%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE147+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 119.69s 15.51s
% Output : Proof 119.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE147+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 13:12:31 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 119.69/15.51 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
% 119.69/15.51
% 119.69/15.51 % SZS status Theorem
% 119.69/15.51
% 119.69/15.53 % SZS output start Proof
% 119.69/15.53 Axiom 1 (multiplicative_left_identity): multiplication(one, X) = X.
% 119.69/15.53 Axiom 2 (idempotence): addition(X, X) = X.
% 119.69/15.53 Axiom 3 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 119.69/15.53 Axiom 4 (star_unfold1): addition(one, multiplication(X, star(X))) = star(X).
% 119.69/15.53 Axiom 5 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 119.69/15.53 Axiom 6 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 119.69/15.53 Axiom 7 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 119.69/15.53 Axiom 8 (infty_unfold1): strong_iteration(X) = addition(multiplication(X, strong_iteration(X)), one).
% 119.69/15.53 Axiom 9 (distributivity2): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 119.69/15.53 Axiom 10 (order): ifeq3(addition(X, Y), Y, leq(X, Y), true) = true.
% 119.69/15.53 Axiom 11 (star_induction1): ifeq(leq(addition(multiplication(X, Y), Z), Y), true, leq(multiplication(star(X), Z), Y), true) = true.
% 119.69/15.53
% 119.69/15.53 Lemma 12: addition(one, star(X)) = star(X).
% 119.69/15.53 Proof:
% 119.69/15.53 addition(one, star(X))
% 119.69/15.53 = { by axiom 4 (star_unfold1) R->L }
% 119.69/15.53 addition(one, addition(one, multiplication(X, star(X))))
% 119.69/15.53 = { by axiom 5 (additive_associativity) }
% 119.69/15.53 addition(addition(one, one), multiplication(X, star(X)))
% 119.69/15.53 = { by axiom 2 (idempotence) }
% 119.69/15.54 addition(one, multiplication(X, star(X)))
% 119.69/15.54 = { by axiom 4 (star_unfold1) }
% 119.69/15.54 star(X)
% 119.69/15.54
% 119.69/15.54 Lemma 13: addition(one, multiplication(X, strong_iteration(X))) = strong_iteration(X).
% 119.69/15.54 Proof:
% 119.69/15.54 addition(one, multiplication(X, strong_iteration(X)))
% 119.69/15.54 = { by axiom 3 (additive_commutativity) R->L }
% 119.69/15.54 addition(multiplication(X, strong_iteration(X)), one)
% 119.69/15.54 = { by axiom 8 (infty_unfold1) R->L }
% 119.69/15.54 strong_iteration(X)
% 119.69/15.54
% 119.69/15.54 Lemma 14: addition(multiplication(X, Y), multiplication(Z, Y)) = multiplication(addition(Z, X), Y).
% 119.69/15.54 Proof:
% 119.69/15.54 addition(multiplication(X, Y), multiplication(Z, Y))
% 119.69/15.54 = { by axiom 9 (distributivity2) R->L }
% 119.69/15.54 multiplication(addition(X, Z), Y)
% 119.69/15.54 = { by axiom 3 (additive_commutativity) }
% 119.69/15.54 multiplication(addition(Z, X), Y)
% 119.69/15.54
% 119.69/15.54 Goal 1 (goals): tuple(leq(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), leq(strong_iteration(multiplication(star(x0_2), x1_2)), multiplication(star(x1_2), strong_iteration(multiplication(star(x0_2), x1_2))))) = tuple(true, true).
% 119.69/15.54 Proof:
% 119.69/15.54 tuple(leq(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), leq(strong_iteration(multiplication(star(x0_2), x1_2)), multiplication(star(x1_2), strong_iteration(multiplication(star(x0_2), x1_2)))))
% 119.69/15.54 = { by axiom 7 (ifeq_axiom) R->L }
% 119.69/15.54 tuple(leq(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), ifeq3(multiplication(star(x1_2), strong_iteration(multiplication(star(x0_2), x1_2))), multiplication(star(x1_2), strong_iteration(multiplication(star(x0_2), x1_2))), leq(strong_iteration(multiplication(star(x0_2), x1_2)), multiplication(star(x1_2), strong_iteration(multiplication(star(x0_2), x1_2)))), true))
% 119.69/15.54 = { by lemma 12 R->L }
% 119.69/15.54 tuple(leq(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), ifeq3(multiplication(addition(one, star(x1_2)), strong_iteration(multiplication(star(x0_2), x1_2))), multiplication(star(x1_2), strong_iteration(multiplication(star(x0_2), x1_2))), leq(strong_iteration(multiplication(star(x0_2), x1_2)), multiplication(star(x1_2), strong_iteration(multiplication(star(x0_2), x1_2)))), true))
% 119.69/15.54 = { by lemma 14 R->L }
% 119.69/15.54 tuple(leq(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), ifeq3(addition(multiplication(star(x1_2), strong_iteration(multiplication(star(x0_2), x1_2))), multiplication(one, strong_iteration(multiplication(star(x0_2), x1_2)))), multiplication(star(x1_2), strong_iteration(multiplication(star(x0_2), x1_2))), leq(strong_iteration(multiplication(star(x0_2), x1_2)), multiplication(star(x1_2), strong_iteration(multiplication(star(x0_2), x1_2)))), true))
% 119.69/15.54 = { by axiom 1 (multiplicative_left_identity) }
% 119.69/15.54 tuple(leq(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), ifeq3(addition(multiplication(star(x1_2), strong_iteration(multiplication(star(x0_2), x1_2))), strong_iteration(multiplication(star(x0_2), x1_2))), multiplication(star(x1_2), strong_iteration(multiplication(star(x0_2), x1_2))), leq(strong_iteration(multiplication(star(x0_2), x1_2)), multiplication(star(x1_2), strong_iteration(multiplication(star(x0_2), x1_2)))), true))
% 119.69/15.54 = { by axiom 3 (additive_commutativity) R->L }
