TSTP Solution File: KLE042+2 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : KLE042+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 05:35:38 EDT 2023
% Result : Theorem 188.94s 24.15s
% Output : Proof 189.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE042+2 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 12:08:28 EDT 2023
% 0.19/0.34 % CPUTime :
% 188.94/24.15 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 188.94/24.15
% 188.94/24.15 % SZS status Theorem
% 188.94/24.15
% 189.74/24.20 % SZS output start Proof
% 189.74/24.20 Take the following subset of the input axioms:
% 189.92/24.20 fof(additive_associativity, axiom, ![A, B, C]: addition(A, addition(B, C))=addition(addition(A, B), C)).
% 189.92/24.20 fof(additive_commutativity, axiom, ![A3, B2]: addition(A3, B2)=addition(B2, A3)).
% 189.92/24.20 fof(additive_idempotence, axiom, ![A3]: addition(A3, A3)=A3).
% 189.92/24.20 fof(goals, conjecture, ![X0, X1]: (leq(multiplication(star(multiplication(X0, X1)), X0), multiplication(X0, star(multiplication(X1, X0)))) & leq(multiplication(X0, star(multiplication(X1, X0))), multiplication(star(multiplication(X0, X1)), X0)))).
% 189.92/24.20 fof(left_distributivity, axiom, ![A3, B2, C2]: multiplication(addition(A3, B2), C2)=addition(multiplication(A3, C2), multiplication(B2, C2))).
% 189.92/24.20 fof(multiplicative_associativity, axiom, ![A3, B2, C2]: multiplication(A3, multiplication(B2, C2))=multiplication(multiplication(A3, B2), C2)).
% 189.92/24.20 fof(multiplicative_left_identity, axiom, ![A3]: multiplication(one, A3)=A3).
% 189.92/24.20 fof(multiplicative_right_identity, axiom, ![A3]: multiplication(A3, one)=A3).
% 189.92/24.20 fof(order, axiom, ![A2, B2]: (leq(A2, B2) <=> addition(A2, B2)=B2)).
% 189.92/24.20 fof(right_distributivity, axiom, ![A3, B2, C2]: multiplication(A3, addition(B2, C2))=addition(multiplication(A3, B2), multiplication(A3, C2))).
% 189.92/24.20 fof(star_induction_left, axiom, ![B2, C2, A2_2]: (leq(addition(multiplication(A2_2, B2), C2), B2) => leq(multiplication(star(A2_2), C2), B2))).
% 189.92/24.20 fof(star_induction_right, axiom, ![B2, C2, A2_2]: (leq(addition(multiplication(A2_2, B2), C2), A2_2) => leq(multiplication(C2, star(B2)), A2_2))).
% 189.92/24.20 fof(star_unfold_left, axiom, ![A3]: leq(addition(one, multiplication(star(A3), A3)), star(A3))).
% 189.92/24.20 fof(star_unfold_right, axiom, ![A3]: leq(addition(one, multiplication(A3, star(A3))), star(A3))).
% 189.92/24.20
% 189.92/24.20 Now clausify the problem and encode Horn clauses using encoding 3 of
% 189.92/24.20 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 189.92/24.20 We repeatedly replace C & s=t => u=v by the two clauses:
% 189.92/24.20 fresh(y, y, x1...xn) = u
% 189.92/24.20 C => fresh(s, t, x1...xn) = v
% 189.92/24.20 where fresh is a fresh function symbol and x1..xn are the free
% 189.92/24.20 variables of u and v.
% 189.92/24.20 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 189.92/24.20 input problem has no model of domain size 1).
% 189.92/24.20
% 189.92/24.20 The encoding turns the above axioms into the following unit equations and goals:
% 189.92/24.20
% 189.92/24.20 Axiom 1 (multiplicative_right_identity): multiplication(X, one) = X.
% 189.92/24.20 Axiom 2 (multiplicative_left_identity): multiplication(one, X) = X.
% 189.92/24.20 Axiom 3 (additive_idempotence): addition(X, X) = X.
% 189.92/24.20 Axiom 4 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 189.92/24.20 Axiom 5 (multiplicative_associativity): multiplication(X, multiplication(Y, Z)) = multiplication(multiplication(X, Y), Z).
% 189.92/24.20 Axiom 6 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 189.92/24.20 Axiom 7 (order_1): fresh(X, X, Y, Z) = Z.
