%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE159+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/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 11:39:56 AM UTC 2026
% Result : Theorem 102.42s 13.44s
% Output : Proof 103.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE159+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n014.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sun Sep 27 13:13:31 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 102.42/13.44 Command-line arguments: --flatten-regeneralise
% 102.42/13.44
% 102.42/13.44 % SZS status Theorem
% 102.42/13.44
% 102.42/13.49 % SZS output start Proof
% 102.42/13.49 Axiom 1 (idempotence): addition(X, X) = X.
% 102.42/13.49 Axiom 2 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 102.42/13.49 Axiom 3 (multiplicative_right_identity): multiplication(X, one) = X.
% 102.42/13.49 Axiom 4 (multiplicative_left_identity): multiplication(one, X) = X.
% 102.42/13.49 Axiom 5 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 102.42/13.49 Axiom 6 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 102.42/13.49 Axiom 7 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 102.42/13.49 Axiom 8 (star_unfold1): addition(one, multiplication(X, star(X))) = star(X).
% 102.42/13.49 Axiom 9 (star_unfold2): addition(one, multiplication(star(X), X)) = star(X).
% 102.42/13.49 Axiom 10 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 102.42/13.49 Axiom 11 (multiplicative_associativity): multiplication(X, multiplication(Y, Z)) = multiplication(multiplication(X, Y), Z).
% 102.42/13.49 Axiom 12 (goals): leq(multiplication(x0, x1), multiplication(x2, x0)) = true.
% 102.42/13.49 Axiom 13 (distributivity1): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 102.42/13.49 Axiom 14 (distributivity2): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 102.42/13.49 Axiom 15 (order): ifeq3(addition(X, Y), Y, leq(X, Y), true) = true.
% 102.42/13.49 Axiom 16 (order_1): ifeq2(leq(X, Y), true, addition(X, Y), Y) = Y.
% 102.42/13.49 Axiom 17 (star_induction2): ifeq(leq(addition(multiplication(X, Y), Z), X), true, leq(multiplication(Z, star(Y)), X), true) = true.
% 102.42/13.49
% 102.42/13.49 Lemma 18: multiplication(addition(X, one), Y) = addition(Y, multiplication(X, Y)).
% 102.42/13.49 Proof:
% 102.42/13.49 multiplication(addition(X, one), Y)
% 102.42/13.49 = { by axiom 2 (additive_commutativity) R->L }
% 102.42/13.49 multiplication(addition(one, X), Y)
% 102.42/13.49 = { by axiom 14 (distributivity2) }
% 102.42/13.49 addition(multiplication(one, Y), multiplication(X, Y))
% 102.42/13.49 = { by axiom 4 (multiplicative_left_identity) }
% 102.42/13.49 addition(Y, multiplication(X, Y))
% 102.42/13.49
% 102.42/13.49 Lemma 19: addition(X, multiplication(Y, multiplication(star(Y), X))) = multiplication(star(Y), X).
% 102.42/13.49 Proof:
% 102.42/13.49 addition(X, multiplication(Y, multiplication(star(Y), X)))
% 102.42/13.49 = { by axiom 11 (multiplicative_associativity) }
% 102.42/13.49 addition(X, multiplication(multiplication(Y, star(Y)), X))
% 102.42/13.49 = { by lemma 18 R->L }
% 102.42/13.49 multiplication(addition(multiplication(Y, star(Y)), one), X)
% 102.42/13.49 = { by axiom 2 (additive_commutativity) }
% 102.42/13.49 multiplication(addition(one, multiplication(Y, star(Y))), X)
% 102.42/13.49 = { by axiom 8 (star_unfold1) }
% 102.42/13.49 multiplication(star(Y), X)
% 102.42/13.49
% 102.42/13.49 Lemma 20: multiplication(X, addition(one, Y)) = addition(X, multiplication(X, Y)).
% 102.42/13.49 Proof:
% 102.42/13.49 multiplication(X, addition(one, Y))
% 102.42/13.49 = { by axiom 13 (distributivity1) }
% 102.42/13.49 addition(multiplication(X, one), multiplication(X, Y))
% 102.42/13.49 = { by axiom 3 (multiplicative_right_identity) }
% 102.42/13.49 addition(X, multiplication(X, Y))
% 102.42/13.49
% 102.42/13.49 Lemma 21: multiplication(star(X), X) = multiplication(X, star(X)).
