%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE046+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 11:39:42 AM UTC 2026
% Result : Theorem 104.63s 13.65s
% Output : Proof 106.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE046+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 : n016.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 13:10:47 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 104.63/13.65 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
% 104.63/13.65
% 104.63/13.65 % SZS status Theorem
% 104.63/13.65
% 105.42/13.76 % SZS output start Proof
% 105.42/13.76 Axiom 1 (multiplicative_right_identity): multiplication(X, one) = X.
% 105.42/13.76 Axiom 2 (multiplicative_left_identity): multiplication(one, X) = X.
% 105.42/13.76 Axiom 3 (additive_idempotence): addition(X, X) = X.
% 105.42/13.76 Axiom 4 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 105.42/13.76 Axiom 5 (multiplicative_associativity): multiplication(X, multiplication(Y, Z)) = multiplication(multiplication(X, Y), Z).
% 105.42/13.76 Axiom 6 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 105.42/13.77 Axiom 7 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 105.42/13.77 Axiom 8 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 105.42/13.77 Axiom 9 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 105.42/13.77 Axiom 10 (right_distributivity): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 105.42/13.77 Axiom 11 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 105.42/13.77 Axiom 12 (goals): leq(multiplication(star(x1), star(x0)), multiplication(star(x0), star(x1))) = true.
% 105.42/13.77 Axiom 13 (star_unfold_right): leq(addition(one, multiplication(X, star(X))), star(X)) = true.
% 105.42/13.77 Axiom 14 (star_unfold_left): leq(addition(one, multiplication(star(X), X)), star(X)) = true.
% 105.42/13.77 Axiom 15 (order): ifeq3(addition(X, Y), Y, leq(X, Y), true) = true.
% 105.42/13.77 Axiom 16 (order_1): ifeq2(leq(X, Y), true, addition(X, Y), Y) = Y.
% 105.42/13.77 Axiom 17 (star_induction_right): ifeq(leq(addition(multiplication(X, Y), Z), X), true, leq(multiplication(Z, star(Y)), X), true) = true.
% 105.42/13.77 Axiom 18 (star_induction_left): ifeq(leq(addition(multiplication(X, Y), Z), Y), true, leq(multiplication(star(X), Z), Y), true) = true.
% 105.42/13.77
% 105.42/13.77 Lemma 19: addition(X, multiplication(Y, X)) = multiplication(addition(Y, one), X).
% 105.42/13.77 Proof:
% 105.42/13.77 addition(X, multiplication(Y, X))
% 105.42/13.77 = { by axiom 2 (multiplicative_left_identity) R->L }
% 105.42/13.77 addition(multiplication(one, X), multiplication(Y, X))
% 105.42/13.77 = { by axiom 11 (left_distributivity) R->L }
% 105.42/13.77 multiplication(addition(one, Y), X)
% 105.42/13.77 = { by axiom 4 (additive_commutativity) }
% 105.42/13.77 multiplication(addition(Y, one), X)
% 105.42/13.77
% 105.42/13.77 Lemma 20: addition(one, multiplication(addition(X, one), star(X))) = star(X).
% 105.42/13.77 Proof:
% 105.42/13.77 addition(one, multiplication(addition(X, one), star(X)))
% 105.42/13.77 = { by lemma 19 R->L }
% 105.42/13.77 addition(one, addition(star(X), multiplication(X, star(X))))
% 105.42/13.77 = { by axiom 4 (additive_commutativity) R->L }
% 105.42/13.77 addition(one, addition(multiplication(X, star(X)), star(X)))
% 105.42/13.77 = { by axiom 6 (additive_associativity) }
% 105.42/13.77 addition(addition(one, multiplication(X, star(X))), star(X))
% 105.42/13.77 = { by axiom 9 (ifeq_axiom) R->L }
% 105.42/13.77 ifeq2(true, true, addition(addition(one, multiplication(X, star(X))), star(X)), star(X))
% 105.42/13.77 = { by axiom 13 (star_unfold_right) R->L }
% 105.42/13.77 ifeq2(leq(addition(one, multiplication(X, star(X))), star(X)), true, addition(addition(one, multiplication(X, star(X))), star(X)), star(X))
% 105.42/13.77 = { by axiom 16 (order_1) }
% 105.42/13.77 star(X)
% 105.42/13.77
% 105.42/13.77 Lemma 21: addition(X, addition(X, Y)) = addition(X, Y).
% 105.42/13.77 Proof:
% 105.42/13.77 addition(X, addition(X, Y))
% 105.42/13.77 = { by axiom 6 (additive_associativity) }
% 105.42/13.77 addition(addition(X, X), Y)
% 105.42/13.77 = { by axiom 3 (additive_idempotence) }
% 105.42/13.77 addition(X, Y)
% 105.42/13.77
% 105.42/13.77 Lemma 22: addition(one, star(X)) = star(X).
% 105.42/13.77 Proof:
% 105.42/13.77 addition(one, star(X))
% 105.42/13.77 = { by lemma 20 R->L }
% 105.42/13.77 addition(one, addition(one, multiplication(addition(X, one), star(X))))
% 105.42/13.77 = { by lemma 21 }
% 105.42/13.77 addition(one, multiplication(addition(X, one), star(X)))
% 105.42/13.77 = { by lemma 20 }
% 105.42/13.77 star(X)
% 105.42/13.77
% 105.42/13.77 Lemma 23: addition(X, addition(Y, X)) = addition(Y, X).
% 105.42/13.77 Proof:
% 105.42/13.77 addition(X, addition(Y, X))
% 105.42/13.77 = { by lemma 21 R->L }
% 105.42/13.77 addition(X, addition(Y, addition(Y, X)))
% 105.42/13.77 = { by axiom 4 (additive_commutativity) R->L }
% 105.42/13.77 addition(X, addition(Y, addition(X, Y)))
% 105.42/13.77 = { by axiom 6 (additive_associativity) }
% 105.42/13.77 addition(addition(X, Y), addition(X, Y))
% 105.42/13.77 = { by axiom 3 (additive_idempotence) }
% 105.42/13.77 addition(X, Y)
% 105.42/13.77 = { by axiom 4 (additive_commutativity) }
% 105.42/13.77 addition(Y, X)
% 105.42/13.77
% 105.42/13.77 Lemma 24: addition(X, addition(Y, Z)) = addition(Y, addition(X, Z)).