% 189.92/24.20 Axiom 8 (order): fresh3(X, X, Y, Z) = true.
% 189.92/24.20 Axiom 9 (star_induction_left): fresh4(X, X, Y, Z, W) = true.
% 189.92/24.20 Axiom 10 (star_induction_right): fresh2(X, X, Y, Z, W) = true.
% 189.92/24.20 Axiom 11 (right_distributivity): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 189.92/24.20 Axiom 12 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 189.92/24.20 Axiom 13 (order_1): fresh(leq(X, Y), true, X, Y) = addition(X, Y).
% 189.92/24.20 Axiom 14 (order): fresh3(addition(X, Y), Y, X, Y) = leq(X, Y).
% 189.92/24.20 Axiom 15 (star_unfold_right): leq(addition(one, multiplication(X, star(X))), star(X)) = true.
% 189.92/24.20 Axiom 16 (star_unfold_left): leq(addition(one, multiplication(star(X), X)), star(X)) = true.
% 189.92/24.20 Axiom 17 (star_induction_left): fresh4(leq(addition(multiplication(X, Y), Z), Y), true, X, Y, Z) = leq(multiplication(star(X), Z), Y).
% 189.92/24.20 Axiom 18 (star_induction_right): fresh2(leq(addition(multiplication(X, Y), Z), X), true, X, Y, Z) = leq(multiplication(Z, star(Y)), X).
% 189.92/24.20
% 189.92/24.20 Lemma 19: addition(one, multiplication(addition(X, one), star(X))) = star(X).
% 189.92/24.20 Proof:
% 189.92/24.20 addition(one, multiplication(addition(X, one), star(X)))
% 189.92/24.20 = { by axiom 4 (additive_commutativity) R->L }
% 189.92/24.20 addition(one, multiplication(addition(one, X), star(X)))
% 189.92/24.20 = { by axiom 12 (left_distributivity) }
% 189.92/24.20 addition(one, addition(multiplication(one, star(X)), multiplication(X, star(X))))
% 189.92/24.20 = { by axiom 2 (multiplicative_left_identity) }
% 189.92/24.20 addition(one, addition(star(X), multiplication(X, star(X))))
% 189.92/24.20 = { by axiom 4 (additive_commutativity) R->L }
% 189.92/24.20 addition(one, addition(multiplication(X, star(X)), star(X)))
% 189.92/24.20 = { by axiom 6 (additive_associativity) }
% 189.92/24.20 addition(addition(one, multiplication(X, star(X))), star(X))
% 189.92/24.20 = { by axiom 13 (order_1) R->L }
% 189.92/24.20 fresh(leq(addition(one, multiplication(X, star(X))), star(X)), true, addition(one, multiplication(X, star(X))), star(X))
% 189.92/24.20 = { by axiom 15 (star_unfold_right) }
% 189.92/24.20 fresh(true, true, addition(one, multiplication(X, star(X))), star(X))
% 189.92/24.20 = { by axiom 7 (order_1) }
% 189.92/24.20 star(X)
% 189.92/24.20
% 189.92/24.20 Lemma 20: addition(X, addition(X, Y)) = addition(X, Y).
% 189.92/24.20 Proof:
% 189.92/24.20 addition(X, addition(X, Y))
% 189.92/24.20 = { by axiom 6 (additive_associativity) }
% 189.92/24.20 addition(addition(X, X), Y)
% 189.92/24.20 = { by axiom 3 (additive_idempotence) }
% 189.92/24.20 addition(X, Y)
% 189.92/24.20
% 189.92/24.20 Lemma 21: addition(one, star(X)) = star(X).
% 189.92/24.20 Proof:
% 189.92/24.20 addition(one, star(X))
% 189.92/24.20 = { by lemma 19 R->L }
% 189.92/24.20 addition(one, addition(one, multiplication(addition(X, one), star(X))))
% 189.92/24.20 = { by lemma 20 }
% 189.92/24.20 addition(one, multiplication(addition(X, one), star(X)))
% 189.92/24.20 = { by lemma 19 }
% 189.92/24.20 star(X)
% 189.92/24.20
% 189.92/24.20 Lemma 22: addition(X, addition(Y, X)) = addition(Y, X).
