%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE042+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 11:39:41 AM UTC 2026
% Result : Theorem 258.83s 33.12s
% Output : Proof 260.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE042+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n005.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 13:05:01 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 258.83/33.12 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
% 258.83/33.12
% 258.83/33.12 % SZS status Theorem
% 258.83/33.12
% 260.18/33.23 % SZS output start Proof
% 260.18/33.23 Axiom 1 (multiplicative_right_identity): multiplication(X, one) = X.
% 260.18/33.23 Axiom 2 (multiplicative_left_identity): multiplication(one, X) = X.
% 260.18/33.23 Axiom 3 (additive_idempotence): addition(X, X) = X.
% 260.18/33.23 Axiom 4 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 260.18/33.23 Axiom 5 (multiplicative_associativity): multiplication(X, multiplication(Y, Z)) = multiplication(multiplication(X, Y), Z).
% 260.18/33.23 Axiom 6 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 260.18/33.23 Axiom 7 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 260.18/33.23 Axiom 8 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 260.18/33.23 Axiom 9 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 260.18/33.23 Axiom 10 (right_distributivity): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 260.18/33.23 Axiom 11 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 260.18/33.23 Axiom 12 (star_unfold_right): leq(addition(one, multiplication(X, star(X))), star(X)) = true.
% 260.18/33.23 Axiom 13 (star_unfold_left): leq(addition(one, multiplication(star(X), X)), star(X)) = true.
% 260.18/33.23 Axiom 14 (order): ifeq3(addition(X, Y), Y, leq(X, Y), true) = true.
% 260.18/33.23 Axiom 15 (order_1): ifeq2(leq(X, Y), true, addition(X, Y), Y) = Y.
% 260.18/33.23 Axiom 16 (star_induction_right): ifeq(leq(addition(multiplication(X, Y), Z), X), true, leq(multiplication(Z, star(Y)), X), true) = true.
% 260.18/33.23 Axiom 17 (star_induction_left): ifeq(leq(addition(multiplication(X, Y), Z), Y), true, leq(multiplication(star(X), Z), Y), true) = true.
% 260.18/33.23
% 260.18/33.23 Lemma 18: addition(X, multiplication(Y, X)) = multiplication(addition(Y, one), X).
% 260.18/33.23 Proof:
% 260.18/33.23 addition(X, multiplication(Y, X))
% 260.18/33.23 = { by axiom 2 (multiplicative_left_identity) R->L }
% 260.18/33.23 addition(multiplication(one, X), multiplication(Y, X))
% 260.18/33.23 = { by axiom 11 (left_distributivity) R->L }
% 260.18/33.23 multiplication(addition(one, Y), X)
% 260.18/33.23 = { by axiom 4 (additive_commutativity) }
% 260.18/33.23 multiplication(addition(Y, one), X)
% 260.18/33.23
% 260.18/33.23 Lemma 19: addition(one, multiplication(addition(X, one), star(X))) = star(X).
% 260.18/33.23 Proof:
% 260.18/33.23 addition(one, multiplication(addition(X, one), star(X)))
% 260.18/33.23 = { by lemma 18 R->L }
% 260.18/33.23 addition(one, addition(star(X), multiplication(X, star(X))))
% 260.18/33.23 = { by axiom 4 (additive_commutativity) R->L }
% 260.18/33.23 addition(one, addition(multiplication(X, star(X)), star(X)))
% 260.18/33.23 = { by axiom 6 (additive_associativity) }
% 260.18/33.23 addition(addition(one, multiplication(X, star(X))), star(X))
% 260.18/33.23 = { by axiom 9 (ifeq_axiom) R->L }
% 260.18/33.23 ifeq2(true, true, addition(addition(one, multiplication(X, star(X))), star(X)), star(X))
% 260.18/33.23 = { by axiom 12 (star_unfold_right) R->L }
% 260.18/33.23 ifeq2(leq(addition(one, multiplication(X, star(X))), star(X)), true, addition(addition(one, multiplication(X, star(X))), star(X)), star(X))
% 260.18/33.23 = { by axiom 15 (order_1) }
% 260.18/33.24 star(X)
% 260.18/33.24
% 260.18/33.24 Lemma 20: addition(X, addition(X, Y)) = addition(X, Y).
% 260.18/33.24 Proof:
% 260.18/33.24 addition(X, addition(X, Y))
% 260.18/33.24 = { by axiom 6 (additive_associativity) }
% 260.18/33.24 addition(addition(X, X), Y)
% 260.18/33.24 = { by axiom 3 (additive_idempotence) }
% 260.18/33.24 addition(X, Y)
% 260.18/33.24
% 260.18/33.24 Lemma 21: addition(one, star(X)) = star(X).
% 260.18/33.24 Proof:
% 260.18/33.24 addition(one, star(X))
% 260.18/33.24 = { by lemma 19 R->L }
% 260.18/33.24 addition(one, addition(one, multiplication(addition(X, one), star(X))))
% 260.18/33.24 = { by lemma 20 }
% 260.18/33.24 addition(one, multiplication(addition(X, one), star(X)))
% 260.18/33.24 = { by lemma 19 }
% 260.18/33.24 star(X)
% 260.18/33.24
% 260.18/33.24 Lemma 22: addition(X, addition(Y, X)) = addition(Y, X).
% 260.18/33.24 Proof:
% 260.18/33.24 addition(X, addition(Y, X))
% 260.18/33.24 = { by lemma 20 R->L }
% 260.18/33.24 addition(X, addition(Y, addition(Y, X)))
% 260.18/33.24 = { by axiom 4 (additive_commutativity) R->L }
% 260.18/33.24 addition(X, addition(Y, addition(X, Y)))
% 260.18/33.24 = { by axiom 6 (additive_associativity) }
% 260.18/33.24 addition(addition(X, Y), addition(X, Y))
% 260.18/33.24 = { by axiom 3 (additive_idempotence) }
% 260.18/33.24 addition(X, Y)
% 260.18/33.24 = { by axiom 4 (additive_commutativity) }
% 260.18/33.24 addition(Y, X)
% 260.18/33.24
% 260.18/33.24 Lemma 23: addition(X, multiplication(X, Y)) = multiplication(X, addition(Y, one)).
% 260.18/33.24 Proof:
% 260.18/33.24 addition(X, multiplication(X, Y))
% 260.18/33.24 = { by axiom 1 (multiplicative_right_identity) R->L }
% 260.18/33.24 addition(multiplication(X, one), multiplication(X, Y))
% 260.18/33.24 = { by axiom 10 (right_distributivity) R->L }
% 260.18/33.24 multiplication(X, addition(one, Y))
% 260.18/33.24 = { by axiom 4 (additive_commutativity) }
% 260.18/33.24 multiplication(X, addition(Y, one))
% 260.18/33.24
% 260.18/33.24 Lemma 24: addition(one, multiplication(star(X), addition(X, one))) = star(X).
% 260.18/33.24 Proof:
% 260.18/33.24 addition(one, multiplication(star(X), addition(X, one)))
% 260.18/33.24 = { by lemma 23 R->L }
% 260.18/33.24 addition(one, addition(star(X), multiplication(star(X), X)))
% 260.18/33.24 = { by axiom 4 (additive_commutativity) R->L }
% 260.18/33.24 addition(one, addition(multiplication(star(X), X), star(X)))
% 260.18/33.24 = { by axiom 6 (additive_associativity) }
% 260.18/33.24 addition(addition(one, multiplication(star(X), X)), star(X))
% 260.18/33.24 = { by axiom 9 (ifeq_axiom) R->L }
% 260.18/33.24 ifeq2(true, true, addition(addition(one, multiplication(star(X), X)), star(X)), star(X))
% 260.18/33.24 = { by axiom 13 (star_unfold_left) R->L }
% 260.18/33.24 ifeq2(leq(addition(one, multiplication(star(X), X)), star(X)), true, addition(addition(one, multiplication(star(X), X)), star(X)), star(X))
% 260.18/33.24 = { by axiom 15 (order_1) }
% 260.18/33.24 star(X)
% 260.18/33.24
% 260.18/33.24 Lemma 25: multiplication(star(X), addition(X, one)) = star(X).