% 105.42/13.77 Proof:
% 105.42/13.77 addition(X, addition(Y, Z))
% 105.42/13.77 = { by axiom 4 (additive_commutativity) R->L }
% 105.42/13.77 addition(addition(Y, Z), X)
% 105.42/13.77 = { by axiom 6 (additive_associativity) R->L }
% 105.42/13.77 addition(Y, addition(Z, X))
% 105.42/13.77 = { by axiom 4 (additive_commutativity) }
% 105.42/13.77 addition(Y, addition(X, Z))
% 105.42/13.77
% 105.42/13.77 Lemma 25: addition(X, multiplication(X, Y)) = multiplication(X, addition(Y, one)).
% 105.42/13.77 Proof:
% 105.42/13.77 addition(X, multiplication(X, Y))
% 105.42/13.77 = { by axiom 1 (multiplicative_right_identity) R->L }
% 105.42/13.77 addition(multiplication(X, one), multiplication(X, Y))
% 105.42/13.77 = { by axiom 10 (right_distributivity) R->L }
% 105.42/13.77 multiplication(X, addition(one, Y))
% 105.42/13.77 = { by axiom 4 (additive_commutativity) }
% 105.42/13.77 multiplication(X, addition(Y, one))
% 105.42/13.77
% 105.42/13.77 Lemma 26: addition(multiplication(X, star(Y)), X) = multiplication(X, star(Y)).
% 105.42/13.77 Proof:
% 105.42/13.77 addition(multiplication(X, star(Y)), X)
% 105.42/13.77 = { by axiom 1 (multiplicative_right_identity) R->L }
% 105.42/13.77 addition(multiplication(X, star(Y)), multiplication(X, one))
% 105.42/13.77 = { by axiom 10 (right_distributivity) R->L }
% 105.42/13.77 multiplication(X, addition(star(Y), one))
% 105.42/13.77 = { by axiom 4 (additive_commutativity) }
% 105.42/13.77 multiplication(X, addition(one, star(Y)))
% 105.42/13.77 = { by lemma 22 }
% 105.42/13.77 multiplication(X, star(Y))
% 105.42/13.77
% 105.42/13.77 Lemma 27: addition(one, multiplication(star(X), addition(X, one))) = star(X).
% 105.42/13.77 Proof:
% 105.42/13.77 addition(one, multiplication(star(X), addition(X, one)))
% 105.42/13.77 = { by lemma 25 R->L }
% 105.42/13.77 addition(one, addition(star(X), multiplication(star(X), X)))
% 105.42/13.77 = { by axiom 4 (additive_commutativity) R->L }
% 105.42/13.77 addition(one, addition(multiplication(star(X), X), star(X)))
% 105.42/13.77 = { by axiom 6 (additive_associativity) }
% 105.42/13.77 addition(addition(one, multiplication(star(X), X)), star(X))
% 105.42/13.77 = { by axiom 9 (ifeq_axiom) R->L }
% 105.42/13.77 ifeq2(true, true, addition(addition(one, multiplication(star(X), X)), star(X)), star(X))
% 105.42/13.77 = { by axiom 14 (star_unfold_left) R->L }
% 105.42/13.77 ifeq2(leq(addition(one, multiplication(star(X), X)), star(X)), true, addition(addition(one, multiplication(star(X), X)), star(X)), star(X))
% 105.42/13.77 = { by axiom 16 (order_1) }
% 105.42/13.77 star(X)
% 105.42/13.77
% 105.42/13.77 Lemma 28: multiplication(star(X), addition(X, one)) = star(X).
% 105.42/13.77 Proof:
% 105.42/13.77 multiplication(star(X), addition(X, one))
% 105.42/13.77 = { by axiom 3 (additive_idempotence) R->L }
% 105.42/13.77 multiplication(star(X), addition(X, addition(one, one)))
% 105.42/13.77 = { by axiom 6 (additive_associativity) }
% 105.42/13.77 multiplication(star(X), addition(addition(X, one), one))
% 105.42/13.77 = { by lemma 25 R->L }
% 105.42/13.77 addition(star(X), multiplication(star(X), addition(X, one)))
% 105.42/13.77 = { by axiom 4 (additive_commutativity) R->L }
% 105.42/13.77 addition(multiplication(star(X), addition(X, one)), star(X))
% 105.42/13.77 = { by lemma 27 R->L }
% 105.42/13.77 addition(multiplication(star(X), addition(X, one)), addition(one, multiplication(star(X), addition(X, one))))
% 105.42/13.77 = { by lemma 23 }
% 105.42/13.77 addition(one, multiplication(star(X), addition(X, one)))
% 105.42/13.77 = { by lemma 27 }
% 105.42/13.77 star(X)
% 105.42/13.77
% 105.42/13.77 Lemma 29: multiplication(addition(X, one), star(X)) = star(X).