% 189.92/24.20 Proof:
% 189.92/24.20 addition(X, addition(Y, X))
% 189.92/24.20 = { by lemma 20 R->L }
% 189.92/24.20 addition(X, addition(Y, addition(Y, X)))
% 189.92/24.20 = { by axiom 4 (additive_commutativity) R->L }
% 189.92/24.20 addition(X, addition(Y, addition(X, Y)))
% 189.92/24.20 = { by axiom 6 (additive_associativity) }
% 189.92/24.20 addition(addition(X, Y), addition(X, Y))
% 189.92/24.20 = { by axiom 3 (additive_idempotence) }
% 189.92/24.20 addition(X, Y)
% 189.92/24.20 = { by axiom 4 (additive_commutativity) }
% 189.92/24.20 addition(Y, X)
% 189.92/24.20
% 189.92/24.20 Lemma 23: addition(X, multiplication(X, Y)) = multiplication(X, addition(Y, one)).
% 189.92/24.20 Proof:
% 189.92/24.20 addition(X, multiplication(X, Y))
% 189.92/24.20 = { by axiom 1 (multiplicative_right_identity) R->L }
% 189.92/24.20 addition(multiplication(X, one), multiplication(X, Y))
% 189.92/24.20 = { by axiom 11 (right_distributivity) R->L }
% 189.92/24.20 multiplication(X, addition(one, Y))
% 189.92/24.20 = { by axiom 4 (additive_commutativity) }
% 189.92/24.20 multiplication(X, addition(Y, one))
% 189.92/24.20
% 189.92/24.20 Lemma 24: leq(X, addition(X, Y)) = true.
% 189.92/24.20 Proof:
% 189.92/24.20 leq(X, addition(X, Y))
% 189.92/24.20 = { by axiom 14 (order) R->L }
% 189.92/24.20 fresh3(addition(X, addition(X, Y)), addition(X, Y), X, addition(X, Y))
% 189.92/24.20 = { by lemma 20 }
% 189.92/24.20 fresh3(addition(X, Y), addition(X, Y), X, addition(X, Y))
% 189.92/24.20 = { by axiom 8 (order) }
% 189.92/24.20 true
% 189.92/24.20
% 189.92/24.20 Lemma 25: addition(multiplication(X, Y), multiplication(Z, Y)) = multiplication(addition(Z, X), Y).
% 189.92/24.20 Proof:
% 189.92/24.20 addition(multiplication(X, Y), multiplication(Z, Y))
% 189.92/24.20 = { by axiom 12 (left_distributivity) R->L }
% 189.92/24.20 multiplication(addition(X, Z), Y)
% 189.92/24.20 = { by axiom 4 (additive_commutativity) }
% 189.92/24.20 multiplication(addition(Z, X), Y)
% 189.92/24.20
% 189.92/24.20 Lemma 26: addition(one, addition(star(multiplication(X, Y)), multiplication(X, multiplication(Y, star(multiplication(X, Y)))))) = star(multiplication(X, Y)).
% 189.92/24.20 Proof:
% 189.92/24.20 addition(one, addition(star(multiplication(X, Y)), multiplication(X, multiplication(Y, star(multiplication(X, Y))))))
% 189.92/24.20 = { by axiom 4 (additive_commutativity) R->L }
% 189.92/24.20 addition(one, addition(multiplication(X, multiplication(Y, star(multiplication(X, Y)))), star(multiplication(X, Y))))
% 189.92/24.20 = { by axiom 5 (multiplicative_associativity) }
% 189.92/24.20 addition(one, addition(multiplication(multiplication(X, Y), star(multiplication(X, Y))), star(multiplication(X, Y))))
% 189.92/24.20 = { by axiom 6 (additive_associativity) }
% 189.92/24.20 addition(addition(one, multiplication(multiplication(X, Y), star(multiplication(X, Y)))), star(multiplication(X, Y)))
% 189.92/24.20 = { by axiom 13 (order_1) R->L }
% 189.92/24.20 fresh(leq(addition(one, multiplication(multiplication(X, Y), star(multiplication(X, Y)))), star(multiplication(X, Y))), true, addition(one, multiplication(multiplication(X, Y), star(multiplication(X, Y)))), star(multiplication(X, Y)))
% 189.92/24.20 = { by axiom 15 (star_unfold_right) }
% 189.92/24.20 fresh(true, true, addition(one, multiplication(multiplication(X, Y), star(multiplication(X, Y)))), star(multiplication(X, Y)))
% 189.92/24.20 = { by axiom 7 (order_1) }
% 189.92/24.20 star(multiplication(X, Y))
% 189.92/24.20
% 189.92/24.20 Lemma 27: addition(one, addition(star(multiplication(X, Y)), multiplication(multiplication(star(multiplication(X, Y)), X), Y))) = star(multiplication(X, Y)).
