%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP009-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 0.02s 0.47s
% Output : Proof 0.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n001.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 09:19:30 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.47 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
% 0.02/0.47
% 0.02/0.47 % SZS status Unsatisfiable
% 0.02/0.47
% 0.02/0.47 % SZS output start Proof
% 0.02/0.47 Axiom 1 (right_identity): product(X, identity, X) = true.
% 0.02/0.47 Axiom 2 (right_inverse): product(X, inverse(X), identity) = true.
% 0.02/0.47 Axiom 3 (left_identity): product(identity, X, X) = true.
% 0.02/0.47 Axiom 4 (a_is_an_inverse_of_b): product(a, b, identity) = true.
% 0.02/0.47 Axiom 5 (c_is_an_inverse_of_b): product(c, b, identity) = true.
% 0.02/0.47 Axiom 6 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.02/0.47 Axiom 7 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.02/0.47 Axiom 8 (total_function2): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 0.02/0.47 Axiom 9 (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.
% 0.02/0.47
% 0.02/0.47 Lemma 10: ifeq2(product(identity, X, Y), true, Y, X) = X.
% 0.02/0.47 Proof:
% 0.02/0.47 ifeq2(product(identity, X, Y), true, Y, X)
% 0.02/0.47 = { by axiom 7 (ifeq_axiom) R->L }
% 0.02/0.47 ifeq2(true, true, ifeq2(product(identity, X, Y), true, Y, X), X)
% 0.02/0.47 = { by axiom 3 (left_identity) R->L }
% 0.02/0.47 ifeq2(product(identity, X, X), true, ifeq2(product(identity, X, Y), true, Y, X), X)
% 0.02/0.47 = { by axiom 8 (total_function2) }
% 0.02/0.47 X
% 0.02/0.47
% 0.02/0.47 Goal 1 (prove_a_equals_c): a = c.
% 0.02/0.47 Proof:
% 0.02/0.47 a
% 0.02/0.47 = { by lemma 10 R->L }
% 0.02/0.48 ifeq2(product(identity, a, c), true, c, a)
% 0.02/0.48 = { by axiom 7 (ifeq_axiom) R->L }
% 0.02/0.48 ifeq2(product(identity, ifeq2(true, true, a, inverse(b)), c), true, c, a)
% 0.02/0.48 = { by axiom 9 (associativity2) R->L }
% 0.02/0.48 ifeq2(product(identity, ifeq2(ifeq(product(b, inverse(b), identity), true, ifeq(product(a, identity, a), true, ifeq(product(a, b, identity), true, product(identity, inverse(b), a), true), true), true), true, a, inverse(b)), c), true, c, a)
% 0.02/0.48 = { by axiom 1 (right_identity) }
% 0.02/0.48 ifeq2(product(identity, ifeq2(ifeq(product(b, inverse(b), identity), true, ifeq(true, true, ifeq(product(a, b, identity), true, product(identity, inverse(b), a), true), true), true), true, a, inverse(b)), c), true, c, a)
% 0.02/0.48 = { by axiom 6 (ifeq_axiom) }
% 0.02/0.48 ifeq2(product(identity, ifeq2(ifeq(product(b, inverse(b), identity), true, ifeq(product(a, b, identity), true, product(identity, inverse(b), a), true), true), true, a, inverse(b)), c), true, c, a)
% 0.02/0.48 = { by axiom 4 (a_is_an_inverse_of_b) }
% 0.02/0.48 ifeq2(product(identity, ifeq2(ifeq(product(b, inverse(b), identity), true, ifeq(true, true, product(identity, inverse(b), a), true), true), true, a, inverse(b)), c), true, c, a)
% 0.02/0.48 = { by axiom 6 (ifeq_axiom) }
% 0.02/0.48 ifeq2(product(identity, ifeq2(ifeq(product(b, inverse(b), identity), true, product(identity, inverse(b), a), true), true, a, inverse(b)), c), true, c, a)
% 0.02/0.48 = { by axiom 2 (right_inverse) }
% 0.02/0.48 ifeq2(product(identity, ifeq2(ifeq(true, true, product(identity, inverse(b), a), true), true, a, inverse(b)), c), true, c, a)
% 0.02/0.48 = { by axiom 6 (ifeq_axiom) }
% 0.02/0.48 ifeq2(product(identity, ifeq2(product(identity, inverse(b), a), true, a, inverse(b)), c), true, c, a)
% 0.02/0.48 = { by lemma 10 }
% 0.02/0.48 ifeq2(product(identity, inverse(b), c), true, c, a)
% 0.02/0.48 = { by axiom 6 (ifeq_axiom) R->L }
% 0.02/0.48 ifeq2(ifeq(true, true, product(identity, inverse(b), c), true), true, c, a)
% 0.02/0.48 = { by axiom 2 (right_inverse) R->L }
% 0.02/0.48 ifeq2(ifeq(product(b, inverse(b), identity), true, product(identity, inverse(b), c), true), true, c, a)
% 0.02/0.48 = { by axiom 6 (ifeq_axiom) R->L }
% 0.02/0.48 ifeq2(ifeq(product(b, inverse(b), identity), true, ifeq(true, true, product(identity, inverse(b), c), true), true), true, c, a)
% 0.02/0.48 = { by axiom 5 (c_is_an_inverse_of_b) R->L }
% 0.02/0.48 ifeq2(ifeq(product(b, inverse(b), identity), true, ifeq(product(c, b, identity), true, product(identity, inverse(b), c), true), true), true, c, a)
% 0.02/0.48 = { by axiom 6 (ifeq_axiom) R->L }
% 0.02/0.48 ifeq2(ifeq(product(b, inverse(b), identity), true, ifeq(true, true, ifeq(product(c, b, identity), true, product(identity, inverse(b), c), true), true), true), true, c, a)
% 0.02/0.48 = { by axiom 1 (right_identity) R->L }
% 0.02/0.48 ifeq2(ifeq(product(b, inverse(b), identity), true, ifeq(product(c, identity, c), true, ifeq(product(c, b, identity), true, product(identity, inverse(b), c), true), true), true), true, c, a)
% 0.02/0.48 = { by axiom 9 (associativity2) }
% 0.02/0.48 ifeq2(true, true, c, a)
% 0.02/0.48 = { by axiom 7 (ifeq_axiom) }
% 0.02/0.48 c
% 0.02/0.48 % SZS output end Proof
% 0.02/0.48
% 0.02/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
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