TSTP Solution File: GRP038-3 by Moca---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : GRP038-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n012.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 10:52:05 EDT 2022
% Result : Unsatisfiable 10.84s 10.78s
% Output : Proof 10.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP038-3 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : moca.sh %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 06:56:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 10.84/10.78 % SZS status Unsatisfiable
% 10.84/10.78 % SZS output start Proof
% 10.84/10.78 The input problem is unsatisfiable because
% 10.84/10.78
% 10.84/10.78 [1] the following set of Horn clauses is unsatisfiable:
% 10.84/10.78
% 10.84/10.78 product(identity, X, X)
% 10.84/10.78 product(X, identity, X)
% 10.84/10.78 product(inverse(X), X, identity)
% 10.84/10.78 product(X, inverse(X), identity)
% 10.84/10.78 product(X, Y, multiply(X, Y))
% 10.84/10.78 product(X, Y, Z) & product(X, Y, W) ==> Z = W
% 10.84/10.78 product(X, Y, U) & product(Y, Z, V) & product(U, Z, W) ==> product(X, V, W)
% 10.84/10.78 product(X, Y, U) & product(Y, Z, V) & product(X, V, W) ==> product(U, Z, W)
% 10.84/10.78 subgroup_member(A) & subgroup_member(B) & product(A, inverse(B), C) ==> subgroup_member(C)
% 10.84/10.78 subgroup_member(A) ==> subgroup_member(inverse(A))
% 10.84/10.78 subgroup_member(identity)
% 10.84/10.78 subgroup_member(a)
% 10.84/10.78 subgroup_member(b)
% 10.84/10.78 product(a, inverse(b), c)
% 10.84/10.78 subgroup_member(c) ==> \bottom
% 10.84/10.78
% 10.84/10.78 This holds because
% 10.84/10.78
% 10.84/10.78 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 10.84/10.78
% 10.84/10.78 E:
% 10.84/10.78 f1(true__, Z, W) = Z
% 10.84/10.78 f10(true__, A, C) = f9(subgroup_member(A), C)
% 10.84/10.78 f11(product(A, inverse(B), C), B, A, C) = true__
% 10.84/10.78 f11(true__, B, A, C) = f10(subgroup_member(B), A, C)
% 10.84/10.78 f12(subgroup_member(A), A) = true__
% 10.84/10.78 f12(true__, A) = subgroup_member(inverse(A))
% 10.84/10.78 f13(subgroup_member(c)) = true__
% 10.84/10.78 f13(true__) = false__
% 10.84/10.78 f2(product(X, Y, W), X, Y, Z, W) = W
% 10.84/10.78 f2(true__, X, Y, Z, W) = f1(product(X, Y, Z), Z, W)
% 10.84/10.78 f3(true__, X, V, W) = product(X, V, W)
% 10.84/10.78 f4(true__, X, Y, U, V, W) = f3(product(X, Y, U), X, V, W)
% 10.84/10.78 f5(product(U, Z, W), Y, Z, V, X, U, W) = true__
% 10.84/10.78 f5(true__, Y, Z, V, X, U, W) = f4(product(Y, Z, V), X, Y, U, V, W)
% 10.84/10.78 f6(true__, U, Z, W) = product(U, Z, W)
% 10.84/10.78 f7(true__, X, Y, U, Z, W) = f6(product(X, Y, U), U, Z, W)
% 10.84/10.78 f8(product(X, V, W), Y, Z, V, X, U, W) = true__
% 10.84/10.78 f8(true__, Y, Z, V, X, U, W) = f7(product(Y, Z, V), X, Y, U, Z, W)
% 10.84/10.78 f9(true__, C) = subgroup_member(C)
