%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE043+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 58.63s 7.81s
% Output : Proof 60.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE043+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n006.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 13:06:55 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 58.63/7.81 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 58.63/7.81
% 58.63/7.81 % SZS status Theorem
% 58.63/7.81
% 59.43/8.02 % SZS output start Proof
% 59.43/8.02 Axiom 1 (multiplicative_right_identity): multiplication(X, one) = X.
% 59.43/8.02 Axiom 2 (multiplicative_left_identity): multiplication(one, X) = X.
% 59.43/8.02 Axiom 3 (additive_idempotence): addition(X, X) = X.
% 59.43/8.02 Axiom 4 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 59.43/8.02 Axiom 5 (multiplicative_associativity): multiplication(X, multiplication(Y, Z)) = multiplication(multiplication(X, Y), Z).
% 59.43/8.02 Axiom 6 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 59.43/8.02 Axiom 7 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 59.43/8.02 Axiom 8 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 59.43/8.02 Axiom 9 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 59.43/8.02 Axiom 10 (right_distributivity): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 59.43/8.02 Axiom 11 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 59.43/8.02 Axiom 12 (star_unfold_right): leq(addition(one, multiplication(X, star(X))), star(X)) = true.
% 59.43/8.02 Axiom 13 (star_unfold_left): leq(addition(one, multiplication(star(X), X)), star(X)) = true.
% 59.43/8.02 Axiom 14 (order): ifeq3(addition(X, Y), Y, leq(X, Y), true) = true.
% 59.43/8.02 Axiom 15 (order_1): ifeq2(leq(X, Y), true, addition(X, Y), Y) = Y.
% 59.43/8.02 Axiom 16 (star_induction_right): ifeq(leq(addition(multiplication(X, Y), Z), X), true, leq(multiplication(Z, star(Y)), X), true) = true.
% 59.43/8.02 Axiom 17 (star_induction_left): ifeq(leq(addition(multiplication(X, Y), Z), Y), true, leq(multiplication(star(X), Z), Y), true) = true.
% 59.43/8.02
% 59.43/8.02 Lemma 18: addition(one, addition(multiplication(X, star(X)), star(X))) = star(X).
% 59.43/8.02 Proof:
% 59.43/8.02 addition(one, addition(multiplication(X, star(X)), star(X)))
% 59.43/8.02 = { by axiom 6 (additive_associativity) }
% 59.43/8.02 addition(addition(one, multiplication(X, star(X))), star(X))
% 59.43/8.02 = { by axiom 9 (ifeq_axiom) R->L }
% 59.43/8.02 ifeq2(true, true, addition(addition(one, multiplication(X, star(X))), star(X)), star(X))
% 59.43/8.02 = { by axiom 12 (star_unfold_right) R->L }
% 59.43/8.02 ifeq2(leq(addition(one, multiplication(X, star(X))), star(X)), true, addition(addition(one, multiplication(X, star(X))), star(X)), star(X))
% 59.43/8.02 = { by axiom 15 (order_1) }
% 59.43/8.02 star(X)
% 59.43/8.02
% 59.43/8.02 Lemma 19: addition(one, star(X)) = star(X).
% 59.43/8.02 Proof:
% 59.43/8.02 addition(one, star(X))
% 59.43/8.02 = { by lemma 18 R->L }
% 59.43/8.02 addition(one, addition(one, addition(multiplication(X, star(X)), star(X))))
% 59.43/8.02 = { by axiom 6 (additive_associativity) }
% 59.43/8.02 addition(addition(one, one), addition(multiplication(X, star(X)), star(X)))
% 59.43/8.02 = { by axiom 3 (additive_idempotence) }
% 59.43/8.02 addition(one, addition(multiplication(X, star(X)), star(X)))
% 59.43/8.02 = { by lemma 18 }
% 59.43/8.02 star(X)
% 59.43/8.02
% 59.43/8.02 Lemma 20: addition(multiplication(X, Y), multiplication(X, Z)) = multiplication(X, addition(Z, Y)).
% 59.43/8.02 Proof:
% 59.43/8.02 addition(multiplication(X, Y), multiplication(X, Z))
% 59.43/8.02 = { by axiom 10 (right_distributivity) R->L }
% 59.43/8.02 multiplication(X, addition(Y, Z))
% 59.43/8.02 = { by axiom 4 (additive_commutativity) }
% 59.43/8.03 multiplication(X, addition(Z, Y))
% 59.43/8.03
% 59.43/8.03 Lemma 21: addition(X, multiplication(X, star(Y))) = multiplication(X, star(Y)).
% 59.43/8.03 Proof:
% 59.43/8.03 addition(X, multiplication(X, star(Y)))
% 59.43/8.03 = { by axiom 4 (additive_commutativity) R->L }
% 59.43/8.03 addition(multiplication(X, star(Y)), X)
% 59.43/8.03 = { by axiom 1 (multiplicative_right_identity) R->L }
% 59.43/8.03 addition(multiplication(X, star(Y)), multiplication(X, one))
% 59.43/8.03 = { by lemma 20 }
% 59.43/8.03 multiplication(X, addition(one, star(Y)))
% 59.43/8.03 = { by lemma 19 }
% 59.43/8.03 multiplication(X, star(Y))
% 59.43/8.03
% 59.43/8.03 Lemma 22: addition(multiplication(X, Y), multiplication(Z, Y)) = multiplication(addition(Z, X), Y).
% 59.43/8.03 Proof:
% 59.43/8.03 addition(multiplication(X, Y), multiplication(Z, Y))
% 59.43/8.03 = { by axiom 11 (left_distributivity) R->L }
% 59.43/8.03 multiplication(addition(X, Z), Y)
% 59.43/8.03 = { by axiom 4 (additive_commutativity) }
% 59.43/8.03 multiplication(addition(Z, X), Y)
% 59.43/8.03
% 59.43/8.03 Lemma 23: addition(Y, addition(X, Z)) = addition(X, addition(Y, Z)).
% 59.43/8.03 Proof:
% 59.43/8.03 addition(Y, addition(X, Z))
% 59.43/8.03 = { by axiom 4 (additive_commutativity) R->L }
% 59.43/8.03 addition(addition(X, Z), Y)
% 59.43/8.03 = { by axiom 6 (additive_associativity) R->L }
% 59.43/8.03 addition(X, addition(Z, Y))
% 59.43/8.03 = { by axiom 4 (additive_commutativity) }
% 59.43/8.03 addition(X, addition(Y, Z))
% 59.43/8.03
% 59.43/8.03 Lemma 24: addition(X, addition(Y, X)) = addition(Y, X).
% 59.43/8.03 Proof:
% 59.43/8.03 addition(X, addition(Y, X))
% 59.43/8.03 = { by lemma 23 }
% 59.43/8.03 addition(Y, addition(X, X))
% 59.43/8.03 = { by axiom 3 (additive_idempotence) }
% 59.43/8.03 addition(Y, X)
% 59.43/8.03
% 59.43/8.03 Lemma 25: addition(multiplication(X, star(X)), star(X)) = star(X).
% 59.43/8.03 Proof:
% 59.43/8.03 addition(multiplication(X, star(X)), star(X))
% 59.43/8.03 = { by axiom 3 (additive_idempotence) R->L }
% 59.43/8.03 addition(multiplication(X, star(X)), addition(star(X), star(X)))
% 59.43/8.03 = { by axiom 6 (additive_associativity) }
% 59.43/8.03 addition(addition(multiplication(X, star(X)), star(X)), star(X))
% 59.43/8.03 = { by lemma 18 R->L }
% 59.43/8.03 addition(addition(multiplication(X, star(X)), star(X)), addition(one, addition(multiplication(X, star(X)), star(X))))
% 59.43/8.03 = { by lemma 24 }
% 59.43/8.03 addition(one, addition(multiplication(X, star(X)), star(X)))
% 59.43/8.03 = { by lemma 18 }
% 59.43/8.03 star(X)
% 59.43/8.03
% 59.43/8.03 Lemma 26: multiplication(addition(X, one), star(X)) = star(X).
% 59.43/8.03 Proof:
% 59.43/8.03 multiplication(addition(X, one), star(X))
% 59.43/8.03 = { by axiom 4 (additive_commutativity) R->L }
% 59.43/8.03 multiplication(addition(one, X), star(X))
% 59.43/8.03 = { by lemma 22 R->L }
% 59.43/8.03 addition(multiplication(X, star(X)), multiplication(one, star(X)))
% 59.43/8.03 = { by axiom 2 (multiplicative_left_identity) }
% 59.43/8.03 addition(multiplication(X, star(X)), star(X))
% 59.43/8.03 = { by lemma 25 }
% 59.43/8.03 star(X)
% 59.43/8.03
% 59.43/8.03 Lemma 27: addition(X, star(X)) = star(X).
% 59.43/8.03 Proof:
% 59.43/8.03 addition(X, star(X))
% 59.43/8.03 = { by lemma 19 R->L }
% 59.43/8.03 addition(X, addition(one, star(X)))
% 59.43/8.03 = { by axiom 6 (additive_associativity) }
% 59.43/8.03 addition(addition(X, one), star(X))
% 59.43/8.03 = { by axiom 9 (ifeq_axiom) R->L }
% 59.43/8.03 ifeq2(true, true, addition(addition(X, one), star(X)), star(X))
% 59.43/8.03 = { by axiom 14 (order) R->L }
% 59.43/8.03 ifeq2(ifeq3(addition(addition(X, one), multiplication(addition(X, one), star(X))), multiplication(addition(X, one), star(X)), leq(addition(X, one), multiplication(addition(X, one), star(X))), true), true, addition(addition(X, one), star(X)), star(X))
% 59.43/8.03 = { by lemma 21 }
% 59.43/8.03 ifeq2(ifeq3(multiplication(addition(X, one), star(X)), multiplication(addition(X, one), star(X)), leq(addition(X, one), multiplication(addition(X, one), star(X))), true), true, addition(addition(X, one), star(X)), star(X))
% 59.43/8.03 = { by axiom 8 (ifeq_axiom) }
% 59.43/8.03 ifeq2(leq(addition(X, one), multiplication(addition(X, one), star(X))), true, addition(addition(X, one), star(X)), star(X))
% 59.43/8.03 = { by lemma 26 }
% 59.43/8.03 ifeq2(leq(addition(X, one), star(X)), true, addition(addition(X, one), star(X)), star(X))
% 59.43/8.03 = { by axiom 15 (order_1) }
% 59.43/8.03 star(X)
% 59.43/8.03
% 59.43/8.03 Lemma 28: addition(X, multiplication(X, Y)) = multiplication(X, addition(Y, one)).
