%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE036+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 11:39:40 AM UTC 2026
% Result : Theorem 13.82s 2.18s
% Output : Proof 13.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE036+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n019.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 13:03:48 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.82/2.18 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
% 13.82/2.18
% 13.82/2.18 % SZS status Theorem
% 13.82/2.18
% 13.82/2.19 % SZS output start Proof
% 13.82/2.19 Axiom 1 (multiplicative_right_identity): multiplication(X, one) = X.
% 13.82/2.19 Axiom 2 (additive_idempotence): addition(X, X) = X.
% 13.82/2.19 Axiom 3 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 13.82/2.19 Axiom 4 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 13.82/2.19 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 13.82/2.19 Axiom 6 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 13.82/2.19 Axiom 7 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 13.82/2.19 Axiom 8 (right_distributivity): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 13.82/2.19 Axiom 9 (star_unfold_right): leq(addition(one, multiplication(X, star(X))), star(X)) = true.
% 13.82/2.19 Axiom 10 (order): ifeq3(addition(X, Y), Y, leq(X, Y), true) = true.
% 13.82/2.19 Axiom 11 (order_1): ifeq2(leq(X, Y), true, addition(X, Y), Y) = Y.
% 13.82/2.19 Axiom 12 (star_induction_left): ifeq(leq(addition(multiplication(X, Y), Z), Y), true, leq(multiplication(star(X), Z), Y), true) = true.
% 13.82/2.19
% 13.82/2.19 Goal 1 (goals): leq(star(x0), addition(one, multiplication(x0, star(x0)))) = true.
% 13.82/2.19 Proof:
% 13.82/2.19 leq(star(x0), addition(one, multiplication(x0, star(x0))))
% 13.82/2.19 = { by axiom 5 (ifeq_axiom) R->L }
% 13.82/2.19 ifeq(true, true, leq(star(x0), addition(one, multiplication(x0, star(x0)))), true)
% 13.82/2.19 = { by axiom 10 (order) R->L }
% 13.82/2.19 ifeq(ifeq3(addition(addition(one, multiplication(x0, addition(one, multiplication(x0, star(x0))))), addition(addition(one, multiplication(x0, addition(one, multiplication(x0, star(x0))))), multiplication(x0, star(x0)))), addition(addition(one, multiplication(x0, addition(one, multiplication(x0, star(x0))))), multiplication(x0, star(x0))), leq(addition(one, multiplication(x0, addition(one, multiplication(x0, star(x0))))), addition(addition(one, multiplication(x0, addition(one, multiplication(x0, star(x0))))), multiplication(x0, star(x0)))), true), true, leq(star(x0), addition(one, multiplication(x0, star(x0)))), true)
% 13.82/2.19 = { by axiom 4 (additive_associativity) }
% 13.82/2.19 ifeq(ifeq3(addition(addition(addition(one, multiplication(x0, addition(one, multiplication(x0, star(x0))))), addition(one, multiplication(x0, addition(one, multiplication(x0, star(x0)))))), multiplication(x0, star(x0))), addition(addition(one, multiplication(x0, addition(one, multiplication(x0, star(x0))))), multiplication(x0, star(x0))), leq(addition(one, multiplication(x0, addition(one, multiplication(x0, star(x0))))), addition(addition(one, multiplication(x0, addition(one, multiplication(x0, star(x0))))), multiplication(x0, star(x0)))), true), true, leq(star(x0), addition(one, multiplication(x0, star(x0)))), true)
% 13.82/2.19 = { by axiom 2 (additive_idempotence) }
% 13.82/2.19 ifeq(ifeq3(addition(addition(one, multiplication(x0, addition(one, multiplication(x0, star(x0))))), multiplication(x0, star(x0))), addition(addition(one, multiplication(x0, addition(one, multiplication(x0, star(x0))))), multiplication(x0, star(x0))), leq(addition(one, multiplication(x0, addition(one, multiplication(x0, star(x0))))), addition(addition(one, multiplication(x0, addition(one, multiplication(x0, star(x0))))), multiplication(x0, star(x0)))), true), true, leq(star(x0), addition(one, multiplication(x0, star(x0)))), true)
% 13.82/2.19 = { by axiom 6 (ifeq_axiom) }