% 260.18/33.24 Proof:
% 260.18/33.24 multiplication(star(X), addition(X, one))
% 260.18/33.24 = { by axiom 3 (additive_idempotence) R->L }
% 260.18/33.24 multiplication(star(X), addition(X, addition(one, one)))
% 260.18/33.24 = { by axiom 6 (additive_associativity) }
% 260.18/33.24 multiplication(star(X), addition(addition(X, one), one))
% 260.18/33.24 = { by lemma 23 R->L }
% 260.18/33.24 addition(star(X), multiplication(star(X), addition(X, one)))
% 260.18/33.24 = { by axiom 4 (additive_commutativity) R->L }
% 260.18/33.24 addition(multiplication(star(X), addition(X, one)), star(X))
% 260.18/33.24 = { by lemma 24 R->L }
% 260.18/33.24 addition(multiplication(star(X), addition(X, one)), addition(one, multiplication(star(X), addition(X, one))))
% 260.18/33.24 = { by lemma 22 }
% 260.18/33.24 addition(one, multiplication(star(X), addition(X, one)))
% 260.18/33.24 = { by lemma 24 }
% 260.18/33.24 star(X)
% 260.18/33.24
% 260.18/33.24 Lemma 26: addition(multiplication(X, Y), multiplication(Z, Y)) = multiplication(addition(Z, X), Y).
% 260.18/33.24 Proof:
% 260.18/33.24 addition(multiplication(X, Y), multiplication(Z, Y))
% 260.18/33.24 = { by axiom 11 (left_distributivity) R->L }
% 260.18/33.24 multiplication(addition(X, Z), Y)
% 260.18/33.24 = { by axiom 4 (additive_commutativity) }
% 260.18/33.24 multiplication(addition(Z, X), Y)
% 260.18/33.24
% 260.18/33.24 Lemma 27: ifeq2(leq(X, Y), true, addition(Y, X), Y) = Y.
% 260.18/33.24 Proof:
% 260.18/33.24 ifeq2(leq(X, Y), true, addition(Y, X), Y)
% 260.18/33.24 = { by axiom 4 (additive_commutativity) R->L }
% 260.18/33.24 ifeq2(leq(X, Y), true, addition(X, Y), Y)
% 260.18/33.24 = { by axiom 15 (order_1) }
% 260.18/33.24 Y
% 260.18/33.24
% 260.18/33.24 Lemma 28: addition(multiplication(X, Y), multiplication(Z, multiplication(W, Y))) = multiplication(addition(X, multiplication(Z, W)), Y).
% 260.18/33.24 Proof:
% 260.18/33.24 addition(multiplication(X, Y), multiplication(Z, multiplication(W, Y)))
% 260.18/33.24 = { by axiom 5 (multiplicative_associativity) }
% 260.18/33.24 addition(multiplication(X, Y), multiplication(multiplication(Z, W), Y))
% 260.18/33.24 = { by lemma 26 }
% 260.18/33.24 multiplication(addition(multiplication(Z, W), X), Y)
% 260.18/33.24 = { by axiom 4 (additive_commutativity) }
% 260.18/33.24 multiplication(addition(X, multiplication(Z, W)), Y)
% 260.18/33.24
% 260.18/33.24 Lemma 29: addition(one, addition(star(multiplication(X, Y)), multiplication(multiplication(star(multiplication(X, Y)), X), Y))) = star(multiplication(X, Y)).
% 260.18/33.24 Proof:
% 260.18/33.24 addition(one, addition(star(multiplication(X, Y)), multiplication(multiplication(star(multiplication(X, Y)), X), Y)))
% 260.18/33.24 = { by axiom 4 (additive_commutativity) R->L }
% 260.18/33.24 addition(one, addition(multiplication(multiplication(star(multiplication(X, Y)), X), Y), star(multiplication(X, Y))))
% 260.18/33.24 = { by axiom 5 (multiplicative_associativity) R->L }
% 260.18/33.24 addition(one, addition(multiplication(star(multiplication(X, Y)), multiplication(X, Y)), star(multiplication(X, Y))))
% 260.18/33.24 = { by axiom 6 (additive_associativity) }
% 260.18/33.24 addition(addition(one, multiplication(star(multiplication(X, Y)), multiplication(X, Y))), star(multiplication(X, Y)))
% 260.18/33.24 = { by axiom 9 (ifeq_axiom) R->L }
% 260.18/33.24 ifeq2(true, true, addition(addition(one, multiplication(star(multiplication(X, Y)), multiplication(X, Y))), star(multiplication(X, Y))), star(multiplication(X, Y)))
% 260.18/33.24 = { by axiom 13 (star_unfold_left) R->L }
% 260.18/33.24 ifeq2(leq(addition(one, multiplication(star(multiplication(X, Y)), multiplication(X, Y))), star(multiplication(X, Y))), true, addition(addition(one, multiplication(star(multiplication(X, Y)), multiplication(X, Y))), star(multiplication(X, Y))), star(multiplication(X, Y)))
% 260.18/33.24 = { by axiom 15 (order_1) }
% 260.18/33.24 star(multiplication(X, Y))
% 260.18/33.24
% 260.18/33.24 Lemma 30: multiplication(multiplication(star(multiplication(X, Y)), X), star(multiplication(Y, X))) = multiplication(star(multiplication(X, Y)), X).
