TSTP Solution File: GRP041-2 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP041-2 : 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 10:52:08 EDT 2022
% Result : Unsatisfiable 1.00s 1.21s
% Output : Proof 1.00s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP041-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n011.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 12:20:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.00/1.21 % SZS status Unsatisfiable
% 1.00/1.21 % SZS output start Proof
% 1.00/1.21 The input problem is unsatisfiable because
% 1.00/1.21
% 1.00/1.21 [1] the following set of Horn clauses is unsatisfiable:
% 1.00/1.21
% 1.00/1.21 product(identity, X, X)
% 1.00/1.21 product(inverse(X), X, identity)
% 1.00/1.21 product(X, Y, multiply(X, Y))
% 1.00/1.21 product(X, Y, Z) & product(X, Y, W) ==> equalish(Z, W)
% 1.00/1.21 product(X, Y, U) & product(Y, Z, V) & product(U, Z, W) ==> product(X, V, W)
% 1.00/1.21 product(X, Y, U) & product(Y, Z, V) & product(X, V, W) ==> product(U, Z, W)
% 1.00/1.21 equalish(X, Y) & product(W, Z, X) ==> product(W, Z, Y)
% 1.00/1.21 equalish(a, a) ==> \bottom
% 1.00/1.21
% 1.00/1.21 This holds because
% 1.00/1.21
% 1.00/1.21 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 1.00/1.21
% 1.00/1.21 E:
% 1.00/1.21 f1(true__, Z, W) = equalish(Z, W)
% 1.00/1.21 f10(product(W, Z, X), X, Y, W, Z) = true__
% 1.00/1.21 f10(true__, X, Y, W, Z) = f9(equalish(X, Y), W, Z, Y)
% 1.00/1.21 f11(equalish(a, a)) = true__
% 1.00/1.21 f11(true__) = false__
% 1.00/1.21 f2(product(X, Y, W), X, Y, Z, W) = true__
% 1.00/1.21 f2(true__, X, Y, Z, W) = f1(product(X, Y, Z), Z, W)
% 1.00/1.21 f3(true__, X, V, W) = product(X, V, W)
% 1.00/1.21 f4(true__, X, Y, U, V, W) = f3(product(X, Y, U), X, V, W)
% 1.00/1.21 f5(product(U, Z, W), Y, Z, V, X, U, W) = true__
% 1.00/1.21 f5(true__, Y, Z, V, X, U, W) = f4(product(Y, Z, V), X, Y, U, V, W)
% 1.00/1.21 f6(true__, U, Z, W) = product(U, Z, W)
% 1.00/1.21 f7(true__, X, Y, U, Z, W) = f6(product(X, Y, U), U, Z, W)
% 1.00/1.21 f8(product(X, V, W), Y, Z, V, X, U, W) = true__
% 1.00/1.21 f8(true__, Y, Z, V, X, U, W) = f7(product(Y, Z, V), X, Y, U, Z, W)
% 1.00/1.21 f9(true__, W, Z, Y) = product(W, Z, Y)
% 1.00/1.21 product(X, Y, multiply(X, Y)) = true__
% 1.00/1.21 product(identity, X, X) = true__
% 1.00/1.21 product(inverse(X), X, identity) = true__
% 1.00/1.21 G:
% 1.00/1.21 true__ = false__
% 1.00/1.21
% 1.00/1.21 This holds because
% 1.00/1.21
% 1.00/1.21 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 1.00/1.21
% 1.00/1.21
% 1.00/1.21 equalish(Z, W) -> f1(true__, Z, W)
% 1.00/1.21 f1(f6(true__, Y0, Y1, Y3), Y3, multiply(Y0, Y1)) -> true__