% 105.42/13.77 Proof:
% 105.42/13.77 multiplication(addition(X, one), star(X))
% 105.42/13.77 = { by axiom 3 (additive_idempotence) R->L }
% 105.42/13.77 multiplication(addition(X, addition(one, one)), star(X))
% 105.42/13.78 = { by axiom 6 (additive_associativity) }
% 105.42/13.78 multiplication(addition(addition(X, one), one), star(X))
% 105.42/13.78 = { by lemma 19 R->L }
% 105.42/13.78 addition(star(X), multiplication(addition(X, one), star(X)))
% 105.42/13.78 = { by axiom 4 (additive_commutativity) R->L }
% 105.42/13.78 addition(multiplication(addition(X, one), star(X)), star(X))
% 105.42/13.78 = { by lemma 20 R->L }
% 105.42/13.78 addition(multiplication(addition(X, one), star(X)), addition(one, multiplication(addition(X, one), star(X))))
% 105.42/13.78 = { by lemma 23 }
% 105.42/13.78 addition(one, multiplication(addition(X, one), star(X)))
% 105.42/13.78 = { by lemma 20 }
% 105.42/13.78 star(X)
% 105.42/13.78
% 105.42/13.78 Lemma 30: addition(multiplication(X, Y), addition(Z, multiplication(W, Y))) = addition(Z, multiplication(addition(X, W), Y)).
% 105.42/13.78 Proof:
% 105.42/13.78 addition(multiplication(X, Y), addition(Z, multiplication(W, Y)))
% 105.42/13.78 = { by axiom 4 (additive_commutativity) R->L }
% 105.42/13.78 addition(multiplication(X, Y), addition(multiplication(W, Y), Z))
% 105.42/13.78 = { by lemma 24 R->L }
% 105.42/13.78 addition(multiplication(W, Y), addition(multiplication(X, Y), Z))
% 105.42/13.78 = { by axiom 6 (additive_associativity) }
% 105.42/13.78 addition(addition(multiplication(W, Y), multiplication(X, Y)), Z)
% 105.42/13.78 = { by axiom 11 (left_distributivity) R->L }
% 105.42/13.78 addition(multiplication(addition(W, X), Y), Z)
% 105.42/13.78 = { by axiom 4 (additive_commutativity) }
% 105.42/13.78 addition(Z, multiplication(addition(W, X), Y))
% 105.42/13.78 = { by axiom 4 (additive_commutativity) }
% 105.42/13.78 addition(Z, multiplication(addition(X, W), Y))
% 105.42/13.78
% 105.42/13.78 Lemma 31: addition(multiplication(star(x0), star(x1)), multiplication(addition(X, star(x1)), star(x0))) = addition(multiplication(star(x0), star(x1)), multiplication(X, star(x0))).
% 105.42/13.78 Proof:
% 105.42/13.78 addition(multiplication(star(x0), star(x1)), multiplication(addition(X, star(x1)), star(x0)))
% 105.42/13.78 = { by lemma 30 R->L }
% 105.42/13.78 addition(multiplication(X, star(x0)), addition(multiplication(star(x0), star(x1)), multiplication(star(x1), star(x0))))
% 105.42/13.78 = { by axiom 4 (additive_commutativity) R->L }
% 105.42/13.78 addition(multiplication(X, star(x0)), addition(multiplication(star(x1), star(x0)), multiplication(star(x0), star(x1))))
% 105.42/13.78 = { by axiom 9 (ifeq_axiom) R->L }
% 105.42/13.78 addition(multiplication(X, star(x0)), ifeq2(true, true, addition(multiplication(star(x1), star(x0)), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))))
% 105.42/13.78 = { by axiom 12 (goals) R->L }
% 105.42/13.78 addition(multiplication(X, star(x0)), ifeq2(leq(multiplication(star(x1), star(x0)), multiplication(star(x0), star(x1))), true, addition(multiplication(star(x1), star(x0)), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))))
% 105.42/13.78 = { by axiom 16 (order_1) }
% 105.42/13.78 addition(multiplication(X, star(x0)), multiplication(star(x0), star(x1)))
% 105.42/13.78 = { by axiom 4 (additive_commutativity) }
% 105.42/13.79 addition(multiplication(star(x0), star(x1)), multiplication(X, star(x0)))
% 105.42/13.79
% 105.42/13.79 Goal 1 (goals_1): leq(star(addition(x0, x1)), multiplication(star(x0), star(x1))) = true.
% 105.42/13.79 Proof:
% 105.42/13.79 leq(star(addition(x0, x1)), multiplication(star(x0), star(x1)))
% 105.42/13.79 = { by axiom 16 (order_1) R->L }
% 105.42/13.79 leq(ifeq2(leq(star(addition(addition(x0, x1), one)), star(addition(x0, x1))), true, addition(star(addition(addition(x0, x1), one)), star(addition(x0, x1))), star(addition(x0, x1))), multiplication(star(x0), star(x1)))
% 105.42/13.79 = { by axiom 7 (ifeq_axiom) R->L }
% 105.42/13.79 leq(ifeq2(ifeq(true, true, leq(star(addition(addition(x0, x1), one)), star(addition(x0, x1))), true), true, addition(star(addition(addition(x0, x1), one)), star(addition(x0, x1))), star(addition(x0, x1))), multiplication(star(x0), star(x1)))
% 105.42/13.79 = { by axiom 15 (order) R->L }
% 105.42/13.79 leq(ifeq2(ifeq(ifeq3(addition(star(addition(x0, x1)), star(addition(x0, x1))), star(addition(x0, x1)), leq(star(addition(x0, x1)), star(addition(x0, x1))), true), true, leq(star(addition(addition(x0, x1), one)), star(addition(x0, x1))), true), true, addition(star(addition(addition(x0, x1), one)), star(addition(x0, x1))), star(addition(x0, x1))), multiplication(star(x0), star(x1)))
% 105.42/13.79 = { by axiom 3 (additive_idempotence) }
% 105.42/13.79 leq(ifeq2(ifeq(ifeq3(star(addition(x0, x1)), star(addition(x0, x1)), leq(star(addition(x0, x1)), star(addition(x0, x1))), true), true, leq(star(addition(addition(x0, x1), one)), star(addition(x0, x1))), true), true, addition(star(addition(addition(x0, x1), one)), star(addition(x0, x1))), star(addition(x0, x1))), multiplication(star(x0), star(x1)))
% 105.42/13.79 = { by axiom 8 (ifeq_axiom) }
% 105.42/13.79 leq(ifeq2(ifeq(leq(star(addition(x0, x1)), star(addition(x0, x1))), true, leq(star(addition(addition(x0, x1), one)), star(addition(x0, x1))), true), true, addition(star(addition(addition(x0, x1), one)), star(addition(x0, x1))), star(addition(x0, x1))), multiplication(star(x0), star(x1)))
% 105.42/13.79 = { by lemma 27 R->L }
% 105.42/13.80 leq(ifeq2(ifeq(leq(addition(one, multiplication(star(addition(x0, x1)), addition(addition(x0, x1), one))), star(addition(x0, x1))), true, leq(star(addition(addition(x0, x1), one)), star(addition(x0, x1))), true), true, addition(star(addition(addition(x0, x1), one)), star(addition(x0, x1))), star(addition(x0, x1))), multiplication(star(x0), star(x1)))
% 105.42/13.80 = { by axiom 4 (additive_commutativity) R->L }
% 105.42/13.80 leq(ifeq2(ifeq(leq(addition(multiplication(star(addition(x0, x1)), addition(addition(x0, x1), one)), one), star(addition(x0, x1))), true, leq(star(addition(addition(x0, x1), one)), star(addition(x0, x1))), true), true, addition(star(addition(addition(x0, x1), one)), star(addition(x0, x1))), star(addition(x0, x1))), multiplication(star(x0), star(x1)))