% 59.43/8.03 Proof:
% 59.43/8.03 addition(X, multiplication(X, Y))
% 59.43/8.03 = { by axiom 1 (multiplicative_right_identity) R->L }
% 59.43/8.03 addition(multiplication(X, one), multiplication(X, Y))
% 59.43/8.03 = { by axiom 10 (right_distributivity) R->L }
% 59.43/8.03 multiplication(X, addition(one, Y))
% 59.43/8.03 = { by axiom 4 (additive_commutativity) }
% 59.43/8.03 multiplication(X, addition(Y, one))
% 59.43/8.03
% 59.43/8.03 Lemma 29: addition(X, multiplication(Y, X)) = multiplication(addition(Y, one), X).
% 59.43/8.03 Proof:
% 59.43/8.03 addition(X, multiplication(Y, X))
% 59.43/8.03 = { by axiom 2 (multiplicative_left_identity) R->L }
% 59.43/8.03 addition(multiplication(one, X), multiplication(Y, X))
% 59.43/8.03 = { by axiom 11 (left_distributivity) R->L }
% 59.43/8.03 multiplication(addition(one, Y), X)
% 59.43/8.03 = { by axiom 4 (additive_commutativity) }
% 59.43/8.03 multiplication(addition(Y, one), X)
% 59.43/8.03
% 59.43/8.03 Lemma 30: addition(Z, addition(X, Y)) = addition(X, addition(Y, Z)).
% 59.43/8.03 Proof:
% 59.43/8.03 addition(Z, addition(X, Y))
% 59.43/8.03 = { by lemma 23 }
% 59.43/8.03 addition(X, addition(Z, Y))
% 59.43/8.03 = { by axiom 4 (additive_commutativity) }
% 59.43/8.03 addition(X, addition(Y, Z))
% 59.43/8.03
% 59.43/8.03 Lemma 31: addition(X, multiplication(star(Y), X)) = multiplication(star(Y), X).
% 59.43/8.03 Proof:
% 59.43/8.03 addition(X, multiplication(star(Y), X))
% 59.43/8.03 = { by axiom 4 (additive_commutativity) R->L }
% 59.43/8.03 addition(multiplication(star(Y), X), X)
% 59.43/8.03 = { by axiom 2 (multiplicative_left_identity) R->L }
% 59.43/8.03 addition(multiplication(star(Y), X), multiplication(one, X))
% 59.43/8.03 = { by lemma 22 }
% 59.43/8.03 multiplication(addition(one, star(Y)), X)
% 59.43/8.03 = { by lemma 19 }
% 59.43/8.03 multiplication(star(Y), X)
% 59.43/8.03
% 59.43/8.03 Lemma 32: ifeq2(leq(X, Y), true, addition(Y, X), Y) = Y.
% 59.43/8.03 Proof:
% 59.43/8.03 ifeq2(leq(X, Y), true, addition(Y, X), Y)
% 59.43/8.03 = { by axiom 4 (additive_commutativity) R->L }
% 59.43/8.03 ifeq2(leq(X, Y), true, addition(X, Y), Y)
% 59.43/8.03 = { by axiom 15 (order_1) }
% 59.43/8.03 Y
% 59.43/8.03
% 59.43/8.03 Lemma 33: multiplication(star(X), addition(one, multiplication(X, star(X)))) = star(X).
% 59.43/8.03 Proof:
% 59.43/8.03 multiplication(star(X), addition(one, multiplication(X, star(X))))
% 59.43/8.03 = { by axiom 4 (additive_commutativity) R->L }
% 59.43/8.03 multiplication(star(X), addition(multiplication(X, star(X)), one))
% 59.43/8.03 = { by lemma 28 R->L }
% 59.43/8.03 addition(star(X), multiplication(star(X), multiplication(X, star(X))))
% 59.43/8.03 = { by axiom 4 (additive_commutativity) R->L }
% 59.43/8.03 addition(multiplication(star(X), multiplication(X, star(X))), star(X))
% 59.43/8.03 = { by axiom 9 (ifeq_axiom) R->L }
% 59.43/8.03 ifeq2(true, true, addition(multiplication(star(X), multiplication(X, star(X))), star(X)), star(X))
% 59.43/8.03 = { by axiom 17 (star_induction_left) R->L }
% 59.43/8.03 ifeq2(ifeq(leq(addition(multiplication(X, star(X)), multiplication(X, star(X))), star(X)), true, leq(multiplication(star(X), multiplication(X, star(X))), star(X)), true), true, addition(multiplication(star(X), multiplication(X, star(X))), star(X)), star(X))
% 59.43/8.03 = { by axiom 3 (additive_idempotence) }
% 59.43/8.03 ifeq2(ifeq(leq(multiplication(X, star(X)), star(X)), true, leq(multiplication(star(X), multiplication(X, star(X))), star(X)), true), true, addition(multiplication(star(X), multiplication(X, star(X))), star(X)), star(X))
% 59.43/8.03 = { by axiom 8 (ifeq_axiom) R->L }
% 59.43/8.03 ifeq2(ifeq(ifeq3(star(X), star(X), leq(multiplication(X, star(X)), star(X)), true), true, leq(multiplication(star(X), multiplication(X, star(X))), star(X)), true), true, addition(multiplication(star(X), multiplication(X, star(X))), star(X)), star(X))
% 59.43/8.03 = { by lemma 25 R->L }
% 59.43/8.03 ifeq2(ifeq(ifeq3(addition(multiplication(X, star(X)), star(X)), star(X), leq(multiplication(X, star(X)), star(X)), true), true, leq(multiplication(star(X), multiplication(X, star(X))), star(X)), true), true, addition(multiplication(star(X), multiplication(X, star(X))), star(X)), star(X))
% 59.43/8.03 = { by axiom 14 (order) }
% 59.43/8.03 ifeq2(ifeq(true, true, leq(multiplication(star(X), multiplication(X, star(X))), star(X)), true), true, addition(multiplication(star(X), multiplication(X, star(X))), star(X)), star(X))
% 59.43/8.03 = { by axiom 7 (ifeq_axiom) }
% 59.43/8.03 ifeq2(leq(multiplication(star(X), multiplication(X, star(X))), star(X)), true, addition(multiplication(star(X), multiplication(X, star(X))), star(X)), star(X))
% 59.43/8.03 = { by axiom 15 (order_1) }
% 59.43/8.03 star(X)
% 59.43/8.03
% 59.43/8.03 Lemma 34: addition(star(X), multiplication(X, star(X))) = star(X).
% 59.43/8.03 Proof:
% 59.43/8.03 addition(star(X), multiplication(X, star(X)))
% 59.43/8.03 = { by axiom 4 (additive_commutativity) R->L }
% 59.43/8.03 addition(multiplication(X, star(X)), star(X))
% 59.43/8.03 = { by axiom 3 (additive_idempotence) R->L }
% 59.43/8.03 addition(multiplication(X, star(X)), addition(star(X), star(X)))
% 59.43/8.03 = { by axiom 6 (additive_associativity) }
% 59.43/8.03 addition(addition(multiplication(X, star(X)), star(X)), star(X))
% 59.43/8.03 = { by lemma 18 R->L }
% 59.43/8.03 addition(addition(multiplication(X, star(X)), star(X)), addition(one, addition(multiplication(X, star(X)), star(X))))
% 59.43/8.03 = { by lemma 24 }
% 59.43/8.03 addition(one, addition(multiplication(X, star(X)), star(X)))
% 59.43/8.03 = { by lemma 18 }
% 59.43/8.03 star(X)
% 59.43/8.03
% 59.43/8.03 Lemma 35: addition(one, multiplication(X, star(X))) = star(multiplication(X, star(X))).
