TSTP Solution File: GRP007-1 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP007-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n007.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 10:51:45 EDT 2022
% Result : Unsatisfiable 1.10s 1.29s
% Output : Proof 1.10s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08 % Problem : GRP007-1 : TPTP v8.1.0. Released v1.0.0.
% 0.02/0.09 % Command : moca.sh %s
% 0.09/0.28 % Computer : n007.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 600
% 0.09/0.28 % DateTime : Mon Jun 13 22:43:54 EDT 2022
% 0.09/0.28 % CPUTime :
% 1.10/1.29 % SZS status Unsatisfiable
% 1.10/1.29 % SZS output start Proof
% 1.10/1.29 The input problem is unsatisfiable because
% 1.10/1.29
% 1.10/1.29 [1] the following set of Horn clauses is unsatisfiable:
% 1.10/1.29
% 1.10/1.29 product(identity, X, X)
% 1.10/1.29 product(X, identity, X)
% 1.10/1.29 product(inverse(X), X, identity)
% 1.10/1.29 product(X, inverse(X), identity)
% 1.10/1.29 product(X, Y, multiply(X, Y))
% 1.10/1.29 product(X, Y, Z) & product(X, Y, W) ==> Z = W
% 1.10/1.29 product(X, Y, U) & product(Y, Z, V) & product(U, Z, W) ==> product(X, V, W)
% 1.10/1.29 product(X, Y, U) & product(Y, Z, V) & product(X, V, W) ==> product(U, Z, W)
% 1.10/1.29 product(c, A, A)
% 1.10/1.29 product(A, c, A)
% 1.10/1.29 identity = c ==> \bottom
% 1.10/1.29
% 1.10/1.29 This holds because
% 1.10/1.29
% 1.10/1.29 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 1.10/1.29
% 1.10/1.29 E:
% 1.10/1.29 f1(true__, Z, W) = Z
% 1.10/1.29 f2(product(X, Y, W), X, Y, Z, W) = W
% 1.10/1.29 f2(true__, X, Y, Z, W) = f1(product(X, Y, Z), Z, W)
% 1.10/1.29 f3(true__, X, V, W) = product(X, V, W)
% 1.10/1.29 f4(true__, X, Y, U, V, W) = f3(product(X, Y, U), X, V, W)
% 1.10/1.29 f5(product(U, Z, W), Y, Z, V, X, U, W) = true__
% 1.10/1.29 f5(true__, Y, Z, V, X, U, W) = f4(product(Y, Z, V), X, Y, U, V, W)
% 1.10/1.29 f6(true__, U, Z, W) = product(U, Z, W)
% 1.10/1.29 f7(true__, X, Y, U, Z, W) = f6(product(X, Y, U), U, Z, W)
% 1.10/1.29 f8(product(X, V, W), Y, Z, V, X, U, W) = true__
% 1.10/1.29 f8(true__, Y, Z, V, X, U, W) = f7(product(Y, Z, V), X, Y, U, Z, W)
% 1.10/1.29 f9(c) = false__
% 1.10/1.29 f9(identity) = true__
% 1.10/1.29 product(A, c, A) = true__
% 1.10/1.29 product(X, Y, multiply(X, Y)) = true__
% 1.10/1.29 product(X, identity, X) = true__
% 1.10/1.29 product(X, inverse(X), identity) = true__
% 1.10/1.29 product(c, A, A) = true__
% 1.10/1.29 product(identity, X, X) = true__
% 1.10/1.29 product(inverse(X), X, identity) = true__
% 1.10/1.29 G:
