%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE146+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 11:39:54 AM UTC 2026
% Result : Theorem 0.09s 0.44s
% Output : Proof 0.09s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE146+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 : n017.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 13:08:04 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.44 Command-line arguments: --flatten --complete-subsets
% 0.09/0.44
% 0.09/0.44 % SZS status Theorem
% 0.09/0.44
% 0.09/0.44 % SZS output start Proof
% 0.09/0.44 Axiom 1 (idempotence): addition(X, X) = X.
% 0.09/0.44 Axiom 2 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 0.09/0.44 Axiom 3 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 0.09/0.44 Axiom 4 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 0.09/0.44 Axiom 5 (infty_unfold1): strong_iteration(X) = addition(multiplication(X, strong_iteration(X)), one).
% 0.09/0.44 Axiom 6 (order): ifeq3(addition(X, Y), Y, leq(X, Y), true) = true.
% 0.09/0.44
% 0.09/0.44 Lemma 7: addition(one, multiplication(X, strong_iteration(X))) = strong_iteration(X).
% 0.09/0.44 Proof:
% 0.09/0.44 addition(one, multiplication(X, strong_iteration(X)))
% 0.09/0.44 = { by axiom 2 (additive_commutativity) R->L }
% 0.09/0.44 addition(multiplication(X, strong_iteration(X)), one)
% 0.09/0.44 = { by axiom 5 (infty_unfold1) R->L }
% 0.09/0.44 strong_iteration(X)
% 0.09/0.44
% 0.09/0.44 Goal 1 (goals): leq(one, strong_iteration(x0)) = true.
% 0.09/0.44 Proof:
% 0.09/0.44 leq(one, strong_iteration(x0))
% 0.09/0.44 = { by axiom 3 (ifeq_axiom) R->L }
% 0.09/0.44 ifeq3(strong_iteration(x0), strong_iteration(x0), leq(one, strong_iteration(x0)), true)
% 0.09/0.44 = { by lemma 7 R->L }
% 0.09/0.44 ifeq3(addition(one, multiplication(x0, strong_iteration(x0))), strong_iteration(x0), leq(one, strong_iteration(x0)), true)
% 0.09/0.44 = { by axiom 1 (idempotence) R->L }
% 0.09/0.44 ifeq3(addition(addition(one, one), multiplication(x0, strong_iteration(x0))), strong_iteration(x0), leq(one, strong_iteration(x0)), true)
% 0.09/0.44 = { by axiom 4 (additive_associativity) R->L }
% 0.09/0.44 ifeq3(addition(one, addition(one, multiplication(x0, strong_iteration(x0)))), strong_iteration(x0), leq(one, strong_iteration(x0)), true)
% 0.09/0.44 = { by lemma 7 }
% 0.09/0.44 ifeq3(addition(one, strong_iteration(x0)), strong_iteration(x0), leq(one, strong_iteration(x0)), true)
% 0.09/0.44 = { by axiom 6 (order) }
% 0.09/0.44 true
% 0.09/0.44 % SZS output end Proof
% 0.09/0.44
% 0.09/0.44 RESULT: Theorem (the conjecture is true).
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