% 102.42/13.49 Proof:
% 102.42/13.49 multiplication(star(X), X)
% 102.42/13.49 = { by lemma 19 R->L }
% 102.42/13.49 addition(X, multiplication(X, multiplication(star(X), X)))
% 102.42/13.49 = { by lemma 20 R->L }
% 102.42/13.49 multiplication(X, addition(one, multiplication(star(X), X)))
% 102.42/13.49 = { by axiom 9 (star_unfold2) }
% 102.42/13.49 multiplication(X, star(X))
% 102.42/13.49
% 102.42/13.49 Lemma 22: addition(X, addition(X, Y)) = addition(X, Y).
% 102.42/13.49 Proof:
% 102.42/13.49 addition(X, addition(X, Y))
% 102.42/13.49 = { by axiom 10 (additive_associativity) }
% 102.42/13.49 addition(addition(X, X), Y)
% 102.42/13.49 = { by axiom 1 (idempotence) }
% 102.42/13.49 addition(X, Y)
% 102.42/13.49
% 102.42/13.49 Lemma 23: multiplication(star(X), multiplication(X, Y)) = multiplication(X, multiplication(star(X), Y)).
% 102.42/13.49 Proof:
% 102.42/13.49 multiplication(star(X), multiplication(X, Y))
% 102.42/13.49 = { by axiom 11 (multiplicative_associativity) }
% 102.42/13.49 multiplication(multiplication(star(X), X), Y)
% 102.42/13.49 = { by lemma 21 }
% 102.42/13.49 multiplication(multiplication(X, star(X)), Y)
% 102.42/13.49 = { by axiom 11 (multiplicative_associativity) R->L }
% 102.42/13.49 multiplication(X, multiplication(star(X), Y))
% 102.42/13.49
% 102.42/13.49 Lemma 24: addition(multiplication(x2, x0), multiplication(x0, x1)) = multiplication(x2, x0).
% 102.42/13.49 Proof:
% 102.42/13.49 addition(multiplication(x2, x0), multiplication(x0, x1))
% 102.42/13.49 = { by axiom 2 (additive_commutativity) R->L }
% 102.42/13.49 addition(multiplication(x0, x1), multiplication(x2, x0))
% 102.42/13.49 = { by axiom 6 (ifeq_axiom) R->L }
% 102.42/13.49 ifeq2(true, true, addition(multiplication(x0, x1), multiplication(x2, x0)), multiplication(x2, x0))
% 102.42/13.49 = { by axiom 12 (goals) R->L }
% 102.42/13.49 ifeq2(leq(multiplication(x0, x1), multiplication(x2, x0)), true, addition(multiplication(x0, x1), multiplication(x2, x0)), multiplication(x2, x0))
% 102.42/13.49 = { by axiom 16 (order_1) }
% 102.42/13.49 multiplication(x2, x0)
% 102.42/13.49
% 102.42/13.49 Goal 1 (goals_1): leq(multiplication(x0, star(x1)), multiplication(star(x2), x0)) = true.
