%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP031-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 0.12s 0.45s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP031-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n020.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 09:16:04 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.45 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
% 0.12/0.45
% 0.12/0.45 % SZS status Unsatisfiable
% 0.12/0.45
% 0.12/0.46 % SZS output start Proof
% 0.12/0.46 Axiom 1 (left_identity): product(identity, X, X) = true.
% 0.12/0.46 Axiom 2 (left_inverse): product(inverse(X), X, identity) = true.
% 0.12/0.46 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.12/0.46 Axiom 4 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.12/0.46 Axiom 5 (total_function1): product(X, Y, multiply(X, Y)) = true.
% 0.12/0.46 Axiom 6 (total_function2): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 0.12/0.46 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.
% 0.12/0.46
% 0.12/0.46 Goal 1 (prove_a_has_an_inverse): product(a, X, identity) = true.
% 0.12/0.46 The goal is true when:
% 0.12/0.46 X = inverse(a)
% 0.12/0.46
% 0.12/0.46 Proof:
% 0.12/0.46 product(a, inverse(a), identity)
% 0.12/0.46 = { by axiom 4 (ifeq_axiom) R->L }
% 0.12/0.46 product(a, inverse(a), ifeq2(true, true, identity, multiply(a, inverse(a))))
% 0.12/0.46 = { by axiom 7 (associativity1) R->L }
% 0.12/0.46 product(a, inverse(a), ifeq2(ifeq(product(identity, multiply(a, inverse(a)), multiply(a, inverse(a))), true, ifeq(product(inverse(a), multiply(a, inverse(a)), inverse(a)), true, ifeq(product(inverse(inverse(a)), inverse(a), identity), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true), true), true, identity, multiply(a, inverse(a))))
% 0.12/0.46 = { by axiom 1 (left_identity) }
% 0.12/0.46 product(a, inverse(a), ifeq2(ifeq(true, true, ifeq(product(inverse(a), multiply(a, inverse(a)), inverse(a)), true, ifeq(product(inverse(inverse(a)), inverse(a), identity), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true), true), true, identity, multiply(a, inverse(a))))
% 0.12/0.46 = { by axiom 3 (ifeq_axiom) }
% 0.12/0.46 product(a, inverse(a), ifeq2(ifeq(product(inverse(a), multiply(a, inverse(a)), inverse(a)), true, ifeq(product(inverse(inverse(a)), inverse(a), identity), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true), true, identity, multiply(a, inverse(a))))
% 0.12/0.46 = { by axiom 2 (left_inverse) }
% 0.12/0.46 product(a, inverse(a), ifeq2(ifeq(product(inverse(a), multiply(a, inverse(a)), inverse(a)), true, ifeq(true, true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true), true, identity, multiply(a, inverse(a))))
% 0.12/0.46 = { by axiom 3 (ifeq_axiom) }
% 0.12/0.46 product(a, inverse(a), ifeq2(ifeq(product(inverse(a), multiply(a, inverse(a)), inverse(a)), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true, identity, multiply(a, inverse(a))))
% 0.12/0.46 = { by axiom 3 (ifeq_axiom) R->L }
% 0.12/0.46 product(a, inverse(a), ifeq2(ifeq(ifeq(true, true, product(inverse(a), multiply(a, inverse(a)), inverse(a)), true), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true, identity, multiply(a, inverse(a))))
% 0.12/0.46 = { by axiom 5 (total_function1) R->L }
% 0.12/0.46 product(a, inverse(a), ifeq2(ifeq(ifeq(product(a, inverse(a), multiply(a, inverse(a))), true, product(inverse(a), multiply(a, inverse(a)), inverse(a)), true), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true, identity, multiply(a, inverse(a))))
% 0.12/0.46 = { by axiom 3 (ifeq_axiom) R->L }
% 0.12/0.46 product(a, inverse(a), ifeq2(ifeq(ifeq(product(a, inverse(a), multiply(a, inverse(a))), true, ifeq(true, true, product(inverse(a), multiply(a, inverse(a)), inverse(a)), true), true), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true, identity, multiply(a, inverse(a))))
% 0.12/0.46 = { by axiom 2 (left_inverse) R->L }
% 0.12/0.46 product(a, inverse(a), ifeq2(ifeq(ifeq(product(a, inverse(a), multiply(a, inverse(a))), true, ifeq(product(inverse(a), a, identity), true, product(inverse(a), multiply(a, inverse(a)), inverse(a)), true), true), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true, identity, multiply(a, inverse(a))))
% 0.12/0.46 = { by axiom 3 (ifeq_axiom) R->L }
% 0.12/0.46 product(a, inverse(a), ifeq2(ifeq(ifeq(true, true, ifeq(product(a, inverse(a), multiply(a, inverse(a))), true, ifeq(product(inverse(a), a, identity), true, product(inverse(a), multiply(a, inverse(a)), inverse(a)), true), true), true), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true, identity, multiply(a, inverse(a))))
% 0.12/0.46 = { by axiom 1 (left_identity) R->L }
% 0.12/0.46 product(a, inverse(a), ifeq2(ifeq(ifeq(product(identity, inverse(a), inverse(a)), true, ifeq(product(a, inverse(a), multiply(a, inverse(a))), true, ifeq(product(inverse(a), a, identity), true, product(inverse(a), multiply(a, inverse(a)), inverse(a)), true), true), true), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true, identity, multiply(a, inverse(a))))
% 0.12/0.46 = { by axiom 7 (associativity1) }
% 0.12/0.46 product(a, inverse(a), ifeq2(ifeq(true, true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true, identity, multiply(a, inverse(a))))
% 0.12/0.46 = { by axiom 3 (ifeq_axiom) }
% 0.12/0.46 product(a, inverse(a), ifeq2(product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true, identity, multiply(a, inverse(a))))
% 0.12/0.46 = { by axiom 4 (ifeq_axiom) R->L }
% 0.12/0.46 product(a, inverse(a), ifeq2(product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true, ifeq2(true, true, identity, multiply(a, inverse(a))), multiply(a, inverse(a))))
% 0.12/0.46 = { by axiom 2 (left_inverse) R->L }
% 0.12/0.46 product(a, inverse(a), ifeq2(product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true, ifeq2(product(inverse(inverse(a)), inverse(a), identity), true, identity, multiply(a, inverse(a))), multiply(a, inverse(a))))
% 0.12/0.46 = { by axiom 6 (total_function2) }
% 0.12/0.46 product(a, inverse(a), multiply(a, inverse(a)))
% 0.12/0.46 = { by axiom 5 (total_function1) }
% 0.12/0.46 true
% 0.12/0.46 % SZS output end Proof
% 0.12/0.46
% 0.12/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------