%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP013-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 10:08:53 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.44s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP013-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n006.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 09:13:40 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.44 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.14/0.44
% 0.14/0.44 % SZS status Unsatisfiable
% 0.14/0.44
% 0.14/0.44 % SZS output start Proof
% 0.14/0.44 Axiom 1 (squareness): product(X, X, identity) = true.
% 0.14/0.44 Axiom 2 (right_identity): product(X, identity, X) = true.
% 0.14/0.44 Axiom 3 (right_inverse): product(X, inverse(X), identity) = true.
% 0.14/0.44 Axiom 4 (a_times_b_is_c): product(a, b, c) = true.
% 0.14/0.44 Axiom 5 (inverse_a_times_inverse_b_is_d): product(inverse(a), inverse(b), d) = true.
% 0.14/0.44 Axiom 6 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.14/0.44 Axiom 7 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.14/0.44 Axiom 8 (inverses_have_property): ifeq(product(inverse(X), inverse(Y), Z), true, product(X, Z, Y), true) = true.
% 0.14/0.44 Axiom 9 (total_function2): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 0.14/0.44
% 0.14/0.44 Lemma 10: inverse(X) = X.
% 0.14/0.44 Proof:
% 0.14/0.44 inverse(X)
% 0.14/0.44 = { by axiom 7 (ifeq_axiom) R->L }
% 0.14/0.44 ifeq2(true, true, inverse(X), X)
% 0.14/0.44 = { by axiom 8 (inverses_have_property) R->L }
% 0.14/0.44 ifeq2(ifeq(product(inverse(X), inverse(inverse(X)), identity), true, product(X, identity, inverse(X)), true), true, inverse(X), X)
% 0.14/0.44 = { by axiom 3 (right_inverse) }
% 0.14/0.44 ifeq2(ifeq(true, true, product(X, identity, inverse(X)), true), true, inverse(X), X)
% 0.14/0.44 = { by axiom 6 (ifeq_axiom) }
% 0.14/0.44 ifeq2(product(X, identity, inverse(X)), true, inverse(X), X)
% 0.14/0.44 = { by axiom 7 (ifeq_axiom) R->L }
% 0.14/0.44 ifeq2(true, true, ifeq2(product(X, identity, inverse(X)), true, inverse(X), X), X)
% 0.14/0.44 = { by axiom 2 (right_identity) R->L }
% 0.14/0.44 ifeq2(product(X, identity, X), true, ifeq2(product(X, identity, inverse(X)), true, inverse(X), X), X)
% 0.14/0.44 = { by axiom 9 (total_function2) }
% 0.14/0.44 X
% 0.14/0.44
% 0.14/0.44 Goal 1 (prove_c_times_d_is_identity): product(c, d, identity) = true.
% 0.14/0.44 Proof:
% 0.14/0.44 product(c, d, identity)
% 0.14/0.44 = { by axiom 9 (total_function2) R->L }
% 0.14/0.44 product(c, ifeq2(product(a, b, d), true, ifeq2(product(a, b, c), true, c, d), d), identity)
% 0.14/0.44 = { by axiom 4 (a_times_b_is_c) }
% 0.14/0.44 product(c, ifeq2(product(a, b, d), true, ifeq2(true, true, c, d), d), identity)
% 0.14/0.44 = { by axiom 7 (ifeq_axiom) }
% 0.14/0.44 product(c, ifeq2(product(a, b, d), true, c, d), identity)
% 0.14/0.44 = { by lemma 10 R->L }
% 0.14/0.44 product(c, ifeq2(product(a, inverse(b), d), true, c, d), identity)
% 0.14/0.44 = { by lemma 10 R->L }
% 0.14/0.44 product(c, ifeq2(product(inverse(a), inverse(b), d), true, c, d), identity)
% 0.14/0.44 = { by axiom 5 (inverse_a_times_inverse_b_is_d) }
% 0.14/0.44 product(c, ifeq2(true, true, c, d), identity)
% 0.14/0.44 = { by axiom 7 (ifeq_axiom) }
% 0.14/0.44 product(c, c, identity)
% 0.14/0.44 = { by axiom 1 (squareness) }
% 0.14/0.44 true
% 0.14/0.44 % SZS output end Proof
% 0.14/0.44
% 0.14/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
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