% 102.42/13.49 Proof:
% 102.42/13.49 leq(multiplication(x0, star(x1)), multiplication(star(x2), x0))
% 102.42/13.49 = { by axiom 16 (order_1) R->L }
% 102.42/13.49 leq(multiplication(x0, star(x1)), ifeq2(leq(multiplication(x2, multiplication(multiplication(star(x2), x0), star(x1))), multiplication(star(x2), x0)), true, addition(multiplication(x2, multiplication(multiplication(star(x2), x0), star(x1))), multiplication(star(x2), x0)), multiplication(star(x2), x0)))
% 102.42/13.49 = { by axiom 11 (multiplicative_associativity) }
% 102.42/13.49 leq(multiplication(x0, star(x1)), ifeq2(leq(multiplication(multiplication(x2, multiplication(star(x2), x0)), star(x1)), multiplication(star(x2), x0)), true, addition(multiplication(x2, multiplication(multiplication(star(x2), x0), star(x1))), multiplication(star(x2), x0)), multiplication(star(x2), x0)))
% 102.42/13.50 = { by axiom 7 (ifeq_axiom) R->L }
% 102.42/13.50 leq(multiplication(x0, star(x1)), ifeq2(ifeq(true, true, leq(multiplication(multiplication(x2, multiplication(star(x2), x0)), star(x1)), multiplication(star(x2), x0)), true), true, addition(multiplication(x2, multiplication(multiplication(star(x2), x0), star(x1))), multiplication(star(x2), x0)), multiplication(star(x2), x0)))
% 102.42/13.50 = { by axiom 15 (order) R->L }
% 102.42/13.50 leq(multiplication(x0, star(x1)), ifeq2(ifeq(ifeq3(addition(multiplication(x2, multiplication(star(x2), x0)), addition(multiplication(x2, multiplication(star(x2), x0)), multiplication(star(x2), x0))), addition(multiplication(x2, multiplication(star(x2), x0)), multiplication(star(x2), x0)), leq(multiplication(x2, multiplication(star(x2), x0)), addition(multiplication(x2, multiplication(star(x2), x0)), multiplication(star(x2), x0))), true), true, leq(multiplication(multiplication(x2, multiplication(star(x2), x0)), star(x1)), multiplication(star(x2), x0)), true), true, addition(multiplication(x2, multiplication(multiplication(star(x2), x0), star(x1))), multiplication(star(x2), x0)), multiplication(star(x2), x0)))
% 102.42/13.50 = { by lemma 22 }
% 102.42/13.50 leq(multiplication(x0, star(x1)), ifeq2(ifeq(ifeq3(addition(multiplication(x2, multiplication(star(x2), x0)), multiplication(star(x2), x0)), addition(multiplication(x2, multiplication(star(x2), x0)), multiplication(star(x2), x0)), leq(multiplication(x2, multiplication(star(x2), x0)), addition(multiplication(x2, multiplication(star(x2), x0)), multiplication(star(x2), x0))), true), true, leq(multiplication(multiplication(x2, multiplication(star(x2), x0)), star(x1)), multiplication(star(x2), x0)), true), true, addition(multiplication(x2, multiplication(multiplication(star(x2), x0), star(x1))), multiplication(star(x2), x0)), multiplication(star(x2), x0)))
% 102.42/13.50 = { by axiom 5 (ifeq_axiom) }
% 102.42/13.50 leq(multiplication(x0, star(x1)), ifeq2(ifeq(leq(multiplication(x2, multiplication(star(x2), x0)), addition(multiplication(x2, multiplication(star(x2), x0)), multiplication(star(x2), x0))), true, leq(multiplication(multiplication(x2, multiplication(star(x2), x0)), star(x1)), multiplication(star(x2), x0)), true), true, addition(multiplication(x2, multiplication(multiplication(star(x2), x0), star(x1))), multiplication(star(x2), x0)), multiplication(star(x2), x0)))
% 102.42/13.50 = { by axiom 2 (additive_commutativity) }
% 102.42/13.50 leq(multiplication(x0, star(x1)), ifeq2(ifeq(leq(multiplication(x2, multiplication(star(x2), x0)), addition(multiplication(star(x2), x0), multiplication(x2, multiplication(star(x2), x0)))), true, leq(multiplication(multiplication(x2, multiplication(star(x2), x0)), star(x1)), multiplication(star(x2), x0)), true), true, addition(multiplication(x2, multiplication(multiplication(star(x2), x0), star(x1))), multiplication(star(x2), x0)), multiplication(star(x2), x0)))