% 105.42/13.80 = { by axiom 2 (multiplicative_left_identity) R->L }
% 105.42/13.80 leq(ifeq2(ifeq(leq(addition(multiplication(star(addition(x0, x1)), addition(addition(x0, x1), one)), one), star(addition(x0, x1))), true, leq(multiplication(one, star(addition(addition(x0, x1), one))), star(addition(x0, x1))), true), true, addition(star(addition(addition(x0, x1), one)), star(addition(x0, x1))), star(addition(x0, x1))), multiplication(star(x0), star(x1)))
% 105.42/13.80 = { by axiom 17 (star_induction_right) }
% 105.42/13.80 leq(ifeq2(true, true, addition(star(addition(addition(x0, x1), one)), star(addition(x0, x1))), star(addition(x0, x1))), multiplication(star(x0), star(x1)))
% 105.42/13.80 = { by axiom 9 (ifeq_axiom) }
% 105.42/13.80 leq(addition(star(addition(addition(x0, x1), one)), star(addition(x0, x1))), multiplication(star(x0), star(x1)))
% 105.42/13.80 = { by axiom 4 (additive_commutativity) }
% 105.42/13.80 leq(addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 105.42/13.80 = { by axiom 9 (ifeq_axiom) R->L }
% 105.42/13.80 leq(ifeq2(true, true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 105.42/13.80 = { by axiom 18 (star_induction_left) R->L }
% 105.42/13.80 leq(ifeq2(ifeq(leq(addition(multiplication(addition(x0, x1), star(addition(addition(x0, x1), one))), multiplication(one, star(addition(addition(x0, x1), one)))), star(addition(addition(x0, x1), one))), true, leq(multiplication(star(addition(x0, x1)), multiplication(one, star(addition(addition(x0, x1), one)))), star(addition(addition(x0, x1), one))), true), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 105.42/13.80 = { by axiom 11 (left_distributivity) R->L }
% 105.42/13.80 leq(ifeq2(ifeq(leq(multiplication(addition(addition(x0, x1), one), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), true, leq(multiplication(star(addition(x0, x1)), multiplication(one, star(addition(addition(x0, x1), one)))), star(addition(addition(x0, x1), one))), true), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 105.42/13.80 = { by axiom 4 (additive_commutativity) R->L }
% 105.42/13.80 leq(ifeq2(ifeq(leq(multiplication(addition(one, addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), true, leq(multiplication(star(addition(x0, x1)), multiplication(one, star(addition(addition(x0, x1), one)))), star(addition(addition(x0, x1), one))), true), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 105.42/13.80 = { by axiom 4 (additive_commutativity) R->L }
% 105.42/13.80 leq(ifeq2(ifeq(leq(multiplication(addition(one, addition(x0, x1)), star(addition(one, addition(x0, x1)))), star(addition(addition(x0, x1), one))), true, leq(multiplication(star(addition(x0, x1)), multiplication(one, star(addition(addition(x0, x1), one)))), star(addition(addition(x0, x1), one))), true), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 105.42/13.80 = { by lemma 21 R->L }
% 105.42/13.80 leq(ifeq2(ifeq(leq(multiplication(addition(one, addition(one, addition(x0, x1))), star(addition(one, addition(x0, x1)))), star(addition(addition(x0, x1), one))), true, leq(multiplication(star(addition(x0, x1)), multiplication(one, star(addition(addition(x0, x1), one)))), star(addition(addition(x0, x1), one))), true), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 105.42/13.80 = { by axiom 4 (additive_commutativity) R->L }
% 105.42/13.80 leq(ifeq2(ifeq(leq(multiplication(addition(addition(one, addition(x0, x1)), one), star(addition(one, addition(x0, x1)))), star(addition(addition(x0, x1), one))), true, leq(multiplication(star(addition(x0, x1)), multiplication(one, star(addition(addition(x0, x1), one)))), star(addition(addition(x0, x1), one))), true), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 105.42/13.80 = { by lemma 29 }
% 105.42/13.80 leq(ifeq2(ifeq(leq(star(addition(one, addition(x0, x1))), star(addition(addition(x0, x1), one))), true, leq(multiplication(star(addition(x0, x1)), multiplication(one, star(addition(addition(x0, x1), one)))), star(addition(addition(x0, x1), one))), true), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 106.19/13.80 = { by axiom 4 (additive_commutativity) }
% 106.19/13.80 leq(ifeq2(ifeq(leq(star(addition(addition(x0, x1), one)), star(addition(addition(x0, x1), one))), true, leq(multiplication(star(addition(x0, x1)), multiplication(one, star(addition(addition(x0, x1), one)))), star(addition(addition(x0, x1), one))), true), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 106.19/13.80 = { by axiom 8 (ifeq_axiom) R->L }
% 106.19/13.80 leq(ifeq2(ifeq(ifeq3(star(addition(addition(x0, x1), one)), star(addition(addition(x0, x1), one)), leq(star(addition(addition(x0, x1), one)), star(addition(addition(x0, x1), one))), true), true, leq(multiplication(star(addition(x0, x1)), multiplication(one, star(addition(addition(x0, x1), one)))), star(addition(addition(x0, x1), one))), true), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 106.19/13.81 = { by axiom 3 (additive_idempotence) R->L }
% 106.19/13.81 leq(ifeq2(ifeq(ifeq3(addition(star(addition(addition(x0, x1), one)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one)), leq(star(addition(addition(x0, x1), one)), star(addition(addition(x0, x1), one))), true), true, leq(multiplication(star(addition(x0, x1)), multiplication(one, star(addition(addition(x0, x1), one)))), star(addition(addition(x0, x1), one))), true), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 106.19/13.81 = { by axiom 15 (order) }
% 106.19/13.81 leq(ifeq2(ifeq(true, true, leq(multiplication(star(addition(x0, x1)), multiplication(one, star(addition(addition(x0, x1), one)))), star(addition(addition(x0, x1), one))), true), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 106.19/13.81 = { by axiom 7 (ifeq_axiom) }
% 106.19/13.81 leq(ifeq2(leq(multiplication(star(addition(x0, x1)), multiplication(one, star(addition(addition(x0, x1), one)))), star(addition(addition(x0, x1), one))), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 106.19/13.81 = { by axiom 2 (multiplicative_left_identity) }
% 106.19/13.81 leq(ifeq2(leq(multiplication(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 106.19/13.81 = { by lemma 22 R->L }
