%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP028-3 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 2.65s 0.80s
% Output : Proof 2.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP028-3 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.39 % Computer : n009.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sun Sep 27 09:14:59 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.65/0.80 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 2.65/0.80
% 2.65/0.80 % SZS status Unsatisfiable
% 2.65/0.80
% 2.65/0.82 % SZS output start Proof
% 2.65/0.82 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 2.65/0.82 Axiom 2 (total_function1): product(X, Y, multiply(X, Y)) = true.
% 2.65/0.82 Axiom 3 (right_soln): product(X, right_solution(X, Y), Y) = true.
% 2.65/0.82 Axiom 4 (left_soln): product(left_solution(X, Y), X, Y) = true.
% 2.65/0.82 Axiom 5 (associativity1): ifeq(product(X, Y, Z), true, ifeq(product(W, Y, V), true, ifeq(product(U, W, X), true, product(U, V, Z), true), true), true) = true.
% 2.65/0.82 Axiom 6 (associativity2): 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.
% 2.65/0.82
% 2.65/0.82 Goal 1 (prove_there_is_a_right_identity): product(not_identity(X), X, not_identity(X)) = true.
% 2.65/0.82 The goal is true when:
% 2.65/0.82 X = right_solution(X, X)
% 2.65/0.82
% 2.65/0.82 Proof:
% 2.65/0.82 product(not_identity(right_solution(X, X)), right_solution(X, X), not_identity(right_solution(X, X)))
% 2.65/0.83 = { by axiom 1 (ifeq_axiom) R->L }
% 2.65/0.83 ifeq(true, true, product(not_identity(right_solution(X, X)), right_solution(X, X), not_identity(right_solution(X, X))), true)
% 2.65/0.83 = { by axiom 5 (associativity1) R->L }
% 2.65/0.83 ifeq(ifeq(product(multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X), right_solution(X, X), not_identity(right_solution(X, X))), true, ifeq(product(X, right_solution(X, X), X), true, ifeq(product(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X, multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X)), true, product(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X, not_identity(right_solution(X, X))), true), true), true), true, product(not_identity(right_solution(X, X)), right_solution(X, X), not_identity(right_solution(X, X))), true)
% 2.65/0.83 = { by axiom 2 (total_function1) }
% 2.65/0.83 ifeq(ifeq(product(multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X), right_solution(X, X), not_identity(right_solution(X, X))), true, ifeq(product(X, right_solution(X, X), X), true, ifeq(true, true, product(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X, not_identity(right_solution(X, X))), true), true), true), true, product(not_identity(right_solution(X, X)), right_solution(X, X), not_identity(right_solution(X, X))), true)
% 2.65/0.83 = { by axiom 1 (ifeq_axiom) }
% 2.65/0.83 ifeq(ifeq(product(multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X), right_solution(X, X), not_identity(right_solution(X, X))), true, ifeq(product(X, right_solution(X, X), X), true, product(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X, not_identity(right_solution(X, X))), true), true), true, product(not_identity(right_solution(X, X)), right_solution(X, X), not_identity(right_solution(X, X))), true)
% 2.65/0.83 = { by axiom 3 (right_soln) }
% 2.65/0.83 ifeq(ifeq(product(multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X), right_solution(X, X), not_identity(right_solution(X, X))), true, ifeq(true, true, product(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X, not_identity(right_solution(X, X))), true), true), true, product(not_identity(right_solution(X, X)), right_solution(X, X), not_identity(right_solution(X, X))), true)
% 2.65/0.83 = { by axiom 1 (ifeq_axiom) }
% 2.65/0.83 ifeq(ifeq(product(multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X), right_solution(X, X), not_identity(right_solution(X, X))), true, product(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X, not_identity(right_solution(X, X))), true), true, product(not_identity(right_solution(X, X)), right_solution(X, X), not_identity(right_solution(X, X))), true)
% 2.65/0.83 = { by axiom 1 (ifeq_axiom) R->L }
% 2.65/0.83 ifeq(ifeq(ifeq(true, true, product(multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X), right_solution(X, X), not_identity(right_solution(X, X))), true), true, product(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X, not_identity(right_solution(X, X))), true), true, product(not_identity(right_solution(X, X)), right_solution(X, X), not_identity(right_solution(X, X))), true)
% 2.65/0.83 = { by axiom 4 (left_soln) R->L }
