%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL014+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 12:33:05 PM UTC 2026
% Result : Theorem 0.20s 0.53s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL014+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.39 % Computer : n010.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sun Sep 27 22:51:18 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.53 Command-line arguments: --no-flatten-goal
% 0.20/0.53
% 0.20/0.53 % SZS status Theorem
% 0.20/0.53
% 0.20/0.53 % SZS output start Proof
% 0.20/0.53 Axiom 1 (converse_idempotence): converse(converse(X)) = X.
% 0.20/0.53 Axiom 2 (composition_identity): composition(X, one) = X.
% 0.20/0.53 Axiom 3 (converse_multiplicativity): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 0.20/0.53 Axiom 4 (composition_associativity): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 0.20/0.53
% 0.20/0.53 Lemma 5: composition(converse(one), X) = X.
% 0.20/0.53 Proof:
% 0.20/0.53 composition(converse(one), X)
% 0.20/0.53 = { by axiom 1 (converse_idempotence) R->L }
% 0.20/0.53 composition(converse(one), converse(converse(X)))
% 0.20/0.53 = { by axiom 3 (converse_multiplicativity) R->L }
% 0.20/0.53 converse(composition(converse(X), one))
% 0.20/0.53 = { by axiom 2 (composition_identity) }
% 0.20/0.53 converse(converse(X))
% 0.20/0.53 = { by axiom 1 (converse_idempotence) }
% 0.20/0.53 X
% 0.20/0.53
% 0.20/0.53 Goal 1 (goals): tuple(composition(one, x0), composition(x0_2, one)) = tuple(x0, x0_2).
% 0.20/0.53 Proof:
% 0.20/0.53 tuple(composition(one, x0), composition(x0_2, one))
% 0.20/0.53 = { by axiom 2 (composition_identity) }
% 0.20/0.53 tuple(composition(one, x0), x0_2)
% 0.20/0.53 = { by lemma 5 R->L }
% 0.20/0.53 tuple(composition(converse(one), composition(one, x0)), x0_2)
% 0.20/0.53 = { by axiom 4 (composition_associativity) }
% 0.20/0.53 tuple(composition(composition(converse(one), one), x0), x0_2)
% 0.20/0.53 = { by axiom 2 (composition_identity) }
% 0.20/0.53 tuple(composition(converse(one), x0), x0_2)
% 0.20/0.53 = { by lemma 5 }
% 0.20/0.53 tuple(x0, x0_2)
% 0.20/0.53 % SZS output end Proof
% 0.20/0.53
% 0.20/0.53 RESULT: Theorem (the conjecture is true).
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