% 260.18/33.24 Proof:
% 260.18/33.24 multiplication(multiplication(star(multiplication(X, Y)), X), star(multiplication(Y, X)))
% 260.18/33.24 = { by lemma 21 R->L }
% 260.18/33.24 multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, star(multiplication(Y, X))))
% 260.18/33.24 = { by axiom 9 (ifeq_axiom) R->L }
% 260.18/33.24 ifeq2(true, true, multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.24 = { by axiom 16 (star_induction_right) R->L }
% 260.18/33.24 ifeq2(ifeq(leq(addition(multiplication(multiplication(star(multiplication(X, Y)), X), multiplication(Y, X)), multiplication(multiplication(star(multiplication(X, Y)), X), one)), multiplication(star(multiplication(X, Y)), X)), true, leq(multiplication(multiplication(multiplication(star(multiplication(X, Y)), X), one), star(multiplication(Y, X))), multiplication(star(multiplication(X, Y)), X)), true), true, multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.24 = { by axiom 10 (right_distributivity) R->L }
% 260.18/33.24 ifeq2(ifeq(leq(multiplication(multiplication(star(multiplication(X, Y)), X), addition(multiplication(Y, X), one)), multiplication(star(multiplication(X, Y)), X)), true, leq(multiplication(multiplication(multiplication(star(multiplication(X, Y)), X), one), star(multiplication(Y, X))), multiplication(star(multiplication(X, Y)), X)), true), true, multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.24 = { by axiom 5 (multiplicative_associativity) R->L }
% 260.18/33.24 ifeq2(ifeq(leq(multiplication(multiplication(star(multiplication(X, Y)), X), addition(multiplication(Y, X), one)), multiplication(star(multiplication(X, Y)), X)), true, leq(multiplication(multiplication(star(multiplication(X, Y)), X), multiplication(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X)), true), true, multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.24 = { by axiom 4 (additive_commutativity) }
% 260.18/33.24 ifeq2(ifeq(leq(multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, multiplication(Y, X))), multiplication(star(multiplication(X, Y)), X)), true, leq(multiplication(multiplication(star(multiplication(X, Y)), X), multiplication(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X)), true), true, multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.24 = { by axiom 5 (multiplicative_associativity) R->L }
% 260.18/33.24 ifeq2(ifeq(leq(multiplication(star(multiplication(X, Y)), multiplication(X, addition(one, multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X)), true, leq(multiplication(multiplication(star(multiplication(X, Y)), X), multiplication(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X)), true), true, multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.24 = { by axiom 4 (additive_commutativity) R->L }
% 260.18/33.25 ifeq2(ifeq(leq(multiplication(star(multiplication(X, Y)), multiplication(X, addition(multiplication(Y, X), one))), multiplication(star(multiplication(X, Y)), X)), true, leq(multiplication(multiplication(star(multiplication(X, Y)), X), multiplication(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X)), true), true, multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.25 = { by lemma 23 R->L }
% 260.18/33.25 ifeq2(ifeq(leq(multiplication(star(multiplication(X, Y)), addition(X, multiplication(X, multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X)), true, leq(multiplication(multiplication(star(multiplication(X, Y)), X), multiplication(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X)), true), true, multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.25 = { by axiom 5 (multiplicative_associativity) }
% 260.18/33.25 ifeq2(ifeq(leq(multiplication(star(multiplication(X, Y)), addition(X, multiplication(multiplication(X, Y), X))), multiplication(star(multiplication(X, Y)), X)), true, leq(multiplication(multiplication(star(multiplication(X, Y)), X), multiplication(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X)), true), true, multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.25 = { by lemma 18 }
% 260.18/33.25 ifeq2(ifeq(leq(multiplication(star(multiplication(X, Y)), multiplication(addition(multiplication(X, Y), one), X)), multiplication(star(multiplication(X, Y)), X)), true, leq(multiplication(multiplication(star(multiplication(X, Y)), X), multiplication(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X)), true), true, multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.25 = { by axiom 5 (multiplicative_associativity) }
% 260.18/33.25 ifeq2(ifeq(leq(multiplication(multiplication(star(multiplication(X, Y)), addition(multiplication(X, Y), one)), X), multiplication(star(multiplication(X, Y)), X)), true, leq(multiplication(multiplication(star(multiplication(X, Y)), X), multiplication(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X)), true), true, multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.25 = { by lemma 23 R->L }
% 260.18/33.25 ifeq2(ifeq(leq(multiplication(addition(star(multiplication(X, Y)), multiplication(star(multiplication(X, Y)), multiplication(X, Y))), X), multiplication(star(multiplication(X, Y)), X)), true, leq(multiplication(multiplication(star(multiplication(X, Y)), X), multiplication(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X)), true), true, multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.25 = { by lemma 28 R->L }
% 260.18/33.25 ifeq2(ifeq(leq(addition(multiplication(star(multiplication(X, Y)), X), multiplication(star(multiplication(X, Y)), multiplication(multiplication(X, Y), X))), multiplication(star(multiplication(X, Y)), X)), true, leq(multiplication(multiplication(star(multiplication(X, Y)), X), multiplication(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X)), true), true, multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.25 = { by axiom 5 (multiplicative_associativity) R->L }
% 260.18/33.25 ifeq2(ifeq(leq(addition(multiplication(star(multiplication(X, Y)), X), multiplication(star(multiplication(X, Y)), multiplication(X, multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X)), true, leq(multiplication(multiplication(star(multiplication(X, Y)), X), multiplication(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X)), true), true, multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.25 = { by axiom 5 (multiplicative_associativity) }
% 260.18/33.25 ifeq2(ifeq(leq(addition(multiplication(star(multiplication(X, Y)), X), multiplication(multiplication(star(multiplication(X, Y)), X), multiplication(Y, X))), multiplication(star(multiplication(X, Y)), X)), true, leq(multiplication(multiplication(star(multiplication(X, Y)), X), multiplication(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X)), true), true, multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.25 = { by lemma 28 }
% 260.18/33.25 ifeq2(ifeq(leq(multiplication(addition(star(multiplication(X, Y)), multiplication(multiplication(star(multiplication(X, Y)), X), Y)), X), multiplication(star(multiplication(X, Y)), X)), true, leq(multiplication(multiplication(star(multiplication(X, Y)), X), multiplication(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X)), true), true, multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.25 = { by axiom 4 (additive_commutativity) R->L }
% 260.18/33.25 ifeq2(ifeq(leq(multiplication(addition(multiplication(multiplication(star(multiplication(X, Y)), X), Y), star(multiplication(X, Y))), X), multiplication(star(multiplication(X, Y)), X)), true, leq(multiplication(multiplication(star(multiplication(X, Y)), X), multiplication(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X)), true), true, multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.25 = { by lemma 22 R->L }
% 260.18/33.25 ifeq2(ifeq(leq(multiplication(addition(star(multiplication(X, Y)), addition(multiplication(multiplication(star(multiplication(X, Y)), X), Y), star(multiplication(X, Y)))), X), multiplication(star(multiplication(X, Y)), X)), true, leq(multiplication(multiplication(star(multiplication(X, Y)), X), multiplication(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X)), true), true, multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.25 = { by axiom 6 (additive_associativity) }
% 260.18/33.25 ifeq2(ifeq(leq(multiplication(addition(addition(star(multiplication(X, Y)), multiplication(multiplication(star(multiplication(X, Y)), X), Y)), star(multiplication(X, Y))), X), multiplication(star(multiplication(X, Y)), X)), true, leq(multiplication(multiplication(star(multiplication(X, Y)), X), multiplication(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X)), true), true, multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.25 = { by lemma 29 R->L }
