%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE140+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 11:39:53 AM UTC 2026
% Result : Theorem 6.07s 1.35s
% Output : Proof 6.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE140+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 % Computer : n001.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Sun Sep 27 13:18:00 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.07/1.35 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 6.07/1.35
% 6.07/1.35 % SZS status Theorem
% 6.07/1.35
% 6.07/1.36 % SZS output start Proof
% 6.07/1.36 Axiom 1 (multiplicative_right_identity): multiplication(X, one) = X.
% 6.07/1.36 Axiom 2 (idempotence): addition(X, X) = X.
% 6.07/1.36 Axiom 3 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 6.07/1.36 Axiom 4 (goals): leq(x0, x1) = true.
% 6.07/1.36 Axiom 5 (infty_unfold1): strong_iteration(X) = addition(multiplication(X, strong_iteration(X)), one).
% 6.07/1.36 Axiom 6 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 6.07/1.36 Axiom 7 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 6.07/1.36 Axiom 8 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 6.07/1.36 Axiom 9 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 6.07/1.36 Axiom 10 (distributivity2): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 6.07/1.36 Axiom 11 (order): ifeq3(addition(X, Y), Y, leq(X, Y), true) = true.
% 6.07/1.36 Axiom 12 (order_1): ifeq2(leq(X, Y), true, addition(X, Y), Y) = Y.
% 6.07/1.36 Axiom 13 (infty_coinduction): ifeq(leq(X, addition(multiplication(Y, X), Z)), true, leq(X, multiplication(strong_iteration(Y), Z)), true) = true.
% 6.07/1.36
% 6.07/1.36 Goal 1 (goals_1): leq(strong_iteration(x0), strong_iteration(x1)) = true.
% 6.07/1.36 Proof:
% 6.07/1.36 leq(strong_iteration(x0), strong_iteration(x1))
% 6.07/1.36 = { by axiom 12 (order_1) R->L }
% 6.07/1.36 leq(strong_iteration(x0), strong_iteration(ifeq2(leq(x0, x1), true, addition(x0, x1), x1)))
% 6.07/1.36 = { by axiom 4 (goals) }
% 6.07/1.36 leq(strong_iteration(x0), strong_iteration(ifeq2(true, true, addition(x0, x1), x1)))
% 6.07/1.36 = { by axiom 9 (ifeq_axiom) }
% 6.07/1.36 leq(strong_iteration(x0), strong_iteration(addition(x0, x1)))
% 6.07/1.36 = { by axiom 3 (additive_commutativity) R->L }
% 6.07/1.36 leq(strong_iteration(x0), strong_iteration(addition(x1, x0)))
% 6.07/1.36 = { by axiom 7 (ifeq_axiom) R->L }
% 6.07/1.36 ifeq(true, true, leq(strong_iteration(x0), strong_iteration(addition(x1, x0))), true)
% 6.07/1.36 = { by axiom 11 (order) R->L }
% 6.07/1.36 ifeq(ifeq3(addition(strong_iteration(x0), addition(strong_iteration(x0), multiplication(x1, strong_iteration(x0)))), addition(strong_iteration(x0), multiplication(x1, strong_iteration(x0))), leq(strong_iteration(x0), addition(strong_iteration(x0), multiplication(x1, strong_iteration(x0)))), true), true, leq(strong_iteration(x0), strong_iteration(addition(x1, x0))), true)
% 6.07/1.36 = { by axiom 6 (additive_associativity) }
% 6.07/1.36 ifeq(ifeq3(addition(addition(strong_iteration(x0), strong_iteration(x0)), multiplication(x1, strong_iteration(x0))), addition(strong_iteration(x0), multiplication(x1, strong_iteration(x0))), leq(strong_iteration(x0), addition(strong_iteration(x0), multiplication(x1, strong_iteration(x0)))), true), true, leq(strong_iteration(x0), strong_iteration(addition(x1, x0))), true)
% 6.07/1.36 = { by axiom 2 (idempotence) }
