%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP028-4 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:09:06 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.51s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP028-4 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n005.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 09:15:16 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.51 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.19/0.51
% 0.19/0.51 % SZS status Unsatisfiable
% 0.19/0.51
% 0.19/0.51 % SZS output start Proof
% 0.19/0.51 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.19/0.51 Axiom 2 (right_soln): product(X, right_solution(X, Y), Y) = true.
% 0.19/0.51 Axiom 3 (left_soln): product(left_solution(X, Y), X, Y) = true.
% 0.19/0.51 Axiom 4 (associativity1): ifeq(product(X, Y, Z), true, ifeq(product(W, Z, V), true, ifeq(product(W, X, U), true, product(U, Y, V), true), true), true) = true.
% 0.19/0.51
% 0.19/0.51 Goal 1 (prove_there_is_a_right_identity): product(not_identity(X), X, not_identity(X)) = true.
% 0.19/0.51 The goal is true when:
% 0.19/0.51 X = right_solution(X, X)
% 0.19/0.51
% 0.19/0.51 Proof:
% 0.19/0.51 product(not_identity(right_solution(X, X)), right_solution(X, X), not_identity(right_solution(X, X)))
% 0.19/0.51 = { by axiom 1 (ifeq_axiom) R->L }
% 0.19/0.51 ifeq(true, true, product(not_identity(right_solution(X, X)), right_solution(X, X), not_identity(right_solution(X, X))), true)
% 0.19/0.51 = { by axiom 3 (left_soln) R->L }
% 0.19/0.51 ifeq(product(left_solution(X, not_identity(right_solution(X, X))), X, not_identity(right_solution(X, X))), true, product(not_identity(right_solution(X, X)), right_solution(X, X), not_identity(right_solution(X, X))), true)
% 0.19/0.51 = { by axiom 1 (ifeq_axiom) R->L }
% 0.19/0.51 ifeq(true, true, ifeq(product(left_solution(X, not_identity(right_solution(X, X))), X, not_identity(right_solution(X, X))), true, product(not_identity(right_solution(X, X)), right_solution(X, X), not_identity(right_solution(X, X))), true), true)
% 0.19/0.51 = { by axiom 3 (left_soln) R->L }
% 0.19/0.51 ifeq(product(left_solution(X, not_identity(right_solution(X, X))), X, not_identity(right_solution(X, X))), true, ifeq(product(left_solution(X, not_identity(right_solution(X, X))), X, not_identity(right_solution(X, X))), true, product(not_identity(right_solution(X, X)), right_solution(X, X), not_identity(right_solution(X, X))), true), true)
% 0.19/0.51 = { by axiom 1 (ifeq_axiom) R->L }
% 0.19/0.51 ifeq(true, true, ifeq(product(left_solution(X, not_identity(right_solution(X, X))), X, not_identity(right_solution(X, X))), true, ifeq(product(left_solution(X, not_identity(right_solution(X, X))), X, not_identity(right_solution(X, X))), true, product(not_identity(right_solution(X, X)), right_solution(X, X), not_identity(right_solution(X, X))), true), true), true)
% 0.19/0.51 = { by axiom 2 (right_soln) R->L }
% 0.19/0.52 ifeq(product(X, right_solution(X, X), X), true, ifeq(product(left_solution(X, not_identity(right_solution(X, X))), X, not_identity(right_solution(X, X))), true, ifeq(product(left_solution(X, not_identity(right_solution(X, X))), X, not_identity(right_solution(X, X))), true, product(not_identity(right_solution(X, X)), right_solution(X, X), not_identity(right_solution(X, X))), true), true), true)
% 0.19/0.52 = { by axiom 4 (associativity1) }
% 0.19/0.52 true
% 0.19/0.52 % SZS output end Proof
% 0.19/0.52
% 0.19/0.52 RESULT: Unsatisfiable (the axioms are contradictory).
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