% 260.18/33.25 ifeq2(ifeq(leq(multiplication(addition(addition(star(multiplication(X, Y)), multiplication(multiplication(star(multiplication(X, Y)), X), Y)), addition(one, addition(star(multiplication(X, Y)), multiplication(multiplication(star(multiplication(X, Y)), X), Y)))), X), multiplication(star(multiplication(X, Y)), X)), true, leq(multiplication(multiplication(star(multiplication(X, Y)), X), multiplication(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X)), true), true, multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.25 = { by lemma 22 }
% 260.18/33.25 ifeq2(ifeq(leq(multiplication(addition(one, addition(star(multiplication(X, Y)), multiplication(multiplication(star(multiplication(X, Y)), X), Y))), X), multiplication(star(multiplication(X, Y)), X)), true, leq(multiplication(multiplication(star(multiplication(X, Y)), X), multiplication(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X)), true), true, multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.25 = { by lemma 29 }
% 260.18/33.25 ifeq2(ifeq(leq(multiplication(star(multiplication(X, Y)), X), multiplication(star(multiplication(X, Y)), X)), true, leq(multiplication(multiplication(star(multiplication(X, Y)), X), multiplication(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X)), true), true, multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.25 = { by axiom 8 (ifeq_axiom) R->L }
% 260.18/33.25 ifeq2(ifeq(ifeq3(multiplication(star(multiplication(X, Y)), X), multiplication(star(multiplication(X, Y)), X), leq(multiplication(star(multiplication(X, Y)), X), multiplication(star(multiplication(X, Y)), X)), true), true, leq(multiplication(multiplication(star(multiplication(X, Y)), X), multiplication(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X)), true), true, multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.25 = { by axiom 3 (additive_idempotence) R->L }
% 260.18/33.25 ifeq2(ifeq(ifeq3(addition(multiplication(star(multiplication(X, Y)), X), multiplication(star(multiplication(X, Y)), X)), multiplication(star(multiplication(X, Y)), X), leq(multiplication(star(multiplication(X, Y)), X), multiplication(star(multiplication(X, Y)), X)), true), true, leq(multiplication(multiplication(star(multiplication(X, Y)), X), multiplication(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X)), true), true, multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.25 = { by axiom 14 (order) }
% 260.18/33.25 ifeq2(ifeq(true, true, leq(multiplication(multiplication(star(multiplication(X, Y)), X), multiplication(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X)), true), true, multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.25 = { by axiom 7 (ifeq_axiom) }
% 260.18/33.25 ifeq2(leq(multiplication(multiplication(star(multiplication(X, Y)), X), multiplication(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X)), true, multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.25 = { by axiom 2 (multiplicative_left_identity) }
% 260.18/33.25 ifeq2(leq(multiplication(multiplication(star(multiplication(X, Y)), X), star(multiplication(Y, X))), multiplication(star(multiplication(X, Y)), X)), true, multiplication(multiplication(star(multiplication(X, Y)), X), addition(one, star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.26 = { by axiom 4 (additive_commutativity) R->L }
% 260.18/33.26 ifeq2(leq(multiplication(multiplication(star(multiplication(X, Y)), X), star(multiplication(Y, X))), multiplication(star(multiplication(X, Y)), X)), true, multiplication(multiplication(star(multiplication(X, Y)), X), addition(star(multiplication(Y, X)), one)), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.26 = { by lemma 23 R->L }
% 260.18/33.26 ifeq2(leq(multiplication(multiplication(star(multiplication(X, Y)), X), star(multiplication(Y, X))), multiplication(star(multiplication(X, Y)), X)), true, addition(multiplication(star(multiplication(X, Y)), X), multiplication(multiplication(star(multiplication(X, Y)), X), star(multiplication(Y, X)))), multiplication(star(multiplication(X, Y)), X))
% 260.18/33.26 = { by lemma 27 }
% 260.18/33.26 multiplication(star(multiplication(X, Y)), X)
% 260.18/33.26
% 260.18/33.26 Lemma 31: addition(one, addition(star(multiplication(X, Y)), multiplication(X, multiplication(Y, star(multiplication(X, Y)))))) = star(multiplication(X, Y)).
% 260.18/33.26 Proof:
% 260.18/33.26 addition(one, addition(star(multiplication(X, Y)), multiplication(X, multiplication(Y, star(multiplication(X, Y))))))
% 260.18/33.26 = { by axiom 4 (additive_commutativity) R->L }
% 260.18/33.26 addition(one, addition(multiplication(X, multiplication(Y, star(multiplication(X, Y)))), star(multiplication(X, Y))))
% 260.18/33.26 = { by axiom 5 (multiplicative_associativity) }
% 260.18/33.26 addition(one, addition(multiplication(multiplication(X, Y), star(multiplication(X, Y))), star(multiplication(X, Y))))
% 260.18/33.26 = { by axiom 6 (additive_associativity) }
% 260.18/33.26 addition(addition(one, multiplication(multiplication(X, Y), star(multiplication(X, Y)))), star(multiplication(X, Y)))
% 260.18/33.26 = { by axiom 9 (ifeq_axiom) R->L }
% 260.18/33.26 ifeq2(true, true, addition(addition(one, multiplication(multiplication(X, Y), star(multiplication(X, Y)))), star(multiplication(X, Y))), star(multiplication(X, Y)))
% 260.18/33.26 = { by axiom 12 (star_unfold_right) R->L }
% 260.18/33.26 ifeq2(leq(addition(one, multiplication(multiplication(X, Y), star(multiplication(X, Y)))), star(multiplication(X, Y))), true, addition(addition(one, multiplication(multiplication(X, Y), star(multiplication(X, Y)))), star(multiplication(X, Y))), star(multiplication(X, Y)))
% 260.18/33.26 = { by axiom 15 (order_1) }
% 260.18/33.26 star(multiplication(X, Y))
% 260.18/33.26
% 260.18/33.26 Lemma 32: multiplication(addition(one, multiplication(X, Y)), multiplication(X, star(multiplication(Y, X)))) = multiplication(X, star(multiplication(Y, X))).
% 260.18/33.26 Proof:
% 260.18/33.26 multiplication(addition(one, multiplication(X, Y)), multiplication(X, star(multiplication(Y, X))))
% 260.18/33.26 = { by axiom 4 (additive_commutativity) R->L }
% 260.18/33.26 multiplication(addition(multiplication(X, Y), one), multiplication(X, star(multiplication(Y, X))))
% 260.18/33.26 = { by lemma 18 R->L }
% 260.18/33.26 addition(multiplication(X, star(multiplication(Y, X))), multiplication(multiplication(X, Y), multiplication(X, star(multiplication(Y, X)))))
% 260.18/33.26 = { by axiom 5 (multiplicative_associativity) R->L }
% 260.18/33.26 addition(multiplication(X, star(multiplication(Y, X))), multiplication(X, multiplication(Y, multiplication(X, star(multiplication(Y, X))))))
% 260.18/33.26 = { by axiom 10 (right_distributivity) R->L }
% 260.18/33.26 multiplication(X, addition(star(multiplication(Y, X)), multiplication(Y, multiplication(X, star(multiplication(Y, X))))))
% 260.18/33.26 = { by axiom 4 (additive_commutativity) R->L }
% 260.18/33.26 multiplication(X, addition(multiplication(Y, multiplication(X, star(multiplication(Y, X)))), star(multiplication(Y, X))))
% 260.18/33.26 = { by lemma 22 R->L }
% 260.18/33.26 multiplication(X, addition(star(multiplication(Y, X)), addition(multiplication(Y, multiplication(X, star(multiplication(Y, X)))), star(multiplication(Y, X)))))
% 260.18/33.26 = { by axiom 6 (additive_associativity) }
% 260.18/33.26 multiplication(X, addition(addition(star(multiplication(Y, X)), multiplication(Y, multiplication(X, star(multiplication(Y, X))))), star(multiplication(Y, X))))
% 260.18/33.26 = { by lemma 31 R->L }
% 260.18/33.26 multiplication(X, addition(addition(star(multiplication(Y, X)), multiplication(Y, multiplication(X, star(multiplication(Y, X))))), addition(one, addition(star(multiplication(Y, X)), multiplication(Y, multiplication(X, star(multiplication(Y, X))))))))
% 260.18/33.26 = { by lemma 22 }
% 260.18/33.26 multiplication(X, addition(one, addition(star(multiplication(Y, X)), multiplication(Y, multiplication(X, star(multiplication(Y, X)))))))
% 260.18/33.26 = { by lemma 31 }
% 260.18/33.26 multiplication(X, star(multiplication(Y, X)))
% 260.18/33.26
% 260.18/33.26 Goal 1 (goals): tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0))) = tuple(true, true).
