TSTP Solution File: GRP004-2 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP004-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n020.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 10:51:44 EDT 2022
% Result : Unsatisfiable 12.81s 12.77s
% Output : Proof 12.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP004-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : moca.sh %s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 06:40:50 EDT 2022
% 0.13/0.33 % CPUTime :
% 12.81/12.77 % SZS status Unsatisfiable
% 12.81/12.77 % SZS output start Proof
% 12.81/12.77 The input problem is unsatisfiable because
% 12.81/12.77
% 12.81/12.77 [1] the following set of Horn clauses is unsatisfiable:
% 12.81/12.77
% 12.81/12.77 product(identity, X, X)
% 12.81/12.77 product(inverse(X), X, identity)
% 12.81/12.77 product(X, Y, multiply(X, Y))
% 12.81/12.77 product(X, Y, Z) & product(X, Y, W) ==> equalish(Z, W)
% 12.81/12.77 product(X, Y, U) & product(Y, Z, V) & product(U, Z, W) ==> product(X, V, W)
% 12.81/12.77 product(X, Y, U) & product(Y, Z, V) & product(X, V, W) ==> product(U, Z, W)
% 12.81/12.77 equalish(X, Y) & product(W, Z, X) ==> product(W, Z, Y)
% 12.81/12.77 product(a, inverse(a), identity) ==> \bottom
% 12.81/12.77
% 12.81/12.77 This holds because
% 12.81/12.77
% 12.81/12.77 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 12.81/12.77
% 12.81/12.77 E:
% 12.81/12.77 f1(true__, Z, W) = equalish(Z, W)
% 12.81/12.77 f10(product(W, Z, X), X, Y, W, Z) = true__
% 12.81/12.77 f10(true__, X, Y, W, Z) = f9(equalish(X, Y), W, Z, Y)
% 12.81/12.77 f11(product(a, inverse(a), identity)) = true__
% 12.81/12.77 f11(true__) = false__
% 12.81/12.77 f2(product(X, Y, W), X, Y, Z, W) = true__
% 12.81/12.77 f2(true__, X, Y, Z, W) = f1(product(X, Y, Z), Z, W)
% 12.81/12.77 f3(true__, X, V, W) = product(X, V, W)
% 12.81/12.77 f4(true__, X, Y, U, V, W) = f3(product(X, Y, U), X, V, W)
% 12.81/12.77 f5(product(U, Z, W), Y, Z, V, X, U, W) = true__
% 12.81/12.77 f5(true__, Y, Z, V, X, U, W) = f4(product(Y, Z, V), X, Y, U, V, W)
% 12.81/12.77 f6(true__, U, Z, W) = product(U, Z, W)
% 12.81/12.77 f7(true__, X, Y, U, Z, W) = f6(product(X, Y, U), U, Z, W)
% 12.81/12.77 f8(product(X, V, W), Y, Z, V, X, U, W) = true__
% 12.81/12.77 f8(true__, Y, Z, V, X, U, W) = f7(product(Y, Z, V), X, Y, U, Z, W)
% 12.81/12.77 f9(true__, W, Z, Y) = product(W, Z, Y)
% 12.81/12.77 product(X, Y, multiply(X, Y)) = true__
% 12.81/12.77 product(identity, X, X) = true__
% 12.81/12.77 product(inverse(X), X, identity) = true__
% 12.81/12.77 G:
% 12.81/12.77 true__ = false__
% 12.81/12.77
% 12.81/12.77 This holds because
% 12.81/12.77
% 12.81/12.77 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 12.81/12.77
% 12.81/12.77
% 12.81/12.77 equalish(Z, W) -> f1(true__, Z, W)
% 12.81/12.77 f1(f6(true__, Y0, Y1, Y3), Y3, multiply(Y0, Y1)) -> true__
% 12.81/12.77 f1(f6(true__, Y0, inverse(Y0), Y3), Y3, identity) -> true__
% 12.81/12.77 f1(f6(true__, identity, Y2, Y3), Y3, Y2) -> true__
% 12.81/12.77 f1(f6(true__, identity, identity, Y3), Y3, inverse(identity)) -> true__
% 12.81/12.77 f1(f6(true__, identity, inverse(identity), Y3), Y3, identity) -> true__
