%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE150+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 0.13s 0.44s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE150+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n018.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 13:15:08 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.44 Command-line arguments: --flatten --complete-subsets
% 0.13/0.44
% 0.13/0.44 % SZS status Theorem
% 0.13/0.44
% 0.13/0.45 % SZS output start Proof
% 0.13/0.45 Axiom 1 (idempotence): addition(X, X) = X.
% 0.13/0.45 Axiom 2 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 0.13/0.45 Axiom 3 (left_annihilation): multiplication(zero, X) = zero.
% 0.13/0.45 Axiom 4 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 0.13/0.45 Axiom 5 (infty_unfold1): strong_iteration(X) = addition(multiplication(X, strong_iteration(X)), one).
% 0.13/0.45 Axiom 6 (multiplicative_associativity): multiplication(X, multiplication(Y, Z)) = multiplication(multiplication(X, Y), Z).
% 0.13/0.45 Axiom 7 (order): ifeq3(addition(X, Y), Y, leq(X, Y), true) = true.
% 0.13/0.45
% 0.13/0.45 Lemma 8: addition(one, multiplication(X, zero)) = strong_iteration(multiplication(X, zero)).
% 0.13/0.45 Proof:
% 0.13/0.45 addition(one, multiplication(X, zero))
% 0.13/0.45 = { by axiom 3 (left_annihilation) R->L }
% 0.13/0.45 addition(one, multiplication(X, multiplication(zero, strong_iteration(multiplication(X, zero)))))
% 0.13/0.45 = { by axiom 6 (multiplicative_associativity) }
% 0.13/0.45 addition(one, multiplication(multiplication(X, zero), strong_iteration(multiplication(X, zero))))
% 0.13/0.45 = { by axiom 2 (additive_commutativity) R->L }
% 0.13/0.45 addition(multiplication(multiplication(X, zero), strong_iteration(multiplication(X, zero))), one)
% 0.13/0.45 = { by axiom 5 (infty_unfold1) R->L }
% 0.13/0.45 strong_iteration(multiplication(X, zero))
% 0.13/0.45
% 0.13/0.45 Goal 1 (goals): tuple(leq(addition(one, multiplication(x0, zero)), strong_iteration(multiplication(x0, zero))), leq(strong_iteration(multiplication(x0_2, zero)), addition(one, multiplication(x0_2, zero)))) = tuple(true, true).
% 0.13/0.45 Proof:
% 0.13/0.45 tuple(leq(addition(one, multiplication(x0, zero)), strong_iteration(multiplication(x0, zero))), leq(strong_iteration(multiplication(x0_2, zero)), addition(one, multiplication(x0_2, zero))))
% 0.13/0.45 = { by lemma 8 R->L }
% 0.13/0.45 tuple(leq(addition(one, multiplication(x0, zero)), strong_iteration(multiplication(x0, zero))), leq(addition(one, multiplication(x0_2, zero)), addition(one, multiplication(x0_2, zero))))
% 0.13/0.45 = { by axiom 4 (ifeq_axiom) R->L }
% 0.13/0.45 tuple(leq(addition(one, multiplication(x0, zero)), strong_iteration(multiplication(x0, zero))), ifeq3(addition(one, multiplication(x0_2, zero)), addition(one, multiplication(x0_2, zero)), leq(addition(one, multiplication(x0_2, zero)), addition(one, multiplication(x0_2, zero))), true))
% 0.13/0.45 = { by axiom 1 (idempotence) R->L }
% 0.13/0.45 tuple(leq(addition(one, multiplication(x0, zero)), strong_iteration(multiplication(x0, zero))), ifeq3(addition(addition(one, multiplication(x0_2, zero)), addition(one, multiplication(x0_2, zero))), addition(one, multiplication(x0_2, zero)), leq(addition(one, multiplication(x0_2, zero)), addition(one, multiplication(x0_2, zero))), true))
% 0.13/0.45 = { by axiom 7 (order) }
% 0.13/0.45 tuple(leq(addition(one, multiplication(x0, zero)), strong_iteration(multiplication(x0, zero))), true)
% 0.13/0.45 = { by lemma 8 R->L }
% 0.13/0.45 tuple(leq(addition(one, multiplication(x0, zero)), addition(one, multiplication(x0, zero))), true)
% 0.13/0.45 = { by axiom 4 (ifeq_axiom) R->L }
% 0.13/0.45 tuple(ifeq3(addition(one, multiplication(x0, zero)), addition(one, multiplication(x0, zero)), leq(addition(one, multiplication(x0, zero)), addition(one, multiplication(x0, zero))), true), true)
% 0.13/0.45 = { by axiom 1 (idempotence) R->L }
% 0.13/0.45 tuple(ifeq3(addition(addition(one, multiplication(x0, zero)), addition(one, multiplication(x0, zero))), addition(one, multiplication(x0, zero)), leq(addition(one, multiplication(x0, zero)), addition(one, multiplication(x0, zero))), true), true)
% 0.13/0.45 = { by axiom 7 (order) }
% 0.13/0.45 tuple(true, true)
% 0.13/0.45 % SZS output end Proof
% 0.13/0.45
% 0.13/0.45 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------