%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE137+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 11:39:52 AM UTC 2026
% Result : Theorem 0.19s 0.52s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE137+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n015.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 13:15:30 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.52 Command-line arguments: --flatten --complete-subsets
% 0.19/0.52
% 0.19/0.52 % SZS status Theorem
% 0.19/0.52
% 0.19/0.52 % SZS output start Proof
% 0.19/0.52 Axiom 1 (idempotence): addition(X, X) = X.
% 0.19/0.52 Axiom 2 (multiplicative_right_identity): multiplication(X, one) = X.
% 0.19/0.52 Axiom 3 (multiplicative_left_identity): multiplication(one, X) = X.
% 0.19/0.52 Axiom 4 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 0.19/0.52 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.19/0.52 Axiom 6 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 0.19/0.52 Axiom 7 (distributivity2): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 0.19/0.52 Axiom 8 (order): ifeq3(addition(X, Y), Y, leq(X, Y), true) = true.
% 0.19/0.52 Axiom 9 (infty_coinduction): ifeq(leq(X, addition(multiplication(Y, X), Z)), true, leq(X, multiplication(strong_iteration(Y), Z)), true) = true.
% 0.19/0.52
% 0.19/0.52 Goal 1 (goals): leq(x0, strong_iteration(one)) = true.
% 0.19/0.52 Proof:
% 0.19/0.52 leq(x0, strong_iteration(one))
% 0.19/0.52 = { by axiom 2 (multiplicative_right_identity) R->L }
% 0.19/0.52 leq(x0, multiplication(strong_iteration(one), one))
% 0.19/0.52 = { by axiom 1 (idempotence) R->L }
% 0.19/0.52 leq(x0, multiplication(strong_iteration(addition(one, one)), one))
% 0.19/0.52 = { by axiom 5 (ifeq_axiom) R->L }
% 0.19/0.52 ifeq(true, true, leq(x0, multiplication(strong_iteration(addition(one, one)), one)), true)
% 0.19/0.52 = { by axiom 8 (order) R->L }
% 0.19/0.52 ifeq(ifeq3(addition(x0, addition(x0, addition(multiplication(one, x0), one))), addition(x0, addition(multiplication(one, x0), one)), leq(x0, addition(x0, addition(multiplication(one, x0), one))), true), true, leq(x0, multiplication(strong_iteration(addition(one, one)), one)), true)
% 0.19/0.52 = { by axiom 6 (additive_associativity) }
% 0.19/0.52 ifeq(ifeq3(addition(addition(x0, x0), addition(multiplication(one, x0), one)), addition(x0, addition(multiplication(one, x0), one)), leq(x0, addition(x0, addition(multiplication(one, x0), one))), true), true, leq(x0, multiplication(strong_iteration(addition(one, one)), one)), true)
% 0.19/0.52 = { by axiom 1 (idempotence) }
% 0.19/0.52 ifeq(ifeq3(addition(x0, addition(multiplication(one, x0), one)), addition(x0, addition(multiplication(one, x0), one)), leq(x0, addition(x0, addition(multiplication(one, x0), one))), true), true, leq(x0, multiplication(strong_iteration(addition(one, one)), one)), true)
% 0.19/0.52 = { by axiom 4 (ifeq_axiom) }
% 0.19/0.52 ifeq(leq(x0, addition(x0, addition(multiplication(one, x0), one))), true, leq(x0, multiplication(strong_iteration(addition(one, one)), one)), true)
% 0.19/0.52 = { by axiom 6 (additive_associativity) }
% 0.19/0.52 ifeq(leq(x0, addition(addition(x0, multiplication(one, x0)), one)), true, leq(x0, multiplication(strong_iteration(addition(one, one)), one)), true)
% 0.19/0.52 = { by axiom 3 (multiplicative_left_identity) R->L }
% 0.19/0.52 ifeq(leq(x0, addition(addition(multiplication(one, x0), multiplication(one, x0)), one)), true, leq(x0, multiplication(strong_iteration(addition(one, one)), one)), true)
% 0.19/0.52 = { by axiom 7 (distributivity2) R->L }
% 0.19/0.52 ifeq(leq(x0, addition(multiplication(addition(one, one), x0), one)), true, leq(x0, multiplication(strong_iteration(addition(one, one)), one)), true)
% 0.19/0.52 = { by axiom 9 (infty_coinduction) }
% 0.19/0.52 true
% 0.19/0.52 % SZS output end Proof
% 0.19/0.52
% 0.19/0.52 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------