% 59.43/8.03 Proof:
% 59.43/8.03 addition(one, multiplication(X, star(X)))
% 59.43/8.03 = { by lemma 32 R->L }
% 59.43/8.03 ifeq2(leq(star(multiplication(X, star(X))), addition(one, multiplication(X, star(X)))), true, addition(addition(one, multiplication(X, star(X))), star(multiplication(X, star(X)))), addition(one, multiplication(X, star(X))))
% 59.43/8.03 = { by axiom 7 (ifeq_axiom) R->L }
% 59.43/8.03 ifeq2(ifeq(true, true, leq(star(multiplication(X, star(X))), addition(one, multiplication(X, star(X)))), true), true, addition(addition(one, multiplication(X, star(X))), star(multiplication(X, star(X)))), addition(one, multiplication(X, star(X))))
% 59.43/8.03 = { by axiom 14 (order) R->L }
% 59.43/8.03 ifeq2(ifeq(ifeq3(addition(addition(one, multiplication(X, star(X))), addition(one, multiplication(X, star(X)))), addition(one, multiplication(X, star(X))), leq(addition(one, multiplication(X, star(X))), addition(one, multiplication(X, star(X)))), true), true, leq(star(multiplication(X, star(X))), addition(one, multiplication(X, star(X)))), true), true, addition(addition(one, multiplication(X, star(X))), star(multiplication(X, star(X)))), addition(one, multiplication(X, star(X))))
% 59.43/8.03 = { by axiom 3 (additive_idempotence) }
% 59.43/8.03 ifeq2(ifeq(ifeq3(addition(one, multiplication(X, star(X))), addition(one, multiplication(X, star(X))), leq(addition(one, multiplication(X, star(X))), addition(one, multiplication(X, star(X)))), true), true, leq(star(multiplication(X, star(X))), addition(one, multiplication(X, star(X)))), true), true, addition(addition(one, multiplication(X, star(X))), star(multiplication(X, star(X)))), addition(one, multiplication(X, star(X))))
% 59.43/8.03 = { by axiom 8 (ifeq_axiom) }
% 59.43/8.03 ifeq2(ifeq(leq(addition(one, multiplication(X, star(X))), addition(one, multiplication(X, star(X)))), true, leq(star(multiplication(X, star(X))), addition(one, multiplication(X, star(X)))), true), true, addition(addition(one, multiplication(X, star(X))), star(multiplication(X, star(X)))), addition(one, multiplication(X, star(X))))
% 59.43/8.03 = { by lemma 33 R->L }
% 59.43/8.03 ifeq2(ifeq(leq(addition(one, multiplication(X, multiplication(star(X), addition(one, multiplication(X, star(X)))))), addition(one, multiplication(X, star(X)))), true, leq(star(multiplication(X, star(X))), addition(one, multiplication(X, star(X)))), true), true, addition(addition(one, multiplication(X, star(X))), star(multiplication(X, star(X)))), addition(one, multiplication(X, star(X))))
% 59.43/8.03 = { by axiom 5 (multiplicative_associativity) }
% 59.43/8.03 ifeq2(ifeq(leq(addition(one, multiplication(multiplication(X, star(X)), addition(one, multiplication(X, star(X))))), addition(one, multiplication(X, star(X)))), true, leq(star(multiplication(X, star(X))), addition(one, multiplication(X, star(X)))), true), true, addition(addition(one, multiplication(X, star(X))), star(multiplication(X, star(X)))), addition(one, multiplication(X, star(X))))
% 59.43/8.03 = { by axiom 4 (additive_commutativity) R->L }
% 59.43/8.03 ifeq2(ifeq(leq(addition(multiplication(multiplication(X, star(X)), addition(one, multiplication(X, star(X)))), one), addition(one, multiplication(X, star(X)))), true, leq(star(multiplication(X, star(X))), addition(one, multiplication(X, star(X)))), true), true, addition(addition(one, multiplication(X, star(X))), star(multiplication(X, star(X)))), addition(one, multiplication(X, star(X))))
% 59.43/8.03 = { by axiom 1 (multiplicative_right_identity) R->L }
% 59.43/8.04 ifeq2(ifeq(leq(addition(multiplication(multiplication(X, star(X)), addition(one, multiplication(X, star(X)))), one), addition(one, multiplication(X, star(X)))), true, leq(multiplication(star(multiplication(X, star(X))), one), addition(one, multiplication(X, star(X)))), true), true, addition(addition(one, multiplication(X, star(X))), star(multiplication(X, star(X)))), addition(one, multiplication(X, star(X))))
% 59.43/8.04 = { by axiom 17 (star_induction_left) }
% 59.43/8.04 ifeq2(true, true, addition(addition(one, multiplication(X, star(X))), star(multiplication(X, star(X)))), addition(one, multiplication(X, star(X))))
% 59.43/8.04 = { by axiom 9 (ifeq_axiom) }
% 59.43/8.04 addition(addition(one, multiplication(X, star(X))), star(multiplication(X, star(X))))
% 59.43/8.04 = { by axiom 6 (additive_associativity) R->L }
% 59.43/8.04 addition(one, addition(multiplication(X, star(X)), star(multiplication(X, star(X)))))
% 59.43/8.04 = { by lemma 34 R->L }
% 59.43/8.04 addition(one, addition(multiplication(X, star(X)), addition(star(multiplication(X, star(X))), multiplication(multiplication(X, star(X)), star(multiplication(X, star(X)))))))
% 59.43/8.04 = { by axiom 4 (additive_commutativity) R->L }
% 59.43/8.04 addition(one, addition(multiplication(X, star(X)), addition(multiplication(multiplication(X, star(X)), star(multiplication(X, star(X)))), star(multiplication(X, star(X))))))
% 59.43/8.04 = { by lemma 23 }
% 59.43/8.04 addition(one, addition(multiplication(multiplication(X, star(X)), star(multiplication(X, star(X)))), addition(multiplication(X, star(X)), star(multiplication(X, star(X))))))
% 59.43/8.04 = { by axiom 4 (additive_commutativity) R->L }
% 59.43/8.04 addition(one, addition(multiplication(multiplication(X, star(X)), star(multiplication(X, star(X)))), addition(star(multiplication(X, star(X))), multiplication(X, star(X)))))
% 59.43/8.04 = { by axiom 6 (additive_associativity) }
% 59.43/8.04 addition(one, addition(addition(multiplication(multiplication(X, star(X)), star(multiplication(X, star(X)))), star(multiplication(X, star(X)))), multiplication(X, star(X))))
% 59.43/8.04 = { by axiom 6 (additive_associativity) }
% 59.43/8.04 addition(addition(one, addition(multiplication(multiplication(X, star(X)), star(multiplication(X, star(X)))), star(multiplication(X, star(X))))), multiplication(X, star(X)))
% 59.43/8.04 = { by lemma 18 }
% 59.43/8.04 addition(star(multiplication(X, star(X))), multiplication(X, star(X)))
% 59.43/8.04 = { by axiom 4 (additive_commutativity) }
% 59.43/8.04 addition(multiplication(X, star(X)), star(multiplication(X, star(X))))
% 59.43/8.04 = { by lemma 27 }
% 59.43/8.04 star(multiplication(X, star(X)))
% 59.43/8.04
% 59.43/8.04 Lemma 36: multiplication(star(X), star(star(X))) = star(star(X)).
% 59.43/8.04 Proof:
% 59.43/8.04 multiplication(star(X), star(star(X)))
% 59.43/8.04 = { by lemma 25 R->L }
% 59.43/8.04 multiplication(star(X), star(addition(multiplication(X, star(X)), star(X))))
% 59.43/8.04 = { by lemma 18 R->L }
% 59.43/8.04 multiplication(addition(one, addition(multiplication(X, star(X)), star(X))), star(addition(multiplication(X, star(X)), star(X))))
% 59.43/8.04 = { by axiom 4 (additive_commutativity) R->L }
% 59.43/8.04 multiplication(addition(addition(multiplication(X, star(X)), star(X)), one), star(addition(multiplication(X, star(X)), star(X))))
% 59.43/8.04 = { by lemma 26 }
% 59.43/8.04 star(addition(multiplication(X, star(X)), star(X)))
% 59.43/8.04 = { by lemma 25 }
% 59.43/8.04 star(star(X))
% 59.43/8.04
% 59.43/8.04 Lemma 37: star(star(multiplication(X, star(X)))) = star(multiplication(X, star(X))).
