%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP009-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n018.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 10:51:46 EDT 2022 % Result : Unsatisfiable 7.09s 7.11s % Output : Proof 7.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : GRP009-1 : TPTP v8.1.0. Released v1.0.0. % 0.04/0.13 % Command : moca.sh %s % 0.14/0.34 % Computer : n018.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Mon Jun 13 21:29:58 EDT 2022 % 0.14/0.35 % CPUTime : % 7.09/7.11 % SZS status Unsatisfiable % 7.09/7.11 % SZS output start Proof % 7.09/7.11 The input problem is unsatisfiable because % 7.09/7.11 % 7.09/7.11 [1] the following set of Horn clauses is unsatisfiable: % 7.09/7.11 % 7.09/7.11 product(identity, X, X) % 7.09/7.11 product(X, identity, X) % 7.09/7.11 product(inverse(X), X, identity) % 7.09/7.11 product(X, inverse(X), identity) % 7.09/7.11 product(X, Y, multiply(X, Y)) % 7.09/7.11 product(X, Y, Z) & product(X, Y, W) ==> Z = W % 7.09/7.11 product(X, Y, U) & product(Y, Z, V) & product(U, Z, W) ==> product(X, V, W) % 7.09/7.11 product(X, Y, U) & product(Y, Z, V) & product(X, V, W) ==> product(U, Z, W) % 7.09/7.11 product(a, b, identity) % 7.09/7.11 product(c, b, identity) % 7.09/7.11 a = c ==> \bottom % 7.09/7.11 % 7.09/7.11 This holds because % 7.09/7.11 % 7.09/7.11 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 7.09/7.11 % 7.09/7.11 E: % 7.09/7.11 f1(true__, Z, W) = Z % 7.09/7.11 f2(product(X, Y, W), X, Y, Z, W) = W % 7.09/7.11 f2(true__, X, Y, Z, W) = f1(product(X, Y, Z), Z, W) % 7.09/7.11 f3(true__, X, V, W) = product(X, V, W) % 7.09/7.11 f4(true__, X, Y, U, V, W) = f3(product(X, Y, U), X, V, W) % 7.09/7.11 f5(product(U, Z, W), Y, Z, V, X, U, W) = true__ % 7.09/7.11 f5(true__, Y, Z, V, X, U, W) = f4(product(Y, Z, V), X, Y, U, V, W) % 7.09/7.11 f6(true__, U, Z, W) = product(U, Z, W) % 7.09/7.11 f7(true__, X, Y, U, Z, W) = f6(product(X, Y, U), U, Z, W) % 7.09/7.11 f8(product(X, V, W), Y, Z, V, X, U, W) = true__ % 7.09/7.11 f8(true__, Y, Z, V, X, U, W) = f7(product(Y, Z, V), X, Y, U, Z, W) % 7.09/7.11 f9(a) = true__ % 7.09/7.11 f9(c) = false__ % 7.09/7.11 product(X, Y, multiply(X, Y)) = true__ % 7.09/7.11 product(X, identity, X) = true__ % 7.09/7.11 product(X, inverse(X), identity) = true__ % 7.09/7.11 product(a, b, identity) = true__ % 7.09/7.11 product(c, b, identity) = true__ % 7.09/7.11 product(identity, X, X) = true__ % 7.09/7.11 product(inverse(X), X, identity) = true__ % 7.09/7.11 G: % 7.09/7.11 true__ = false__ % 7.09/7.11 % 7.09/7.11 This holds because % 7.09/7.11 % 7.09/7.11 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 