% 6.07/1.36 ifeq(ifeq3(addition(strong_iteration(x0), multiplication(x1, strong_iteration(x0))), addition(strong_iteration(x0), multiplication(x1, strong_iteration(x0))), leq(strong_iteration(x0), addition(strong_iteration(x0), multiplication(x1, strong_iteration(x0)))), true), true, leq(strong_iteration(x0), strong_iteration(addition(x1, x0))), true)
% 6.07/1.36 = { by axiom 8 (ifeq_axiom) }
% 6.07/1.37 ifeq(leq(strong_iteration(x0), addition(strong_iteration(x0), multiplication(x1, strong_iteration(x0)))), true, leq(strong_iteration(x0), strong_iteration(addition(x1, x0))), true)
% 6.07/1.37 = { by axiom 3 (additive_commutativity) R->L }
% 6.07/1.37 ifeq(leq(strong_iteration(x0), addition(multiplication(x1, strong_iteration(x0)), strong_iteration(x0))), true, leq(strong_iteration(x0), strong_iteration(addition(x1, x0))), true)
% 6.07/1.37 = { by axiom 5 (infty_unfold1) }
% 6.07/1.37 ifeq(leq(strong_iteration(x0), addition(multiplication(x1, strong_iteration(x0)), addition(multiplication(x0, strong_iteration(x0)), one))), true, leq(strong_iteration(x0), strong_iteration(addition(x1, x0))), true)
% 6.07/1.37 = { by axiom 3 (additive_commutativity) R->L }
% 6.07/1.37 ifeq(leq(strong_iteration(x0), addition(addition(multiplication(x0, strong_iteration(x0)), one), multiplication(x1, strong_iteration(x0)))), true, leq(strong_iteration(x0), strong_iteration(addition(x1, x0))), true)
% 6.07/1.37 = { by axiom 6 (additive_associativity) R->L }
% 6.07/1.37 ifeq(leq(strong_iteration(x0), addition(multiplication(x0, strong_iteration(x0)), addition(one, multiplication(x1, strong_iteration(x0))))), true, leq(strong_iteration(x0), strong_iteration(addition(x1, x0))), true)
% 6.07/1.37 = { by axiom 3 (additive_commutativity) }
% 6.07/1.37 ifeq(leq(strong_iteration(x0), addition(multiplication(x0, strong_iteration(x0)), addition(multiplication(x1, strong_iteration(x0)), one))), true, leq(strong_iteration(x0), strong_iteration(addition(x1, x0))), true)
% 6.07/1.37 = { by axiom 6 (additive_associativity) }
% 6.07/1.37 ifeq(leq(strong_iteration(x0), addition(addition(multiplication(x0, strong_iteration(x0)), multiplication(x1, strong_iteration(x0))), one)), true, leq(strong_iteration(x0), strong_iteration(addition(x1, x0))), true)
% 6.07/1.37 = { by axiom 10 (distributivity2) R->L }
% 6.07/1.37 ifeq(leq(strong_iteration(x0), addition(multiplication(addition(x0, x1), strong_iteration(x0)), one)), true, leq(strong_iteration(x0), strong_iteration(addition(x1, x0))), true)
% 6.07/1.37 = { by axiom 3 (additive_commutativity) }
% 6.07/1.37 ifeq(leq(strong_iteration(x0), addition(one, multiplication(addition(x0, x1), strong_iteration(x0)))), true, leq(strong_iteration(x0), strong_iteration(addition(x1, x0))), true)
% 6.07/1.37 = { by axiom 3 (additive_commutativity) }
% 6.07/1.37 ifeq(leq(strong_iteration(x0), addition(one, multiplication(addition(x1, x0), strong_iteration(x0)))), true, leq(strong_iteration(x0), strong_iteration(addition(x1, x0))), true)
% 6.07/1.37 = { by axiom 3 (additive_commutativity) R->L }
% 6.07/1.37 ifeq(leq(strong_iteration(x0), addition(multiplication(addition(x1, x0), strong_iteration(x0)), one)), true, leq(strong_iteration(x0), strong_iteration(addition(x1, x0))), true)
% 6.07/1.37 = { by axiom 1 (multiplicative_right_identity) R->L }
% 6.07/1.37 ifeq(leq(strong_iteration(x0), addition(multiplication(addition(x1, x0), strong_iteration(x0)), one)), true, leq(strong_iteration(x0), multiplication(strong_iteration(addition(x1, x0)), one)), true)
% 6.07/1.37 = { by axiom 13 (infty_coinduction) }
% 6.07/1.37 true
% 6.07/1.37 % SZS output end Proof
% 6.07/1.37
% 6.07/1.37 RESULT: Theorem (the conjecture is true).
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