% 59.43/8.04 Proof:
% 59.43/8.04 star(star(multiplication(X, star(X))))
% 59.43/8.04 = { by lemma 27 R->L }
% 59.43/8.04 addition(star(multiplication(X, star(X))), star(star(multiplication(X, star(X)))))
% 59.43/8.04 = { by axiom 9 (ifeq_axiom) R->L }
% 59.43/8.04 ifeq2(true, true, addition(star(multiplication(X, star(X))), star(star(multiplication(X, star(X))))), star(multiplication(X, star(X))))
% 59.43/8.04 = { by axiom 16 (star_induction_right) R->L }
% 59.43/8.04 ifeq2(ifeq(leq(addition(multiplication(star(addition(X, multiplication(X, star(X)))), addition(addition(X, multiplication(X, star(X))), one)), one), star(addition(X, multiplication(X, star(X))))), true, leq(multiplication(one, star(addition(addition(X, multiplication(X, star(X))), one))), star(addition(X, multiplication(X, star(X))))), true), true, addition(star(multiplication(X, star(X))), star(star(multiplication(X, star(X))))), star(multiplication(X, star(X))))
% 59.43/8.04 = { by axiom 2 (multiplicative_left_identity) }
% 59.43/8.04 ifeq2(ifeq(leq(addition(multiplication(star(addition(X, multiplication(X, star(X)))), addition(addition(X, multiplication(X, star(X))), one)), one), star(addition(X, multiplication(X, star(X))))), true, leq(star(addition(addition(X, multiplication(X, star(X))), one)), star(addition(X, multiplication(X, star(X))))), true), true, addition(star(multiplication(X, star(X))), star(star(multiplication(X, star(X))))), star(multiplication(X, star(X))))
% 60.52/8.04 = { by axiom 4 (additive_commutativity) }
% 60.52/8.04 ifeq2(ifeq(leq(addition(one, multiplication(star(addition(X, multiplication(X, star(X)))), addition(addition(X, multiplication(X, star(X))), one))), star(addition(X, multiplication(X, star(X))))), true, leq(star(addition(addition(X, multiplication(X, star(X))), one)), star(addition(X, multiplication(X, star(X))))), true), true, addition(star(multiplication(X, star(X))), star(star(multiplication(X, star(X))))), star(multiplication(X, star(X))))
% 60.52/8.04 = { by lemma 28 R->L }
% 60.52/8.04 ifeq2(ifeq(leq(addition(one, addition(star(addition(X, multiplication(X, star(X)))), multiplication(star(addition(X, multiplication(X, star(X)))), addition(X, multiplication(X, star(X)))))), star(addition(X, multiplication(X, star(X))))), true, leq(star(addition(addition(X, multiplication(X, star(X))), one)), star(addition(X, multiplication(X, star(X))))), true), true, addition(star(multiplication(X, star(X))), star(star(multiplication(X, star(X))))), star(multiplication(X, star(X))))
% 60.52/8.04 = { by axiom 4 (additive_commutativity) R->L }
% 60.52/8.04 ifeq2(ifeq(leq(addition(one, addition(multiplication(star(addition(X, multiplication(X, star(X)))), addition(X, multiplication(X, star(X)))), star(addition(X, multiplication(X, star(X)))))), star(addition(X, multiplication(X, star(X))))), true, leq(star(addition(addition(X, multiplication(X, star(X))), one)), star(addition(X, multiplication(X, star(X))))), true), true, addition(star(multiplication(X, star(X))), star(star(multiplication(X, star(X))))), star(multiplication(X, star(X))))
% 60.52/8.04 = { by axiom 6 (additive_associativity) }
% 60.52/8.04 ifeq2(ifeq(leq(addition(addition(one, multiplication(star(addition(X, multiplication(X, star(X)))), addition(X, multiplication(X, star(X))))), star(addition(X, multiplication(X, star(X))))), star(addition(X, multiplication(X, star(X))))), true, leq(star(addition(addition(X, multiplication(X, star(X))), one)), star(addition(X, multiplication(X, star(X))))), true), true, addition(star(multiplication(X, star(X))), star(star(multiplication(X, star(X))))), star(multiplication(X, star(X))))
% 60.52/8.04 = { by axiom 9 (ifeq_axiom) R->L }
% 60.52/8.04 ifeq2(ifeq(leq(ifeq2(true, true, addition(addition(one, multiplication(star(addition(X, multiplication(X, star(X)))), addition(X, multiplication(X, star(X))))), star(addition(X, multiplication(X, star(X))))), star(addition(X, multiplication(X, star(X))))), star(addition(X, multiplication(X, star(X))))), true, leq(star(addition(addition(X, multiplication(X, star(X))), one)), star(addition(X, multiplication(X, star(X))))), true), true, addition(star(multiplication(X, star(X))), star(star(multiplication(X, star(X))))), star(multiplication(X, star(X))))
% 60.52/8.04 = { by axiom 13 (star_unfold_left) R->L }
% 60.52/8.04 ifeq2(ifeq(leq(ifeq2(leq(addition(one, multiplication(star(addition(X, multiplication(X, star(X)))), addition(X, multiplication(X, star(X))))), star(addition(X, multiplication(X, star(X))))), true, addition(addition(one, multiplication(star(addition(X, multiplication(X, star(X)))), addition(X, multiplication(X, star(X))))), star(addition(X, multiplication(X, star(X))))), star(addition(X, multiplication(X, star(X))))), star(addition(X, multiplication(X, star(X))))), true, leq(star(addition(addition(X, multiplication(X, star(X))), one)), star(addition(X, multiplication(X, star(X))))), true), true, addition(star(multiplication(X, star(X))), star(star(multiplication(X, star(X))))), star(multiplication(X, star(X))))
% 60.52/8.04 = { by axiom 15 (order_1) }
% 60.52/8.04 ifeq2(ifeq(leq(star(addition(X, multiplication(X, star(X)))), star(addition(X, multiplication(X, star(X))))), true, leq(star(addition(addition(X, multiplication(X, star(X))), one)), star(addition(X, multiplication(X, star(X))))), true), true, addition(star(multiplication(X, star(X))), star(star(multiplication(X, star(X))))), star(multiplication(X, star(X))))
% 60.52/8.04 = { by axiom 8 (ifeq_axiom) R->L }
% 60.52/8.04 ifeq2(ifeq(ifeq3(star(addition(X, multiplication(X, star(X)))), star(addition(X, multiplication(X, star(X)))), leq(star(addition(X, multiplication(X, star(X)))), star(addition(X, multiplication(X, star(X))))), true), true, leq(star(addition(addition(X, multiplication(X, star(X))), one)), star(addition(X, multiplication(X, star(X))))), true), true, addition(star(multiplication(X, star(X))), star(star(multiplication(X, star(X))))), star(multiplication(X, star(X))))
% 60.52/8.04 = { by axiom 3 (additive_idempotence) R->L }
% 60.52/8.04 ifeq2(ifeq(ifeq3(addition(star(addition(X, multiplication(X, star(X)))), star(addition(X, multiplication(X, star(X))))), star(addition(X, multiplication(X, star(X)))), leq(star(addition(X, multiplication(X, star(X)))), star(addition(X, multiplication(X, star(X))))), true), true, leq(star(addition(addition(X, multiplication(X, star(X))), one)), star(addition(X, multiplication(X, star(X))))), true), true, addition(star(multiplication(X, star(X))), star(star(multiplication(X, star(X))))), star(multiplication(X, star(X))))
% 60.52/8.04 = { by axiom 14 (order) }
% 60.52/8.05 ifeq2(ifeq(true, true, leq(star(addition(addition(X, multiplication(X, star(X))), one)), star(addition(X, multiplication(X, star(X))))), true), true, addition(star(multiplication(X, star(X))), star(star(multiplication(X, star(X))))), star(multiplication(X, star(X))))
% 60.52/8.05 = { by axiom 7 (ifeq_axiom) }
% 60.52/8.05 ifeq2(leq(star(addition(addition(X, multiplication(X, star(X))), one)), star(addition(X, multiplication(X, star(X))))), true, addition(star(multiplication(X, star(X))), star(star(multiplication(X, star(X))))), star(multiplication(X, star(X))))
% 60.52/8.05 = { by lemma 21 }
% 60.52/8.05 ifeq2(leq(star(addition(multiplication(X, star(X)), one)), star(addition(X, multiplication(X, star(X))))), true, addition(star(multiplication(X, star(X))), star(star(multiplication(X, star(X))))), star(multiplication(X, star(X))))
% 60.52/8.05 = { by axiom 4 (additive_commutativity) }
% 60.52/8.05 ifeq2(leq(star(addition(one, multiplication(X, star(X)))), star(addition(X, multiplication(X, star(X))))), true, addition(star(multiplication(X, star(X))), star(star(multiplication(X, star(X))))), star(multiplication(X, star(X))))
% 60.52/8.05 = { by lemma 35 }
% 60.52/8.05 ifeq2(leq(star(star(multiplication(X, star(X)))), star(addition(X, multiplication(X, star(X))))), true, addition(star(multiplication(X, star(X))), star(star(multiplication(X, star(X))))), star(multiplication(X, star(X))))
% 60.52/8.05 = { by lemma 21 }
% 60.52/8.05 ifeq2(leq(star(star(multiplication(X, star(X)))), star(multiplication(X, star(X)))), true, addition(star(multiplication(X, star(X))), star(star(multiplication(X, star(X))))), star(multiplication(X, star(X))))
% 60.52/8.05 = { by lemma 32 }
% 60.52/8.05 star(multiplication(X, star(X)))
% 60.52/8.05
% 60.52/8.05 Lemma 38: addition(multiplication(multiplication(X, star(X)), Y), multiplication(star(X), Y)) = multiplication(star(X), Y).
% 60.52/8.05 Proof:
% 60.52/8.05 addition(multiplication(multiplication(X, star(X)), Y), multiplication(star(X), Y))
% 60.52/8.05 = { by axiom 4 (additive_commutativity) R->L }
% 60.52/8.05 addition(multiplication(star(X), Y), multiplication(multiplication(X, star(X)), Y))
% 60.52/8.05 = { by lemma 22 }
% 60.52/8.05 multiplication(addition(multiplication(X, star(X)), star(X)), Y)
% 60.52/8.05 = { by lemma 25 }
% 60.52/8.05 multiplication(star(X), Y)
% 60.52/8.05
% 60.52/8.05 Lemma 39: multiplication(star(X), addition(Y, multiplication(multiplication(X, star(X)), Y))) = multiplication(star(X), Y).