% 12.81/12.77 f1(f6(true__, identity, multiply(identity, Y2), Y3), Y3, Y2) -> true__
% 12.81/12.77 f1(f6(true__, inverse(Y1), Y1, Y3), Y3, identity) -> true__
% 12.81/12.77 f1(f6(true__, inverse(Y1), Y1, Y3), Y3, inverse(identity)) -> true__
% 12.81/12.77 f1(f6(true__, inverse(identity), Y2, Y3), Y3, Y2) -> true__
% 12.81/12.77 f1(f6(true__, inverse(identity), inverse(identity), Y3), Y3, identity) -> true__
% 12.81/12.77 f1(f6(true__, inverse(inverse(Y2)), identity, Y3), Y3, Y2) -> true__
% 12.81/12.77 f1(f6(true__, inverse(inverse(identity)), Y2, Y3), Y3, Y2) -> true__
% 12.81/12.77 f1(f6(true__, multiply(identity, identity), Y2, Y3), Y3, Y2) -> true__
% 12.81/12.77 f1(true__, Y1, Y1) -> true__
% 12.81/12.77 f1(true__, Y2, multiply(identity, Y2)) -> true__
% 12.81/12.77 f1(true__, Y2, multiply(identity, multiply(identity, Y2))) -> true__
% 12.81/12.77 f1(true__, Y2, multiply(inverse(identity), Y2)) -> true__
% 12.81/12.77 f1(true__, Y2, multiply(inverse(inverse(Y2)), identity)) -> true__
% 12.81/12.77 f1(true__, Y2, multiply(inverse(inverse(identity)), Y2)) -> true__
% 12.81/12.77 f1(true__, Y2, multiply(multiply(identity, identity), Y2)) -> true__
% 12.81/12.77 f1(true__, identity, inverse(identity)) -> true__
% 12.81/12.77 f1(true__, identity, inverse(inverse(identity))) -> true__
% 12.81/12.77 f1(true__, identity, inverse(multiply(identity, identity))) -> true__
% 12.81/12.77 f1(true__, identity, multiply(Y0, inverse(Y0))) -> true__
% 12.81/12.77 f1(true__, identity, multiply(identity, inverse(identity))) -> true__
% 12.81/12.77 f1(true__, identity, multiply(inverse(Y1), Y1)) -> true__
% 12.81/12.77 f1(true__, identity, multiply(inverse(identity), inverse(identity))) -> true__
% 12.81/12.77 f1(true__, inverse(identity), identity) -> true__
% 12.81/12.77 f1(true__, inverse(identity), multiply(identity, identity)) -> true__
% 12.81/12.77 f1(true__, inverse(identity), multiply(inverse(Y1), Y1)) -> true__
% 12.81/12.77 f1(true__, inverse(identity), multiply(inverse(identity), identity)) -> true__
% 12.81/12.77 f1(true__, multiply(identity, Y0), Y0) -> true__
% 12.81/12.77 f1(true__, multiply(identity, identity), inverse(identity)) -> true__
% 12.81/12.77 f1(true__, multiply(identity, inverse(identity)), identity) -> true__
% 12.81/12.77 f1(true__, multiply(identity, multiply(identity, Y0)), Y0) -> true__
% 12.81/12.77 f1(true__, multiply(inverse(X0), X0), inverse(identity)) -> true__
% 12.81/12.77 f1(true__, multiply(inverse(Y0), Y0), identity) -> true__
% 12.81/12.77 f1(true__, multiply(inverse(identity), Y0), Y0) -> true__
% 12.81/12.77 f1(true__, multiply(inverse(identity), identity), inverse(identity)) -> true__
% 12.81/12.77 f1(true__, multiply(inverse(identity), inverse(identity)), identity) -> true__
% 12.81/12.77 f1(true__, multiply(inverse(inverse(Y0)), identity), Y0) -> true__
% 12.81/12.77 f1(true__, multiply(multiply(identity, identity), Y0), Y0) -> true__
% 12.81/12.77 f10(f6(true__, Y0, Y1, Y2), Y2, Y3, Y0, Y1) -> true__
% 12.81/12.77 f10(product(W, Z, X), X, Y, W, Z) -> true__
% 12.81/12.77 f10(true__, X, Y, W, Z) -> f9(equalish(X, Y), W, Z, Y)
% 12.81/12.77 f11(f6(true__, a, inverse(a), identity)) -> true__
