%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP031-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n010.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 10:52:01 EDT 2022 % Result : Unsatisfiable 6.34s 6.38s % Output : Proof 6.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : GRP031-1 : TPTP v8.1.0. Released v1.0.0. % 0.07/0.13 % Command : moca.sh %s % 0.13/0.35 % Computer : n010.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 : Tue Jun 14 05:18:39 EDT 2022 % 0.13/0.35 % CPUTime : % 6.34/6.38 % SZS status Unsatisfiable % 6.34/6.38 % SZS output start Proof % 6.34/6.38 The input problem is unsatisfiable because % 6.34/6.38 % 6.34/6.38 [1] the following set of Horn clauses is unsatisfiable: % 6.34/6.38 % 6.34/6.38 product(X, Y, multiply(X, Y)) % 6.34/6.38 product(X, Y, Z) & product(X, Y, W) ==> Z = W % 6.34/6.38 product(X, Y, U) & product(Y, Z, V) & product(U, Z, W) ==> product(X, V, W) % 6.34/6.38 product(X, Y, U) & product(Y, Z, V) & product(X, V, W) ==> product(U, Z, W) % 6.34/6.38 product(identity, A, A) % 6.34/6.38 product(inverse(A), A, identity) % 6.34/6.38 product(a, A, identity) ==> \bottom % 6.34/6.38 % 6.34/6.38 This holds because % 6.34/6.38 % 6.34/6.38 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 6.34/6.38 % 6.34/6.38 E: % 6.34/6.38 f1(true__, Z, W) = Z % 6.34/6.38 f2(product(X, Y, W), X, Y, Z, W) = W % 6.34/6.38 f2(true__, X, Y, Z, W) = f1(product(X, Y, Z), Z, W) % 6.34/6.38 f3(true__, X, V, W) = product(X, V, W) % 6.34/6.38 f4(true__, X, Y, U, V, W) = f3(product(X, Y, U), X, V, W) % 6.34/6.38 f5(product(U, Z, W), Y, Z, V, X, U, W) = true__ % 6.34/6.38 f5(true__, Y, Z, V, X, U, W) = f4(product(Y, Z, V), X, Y, U, V, W) % 6.34/6.38 f6(true__, U, Z, W) = product(U, Z, W) % 6.34/6.38 f7(true__, X, Y, U, Z, W) = f6(product(X, Y, U), U, Z, W) % 6.34/6.38 f8(product(X, V, W), Y, Z, V, X, U, W) = true__ % 6.34/6.38 f8(true__, Y, Z, V, X, U, W) = f7(product(Y, Z, V), X, Y, U, Z, W) % 6.34/6.38 f9(product(a, A, identity)) = true__ % 6.34/6.38 f9(true__) = false__ % 6.34/6.38 product(X, Y, multiply(X, Y)) = true__ % 6.34/6.38 product(identity, A, A) = true__ % 6.34/6.38 product(inverse(A), A, identity) = true__ % 6.34/6.38 G: % 6.34/6.38 true__ = false__ % 6.34/6.38 % 6.34/6.38 This holds because % 6.34/6.38 % 6.34/6.38 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 6.34/6.38 % 6.34/6.38 % 6.34/6.38 f1(f3(true__, Y0, Y1, Y3), Y3, multiply(Y0, Y1)) -> multiply(Y0, Y1) % 6.34/6.38 f1(f3(true__, Y0, inverse(Y0), Y3), Y3, identity) -> identity % 6.34/6.38 f1(f3(true__, identity, Y2, Y3), Y3, Y2) -> Y2 % 6.34/6.38 f1(f3(true__, inverse(Y1), Y1, Y3), Y3, identity) -> identity % 6.34/6.38 f1(f3(true__, inverse(identity), Y2, Y3), Y3, Y2) -> Y2 % 6.34/6.38 f1(f3(true__, inverse(inverse(Y2)), identity, Y3), Y3, Y2) -> Y2 % 6.34/6.38 f1(f3(true__, inverse(inverse(identity)), Y2, Y3), Y3, Y2) -> Y2 % 6.34/6.38 f1(true__, Z, W) -> Z % 6.34/6.38 f2(f3(true__, Y0, Y1, Y2), Y0, Y1, Y3, Y2) -> Y2 % 6.34/6.38 f2(product(X, Y, W), X, Y, Z, W) -> W % 6.34/6.38 f2(true__, X, Y, Z, W) -> f1(product(X, Y, Z), Z, W) % 6.34/6.38 f3(f3(true__, Y3, identity, identity), Y3, Y2, Y2) -> true__ % 6.34/6.38 f3(f3(true__, Y3, identity, inverse(Y2)), Y3, Y2, identity) -> true__ % 6.34/6.38 f3(f3(true__, Y3, inverse(Y1), identity), Y3, identity, Y1) -> true__ % 6.34/6.38 f3(f3(true__, Y3, inverse(Y1), inverse(Y1)), Y3, identity, identity) -> true__ % 6.34/6.38 f3(f3(true__, Y3, inverse(identity), identity), Y3, Y2, Y2) -> true__ % 6.34/6.38 f3(true__, Y0, Y1, multiply(Y0, Y1)) -> true__ % 6.34/6.38 f3(true__, Y1, identity, Y1) -> true__ % 6.34/6.38 f3(true__, Y1, inverse(Y1), identity) -> true__ % 6.34/6.38 f3(true__, identity, Y2, Y2) -> true__ % 6.34/6.38 f3(true__, inverse(Y1), Y1, identity) -> true__ % 6.34/6.38 f3(true__, inverse(identity), Y1, Y1) -> true__ % 6.34/6.38 f3(true__, inverse(inverse(Y1)), identity, Y1) -> true__ % 6.34/6.38 f3(true__, inverse(inverse(identity)), Y1, Y1) -> true__ % 6.34/6.38 f3(true__, inverse(inverse(inverse(Y1))), Y1, identity) -> true__ % 6.34/6.38 f3(true__, inverse(inverse(inverse(identity))), Y1, Y1) -> true__ % 6.34/6.38 f3(true__, multiply(inverse(Y0), identity), Y0, identity) -> true__ % 6.34/6.38 f4(f3(true__, Y3, Y1, Y4), Y5, Y3, Y0, Y4, multiply(Y0, Y1)) -> true__ % 6.34/6.38 f4(f3(true__, Y3, Y1, Y4), Y5, Y3, inverse(Y1), Y4, identity) -> true__ % 6.34/6.38 f4(f3(true__, Y3, Y2, Y4), Y5, Y3, identity, Y4, Y2) -> true__ % 6.34/6.38 f4(true__, X, Y, U, V, W) -> f3(product(X, Y, U), X, V, W) % 6.34/6.38 f5(f3(true__, Y0, Y1, Y2), Y3, Y1, Y4, Y5, Y0, Y2) -> true__ % 6.34/6.38 f5(product(U, Z, W), Y, Z, V, X, U, W) -> true__ % 6.34/6.38 f5(true__, Y, Z, V, X, U, W) -> f4(product(Y, Z, V), X, Y, U, V, W) % 6.34/6.38 f6(f3(true__, identity, identity, Y3), Y3, Y2, Y2) -> true__ % 6.34/6.38 f6(f3(true__, identity, inverse(Y1), Y3), Y3, Y1, identity) -> true__ % 6.34/6.38 f6(f3(true__, identity, inverse(identity), Y3), Y3, Y2, Y2) -> true__ % 6.34/6.38 f6(f3(true__, inverse(Y2), identity, Y3), Y3, Y2, identity) -> true__ % 6.34/6.38 f6(true__, U, Z, W) -> product(U, Z, W) % 6.34/6.38 f7(f3(true__, Y3, Y4, Y1), Y0, Y3, Y5, Y4, multiply(Y0, Y1)) -> true__ % 6.34/6.38 f7(f3(true__, Y3, Y4, Y1), inverse(Y1), Y3, Y5, Y4, identity) -> true__ % 6.34/6.38 f7(f3(true__, Y3, Y4, Y2), identity, Y3, Y5, Y4, Y2) -> true__ % 6.34/6.38 f7(true__, X, Y, U, Z, W) -> f6(product(X, Y, U), U, Z, W) % 6.34/6.38 f8(product(X, V, W), Y, Z, V, X, U, W) -> true__ % 6.34/6.38 f8(true__, Y, Z, V, X, U, W) -> f7(product(Y, Z, V), X, Y, U, Z, W) % 6.34/6.38 f9(f3(true__, a, Y0, identity)) -> true__ % 6.34/6.38 f9(product(a, A, identity)) -> true__ % 6.34/6.38 f9(true__) -> false__ % 6.34/6.38 false__ -> true__ % 6.34/6.38 inverse(identity) -> identity % 6.34/6.38 inverse(inverse(identity)) -> identity % 6.34/6.38 multiply(identity, Y0) -> Y0 % 6.34/6.38 multiply(inverse(Y0), Y0) -> identity % 6.34/6.38 multiply(inverse(identity), Y0) -> Y0 % 6.34/6.38 product(X, V, W) -> f3(true__, X, V, W) % 6.34/6.38 product(X, Y, multiply(X, Y)) -> true__ % 6.34/6.38 product(identity, A, A) -> true__ % 6.34/6.38 product(inverse(A), A, identity) -> true__ % 6.34/6.38 with the LPO induced by % 6.34/6.38 a > f9 > inverse > identity > f2 > f1 > f8 > f7 > f6 > f5 > f4 > product > f3 > multiply > false__ > true__ % 6.34/6.38 % 6.34/6.38 % SZS output end Proof % 6.34/6.38 %------------------------------------------------------------------------------