% 119.69/15.54 tuple(leq(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), ifeq3(addition(strong_iteration(multiplication(star(x0_2), x1_2)), multiplication(star(x1_2), strong_iteration(multiplication(star(x0_2), x1_2)))), multiplication(star(x1_2), strong_iteration(multiplication(star(x0_2), x1_2))), leq(strong_iteration(multiplication(star(x0_2), x1_2)), multiplication(star(x1_2), strong_iteration(multiplication(star(x0_2), x1_2)))), true))
% 119.69/15.54 = { by axiom 10 (order) }
% 119.69/15.54 tuple(leq(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), true)
% 119.69/15.54 = { by axiom 6 (ifeq_axiom) R->L }
% 119.69/15.54 tuple(ifeq(true, true, leq(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), true), true)
% 119.69/15.54 = { by axiom 10 (order) R->L }
% 119.69/15.54 tuple(ifeq(ifeq3(addition(strong_iteration(multiplication(star(x0), x1)), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1)), leq(strong_iteration(multiplication(star(x0), x1)), strong_iteration(multiplication(star(x0), x1))), true), true, leq(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), true), true)
% 119.69/15.54 = { by axiom 2 (idempotence) }
% 119.69/15.54 tuple(ifeq(ifeq3(strong_iteration(multiplication(star(x0), x1)), strong_iteration(multiplication(star(x0), x1)), leq(strong_iteration(multiplication(star(x0), x1)), strong_iteration(multiplication(star(x0), x1))), true), true, leq(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), true), true)
% 119.69/15.54 = { by axiom 7 (ifeq_axiom) }
% 119.69/15.54 tuple(ifeq(leq(strong_iteration(multiplication(star(x0), x1)), strong_iteration(multiplication(star(x0), x1))), true, leq(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), true), true)
% 119.69/15.54 = { by lemma 13 R->L }
% 119.69/15.54 tuple(ifeq(leq(addition(one, multiplication(multiplication(star(x0), x1), strong_iteration(multiplication(star(x0), x1)))), strong_iteration(multiplication(star(x0), x1))), true, leq(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), true), true)
% 119.69/15.54 = { by lemma 12 R->L }
% 119.69/15.54 tuple(ifeq(leq(addition(one, multiplication(multiplication(addition(one, star(x0)), x1), strong_iteration(multiplication(star(x0), x1)))), strong_iteration(multiplication(star(x0), x1))), true, leq(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), true), true)
% 119.69/15.54 = { by lemma 14 R->L }
% 119.69/15.54 tuple(ifeq(leq(addition(one, multiplication(addition(multiplication(star(x0), x1), multiplication(one, x1)), strong_iteration(multiplication(star(x0), x1)))), strong_iteration(multiplication(star(x0), x1))), true, leq(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), true), true)
% 119.69/15.54 = { by axiom 1 (multiplicative_left_identity) }
% 119.69/15.54 tuple(ifeq(leq(addition(one, multiplication(addition(multiplication(star(x0), x1), x1), strong_iteration(multiplication(star(x0), x1)))), strong_iteration(multiplication(star(x0), x1))), true, leq(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), true), true)
% 119.69/15.54 = { by axiom 3 (additive_commutativity) R->L }
% 119.69/15.54 tuple(ifeq(leq(addition(multiplication(addition(multiplication(star(x0), x1), x1), strong_iteration(multiplication(star(x0), x1))), one), strong_iteration(multiplication(star(x0), x1))), true, leq(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), true), true)
% 119.69/15.54 = { by axiom 9 (distributivity2) }
% 119.69/15.54 tuple(ifeq(leq(addition(addition(multiplication(multiplication(star(x0), x1), strong_iteration(multiplication(star(x0), x1))), multiplication(x1, strong_iteration(multiplication(star(x0), x1)))), one), strong_iteration(multiplication(star(x0), x1))), true, leq(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), true), true)
% 119.69/15.54 = { by axiom 5 (additive_associativity) R->L }
% 119.69/15.54 tuple(ifeq(leq(addition(multiplication(multiplication(star(x0), x1), strong_iteration(multiplication(star(x0), x1))), addition(multiplication(x1, strong_iteration(multiplication(star(x0), x1))), one)), strong_iteration(multiplication(star(x0), x1))), true, leq(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), true), true)
% 119.69/15.54 = { by axiom 3 (additive_commutativity) R->L }
% 119.69/15.54 tuple(ifeq(leq(addition(addition(multiplication(x1, strong_iteration(multiplication(star(x0), x1))), one), multiplication(multiplication(star(x0), x1), strong_iteration(multiplication(star(x0), x1)))), strong_iteration(multiplication(star(x0), x1))), true, leq(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), true), true)
% 119.69/15.54 = { by axiom 5 (additive_associativity) R->L }
% 119.69/15.54 tuple(ifeq(leq(addition(multiplication(x1, strong_iteration(multiplication(star(x0), x1))), addition(one, multiplication(multiplication(star(x0), x1), strong_iteration(multiplication(star(x0), x1))))), strong_iteration(multiplication(star(x0), x1))), true, leq(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), true), true)
% 119.69/15.54 = { by lemma 13 }
% 119.69/15.55 tuple(ifeq(leq(addition(multiplication(x1, strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), true, leq(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), true), true)
% 119.69/15.55 = { by axiom 11 (star_induction1) }
% 119.69/15.55 tuple(true, true)
% 119.69/15.55 % SZS output end Proof
% 119.69/15.55
% 119.69/15.55 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------