% 102.42/13.50 = { by axiom 11 (multiplicative_associativity) }
% 102.42/13.50 leq(multiplication(x0, star(x1)), ifeq2(ifeq(leq(multiplication(x2, multiplication(star(x2), x0)), addition(multiplication(star(x2), x0), multiplication(multiplication(x2, star(x2)), x0))), true, leq(multiplication(multiplication(x2, multiplication(star(x2), x0)), star(x1)), multiplication(star(x2), x0)), true), true, addition(multiplication(x2, multiplication(multiplication(star(x2), x0), star(x1))), multiplication(star(x2), x0)), multiplication(star(x2), x0)))
% 102.42/13.50 = { by axiom 14 (distributivity2) R->L }
% 102.42/13.50 leq(multiplication(x0, star(x1)), ifeq2(ifeq(leq(multiplication(x2, multiplication(star(x2), x0)), multiplication(addition(star(x2), multiplication(x2, star(x2))), x0)), true, leq(multiplication(multiplication(x2, multiplication(star(x2), x0)), star(x1)), multiplication(star(x2), x0)), true), true, addition(multiplication(x2, multiplication(multiplication(star(x2), x0), star(x1))), multiplication(star(x2), x0)), multiplication(star(x2), x0)))
% 102.42/13.50 = { by axiom 2 (additive_commutativity) R->L }
% 102.42/13.50 leq(multiplication(x0, star(x1)), ifeq2(ifeq(leq(multiplication(x2, multiplication(star(x2), x0)), multiplication(addition(multiplication(x2, star(x2)), star(x2)), x0)), true, leq(multiplication(multiplication(x2, multiplication(star(x2), x0)), star(x1)), multiplication(star(x2), x0)), true), true, addition(multiplication(x2, multiplication(multiplication(star(x2), x0), star(x1))), multiplication(star(x2), x0)), multiplication(star(x2), x0)))
% 103.18/13.50 = { by axiom 8 (star_unfold1) R->L }
% 103.18/13.50 leq(multiplication(x0, star(x1)), ifeq2(ifeq(leq(multiplication(x2, multiplication(star(x2), x0)), multiplication(addition(multiplication(x2, star(x2)), addition(one, multiplication(x2, star(x2)))), x0)), true, leq(multiplication(multiplication(x2, multiplication(star(x2), x0)), star(x1)), multiplication(star(x2), x0)), true), true, addition(multiplication(x2, multiplication(multiplication(star(x2), x0), star(x1))), multiplication(star(x2), x0)), multiplication(star(x2), x0)))
% 103.18/13.50 = { by axiom 2 (additive_commutativity) R->L }
% 103.18/13.50 leq(multiplication(x0, star(x1)), ifeq2(ifeq(leq(multiplication(x2, multiplication(star(x2), x0)), multiplication(addition(multiplication(x2, star(x2)), addition(multiplication(x2, star(x2)), one)), x0)), true, leq(multiplication(multiplication(x2, multiplication(star(x2), x0)), star(x1)), multiplication(star(x2), x0)), true), true, addition(multiplication(x2, multiplication(multiplication(star(x2), x0), star(x1))), multiplication(star(x2), x0)), multiplication(star(x2), x0)))
% 103.18/13.50 = { by lemma 22 }
% 103.18/13.50 leq(multiplication(x0, star(x1)), ifeq2(ifeq(leq(multiplication(x2, multiplication(star(x2), x0)), multiplication(addition(multiplication(x2, star(x2)), one), x0)), true, leq(multiplication(multiplication(x2, multiplication(star(x2), x0)), star(x1)), multiplication(star(x2), x0)), true), true, addition(multiplication(x2, multiplication(multiplication(star(x2), x0), star(x1))), multiplication(star(x2), x0)), multiplication(star(x2), x0)))
% 103.18/13.50 = { by axiom 2 (additive_commutativity) }
% 103.18/13.50 leq(multiplication(x0, star(x1)), ifeq2(ifeq(leq(multiplication(x2, multiplication(star(x2), x0)), multiplication(addition(one, multiplication(x2, star(x2))), x0)), true, leq(multiplication(multiplication(x2, multiplication(star(x2), x0)), star(x1)), multiplication(star(x2), x0)), true), true, addition(multiplication(x2, multiplication(multiplication(star(x2), x0), star(x1))), multiplication(star(x2), x0)), multiplication(star(x2), x0)))