% 189.92/24.20 Proof:
% 189.92/24.20 addition(one, addition(star(multiplication(X, Y)), multiplication(multiplication(star(multiplication(X, Y)), X), Y)))
% 189.92/24.20 = { by axiom 4 (additive_commutativity) R->L }
% 189.92/24.20 addition(one, addition(multiplication(multiplication(star(multiplication(X, Y)), X), Y), star(multiplication(X, Y))))
% 189.92/24.20 = { by axiom 5 (multiplicative_associativity) R->L }
% 189.92/24.20 addition(one, addition(multiplication(star(multiplication(X, Y)), multiplication(X, Y)), star(multiplication(X, Y))))
% 189.92/24.20 = { by axiom 6 (additive_associativity) }
% 189.92/24.20 addition(addition(one, multiplication(star(multiplication(X, Y)), multiplication(X, Y))), star(multiplication(X, Y)))
% 189.92/24.20 = { by axiom 13 (order_1) R->L }
% 189.92/24.20 fresh(leq(addition(one, multiplication(star(multiplication(X, Y)), multiplication(X, Y))), star(multiplication(X, Y))), true, addition(one, multiplication(star(multiplication(X, Y)), multiplication(X, Y))), star(multiplication(X, Y)))
% 189.92/24.20 = { by axiom 16 (star_unfold_left) }
% 189.92/24.20 fresh(true, true, addition(one, multiplication(star(multiplication(X, Y)), multiplication(X, Y))), star(multiplication(X, Y)))
% 189.92/24.20 = { by axiom 7 (order_1) }
% 189.92/24.20 star(multiplication(X, Y))
% 189.92/24.20
% 189.92/24.20 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).
% 189.92/24.20 Proof:
% 189.92/24.20 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)))
% 189.92/24.20 = { by axiom 18 (star_induction_right) R->L }
% 189.92/24.20 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), fresh2(leq(addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0)), x0), multiplication(star(multiplication(x0, x1)), x0)), true, multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0), x0))
% 189.92/24.21 = { by axiom 3 (additive_idempotence) R->L }
% 189.92/24.21 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), fresh2(leq(addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0)), x0), addition(multiplication(star(multiplication(x0, x1)), x0), multiplication(star(multiplication(x0, x1)), x0))), true, multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0), x0))
% 189.92/24.21 = { by lemma 27 R->L }
% 189.92/24.21 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), fresh2(leq(addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0)), x0), addition(multiplication(addition(one, addition(star(multiplication(x0, x1)), multiplication(multiplication(star(multiplication(x0, x1)), x0), x1))), x0), multiplication(star(multiplication(x0, x1)), x0))), true, multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0), x0))
% 189.92/24.21 = { by lemma 22 R->L }
% 189.92/24.21 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), fresh2(leq(addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0)), x0), addition(multiplication(addition(addition(star(multiplication(x0, x1)), multiplication(multiplication(star(multiplication(x0, x1)), x0), x1)), addition(one, addition(star(multiplication(x0, x1)), multiplication(multiplication(star(multiplication(x0, x1)), x0), x1)))), x0), multiplication(star(multiplication(x0, x1)), x0))), true, multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0), x0))
% 189.92/24.21 = { by lemma 27 }
% 189.92/24.21 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), fresh2(leq(addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0)), x0), addition(multiplication(addition(addition(star(multiplication(x0, x1)), multiplication(multiplication(star(multiplication(x0, x1)), x0), x1)), star(multiplication(x0, x1))), x0), multiplication(star(multiplication(x0, x1)), x0))), true, multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0), x0))
% 189.92/24.21 = { by axiom 6 (additive_associativity) R->L }
% 189.92/24.21 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), fresh2(leq(addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0)), x0), addition(multiplication(addition(star(multiplication(x0, x1)), addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), x1), star(multiplication(x0, x1)))), x0), multiplication(star(multiplication(x0, x1)), x0))), true, multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0), x0))
% 189.92/24.21 = { by lemma 22 }
% 189.92/24.21 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), fresh2(leq(addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0)), x0), addition(multiplication(addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), x1), star(multiplication(x0, x1))), x0), multiplication(star(multiplication(x0, x1)), x0))), true, multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0), x0))
% 189.92/24.21 = { by lemma 25 R->L }
% 189.92/24.21 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), fresh2(leq(addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0)), x0), addition(addition(multiplication(star(multiplication(x0, x1)), x0), multiplication(multiplication(multiplication(star(multiplication(x0, x1)), x0), x1), x0)), multiplication(star(multiplication(x0, x1)), x0))), true, multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0), x0))