% 12.81/12.77 f11(product(a, inverse(a), identity)) -> true__
% 12.81/12.77 f11(true__) -> false__
% 12.81/12.77 f2(f6(true__, Y0, Y1, Y2), Y0, Y1, Y3, Y2) -> true__
% 12.81/12.77 f2(product(X, Y, W), X, Y, Z, W) -> true__
% 12.81/12.77 f2(true__, X, Y, Z, W) -> f1(product(X, Y, Z), Z, W)
% 12.81/12.77 f3(f6(true__, Y3, identity, Y4), Y3, Y2, multiply(Y4, Y2)) -> true__
% 12.81/12.77 f3(f6(true__, Y3, identity, identity), Y3, Y2, Y2) -> true__
% 12.81/12.77 f3(f6(true__, Y3, identity, inverse(Y2)), Y3, Y2, identity) -> true__
% 12.81/12.77 f3(f6(true__, Y3, inverse(Y1), identity), Y3, identity, Y1) -> true__
% 12.81/12.77 f3(true__, X, V, W) -> product(X, V, W)
% 12.81/12.77 f4(f6(true__, Y3, Y1, Y4), Y5, Y3, Y0, Y4, multiply(Y0, Y1)) -> true__
% 12.81/12.77 f4(f6(true__, Y3, Y1, Y4), Y5, Y3, inverse(Y1), Y4, identity) -> true__
% 12.81/12.77 f4(f6(true__, Y3, Y2, Y4), Y5, Y3, identity, Y4, Y2) -> true__
% 12.81/12.77 f4(true__, X, Y, U, V, W) -> f3(product(X, Y, U), X, V, W)
% 12.81/12.77 f5(product(U, Z, W), Y, Z, V, X, U, W) -> true__
% 12.81/12.77 f5(true__, Y, Z, V, X, U, W) -> f4(product(Y, Z, V), X, Y, U, V, W)
% 12.81/12.77 f6(f6(true__, identity, identity, Y3), Y3, Y2, Y2) -> true__
% 12.81/12.77 f6(f6(true__, identity, inverse(Y1), Y3), Y3, Y1, identity) -> true__
% 12.81/12.77 f6(f6(true__, inverse(Y2), identity, Y3), Y3, Y2, identity) -> true__
% 12.81/12.77 f6(true__, Y0, Y1, multiply(Y0, Y1)) -> true__
% 12.81/12.77 f6(true__, Y0, Y1, multiply(identity, multiply(Y0, Y1))) -> true__
% 12.81/12.77 f6(true__, Y0, Y1, multiply(inverse(identity), multiply(Y0, Y1))) -> true__
% 12.81/12.77 f6(true__, Y1, identity, Y1) -> true__
% 12.81/12.77 f6(true__, Y1, inverse(Y1), identity) -> true__
% 12.81/12.77 f6(true__, identity, Y0, multiply(inverse(identity), Y0)) -> true__
% 12.81/12.77 f6(true__, identity, Y0, multiply(inverse(inverse(Y0)), identity)) -> true__
% 12.81/12.77 f6(true__, identity, Y0, multiply(inverse(inverse(identity)), Y0)) -> true__
% 12.81/12.77 f6(true__, identity, Y0, multiply(multiply(identity, identity), Y0)) -> true__
% 12.81/12.77 f6(true__, identity, Y2, Y2) -> true__
% 12.81/12.77 f6(true__, identity, identity, inverse(identity)) -> true__
% 12.81/12.77 f6(true__, identity, identity, multiply(identity, inverse(identity))) -> true__
% 12.81/12.77 f6(true__, identity, identity, multiply(identity, multiply(identity, inverse(identity)))) -> true__
% 12.81/12.77 f6(true__, identity, identity, multiply(inverse(X0), X0)) -> true__
% 12.81/12.77 f6(true__, identity, identity, multiply(inverse(identity), inverse(identity))) -> true__
% 12.81/12.77 f6(true__, identity, inverse(identity), identity) -> true__
% 12.81/12.77 f6(true__, identity, inverse(identity), multiply(identity, identity)) -> true__
% 12.81/12.77 f6(true__, identity, inverse(identity), multiply(identity, multiply(identity, identity))) -> true__
% 12.81/12.77 f6(true__, identity, inverse(identity), multiply(inverse(X0), X0)) -> true__
% 12.81/12.77 f6(true__, identity, inverse(identity), multiply(inverse(identity), identity)) -> true__
% 12.81/12.77 f6(true__, identity, inverse(identity), multiply(multiply(identity, identity), identity)) -> true__