% 103.18/13.50 = { by axiom 8 (star_unfold1) }
% 103.18/13.50 leq(multiplication(x0, star(x1)), ifeq2(ifeq(leq(multiplication(x2, multiplication(star(x2), x0)), multiplication(star(x2), x0)), true, leq(multiplication(multiplication(x2, multiplication(star(x2), x0)), star(x1)), multiplication(star(x2), x0)), true), true, addition(multiplication(x2, multiplication(multiplication(star(x2), x0), star(x1))), multiplication(star(x2), x0)), multiplication(star(x2), x0)))
% 103.18/13.50 = { by lemma 23 R->L }
% 103.18/13.50 leq(multiplication(x0, star(x1)), ifeq2(ifeq(leq(multiplication(star(x2), multiplication(x2, x0)), multiplication(star(x2), x0)), true, leq(multiplication(multiplication(x2, multiplication(star(x2), x0)), star(x1)), multiplication(star(x2), x0)), true), true, addition(multiplication(x2, multiplication(multiplication(star(x2), x0), star(x1))), multiplication(star(x2), x0)), multiplication(star(x2), x0)))
% 103.18/13.50 = { by lemma 24 R->L }
% 103.18/13.50 leq(multiplication(x0, star(x1)), ifeq2(ifeq(leq(multiplication(star(x2), addition(multiplication(x2, x0), multiplication(x0, x1))), multiplication(star(x2), x0)), true, leq(multiplication(multiplication(x2, multiplication(star(x2), x0)), star(x1)), multiplication(star(x2), x0)), true), true, addition(multiplication(x2, multiplication(multiplication(star(x2), x0), star(x1))), multiplication(star(x2), x0)), multiplication(star(x2), x0)))
% 103.18/13.50 = { by axiom 2 (additive_commutativity) R->L }
% 103.18/13.51 leq(multiplication(x0, star(x1)), ifeq2(ifeq(leq(multiplication(star(x2), addition(multiplication(x0, x1), multiplication(x2, x0))), multiplication(star(x2), x0)), true, leq(multiplication(multiplication(x2, multiplication(star(x2), x0)), star(x1)), multiplication(star(x2), x0)), true), true, addition(multiplication(x2, multiplication(multiplication(star(x2), x0), star(x1))), multiplication(star(x2), x0)), multiplication(star(x2), x0)))
% 103.18/13.51 = { by axiom 13 (distributivity1) }
% 103.18/13.51 leq(multiplication(x0, star(x1)), ifeq2(ifeq(leq(addition(multiplication(star(x2), multiplication(x0, x1)), multiplication(star(x2), multiplication(x2, x0))), multiplication(star(x2), x0)), true, leq(multiplication(multiplication(x2, multiplication(star(x2), x0)), star(x1)), multiplication(star(x2), x0)), true), true, addition(multiplication(x2, multiplication(multiplication(star(x2), x0), star(x1))), multiplication(star(x2), x0)), multiplication(star(x2), x0)))
% 103.18/13.51 = { by axiom 11 (multiplicative_associativity) }
% 103.18/13.51 leq(multiplication(x0, star(x1)), ifeq2(ifeq(leq(addition(multiplication(multiplication(star(x2), x0), x1), multiplication(star(x2), multiplication(x2, x0))), multiplication(star(x2), x0)), true, leq(multiplication(multiplication(x2, multiplication(star(x2), x0)), star(x1)), multiplication(star(x2), x0)), true), true, addition(multiplication(x2, multiplication(multiplication(star(x2), x0), star(x1))), multiplication(star(x2), x0)), multiplication(star(x2), x0)))
% 103.18/13.51 = { by lemma 23 }
% 103.18/13.51 leq(multiplication(x0, star(x1)), ifeq2(ifeq(leq(addition(multiplication(multiplication(star(x2), x0), x1), multiplication(x2, multiplication(star(x2), x0))), multiplication(star(x2), x0)), true, leq(multiplication(multiplication(x2, multiplication(star(x2), x0)), star(x1)), multiplication(star(x2), x0)), true), true, addition(multiplication(x2, multiplication(multiplication(star(x2), x0), star(x1))), multiplication(star(x2), x0)), multiplication(star(x2), x0)))
% 103.18/13.51 = { by axiom 17 (star_induction2) }
% 103.18/13.51 leq(multiplication(x0, star(x1)), ifeq2(true, true, addition(multiplication(x2, multiplication(multiplication(star(x2), x0), star(x1))), multiplication(star(x2), x0)), multiplication(star(x2), x0)))