% 189.92/24.21 = { by axiom 5 (multiplicative_associativity) R->L }
% 189.92/24.21 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), fresh2(leq(addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0)), x0), addition(addition(multiplication(star(multiplication(x0, x1)), x0), multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0))), multiplication(star(multiplication(x0, x1)), x0))), true, multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0), x0))
% 189.92/24.21 = { by axiom 6 (additive_associativity) R->L }
% 189.92/24.21 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), fresh2(leq(addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0)), x0), addition(multiplication(star(multiplication(x0, x1)), x0), addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0)), multiplication(star(multiplication(x0, x1)), x0)))), true, multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0), x0))
% 189.92/24.21 = { by axiom 4 (additive_commutativity) }
% 189.92/24.21 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), fresh2(leq(addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0)), x0), addition(multiplication(star(multiplication(x0, x1)), x0), addition(multiplication(star(multiplication(x0, x1)), x0), multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0))))), true, multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0), x0))
% 189.92/24.21 = { by axiom 6 (additive_associativity) }
% 189.92/24.21 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), fresh2(leq(addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0)), x0), addition(addition(multiplication(star(multiplication(x0, x1)), x0), multiplication(star(multiplication(x0, x1)), x0)), multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0)))), true, multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0), x0))
% 189.92/24.21 = { by axiom 4 (additive_commutativity) R->L }
% 189.92/24.21 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), fresh2(leq(addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0)), x0), addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0)), addition(multiplication(star(multiplication(x0, x1)), x0), multiplication(star(multiplication(x0, x1)), x0)))), true, multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0), x0))
% 189.92/24.21 = { by lemma 21 R->L }
% 189.92/24.21 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), fresh2(leq(addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0)), x0), addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0)), addition(multiplication(addition(one, star(multiplication(x0, x1))), x0), multiplication(star(multiplication(x0, x1)), x0)))), true, multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0), x0))
% 189.92/24.21 = { by lemma 25 R->L }
% 189.92/24.21 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), fresh2(leq(addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0)), x0), addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0)), addition(addition(multiplication(star(multiplication(x0, x1)), x0), multiplication(one, x0)), multiplication(star(multiplication(x0, x1)), x0)))), true, multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0), x0))
% 189.92/24.21 = { by axiom 2 (multiplicative_left_identity) }
% 189.92/24.21 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), fresh2(leq(addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0)), x0), addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0)), addition(addition(multiplication(star(multiplication(x0, x1)), x0), x0), multiplication(star(multiplication(x0, x1)), x0)))), true, multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0), x0))
% 189.92/24.21 = { by axiom 4 (additive_commutativity) }
% 189.92/24.21 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), fresh2(leq(addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0)), x0), addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0)), addition(addition(x0, multiplication(star(multiplication(x0, x1)), x0)), multiplication(star(multiplication(x0, x1)), x0)))), true, multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0), x0))
% 189.92/24.21 = { by axiom 6 (additive_associativity) R->L }
% 189.92/24.21 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), fresh2(leq(addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0)), x0), addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0)), addition(x0, addition(multiplication(star(multiplication(x0, x1)), x0), multiplication(star(multiplication(x0, x1)), x0))))), true, multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0), x0))
% 189.92/24.21 = { by axiom 6 (additive_associativity) }
% 189.92/24.21 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), fresh2(leq(addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0)), x0), addition(addition(multiplication(multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0)), x0), addition(multiplication(star(multiplication(x0, x1)), x0), multiplication(star(multiplication(x0, x1)), x0)))), true, multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0), x0))
