%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE056+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 11:39:44 AM UTC 2026
% Result : Theorem 0.12s 0.43s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE056+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.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 13:07:44 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.43 Command-line arguments: --no-flatten-goal
% 0.12/0.43
% 0.12/0.43 % SZS status Theorem
% 0.12/0.43
% 0.12/0.43 % SZS output start Proof
% 0.12/0.43 Axiom 1 (goals): domain(x0) = zero.
% 0.12/0.43 Axiom 2 (additive_identity): addition(X, zero) = X.
% 0.12/0.43 Axiom 3 (left_annihilation): multiplication(zero, X) = zero.
% 0.12/0.43 Axiom 4 (domain1): addition(X, multiplication(domain(X), X)) = multiplication(domain(X), X).
% 0.12/0.43
% 0.12/0.43 Goal 1 (goals_1): x0 = zero.
% 0.12/0.43 Proof:
% 0.12/0.43 x0
% 0.12/0.43 = { by axiom 2 (additive_identity) R->L }
% 0.12/0.43 addition(x0, zero)
% 0.12/0.43 = { by axiom 3 (left_annihilation) R->L }
% 0.12/0.43 addition(x0, multiplication(zero, x0))
% 0.12/0.43 = { by axiom 1 (goals) R->L }
% 0.12/0.43 addition(x0, multiplication(domain(x0), x0))
% 0.12/0.43 = { by axiom 4 (domain1) }
% 0.12/0.43 multiplication(domain(x0), x0)
% 0.12/0.43 = { by axiom 1 (goals) }
% 0.12/0.43 multiplication(zero, x0)
% 0.12/0.43 = { by axiom 3 (left_annihilation) }
% 0.12/0.43 zero
% 0.12/0.43 % SZS output end Proof
% 0.12/0.43
% 0.12/0.43 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------