% 60.52/8.05 Proof:
% 60.52/8.05 multiplication(star(X), addition(Y, multiplication(multiplication(X, star(X)), Y)))
% 60.52/8.05 = { by axiom 4 (additive_commutativity) R->L }
% 60.52/8.05 multiplication(star(X), addition(multiplication(multiplication(X, star(X)), Y), Y))
% 60.52/8.05 = { by lemma 20 R->L }
% 60.52/8.05 addition(multiplication(star(X), Y), multiplication(star(X), multiplication(multiplication(X, star(X)), Y)))
% 60.52/8.05 = { by axiom 4 (additive_commutativity) R->L }
% 60.52/8.05 addition(multiplication(star(X), multiplication(multiplication(X, star(X)), Y)), multiplication(star(X), Y))
% 60.52/8.05 = { by axiom 9 (ifeq_axiom) R->L }
% 60.52/8.05 ifeq2(true, true, addition(multiplication(star(X), multiplication(multiplication(X, star(X)), Y)), multiplication(star(X), Y)), multiplication(star(X), Y))
% 60.52/8.05 = { by axiom 17 (star_induction_left) R->L }
% 60.52/8.05 ifeq2(ifeq(leq(addition(multiplication(X, multiplication(star(X), Y)), multiplication(multiplication(X, star(X)), Y)), multiplication(star(X), Y)), true, leq(multiplication(star(X), multiplication(multiplication(X, star(X)), Y)), multiplication(star(X), Y)), true), true, addition(multiplication(star(X), multiplication(multiplication(X, star(X)), Y)), multiplication(star(X), Y)), multiplication(star(X), Y))
% 60.52/8.05 = { by axiom 5 (multiplicative_associativity) }
% 60.52/8.05 ifeq2(ifeq(leq(addition(multiplication(multiplication(X, star(X)), Y), multiplication(multiplication(X, star(X)), Y)), multiplication(star(X), Y)), true, leq(multiplication(star(X), multiplication(multiplication(X, star(X)), Y)), multiplication(star(X), Y)), true), true, addition(multiplication(star(X), multiplication(multiplication(X, star(X)), Y)), multiplication(star(X), Y)), multiplication(star(X), Y))
% 60.52/8.05 = { by axiom 3 (additive_idempotence) }
% 60.52/8.05 ifeq2(ifeq(leq(multiplication(multiplication(X, star(X)), Y), multiplication(star(X), Y)), true, leq(multiplication(star(X), multiplication(multiplication(X, star(X)), Y)), multiplication(star(X), Y)), true), true, addition(multiplication(star(X), multiplication(multiplication(X, star(X)), Y)), multiplication(star(X), Y)), multiplication(star(X), Y))
% 60.52/8.05 = { by axiom 8 (ifeq_axiom) R->L }
% 60.52/8.05 ifeq2(ifeq(ifeq3(multiplication(star(X), Y), multiplication(star(X), Y), leq(multiplication(multiplication(X, star(X)), Y), multiplication(star(X), Y)), true), true, leq(multiplication(star(X), multiplication(multiplication(X, star(X)), Y)), multiplication(star(X), Y)), true), true, addition(multiplication(star(X), multiplication(multiplication(X, star(X)), Y)), multiplication(star(X), Y)), multiplication(star(X), Y))
% 60.52/8.05 = { by lemma 38 R->L }
% 60.52/8.05 ifeq2(ifeq(ifeq3(addition(multiplication(multiplication(X, star(X)), Y), multiplication(star(X), Y)), multiplication(star(X), Y), leq(multiplication(multiplication(X, star(X)), Y), multiplication(star(X), Y)), true), true, leq(multiplication(star(X), multiplication(multiplication(X, star(X)), Y)), multiplication(star(X), Y)), true), true, addition(multiplication(star(X), multiplication(multiplication(X, star(X)), Y)), multiplication(star(X), Y)), multiplication(star(X), Y))
% 60.52/8.05 = { by axiom 14 (order) }
% 60.52/8.05 ifeq2(ifeq(true, true, leq(multiplication(star(X), multiplication(multiplication(X, star(X)), Y)), multiplication(star(X), Y)), true), true, addition(multiplication(star(X), multiplication(multiplication(X, star(X)), Y)), multiplication(star(X), Y)), multiplication(star(X), Y))
% 60.52/8.05 = { by axiom 7 (ifeq_axiom) }
% 60.52/8.05 ifeq2(leq(multiplication(star(X), multiplication(multiplication(X, star(X)), Y)), multiplication(star(X), Y)), true, addition(multiplication(star(X), multiplication(multiplication(X, star(X)), Y)), multiplication(star(X), Y)), multiplication(star(X), Y))
% 60.52/8.05 = { by axiom 15 (order_1) }
% 60.52/8.06 multiplication(star(X), Y)
% 60.52/8.06
% 60.52/8.06 Goal 1 (goals): multiplication(star(x0), x1) = addition(x1, multiplication(multiplication(x0, star(x0)), x1)).
% 60.52/8.06 Proof:
% 60.52/8.06 multiplication(star(x0), x1)
% 60.52/8.06 = { by lemma 31 R->L }
% 60.52/8.06 addition(x1, multiplication(star(x0), x1))
% 60.52/8.06 = { by lemma 38 R->L }
% 60.52/8.06 addition(x1, addition(multiplication(multiplication(x0, star(x0)), x1), multiplication(star(x0), x1)))
% 60.52/8.06 = { by lemma 30 R->L }
% 60.52/8.06 addition(multiplication(star(x0), x1), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.06 = { by axiom 4 (additive_commutativity) }
% 60.52/8.06 addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1))
% 60.52/8.06 = { by axiom 9 (ifeq_axiom) R->L }
% 60.52/8.06 ifeq2(true, true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.06 = { by axiom 17 (star_induction_left) R->L }
% 60.52/8.06 ifeq2(ifeq(leq(addition(multiplication(star(x0), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(star(x0)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.06 = { by axiom 4 (additive_commutativity) }
% 60.52/8.06 ifeq2(ifeq(leq(addition(multiplication(star(x0), x1), multiplication(star(x0), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(star(x0)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.06 = { by lemma 27 R->L }
% 60.52/8.06 ifeq2(ifeq(leq(addition(multiplication(star(x0), x1), multiplication(star(x0), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(addition(star(x0), star(star(x0))), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.06 = { by axiom 9 (ifeq_axiom) R->L }
% 60.52/8.06 ifeq2(ifeq(leq(addition(multiplication(star(x0), x1), multiplication(star(x0), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(ifeq2(true, true, addition(star(x0), star(star(x0))), star(x0)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.06 = { by axiom 16 (star_induction_right) R->L }
% 60.52/8.06 ifeq2(ifeq(leq(addition(multiplication(star(x0), x1), multiplication(star(x0), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(ifeq2(ifeq(leq(addition(multiplication(star(x0), star(x0)), multiplication(star(x0), star(x0))), star(x0)), true, leq(multiplication(multiplication(star(x0), star(x0)), star(star(x0))), star(x0)), true), true, addition(star(x0), star(star(x0))), star(x0)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.06 = { by axiom 3 (additive_idempotence) }
% 60.52/8.06 ifeq2(ifeq(leq(addition(multiplication(star(x0), x1), multiplication(star(x0), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(ifeq2(ifeq(leq(multiplication(star(x0), star(x0)), star(x0)), true, leq(multiplication(multiplication(star(x0), star(x0)), star(star(x0))), star(x0)), true), true, addition(star(x0), star(star(x0))), star(x0)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.06 = { by axiom 5 (multiplicative_associativity) R->L }
% 60.52/8.06 ifeq2(ifeq(leq(addition(multiplication(star(x0), x1), multiplication(star(x0), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(ifeq2(ifeq(leq(multiplication(star(x0), star(x0)), star(x0)), true, leq(multiplication(star(x0), multiplication(star(x0), star(star(x0)))), star(x0)), true), true, addition(star(x0), star(star(x0))), star(x0)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.06 = { by axiom 7 (ifeq_axiom) R->L }
% 60.52/8.06 ifeq2(ifeq(leq(addition(multiplication(star(x0), x1), multiplication(star(x0), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(ifeq2(ifeq(ifeq(true, true, leq(multiplication(star(x0), star(x0)), star(x0)), true), true, leq(multiplication(star(x0), multiplication(star(x0), star(star(x0)))), star(x0)), true), true, addition(star(x0), star(star(x0))), star(x0)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.06 = { by axiom 14 (order) R->L }
% 60.52/8.07 ifeq2(ifeq(leq(addition(multiplication(star(x0), x1), multiplication(star(x0), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(ifeq2(ifeq(ifeq(ifeq3(addition(star(x0), star(x0)), star(x0), leq(star(x0), star(x0)), true), true, leq(multiplication(star(x0), star(x0)), star(x0)), true), true, leq(multiplication(star(x0), multiplication(star(x0), star(star(x0)))), star(x0)), true), true, addition(star(x0), star(star(x0))), star(x0)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.07 = { by axiom 3 (additive_idempotence) }
% 60.52/8.07 ifeq2(ifeq(leq(addition(multiplication(star(x0), x1), multiplication(star(x0), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(ifeq2(ifeq(ifeq(ifeq3(star(x0), star(x0), leq(star(x0), star(x0)), true), true, leq(multiplication(star(x0), star(x0)), star(x0)), true), true, leq(multiplication(star(x0), multiplication(star(x0), star(star(x0)))), star(x0)), true), true, addition(star(x0), star(star(x0))), star(x0)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.07 = { by axiom 8 (ifeq_axiom) }
% 60.52/8.07 ifeq2(ifeq(leq(addition(multiplication(star(x0), x1), multiplication(star(x0), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(ifeq2(ifeq(ifeq(leq(star(x0), star(x0)), true, leq(multiplication(star(x0), star(x0)), star(x0)), true), true, leq(multiplication(star(x0), multiplication(star(x0), star(star(x0)))), star(x0)), true), true, addition(star(x0), star(star(x0))), star(x0)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.07 = { by lemma 34 R->L }
% 60.52/8.07 ifeq2(ifeq(leq(addition(multiplication(star(x0), x1), multiplication(star(x0), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(ifeq2(ifeq(ifeq(leq(addition(star(x0), multiplication(x0, star(x0))), star(x0)), true, leq(multiplication(star(x0), star(x0)), star(x0)), true), true, leq(multiplication(star(x0), multiplication(star(x0), star(star(x0)))), star(x0)), true), true, addition(star(x0), star(star(x0))), star(x0)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.07 = { by axiom 4 (additive_commutativity) R->L }