% 2.65/0.83 ifeq(ifeq(ifeq(product(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), true, product(multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X), right_solution(X, X), not_identity(right_solution(X, X))), true), true, product(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X, not_identity(right_solution(X, X))), true), true, product(not_identity(right_solution(X, X)), right_solution(X, X), not_identity(right_solution(X, X))), true)
% 2.65/0.83 = { by axiom 1 (ifeq_axiom) R->L }
% 2.65/0.83 ifeq(ifeq(ifeq(product(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), true, ifeq(true, true, product(multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X), right_solution(X, X), not_identity(right_solution(X, X))), true), true), true, product(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X, not_identity(right_solution(X, X))), true), true, product(not_identity(right_solution(X, X)), right_solution(X, X), not_identity(right_solution(X, X))), true)
% 2.65/0.83 = { by axiom 2 (total_function1) R->L }
% 2.65/0.83 ifeq(ifeq(ifeq(product(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), true, ifeq(product(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X, multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X)), true, product(multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X), right_solution(X, X), not_identity(right_solution(X, X))), true), true), true, product(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X, not_identity(right_solution(X, X))), true), true, product(not_identity(right_solution(X, X)), right_solution(X, X), not_identity(right_solution(X, X))), true)
% 2.65/0.83 = { by axiom 1 (ifeq_axiom) R->L }
% 2.65/0.83 ifeq(ifeq(ifeq(true, true, ifeq(product(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), true, ifeq(product(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X, multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X)), true, product(multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X), right_solution(X, X), not_identity(right_solution(X, X))), true), true), true), true, product(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X, not_identity(right_solution(X, X))), true), true, product(not_identity(right_solution(X, X)), right_solution(X, X), not_identity(right_solution(X, X))), true)
% 2.65/0.83 = { by axiom 2 (total_function1) R->L }
% 2.65/0.83 ifeq(ifeq(ifeq(product(X, right_solution(X, X), multiply(X, right_solution(X, X))), true, ifeq(product(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), true, ifeq(product(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X, multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X)), true, product(multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X), right_solution(X, X), not_identity(right_solution(X, X))), true), true), true), true, product(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X, not_identity(right_solution(X, X))), true), true, product(not_identity(right_solution(X, X)), right_solution(X, X), not_identity(right_solution(X, X))), true)
% 2.65/0.84 = { by axiom 6 (associativity2) }
% 2.65/0.84 ifeq(ifeq(true, true, product(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X, not_identity(right_solution(X, X))), true), true, product(not_identity(right_solution(X, X)), right_solution(X, X), not_identity(right_solution(X, X))), true)
% 2.65/0.84 = { by axiom 1 (ifeq_axiom) }
% 2.65/0.84 ifeq(product(left_solution(multiply(X, right_solution(X, 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)
% 2.65/0.84 = { by axiom 1 (ifeq_axiom) R->L }
% 2.65/0.84 ifeq(true, true, ifeq(product(left_solution(multiply(X, right_solution(X, 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)
% 2.65/0.84 = { by axiom 4 (left_soln) R->L }
% 2.65/0.84 ifeq(product(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), true, ifeq(product(left_solution(multiply(X, right_solution(X, 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)
% 2.65/0.84 = { by axiom 1 (ifeq_axiom) R->L }
% 2.65/0.84 ifeq(true, true, ifeq(product(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), true, ifeq(product(left_solution(multiply(X, right_solution(X, 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)
% 2.65/0.84 = { by axiom 2 (total_function1) R->L }
% 2.65/0.84 ifeq(product(X, right_solution(X, X), multiply(X, right_solution(X, X))), true, ifeq(product(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), true, ifeq(product(left_solution(multiply(X, right_solution(X, 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)
% 2.65/0.84 = { by axiom 6 (associativity2) }
% 2.65/0.84 true
% 2.65/0.84 % SZS output end Proof
% 2.65/0.84
% 2.65/0.84 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------