% 12.81/12.77 f6(true__, identity, multiply(identity, Y1), Y1) -> true__
% 12.81/12.77 f6(true__, identity, multiply(identity, identity), inverse(identity)) -> true__
% 12.81/12.77 f6(true__, identity, multiply(identity, identity), multiply(inverse(X0), X0)) -> true__
% 12.81/12.77 f6(true__, identity, multiply(identity, inverse(identity)), identity) -> true__
% 12.81/12.77 f6(true__, identity, multiply(identity, multiply(identity, Y1)), Y1) -> true__
% 12.81/12.77 f6(true__, identity, multiply(identity, multiply(inverse(X0), X0)), identity) -> true__
% 12.81/12.77 f6(true__, identity, multiply(inverse(X0), X0), identity) -> true__
% 12.81/12.77 f6(true__, identity, multiply(inverse(X0), X0), inverse(identity)) -> true__
% 12.81/12.77 f6(true__, identity, multiply(inverse(identity), Y1), Y1) -> true__
% 12.81/12.77 f6(true__, identity, multiply(inverse(identity), identity), inverse(identity)) -> true__
% 12.81/12.78 f6(true__, identity, multiply(inverse(identity), inverse(identity)), identity) -> true__
% 12.81/12.78 f6(true__, identity, multiply(inverse(inverse(Y1)), identity), Y1) -> true__
% 12.81/12.78 f6(true__, identity, multiply(multiply(identity, identity), Y1), Y1) -> true__
% 12.81/12.78 f6(true__, inverse(Y1), Y1, identity) -> true__
% 12.81/12.78 f6(true__, inverse(Y1), Y1, inverse(identity)) -> true__
% 12.81/12.78 f6(true__, inverse(Y1), Y1, multiply(identity, identity)) -> true__
% 12.81/12.78 f6(true__, inverse(Y1), Y1, multiply(identity, inverse(identity))) -> true__
% 12.81/12.78 f6(true__, inverse(Y1), Y1, multiply(identity, multiply(identity, identity))) -> true__
% 12.81/12.78 f6(true__, inverse(Y1), Y1, multiply(inverse(X0), X0)) -> true__
% 12.81/12.78 f6(true__, inverse(Y1), Y1, multiply(inverse(identity), identity)) -> true__
% 12.81/12.78 f6(true__, inverse(Y1), Y1, multiply(inverse(identity), inverse(identity))) -> true__
% 12.81/12.78 f6(true__, inverse(Y1), Y1, multiply(inverse(inverse(identity)), identity)) -> true__
% 12.81/12.78 f6(true__, inverse(Y1), Y1, multiply(multiply(identity, identity), identity)) -> true__
% 12.81/12.78 f6(true__, inverse(identity), Y0, multiply(identity, Y0)) -> true__
% 12.81/12.78 f6(true__, inverse(identity), Y0, multiply(identity, multiply(identity, Y0))) -> true__
% 12.81/12.78 f6(true__, inverse(identity), Y0, multiply(multiply(identity, identity), Y0)) -> true__
% 12.81/12.78 f6(true__, inverse(identity), Y1, Y1) -> true__
% 12.81/12.78 f6(true__, inverse(identity), identity, inverse(identity)) -> true__
% 12.81/12.78 f6(true__, inverse(identity), inverse(identity), identity) -> true__
% 12.81/12.78 f6(true__, inverse(identity), inverse(identity), multiply(identity, identity)) -> true__
% 12.81/12.78 f6(true__, inverse(identity), multiply(identity, Y1), Y1) -> true__
% 12.81/12.78 f6(true__, inverse(identity), multiply(identity, identity), inverse(identity)) -> true__
% 12.81/12.78 f6(true__, inverse(identity), multiply(identity, inverse(identity)), identity) -> true__
% 12.81/12.78 f6(true__, inverse(identity), multiply(identity, multiply(identity, Y1)), Y1) -> true__
