%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE147+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 11:39:54 AM UTC 2026
% Result : Theorem 52.51s 7.19s
% Output : Proof 53.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE147+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 13:18:30 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 52.51/7.19 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
% 52.51/7.19
% 52.51/7.19 % SZS status Theorem
% 52.51/7.19
% 53.33/7.21 % SZS output start Proof
% 53.33/7.21 Axiom 1 (multiplicative_left_identity): multiplication(one, X) = X.
% 53.33/7.21 Axiom 2 (idempotence): addition(X, X) = X.
% 53.33/7.21 Axiom 3 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 53.33/7.21 Axiom 4 (star_unfold1): addition(one, multiplication(X, star(X))) = star(X).
% 53.33/7.21 Axiom 5 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 53.33/7.21 Axiom 6 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 53.33/7.21 Axiom 7 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 53.33/7.21 Axiom 8 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 53.33/7.21 Axiom 9 (infty_unfold1): strong_iteration(X) = addition(multiplication(X, strong_iteration(X)), one).
% 53.33/7.21 Axiom 10 (distributivity2): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 53.33/7.21 Axiom 11 (order): ifeq3(addition(X, Y), Y, leq(X, Y), true) = true.
% 53.33/7.21 Axiom 12 (order_1): ifeq2(leq(X, Y), true, addition(X, Y), Y) = Y.
% 53.33/7.21 Axiom 13 (star_induction1): ifeq(leq(addition(multiplication(X, Y), Z), Y), true, leq(multiplication(star(X), Z), Y), true) = true.
% 53.33/7.21
% 53.33/7.21 Lemma 14: addition(one, star(X)) = star(X).
% 53.33/7.21 Proof:
% 53.33/7.21 addition(one, star(X))
% 53.33/7.21 = { by axiom 4 (star_unfold1) R->L }
% 53.33/7.21 addition(one, addition(one, multiplication(X, star(X))))
% 53.33/7.21 = { by axiom 5 (additive_associativity) }
% 53.33/7.21 addition(addition(one, one), multiplication(X, star(X)))
% 53.33/7.21 = { by axiom 2 (idempotence) }
% 53.33/7.21 addition(one, multiplication(X, star(X)))
% 53.33/7.21 = { by axiom 4 (star_unfold1) }
% 53.33/7.21 star(X)
% 53.33/7.21
% 53.33/7.21 Lemma 15: addition(one, multiplication(X, strong_iteration(X))) = strong_iteration(X).
% 53.33/7.21 Proof:
% 53.33/7.21 addition(one, multiplication(X, strong_iteration(X)))
% 53.33/7.21 = { by axiom 3 (additive_commutativity) R->L }
% 53.33/7.21 addition(multiplication(X, strong_iteration(X)), one)
% 53.33/7.21 = { by axiom 9 (infty_unfold1) R->L }
% 53.33/7.21 strong_iteration(X)
% 53.33/7.21
% 53.33/7.21 Lemma 16: addition(multiplication(X, Y), multiplication(Z, Y)) = multiplication(addition(Z, X), Y).
% 53.33/7.21 Proof:
% 53.33/7.21 addition(multiplication(X, Y), multiplication(Z, Y))
% 53.33/7.21 = { by axiom 10 (distributivity2) R->L }
% 53.33/7.21 multiplication(addition(X, Z), Y)
% 53.33/7.21 = { by axiom 3 (additive_commutativity) }
% 53.33/7.21 multiplication(addition(Z, X), Y)
% 53.33/7.21
% 53.33/7.21 Goal 1 (goals): strong_iteration(multiplication(star(x0), x1)) = multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))).
% 53.33/7.21 Proof:
% 53.33/7.21 strong_iteration(multiplication(star(x0), x1))
% 53.33/7.21 = { by axiom 12 (order_1) R->L }
% 53.33/7.21 ifeq2(leq(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), true, addition(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1)))
% 53.33/7.21 = { by axiom 6 (ifeq_axiom) R->L }
% 53.33/7.21 ifeq2(ifeq(true, true, leq(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), true), true, addition(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1)))
% 53.33/7.21 = { by axiom 11 (order) R->L }
% 53.33/7.21 ifeq2(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, addition(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1)))
% 53.33/7.21 = { by axiom 2 (idempotence) }
% 53.33/7.22 ifeq2(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, addition(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1)))
% 53.33/7.22 = { by axiom 7 (ifeq_axiom) }
% 53.33/7.22 ifeq2(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, addition(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1)))
% 53.33/7.22 = { by lemma 15 R->L }
% 53.33/7.22 ifeq2(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, addition(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1)))
% 53.33/7.22 = { by lemma 14 R->L }
% 53.33/7.22 ifeq2(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, addition(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1)))
% 53.33/7.22 = { by lemma 16 R->L }
% 53.33/7.22 ifeq2(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, addition(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1)))
% 53.33/7.22 = { by axiom 1 (multiplicative_left_identity) }
% 53.33/7.22 ifeq2(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, addition(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1)))
% 53.33/7.22 = { by axiom 3 (additive_commutativity) R->L }
% 53.33/7.22 ifeq2(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, addition(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1)))
% 53.33/7.22 = { by axiom 10 (distributivity2) }
% 53.33/7.22 ifeq2(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, addition(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1)))
% 53.33/7.22 = { by axiom 5 (additive_associativity) R->L }
% 53.33/7.22 ifeq2(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, addition(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1)))
% 53.33/7.22 = { by axiom 3 (additive_commutativity) R->L }
% 53.33/7.22 ifeq2(ifeq(leq(addition(multiplication(multiplication(star(x0), x1), strong_iteration(multiplication(star(x0), x1))), addition(one, multiplication(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, addition(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1)))
% 53.33/7.22 = { by axiom 5 (additive_associativity) }
% 53.33/7.22 ifeq2(ifeq(leq(addition(addition(multiplication(multiplication(star(x0), x1), strong_iteration(multiplication(star(x0), x1))), one), multiplication(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, addition(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1)))
% 53.33/7.22 = { by axiom 3 (additive_commutativity) }
% 53.33/7.22 ifeq2(ifeq(leq(addition(multiplication(x1, strong_iteration(multiplication(star(x0), x1))), addition(multiplication(multiplication(star(x0), 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, addition(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1)))
% 53.33/7.22 = { by axiom 3 (additive_commutativity) }
% 53.33/7.22 ifeq2(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, addition(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1)))
% 53.33/7.22 = { by lemma 15 }
% 53.33/7.22 ifeq2(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, addition(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1)))
% 53.33/7.22 = { by axiom 13 (star_induction1) }
% 53.33/7.22 ifeq2(true, true, addition(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1)))
% 53.33/7.22 = { by axiom 8 (ifeq_axiom) }
% 53.33/7.22 addition(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), strong_iteration(multiplication(star(x0), x1)))
% 53.33/7.22 = { by axiom 1 (multiplicative_left_identity) R->L }
% 53.33/7.22 addition(multiplication(star(x1), strong_iteration(multiplication(star(x0), x1))), multiplication(one, strong_iteration(multiplication(star(x0), x1))))
% 53.33/7.23 = { by lemma 16 }
% 53.33/7.23 multiplication(addition(one, star(x1)), strong_iteration(multiplication(star(x0), x1)))
% 53.33/7.23 = { by lemma 14 }
% 53.33/7.23 multiplication(star(x1), strong_iteration(multiplication(star(x0), x1)))
% 53.33/7.23 % SZS output end Proof
% 53.33/7.23
% 53.33/7.23 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------