%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE053+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 11:39:43 AM UTC 2026
% Result : Theorem 0.10s 0.44s
% Output : Proof 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE053+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 13:07:44 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.44 Command-line arguments: --flatten-regeneralise
% 0.10/0.44
% 0.10/0.44 % SZS status Theorem
% 0.10/0.44
% 0.10/0.44 % SZS output start Proof
% 0.10/0.44 Axiom 1 (multiplicative_left_identity): multiplication(one, X) = X.
% 0.10/0.44 Axiom 2 (domain2): domain(multiplication(X, Y)) = domain(multiplication(X, domain(Y))).
% 0.10/0.44
% 0.10/0.44 Goal 1 (goals): domain(domain(x0)) = domain(x0).
% 0.10/0.44 Proof:
% 0.10/0.44 domain(domain(x0))
% 0.10/0.44 = { by axiom 1 (multiplicative_left_identity) R->L }
% 0.10/0.44 domain(multiplication(one, domain(x0)))
% 0.10/0.44 = { by axiom 2 (domain2) R->L }
% 0.10/0.44 domain(multiplication(one, x0))
% 0.10/0.44 = { by axiom 1 (multiplicative_left_identity) }
% 0.10/0.44 domain(x0)
% 0.10/0.44 % SZS output end Proof
% 0.10/0.44
% 0.10/0.44 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------