% 106.19/13.81 leq(ifeq2(leq(multiplication(star(addition(x0, x1)), addition(one, star(addition(addition(x0, x1), one)))), star(addition(addition(x0, x1), one))), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 106.19/13.81 = { by axiom 4 (additive_commutativity) R->L }
% 106.19/13.81 leq(ifeq2(leq(multiplication(star(addition(x0, x1)), addition(star(addition(addition(x0, x1), one)), one)), star(addition(addition(x0, x1), one))), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 106.19/13.81 = { by lemma 25 R->L }
% 106.19/13.81 leq(ifeq2(leq(addition(star(addition(x0, x1)), multiplication(star(addition(x0, x1)), star(addition(addition(x0, x1), one)))), star(addition(addition(x0, x1), one))), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 106.19/13.81 = { by axiom 4 (additive_commutativity) R->L }
% 106.19/13.81 leq(ifeq2(leq(addition(multiplication(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(x0, x1))), star(addition(addition(x0, x1), one))), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 106.19/13.81 = { by axiom 9 (ifeq_axiom) R->L }
% 106.19/13.81 leq(ifeq2(leq(ifeq2(true, true, addition(multiplication(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(x0, x1))), star(addition(x0, x1))), star(addition(addition(x0, x1), one))), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 106.19/13.81 = { by axiom 17 (star_induction_right) R->L }
% 106.19/13.81 leq(ifeq2(leq(ifeq2(ifeq(leq(addition(multiplication(star(addition(x0, x1)), addition(addition(x0, x1), one)), multiplication(star(addition(x0, x1)), addition(addition(x0, x1), one))), star(addition(x0, x1))), true, leq(multiplication(multiplication(star(addition(x0, x1)), addition(addition(x0, x1), one)), star(addition(addition(x0, x1), one))), star(addition(x0, x1))), true), true, addition(multiplication(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(x0, x1))), star(addition(x0, x1))), star(addition(addition(x0, x1), one))), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 106.19/13.81 = { by axiom 3 (additive_idempotence) }
% 106.19/13.81 leq(ifeq2(leq(ifeq2(ifeq(leq(multiplication(star(addition(x0, x1)), addition(addition(x0, x1), one)), star(addition(x0, x1))), true, leq(multiplication(multiplication(star(addition(x0, x1)), addition(addition(x0, x1), one)), star(addition(addition(x0, x1), one))), star(addition(x0, x1))), true), true, addition(multiplication(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(x0, x1))), star(addition(x0, x1))), star(addition(addition(x0, x1), one))), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 106.19/13.81 = { by axiom 5 (multiplicative_associativity) R->L }
% 106.19/13.81 leq(ifeq2(leq(ifeq2(ifeq(leq(multiplication(star(addition(x0, x1)), addition(addition(x0, x1), one)), star(addition(x0, x1))), true, leq(multiplication(star(addition(x0, x1)), multiplication(addition(addition(x0, x1), one), star(addition(addition(x0, x1), one)))), star(addition(x0, x1))), true), true, addition(multiplication(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(x0, x1))), star(addition(x0, x1))), star(addition(addition(x0, x1), one))), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 106.19/13.81 = { by lemma 28 }
% 106.19/13.81 leq(ifeq2(leq(ifeq2(ifeq(leq(star(addition(x0, x1)), star(addition(x0, x1))), true, leq(multiplication(star(addition(x0, x1)), multiplication(addition(addition(x0, x1), one), star(addition(addition(x0, x1), one)))), star(addition(x0, x1))), true), true, addition(multiplication(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(x0, x1))), star(addition(x0, x1))), star(addition(addition(x0, x1), one))), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 106.19/13.81 = { by axiom 8 (ifeq_axiom) R->L }
% 106.19/13.81 leq(ifeq2(leq(ifeq2(ifeq(ifeq3(star(addition(x0, x1)), star(addition(x0, x1)), leq(star(addition(x0, x1)), star(addition(x0, x1))), true), true, leq(multiplication(star(addition(x0, x1)), multiplication(addition(addition(x0, x1), one), star(addition(addition(x0, x1), one)))), star(addition(x0, x1))), true), true, addition(multiplication(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(x0, x1))), star(addition(x0, x1))), star(addition(addition(x0, x1), one))), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 106.19/13.81 = { by axiom 3 (additive_idempotence) R->L }
% 106.19/13.81 leq(ifeq2(leq(ifeq2(ifeq(ifeq3(addition(star(addition(x0, x1)), star(addition(x0, x1))), star(addition(x0, x1)), leq(star(addition(x0, x1)), star(addition(x0, x1))), true), true, leq(multiplication(star(addition(x0, x1)), multiplication(addition(addition(x0, x1), one), star(addition(addition(x0, x1), one)))), star(addition(x0, x1))), true), true, addition(multiplication(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(x0, x1))), star(addition(x0, x1))), star(addition(addition(x0, x1), one))), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 106.19/13.81 = { by axiom 15 (order) }
% 106.19/13.81 leq(ifeq2(leq(ifeq2(ifeq(true, true, leq(multiplication(star(addition(x0, x1)), multiplication(addition(addition(x0, x1), one), star(addition(addition(x0, x1), one)))), star(addition(x0, x1))), true), true, addition(multiplication(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(x0, x1))), star(addition(x0, x1))), star(addition(addition(x0, x1), one))), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 106.19/13.82 = { by axiom 7 (ifeq_axiom) }
% 106.19/13.82 leq(ifeq2(leq(ifeq2(leq(multiplication(star(addition(x0, x1)), multiplication(addition(addition(x0, x1), one), star(addition(addition(x0, x1), one)))), star(addition(x0, x1))), true, addition(multiplication(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(x0, x1))), star(addition(x0, x1))), star(addition(addition(x0, x1), one))), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 106.19/13.82 = { by axiom 5 (multiplicative_associativity) }
% 106.19/13.82 leq(ifeq2(leq(ifeq2(leq(multiplication(multiplication(star(addition(x0, x1)), addition(addition(x0, x1), one)), star(addition(addition(x0, x1), one))), star(addition(x0, x1))), true, addition(multiplication(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(x0, x1))), star(addition(x0, x1))), star(addition(addition(x0, x1), one))), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 106.19/13.82 = { by lemma 28 }