7.09/7.11 % 7.09/7.11 % 7.09/7.11 b -> inverse(a) % 7.09/7.11 c -> a % 7.09/7.11 f1(f3(true__, Y0, Y1, Y3), Y3, multiply(Y0, Y1)) -> multiply(Y0, Y1) % 7.09/7.11 f1(f3(true__, Y0, inverse(Y0), Y3), Y3, identity) -> identity % 7.09/7.11 f1(f3(true__, Y2, identity, Y3), Y3, Y2) -> Y2 % 7.09/7.11 f1(f3(true__, a, b, Y3), Y3, identity) -> identity % 7.09/7.11 f1(f3(true__, a, identity, Y1), Y1, c) -> c % 7.09/7.11 f1(f3(true__, c, b, Y3), Y3, identity) -> identity % 7.09/7.11 f1(f3(true__, c, identity, Y3), Y3, a) -> a % 7.09/7.11 f1(f3(true__, c, inverse(a), Y0), Y0, identity) -> identity % 7.09/7.11 f1(f3(true__, identity, Y2, Y3), Y3, Y2) -> Y2 % 7.09/7.11 f1(f3(true__, inverse(Y1), Y1, Y3), Y3, identity) -> identity % 7.09/7.11 f1(f3(true__, inverse(a), c, Y1), Y1, identity) -> identity % 7.09/7.11 f1(f3(true__, inverse(a), identity, Y3), Y3, b) -> b % 7.09/7.11 f1(f3(true__, inverse(inverse(Y2)), identity, Y3), Y3, Y2) -> Y2 % 7.09/7.11 f1(true__, Z, W) -> Z % 7.09/7.11 f2(f3(true__, Y0, Y1, Y2), Y0, Y1, Y3, Y2) -> Y2 % 7.09/7.11 f2(product(X, Y, W), X, Y, Z, W) -> W % 7.09/7.11 f2(true__, X, Y, Z, W) -> f1(product(X, Y, Z), Z, W) % 7.09/7.11 f3(f3(true__, Y0, X0, identity), Y0, identity, inverse(X0)) -> true__ % 7.09/7.11 f3(f3(true__, Y0, a, identity), Y0, identity, inverse(a)) -> true__ % 7.09/7.11 f3(f3(true__, Y0, c, identity), Y0, identity, inverse(a)) -> true__ % 7.09/7.11 f3(f3(true__, Y0, identity, a), Y0, inverse(a), identity) -> true__ % 7.09/7.11 f3(f3(true__, Y0, inverse(a), identity), Y0, identity, c) -> true__ % 7.09/7.11 f3(f3(true__, Y2, Y1, Y3), Y2, Y1, Y3) -> true__ % 7.09/7.11 f3(f3(true__, Y2, a, a), Y2, identity, identity) -> true__ % 7.09/7.11 f3(f3(true__, Y2, identity, Y3), Y2, identity, Y3) -> true__ % 7.09/7.11 f3(f3(true__, Y2, identity, a), Y2, b, identity) -> true__ % 7.09/7.11 f3(f3(true__, Y3, Y2, identity), Y3, Y2, identity) -> true__ % 7.09/7.11 f3(f3(true__, Y3, a, identity), Y3, c, identity) -> true__ % 7.09/7.11 f3(f3(true__, Y3, a, identity), Y3, identity, b) -> true__ % 7.09/7.11 f3(f3(true__, Y3, c, identity), Y3, a, identity) -> true__ % 7.09/7.11 f3(f3(true__, Y3, c, identity), Y3, identity, b) -> true__ % 7.09/7.11 f3(f3(true__, Y3, identity, identity), Y3, Y2, Y2) -> true__ % 7.09/7.11 f3(f3(true__, Y3, identity, inverse(Y2)), Y3, Y2, identity) -> true__ % 7.09/7.11 f3(f3(true__, Y3, inverse(Y1), identity), Y3, identity, Y1) -> true__ % 7.09/7.11 f3(true__, Y0, Y1, multiply(Y0, Y1)) -> true__ % 7.09/7.11 f3(true__, Y0, inverse(Y0), identity) -> true__ % 7.09/7.11 f3(true__, Y1, identity, inverse(inverse(Y1))) -> true__ % 7.09/7.11 