% 103.18/13.51 = { by axiom 6 (ifeq_axiom) }
% 103.18/13.51 leq(multiplication(x0, star(x1)), addition(multiplication(x2, multiplication(multiplication(star(x2), x0), star(x1))), multiplication(star(x2), x0)))
% 103.18/13.51 = { by axiom 11 (multiplicative_associativity) R->L }
% 103.18/13.51 leq(multiplication(x0, star(x1)), addition(multiplication(x2, multiplication(star(x2), multiplication(x0, star(x1)))), multiplication(star(x2), x0)))
% 103.18/13.51 = { by lemma 23 R->L }
% 103.18/13.51 leq(multiplication(x0, star(x1)), addition(multiplication(star(x2), multiplication(x2, multiplication(x0, star(x1)))), multiplication(star(x2), x0)))
% 103.18/13.51 = { by axiom 2 (additive_commutativity) }
% 103.18/13.51 leq(multiplication(x0, star(x1)), addition(multiplication(star(x2), x0), multiplication(star(x2), multiplication(x2, multiplication(x0, star(x1))))))
% 103.18/13.51 = { by axiom 13 (distributivity1) R->L }
% 103.18/13.51 leq(multiplication(x0, star(x1)), multiplication(star(x2), addition(x0, multiplication(x2, multiplication(x0, star(x1))))))
% 103.18/13.51 = { by axiom 11 (multiplicative_associativity) }
% 103.18/13.51 leq(multiplication(x0, star(x1)), multiplication(star(x2), addition(x0, multiplication(multiplication(x2, x0), star(x1)))))
% 103.18/13.51 = { by lemma 24 R->L }
% 103.18/13.51 leq(multiplication(x0, star(x1)), multiplication(star(x2), addition(x0, multiplication(addition(multiplication(x2, x0), multiplication(x0, x1)), star(x1)))))
% 103.18/13.51 = { by axiom 14 (distributivity2) }
% 103.18/13.51 leq(multiplication(x0, star(x1)), multiplication(star(x2), addition(x0, addition(multiplication(multiplication(x2, x0), star(x1)), multiplication(multiplication(x0, x1), star(x1))))))
% 103.18/13.51 = { by axiom 11 (multiplicative_associativity) R->L }
% 103.18/13.51 leq(multiplication(x0, star(x1)), multiplication(star(x2), addition(x0, addition(multiplication(x2, multiplication(x0, star(x1))), multiplication(multiplication(x0, x1), star(x1))))))
% 103.18/13.51 = { by axiom 11 (multiplicative_associativity) R->L }
% 103.18/13.51 leq(multiplication(x0, star(x1)), multiplication(star(x2), addition(x0, addition(multiplication(x2, multiplication(x0, star(x1))), multiplication(x0, multiplication(x1, star(x1)))))))
% 103.18/13.51 = { by lemma 21 R->L }
% 103.18/13.51 leq(multiplication(x0, star(x1)), multiplication(star(x2), addition(x0, addition(multiplication(x2, multiplication(x0, star(x1))), multiplication(x0, multiplication(star(x1), x1))))))
% 103.18/13.51 = { by axiom 11 (multiplicative_associativity) }
% 103.18/13.51 leq(multiplication(x0, star(x1)), multiplication(star(x2), addition(x0, addition(multiplication(x2, multiplication(x0, star(x1))), multiplication(multiplication(x0, star(x1)), x1)))))
% 103.18/13.51 = { by axiom 2 (additive_commutativity) R->L }
% 103.18/13.51 leq(multiplication(x0, star(x1)), multiplication(star(x2), addition(x0, addition(multiplication(multiplication(x0, star(x1)), x1), multiplication(x2, multiplication(x0, star(x1)))))))
% 103.18/13.51 = { by axiom 10 (additive_associativity) }
% 103.18/13.51 leq(multiplication(x0, star(x1)), multiplication(star(x2), addition(addition(x0, multiplication(multiplication(x0, star(x1)), x1)), multiplication(x2, multiplication(x0, star(x1))))))
% 103.18/13.51 = { by axiom 11 (multiplicative_associativity) R->L }
% 103.18/13.51 leq(multiplication(x0, star(x1)), multiplication(star(x2), addition(addition(x0, multiplication(x0, multiplication(star(x1), x1))), multiplication(x2, multiplication(x0, star(x1))))))
% 103.18/13.51 = { by lemma 20 R->L }
% 103.18/13.51 leq(multiplication(x0, star(x1)), multiplication(star(x2), addition(multiplication(x0, addition(one, multiplication(star(x1), x1))), multiplication(x2, multiplication(x0, star(x1))))))