% 10.84/10.78 product(X, Y, multiply(X, Y)) = true__
% 10.84/10.78 product(X, identity, X) = true__
% 10.84/10.78 product(X, inverse(X), identity) = true__
% 10.84/10.78 product(a, inverse(b), c) = true__
% 10.84/10.78 product(identity, X, X) = true__
% 10.84/10.78 product(inverse(X), X, identity) = true__
% 10.84/10.78 subgroup_member(a) = true__
% 10.84/10.78 subgroup_member(b) = true__
% 10.84/10.78 subgroup_member(identity) = true__
% 10.84/10.78 G:
% 10.84/10.78 true__ = false__
% 10.84/10.78
% 10.84/10.78 This holds because
% 10.84/10.78
% 10.84/10.78 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 10.84/10.78
% 10.84/10.78
% 10.84/10.78 f1(f3(true__, Y0, inverse(Y0), Y3), Y3, identity) -> identity
% 10.84/10.78 f1(f3(true__, Y2, identity, Y3), Y3, Y2) -> Y2
% 10.84/10.78 f1(f3(true__, a, inverse(b), Y3), Y3, c) -> c
% 10.84/10.78 f1(f3(true__, identity, Y2, Y3), Y3, Y2) -> Y2
% 10.84/10.78 f1(f3(true__, inverse(Y1), Y1, Y3), Y3, identity) -> identity
% 10.84/10.78 f1(true__, Z, W) -> Z
% 10.84/10.78 f10(f9(true__, Y1), Y1, identity) -> true__
% 10.84/10.78 f10(f9(true__, Y1), identity, inverse(Y1)) -> true__
% 10.84/10.78 f10(f9(true__, Y1), inverse(inverse(Y1)), identity) -> true__
% 10.84/10.78 f10(true__, A, C) -> f9(subgroup_member(A), C)
% 10.84/10.78 f11(product(A, inverse(B), C), B, A, C) -> true__
% 10.84/10.78 f11(true__, B, A, C) -> f10(subgroup_member(B), A, C)
% 10.84/10.78 f12(f9(true__, Y0), Y0) -> true__
% 10.84/10.78 f12(subgroup_member(A), A) -> true__
% 10.84/10.78 f12(true__, A) -> subgroup_member(inverse(A))
% 10.84/10.78 f13(f9(true__, c)) -> true__
% 10.84/10.78 f13(subgroup_member(c)) -> true__
% 10.84/10.78 f13(true__) -> false__
% 10.84/10.78 f2(product(X, Y, W), X, Y, Z, W) -> W
% 10.84/10.78 f2(true__, X, Y, Z, W) -> f1(product(X, Y, Z), Z, W)
% 10.84/10.78 f3(true__, Y0, Y1, multiply(Y0, Y1)) -> true__
% 10.84/10.78 f3(true__, Y0, inverse(Y0), identity) -> true__
% 10.84/10.78 f3(true__, Y2, identity, Y2) -> true__
% 10.84/10.78 f3(true__, a, inverse(b), c) -> true__
% 10.84/10.78 f3(true__, identity, Y2, Y2) -> true__
% 10.84/10.78 f3(true__, inverse(Y1), Y1, identity) -> true__
% 10.84/10.78 f4(f3(true__, Y3, Y1, Y4), Y5, Y3, inverse(Y1), Y4, identity) -> true__
% 10.84/10.78 f4(f3(true__, Y3, Y2, Y4), Y5, Y3, identity, Y4, Y2) -> true__
% 10.84/10.78 f4(f3(true__, Y3, identity, Y4), Y5, Y3, Y2, Y4, Y2) -> true__
% 10.84/10.78 f4(f3(true__, Y3, inverse(Y0), Y4), Y5, Y3, Y0, Y4, identity) -> true__
% 10.84/10.78 f4(true__, X, Y, U, V, W) -> f3(product(X, Y, U), X, V, W)
% 10.84/10.78 f5(product(U, Z, W), Y, Z, V, X, U, W) -> true__
% 10.84/10.78 f5(true__, Y, Z, V, X, U, W) -> f4(product(Y, Z, V), X, Y, U, V, W)
% 10.84/10.78 f6(true__, U, Z, W) -> product(U, Z, W)
% 10.84/10.78 f7(f3(true__, Y3, Y4, Y1), inverse(Y1), Y3, Y5, Y4, identity) -> true__
