%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP402-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/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 10:09:55 AM UTC 2026
% Result : Unsatisfiable 34.13s 4.74s
% Output : Proof 34.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP402-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/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 10:01:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.13/4.74 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
% 34.13/4.74
% 34.13/4.74 % SZS status Unsatisfiable
% 34.13/4.74
% 34.13/4.74 % SZS output start Proof
% 34.13/4.75 Axiom 1 (associativity_of_multiply): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 34.13/4.75 Axiom 2 (nilpotency): multiply(commutator(X, Y), Z) = multiply(Z, commutator(X, Y)).
% 34.13/4.75 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 34.13/4.75 Axiom 4 (commutator): multiply(X, Y) = multiply(Y, multiply(X, commutator(X, Y))).
% 34.13/4.75 Axiom 5 (left_cancellation): ifeq(multiply(X, Y), multiply(X, Z), Y, Z) = Z.
% 34.13/4.75
% 34.13/4.75 Lemma 6: ifeq(multiply(X, commutator(Y, Z)), multiply(X, W), multiply(commutator(Y, Z), commutator(commutator(Y, Z), X)), W) = W.
% 34.13/4.75 Proof:
% 34.13/4.75 ifeq(multiply(X, commutator(Y, Z)), multiply(X, W), multiply(commutator(Y, Z), commutator(commutator(Y, Z), X)), W)
% 34.13/4.75 = { by axiom 2 (nilpotency) R->L }
% 34.13/4.75 ifeq(multiply(commutator(Y, Z), X), multiply(X, W), multiply(commutator(Y, Z), commutator(commutator(Y, Z), X)), W)
% 34.13/4.75 = { by axiom 4 (commutator) }
% 34.13/4.75 ifeq(multiply(X, multiply(commutator(Y, Z), commutator(commutator(Y, Z), X))), multiply(X, W), multiply(commutator(Y, Z), commutator(commutator(Y, Z), X)), W)
% 34.13/4.75 = { by axiom 5 (left_cancellation) }
% 34.13/4.75 W
% 34.13/4.75
% 34.13/4.75 Lemma 7: multiply(commutator(X, Y), commutator(commutator(X, Y), Z)) = commutator(X, Y).
% 34.13/4.75 Proof:
% 34.13/4.75 multiply(commutator(X, Y), commutator(commutator(X, Y), Z))
% 34.13/4.75 = { by axiom 3 (ifeq_axiom) R->L }
% 34.13/4.75 ifeq(multiply(Z, commutator(X, Y)), multiply(Z, commutator(X, Y)), multiply(commutator(X, Y), commutator(commutator(X, Y), Z)), commutator(X, Y))
% 34.13/4.75 = { by lemma 6 }
% 34.13/4.75 commutator(X, Y)
% 34.13/4.75
% 34.13/4.75 Goal 1 (prove_commutator_is_associative): commutator(commutator(a, b), c) = commutator(a, commutator(b, c)).
% 34.13/4.75 Proof:
% 34.13/4.75 commutator(commutator(a, b), c)
% 34.13/4.75 = { by axiom 3 (ifeq_axiom) R->L }
% 34.13/4.75 ifeq(commutator(a, b), commutator(a, b), commutator(commutator(a, b), c), commutator(commutator(a, b), commutator(b, c)))
% 34.13/4.75 = { by axiom 5 (left_cancellation) R->L }
% 34.13/4.75 ifeq(ifeq(multiply(c, multiply(commutator(commutator(a, b), c), commutator(a, b))), multiply(c, commutator(a, b)), multiply(commutator(commutator(a, b), c), commutator(a, b)), commutator(a, b)), commutator(a, b), commutator(commutator(a, b), c), commutator(commutator(a, b), commutator(b, c)))
% 34.13/4.75 = { by axiom 2 (nilpotency) R->L }
% 34.13/4.75 ifeq(ifeq(multiply(c, multiply(commutator(a, b), commutator(commutator(a, b), c))), multiply(c, commutator(a, b)), multiply(commutator(commutator(a, b), c), commutator(a, b)), commutator(a, b)), commutator(a, b), commutator(commutator(a, b), c), commutator(commutator(a, b), commutator(b, c)))
