%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE150+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 11:39:55 AM UTC 2026
% Result : Theorem 0.24s 0.58s
% Output : Proof 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE150+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n001.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 27 13:18:45 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.24/0.58 Command-line arguments: --flatten --complete-subsets
% 0.24/0.58
% 0.24/0.58 % SZS status Theorem
% 0.24/0.58
% 0.24/0.58 % SZS output start Proof
% 0.24/0.58 Axiom 1 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 0.24/0.58 Axiom 2 (left_annihilation): multiplication(zero, X) = zero.
% 0.24/0.58 Axiom 3 (infty_unfold1): strong_iteration(X) = addition(multiplication(X, strong_iteration(X)), one).
% 0.24/0.58 Axiom 4 (multiplicative_associativity): multiplication(X, multiplication(Y, Z)) = multiplication(multiplication(X, Y), Z).
% 0.24/0.58
% 0.24/0.58 Goal 1 (goals): strong_iteration(multiplication(x0, zero)) = addition(one, multiplication(x0, zero)).
% 0.24/0.58 Proof:
% 0.24/0.58 strong_iteration(multiplication(x0, zero))
% 0.24/0.58 = { by axiom 3 (infty_unfold1) }
% 0.24/0.58 addition(multiplication(multiplication(x0, zero), strong_iteration(multiplication(x0, zero))), one)
% 0.24/0.58 = { by axiom 1 (additive_commutativity) }
% 0.24/0.58 addition(one, multiplication(multiplication(x0, zero), strong_iteration(multiplication(x0, zero))))
% 0.24/0.58 = { by axiom 4 (multiplicative_associativity) R->L }
% 0.24/0.58 addition(one, multiplication(x0, multiplication(zero, strong_iteration(multiplication(x0, zero)))))
% 0.24/0.58 = { by axiom 2 (left_annihilation) }
% 0.24/0.58 addition(one, multiplication(x0, zero))
% 0.24/0.58 % SZS output end Proof
% 0.24/0.58
% 0.24/0.58 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------