% 260.18/33.26 Proof:
% 260.18/33.26 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.26 = { by lemma 27 R->L }
% 260.18/33.26 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), ifeq2(leq(multiplication(star(addition(one, multiplication(x0_2, x1_2))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), true, addition(multiplication(x0_2, star(multiplication(x1_2, x0_2))), multiplication(star(addition(one, multiplication(x0_2, x1_2))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.26 = { by lemma 18 }
% 260.18/33.26 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), ifeq2(leq(multiplication(star(addition(one, multiplication(x0_2, x1_2))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), true, multiplication(addition(star(addition(one, multiplication(x0_2, x1_2))), one), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.26 = { by axiom 4 (additive_commutativity) }
% 260.18/33.26 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), ifeq2(leq(multiplication(star(addition(one, multiplication(x0_2, x1_2))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), true, multiplication(addition(one, star(addition(one, multiplication(x0_2, x1_2)))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.26 = { by lemma 32 R->L }
% 260.18/33.26 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), ifeq2(leq(multiplication(star(addition(one, multiplication(x0_2, x1_2))), multiplication(addition(one, multiplication(x0_2, x1_2)), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), true, multiplication(addition(one, star(addition(one, multiplication(x0_2, x1_2)))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.26 = { by axiom 7 (ifeq_axiom) R->L }
% 260.18/33.26 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), ifeq2(ifeq(true, true, leq(multiplication(star(addition(one, multiplication(x0_2, x1_2))), multiplication(addition(one, multiplication(x0_2, x1_2)), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), true), true, multiplication(addition(one, star(addition(one, multiplication(x0_2, x1_2)))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.26 = { by axiom 14 (order) R->L }
% 260.18/33.27 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), ifeq2(ifeq(ifeq3(addition(multiplication(x0_2, star(multiplication(x1_2, x0_2))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), multiplication(x0_2, star(multiplication(x1_2, x0_2))), leq(multiplication(x0_2, star(multiplication(x1_2, x0_2))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), true), true, leq(multiplication(star(addition(one, multiplication(x0_2, x1_2))), multiplication(addition(one, multiplication(x0_2, x1_2)), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), true), true, multiplication(addition(one, star(addition(one, multiplication(x0_2, x1_2)))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.27 = { by axiom 3 (additive_idempotence) }
% 260.18/33.27 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), ifeq2(ifeq(ifeq3(multiplication(x0_2, star(multiplication(x1_2, x0_2))), multiplication(x0_2, star(multiplication(x1_2, x0_2))), leq(multiplication(x0_2, star(multiplication(x1_2, x0_2))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), true), true, leq(multiplication(star(addition(one, multiplication(x0_2, x1_2))), multiplication(addition(one, multiplication(x0_2, x1_2)), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), true), true, multiplication(addition(one, star(addition(one, multiplication(x0_2, x1_2)))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.27 = { by axiom 8 (ifeq_axiom) }
% 260.18/33.27 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), ifeq2(ifeq(leq(multiplication(x0_2, star(multiplication(x1_2, x0_2))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), true, leq(multiplication(star(addition(one, multiplication(x0_2, x1_2))), multiplication(addition(one, multiplication(x0_2, x1_2)), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), true), true, multiplication(addition(one, star(addition(one, multiplication(x0_2, x1_2)))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.27 = { by lemma 32 R->L }
% 260.18/33.27 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), ifeq2(ifeq(leq(multiplication(addition(one, multiplication(x0_2, x1_2)), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), true, leq(multiplication(star(addition(one, multiplication(x0_2, x1_2))), multiplication(addition(one, multiplication(x0_2, x1_2)), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), true), true, multiplication(addition(one, star(addition(one, multiplication(x0_2, x1_2)))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.27 = { by axiom 3 (additive_idempotence) R->L }
% 260.18/33.27 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), ifeq2(ifeq(leq(addition(multiplication(addition(one, multiplication(x0_2, x1_2)), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), multiplication(addition(one, multiplication(x0_2, x1_2)), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), true, leq(multiplication(star(addition(one, multiplication(x0_2, x1_2))), multiplication(addition(one, multiplication(x0_2, x1_2)), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), true), true, multiplication(addition(one, star(addition(one, multiplication(x0_2, x1_2)))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.27 = { by axiom 17 (star_induction_left) }
% 260.18/33.27 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), ifeq2(true, true, multiplication(addition(one, star(addition(one, multiplication(x0_2, x1_2)))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.27 = { by axiom 9 (ifeq_axiom) }
% 260.18/33.27 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(addition(one, star(addition(one, multiplication(x0_2, x1_2)))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.27 = { by lemma 21 }
% 260.18/33.27 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(star(addition(one, multiplication(x0_2, x1_2))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.27 = { by axiom 4 (additive_commutativity) R->L }
% 260.18/33.27 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(star(addition(multiplication(x0_2, x1_2), one)), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.27 = { by axiom 15 (order_1) R->L }
% 260.18/33.27 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(leq(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.27 = { by axiom 15 (order_1) R->L }
% 260.18/33.27 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(leq(ifeq2(leq(multiplication(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(multiplication(x0_2, x1_2))), true, addition(multiplication(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(multiplication(x0_2, x1_2))), star(multiplication(x0_2, x1_2))), star(addition(multiplication(x0_2, x1_2), one))), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.27 = { by lemma 25 R->L }
% 260.18/33.27 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(leq(ifeq2(leq(multiplication(multiplication(star(multiplication(x0_2, x1_2)), addition(multiplication(x0_2, x1_2), one)), star(addition(multiplication(x0_2, x1_2), one))), star(multiplication(x0_2, x1_2))), true, addition(multiplication(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(multiplication(x0_2, x1_2))), star(multiplication(x0_2, x1_2))), star(addition(multiplication(x0_2, x1_2), one))), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.28 = { by axiom 5 (multiplicative_associativity) R->L }
% 260.18/33.28 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(leq(ifeq2(leq(multiplication(star(multiplication(x0_2, x1_2)), multiplication(addition(multiplication(x0_2, x1_2), one), star(addition(multiplication(x0_2, x1_2), one)))), star(multiplication(x0_2, x1_2))), true, addition(multiplication(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(multiplication(x0_2, x1_2))), star(multiplication(x0_2, x1_2))), star(addition(multiplication(x0_2, x1_2), one))), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.28 = { by axiom 7 (ifeq_axiom) R->L }
% 260.18/33.28 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(leq(ifeq2(ifeq(true, true, leq(multiplication(star(multiplication(x0_2, x1_2)), multiplication(addition(multiplication(x0_2, x1_2), one), star(addition(multiplication(x0_2, x1_2), one)))), star(multiplication(x0_2, x1_2))), true), true, addition(multiplication(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(multiplication(x0_2, x1_2))), star(multiplication(x0_2, x1_2))), star(addition(multiplication(x0_2, x1_2), one))), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.28 = { by axiom 14 (order) R->L }
