%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP010-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n029.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 10:51:47 EDT 2022 % Result : Unsatisfiable 7.25s 7.24s % Output : Proof 7.25s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : GRP010-1 : TPTP v8.1.0. Released v1.0.0. % 0.04/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n029.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Tue Jun 14 10:45:41 EDT 2022 % 0.13/0.34 % CPUTime : % 7.25/7.24 % SZS status Unsatisfiable % 7.25/7.24 % SZS output start Proof % 7.25/7.24 The input problem is unsatisfiable because % 7.25/7.24 % 7.25/7.24 [1] the following set of Horn clauses is unsatisfiable: % 7.25/7.24 % 7.25/7.24 product(identity, X, X) % 7.25/7.24 product(X, identity, X) % 7.25/7.24 product(inverse(X), X, identity) % 7.25/7.24 product(X, inverse(X), identity) % 7.25/7.24 product(X, Y, multiply(X, Y)) % 7.25/7.24 product(X, Y, Z) & product(X, Y, W) ==> Z = W % 7.25/7.24 product(X, Y, U) & product(Y, Z, V) & product(U, Z, W) ==> product(X, V, W) % 7.25/7.24 product(X, Y, U) & product(Y, Z, V) & product(X, V, W) ==> product(U, Z, W) % 7.25/7.24 product(a, b, identity) % 7.25/7.24 product(b, a, identity) ==> \bottom % 7.25/7.24 % 7.25/7.24 This holds because % 7.25/7.24 % 7.25/7.24 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 7.25/7.24 % 7.25/7.24 E: % 7.25/7.24 f1(true__, Z, W) = Z % 7.25/7.24 f2(product(X, Y, W), X, Y, Z, W) = W % 7.25/7.24 f2(true__, X, Y, Z, W) = f1(product(X, Y, Z), Z, W) % 7.25/7.24 f3(true__, X, V, W) = product(X, V, W) % 7.25/7.24 f4(true__, X, Y, U, V, W) = f3(product(X, Y, U), X, V, W) % 7.25/7.24 f5(product(U, Z, W), Y, Z, V, X, U, W) = true__ % 7.25/7.24 f5(true__, Y, Z, V, X, U, W) = f4(product(Y, Z, V), X, Y, U, V, W) % 7.25/7.24 f6(true__, U, Z, W) = product(U, Z, W) % 7.25/7.24 f7(true__, X, Y, U, Z, W) = f6(product(X, Y, U), U, Z, W) % 7.25/7.24 f8(product(X, V, W), Y, Z, V, X, U, W) = true__ % 7.25/7.24 f8(true__, Y, Z, V, X, U, W) = f7(product(Y, Z, V), X, Y, U, Z, W) % 7.25/7.24 f9(product(b, a, identity)) = true__ % 7.25/7.24 f9(true__) = false__ % 7.25/7.24 product(X, Y, multiply(X, Y)) = true__ % 7.25/7.24 product(X, identity, X) = true__ % 7.25/7.24 product(X, inverse(X), identity) = true__ % 7.25/7.24 product(a, b, identity) = true__ % 7.25/7.24 product(identity, X, X) = true__ % 7.25/7.24 product(inverse(X), X, identity) = true__ % 7.25/7.24 G: % 7.25/7.24 true__ = false__ % 7.25/7.24 % 7.25/7.24 This holds because % 7.25/7.24 % 7.25/7.24 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 7.25/7.24 % 7.25/7.24 % 7.25/7.24 b -> inverse(a) % 7.25/7.24 f1(f3(true__, Y0, Y1, Y3), Y3, multiply(Y0, Y1)) -> multiply(Y0, Y1) % 