% 189.92/24.21 = { by lemma 24 }
% 189.92/24.21 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), fresh2(true, true, multiplication(star(multiplication(x0, x1)), x0), multiplication(x1, x0), x0))
% 189.92/24.21 = { by axiom 10 (star_induction_right) }
% 189.92/24.21 tuple(leq(multiplication(star(multiplication(x0_2, x1_2)), x0_2), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), true)
% 189.92/24.21 = { by axiom 17 (star_induction_left) R->L }
% 189.92/24.21 tuple(fresh4(leq(addition(multiplication(multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), x0_2), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.21 = { by axiom 4 (additive_commutativity) }
% 189.92/24.21 tuple(fresh4(leq(addition(x0_2, multiplication(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(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.21 = { by axiom 5 (multiplicative_associativity) R->L }
% 189.92/24.21 tuple(fresh4(leq(addition(x0_2, multiplication(x0_2, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.21 = { by lemma 23 }
% 189.92/24.21 tuple(fresh4(leq(multiplication(x0_2, addition(multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))), one)), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.21 = { by axiom 4 (additive_commutativity) }
% 189.92/24.21 tuple(fresh4(leq(multiplication(x0_2, addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))), multiplication(x0_2, star(multiplication(x1_2, x0_2)))), true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.21 = { by axiom 7 (order_1) R->L }
% 189.92/24.21 tuple(fresh4(leq(multiplication(x0_2, addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))), multiplication(x0_2, fresh(true, true, multiplication(star(multiplication(x1_2, x0_2)), multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2))))), star(multiplication(x1_2, x0_2))))), true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.21 = { by axiom 9 (star_induction_left) R->L }
% 189.92/24.21 tuple(fresh4(leq(multiplication(x0_2, addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))), multiplication(x0_2, fresh(fresh4(true, true, multiplication(x1_2, x0_2), star(multiplication(x1_2, x0_2)), multiplication(multiplication(x1_2, x0_2), star(multiplication(x1_2, x0_2)))), true, multiplication(star(multiplication(x1_2, x0_2)), multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2))))), star(multiplication(x1_2, x0_2))))), true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.21 = { by axiom 8 (order) R->L }
% 189.92/24.21 tuple(fresh4(leq(multiplication(x0_2, addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))), multiplication(x0_2, fresh(fresh4(fresh3(star(multiplication(x1_2, x0_2)), star(multiplication(x1_2, x0_2)), multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))), star(multiplication(x1_2, x0_2))), true, multiplication(x1_2, x0_2), star(multiplication(x1_2, x0_2)), multiplication(multiplication(x1_2, x0_2), star(multiplication(x1_2, x0_2)))), true, multiplication(star(multiplication(x1_2, x0_2)), multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2))))), star(multiplication(x1_2, x0_2))))), true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.21 = { by lemma 26 R->L }
% 189.92/24.21 tuple(fresh4(leq(multiplication(x0_2, addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))), multiplication(x0_2, fresh(fresh4(fresh3(addition(one, addition(star(multiplication(x1_2, x0_2)), multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))), star(multiplication(x1_2, x0_2)), multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))), star(multiplication(x1_2, x0_2))), true, multiplication(x1_2, x0_2), star(multiplication(x1_2, x0_2)), multiplication(multiplication(x1_2, x0_2), star(multiplication(x1_2, x0_2)))), true, multiplication(star(multiplication(x1_2, x0_2)), multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2))))), star(multiplication(x1_2, x0_2))))), true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.21 = { by lemma 22 R->L }
% 189.92/24.22 tuple(fresh4(leq(multiplication(x0_2, addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))), multiplication(x0_2, fresh(fresh4(fresh3(addition(addition(star(multiplication(x1_2, x0_2)), multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2))))), addition(one, addition(star(multiplication(x1_2, x0_2)), multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2))))))), star(multiplication(x1_2, x0_2)), multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))), star(multiplication(x1_2, x0_2))), true, multiplication(x1_2, x0_2), star(multiplication(x1_2, x0_2)), multiplication(multiplication(x1_2, x0_2), star(multiplication(x1_2, x0_2)))), true, multiplication(star(multiplication(x1_2, x0_2)), multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2))))), star(multiplication(x1_2, x0_2))))), true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.22 = { by lemma 26 }