% 260.18/33.28 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(leq(ifeq2(ifeq(ifeq3(addition(star(multiplication(x0_2, x1_2)), star(multiplication(x0_2, x1_2))), star(multiplication(x0_2, x1_2)), leq(star(multiplication(x0_2, x1_2)), star(multiplication(x0_2, x1_2))), true), true, leq(multiplication(star(multiplication(x0_2, x1_2)), multiplication(addition(multiplication(x0_2, x1_2), one), star(addition(multiplication(x0_2, x1_2), one)))), star(multiplication(x0_2, x1_2))), true), true, addition(multiplication(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(multiplication(x0_2, x1_2))), star(multiplication(x0_2, x1_2))), star(addition(multiplication(x0_2, x1_2), one))), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.28 = { by axiom 3 (additive_idempotence) }
% 260.18/33.28 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(leq(ifeq2(ifeq(ifeq3(star(multiplication(x0_2, x1_2)), star(multiplication(x0_2, x1_2)), leq(star(multiplication(x0_2, x1_2)), star(multiplication(x0_2, x1_2))), true), true, leq(multiplication(star(multiplication(x0_2, x1_2)), multiplication(addition(multiplication(x0_2, x1_2), one), star(addition(multiplication(x0_2, x1_2), one)))), star(multiplication(x0_2, x1_2))), true), true, addition(multiplication(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(multiplication(x0_2, x1_2))), star(multiplication(x0_2, x1_2))), star(addition(multiplication(x0_2, x1_2), one))), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.28 = { by axiom 8 (ifeq_axiom) }
% 260.18/33.28 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(leq(ifeq2(ifeq(leq(star(multiplication(x0_2, x1_2)), star(multiplication(x0_2, x1_2))), true, leq(multiplication(star(multiplication(x0_2, x1_2)), multiplication(addition(multiplication(x0_2, x1_2), one), star(addition(multiplication(x0_2, x1_2), one)))), star(multiplication(x0_2, x1_2))), true), true, addition(multiplication(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(multiplication(x0_2, x1_2))), star(multiplication(x0_2, x1_2))), star(addition(multiplication(x0_2, x1_2), one))), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.28 = { by lemma 25 R->L }
% 260.18/33.28 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(leq(ifeq2(ifeq(leq(multiplication(star(multiplication(x0_2, x1_2)), addition(multiplication(x0_2, x1_2), one)), star(multiplication(x0_2, x1_2))), true, leq(multiplication(star(multiplication(x0_2, x1_2)), multiplication(addition(multiplication(x0_2, x1_2), one), star(addition(multiplication(x0_2, x1_2), one)))), star(multiplication(x0_2, x1_2))), true), true, addition(multiplication(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(multiplication(x0_2, x1_2))), star(multiplication(x0_2, x1_2))), star(addition(multiplication(x0_2, x1_2), one))), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.28 = { by axiom 5 (multiplicative_associativity) }
% 260.18/33.28 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(leq(ifeq2(ifeq(leq(multiplication(star(multiplication(x0_2, x1_2)), addition(multiplication(x0_2, x1_2), one)), star(multiplication(x0_2, x1_2))), true, leq(multiplication(multiplication(star(multiplication(x0_2, x1_2)), addition(multiplication(x0_2, x1_2), one)), star(addition(multiplication(x0_2, x1_2), one))), star(multiplication(x0_2, x1_2))), true), true, addition(multiplication(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(multiplication(x0_2, x1_2))), star(multiplication(x0_2, x1_2))), star(addition(multiplication(x0_2, x1_2), one))), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.28 = { by axiom 3 (additive_idempotence) R->L }
% 260.18/33.28 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(leq(ifeq2(ifeq(leq(addition(multiplication(star(multiplication(x0_2, x1_2)), addition(multiplication(x0_2, x1_2), one)), multiplication(star(multiplication(x0_2, x1_2)), addition(multiplication(x0_2, x1_2), one))), star(multiplication(x0_2, x1_2))), true, leq(multiplication(multiplication(star(multiplication(x0_2, x1_2)), addition(multiplication(x0_2, x1_2), one)), star(addition(multiplication(x0_2, x1_2), one))), star(multiplication(x0_2, x1_2))), true), true, addition(multiplication(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(multiplication(x0_2, x1_2))), star(multiplication(x0_2, x1_2))), star(addition(multiplication(x0_2, x1_2), one))), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.28 = { by axiom 16 (star_induction_right) }
% 260.18/33.28 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(leq(ifeq2(true, true, addition(multiplication(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(multiplication(x0_2, x1_2))), star(multiplication(x0_2, x1_2))), star(addition(multiplication(x0_2, x1_2), one))), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.29 = { by axiom 9 (ifeq_axiom) }
% 260.18/33.29 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(leq(addition(multiplication(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(multiplication(x0_2, x1_2))), star(addition(multiplication(x0_2, x1_2), one))), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.29 = { by axiom 4 (additive_commutativity) }
% 260.18/33.29 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(leq(addition(star(multiplication(x0_2, x1_2)), multiplication(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one)))), star(addition(multiplication(x0_2, x1_2), one))), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.29 = { by lemma 23 }
% 260.18/33.29 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(leq(multiplication(star(multiplication(x0_2, x1_2)), addition(star(addition(multiplication(x0_2, x1_2), one)), one)), star(addition(multiplication(x0_2, x1_2), one))), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.29 = { by axiom 4 (additive_commutativity) }
% 260.18/33.29 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(leq(multiplication(star(multiplication(x0_2, x1_2)), addition(one, star(addition(multiplication(x0_2, x1_2), one)))), star(addition(multiplication(x0_2, x1_2), one))), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.29 = { by lemma 21 }
% 260.18/33.29 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(leq(multiplication(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.29 = { by axiom 2 (multiplicative_left_identity) R->L }
% 260.18/33.29 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(leq(multiplication(star(multiplication(x0_2, x1_2)), multiplication(one, star(addition(multiplication(x0_2, x1_2), one)))), star(addition(multiplication(x0_2, x1_2), one))), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.29 = { by axiom 7 (ifeq_axiom) R->L }
% 260.18/33.29 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(ifeq(true, true, leq(multiplication(star(multiplication(x0_2, x1_2)), multiplication(one, star(addition(multiplication(x0_2, x1_2), one)))), star(addition(multiplication(x0_2, x1_2), one))), true), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.29 = { by axiom 14 (order) R->L }
% 260.18/33.29 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(ifeq(ifeq3(addition(star(addition(multiplication(x0_2, x1_2), one)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one)), leq(star(addition(multiplication(x0_2, x1_2), one)), star(addition(multiplication(x0_2, x1_2), one))), true), true, leq(multiplication(star(multiplication(x0_2, x1_2)), multiplication(one, star(addition(multiplication(x0_2, x1_2), one)))), star(addition(multiplication(x0_2, x1_2), one))), true), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.29 = { by axiom 3 (additive_idempotence) }
% 260.18/33.29 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(ifeq(ifeq3(star(addition(multiplication(x0_2, x1_2), one)), star(addition(multiplication(x0_2, x1_2), one)), leq(star(addition(multiplication(x0_2, x1_2), one)), star(addition(multiplication(x0_2, x1_2), one))), true), true, leq(multiplication(star(multiplication(x0_2, x1_2)), multiplication(one, star(addition(multiplication(x0_2, x1_2), one)))), star(addition(multiplication(x0_2, x1_2), one))), true), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.29 = { by axiom 8 (ifeq_axiom) }
% 260.18/33.29 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(ifeq(leq(star(addition(multiplication(x0_2, x1_2), one)), star(addition(multiplication(x0_2, x1_2), one))), true, leq(multiplication(star(multiplication(x0_2, x1_2)), multiplication(one, star(addition(multiplication(x0_2, x1_2), one)))), star(addition(multiplication(x0_2, x1_2), one))), true), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.29 = { by axiom 4 (additive_commutativity) R->L }