% 106.19/13.82 leq(ifeq2(leq(ifeq2(leq(multiplication(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(x0, x1))), true, addition(multiplication(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(x0, x1))), star(addition(x0, x1))), star(addition(addition(x0, x1), one))), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 106.19/13.82 = { by axiom 16 (order_1) }
% 106.19/13.82 leq(ifeq2(leq(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), true, addition(star(addition(x0, x1)), star(addition(addition(x0, x1), one))), star(addition(addition(x0, x1), one))), multiplication(star(x0), star(x1)))
% 106.19/13.82 = { by axiom 16 (order_1) }
% 106.19/13.82 leq(star(addition(addition(x0, x1), one)), multiplication(star(x0), star(x1)))
% 106.19/13.82 = { by axiom 4 (additive_commutativity) }
% 106.19/13.82 leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1)))
% 106.19/13.82 = { by axiom 7 (ifeq_axiom) R->L }
% 106.19/13.82 ifeq(true, true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.82 = { by axiom 15 (order) R->L }
% 106.19/13.82 ifeq(ifeq3(addition(multiplication(star(x0), star(x1)), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)), leq(multiplication(star(x0), star(x1)), multiplication(star(x0), star(x1))), true), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.82 = { by axiom 3 (additive_idempotence) }
% 106.19/13.82 ifeq(ifeq3(multiplication(star(x0), star(x1)), multiplication(star(x0), star(x1)), leq(multiplication(star(x0), star(x1)), multiplication(star(x0), star(x1))), true), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.82 = { by axiom 8 (ifeq_axiom) }
% 106.19/13.82 ifeq(leq(multiplication(star(x0), star(x1)), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.82 = { by lemma 26 R->L }
% 106.19/13.82 ifeq(leq(addition(multiplication(star(x0), star(x1)), star(x0)), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.82 = { by lemma 22 R->L }
% 106.19/13.82 ifeq(leq(addition(multiplication(star(x0), star(x1)), addition(one, star(x0))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.82 = { by axiom 4 (additive_commutativity) R->L }
% 106.19/13.82 ifeq(leq(addition(multiplication(star(x0), star(x1)), addition(star(x0), one)), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.82 = { by axiom 6 (additive_associativity) }
% 106.19/13.82 ifeq(leq(addition(addition(multiplication(star(x0), star(x1)), star(x0)), one), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.82 = { by lemma 26 }
% 106.19/13.82 ifeq(leq(addition(multiplication(star(x0), star(x1)), one), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.82 = { by axiom 4 (additive_commutativity) }
% 106.19/13.82 ifeq(leq(addition(one, multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.82 = { by axiom 16 (order_1) R->L }
% 106.19/13.82 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.82 = { by axiom 16 (order_1) R->L }
% 106.19/13.82 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), ifeq2(leq(multiplication(star(x1), star(x1)), star(x1)), true, addition(multiplication(star(x1), star(x1)), star(x1)), star(x1)))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.82 = { by axiom 4 (additive_commutativity) }
% 106.19/13.82 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), ifeq2(leq(multiplication(star(x1), star(x1)), star(x1)), true, addition(star(x1), multiplication(star(x1), star(x1))), star(x1)))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.82 = { by lemma 19 }
% 106.19/13.82 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), ifeq2(leq(multiplication(star(x1), star(x1)), star(x1)), true, multiplication(addition(star(x1), one), star(x1)), star(x1)))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.82 = { by axiom 4 (additive_commutativity) }
% 106.19/13.82 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), ifeq2(leq(multiplication(star(x1), star(x1)), star(x1)), true, multiplication(addition(one, star(x1)), star(x1)), star(x1)))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.82 = { by lemma 22 }
% 106.19/13.82 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), ifeq2(leq(multiplication(star(x1), star(x1)), star(x1)), true, multiplication(star(x1), star(x1)), star(x1)))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.82 = { by axiom 2 (multiplicative_left_identity) R->L }
% 106.19/13.82 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), ifeq2(leq(multiplication(star(x1), multiplication(one, star(x1))), star(x1)), true, multiplication(star(x1), star(x1)), star(x1)))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.82 = { by axiom 7 (ifeq_axiom) R->L }
% 106.19/13.82 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), ifeq2(ifeq(true, true, leq(multiplication(star(x1), multiplication(one, star(x1))), star(x1)), true), true, multiplication(star(x1), star(x1)), star(x1)))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.82 = { by axiom 15 (order) R->L }
% 106.19/13.82 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), ifeq2(ifeq(ifeq3(addition(star(x1), star(x1)), star(x1), leq(star(x1), star(x1)), true), true, leq(multiplication(star(x1), multiplication(one, star(x1))), star(x1)), true), true, multiplication(star(x1), star(x1)), star(x1)))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.83 = { by axiom 3 (additive_idempotence) }
% 106.19/13.83 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), ifeq2(ifeq(ifeq3(star(x1), star(x1), leq(star(x1), star(x1)), true), true, leq(multiplication(star(x1), multiplication(one, star(x1))), star(x1)), true), true, multiplication(star(x1), star(x1)), star(x1)))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.83 = { by axiom 8 (ifeq_axiom) }
% 106.19/13.83 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), ifeq2(ifeq(leq(star(x1), star(x1)), true, leq(multiplication(star(x1), multiplication(one, star(x1))), star(x1)), true), true, multiplication(star(x1), star(x1)), star(x1)))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.83 = { by lemma 28 R->L }