% 12.81/12.78 f6(true__, inverse(identity), multiply(inverse(X0), X0), identity) -> true__
% 12.81/12.78 f6(true__, inverse(identity), multiply(inverse(identity), Y1), Y1) -> true__
% 12.81/12.78 f6(true__, inverse(inverse(Y1)), identity, Y1) -> true__
% 12.81/12.78 f6(true__, inverse(inverse(identity)), Y1, Y1) -> true__
% 12.81/12.78 f6(true__, inverse(inverse(inverse(Y1))), Y1, identity) -> true__
% 12.81/12.78 f6(true__, inverse(inverse(inverse(identity))), Y1, Y1) -> true__
% 12.81/12.78 f6(true__, multiply(identity, identity), Y0, multiply(identity, Y0)) -> true__
% 12.81/12.78 f6(true__, multiply(identity, identity), Y1, Y1) -> true__
% 12.81/12.78 f6(true__, multiply(identity, identity), identity, inverse(identity)) -> true__
% 12.81/12.78 f6(true__, multiply(identity, identity), inverse(identity), identity) -> true__
% 12.81/12.78 f6(true__, multiply(identity, identity), multiply(identity, Y1), Y1) -> true__
% 12.81/12.78 f6(true__, multiply(identity, inverse(Y0)), Y0, identity) -> true__
% 12.81/12.78 f6(true__, multiply(identity, inverse(identity)), Y1, Y1) -> true__
% 12.81/12.78 f6(true__, multiply(inverse(X0), X0), Y1, Y1) -> true__
% 12.81/12.78 f6(true__, multiply(inverse(Y0), identity), Y0, identity) -> true__
% 12.81/12.78 f7(f6(true__, Y3, Y4, Y1), Y0, Y3, Y5, Y4, multiply(Y0, Y1)) -> true__
% 12.81/12.78 f7(f6(true__, Y3, Y4, Y1), inverse(Y1), Y3, Y5, Y4, identity) -> true__
% 12.81/12.78 f7(f6(true__, Y3, Y4, Y2), identity, Y3, Y5, Y4, Y2) -> true__
% 12.81/12.78 f7(true__, X, Y, U, Z, W) -> f6(product(X, Y, U), U, Z, W)
% 12.81/12.78 f8(product(X, V, W), Y, Z, V, X, U, W) -> true__
% 12.81/12.78 f8(true__, Y, Z, V, X, U, W) -> f7(product(Y, Z, V), X, Y, U, Z, W)
% 12.81/12.78 f9(f1(true__, Y2, Y3), identity, Y2, Y3) -> true__
% 12.81/12.78 f9(f1(true__, Y2, Y3), identity, multiply(identity, Y2), Y3) -> true__
% 12.81/12.78 f9(f1(true__, Y2, Y3), inverse(identity), Y2, Y3) -> true__
% 12.81/12.78 f9(f1(true__, Y2, Y3), inverse(inverse(Y2)), identity, Y3) -> true__
% 12.81/12.78 f9(f1(true__, Y2, Y3), inverse(inverse(identity)), Y2, Y3) -> true__
% 12.81/12.78 f9(f1(true__, Y2, Y3), multiply(identity, identity), Y2, Y3) -> true__
% 12.81/12.78 f9(f1(true__, identity, Y3), Y0, inverse(Y0), Y3) -> true__
% 12.81/12.78 f9(f1(true__, identity, Y3), identity, inverse(identity), Y3) -> true__
% 12.81/12.78 f9(f1(true__, identity, Y3), inverse(Y1), Y1, Y3) -> true__
% 12.81/12.78 f9(f1(true__, inverse(identity), Y3), identity, identity, Y3) -> true__
% 12.81/12.78 f9(f1(true__, multiply(Y0, Y1), Y3), Y0, Y1, Y3) -> true__
% 12.81/12.78 f9(true__, W, Z, Y) -> product(W, Z, Y)
% 12.81/12.78 false__ -> true__
% 12.81/12.78 product(U, Z, W) -> f6(true__, U, Z, W)
% 12.81/12.78 product(X, Y, multiply(X, Y)) -> true__
% 12.81/12.78 product(identity, X, X) -> true__
% 12.81/12.78 product(inverse(X), X, identity) -> true__
% 12.81/12.78 with the LPO induced by
% 12.81/12.78 a > f11 > f10 > f2 > f8 > f7 > f9 > f5 > f4 > f3 > equalish > f1 > product > f6 > multiply > inverse > identity > false__ > true__
% 12.81/12.78
% 12.81/12.78 % SZS output end Proof
% 12.81/12.78
%------------------------------------------------------------------------------