f3(true__, Y2, identity, Y2) -> true__ % 7.09/7.11 f3(true__, a, b, identity) -> true__ % 7.09/7.11 f3(true__, a, identity, c) -> true__ % 7.09/7.11 f3(true__, b, identity, inverse(a)) -> true__ % 7.09/7.11 f3(true__, c, b, identity) -> true__ % 7.09/7.11 f3(true__, c, identity, a) -> true__ % 7.09/7.11 f3(true__, c, inverse(a), identity) -> true__ % 7.09/7.11 f3(true__, identity, Y2, Y2) -> true__ % 7.09/7.11 f3(true__, inverse(Y1), Y1, identity) -> true__ % 7.09/7.11 f3(true__, inverse(a), c, identity) -> true__ % 7.09/7.11 f3(true__, inverse(a), identity, b) -> true__ % 7.09/7.11 f3(true__, inverse(c), identity, b) -> true__ % 7.09/7.11 f3(true__, inverse(c), identity, inverse(a)) -> true__ % 7.09/7.11 f3(true__, inverse(inverse(Y1)), identity, Y1) -> true__ % 7.09/7.11 f3(true__, inverse(inverse(a)), identity, c) -> true__ % 7.09/7.11 f3(true__, multiply(Y0, a), inverse(a), Y0) -> true__ % 7.09/7.11 f4(f3(true__, Y0, c, Y2), Y3, Y0, inverse(a), Y2, identity) -> true__ % 7.09/7.11 f4(f3(true__, Y0, inverse(a), Y1), Y2, Y0, c, Y1, identity) -> true__ % 7.09/7.11 f4(f3(true__, Y3, Y1, Y4), Y5, Y3, Y0, Y4, multiply(Y0, Y1)) -> true__ % 7.09/7.11 f4(f3(true__, Y3, Y1, Y4), Y5, Y3, inverse(Y1), Y4, identity) -> true__ % 7.09/7.11 f4(f3(true__, Y3, Y2, Y4), Y5, Y3, identity, Y4, Y2) -> true__ % 7.09/7.11 f4(f3(true__, Y3, b, Y4), Y5, Y3, a, Y4, identity) -> true__ % 7.09/7.11 f4(f3(true__, Y3, b, Y4), Y5, Y3, c, Y4, identity) -> true__ % 7.09/7.11 f4(f3(true__, Y3, identity, Y4), Y5, Y3, Y2, Y4, Y2) -> true__ % 7.09/7.11 f4(f3(true__, Y3, inverse(Y0), Y4), Y5, Y3, Y0, Y4, identity) -> true__ % 7.09/7.11 f4(true__, X, Y, U, V, W) -> f3(product(X, Y, U), X, V, W) % 7.09/7.11 f5(product(U, Z, W), Y, Z, V, X, U, W) -> true__ % 7.09/7.11 f5(true__, Y, Z, V, X, U, W) -> f4(product(Y, Z, V), X, Y, U, V, W) % 7.09/7.11 f6(f3(true__, Y0, a, Y1), Y1, inverse(a), Y0) -> true__ % 7.09/7.11 f6(f3(true__, Y2, a, Y3), Y3, b, Y2) -> true__ % 7.09/7.11 f6(f3(true__, Y2, identity, Y3), Y3, identity, Y2) -> true__ % 7.09/7.11 f6(f3(true__, a, identity, Y0), Y0, inverse(a), identity) -> true__ % 7.09/7.11 f6(f3(true__, a, identity, Y2), Y2, b, identity) -> true__ % 7.09/7.11 f6(f3(true__, a, inverse(a), Y2), Y2, identity, identity) -> true__ % 7.09/7.11 f6(f3(true__, identity, Y0, Y3), Y3, inverse(Y0), identity) -> true__ % 7.09/7.11 f6(f3(true__, identity, Y2, Y3), Y3, identity, Y2) -> true__ % 7.09/7.11 f6(f3(true__, identity, a, Y0), Y0, inverse(a), identity) -> true__ % 7.09/7.11 f6(f3(true__, identity, a, Y3), Y3, b, identity) -> true__ % 7.09/7.11 f6(f3(true__, identity, c, Y0), Y0, inverse(a), identity) -> true__ % 7.09/7.11 f6(f3(true__, identity, c, Y3), Y3, b, identity) -> true__ % 7.09/7.11 f6(f3(true__, identity, c, Y3), Y3, identity, a) -> true__ % 7.09/7.11 f6(f3(true__, identity, identity, Y3), Y3, Y2, Y2) -> true__ % 7.09/7.11 f6(f3(true__, identity, inverse(Y1), Y3), Y3, Y1, identity) -> true__ % 7.09/7.11 f6(f3(true__, inverse(Y2), identity, Y3), Y3, Y2, identity) -> true__ % 7.09/7.11 f6(true__, U, Z, W) -> product(U, Z, W) % 7.09/7.11 f7(f3(true__, Y0, Y1, c), inverse(a), Y0, Y3, Y1, identity) -> true__ % 7.09/7.11 f7(f3(true__, Y0, Y1, inverse(a)), c, Y0, Y2, Y1, identity) -> true__ % 7.09/7.11 f7(f3(true__, Y3, Y4, Y1), Y0, Y3, Y5, Y4, multiply(Y0, Y1)) -> true__ % 7.09/7.11 f7(f3(true__, Y3, Y4, Y1), inverse(Y1), Y3, Y5, Y4, identity) -> true__ % 7.09/7.11 f7(f3(true__, Y3, Y4, Y2), identity, Y3, Y5, Y4, Y2) -> true__ % 7.09/7.11 f7(f3(true__, Y3, Y4, b), a, Y3, Y5, Y4, identity) -> true__ % 7.09/7.11 f7(f3(true__, Y3, Y4, b), c, Y3, Y5, Y4, identity) -> true__ % 7.09/7.11 f7(f3(true__, Y3, Y4, identity), Y2, Y3, Y5, Y4, Y2) -> true__ % 7.09/7.11 f7(f3(true__, Y3, Y4, inverse(Y0)), Y0, Y3, Y5, Y4, identity) -> true__ % 7.09/7.11 f7(true__, X, Y, U, Z, W) -> f6(product(X, Y, U), U, Z, W) % 7.09/7.11 f8(product(X, V, W), Y, Z, V, X, U, W) -> true__ % 7.09/7.11 f8(true__, Y, Z, V, X, U, W) -> f7(product(Y, Z, V), X, Y, U, Z, W) % 7.09/7.11 f9(a) -> true__ % 7.09/7.11 f9(c) -> false__ % 7.09/7.11 false__ -> true__ % 7.09/7.11 inverse(c) -> inverse(a) % 7.09/7.11 inverse(identity) -> identity % 7.09/7.11 inverse(inverse(Y1)) -> Y1 % 7.09/7.11 multiply(Y0, identity) -> Y0 % 7.09/7.11 multiply(Y0, inverse(Y0)) -> identity % 7.09/7.11 multiply(a, b) -> identity % 7.09/7.11 multiply(c, b) -> identity % 7.09/7.11 multiply(c, inverse(a)) -> identity % 7.09/7.11 multiply(identity, Y0) -> Y0 % 7.09/7.11 multiply(inverse(Y0), Y0) -> identity % 7.09/7.11 multiply(inverse(a), c) -> identity % 7.09/7.11 product(X, V, W) -> f3(true__, X, V, W) % 7.09/7.11 product(X, Y, multiply(X, Y)) -> true__ % 7.09/7.11 product(X, identity, X) -> true__ % 7.09/7.11 product(X, inverse(X), identity) -> true__ % 7.09/7.11 product(a, b, identity) -> true__ % 7.09/7.11 product(c, b, identity) -> true__ % 7.09/7.11 product(identity, X, X) -> true__ % 7.09/7.11 product(inverse(X), X, identity) -> true__ % 7.09/7.11 with the LPO induced by % 7.09/7.11 f9 > c > b > a > f5 > f4 > f8 > f7 > f6 > f2 > product > f3 > f1 > multiply > inverse > identity > false__ > true__ % 7.09/7.11 % 7.09/7.11 % SZS output end Proof % 7.09/7.11 %------------------------------------------------------------------------------