TSTP Solution File: GRP013-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% 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
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