%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP028-2 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/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 0.17s 0.46s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP028-2 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n005.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 09:15:01 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.46 Command-line arguments: --no-flatten-goal
% 0.17/0.46
% 0.17/0.46 % SZS status Unsatisfiable
% 0.17/0.46
% 0.17/0.48 % SZS output start Proof
% 0.17/0.48 Axiom 1 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.17/0.48 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.17/0.48 Axiom 3 (total_function1): product(X, Y, multiply(X, Y)) = true.
% 0.17/0.48 Axiom 4 (right_soln): product(X, right_solution(X, Y), Y) = true.
% 0.17/0.48 Axiom 5 (left_soln): product(left_solution(X, Y), X, Y) = true.
% 0.17/0.48 Axiom 6 (total_function2): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 0.17/0.48 Axiom 7 (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.
% 0.17/0.48
% 0.17/0.48 Lemma 8: ifeq2(product(X, Y, Z), true, multiply(X, Y), Z) = Z.
% 0.17/0.48 Proof:
% 0.17/0.48 ifeq2(product(X, Y, Z), true, multiply(X, Y), Z)
% 0.17/0.48 = { by axiom 1 (ifeq_axiom) R->L }
% 0.17/0.48 ifeq2(product(X, Y, Z), true, ifeq2(true, true, multiply(X, Y), Z), Z)
% 0.17/0.48 = { by axiom 3 (total_function1) R->L }
% 0.17/0.48 ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, multiply(X, Y)), true, multiply(X, Y), Z), Z)
% 0.17/0.48 = { by axiom 6 (total_function2) }
% 0.17/0.48 Z
% 0.17/0.48
% 0.17/0.48 Lemma 9: multiply(left_solution(X, Y), X) = Y.
% 0.17/0.48 Proof:
% 0.17/0.48 multiply(left_solution(X, Y), X)
% 0.17/0.48 = { by axiom 1 (ifeq_axiom) R->L }
% 0.17/0.48 ifeq2(true, true, multiply(left_solution(X, Y), X), Y)
% 0.17/0.48 = { by axiom 5 (left_soln) R->L }
% 0.17/0.48 ifeq2(product(left_solution(X, Y), X, Y), true, multiply(left_solution(X, Y), X), Y)
% 0.17/0.48 = { by lemma 8 }
% 0.17/0.48 Y
% 0.17/0.48
% 0.17/0.48 Goal 1 (prove_there_is_a_right_identity): product(not_identity(X), X, not_identity(X)) = true.
% 0.17/0.48 The goal is true when:
% 0.17/0.48 X = right_solution(X, X)
% 0.17/0.48
% 0.17/0.48 Proof:
% 0.17/0.48 product(not_identity(right_solution(X, X)), right_solution(X, X), not_identity(right_solution(X, X)))
% 0.17/0.48 = { by lemma 9 R->L }
% 0.17/0.48 product(not_identity(right_solution(X, X)), right_solution(X, X), multiply(left_solution(X, not_identity(right_solution(X, X))), X))
% 0.17/0.48 = { by lemma 8 R->L }
% 0.17/0.48 product(not_identity(right_solution(X, X)), right_solution(X, X), multiply(left_solution(X, not_identity(right_solution(X, X))), ifeq2(product(X, right_solution(X, X), X), true, multiply(X, right_solution(X, X)), X)))
% 0.17/0.48 = { by axiom 4 (right_soln) }
% 0.17/0.48 product(not_identity(right_solution(X, X)), right_solution(X, X), multiply(left_solution(X, not_identity(right_solution(X, X))), ifeq2(true, true, multiply(X, right_solution(X, X)), X)))
% 0.17/0.48 = { by axiom 1 (ifeq_axiom) }
% 0.17/0.48 product(not_identity(right_solution(X, X)), right_solution(X, X), multiply(left_solution(X, not_identity(right_solution(X, X))), multiply(X, right_solution(X, X))))
% 0.17/0.48 = { by axiom 1 (ifeq_axiom) R->L }
% 0.17/0.48 product(not_identity(right_solution(X, X)), right_solution(X, X), ifeq2(true, true, multiply(left_solution(X, not_identity(right_solution(X, X))), multiply(X, right_solution(X, X))), multiply(multiply(left_solution(X, not_identity(right_solution(X, X))), X), right_solution(X, X))))
% 0.17/0.48 = { by axiom 7 (associativity1) R->L }
% 0.17/0.48 product(not_identity(right_solution(X, X)), right_solution(X, X), ifeq2(ifeq(product(multiply(left_solution(X, not_identity(right_solution(X, X))), X), right_solution(X, X), multiply(multiply(left_solution(X, not_identity(right_solution(X, X))), X), right_solution(X, X))), true, ifeq(product(X, right_solution(X, X), multiply(X, right_solution(X, X))), true, ifeq(product(left_solution(X, not_identity(right_solution(X, X))), X, multiply(left_solution(X, not_identity(right_solution(X, X))), X)), true, product(left_solution(X, not_identity(right_solution(X, X))), multiply(X, right_solution(X, X)), multiply(multiply(left_solution(X, not_identity(right_solution(X, X))), X), right_solution(X, X))), true), true), true), true, multiply(left_solution(X, not_identity(right_solution(X, X))), multiply(X, right_solution(X, X))), multiply(multiply(left_solution(X, not_identity(right_solution(X, X))), X), right_solution(X, X))))
