%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE001+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 11:39:36 AM UTC 2026
% Result : Theorem 0.10s 0.43s
% Output : Proof 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE001+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 12:59:40 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.43 Command-line arguments: --flatten --complete-subsets
% 0.10/0.43
% 0.10/0.43 % SZS status Theorem
% 0.10/0.43
% 0.10/0.43 % SZS output start Proof
% 0.10/0.43 Axiom 1 (goals): leq(x0, x1) = true.
% 0.10/0.43 Axiom 2 (additive_idempotence): addition(X, X) = X.
% 0.10/0.43 Axiom 3 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.10/0.43 Axiom 4 (order): ifeq2(addition(X, Y), Y, leq(X, Y), true) = true.
% 0.10/0.43
% 0.10/0.43 Goal 1 (goals_1): leq(addition(x0, x2), addition(x0, x2)) = true.
% 0.10/0.43 Proof:
% 0.10/0.43 leq(addition(x0, x2), addition(x0, x2))
% 0.10/0.43 = { by axiom 3 (ifeq_axiom) R->L }
% 0.10/0.43 ifeq2(addition(x0, x2), addition(x0, x2), leq(addition(x0, x2), addition(x0, x2)), leq(x0, x1))
% 0.10/0.43 = { by axiom 2 (additive_idempotence) R->L }
% 0.10/0.43 ifeq2(addition(addition(x0, x2), addition(x0, x2)), addition(x0, x2), leq(addition(x0, x2), addition(x0, x2)), leq(x0, x1))
% 0.10/0.43 = { by axiom 1 (goals) }
% 0.10/0.43 ifeq2(addition(addition(x0, x2), addition(x0, x2)), addition(x0, x2), leq(addition(x0, x2), addition(x0, x2)), true)
% 0.10/0.43 = { by axiom 4 (order) }
% 0.10/0.43 true
% 0.10/0.43 % SZS output end Proof
% 0.10/0.43
% 0.10/0.43 RESULT: Theorem (the conjecture is true).
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