% 189.92/24.22 tuple(fresh4(leq(multiplication(x0_2, addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))), multiplication(x0_2, fresh(fresh4(fresh3(addition(addition(star(multiplication(x1_2, x0_2)), multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2))))), star(multiplication(x1_2, x0_2))), star(multiplication(x1_2, x0_2)), multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))), star(multiplication(x1_2, x0_2))), true, multiplication(x1_2, x0_2), star(multiplication(x1_2, x0_2)), multiplication(multiplication(x1_2, x0_2), star(multiplication(x1_2, x0_2)))), true, multiplication(star(multiplication(x1_2, x0_2)), multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2))))), star(multiplication(x1_2, x0_2))))), true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.22 = { by axiom 6 (additive_associativity) R->L }
% 189.92/24.22 tuple(fresh4(leq(multiplication(x0_2, addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))), multiplication(x0_2, fresh(fresh4(fresh3(addition(star(multiplication(x1_2, x0_2)), addition(multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))), star(multiplication(x1_2, x0_2)))), star(multiplication(x1_2, x0_2)), multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))), star(multiplication(x1_2, x0_2))), true, multiplication(x1_2, x0_2), star(multiplication(x1_2, x0_2)), multiplication(multiplication(x1_2, x0_2), star(multiplication(x1_2, x0_2)))), true, multiplication(star(multiplication(x1_2, x0_2)), multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2))))), star(multiplication(x1_2, x0_2))))), true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.22 = { by lemma 22 }
% 189.92/24.22 tuple(fresh4(leq(multiplication(x0_2, addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))), multiplication(x0_2, fresh(fresh4(fresh3(addition(multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))), star(multiplication(x1_2, x0_2))), star(multiplication(x1_2, x0_2)), multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))), star(multiplication(x1_2, x0_2))), true, multiplication(x1_2, x0_2), star(multiplication(x1_2, x0_2)), multiplication(multiplication(x1_2, x0_2), star(multiplication(x1_2, x0_2)))), true, multiplication(star(multiplication(x1_2, x0_2)), multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2))))), star(multiplication(x1_2, x0_2))))), true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.22 = { by axiom 14 (order) }
% 189.92/24.22 tuple(fresh4(leq(multiplication(x0_2, addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))), multiplication(x0_2, fresh(fresh4(leq(multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))), star(multiplication(x1_2, x0_2))), true, multiplication(x1_2, x0_2), star(multiplication(x1_2, x0_2)), multiplication(multiplication(x1_2, x0_2), star(multiplication(x1_2, x0_2)))), true, multiplication(star(multiplication(x1_2, x0_2)), multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2))))), star(multiplication(x1_2, x0_2))))), true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.22 = { by axiom 5 (multiplicative_associativity) }
% 189.92/24.22 tuple(fresh4(leq(multiplication(x0_2, addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))), multiplication(x0_2, fresh(fresh4(leq(multiplication(multiplication(x1_2, x0_2), star(multiplication(x1_2, x0_2))), star(multiplication(x1_2, x0_2))), true, multiplication(x1_2, x0_2), star(multiplication(x1_2, x0_2)), multiplication(multiplication(x1_2, x0_2), star(multiplication(x1_2, x0_2)))), true, multiplication(star(multiplication(x1_2, x0_2)), multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2))))), star(multiplication(x1_2, x0_2))))), true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.22 = { by axiom 3 (additive_idempotence) R->L }
% 189.92/24.22 tuple(fresh4(leq(multiplication(x0_2, addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))), multiplication(x0_2, fresh(fresh4(leq(addition(multiplication(multiplication(x1_2, x0_2), star(multiplication(x1_2, x0_2))), multiplication(multiplication(x1_2, x0_2), star(multiplication(x1_2, x0_2)))), star(multiplication(x1_2, x0_2))), true, multiplication(x1_2, x0_2), star(multiplication(x1_2, x0_2)), multiplication(multiplication(x1_2, x0_2), star(multiplication(x1_2, x0_2)))), true, multiplication(star(multiplication(x1_2, x0_2)), multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2))))), star(multiplication(x1_2, x0_2))))), true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.22 = { by axiom 17 (star_induction_left) }
% 189.92/24.22 tuple(fresh4(leq(multiplication(x0_2, addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))), multiplication(x0_2, fresh(leq(multiplication(star(multiplication(x1_2, x0_2)), multiplication(multiplication(x1_2, x0_2), star(multiplication(x1_2, x0_2)))), star(multiplication(x1_2, x0_2))), true, multiplication(star(multiplication(x1_2, x0_2)), multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2))))), star(multiplication(x1_2, x0_2))))), true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.22 = { by axiom 5 (multiplicative_associativity) R->L }
