%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE151+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 16.36s 2.59s
% Output : Proof 16.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE151+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 13:17:31 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.36/2.59 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 16.36/2.59
% 16.36/2.59 % SZS status Theorem
% 16.36/2.59
% 16.36/2.59 % SZS output start Proof
% 16.36/2.60 Axiom 1 (multiplicative_right_identity): multiplication(X, one) = X.
% 16.36/2.60 Axiom 2 (idempotence): addition(X, X) = X.
% 16.36/2.60 Axiom 3 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 16.36/2.60 Axiom 4 (multiplicative_associativity): multiplication(X, multiplication(Y, Z)) = multiplication(multiplication(X, Y), Z).
% 16.36/2.60 Axiom 5 (infty_unfold1): strong_iteration(X) = addition(multiplication(X, strong_iteration(X)), one).
% 16.36/2.60 Axiom 6 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 16.36/2.60 Axiom 7 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 16.36/2.60 Axiom 8 (distributivity1): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 16.36/2.60 Axiom 9 (order): ifeq3(addition(X, Y), Y, leq(X, Y), true) = true.
% 16.36/2.60 Axiom 10 (infty_coinduction): ifeq(leq(X, addition(multiplication(Y, X), Z)), true, leq(X, multiplication(strong_iteration(Y), Z)), true) = true.
% 16.36/2.60
% 16.36/2.60 Goal 1 (goals): leq(multiplication(x0, strong_iteration(multiplication(x1, x0))), multiplication(strong_iteration(multiplication(x0, x1)), x0)) = true.
% 16.36/2.60 Proof:
% 16.36/2.60 leq(multiplication(x0, strong_iteration(multiplication(x1, x0))), multiplication(strong_iteration(multiplication(x0, x1)), x0))
% 16.36/2.60 = { by axiom 6 (ifeq_axiom) R->L }
% 16.36/2.60 ifeq(true, true, leq(multiplication(x0, strong_iteration(multiplication(x1, x0))), multiplication(strong_iteration(multiplication(x0, x1)), x0)), true)
% 16.36/2.60 = { by axiom 9 (order) R->L }
% 16.36/2.60 ifeq(ifeq3(addition(multiplication(x0, strong_iteration(multiplication(x1, x0))), multiplication(x0, strong_iteration(multiplication(x1, x0)))), multiplication(x0, strong_iteration(multiplication(x1, x0))), leq(multiplication(x0, strong_iteration(multiplication(x1, x0))), multiplication(x0, strong_iteration(multiplication(x1, x0)))), true), true, leq(multiplication(x0, strong_iteration(multiplication(x1, x0))), multiplication(strong_iteration(multiplication(x0, x1)), x0)), true)
% 16.36/2.60 = { by axiom 2 (idempotence) }
% 16.36/2.60 ifeq(ifeq3(multiplication(x0, strong_iteration(multiplication(x1, x0))), multiplication(x0, strong_iteration(multiplication(x1, x0))), leq(multiplication(x0, strong_iteration(multiplication(x1, x0))), multiplication(x0, strong_iteration(multiplication(x1, x0)))), true), true, leq(multiplication(x0, strong_iteration(multiplication(x1, x0))), multiplication(strong_iteration(multiplication(x0, x1)), x0)), true)
% 16.36/2.60 = { by axiom 7 (ifeq_axiom) }
% 16.36/2.60 ifeq(leq(multiplication(x0, strong_iteration(multiplication(x1, x0))), multiplication(x0, strong_iteration(multiplication(x1, x0)))), true, leq(multiplication(x0, strong_iteration(multiplication(x1, x0))), multiplication(strong_iteration(multiplication(x0, x1)), x0)), true)
% 16.36/2.60 = { by axiom 5 (infty_unfold1) }
% 16.36/2.60 ifeq(leq(multiplication(x0, strong_iteration(multiplication(x1, x0))), multiplication(x0, addition(multiplication(multiplication(x1, x0), strong_iteration(multiplication(x1, x0))), one))), true, leq(multiplication(x0, strong_iteration(multiplication(x1, x0))), multiplication(strong_iteration(multiplication(x0, x1)), x0)), true)
% 16.36/2.60 = { by axiom 3 (additive_commutativity) }
% 16.36/2.60 ifeq(leq(multiplication(x0, strong_iteration(multiplication(x1, x0))), multiplication(x0, addition(one, multiplication(multiplication(x1, x0), strong_iteration(multiplication(x1, x0)))))), true, leq(multiplication(x0, strong_iteration(multiplication(x1, x0))), multiplication(strong_iteration(multiplication(x0, x1)), x0)), true)
% 16.36/2.60 = { by axiom 4 (multiplicative_associativity) R->L }
% 16.36/2.60 ifeq(leq(multiplication(x0, strong_iteration(multiplication(x1, x0))), multiplication(x0, addition(one, multiplication(x1, multiplication(x0, strong_iteration(multiplication(x1, x0))))))), true, leq(multiplication(x0, strong_iteration(multiplication(x1, x0))), multiplication(strong_iteration(multiplication(x0, x1)), x0)), true)
% 16.36/2.60 = { by axiom 8 (distributivity1) }
% 16.36/2.60 ifeq(leq(multiplication(x0, strong_iteration(multiplication(x1, x0))), addition(multiplication(x0, one), multiplication(x0, multiplication(x1, multiplication(x0, strong_iteration(multiplication(x1, x0))))))), true, leq(multiplication(x0, strong_iteration(multiplication(x1, x0))), multiplication(strong_iteration(multiplication(x0, x1)), x0)), true)
% 16.36/2.60 = { by axiom 1 (multiplicative_right_identity) }
% 16.36/2.60 ifeq(leq(multiplication(x0, strong_iteration(multiplication(x1, x0))), addition(x0, multiplication(x0, multiplication(x1, multiplication(x0, strong_iteration(multiplication(x1, x0))))))), true, leq(multiplication(x0, strong_iteration(multiplication(x1, x0))), multiplication(strong_iteration(multiplication(x0, x1)), x0)), true)
% 16.36/2.60 = { by axiom 4 (multiplicative_associativity) }
% 16.36/2.60 ifeq(leq(multiplication(x0, strong_iteration(multiplication(x1, x0))), addition(x0, multiplication(multiplication(x0, x1), multiplication(x0, strong_iteration(multiplication(x1, x0)))))), true, leq(multiplication(x0, strong_iteration(multiplication(x1, x0))), multiplication(strong_iteration(multiplication(x0, x1)), x0)), true)
% 16.36/2.60 = { by axiom 3 (additive_commutativity) R->L }
% 16.36/2.60 ifeq(leq(multiplication(x0, strong_iteration(multiplication(x1, x0))), addition(multiplication(multiplication(x0, x1), multiplication(x0, strong_iteration(multiplication(x1, x0)))), x0)), true, leq(multiplication(x0, strong_iteration(multiplication(x1, x0))), multiplication(strong_iteration(multiplication(x0, x1)), x0)), true)
% 16.36/2.60 = { by axiom 10 (infty_coinduction) }
% 16.36/2.60 true
% 16.36/2.60 % SZS output end Proof
% 16.36/2.60
% 16.36/2.60 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------