% 60.52/8.07 ifeq2(ifeq(leq(addition(multiplication(star(x0), x1), multiplication(star(x0), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(ifeq2(ifeq(ifeq(leq(addition(multiplication(x0, star(x0)), star(x0)), star(x0)), true, leq(multiplication(star(x0), star(x0)), star(x0)), true), true, leq(multiplication(star(x0), multiplication(star(x0), star(star(x0)))), star(x0)), true), true, addition(star(x0), star(star(x0))), star(x0)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.07 = { by axiom 17 (star_induction_left) }
% 60.52/8.07 ifeq2(ifeq(leq(addition(multiplication(star(x0), x1), multiplication(star(x0), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(ifeq2(ifeq(true, true, leq(multiplication(star(x0), multiplication(star(x0), star(star(x0)))), star(x0)), true), true, addition(star(x0), star(star(x0))), star(x0)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.07 = { by axiom 7 (ifeq_axiom) }
% 60.52/8.07 ifeq2(ifeq(leq(addition(multiplication(star(x0), x1), multiplication(star(x0), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(ifeq2(leq(multiplication(star(x0), multiplication(star(x0), star(star(x0)))), star(x0)), true, addition(star(x0), star(star(x0))), star(x0)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.07 = { by lemma 36 }
% 60.52/8.08 ifeq2(ifeq(leq(addition(multiplication(star(x0), x1), multiplication(star(x0), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(ifeq2(leq(multiplication(star(x0), star(star(x0))), star(x0)), true, addition(star(x0), star(star(x0))), star(x0)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.08 = { by lemma 36 }
% 60.52/8.08 ifeq2(ifeq(leq(addition(multiplication(star(x0), x1), multiplication(star(x0), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(ifeq2(leq(star(star(x0)), star(x0)), true, addition(star(x0), star(star(x0))), star(x0)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.08 = { by lemma 32 }
% 60.52/8.08 ifeq2(ifeq(leq(addition(multiplication(star(x0), x1), multiplication(star(x0), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.08 = { by lemma 39 R->L }
% 60.52/8.08 ifeq2(ifeq(leq(addition(multiplication(star(x0), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), multiplication(star(x0), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.08 = { by axiom 11 (left_distributivity) R->L }
% 60.52/8.08 ifeq2(ifeq(leq(multiplication(addition(star(x0), star(x0)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.08 = { by axiom 3 (additive_idempotence) }
% 60.52/8.08 ifeq2(ifeq(leq(multiplication(star(x0), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.08 = { by axiom 15 (order_1) R->L }
% 60.52/8.08 ifeq2(ifeq(leq(multiplication(ifeq2(leq(star(addition(one, multiplication(x0, star(x0)))), star(x0)), true, addition(star(addition(one, multiplication(x0, star(x0)))), star(x0)), star(x0)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.08 = { by axiom 7 (ifeq_axiom) R->L }
% 60.52/8.08 ifeq2(ifeq(leq(multiplication(ifeq2(ifeq(true, true, leq(star(addition(one, multiplication(x0, star(x0)))), star(x0)), true), true, addition(star(addition(one, multiplication(x0, star(x0)))), star(x0)), star(x0)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.08 = { by axiom 14 (order) R->L }
% 60.52/8.08 ifeq2(ifeq(leq(multiplication(ifeq2(ifeq(ifeq3(addition(star(x0), star(x0)), star(x0), leq(star(x0), star(x0)), true), true, leq(star(addition(one, multiplication(x0, star(x0)))), star(x0)), true), true, addition(star(addition(one, multiplication(x0, star(x0)))), star(x0)), star(x0)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.08 = { by axiom 3 (additive_idempotence) }
% 60.52/8.08 ifeq2(ifeq(leq(multiplication(ifeq2(ifeq(ifeq3(star(x0), star(x0), leq(star(x0), star(x0)), true), true, leq(star(addition(one, multiplication(x0, star(x0)))), star(x0)), true), true, addition(star(addition(one, multiplication(x0, star(x0)))), star(x0)), star(x0)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.08 = { by axiom 8 (ifeq_axiom) }
% 60.52/8.08 ifeq2(ifeq(leq(multiplication(ifeq2(ifeq(leq(star(x0), star(x0)), true, leq(star(addition(one, multiplication(x0, star(x0)))), star(x0)), true), true, addition(star(addition(one, multiplication(x0, star(x0)))), star(x0)), star(x0)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.09 = { by lemma 19 R->L }
% 60.52/8.09 ifeq2(ifeq(leq(multiplication(ifeq2(ifeq(leq(addition(one, star(x0)), star(x0)), true, leq(star(addition(one, multiplication(x0, star(x0)))), star(x0)), true), true, addition(star(addition(one, multiplication(x0, star(x0)))), star(x0)), star(x0)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.09 = { by lemma 33 R->L }
% 60.52/8.09 ifeq2(ifeq(leq(multiplication(ifeq2(ifeq(leq(addition(one, multiplication(star(x0), addition(one, multiplication(x0, star(x0))))), star(x0)), true, leq(star(addition(one, multiplication(x0, star(x0)))), star(x0)), true), true, addition(star(addition(one, multiplication(x0, star(x0)))), star(x0)), star(x0)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.09 = { by axiom 4 (additive_commutativity) R->L }
% 60.52/8.09 ifeq2(ifeq(leq(multiplication(ifeq2(ifeq(leq(addition(multiplication(star(x0), addition(one, multiplication(x0, star(x0)))), one), star(x0)), true, leq(star(addition(one, multiplication(x0, star(x0)))), star(x0)), true), true, addition(star(addition(one, multiplication(x0, star(x0)))), star(x0)), star(x0)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.09 = { by axiom 2 (multiplicative_left_identity) R->L }
% 60.52/8.09 ifeq2(ifeq(leq(multiplication(ifeq2(ifeq(leq(addition(multiplication(star(x0), addition(one, multiplication(x0, star(x0)))), one), star(x0)), true, leq(multiplication(one, star(addition(one, multiplication(x0, star(x0))))), star(x0)), true), true, addition(star(addition(one, multiplication(x0, star(x0)))), star(x0)), star(x0)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.09 = { by axiom 16 (star_induction_right) }
% 60.52/8.09 ifeq2(ifeq(leq(multiplication(ifeq2(true, true, addition(star(addition(one, multiplication(x0, star(x0)))), star(x0)), star(x0)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.09 = { by axiom 9 (ifeq_axiom) }
% 60.52/8.09 ifeq2(ifeq(leq(multiplication(addition(star(addition(one, multiplication(x0, star(x0)))), star(x0)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.09 = { by axiom 4 (additive_commutativity) }
% 60.52/8.09 ifeq2(ifeq(leq(multiplication(addition(star(x0), star(addition(one, multiplication(x0, star(x0))))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.09 = { by lemma 35 }
% 60.52/8.09 ifeq2(ifeq(leq(multiplication(addition(star(x0), star(star(multiplication(x0, star(x0))))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.09 = { by lemma 37 }
% 60.52/8.09 ifeq2(ifeq(leq(multiplication(addition(star(x0), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.09 = { by axiom 9 (ifeq_axiom) R->L }
% 60.52/8.09 ifeq2(ifeq(leq(multiplication(ifeq2(true, true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.09 = { by axiom 17 (star_induction_left) R->L }
% 60.52/8.09 ifeq2(ifeq(leq(multiplication(ifeq2(ifeq(leq(addition(multiplication(x0, star(star(multiplication(x0, star(x0))))), addition(star(star(multiplication(x0, star(x0)))), multiplication(multiplication(x0, star(x0)), star(star(multiplication(x0, star(x0))))))), star(star(multiplication(x0, star(x0))))), true, leq(multiplication(star(x0), addition(star(star(multiplication(x0, star(x0)))), multiplication(multiplication(x0, star(x0)), star(star(multiplication(x0, star(x0))))))), star(star(multiplication(x0, star(x0))))), true), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.09 = { by lemma 30 }
% 60.52/8.09 ifeq2(ifeq(leq(multiplication(ifeq2(ifeq(leq(addition(star(star(multiplication(x0, star(x0)))), addition(multiplication(multiplication(x0, star(x0)), star(star(multiplication(x0, star(x0))))), multiplication(x0, star(star(multiplication(x0, star(x0))))))), star(star(multiplication(x0, star(x0))))), true, leq(multiplication(star(x0), addition(star(star(multiplication(x0, star(x0)))), multiplication(multiplication(x0, star(x0)), star(star(multiplication(x0, star(x0))))))), star(star(multiplication(x0, star(x0))))), true), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.09 = { by axiom 5 (multiplicative_associativity) R->L }
% 60.52/8.09 ifeq2(ifeq(leq(multiplication(ifeq2(ifeq(leq(addition(star(star(multiplication(x0, star(x0)))), addition(multiplication(x0, multiplication(star(x0), star(star(multiplication(x0, star(x0)))))), multiplication(x0, star(star(multiplication(x0, star(x0))))))), star(star(multiplication(x0, star(x0))))), true, leq(multiplication(star(x0), addition(star(star(multiplication(x0, star(x0)))), multiplication(multiplication(x0, star(x0)), star(star(multiplication(x0, star(x0))))))), star(star(multiplication(x0, star(x0))))), true), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.09 = { by axiom 10 (right_distributivity) R->L }
% 60.52/8.10 ifeq2(ifeq(leq(multiplication(ifeq2(ifeq(leq(addition(star(star(multiplication(x0, star(x0)))), multiplication(x0, addition(multiplication(star(x0), star(star(multiplication(x0, star(x0))))), star(star(multiplication(x0, star(x0))))))), star(star(multiplication(x0, star(x0))))), true, leq(multiplication(star(x0), addition(star(star(multiplication(x0, star(x0)))), multiplication(multiplication(x0, star(x0)), star(star(multiplication(x0, star(x0))))))), star(star(multiplication(x0, star(x0))))), true), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.10 = { by axiom 4 (additive_commutativity) }