% 1.10/1.29 true__ = false__
% 1.10/1.29
% 1.10/1.29 This holds because
% 1.10/1.29
% 1.10/1.29 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 1.10/1.29
% 1.10/1.29
% 1.10/1.29 f1(f3(true__, Y0, Y1, Y3), Y3, multiply(Y0, Y1)) -> multiply(Y0, Y1)
% 1.10/1.29 f1(f3(true__, Y2, c, Y3), Y3, Y2) -> Y2
% 1.10/1.29 f1(f3(true__, c, Y0, Y1), Y1, Y0) -> Y0
% 1.10/1.29 f1(f3(true__, identity, Y2, Y3), Y3, Y2) -> Y2
% 1.10/1.29 f1(f3(true__, inverse(Y0), Y0, Y1), Y1, c) -> c
% 1.10/1.29 f1(f3(true__, inverse(Y1), Y1, Y3), Y3, identity) -> c
% 1.10/1.29 f1(true__, Z, W) -> Z
% 1.10/1.29 f2(product(X, Y, W), X, Y, Z, W) -> W
% 1.10/1.29 f2(true__, X, Y, Z, W) -> f1(f3(true__, X, Y, Z), Z, W)
% 1.10/1.29 f3(f3(true__, Y0, c, c), Y0, Y1, Y1) -> true__
% 1.10/1.29 f3(f3(true__, Y3, identity, identity), Y3, Y2, Y2) -> true__
% 1.10/1.29 f3(true__, Y0, Y1, multiply(Y0, Y1)) -> true__
% 1.10/1.29 f3(true__, Y0, inverse(Y0), c) -> true__
% 1.10/1.29 f3(true__, Y0, inverse(Y0), identity) -> true__
% 1.10/1.29 f3(true__, Y2, c, Y2) -> true__
% 1.10/1.29 f3(true__, c, Y2, Y2) -> true__
% 1.10/1.29 f3(true__, inverse(Y0), Y0, c) -> true__
% 1.10/1.29 f3(true__, inverse(Y1), Y1, identity) -> true__
% 1.10/1.29 f4(f3(true__, Y3, Y2, Y4), Y5, Y3, identity, Y4, Y2) -> true__
% 1.10/1.29 f4(f3(true__, Y3, c, Y4), Y5, Y3, Y2, Y4, Y2) -> true__
% 1.10/1.29 f4(true__, X, Y, U, V, W) -> f3(f3(true__, X, Y, U), X, V, W)
% 1.10/1.29 f5(product(U, Z, W), Y, Z, V, X, U, W) -> true__
% 1.10/1.29 f5(true__, Y, Z, V, X, U, W) -> f4(f3(true__, Y, Z, V), X, Y, U, V, W)
% 1.10/1.29 f6(f3(true__, c, c, Y0), Y0, Y1, Y1) -> true__
% 1.10/1.29 f6(f3(true__, identity, identity, Y3), Y3, Y2, Y2) -> true__
% 1.10/1.29 f6(true__, U, Z, W) -> f3(true__, U, Z, W)
% 1.10/1.29 f7(f3(true__, Y3, Y4, Y2), identity, Y3, Y5, Y4, Y2) -> true__
% 1.10/1.29 f7(f3(true__, Y3, Y4, c), Y2, Y3, Y5, Y4, Y2) -> true__
% 1.10/1.29 f7(true__, X, Y, U, Z, W) -> f6(f3(true__, X, Y, U), U, Z, W)
% 1.10/1.29 f8(product(X, V, W), Y, Z, V, X, U, W) -> true__
% 1.10/1.29 f8(true__, Y, Z, V, X, U, W) -> f7(f3(true__, Y, Z, V), X, Y, U, Z, W)
% 1.10/1.29 f9(c) -> false__
% 1.10/1.29 f9(identity) -> true__
% 1.10/1.29 identity -> c
% 1.10/1.29 inverse(c) -> c
% 1.10/1.29 product(X, V, W) -> f3(true__, X, V, W)
% 1.10/1.29 true__ -> false__
% 1.10/1.29 with the LPO induced by
% 1.10/1.29 f9 > f2 > f1 > f8 > f5 > f4 > f7 > f6 > product > f3 > inverse > multiply > identity > c > true__ > false__
% 1.10/1.29
% 1.10/1.29 % SZS output end Proof
% 1.10/1.29
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