% 103.18/13.51 = { by axiom 9 (star_unfold2) }
% 103.18/13.51 leq(multiplication(x0, star(x1)), multiplication(star(x2), addition(multiplication(x0, star(x1)), multiplication(x2, multiplication(x0, star(x1))))))
% 103.18/13.51 = { by axiom 2 (additive_commutativity) R->L }
% 103.18/13.51 leq(multiplication(x0, star(x1)), multiplication(star(x2), addition(multiplication(x2, multiplication(x0, star(x1))), multiplication(x0, star(x1)))))
% 103.18/13.51 = { by axiom 13 (distributivity1) }
% 103.18/13.51 leq(multiplication(x0, star(x1)), addition(multiplication(star(x2), multiplication(x2, multiplication(x0, star(x1)))), multiplication(star(x2), multiplication(x0, star(x1)))))
% 103.18/13.51 = { by axiom 6 (ifeq_axiom) R->L }
% 103.18/13.51 leq(multiplication(x0, star(x1)), ifeq2(true, true, addition(multiplication(star(x2), multiplication(x2, multiplication(x0, star(x1)))), multiplication(star(x2), multiplication(x0, star(x1)))), multiplication(star(x2), multiplication(x0, star(x1)))))
% 103.18/13.51 = { by axiom 15 (order) R->L }
% 103.18/13.51 leq(multiplication(x0, star(x1)), ifeq2(ifeq3(addition(multiplication(x2, multiplication(star(x2), multiplication(x0, star(x1)))), addition(multiplication(x2, multiplication(star(x2), multiplication(x0, star(x1)))), multiplication(x0, star(x1)))), addition(multiplication(x2, multiplication(star(x2), multiplication(x0, star(x1)))), multiplication(x0, star(x1))), leq(multiplication(x2, multiplication(star(x2), multiplication(x0, star(x1)))), addition(multiplication(x2, multiplication(star(x2), multiplication(x0, star(x1)))), multiplication(x0, star(x1)))), true), true, addition(multiplication(star(x2), multiplication(x2, multiplication(x0, star(x1)))), multiplication(star(x2), multiplication(x0, star(x1)))), multiplication(star(x2), multiplication(x0, star(x1)))))
% 103.18/13.51 = { by lemma 22 }
% 103.18/13.51 leq(multiplication(x0, star(x1)), ifeq2(ifeq3(addition(multiplication(x2, multiplication(star(x2), multiplication(x0, star(x1)))), multiplication(x0, star(x1))), addition(multiplication(x2, multiplication(star(x2), multiplication(x0, star(x1)))), multiplication(x0, star(x1))), leq(multiplication(x2, multiplication(star(x2), multiplication(x0, star(x1)))), addition(multiplication(x2, multiplication(star(x2), multiplication(x0, star(x1)))), multiplication(x0, star(x1)))), true), true, addition(multiplication(star(x2), multiplication(x2, multiplication(x0, star(x1)))), multiplication(star(x2), multiplication(x0, star(x1)))), multiplication(star(x2), multiplication(x0, star(x1)))))
% 103.18/13.51 = { by axiom 5 (ifeq_axiom) }
% 103.18/13.51 leq(multiplication(x0, star(x1)), ifeq2(leq(multiplication(x2, multiplication(star(x2), multiplication(x0, star(x1)))), addition(multiplication(x2, multiplication(star(x2), multiplication(x0, star(x1)))), multiplication(x0, star(x1)))), true, addition(multiplication(star(x2), multiplication(x2, multiplication(x0, star(x1)))), multiplication(star(x2), multiplication(x0, star(x1)))), multiplication(star(x2), multiplication(x0, star(x1)))))
% 103.18/13.51 = { by axiom 2 (additive_commutativity) }
% 103.18/13.51 leq(multiplication(x0, star(x1)), ifeq2(leq(multiplication(x2, multiplication(star(x2), multiplication(x0, star(x1)))), addition(multiplication(x0, star(x1)), multiplication(x2, multiplication(star(x2), multiplication(x0, star(x1)))))), true, addition(multiplication(star(x2), multiplication(x2, multiplication(x0, star(x1)))), multiplication(star(x2), multiplication(x0, star(x1)))), multiplication(star(x2), multiplication(x0, star(x1)))))
% 103.18/13.51 = { by lemma 19 }