% 60.52/8.10 ifeq2(ifeq(leq(multiplication(ifeq2(ifeq(leq(addition(star(star(multiplication(x0, star(x0)))), multiplication(x0, addition(star(star(multiplication(x0, star(x0)))), multiplication(star(x0), star(star(multiplication(x0, star(x0)))))))), star(star(multiplication(x0, star(x0))))), true, leq(multiplication(star(x0), addition(star(star(multiplication(x0, star(x0)))), multiplication(multiplication(x0, star(x0)), star(star(multiplication(x0, star(x0))))))), star(star(multiplication(x0, star(x0))))), true), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.10 = { by lemma 31 }
% 60.52/8.10 ifeq2(ifeq(leq(multiplication(ifeq2(ifeq(leq(addition(star(star(multiplication(x0, star(x0)))), multiplication(x0, multiplication(star(x0), star(star(multiplication(x0, star(x0))))))), star(star(multiplication(x0, star(x0))))), true, leq(multiplication(star(x0), addition(star(star(multiplication(x0, star(x0)))), multiplication(multiplication(x0, star(x0)), star(star(multiplication(x0, star(x0))))))), star(star(multiplication(x0, star(x0))))), true), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.10 = { by axiom 5 (multiplicative_associativity) }
% 60.52/8.10 ifeq2(ifeq(leq(multiplication(ifeq2(ifeq(leq(addition(star(star(multiplication(x0, star(x0)))), multiplication(multiplication(x0, star(x0)), star(star(multiplication(x0, star(x0)))))), star(star(multiplication(x0, star(x0))))), true, leq(multiplication(star(x0), addition(star(star(multiplication(x0, star(x0)))), multiplication(multiplication(x0, star(x0)), star(star(multiplication(x0, star(x0))))))), star(star(multiplication(x0, star(x0))))), true), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.10 = { by lemma 39 }
% 60.52/8.10 ifeq2(ifeq(leq(multiplication(ifeq2(ifeq(leq(addition(star(star(multiplication(x0, star(x0)))), multiplication(multiplication(x0, star(x0)), star(star(multiplication(x0, star(x0)))))), star(star(multiplication(x0, star(x0))))), true, leq(multiplication(star(x0), star(star(multiplication(x0, star(x0))))), star(star(multiplication(x0, star(x0))))), true), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.10 = { by lemma 29 }
% 60.52/8.10 ifeq2(ifeq(leq(multiplication(ifeq2(ifeq(leq(multiplication(addition(multiplication(x0, star(x0)), one), star(star(multiplication(x0, star(x0))))), star(star(multiplication(x0, star(x0))))), true, leq(multiplication(star(x0), star(star(multiplication(x0, star(x0))))), star(star(multiplication(x0, star(x0))))), true), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.10 = { by axiom 4 (additive_commutativity) }
% 60.52/8.10 ifeq2(ifeq(leq(multiplication(ifeq2(ifeq(leq(multiplication(addition(one, multiplication(x0, star(x0))), star(star(multiplication(x0, star(x0))))), star(star(multiplication(x0, star(x0))))), true, leq(multiplication(star(x0), star(star(multiplication(x0, star(x0))))), star(star(multiplication(x0, star(x0))))), true), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.10 = { by lemma 35 }
% 60.52/8.10 ifeq2(ifeq(leq(multiplication(ifeq2(ifeq(leq(multiplication(star(multiplication(x0, star(x0))), star(star(multiplication(x0, star(x0))))), star(star(multiplication(x0, star(x0))))), true, leq(multiplication(star(x0), star(star(multiplication(x0, star(x0))))), star(star(multiplication(x0, star(x0))))), true), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.10 = { by axiom 8 (ifeq_axiom) R->L }
% 60.52/8.10 ifeq2(ifeq(leq(multiplication(ifeq2(ifeq(ifeq3(star(star(multiplication(x0, star(x0)))), star(star(multiplication(x0, star(x0)))), leq(multiplication(star(multiplication(x0, star(x0))), star(star(multiplication(x0, star(x0))))), star(star(multiplication(x0, star(x0))))), true), true, leq(multiplication(star(x0), star(star(multiplication(x0, star(x0))))), star(star(multiplication(x0, star(x0))))), true), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.10 = { by lemma 25 R->L }
% 60.52/8.10 ifeq2(ifeq(leq(multiplication(ifeq2(ifeq(ifeq3(addition(multiplication(star(multiplication(x0, star(x0))), star(star(multiplication(x0, star(x0))))), star(star(multiplication(x0, star(x0))))), star(star(multiplication(x0, star(x0)))), leq(multiplication(star(multiplication(x0, star(x0))), star(star(multiplication(x0, star(x0))))), star(star(multiplication(x0, star(x0))))), true), true, leq(multiplication(star(x0), star(star(multiplication(x0, star(x0))))), star(star(multiplication(x0, star(x0))))), true), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.10 = { by axiom 14 (order) }
% 60.52/8.10 ifeq2(ifeq(leq(multiplication(ifeq2(ifeq(true, true, leq(multiplication(star(x0), star(star(multiplication(x0, star(x0))))), star(star(multiplication(x0, star(x0))))), true), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.10 = { by axiom 7 (ifeq_axiom) }
% 60.52/8.10 ifeq2(ifeq(leq(multiplication(ifeq2(leq(multiplication(star(x0), star(star(multiplication(x0, star(x0))))), star(star(multiplication(x0, star(x0))))), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.10 = { by lemma 37 }
% 60.52/8.10 ifeq2(ifeq(leq(multiplication(ifeq2(leq(multiplication(star(x0), star(star(multiplication(x0, star(x0))))), star(multiplication(x0, star(x0)))), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.10 = { by lemma 37 }
% 60.52/8.10 ifeq2(ifeq(leq(multiplication(ifeq2(leq(multiplication(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.11 = { by lemma 19 R->L }
% 60.52/8.11 ifeq2(ifeq(leq(multiplication(ifeq2(leq(multiplication(star(x0), addition(one, star(multiplication(x0, star(x0))))), star(multiplication(x0, star(x0)))), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.11 = { by axiom 4 (additive_commutativity) R->L }
% 60.52/8.11 ifeq2(ifeq(leq(multiplication(ifeq2(leq(multiplication(star(x0), addition(star(multiplication(x0, star(x0))), one)), star(multiplication(x0, star(x0)))), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.11 = { by lemma 28 R->L }
% 60.52/8.11 ifeq2(ifeq(leq(multiplication(ifeq2(leq(addition(star(x0), multiplication(star(x0), star(multiplication(x0, star(x0))))), star(multiplication(x0, star(x0)))), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.11 = { by axiom 4 (additive_commutativity) R->L }
% 60.52/8.11 ifeq2(ifeq(leq(multiplication(ifeq2(leq(addition(multiplication(star(x0), star(multiplication(x0, star(x0)))), star(x0)), star(multiplication(x0, star(x0)))), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.11 = { by axiom 9 (ifeq_axiom) R->L }
% 60.52/8.11 ifeq2(ifeq(leq(multiplication(ifeq2(leq(ifeq2(true, true, addition(multiplication(star(x0), star(multiplication(x0, star(x0)))), star(x0)), star(x0)), star(multiplication(x0, star(x0)))), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.11 = { by axiom 16 (star_induction_right) R->L }
% 60.52/8.11 ifeq2(ifeq(leq(multiplication(ifeq2(leq(ifeq2(ifeq(leq(addition(multiplication(star(x0), addition(one, multiplication(x0, star(x0)))), multiplication(star(x0), addition(one, multiplication(x0, star(x0))))), star(x0)), true, leq(multiplication(multiplication(star(x0), addition(one, multiplication(x0, star(x0)))), star(addition(one, multiplication(x0, star(x0))))), star(x0)), true), true, addition(multiplication(star(x0), star(multiplication(x0, star(x0)))), star(x0)), star(x0)), star(multiplication(x0, star(x0)))), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.11 = { by axiom 3 (additive_idempotence) }
% 60.52/8.11 ifeq2(ifeq(leq(multiplication(ifeq2(leq(ifeq2(ifeq(leq(multiplication(star(x0), addition(one, multiplication(x0, star(x0)))), star(x0)), true, leq(multiplication(multiplication(star(x0), addition(one, multiplication(x0, star(x0)))), star(addition(one, multiplication(x0, star(x0))))), star(x0)), true), true, addition(multiplication(star(x0), star(multiplication(x0, star(x0)))), star(x0)), star(x0)), star(multiplication(x0, star(x0)))), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.11 = { by axiom 5 (multiplicative_associativity) R->L }
% 60.52/8.11 ifeq2(ifeq(leq(multiplication(ifeq2(leq(ifeq2(ifeq(leq(multiplication(star(x0), addition(one, multiplication(x0, star(x0)))), star(x0)), true, leq(multiplication(star(x0), multiplication(addition(one, multiplication(x0, star(x0))), star(addition(one, multiplication(x0, star(x0)))))), star(x0)), true), true, addition(multiplication(star(x0), star(multiplication(x0, star(x0)))), star(x0)), star(x0)), star(multiplication(x0, star(x0)))), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.11 = { by lemma 33 }
% 60.52/8.12 ifeq2(ifeq(leq(multiplication(ifeq2(leq(ifeq2(ifeq(leq(star(x0), star(x0)), true, leq(multiplication(star(x0), multiplication(addition(one, multiplication(x0, star(x0))), star(addition(one, multiplication(x0, star(x0)))))), star(x0)), true), true, addition(multiplication(star(x0), star(multiplication(x0, star(x0)))), star(x0)), star(x0)), star(multiplication(x0, star(x0)))), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.12 = { by axiom 8 (ifeq_axiom) R->L }
% 60.52/8.12 ifeq2(ifeq(leq(multiplication(ifeq2(leq(ifeq2(ifeq(ifeq3(star(x0), star(x0), leq(star(x0), star(x0)), true), true, leq(multiplication(star(x0), multiplication(addition(one, multiplication(x0, star(x0))), star(addition(one, multiplication(x0, star(x0)))))), star(x0)), true), true, addition(multiplication(star(x0), star(multiplication(x0, star(x0)))), star(x0)), star(x0)), star(multiplication(x0, star(x0)))), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.12 = { by axiom 3 (additive_idempotence) R->L }
% 60.52/8.12 ifeq2(ifeq(leq(multiplication(ifeq2(leq(ifeq2(ifeq(ifeq3(addition(star(x0), star(x0)), star(x0), leq(star(x0), star(x0)), true), true, leq(multiplication(star(x0), multiplication(addition(one, multiplication(x0, star(x0))), star(addition(one, multiplication(x0, star(x0)))))), star(x0)), true), true, addition(multiplication(star(x0), star(multiplication(x0, star(x0)))), star(x0)), star(x0)), star(multiplication(x0, star(x0)))), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.12 = { by axiom 14 (order) }