% 0.17/0.48 = { by axiom 3 (total_function1) }
% 0.17/0.48 product(not_identity(right_solution(X, X)), right_solution(X, X), ifeq2(ifeq(true, true, ifeq(product(X, right_solution(X, X), multiply(X, right_solution(X, X))), true, ifeq(product(left_solution(X, not_identity(right_solution(X, X))), X, multiply(left_solution(X, not_identity(right_solution(X, X))), X)), true, product(left_solution(X, not_identity(right_solution(X, X))), multiply(X, right_solution(X, X)), multiply(multiply(left_solution(X, not_identity(right_solution(X, X))), X), right_solution(X, X))), true), true), true), true, multiply(left_solution(X, not_identity(right_solution(X, X))), multiply(X, right_solution(X, X))), multiply(multiply(left_solution(X, not_identity(right_solution(X, X))), X), right_solution(X, X))))
% 0.17/0.48 = { by axiom 2 (ifeq_axiom) }
% 0.17/0.48 product(not_identity(right_solution(X, X)), right_solution(X, X), ifeq2(ifeq(product(X, right_solution(X, X), multiply(X, right_solution(X, X))), true, ifeq(product(left_solution(X, not_identity(right_solution(X, X))), X, multiply(left_solution(X, not_identity(right_solution(X, X))), X)), true, product(left_solution(X, not_identity(right_solution(X, X))), multiply(X, right_solution(X, X)), multiply(multiply(left_solution(X, not_identity(right_solution(X, X))), X), right_solution(X, X))), true), true), true, multiply(left_solution(X, not_identity(right_solution(X, X))), multiply(X, right_solution(X, X))), multiply(multiply(left_solution(X, not_identity(right_solution(X, X))), X), right_solution(X, X))))
% 0.17/0.48 = { by axiom 3 (total_function1) }
% 0.17/0.48 product(not_identity(right_solution(X, X)), right_solution(X, X), ifeq2(ifeq(true, true, ifeq(product(left_solution(X, not_identity(right_solution(X, X))), X, multiply(left_solution(X, not_identity(right_solution(X, X))), X)), true, product(left_solution(X, not_identity(right_solution(X, X))), multiply(X, right_solution(X, X)), multiply(multiply(left_solution(X, not_identity(right_solution(X, X))), X), right_solution(X, X))), true), true), true, multiply(left_solution(X, not_identity(right_solution(X, X))), multiply(X, right_solution(X, X))), multiply(multiply(left_solution(X, not_identity(right_solution(X, X))), X), right_solution(X, X))))
% 0.17/0.48 = { by axiom 2 (ifeq_axiom) }
% 0.17/0.48 product(not_identity(right_solution(X, X)), right_solution(X, X), ifeq2(ifeq(product(left_solution(X, not_identity(right_solution(X, X))), X, multiply(left_solution(X, not_identity(right_solution(X, X))), X)), true, product(left_solution(X, not_identity(right_solution(X, X))), multiply(X, right_solution(X, X)), multiply(multiply(left_solution(X, not_identity(right_solution(X, X))), X), right_solution(X, X))), true), true, multiply(left_solution(X, not_identity(right_solution(X, X))), multiply(X, right_solution(X, X))), multiply(multiply(left_solution(X, not_identity(right_solution(X, X))), X), right_solution(X, X))))
% 0.17/0.48 = { by axiom 3 (total_function1) }
% 0.17/0.49 product(not_identity(right_solution(X, X)), right_solution(X, X), ifeq2(ifeq(true, true, product(left_solution(X, not_identity(right_solution(X, X))), multiply(X, right_solution(X, X)), multiply(multiply(left_solution(X, not_identity(right_solution(X, X))), X), right_solution(X, X))), true), true, multiply(left_solution(X, not_identity(right_solution(X, X))), multiply(X, right_solution(X, X))), multiply(multiply(left_solution(X, not_identity(right_solution(X, X))), X), right_solution(X, X))))
% 0.17/0.49 = { by axiom 2 (ifeq_axiom) }
% 0.17/0.49 product(not_identity(right_solution(X, X)), right_solution(X, X), ifeq2(product(left_solution(X, not_identity(right_solution(X, X))), multiply(X, right_solution(X, X)), multiply(multiply(left_solution(X, not_identity(right_solution(X, X))), X), right_solution(X, X))), true, multiply(left_solution(X, not_identity(right_solution(X, X))), multiply(X, right_solution(X, X))), multiply(multiply(left_solution(X, not_identity(right_solution(X, X))), X), right_solution(X, X))))
% 0.17/0.49 = { by lemma 8 }
% 0.17/0.49 product(not_identity(right_solution(X, X)), right_solution(X, X), multiply(multiply(left_solution(X, not_identity(right_solution(X, X))), X), right_solution(X, X)))
% 0.17/0.49 = { by lemma 9 }
% 0.17/0.49 product(not_identity(right_solution(X, X)), right_solution(X, X), multiply(not_identity(right_solution(X, X)), right_solution(X, X)))
% 0.17/0.49 = { by axiom 3 (total_function1) }
% 0.17/0.49 true
% 0.17/0.49 % SZS output end Proof
% 0.17/0.49
% 0.17/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------