%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP010-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 10:08:52 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.48s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 09:12:51 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.48 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
% 0.12/0.48
% 0.12/0.48 % SZS status Unsatisfiable
% 0.12/0.48
% 0.12/0.48 % SZS output start Proof
% 0.12/0.48 Axiom 1 (right_identity): product(X, identity, X) = true.
% 0.12/0.48 Axiom 2 (left_identity): product(identity, X, X) = true.
% 0.12/0.48 Axiom 3 (a_multiply_b_is_identity): product(a, b, identity) = true.
% 0.12/0.48 Axiom 4 (left_inverse): product(inverse(X), X, identity) = true.
% 0.12/0.48 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.12/0.48 Axiom 6 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.12/0.48 Axiom 7 (total_function2): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 0.12/0.48 Axiom 8 (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.
% 0.12/0.48
% 0.12/0.48 Goal 1 (prove_b_multiply_a_is_identity): product(b, a, identity) = true.
% 0.12/0.48 Proof:
% 0.12/0.48 product(b, a, identity)
% 0.12/0.48 = { by axiom 7 (total_function2) R->L }
% 0.12/0.48 product(ifeq2(product(identity, b, b), true, ifeq2(product(identity, b, inverse(a)), true, inverse(a), b), b), a, identity)
% 0.12/0.48 = { by axiom 2 (left_identity) }
% 0.12/0.48 product(ifeq2(true, true, ifeq2(product(identity, b, inverse(a)), true, inverse(a), b), b), a, identity)
% 0.12/0.48 = { by axiom 6 (ifeq_axiom) }
% 0.12/0.48 product(ifeq2(product(identity, b, inverse(a)), true, inverse(a), b), a, identity)
% 0.12/0.48 = { by axiom 5 (ifeq_axiom) R->L }
% 0.12/0.48 product(ifeq2(ifeq(true, true, product(identity, b, inverse(a)), true), true, inverse(a), b), a, identity)
% 0.12/0.48 = { by axiom 4 (left_inverse) R->L }
% 0.12/0.48 product(ifeq2(ifeq(product(inverse(a), a, identity), true, product(identity, b, inverse(a)), true), true, inverse(a), b), a, identity)
% 0.12/0.48 = { by axiom 5 (ifeq_axiom) R->L }
% 0.12/0.48 product(ifeq2(ifeq(true, true, ifeq(product(inverse(a), a, identity), true, product(identity, b, inverse(a)), true), true), true, inverse(a), b), a, identity)
% 0.12/0.48 = { by axiom 3 (a_multiply_b_is_identity) R->L }
% 0.12/0.48 product(ifeq2(ifeq(product(a, b, identity), true, ifeq(product(inverse(a), a, identity), true, product(identity, b, inverse(a)), true), true), true, inverse(a), b), a, identity)
% 0.12/0.48 = { by axiom 5 (ifeq_axiom) R->L }
% 0.12/0.48 product(ifeq2(ifeq(product(a, b, identity), true, ifeq(true, true, ifeq(product(inverse(a), a, identity), true, product(identity, b, inverse(a)), true), true), true), true, inverse(a), b), a, identity)
% 0.12/0.48 = { by axiom 1 (right_identity) R->L }
% 0.12/0.48 product(ifeq2(ifeq(product(a, b, identity), true, ifeq(product(inverse(a), identity, inverse(a)), true, ifeq(product(inverse(a), a, identity), true, product(identity, b, inverse(a)), true), true), true), true, inverse(a), b), a, identity)
% 0.12/0.48 = { by axiom 8 (associativity2) }
% 0.12/0.48 product(ifeq2(true, true, inverse(a), b), a, identity)
% 0.12/0.48 = { by axiom 6 (ifeq_axiom) }
% 0.12/0.48 product(inverse(a), a, identity)
% 0.12/0.48 = { by axiom 4 (left_inverse) }
% 0.12/0.48 true
% 0.12/0.48 % SZS output end Proof
% 0.12/0.48
% 0.12/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------