% 13.82/2.19 ifeq(leq(addition(one, multiplication(x0, addition(one, multiplication(x0, star(x0))))), addition(addition(one, multiplication(x0, addition(one, multiplication(x0, star(x0))))), multiplication(x0, star(x0)))), true, leq(star(x0), addition(one, multiplication(x0, star(x0)))), true)
% 13.82/2.19 = { by axiom 3 (additive_commutativity) }
% 13.82/2.19 ifeq(leq(addition(one, multiplication(x0, addition(one, multiplication(x0, star(x0))))), addition(multiplication(x0, star(x0)), addition(one, multiplication(x0, addition(one, multiplication(x0, star(x0))))))), true, leq(star(x0), addition(one, multiplication(x0, star(x0)))), true)
% 13.82/2.19 = { by axiom 3 (additive_commutativity) R->L }
% 13.82/2.19 ifeq(leq(addition(one, multiplication(x0, addition(one, multiplication(x0, star(x0))))), addition(multiplication(x0, star(x0)), addition(multiplication(x0, addition(one, multiplication(x0, star(x0)))), one))), true, leq(star(x0), addition(one, multiplication(x0, star(x0)))), true)
% 13.82/2.19 = { by axiom 4 (additive_associativity) }
% 13.82/2.19 ifeq(leq(addition(one, multiplication(x0, addition(one, multiplication(x0, star(x0))))), addition(addition(multiplication(x0, star(x0)), multiplication(x0, addition(one, multiplication(x0, star(x0))))), one)), true, leq(star(x0), addition(one, multiplication(x0, star(x0)))), true)
% 13.82/2.19 = { by axiom 8 (right_distributivity) R->L }
% 13.82/2.20 ifeq(leq(addition(one, multiplication(x0, addition(one, multiplication(x0, star(x0))))), addition(multiplication(x0, addition(star(x0), addition(one, multiplication(x0, star(x0))))), one)), true, leq(star(x0), addition(one, multiplication(x0, star(x0)))), true)
% 13.82/2.20 = { by axiom 3 (additive_commutativity) }
% 13.82/2.20 ifeq(leq(addition(one, multiplication(x0, addition(one, multiplication(x0, star(x0))))), addition(multiplication(x0, addition(addition(one, multiplication(x0, star(x0))), star(x0))), one)), true, leq(star(x0), addition(one, multiplication(x0, star(x0)))), true)
% 13.82/2.20 = { by axiom 7 (ifeq_axiom) R->L }
% 13.82/2.20 ifeq(leq(addition(one, multiplication(x0, addition(one, multiplication(x0, star(x0))))), addition(multiplication(x0, ifeq2(true, true, addition(addition(one, multiplication(x0, star(x0))), star(x0)), star(x0))), one)), true, leq(star(x0), addition(one, multiplication(x0, star(x0)))), true)
% 13.82/2.20 = { by axiom 9 (star_unfold_right) R->L }
% 13.82/2.20 ifeq(leq(addition(one, multiplication(x0, addition(one, multiplication(x0, star(x0))))), addition(multiplication(x0, ifeq2(leq(addition(one, multiplication(x0, star(x0))), star(x0)), true, addition(addition(one, multiplication(x0, star(x0))), star(x0)), star(x0))), one)), true, leq(star(x0), addition(one, multiplication(x0, star(x0)))), true)
% 13.82/2.20 = { by axiom 11 (order_1) }
% 13.82/2.20 ifeq(leq(addition(one, multiplication(x0, addition(one, multiplication(x0, star(x0))))), addition(multiplication(x0, star(x0)), one)), true, leq(star(x0), addition(one, multiplication(x0, star(x0)))), true)
% 13.82/2.20 = { by axiom 3 (additive_commutativity) }
% 13.82/2.20 ifeq(leq(addition(one, multiplication(x0, addition(one, multiplication(x0, star(x0))))), addition(one, multiplication(x0, star(x0)))), true, leq(star(x0), addition(one, multiplication(x0, star(x0)))), true)
% 13.82/2.20 = { by axiom 3 (additive_commutativity) R->L }
% 13.82/2.20 ifeq(leq(addition(multiplication(x0, addition(one, multiplication(x0, star(x0)))), one), addition(one, multiplication(x0, star(x0)))), true, leq(star(x0), addition(one, multiplication(x0, star(x0)))), true)
% 13.82/2.20 = { by axiom 1 (multiplicative_right_identity) R->L }
% 13.82/2.20 ifeq(leq(addition(multiplication(x0, addition(one, multiplication(x0, star(x0)))), one), addition(one, multiplication(x0, star(x0)))), true, leq(multiplication(star(x0), one), addition(one, multiplication(x0, star(x0)))), true)
% 13.82/2.20 = { by axiom 12 (star_induction_left) }
% 13.82/2.20 true
% 13.82/2.20 % SZS output end Proof
% 13.82/2.20
% 13.82/2.20 RESULT: Theorem (the conjecture is true).
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