% 10.84/10.78 f7(f3(true__, Y3, Y4, Y2), identity, Y3, Y5, Y4, Y2) -> true__
% 10.84/10.78 f7(f3(true__, Y3, Y4, identity), Y2, Y3, Y5, Y4, Y2) -> true__
% 10.84/10.78 f7(true__, X, Y, U, Z, W) -> f6(product(X, Y, U), U, Z, W)
% 10.84/10.78 f8(product(X, V, W), Y, Z, V, X, U, W) -> true__
% 10.84/10.78 f8(true__, Y, Z, V, X, U, W) -> f7(product(Y, Z, V), X, Y, U, Z, W)
% 10.84/10.78 f9(f9(true__, inverse(inverse(c))), identity) -> true__
% 10.84/10.78 f9(true__, a) -> true__
% 10.84/10.78 f9(true__, b) -> true__
% 10.84/10.78 f9(true__, c) -> true__
% 10.84/10.78 f9(true__, identity) -> true__
% 10.84/10.78 f9(true__, inverse(a)) -> true__
% 10.84/10.78 f9(true__, inverse(b)) -> true__
% 10.84/10.78 f9(true__, inverse(c)) -> true__
% 10.84/10.78 f9(true__, inverse(identity)) -> true__
% 10.84/10.78 f9(true__, inverse(inverse(a))) -> true__
% 10.84/10.78 f9(true__, inverse(inverse(b))) -> true__
% 10.84/10.78 f9(true__, inverse(inverse(identity))) -> true__
% 10.84/10.78 f9(true__, inverse(inverse(inverse(a)))) -> true__
% 10.84/10.78 f9(true__, inverse(inverse(inverse(b)))) -> true__
% 10.84/10.78 f9(true__, inverse(inverse(inverse(identity)))) -> true__
% 10.84/10.78 f9(true__, inverse(inverse(inverse(inverse(a))))) -> true__
% 10.84/10.78 f9(true__, inverse(inverse(inverse(inverse(b))))) -> true__
% 10.84/10.78 f9(true__, inverse(inverse(inverse(inverse(identity))))) -> true__
% 10.84/10.78 f9(true__, inverse(inverse(inverse(inverse(inverse(a)))))) -> true__
% 10.84/10.78 f9(true__, inverse(inverse(inverse(inverse(inverse(b)))))) -> true__
% 10.84/10.78 f9(true__, inverse(inverse(inverse(inverse(inverse(identity)))))) -> true__
% 10.84/10.78 f9(true__, inverse(inverse(inverse(inverse(inverse(inverse(a))))))) -> true__
% 10.84/10.78 f9(true__, inverse(inverse(inverse(inverse(inverse(inverse(b))))))) -> true__
% 10.84/10.78 f9(true__, inverse(inverse(inverse(inverse(inverse(inverse(identity))))))) -> true__
% 10.84/10.78 false__ -> true__
% 10.84/10.78 inverse(identity) -> identity
% 10.84/10.78 product(X, V, W) -> f3(true__, X, V, W)
% 10.84/10.78 product(X, Y, multiply(X, Y)) -> true__
% 10.84/10.78 product(X, identity, X) -> true__
% 10.84/10.78 product(X, inverse(X), identity) -> true__
% 10.84/10.78 product(a, inverse(b), c) -> true__
% 10.84/10.78 product(identity, X, X) -> true__
% 10.84/10.78 product(inverse(X), X, identity) -> true__
% 10.84/10.78 subgroup_member(C) -> f9(true__, C)
% 10.84/10.78 subgroup_member(a) -> true__
% 10.84/10.78 subgroup_member(b) -> true__
% 10.84/10.78 subgroup_member(identity) -> true__
% 10.84/10.78 with the LPO induced by
% 10.84/10.78 f13 > c > f8 > f7 > f6 > f5 > f4 > f2 > product > f3 > f1 > identity > b > a > f11 > f10 > f12 > subgroup_member > f9 > inverse > multiply > false__ > true__
% 10.84/10.78
% 10.84/10.78 % SZS output end Proof
% 10.84/10.78
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