7.25/7.24 f1(f3(true__, Y0, inverse(Y0), Y3), Y3, identity) -> identity % 7.25/7.24 f1(f3(true__, Y2, identity, Y3), Y3, Y2) -> Y2 % 7.25/7.24 f1(f3(true__, a, b, Y3), Y3, identity) -> identity % 7.25/7.24 f1(f3(true__, identity, Y2, Y3), Y3, Y2) -> Y2 % 7.25/7.24 f1(f3(true__, inverse(Y1), Y1, Y3), Y3, identity) -> identity % 7.25/7.24 f1(f3(true__, inverse(a), identity, Y3), Y3, b) -> b % 7.25/7.24 f1(true__, Z, W) -> Z % 7.25/7.24 f2(f3(true__, Y0, Y1, Y2), Y0, Y1, Y3, Y2) -> Y2 % 7.25/7.24 f2(product(X, Y, W), X, Y, Z, W) -> W % 7.25/7.24 f2(true__, X, Y, Z, W) -> f1(product(X, Y, Z), Z, W) % 7.25/7.24 f3(f3(true__, Y0, identity, a), Y0, inverse(a), identity) -> true__ % 7.25/7.24 f3(f3(true__, Y2, Y1, Y3), Y2, Y1, Y3) -> true__ % 7.25/7.24 f3(f3(true__, Y2, identity, Y3), Y2, identity, Y3) -> true__ % 7.25/7.24 f3(f3(true__, Y2, identity, a), Y2, b, identity) -> true__ % 7.25/7.24 f3(f3(true__, Y3, Y0, identity), Y3, identity, inverse(Y0)) -> true__ % 7.25/7.24 f3(f3(true__, Y3, Y2, identity), Y3, Y2, identity) -> true__ % 7.25/7.24 f3(f3(true__, Y3, a, identity), Y3, identity, b) -> true__ % 7.25/7.24 f3(f3(true__, Y3, identity, identity), Y3, Y2, Y2) -> true__ % 7.25/7.24 f3(f3(true__, Y3, inverse(Y1), identity), Y3, identity, Y1) -> true__ % 7.25/7.24 f3(true__, Y0, Y1, multiply(Y0, Y1)) -> true__ % 7.25/7.24 f3(true__, Y0, inverse(Y0), identity) -> true__ % 7.25/7.24 f3(true__, Y2, identity, Y2) -> true__ % 7.25/7.24 f3(true__, a, b, identity) -> true__ % 7.25/7.24 f3(true__, a, identity, inverse(b)) -> true__ % 7.25/7.24 f3(true__, a, identity, inverse(inverse(a))) -> true__ % 7.25/7.24 f3(true__, b, identity, inverse(a)) -> true__ % 7.25/7.24 f3(true__, identity, Y2, Y2) -> true__ % 7.25/7.24 f3(true__, identity, b, inverse(a)) -> true__ % 7.25/7.24 f3(true__, inverse(Y1), Y1, identity) -> true__ % 7.25/7.24 f3(true__, inverse(a), identity, b) -> true__ % 7.25/7.24 f3(true__, inverse(inverse(Y1)), identity, Y1) -> true__ % 7.25/7.24 f3(true__, multiply(Y0, a), b, Y0) -> true__ % 7.25/7.24 f3(true__, multiply(Y0, a), inverse(a), Y0) -> true__ % 7.25/7.24 f4(f3(true__, Y3, Y1, Y4), Y5, Y3, Y0, Y4, multiply(Y0, Y1)) -> true__ % 7.25/7.24 f4(f3(true__, Y3, Y1, Y4), Y5, Y3, inverse(Y1), Y4, identity) -> true__ % 7.25/7.24 f4(f3(true__, Y3, Y2, Y4), Y5, Y3, identity, Y4, Y2) -> true__ % 7.25/7.24 f4(f3(true__, Y3, b, Y4), Y5, Y3, a, Y4, identity) -> true__ % 7.25/7.24 f4(f3(true__, Y3, identity, Y4), Y5, Y3, Y2, Y4, Y2) -> true__ % 7.25/7.24 f4(f3(true__, Y3, inverse(Y0), Y4), Y5, Y3, Y0, Y4, identity) -> true__ % 7.25/7.24 f4(true__, X, Y, U, V, W) -> f3(product(X, Y, U), X, V, W) % 7.25/7.24 f5(product(U, Z, W), Y, Z, V, X, U, W) -> true__ % 7.25/7.24 f5(true__, Y, Z, V, X, U, W) -> f4(product(Y, Z, V), X, Y, U, V, W) % 7.25/7.24 f6(f3(true__, Y0, a, Y1), Y1, inverse(a), Y0) -> true__ % 7.25/7.24 f6(f3(true__, Y2, a, Y3), Y3, b, Y2) -> true__ % 7.25/7.24 f6(f3(true__, Y2, identity, Y3), Y3, identity, Y2) -> true__ % 7.25/7.24 f6(f3(true__, a, b, Y2), Y2, identity, identity) -> true__ % 7.25/7.24 f6(f3(true__, a, identity, Y0), Y0, inverse(a), identity) -> true__ % 7.25/7.24 f6(f3(true__, a, identity, Y2), Y2, b, identity) -> true__ % 7.25/7.24 f6(f3(true__, identity, Y2, Y3), Y3, identity, Y2) -> true__ % 7.25/7.24 f6(f3(true__, identity, a, Y0), Y0, inverse(a), identity) -> true__ % 7.25/7.24 f6(f3(true__, identity, a, Y3), Y3, b, identity) -> true__ % 7.25/7.24 f6(f3(true__, identity, identity, Y3), Y3, Y2, Y2) -> true__ % 7.25/7.24 f6(f3(true__, identity, inverse(Y1), Y3), Y3, Y1, identity) -> true__ % 7.25/7.24 f6(true__, U, Z, W) -> product(U, Z, W) % 7.25/7.24 f7(f3(true__, Y3, Y4, Y1), Y0, Y3, Y5, Y4, multiply(Y0, Y1)) -> true__ % 7.25/7.24 f7(f3(true__, Y3, Y4, Y1), inverse(Y1), Y3, Y5, Y4, identity) -> true__ % 7.25/7.24 f7(f3(true__, Y3, Y4, Y2), identity, Y3, Y5, Y4, Y2) -> true__ % 7.25/7.24 f7(f3(true__, Y3, Y4, b), a, Y3, Y5, Y4, identity) -> true__ % 7.25/7.24 f7(f3(true__, Y3, Y4, identity), Y2, Y3, Y5, Y4, Y2) -> true__ % 7.25/7.24 f7(f3(true__, Y3, Y4, inverse(Y0)), Y0, Y3, Y5, Y4, identity) -> true__ % 7.25/7.24 f7(true__, X, Y, U, Z, W) -> f6(product(X, Y, U), U, Z, W) % 7.25/7.24 f8(product(X, V, W), Y, Z, V, X, U, W) -> true__ % 7.25/7.24 f8(true__, Y, Z, V, X, U, W) -> f7(product(Y, Z, V), X, Y, U, Z, W) % 7.25/7.24 f9(f3(true__, b, a, identity)) -> true__ % 7.25/7.24 f9(product(b, a, identity)) -> true__ % 7.25/7.24 f9(true__) -> false__ % 7.25/7.24 false__ -> true__ % 7.25/7.24 inverse(identity) -> identity % 7.25/7.24 multiply(Y0, identity) -> Y0 % 7.25/7.24 multiply(Y0, inverse(Y0)) -> identity % 7.25/7.24 multiply(a, b) -> identity % 7.25/7.24 multiply(identity, Y0) -> Y0 % 7.25/7.24 multiply(inverse(Y0), Y0) -> identity % 7.25/7.24 product(X, V, W) -> f3(true__, X, V, W) % 7.25/7.24 product(X, Y, multiply(X, Y)) -> true__ % 7.25/7.24 product(X, identity, X) -> true__ % 7.25/7.24 product(X, inverse(X), identity) -> true__ % 7.25/7.24 product(a, b, identity) -> true__ % 7.25/7.24 product(identity, X, X) -> true__ % 7.25/7.24 product(inverse(X), X, identity) -> true__ % 7.25/7.24 with the LPO induced by % 7.25/7.24 f2 > f1 > f9 > b > a > f8 > f7 > f6 > f5 > f4 > product > f3 > multiply > inverse > identity > false__ > true__ % 7.25/7.24 % 7.25/7.24 % SZS output end Proof % 7.25/7.24 %------------------------------------------------------------------------------