% 1.00/1.21 f1(f6(true__, identity, Y2, Y3), Y3, Y2) -> true__
% 1.00/1.21 f1(f6(true__, inverse(Y1), Y1, Y3), Y3, identity) -> true__
% 1.00/1.21 f1(true__, Y1, Y1) -> true__
% 1.00/1.21 f1(true__, Y2, multiply(identity, Y2)) -> true__
% 1.00/1.21 f1(true__, multiply(identity, Y0), Y0) -> true__
% 1.00/1.21 f1(true__, multiply(inverse(Y0), Y0), identity) -> true__
% 1.00/1.21 f10(product(W, Z, X), X, Y, W, Z) -> true__
% 1.00/1.21 f10(true__, X, Y, W, Z) -> f9(equalish(X, Y), W, Z, Y)
% 1.00/1.21 f11(equalish(a, a)) -> true__
% 1.00/1.21 f11(f1(true__, a, a)) -> true__
% 1.00/1.21 f11(true__) -> false__
% 1.00/1.21 f2(product(X, Y, W), X, Y, Z, W) -> true__
% 1.00/1.21 f2(true__, X, Y, Z, W) -> f1(product(X, Y, Z), Z, W)
% 1.00/1.21 f3(f6(true__, Y3, identity, identity), Y3, Y2, Y2) -> true__
% 1.00/1.21 f3(true__, X, V, W) -> product(X, V, W)
% 1.00/1.21 f4(f6(true__, Y3, Y1, Y4), Y5, Y3, Y0, Y4, multiply(Y0, Y1)) -> true__
% 1.00/1.21 f4(f6(true__, Y3, Y1, Y4), Y5, Y3, inverse(Y1), Y4, identity) -> true__
% 1.00/1.21 f4(f6(true__, Y3, Y2, Y4), Y5, Y3, identity, Y4, Y2) -> true__
% 1.00/1.21 f4(true__, X, Y, U, V, W) -> f3(product(X, Y, U), X, V, W)
% 1.00/1.21 f5(product(U, Z, W), Y, Z, V, X, U, W) -> true__
% 1.00/1.21 f5(true__, Y, Z, V, X, U, W) -> f4(product(Y, Z, V), X, Y, U, V, W)
% 1.00/1.21 f6(true__, Y0, Y1, multiply(Y0, Y1)) -> true__
% 1.00/1.21 f6(true__, identity, Y2, Y2) -> true__
% 1.00/1.21 f6(true__, inverse(Y1), Y1, identity) -> true__
% 1.00/1.21 f7(f6(true__, Y3, Y4, Y1), inverse(Y1), Y3, Y5, Y4, identity) -> true__
% 1.00/1.21 f7(f6(true__, Y3, Y4, Y2), identity, Y3, Y5, Y4, Y2) -> true__
% 1.00/1.21 f7(true__, X, Y, U, Z, W) -> f6(product(X, Y, U), U, Z, W)
% 1.00/1.21 f8(product(X, V, W), Y, Z, V, X, U, W) -> true__
% 1.00/1.21 f8(true__, Y, Z, V, X, U, W) -> f7(product(Y, Z, V), X, Y, U, Z, W)
% 1.00/1.21 f9(f1(true__, Y2, Y3), identity, Y2, Y3) -> true__
% 1.00/1.21 f9(f1(true__, identity, Y3), inverse(Y1), Y1, Y3) -> true__
% 1.00/1.21 f9(f1(true__, multiply(Y0, Y1), Y3), Y0, Y1, Y3) -> true__
% 1.00/1.21 f9(true__, W, Z, Y) -> product(W, Z, Y)
% 1.00/1.21 false__ -> true__
% 1.00/1.21 product(U, Z, W) -> f6(true__, U, Z, W)
% 1.00/1.21 product(X, Y, multiply(X, Y)) -> true__
% 1.00/1.21 product(identity, X, X) -> true__
% 1.00/1.21 product(inverse(X), X, identity) -> true__
% 1.00/1.21 with the LPO induced by
% 1.00/1.21 a > f11 > f10 > f2 > f8 > f7 > f9 > f5 > f4 > f3 > equalish > f1 > product > f6 > multiply > inverse > identity > false__ > true__
% 1.00/1.21
% 1.00/1.21 % SZS output end Proof
% 1.00/1.21
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