% 103.18/13.51 leq(multiplication(x0, star(x1)), ifeq2(leq(multiplication(x2, multiplication(star(x2), multiplication(x0, star(x1)))), multiplication(star(x2), multiplication(x0, star(x1)))), true, addition(multiplication(star(x2), multiplication(x2, multiplication(x0, star(x1)))), multiplication(star(x2), multiplication(x0, star(x1)))), multiplication(star(x2), multiplication(x0, star(x1)))))
% 103.18/13.51 = { by lemma 23 R->L }
% 103.18/13.51 leq(multiplication(x0, star(x1)), ifeq2(leq(multiplication(star(x2), multiplication(x2, multiplication(x0, star(x1)))), multiplication(star(x2), multiplication(x0, star(x1)))), true, addition(multiplication(star(x2), multiplication(x2, multiplication(x0, star(x1)))), multiplication(star(x2), multiplication(x0, star(x1)))), multiplication(star(x2), multiplication(x0, star(x1)))))
% 103.18/13.51 = { by axiom 16 (order_1) }
% 103.18/13.51 leq(multiplication(x0, star(x1)), multiplication(star(x2), multiplication(x0, star(x1))))
% 103.18/13.52 = { by axiom 11 (multiplicative_associativity) }
% 103.18/13.52 leq(multiplication(x0, star(x1)), multiplication(multiplication(star(x2), x0), star(x1)))
% 103.18/13.52 = { by axiom 5 (ifeq_axiom) R->L }
% 103.18/13.52 ifeq3(multiplication(multiplication(star(x2), x0), star(x1)), multiplication(multiplication(star(x2), x0), star(x1)), leq(multiplication(x0, star(x1)), multiplication(multiplication(star(x2), x0), star(x1))), true)
% 103.18/13.52 = { by axiom 11 (multiplicative_associativity) R->L }
% 103.18/13.52 ifeq3(multiplication(star(x2), multiplication(x0, star(x1))), multiplication(multiplication(star(x2), x0), star(x1)), leq(multiplication(x0, star(x1)), multiplication(multiplication(star(x2), x0), star(x1))), true)
% 103.18/13.52 = { by axiom 8 (star_unfold1) R->L }
% 103.18/13.52 ifeq3(multiplication(addition(one, multiplication(x2, star(x2))), multiplication(x0, star(x1))), multiplication(multiplication(star(x2), x0), star(x1)), leq(multiplication(x0, star(x1)), multiplication(multiplication(star(x2), x0), star(x1))), true)
% 103.18/13.52 = { by lemma 22 R->L }
% 103.18/13.52 ifeq3(multiplication(addition(one, addition(one, multiplication(x2, star(x2)))), multiplication(x0, star(x1))), multiplication(multiplication(star(x2), x0), star(x1)), leq(multiplication(x0, star(x1)), multiplication(multiplication(star(x2), x0), star(x1))), true)
% 103.18/13.52 = { by axiom 8 (star_unfold1) }
% 103.18/13.52 ifeq3(multiplication(addition(one, star(x2)), multiplication(x0, star(x1))), multiplication(multiplication(star(x2), x0), star(x1)), leq(multiplication(x0, star(x1)), multiplication(multiplication(star(x2), x0), star(x1))), true)
% 103.18/13.52 = { by axiom 2 (additive_commutativity) }
% 103.18/13.52 ifeq3(multiplication(addition(star(x2), one), multiplication(x0, star(x1))), multiplication(multiplication(star(x2), x0), star(x1)), leq(multiplication(x0, star(x1)), multiplication(multiplication(star(x2), x0), star(x1))), true)
% 103.18/13.52 = { by lemma 18 }
% 103.18/13.52 ifeq3(addition(multiplication(x0, star(x1)), multiplication(star(x2), multiplication(x0, star(x1)))), multiplication(multiplication(star(x2), x0), star(x1)), leq(multiplication(x0, star(x1)), multiplication(multiplication(star(x2), x0), star(x1))), true)
% 103.18/13.52 = { by axiom 11 (multiplicative_associativity) }
% 103.18/13.52 ifeq3(addition(multiplication(x0, star(x1)), multiplication(multiplication(star(x2), x0), star(x1))), multiplication(multiplication(star(x2), x0), star(x1)), leq(multiplication(x0, star(x1)), multiplication(multiplication(star(x2), x0), star(x1))), true)
% 103.18/13.52 = { by axiom 15 (order) }
% 103.18/13.52 true
% 103.18/13.52 % SZS output end Proof
% 103.18/13.52
% 103.18/13.52 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------