% 34.13/4.75 = { by axiom 4 (commutator) R->L }
% 34.13/4.75 ifeq(ifeq(multiply(commutator(a, b), c), multiply(c, commutator(a, b)), multiply(commutator(commutator(a, b), c), commutator(a, b)), commutator(a, b)), commutator(a, b), commutator(commutator(a, b), c), commutator(commutator(a, b), commutator(b, c)))
% 34.13/4.75 = { by axiom 2 (nilpotency) }
% 34.13/4.75 ifeq(ifeq(multiply(c, commutator(a, b)), multiply(c, commutator(a, b)), multiply(commutator(commutator(a, b), c), commutator(a, b)), commutator(a, b)), commutator(a, b), commutator(commutator(a, b), c), commutator(commutator(a, b), commutator(b, c)))
% 34.13/4.75 = { by axiom 3 (ifeq_axiom) }
% 34.13/4.75 ifeq(multiply(commutator(commutator(a, b), c), commutator(a, b)), commutator(a, b), commutator(commutator(a, b), c), commutator(commutator(a, b), commutator(b, c)))
% 34.13/4.75 = { by lemma 7 R->L }
% 34.13/4.75 ifeq(multiply(commutator(commutator(a, b), c), commutator(a, b)), multiply(commutator(a, b), commutator(commutator(a, b), commutator(b, c))), commutator(commutator(a, b), c), commutator(commutator(a, b), commutator(b, c)))
% 34.13/4.75 = { by axiom 2 (nilpotency) }
% 34.13/4.75 ifeq(multiply(commutator(a, b), commutator(commutator(a, b), c)), multiply(commutator(a, b), commutator(commutator(a, b), commutator(b, c))), commutator(commutator(a, b), c), commutator(commutator(a, b), commutator(b, c)))
% 34.13/4.75 = { by axiom 5 (left_cancellation) }
% 34.13/4.75 commutator(commutator(a, b), commutator(b, c))
% 34.13/4.75 = { by axiom 5 (left_cancellation) R->L }
% 34.13/4.75 ifeq(multiply(multiply(commutator(a, b), commutator(b, c)), commutator(a, commutator(b, c))), multiply(multiply(commutator(a, b), commutator(b, c)), commutator(commutator(a, b), commutator(b, c))), commutator(a, commutator(b, c)), commutator(commutator(a, b), commutator(b, c)))
% 34.13/4.75 = { by axiom 1 (associativity_of_multiply) }
% 34.13/4.75 ifeq(multiply(commutator(a, b), multiply(commutator(b, c), commutator(a, commutator(b, c)))), multiply(multiply(commutator(a, b), commutator(b, c)), commutator(commutator(a, b), commutator(b, c))), commutator(a, commutator(b, c)), commutator(commutator(a, b), commutator(b, c)))
% 34.13/4.75 = { by axiom 1 (associativity_of_multiply) }
% 34.13/4.75 ifeq(multiply(commutator(a, b), multiply(commutator(b, c), commutator(a, commutator(b, c)))), multiply(commutator(a, b), multiply(commutator(b, c), commutator(commutator(a, b), commutator(b, c)))), commutator(a, commutator(b, c)), commutator(commutator(a, b), commutator(b, c)))
% 34.13/4.75 = { by axiom 2 (nilpotency) R->L }
% 34.13/4.75 ifeq(multiply(commutator(a, b), multiply(commutator(a, commutator(b, c)), commutator(b, c))), multiply(commutator(a, b), multiply(commutator(b, c), commutator(commutator(a, b), commutator(b, c)))), commutator(a, commutator(b, c)), commutator(commutator(a, b), commutator(b, c)))
% 34.13/4.75 = { by axiom 2 (nilpotency) R->L }
% 34.13/4.75 ifeq(multiply(commutator(a, b), multiply(commutator(a, commutator(b, c)), commutator(b, c))), multiply(commutator(a, b), multiply(commutator(commutator(a, b), commutator(b, c)), commutator(b, c))), commutator(a, commutator(b, c)), commutator(commutator(a, b), commutator(b, c)))
% 34.13/4.75 = { by axiom 1 (associativity_of_multiply) R->L }