% 60.52/8.12 ifeq2(ifeq(leq(multiplication(ifeq2(leq(ifeq2(ifeq(true, true, leq(multiplication(star(x0), multiplication(addition(one, multiplication(x0, star(x0))), star(addition(one, multiplication(x0, star(x0)))))), star(x0)), true), true, addition(multiplication(star(x0), star(multiplication(x0, star(x0)))), star(x0)), star(x0)), star(multiplication(x0, star(x0)))), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.12 = { by axiom 7 (ifeq_axiom) }
% 60.52/8.12 ifeq2(ifeq(leq(multiplication(ifeq2(leq(ifeq2(leq(multiplication(star(x0), multiplication(addition(one, multiplication(x0, star(x0))), star(addition(one, multiplication(x0, star(x0)))))), star(x0)), true, addition(multiplication(star(x0), star(multiplication(x0, star(x0)))), star(x0)), star(x0)), star(multiplication(x0, star(x0)))), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.12 = { by lemma 35 }
% 60.52/8.12 ifeq2(ifeq(leq(multiplication(ifeq2(leq(ifeq2(leq(multiplication(star(x0), multiplication(addition(one, multiplication(x0, star(x0))), star(star(multiplication(x0, star(x0)))))), star(x0)), true, addition(multiplication(star(x0), star(multiplication(x0, star(x0)))), star(x0)), star(x0)), star(multiplication(x0, star(x0)))), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.12 = { by lemma 35 }
% 60.52/8.12 ifeq2(ifeq(leq(multiplication(ifeq2(leq(ifeq2(leq(multiplication(star(x0), multiplication(star(multiplication(x0, star(x0))), star(star(multiplication(x0, star(x0)))))), star(x0)), true, addition(multiplication(star(x0), star(multiplication(x0, star(x0)))), star(x0)), star(x0)), star(multiplication(x0, star(x0)))), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.12 = { by lemma 36 }
% 60.52/8.12 ifeq2(ifeq(leq(multiplication(ifeq2(leq(ifeq2(leq(multiplication(star(x0), star(star(multiplication(x0, star(x0))))), star(x0)), true, addition(multiplication(star(x0), star(multiplication(x0, star(x0)))), star(x0)), star(x0)), star(multiplication(x0, star(x0)))), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.12 = { by lemma 37 }
% 60.52/8.12 ifeq2(ifeq(leq(multiplication(ifeq2(leq(ifeq2(leq(multiplication(star(x0), star(multiplication(x0, star(x0)))), star(x0)), true, addition(multiplication(star(x0), star(multiplication(x0, star(x0)))), star(x0)), star(x0)), star(multiplication(x0, star(x0)))), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.12 = { by axiom 15 (order_1) }
% 60.52/8.12 ifeq2(ifeq(leq(multiplication(ifeq2(leq(star(x0), star(multiplication(x0, star(x0)))), true, addition(star(x0), star(multiplication(x0, star(x0)))), star(multiplication(x0, star(x0)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.12 = { by axiom 15 (order_1) }
% 60.52/8.12 ifeq2(ifeq(leq(multiplication(star(multiplication(x0, star(x0))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.12 = { by lemma 35 R->L }
% 60.52/8.12 ifeq2(ifeq(leq(multiplication(addition(one, multiplication(x0, star(x0))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.12 = { by axiom 4 (additive_commutativity) R->L }
% 60.52/8.12 ifeq2(ifeq(leq(multiplication(addition(multiplication(x0, star(x0)), one), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.12 = { by lemma 29 R->L }
% 60.52/8.12 ifeq2(ifeq(leq(addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(multiplication(x0, star(x0)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.12 = { by axiom 5 (multiplicative_associativity) R->L }
% 60.52/8.12 ifeq2(ifeq(leq(addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(x0, multiplication(star(x0), addition(x1, multiplication(multiplication(x0, star(x0)), x1))))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.12 = { by lemma 39 }
% 60.52/8.12 ifeq2(ifeq(leq(addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(x0, multiplication(star(x0), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.12 = { by axiom 5 (multiplicative_associativity) }
% 60.52/8.12 ifeq2(ifeq(leq(addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(multiplication(x0, star(x0)), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.12 = { by axiom 4 (additive_commutativity) R->L }
% 60.52/8.12 ifeq2(ifeq(leq(addition(multiplication(multiplication(x0, star(x0)), x1), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.12 = { by lemma 23 }
% 60.52/8.12 ifeq2(ifeq(leq(addition(x1, addition(multiplication(multiplication(x0, star(x0)), x1), multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.12 = { by axiom 3 (additive_idempotence) }
% 60.52/8.12 ifeq2(ifeq(leq(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.12 = { by axiom 8 (ifeq_axiom) R->L }
% 60.52/8.12 ifeq2(ifeq(ifeq3(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)), leq(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.12 = { by axiom 3 (additive_idempotence) R->L }
% 60.52/8.12 ifeq2(ifeq(ifeq3(addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1)), leq(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.12 = { by axiom 14 (order) }
% 60.52/8.12 ifeq2(ifeq(true, true, leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.12 = { by axiom 7 (ifeq_axiom) }
% 60.52/8.13 ifeq2(leq(multiplication(star(x0), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.13 = { by lemma 31 R->L }
% 60.52/8.13 ifeq2(leq(multiplication(star(x0), addition(x1, multiplication(star(x0), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.13 = { by axiom 4 (additive_commutativity) R->L }
% 60.52/8.13 ifeq2(leq(multiplication(star(x0), addition(multiplication(star(x0), x1), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.13 = { by lemma 20 R->L }
% 60.52/8.13 ifeq2(leq(addition(multiplication(star(x0), x1), multiplication(star(x0), multiplication(star(x0), x1))), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.13 = { by axiom 4 (additive_commutativity) R->L }
% 60.52/8.13 ifeq2(leq(addition(multiplication(star(x0), multiplication(star(x0), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.13 = { by axiom 9 (ifeq_axiom) R->L }
% 60.52/8.13 ifeq2(leq(ifeq2(true, true, addition(multiplication(star(x0), multiplication(star(x0), x1)), multiplication(star(x0), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.13 = { by axiom 17 (star_induction_left) R->L }
% 60.52/8.13 ifeq2(leq(ifeq2(ifeq(leq(addition(multiplication(x0, multiplication(star(x0), x1)), multiplication(star(x0), x1)), multiplication(star(x0), x1)), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), multiplication(star(x0), x1)), true), true, addition(multiplication(star(x0), multiplication(star(x0), x1)), multiplication(star(x0), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.13 = { by axiom 5 (multiplicative_associativity) }
% 60.52/8.13 ifeq2(leq(ifeq2(ifeq(leq(addition(multiplication(multiplication(x0, star(x0)), x1), multiplication(star(x0), x1)), multiplication(star(x0), x1)), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), multiplication(star(x0), x1)), true), true, addition(multiplication(star(x0), multiplication(star(x0), x1)), multiplication(star(x0), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.13 = { by lemma 38 }
% 60.52/8.13 ifeq2(leq(ifeq2(ifeq(leq(multiplication(star(x0), x1), multiplication(star(x0), x1)), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), multiplication(star(x0), x1)), true), true, addition(multiplication(star(x0), multiplication(star(x0), x1)), multiplication(star(x0), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.13 = { by axiom 8 (ifeq_axiom) R->L }
% 60.52/8.13 ifeq2(leq(ifeq2(ifeq(ifeq3(multiplication(star(x0), x1), multiplication(star(x0), x1), leq(multiplication(star(x0), x1), multiplication(star(x0), x1)), true), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), multiplication(star(x0), x1)), true), true, addition(multiplication(star(x0), multiplication(star(x0), x1)), multiplication(star(x0), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.13 = { by axiom 3 (additive_idempotence) R->L }
% 60.52/8.13 ifeq2(leq(ifeq2(ifeq(ifeq3(addition(multiplication(star(x0), x1), multiplication(star(x0), x1)), multiplication(star(x0), x1), leq(multiplication(star(x0), x1), multiplication(star(x0), x1)), true), true, leq(multiplication(star(x0), multiplication(star(x0), x1)), multiplication(star(x0), x1)), true), true, addition(multiplication(star(x0), multiplication(star(x0), x1)), multiplication(star(x0), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.13 = { by axiom 14 (order) }
% 60.52/8.13 ifeq2(leq(ifeq2(ifeq(true, true, leq(multiplication(star(x0), multiplication(star(x0), x1)), multiplication(star(x0), x1)), true), true, addition(multiplication(star(x0), multiplication(star(x0), x1)), multiplication(star(x0), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.13 = { by axiom 7 (ifeq_axiom) }
% 60.52/8.13 ifeq2(leq(ifeq2(leq(multiplication(star(x0), multiplication(star(x0), x1)), multiplication(star(x0), x1)), true, addition(multiplication(star(x0), multiplication(star(x0), x1)), multiplication(star(x0), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.13 = { by axiom 15 (order_1) }
% 60.52/8.13 ifeq2(leq(multiplication(star(x0), x1), addition(x1, multiplication(multiplication(x0, star(x0)), x1))), true, addition(addition(x1, multiplication(multiplication(x0, star(x0)), x1)), multiplication(star(x0), x1)), addition(x1, multiplication(multiplication(x0, star(x0)), x1)))
% 60.52/8.13 = { by lemma 32 }
% 60.52/8.13 addition(x1, multiplication(multiplication(x0, star(x0)), x1))
% 60.52/8.13 % SZS output end Proof
% 60.52/8.13
% 60.52/8.13 RESULT: Theorem (the conjecture is true).
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