% 260.18/33.29 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(ifeq(leq(star(addition(one, multiplication(x0_2, x1_2))), star(addition(multiplication(x0_2, x1_2), one))), true, leq(multiplication(star(multiplication(x0_2, x1_2)), multiplication(one, star(addition(multiplication(x0_2, x1_2), one)))), star(addition(multiplication(x0_2, x1_2), one))), true), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.30 = { by lemma 19 R->L }
% 260.18/33.30 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(ifeq(leq(addition(one, multiplication(addition(addition(one, multiplication(x0_2, x1_2)), one), star(addition(one, multiplication(x0_2, x1_2))))), star(addition(multiplication(x0_2, x1_2), one))), true, leq(multiplication(star(multiplication(x0_2, x1_2)), multiplication(one, star(addition(multiplication(x0_2, x1_2), one)))), star(addition(multiplication(x0_2, x1_2), one))), true), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.30 = { by lemma 22 R->L }
% 260.18/33.30 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(ifeq(leq(addition(multiplication(addition(addition(one, multiplication(x0_2, x1_2)), one), star(addition(one, multiplication(x0_2, x1_2)))), addition(one, multiplication(addition(addition(one, multiplication(x0_2, x1_2)), one), star(addition(one, multiplication(x0_2, x1_2)))))), star(addition(multiplication(x0_2, x1_2), one))), true, leq(multiplication(star(multiplication(x0_2, x1_2)), multiplication(one, star(addition(multiplication(x0_2, x1_2), one)))), star(addition(multiplication(x0_2, x1_2), one))), true), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.30 = { by lemma 19 }
% 260.18/33.30 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(ifeq(leq(addition(multiplication(addition(addition(one, multiplication(x0_2, x1_2)), one), star(addition(one, multiplication(x0_2, x1_2)))), star(addition(one, multiplication(x0_2, x1_2)))), star(addition(multiplication(x0_2, x1_2), one))), true, leq(multiplication(star(multiplication(x0_2, x1_2)), multiplication(one, star(addition(multiplication(x0_2, x1_2), one)))), star(addition(multiplication(x0_2, x1_2), one))), true), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.30 = { by axiom 4 (additive_commutativity) }
% 260.18/33.30 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(ifeq(leq(addition(star(addition(one, multiplication(x0_2, x1_2))), multiplication(addition(addition(one, multiplication(x0_2, x1_2)), one), star(addition(one, multiplication(x0_2, x1_2))))), star(addition(multiplication(x0_2, x1_2), one))), true, leq(multiplication(star(multiplication(x0_2, x1_2)), multiplication(one, star(addition(multiplication(x0_2, x1_2), one)))), star(addition(multiplication(x0_2, x1_2), one))), true), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.30 = { by lemma 18 }
% 260.18/33.30 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(ifeq(leq(multiplication(addition(addition(addition(one, multiplication(x0_2, x1_2)), one), one), star(addition(one, multiplication(x0_2, x1_2)))), star(addition(multiplication(x0_2, x1_2), one))), true, leq(multiplication(star(multiplication(x0_2, x1_2)), multiplication(one, star(addition(multiplication(x0_2, x1_2), one)))), star(addition(multiplication(x0_2, x1_2), one))), true), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.30 = { by axiom 6 (additive_associativity) R->L }
% 260.18/33.30 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(ifeq(leq(multiplication(addition(addition(one, multiplication(x0_2, x1_2)), addition(one, one)), star(addition(one, multiplication(x0_2, x1_2)))), star(addition(multiplication(x0_2, x1_2), one))), true, leq(multiplication(star(multiplication(x0_2, x1_2)), multiplication(one, star(addition(multiplication(x0_2, x1_2), one)))), star(addition(multiplication(x0_2, x1_2), one))), true), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.30 = { by axiom 3 (additive_idempotence) }
% 260.18/33.30 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(ifeq(leq(multiplication(addition(addition(one, multiplication(x0_2, x1_2)), one), star(addition(one, multiplication(x0_2, x1_2)))), star(addition(multiplication(x0_2, x1_2), one))), true, leq(multiplication(star(multiplication(x0_2, x1_2)), multiplication(one, star(addition(multiplication(x0_2, x1_2), one)))), star(addition(multiplication(x0_2, x1_2), one))), true), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.30 = { by axiom 6 (additive_associativity) R->L }
% 260.18/33.30 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(ifeq(leq(multiplication(addition(one, addition(multiplication(x0_2, x1_2), one)), star(addition(one, multiplication(x0_2, x1_2)))), star(addition(multiplication(x0_2, x1_2), one))), true, leq(multiplication(star(multiplication(x0_2, x1_2)), multiplication(one, star(addition(multiplication(x0_2, x1_2), one)))), star(addition(multiplication(x0_2, x1_2), one))), true), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.30 = { by axiom 4 (additive_commutativity) R->L }
% 260.18/33.30 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(ifeq(leq(multiplication(addition(addition(multiplication(x0_2, x1_2), one), one), star(addition(one, multiplication(x0_2, x1_2)))), star(addition(multiplication(x0_2, x1_2), one))), true, leq(multiplication(star(multiplication(x0_2, x1_2)), multiplication(one, star(addition(multiplication(x0_2, x1_2), one)))), star(addition(multiplication(x0_2, x1_2), one))), true), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.30 = { by axiom 6 (additive_associativity) R->L }
% 260.18/33.30 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(ifeq(leq(multiplication(addition(multiplication(x0_2, x1_2), addition(one, one)), star(addition(one, multiplication(x0_2, x1_2)))), star(addition(multiplication(x0_2, x1_2), one))), true, leq(multiplication(star(multiplication(x0_2, x1_2)), multiplication(one, star(addition(multiplication(x0_2, x1_2), one)))), star(addition(multiplication(x0_2, x1_2), one))), true), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.31 = { by axiom 4 (additive_commutativity) }
% 260.18/33.31 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(ifeq(leq(multiplication(addition(multiplication(x0_2, x1_2), addition(one, one)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), true, leq(multiplication(star(multiplication(x0_2, x1_2)), multiplication(one, star(addition(multiplication(x0_2, x1_2), one)))), star(addition(multiplication(x0_2, x1_2), one))), true), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.31 = { by axiom 3 (additive_idempotence) }
% 260.18/33.31 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(ifeq(leq(multiplication(addition(multiplication(x0_2, x1_2), one), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), true, leq(multiplication(star(multiplication(x0_2, x1_2)), multiplication(one, star(addition(multiplication(x0_2, x1_2), one)))), star(addition(multiplication(x0_2, x1_2), one))), true), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.31 = { by axiom 11 (left_distributivity) }
% 260.18/33.31 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(ifeq(leq(addition(multiplication(multiplication(x0_2, x1_2), star(addition(multiplication(x0_2, x1_2), one))), multiplication(one, star(addition(multiplication(x0_2, x1_2), one)))), star(addition(multiplication(x0_2, x1_2), one))), true, leq(multiplication(star(multiplication(x0_2, x1_2)), multiplication(one, star(addition(multiplication(x0_2, x1_2), one)))), star(addition(multiplication(x0_2, x1_2), one))), true), true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.31 = { by axiom 17 (star_induction_left) }
% 260.18/33.31 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(true, true, addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.31 = { by axiom 9 (ifeq_axiom) }
% 260.18/33.31 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(addition(star(multiplication(x0_2, x1_2)), star(addition(multiplication(x0_2, x1_2), one))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.31 = { by axiom 4 (additive_commutativity) R->L }
% 260.18/33.31 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(addition(star(addition(multiplication(x0_2, x1_2), one)), star(multiplication(x0_2, x1_2))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.31 = { by axiom 9 (ifeq_axiom) R->L }
% 260.18/33.31 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(true, true, addition(star(addition(multiplication(x0_2, x1_2), one)), star(multiplication(x0_2, x1_2))), star(multiplication(x0_2, x1_2))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.31 = { by axiom 16 (star_induction_right) R->L }