% 106.19/13.83 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), ifeq2(ifeq(leq(multiplication(star(x1), addition(x1, one)), star(x1)), true, leq(multiplication(star(x1), multiplication(one, star(x1))), star(x1)), true), true, multiplication(star(x1), star(x1)), star(x1)))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.83 = { by axiom 5 (multiplicative_associativity) }
% 106.19/13.83 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), ifeq2(ifeq(leq(multiplication(star(x1), addition(x1, one)), star(x1)), true, leq(multiplication(multiplication(star(x1), one), star(x1)), star(x1)), true), true, multiplication(star(x1), star(x1)), star(x1)))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.83 = { by axiom 10 (right_distributivity) }
% 106.19/13.83 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), ifeq2(ifeq(leq(addition(multiplication(star(x1), x1), multiplication(star(x1), one)), star(x1)), true, leq(multiplication(multiplication(star(x1), one), star(x1)), star(x1)), true), true, multiplication(star(x1), star(x1)), star(x1)))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.83 = { by axiom 17 (star_induction_right) }
% 106.19/13.83 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), ifeq2(true, true, multiplication(star(x1), star(x1)), star(x1)))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.83 = { by axiom 9 (ifeq_axiom) }
% 106.19/13.83 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), multiplication(star(x1), star(x1)))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.83 = { by axiom 5 (multiplicative_associativity) }
% 106.19/13.83 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(multiplication(star(x0), star(x1)), star(x1))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.83 = { by axiom 16 (order_1) R->L }
% 106.19/13.83 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(ifeq2(leq(multiplication(x0, star(x0)), multiplication(star(x0), star(x1))), true, addition(multiplication(x0, star(x0)), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), star(x1))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.83 = { by lemma 26 R->L }
% 106.19/13.83 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(ifeq2(leq(multiplication(x0, star(x0)), addition(multiplication(star(x0), star(x1)), star(x0))), true, addition(multiplication(x0, star(x0)), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), star(x1))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.83 = { by lemma 29 R->L }
% 106.19/13.83 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(ifeq2(leq(multiplication(x0, star(x0)), addition(multiplication(star(x0), star(x1)), multiplication(addition(x0, one), star(x0)))), true, addition(multiplication(x0, star(x0)), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), star(x1))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.83 = { by lemma 30 R->L }
% 106.19/13.83 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(ifeq2(leq(multiplication(x0, star(x0)), addition(multiplication(x0, star(x0)), addition(multiplication(star(x0), star(x1)), multiplication(one, star(x0))))), true, addition(multiplication(x0, star(x0)), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), star(x1))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.83 = { by axiom 8 (ifeq_axiom) R->L }
% 106.19/13.83 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(ifeq2(ifeq3(addition(multiplication(x0, star(x0)), addition(multiplication(star(x0), star(x1)), multiplication(one, star(x0)))), addition(multiplication(x0, star(x0)), addition(multiplication(star(x0), star(x1)), multiplication(one, star(x0)))), leq(multiplication(x0, star(x0)), addition(multiplication(x0, star(x0)), addition(multiplication(star(x0), star(x1)), multiplication(one, star(x0))))), true), true, addition(multiplication(x0, star(x0)), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), star(x1))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.84 = { by lemma 21 R->L }
% 106.19/13.84 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(ifeq2(ifeq3(addition(multiplication(x0, star(x0)), addition(multiplication(x0, star(x0)), addition(multiplication(star(x0), star(x1)), multiplication(one, star(x0))))), addition(multiplication(x0, star(x0)), addition(multiplication(star(x0), star(x1)), multiplication(one, star(x0)))), leq(multiplication(x0, star(x0)), addition(multiplication(x0, star(x0)), addition(multiplication(star(x0), star(x1)), multiplication(one, star(x0))))), true), true, addition(multiplication(x0, star(x0)), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), star(x1))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.84 = { by axiom 15 (order) }
% 106.19/13.84 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(ifeq2(true, true, addition(multiplication(x0, star(x0)), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), star(x1))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.84 = { by axiom 9 (ifeq_axiom) }
% 106.19/13.84 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(addition(multiplication(x0, star(x0)), multiplication(star(x0), star(x1))), star(x1))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.84 = { by axiom 4 (additive_commutativity) }
% 106.19/13.84 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(addition(multiplication(star(x0), star(x1)), multiplication(x0, star(x0))), star(x1))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.84 = { by lemma 31 R->L }
% 106.19/13.84 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(addition(multiplication(star(x0), star(x1)), multiplication(addition(x0, star(x1)), star(x0))), star(x1))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.84 = { by lemma 29 R->L }
% 106.19/13.84 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(addition(multiplication(star(x0), star(x1)), multiplication(addition(x0, multiplication(addition(x1, one), star(x1))), star(x0))), star(x1))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.84 = { by lemma 22 R->L }
% 106.19/13.84 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(addition(multiplication(star(x0), star(x1)), multiplication(addition(x0, multiplication(addition(x1, one), addition(one, star(x1)))), star(x0))), star(x1))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.84 = { by axiom 4 (additive_commutativity) R->L }