% 34.13/4.75 ifeq(multiply(commutator(a, b), multiply(commutator(a, commutator(b, c)), commutator(b, c))), multiply(multiply(commutator(a, b), commutator(commutator(a, b), commutator(b, c))), commutator(b, c)), commutator(a, commutator(b, c)), commutator(commutator(a, b), commutator(b, c)))
% 34.13/4.75 = { by axiom 2 (nilpotency) R->L }
% 34.13/4.75 ifeq(multiply(commutator(a, b), multiply(commutator(a, commutator(b, c)), commutator(b, c))), multiply(commutator(b, c), multiply(commutator(a, b), commutator(commutator(a, b), commutator(b, c)))), commutator(a, commutator(b, c)), commutator(commutator(a, b), commutator(b, c)))
% 34.13/4.75 = { by axiom 4 (commutator) R->L }
% 34.13/4.75 ifeq(multiply(commutator(a, b), multiply(commutator(a, commutator(b, c)), commutator(b, c))), multiply(commutator(a, b), commutator(b, c)), commutator(a, commutator(b, c)), commutator(commutator(a, b), commutator(b, c)))
% 34.13/4.75 = { by lemma 6 R->L }
% 34.13/4.75 ifeq(multiply(commutator(a, b), ifeq(multiply(a, commutator(b, c)), multiply(a, multiply(commutator(a, commutator(b, c)), commutator(b, c))), multiply(commutator(b, c), commutator(commutator(b, c), a)), multiply(commutator(a, commutator(b, c)), commutator(b, c)))), multiply(commutator(a, b), commutator(b, c)), commutator(a, commutator(b, c)), commutator(commutator(a, b), commutator(b, c)))
% 34.13/4.75 = { by axiom 1 (associativity_of_multiply) R->L }
% 34.13/4.75 ifeq(multiply(commutator(a, b), ifeq(multiply(a, commutator(b, c)), multiply(multiply(a, commutator(a, commutator(b, c))), commutator(b, c)), multiply(commutator(b, c), commutator(commutator(b, c), a)), multiply(commutator(a, commutator(b, c)), commutator(b, c)))), multiply(commutator(a, b), commutator(b, c)), commutator(a, commutator(b, c)), commutator(commutator(a, b), commutator(b, c)))
% 34.13/4.75 = { by axiom 2 (nilpotency) R->L }
% 34.13/4.75 ifeq(multiply(commutator(a, b), ifeq(multiply(a, commutator(b, c)), multiply(commutator(b, c), multiply(a, commutator(a, commutator(b, c)))), multiply(commutator(b, c), commutator(commutator(b, c), a)), multiply(commutator(a, commutator(b, c)), commutator(b, c)))), multiply(commutator(a, b), commutator(b, c)), commutator(a, commutator(b, c)), commutator(commutator(a, b), commutator(b, c)))
% 34.13/4.75 = { by axiom 4 (commutator) R->L }
% 34.13/4.75 ifeq(multiply(commutator(a, b), ifeq(multiply(a, commutator(b, c)), multiply(a, commutator(b, c)), multiply(commutator(b, c), commutator(commutator(b, c), a)), multiply(commutator(a, commutator(b, c)), commutator(b, c)))), multiply(commutator(a, b), commutator(b, c)), commutator(a, commutator(b, c)), commutator(commutator(a, b), commutator(b, c)))
% 34.13/4.75 = { by axiom 3 (ifeq_axiom) }
% 34.13/4.75 ifeq(multiply(commutator(a, b), multiply(commutator(b, c), commutator(commutator(b, c), a))), multiply(commutator(a, b), commutator(b, c)), commutator(a, commutator(b, c)), commutator(commutator(a, b), commutator(b, c)))
% 34.13/4.75 = { by lemma 7 }
% 34.13/4.75 ifeq(multiply(commutator(a, b), commutator(b, c)), multiply(commutator(a, b), commutator(b, c)), commutator(a, commutator(b, c)), commutator(commutator(a, b), commutator(b, c)))
% 34.13/4.75 = { by axiom 3 (ifeq_axiom) }
% 34.13/4.75 commutator(a, commutator(b, c))
% 34.13/4.75 % SZS output end Proof
% 34.13/4.75
% 34.13/4.75 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------