% 189.92/24.22 tuple(fresh4(leq(multiplication(x0_2, addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))), multiplication(x0_2, fresh(leq(multiplication(star(multiplication(x1_2, x0_2)), multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2))))), star(multiplication(x1_2, x0_2))), true, multiplication(star(multiplication(x1_2, x0_2)), multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2))))), star(multiplication(x1_2, x0_2))))), true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.22 = { by axiom 13 (order_1) }
% 189.92/24.22 tuple(fresh4(leq(multiplication(x0_2, addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))), multiplication(x0_2, addition(multiplication(star(multiplication(x1_2, x0_2)), multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2))))), star(multiplication(x1_2, x0_2))))), true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.22 = { by axiom 4 (additive_commutativity) }
% 189.92/24.22 tuple(fresh4(leq(multiplication(x0_2, addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))), multiplication(x0_2, addition(star(multiplication(x1_2, x0_2)), multiplication(star(multiplication(x1_2, x0_2)), multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))))), true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.22 = { by lemma 23 }
% 189.92/24.22 tuple(fresh4(leq(multiplication(x0_2, addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))), multiplication(x0_2, multiplication(star(multiplication(x1_2, x0_2)), addition(multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))), one)))), true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.22 = { by axiom 4 (additive_commutativity) }
% 189.92/24.22 tuple(fresh4(leq(multiplication(x0_2, addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))), multiplication(x0_2, multiplication(star(multiplication(x1_2, x0_2)), addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))))), true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.22 = { by axiom 5 (multiplicative_associativity) }
% 189.92/24.22 tuple(fresh4(leq(multiplication(x0_2, addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))), multiplication(multiplication(x0_2, star(multiplication(x1_2, x0_2))), addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2))))))), true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.22 = { by lemma 21 R->L }
% 189.92/24.22 tuple(fresh4(leq(multiplication(x0_2, addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))), multiplication(multiplication(x0_2, addition(one, star(multiplication(x1_2, x0_2)))), addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2))))))), true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.22 = { by axiom 4 (additive_commutativity) R->L }
% 189.92/24.22 tuple(fresh4(leq(multiplication(x0_2, addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))), multiplication(multiplication(x0_2, addition(star(multiplication(x1_2, x0_2)), one)), addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2))))))), true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.22 = { by axiom 11 (right_distributivity) }
% 189.92/24.22 tuple(fresh4(leq(multiplication(x0_2, addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))), multiplication(addition(multiplication(x0_2, star(multiplication(x1_2, x0_2))), multiplication(x0_2, one)), addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2))))))), true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.22 = { by axiom 1 (multiplicative_right_identity) }
% 189.92/24.22 tuple(fresh4(leq(multiplication(x0_2, addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))), multiplication(addition(multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2))))))), true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.22 = { by axiom 4 (additive_commutativity) }
% 189.92/24.22 tuple(fresh4(leq(multiplication(x0_2, addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))), multiplication(addition(x0_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))), addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2))))))), true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.22 = { by axiom 12 (left_distributivity) }
% 189.92/24.22 tuple(fresh4(leq(multiplication(x0_2, addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))), addition(multiplication(x0_2, addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))), multiplication(multiplication(x0_2, star(multiplication(x1_2, x0_2))), addition(one, multiplication(x1_2, multiplication(x0_2, star(multiplication(x1_2, x0_2)))))))), true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.22 = { by lemma 24 }
% 189.92/24.22 tuple(fresh4(true, true, multiplication(x0_2, x1_2), multiplication(x0_2, star(multiplication(x1_2, x0_2))), x0_2), true)
% 189.92/24.22 = { by axiom 9 (star_induction_left) }
% 189.92/24.22 tuple(true, true)
% 189.92/24.22 % SZS output end Proof
% 189.92/24.22
% 189.92/24.22 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------