > b > multiply > identity > inverse > false__ > true__ % 7.34/7.39 % 7.34/7.39 % SZS output end Proof % 7.34/7.39 %------------------------------------------------------------------------------