%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP031-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/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 10:09:06 AM UTC 2026
% Result : Unsatisfiable 0.62s 0.54s
% Output : Proof 0.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP031-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n001.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
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 09:21:30 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.62/0.54 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
% 0.62/0.54
% 0.62/0.54 % SZS status Unsatisfiable
% 0.62/0.54
% 0.62/0.54 % SZS output start Proof
% 0.62/0.54 Axiom 1 (right_identity): product(X, identity, X) = true.
% 0.62/0.54 Axiom 2 (right_inverse): product(X, inverse(X), identity) = true.
% 0.62/0.54 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.62/0.54 Axiom 4 (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.
% 0.62/0.54 Axiom 5 (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.
% 0.62/0.54
% 0.62/0.54 Goal 1 (prove_a_has_a_left_inverse): product(X, a, identity) = true.
% 0.62/0.54 The goal is true when:
% 0.62/0.54 X = inverse(a)
% 0.62/0.54
% 0.62/0.54 Proof:
% 0.62/0.54 product(inverse(a), a, identity)
% 0.62/0.54 = { by axiom 3 (ifeq_axiom) R->L }
% 0.62/0.54 ifeq(true, true, product(inverse(a), a, identity), true)
% 0.62/0.54 = { by axiom 5 (associativity2) R->L }
% 0.62/0.54 ifeq(ifeq(product(inverse(a), inverse(inverse(a)), identity), true, ifeq(product(a, identity, a), true, ifeq(product(a, inverse(a), identity), true, product(identity, inverse(inverse(a)), a), true), true), true), true, product(inverse(a), a, identity), true)
% 0.62/0.54 = { by axiom 1 (right_identity) }
% 0.62/0.54 ifeq(ifeq(product(inverse(a), inverse(inverse(a)), identity), true, ifeq(true, true, ifeq(product(a, inverse(a), identity), true, product(identity, inverse(inverse(a)), a), true), true), true), true, product(inverse(a), a, identity), true)
% 0.62/0.54 = { by axiom 3 (ifeq_axiom) }
% 0.62/0.55 ifeq(ifeq(product(inverse(a), inverse(inverse(a)), identity), true, ifeq(product(a, inverse(a), identity), true, product(identity, inverse(inverse(a)), a), true), true), true, product(inverse(a), a, identity), true)
% 0.62/0.55 = { by axiom 2 (right_inverse) }
% 0.62/0.55 ifeq(ifeq(true, true, ifeq(product(a, inverse(a), identity), true, product(identity, inverse(inverse(a)), a), true), true), true, product(inverse(a), a, identity), true)
% 0.62/0.55 = { by axiom 3 (ifeq_axiom) }
% 0.62/0.55 ifeq(ifeq(product(a, inverse(a), identity), true, product(identity, inverse(inverse(a)), a), true), true, product(inverse(a), a, identity), true)
% 0.62/0.55 = { by axiom 2 (right_inverse) }
% 0.62/0.55 ifeq(ifeq(true, true, product(identity, inverse(inverse(a)), a), true), true, product(inverse(a), a, identity), true)
% 0.62/0.55 = { by axiom 3 (ifeq_axiom) }
% 0.62/0.55 ifeq(product(identity, inverse(inverse(a)), a), true, product(inverse(a), a, identity), true)
% 0.62/0.55 = { by axiom 3 (ifeq_axiom) R->L }
% 0.62/0.55 ifeq(true, true, ifeq(product(identity, inverse(inverse(a)), a), true, product(inverse(a), a, identity), true), true)
% 0.62/0.55 = { by axiom 2 (right_inverse) R->L }
% 0.62/0.55 ifeq(product(inverse(a), inverse(inverse(a)), identity), true, ifeq(product(identity, inverse(inverse(a)), a), true, product(inverse(a), a, identity), true), true)
% 0.62/0.55 = { by axiom 3 (ifeq_axiom) R->L }
% 0.62/0.55 ifeq(product(inverse(a), inverse(inverse(a)), identity), true, ifeq(product(identity, inverse(inverse(a)), a), true, ifeq(true, true, product(inverse(a), a, identity), true), true), true)
% 0.62/0.55 = { by axiom 1 (right_identity) R->L }
% 0.62/0.55 ifeq(product(inverse(a), inverse(inverse(a)), identity), true, ifeq(product(identity, inverse(inverse(a)), a), true, ifeq(product(inverse(a), identity, inverse(a)), true, product(inverse(a), a, identity), true), true), true)
% 0.62/0.55 = { by axiom 4 (associativity1) }
% 0.62/0.55 true
% 0.62/0.55 % SZS output end Proof
% 0.62/0.55
% 0.62/0.55 RESULT: Unsatisfiable (the axioms are contradictory).
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