% 260.18/33.31 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(ifeq(leq(addition(multiplication(star(multiplication(x0_2, x1_2)), addition(multiplication(x0_2, x1_2), one)), one), star(multiplication(x0_2, x1_2))), true, leq(multiplication(one, star(addition(multiplication(x0_2, x1_2), one))), star(multiplication(x0_2, x1_2))), true), true, addition(star(addition(multiplication(x0_2, x1_2), one)), star(multiplication(x0_2, x1_2))), star(multiplication(x0_2, x1_2))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.31 = { by axiom 2 (multiplicative_left_identity) }
% 260.18/33.31 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(ifeq(leq(addition(multiplication(star(multiplication(x0_2, x1_2)), addition(multiplication(x0_2, x1_2), one)), one), star(multiplication(x0_2, x1_2))), true, leq(star(addition(multiplication(x0_2, x1_2), one)), star(multiplication(x0_2, x1_2))), true), true, addition(star(addition(multiplication(x0_2, x1_2), one)), star(multiplication(x0_2, x1_2))), star(multiplication(x0_2, x1_2))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.31 = { by axiom 4 (additive_commutativity) }
% 260.18/33.31 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(ifeq(leq(addition(one, multiplication(star(multiplication(x0_2, x1_2)), addition(multiplication(x0_2, x1_2), one))), star(multiplication(x0_2, x1_2))), true, leq(star(addition(multiplication(x0_2, x1_2), one)), star(multiplication(x0_2, x1_2))), true), true, addition(star(addition(multiplication(x0_2, x1_2), one)), star(multiplication(x0_2, x1_2))), star(multiplication(x0_2, x1_2))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.31 = { by lemma 24 }
% 260.18/33.31 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(ifeq(leq(star(multiplication(x0_2, x1_2)), star(multiplication(x0_2, x1_2))), true, leq(star(addition(multiplication(x0_2, x1_2), one)), star(multiplication(x0_2, x1_2))), true), true, addition(star(addition(multiplication(x0_2, x1_2), one)), star(multiplication(x0_2, x1_2))), star(multiplication(x0_2, x1_2))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.31 = { by axiom 8 (ifeq_axiom) R->L }
% 260.18/33.31 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(ifeq(ifeq3(star(multiplication(x0_2, x1_2)), star(multiplication(x0_2, x1_2)), leq(star(multiplication(x0_2, x1_2)), star(multiplication(x0_2, x1_2))), true), true, leq(star(addition(multiplication(x0_2, x1_2), one)), star(multiplication(x0_2, x1_2))), true), true, addition(star(addition(multiplication(x0_2, x1_2), one)), star(multiplication(x0_2, x1_2))), star(multiplication(x0_2, x1_2))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.31 = { by axiom 3 (additive_idempotence) R->L }
% 260.18/33.31 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(ifeq(ifeq3(addition(star(multiplication(x0_2, x1_2)), star(multiplication(x0_2, x1_2))), star(multiplication(x0_2, x1_2)), leq(star(multiplication(x0_2, x1_2)), star(multiplication(x0_2, x1_2))), true), true, leq(star(addition(multiplication(x0_2, x1_2), one)), star(multiplication(x0_2, x1_2))), true), true, addition(star(addition(multiplication(x0_2, x1_2), one)), star(multiplication(x0_2, x1_2))), star(multiplication(x0_2, x1_2))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.31 = { by axiom 14 (order) }
% 260.18/33.31 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(ifeq(true, true, leq(star(addition(multiplication(x0_2, x1_2), one)), star(multiplication(x0_2, x1_2))), true), true, addition(star(addition(multiplication(x0_2, x1_2), one)), star(multiplication(x0_2, x1_2))), star(multiplication(x0_2, x1_2))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.31 = { by axiom 7 (ifeq_axiom) }
% 260.18/33.31 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(ifeq2(leq(star(addition(multiplication(x0_2, x1_2), one)), star(multiplication(x0_2, x1_2))), true, addition(star(addition(multiplication(x0_2, x1_2), one)), star(multiplication(x0_2, x1_2))), star(multiplication(x0_2, x1_2))), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.31 = { by axiom 15 (order_1) }
% 260.18/33.31 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(star(multiplication(x0_2, x1_2)), multiplication(x0_2, star(multiplication(x1_2, x0_2))))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.31 = { by axiom 5 (multiplicative_associativity) }
% 260.18/33.31 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(multiplication(star(multiplication(x0_2, x1_2)), x0_2), star(multiplication(x1_2, x0_2)))), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.31 = { by lemma 30 }
% 260.18/33.31 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(star(multiplication(x0_2, x1_2)), x0_2)), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.31 = { by axiom 8 (ifeq_axiom) R->L }
% 260.18/33.31 tuple(ifeq3(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(star(multiplication(x0_2, x1_2)), x0_2), leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(star(multiplication(x0_2, x1_2)), x0_2)), true), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.31 = { by axiom 3 (additive_idempotence) R->L }
% 260.18/33.31 tuple(ifeq3(addition(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(star(multiplication(x0_2, x1_2)), x0_2)), multiplication(star(multiplication(x0_2, x1_2)), x0_2), leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(star(multiplication(x0_2, x1_2)), x0_2)), true), leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.32 = { by axiom 14 (order) }
% 260.18/33.32 tuple(true, leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0)))
% 260.18/33.32 = { by lemma 30 R->L }
% 260.18/33.32 tuple(true, leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(multiplication(star(multiplication(x0, x1)), x0), star(multiplication(x1, x0)))))
% 260.18/33.32 = { by lemma 21 R->L }
% 260.18/33.32 tuple(true, leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(multiplication(addition(one, star(multiplication(x0, x1))), x0), star(multiplication(x1, x0)))))
% 260.18/33.32 = { by lemma 26 R->L }
% 260.18/33.32 tuple(true, leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(addition(multiplication(star(multiplication(x0, x1)), x0), multiplication(one, x0)), star(multiplication(x1, x0)))))
% 260.18/33.32 = { by axiom 2 (multiplicative_left_identity) }
% 260.18/33.32 tuple(true, leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(addition(multiplication(star(multiplication(x0, x1)), x0), x0), star(multiplication(x1, x0)))))
% 260.18/33.32 = { by axiom 4 (additive_commutativity) }
% 260.18/33.32 tuple(true, leq(multiplication(x0, star(multiplication(x1, x0))), multiplication(addition(x0, multiplication(star(multiplication(x0, x1)), x0)), star(multiplication(x1, x0)))))
% 260.18/33.32 = { by axiom 11 (left_distributivity) }
% 260.18/33.32 tuple(true, leq(multiplication(x0, star(multiplication(x1, x0))), addition(multiplication(x0, star(multiplication(x1, x0))), multiplication(multiplication(star(multiplication(x0, x1)), x0), star(multiplication(x1, x0))))))
% 260.18/33.32 = { by axiom 8 (ifeq_axiom) R->L }
% 260.18/33.32 tuple(true, ifeq3(addition(multiplication(x0, star(multiplication(x1, x0))), multiplication(multiplication(star(multiplication(x0, x1)), x0), star(multiplication(x1, x0)))), addition(multiplication(x0, star(multiplication(x1, x0))), multiplication(multiplication(star(multiplication(x0, x1)), x0), star(multiplication(x1, x0)))), leq(multiplication(x0, star(multiplication(x1, x0))), addition(multiplication(x0, star(multiplication(x1, x0))), multiplication(multiplication(star(multiplication(x0, x1)), x0), star(multiplication(x1, x0))))), true))
% 260.18/33.32 = { by lemma 20 R->L }
% 260.18/33.32 tuple(true, ifeq3(addition(multiplication(x0, star(multiplication(x1, x0))), addition(multiplication(x0, star(multiplication(x1, x0))), multiplication(multiplication(star(multiplication(x0, x1)), x0), star(multiplication(x1, x0))))), addition(multiplication(x0, star(multiplication(x1, x0))), multiplication(multiplication(star(multiplication(x0, x1)), x0), star(multiplication(x1, x0)))), leq(multiplication(x0, star(multiplication(x1, x0))), addition(multiplication(x0, star(multiplication(x1, x0))), multiplication(multiplication(star(multiplication(x0, x1)), x0), star(multiplication(x1, x0))))), true))
% 260.18/33.32 = { by axiom 14 (order) }
% 260.18/33.32 tuple(true, true)
% 260.18/33.32 % SZS output end Proof
% 260.18/33.32
% 260.18/33.32 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------