% 106.19/13.84 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(addition(multiplication(star(x0), star(x1)), multiplication(addition(x0, multiplication(addition(x1, one), addition(star(x1), one))), star(x0))), star(x1))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.84 = { by lemma 25 R->L }
% 106.19/13.84 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(addition(multiplication(star(x0), star(x1)), multiplication(addition(x0, addition(addition(x1, one), multiplication(addition(x1, one), star(x1)))), star(x0))), star(x1))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.84 = { by lemma 29 }
% 106.19/13.84 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(addition(multiplication(star(x0), star(x1)), multiplication(addition(x0, addition(addition(x1, one), star(x1))), star(x0))), star(x1))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.84 = { by axiom 6 (additive_associativity) R->L }
% 106.19/13.84 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(addition(multiplication(star(x0), star(x1)), multiplication(addition(x0, addition(x1, addition(one, star(x1)))), star(x0))), star(x1))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.84 = { by lemma 22 }
% 106.19/13.84 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(addition(multiplication(star(x0), star(x1)), multiplication(addition(x0, addition(x1, star(x1))), star(x0))), star(x1))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.85 = { by axiom 4 (additive_commutativity) R->L }
% 106.19/13.85 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(addition(multiplication(star(x0), star(x1)), multiplication(addition(x0, addition(star(x1), x1)), star(x0))), star(x1))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.85 = { by lemma 24 }
% 106.19/13.85 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(addition(multiplication(star(x0), star(x1)), multiplication(addition(star(x1), addition(x0, x1)), star(x0))), star(x1))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.85 = { by axiom 4 (additive_commutativity) }
% 106.19/13.85 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(addition(multiplication(star(x0), star(x1)), multiplication(addition(addition(x0, x1), star(x1)), star(x0))), star(x1))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.85 = { by lemma 31 }
% 106.19/13.85 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(addition(multiplication(star(x0), star(x1)), multiplication(addition(x0, x1), star(x0))), star(x1))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.85 = { by axiom 4 (additive_commutativity) R->L }
% 106.19/13.85 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(addition(multiplication(addition(x0, x1), star(x0)), multiplication(star(x0), star(x1))), star(x1))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.85 = { by axiom 11 (left_distributivity) }
% 106.19/13.85 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), addition(multiplication(multiplication(addition(x0, x1), star(x0)), star(x1)), multiplication(multiplication(star(x0), star(x1)), star(x1)))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.85 = { by axiom 5 (multiplicative_associativity) R->L }
% 106.19/13.85 ifeq(leq(addition(one, ifeq2(leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(multiplication(star(x0), star(x1)), star(x1)))), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.85 = { by axiom 8 (ifeq_axiom) R->L }
% 106.19/13.85 ifeq(leq(addition(one, ifeq2(ifeq3(addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(multiplication(star(x0), star(x1)), star(x1))), addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(multiplication(star(x0), star(x1)), star(x1))), leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(multiplication(star(x0), star(x1)), star(x1)))), true), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.85 = { by lemma 21 R->L }
% 106.19/13.85 ifeq(leq(addition(one, ifeq2(ifeq3(addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(multiplication(star(x0), star(x1)), star(x1)))), addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(multiplication(star(x0), star(x1)), star(x1))), leq(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(multiplication(star(x0), star(x1)), star(x1)))), true), true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.85 = { by axiom 15 (order) }
% 106.19/13.85 ifeq(leq(addition(one, ifeq2(true, true, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.85 = { by axiom 9 (ifeq_axiom) }
% 106.19/13.85 ifeq(leq(addition(one, addition(multiplication(addition(x0, x1), multiplication(star(x0), star(x1))), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.85 = { by axiom 4 (additive_commutativity) }
% 106.19/13.85 ifeq(leq(addition(one, addition(multiplication(star(x0), star(x1)), multiplication(addition(x0, x1), multiplication(star(x0), star(x1))))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.85 = { by lemma 19 }
% 106.19/13.85 ifeq(leq(addition(one, multiplication(addition(addition(x0, x1), one), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.85 = { by axiom 4 (additive_commutativity) }
% 106.19/13.85 ifeq(leq(addition(one, multiplication(addition(one, addition(x0, x1)), multiplication(star(x0), star(x1)))), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.85 = { by axiom 4 (additive_commutativity) R->L }
% 106.19/13.85 ifeq(leq(addition(multiplication(addition(one, addition(x0, x1)), multiplication(star(x0), star(x1))), one), multiplication(star(x0), star(x1))), true, leq(star(addition(one, addition(x0, x1))), multiplication(star(x0), star(x1))), true)
% 106.19/13.85 = { by axiom 1 (multiplicative_right_identity) R->L }
% 106.19/13.85 ifeq(leq(addition(multiplication(addition(one, addition(x0, x1)), multiplication(star(x0), star(x1))), one), multiplication(star(x0), star(x1))), true, leq(multiplication(star(addition(one, addition(x0, x1))), one), multiplication(star(x0), star(x1))), true)
% 106.19/13.85 = { by axiom 18 (star_induction_left) }
% 106.19/13.85 true
% 106.19/13.85 % SZS output end Proof
% 106.19/13.85
% 106.19/13.85 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------