TSTP Solution File: KLE043+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : KLE043+1 : 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 : n004.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 48.43s 6.55s
% Output : Proof 48.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE043+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % 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 : n004.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 11:35:37 EDT 2023
% 0.13/0.34 % CPUTime :
% 48.43/6.55 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 48.43/6.55
% 48.43/6.55 % SZS status Theorem
% 48.43/6.55
% 48.69/6.57 % SZS output start Proof
% 48.69/6.57 Take the following subset of the input axioms:
% 48.69/6.58 fof(additive_associativity, axiom, ![A, B, C]: addition(A, addition(B, C))=addition(addition(A, B), C)).
% 48.69/6.58 fof(additive_commutativity, axiom, ![A3, B2]: addition(A3, B2)=addition(B2, A3)).
% 48.69/6.58 fof(additive_idempotence, axiom, ![A3]: addition(A3, A3)=A3).
% 48.69/6.58 fof(goals, conjecture, ![X0, X1]: multiplication(star(X0), X1)=addition(X1, multiplication(multiplication(X0, star(X0)), X1))).
% 48.69/6.58 fof(left_distributivity, axiom, ![A3, B2, C2]: multiplication(addition(A3, B2), C2)=addition(multiplication(A3, C2), multiplication(B2, C2))).
% 48.69/6.58 fof(multiplicative_left_identity, axiom, ![A3]: multiplication(one, A3)=A3).
% 48.69/6.58 fof(multiplicative_right_identity, axiom, ![A3]: multiplication(A3, one)=A3).
% 48.69/6.58 fof(order, axiom, ![A2, B2]: (leq(A2, B2) <=> addition(A2, B2)=B2)).
% 48.69/6.58 fof(right_distributivity, axiom, ![A3, B2, C2]: multiplication(A3, addition(B2, C2))=addition(multiplication(A3, B2), multiplication(A3, C2))).
% 48.69/6.58 fof(star_induction_left, axiom, ![B2, C2, A2_2]: (leq(addition(multiplication(A2_2, B2), C2), B2) => leq(multiplication(star(A2_2), C2), B2))).
% 48.69/6.58 fof(star_unfold_right, axiom, ![A3]: leq(addition(one, multiplication(A3, star(A3))), star(A3))).
% 48.69/6.58
% 48.69/6.58 Now clausify the problem and encode Horn clauses using encoding 3 of
% 48.69/6.58 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 48.69/6.58 We repeatedly replace C & s=t => u=v by the two clauses:
% 48.69/6.58 fresh(y, y, x1...xn) = u
% 48.69/6.58 C => fresh(s, t, x1...xn) = v
% 48.69/6.58 where fresh is a fresh function symbol and x1..xn are the free
% 48.69/6.58 variables of u and v.
% 48.69/6.58 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 48.69/6.58 input problem has no model of domain size 1).
% 48.69/6.58
% 48.69/6.58 The encoding turns the above axioms into the following unit equations and goals:
% 48.69/6.58
% 48.69/6.58 Axiom 1 (multiplicative_right_identity): multiplication(X, one) = X.
% 48.69/6.58 Axiom 2 (multiplicative_left_identity): multiplication(one, X) = X.
% 48.69/6.58 Axiom 3 (additive_idempotence): addition(X, X) = X.
% 48.69/6.58 Axiom 4 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 48.69/6.58 Axiom 5 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 48.69/6.58 Axiom 6 (order_1): fresh(X, X, Y, Z) = Z.
% 48.69/6.58 Axiom 7 (order): fresh3(X, X, Y, Z) = true.
% 48.69/6.58 Axiom 8 (star_induction_left): fresh4(X, X, Y, Z, W) = true.
% 48.69/6.58 Axiom 9 (right_distributivity): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 48.69/6.58 Axiom 10 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 48.69/6.58 Axiom 11 (order_1): fresh(leq(X, Y), true, X, Y) = addition(X, Y).
% 48.69/6.58 Axiom 12 (order): fresh3(addition(X, Y), Y, X, Y) = leq(X, Y).
% 48.69/6.58 Axiom 13 (star_unfold_right): leq(addition(one, multiplication(X, star(X))), star(X)) = true.
% 48.69/6.58 Axiom 14 (star_induction_left): fresh4(leq(addition(multiplication(X, Y), Z), Y), true, X, Y, Z) = leq(multiplication(star(X), Z), Y).
% 48.69/6.58
% 48.69/6.58 Lemma 15: addition(one, addition(multiplication(X, star(X)), star(X))) = star(X).
% 48.69/6.58 Proof:
% 48.69/6.58 addition(one, addition(multiplication(X, star(X)), star(X)))
% 48.69/6.58 = { by axiom 5 (additive_associativity) }
% 48.69/6.58 addition(addition(one, multiplication(X, star(X))), star(X))
% 48.69/6.58 = { by axiom 11 (order_1) R->L }
% 48.69/6.58 fresh(leq(addition(one, multiplication(X, star(X))), star(X)), true, addition(one, multiplication(X, star(X))), star(X))
% 48.69/6.58 = { by axiom 13 (star_unfold_right) }
% 48.69/6.58 fresh(true, true, addition(one, multiplication(X, star(X))), star(X))
% 48.69/6.58 = { by axiom 6 (order_1) }
% 48.69/6.58 star(X)
% 48.69/6.58
% 48.69/6.58 Lemma 16: addition(X, addition(X, Y)) = addition(X, Y).
% 48.69/6.58 Proof:
% 48.69/6.58 addition(X, addition(X, Y))
% 48.69/6.58 = { by axiom 5 (additive_associativity) }
% 48.69/6.58 addition(addition(X, X), Y)
% 48.69/6.58 = { by axiom 3 (additive_idempotence) }
% 48.69/6.58 addition(X, Y)
% 48.69/6.58
% 48.69/6.58 Lemma 17: addition(one, star(X)) = star(X).
% 48.69/6.58 Proof:
% 48.69/6.58 addition(one, star(X))
% 48.69/6.58 = { by lemma 15 R->L }
% 48.69/6.58 addition(one, addition(one, addition(multiplication(X, star(X)), star(X))))
% 48.69/6.58 = { by lemma 16 }
% 48.69/6.58 addition(one, addition(multiplication(X, star(X)), star(X)))
% 48.69/6.58 = { by lemma 15 }
% 48.69/6.58 star(X)
% 48.69/6.58
% 48.69/6.58 Lemma 18: addition(X, multiplication(X, Y)) = multiplication(X, addition(Y, one)).
% 48.69/6.58 Proof:
% 48.69/6.58 addition(X, multiplication(X, Y))
% 48.69/6.58 = { by axiom 1 (multiplicative_right_identity) R->L }
% 48.69/6.58 addition(multiplication(X, one), multiplication(X, Y))
% 48.69/6.58 = { by axiom 9 (right_distributivity) R->L }
% 48.69/6.58 multiplication(X, addition(one, Y))
% 48.69/6.58 = { by axiom 4 (additive_commutativity) }
% 48.69/6.58 multiplication(X, addition(Y, one))
% 48.69/6.58
% 48.69/6.58 Lemma 19: addition(X, multiplication(Y, X)) = multiplication(addition(Y, one), X).
% 48.69/6.58 Proof:
% 48.69/6.58 addition(X, multiplication(Y, X))
% 48.69/6.58 = { by axiom 2 (multiplicative_left_identity) R->L }
% 48.69/6.58 addition(multiplication(one, X), multiplication(Y, X))
% 48.69/6.58 = { by axiom 10 (left_distributivity) R->L }
% 48.69/6.58 multiplication(addition(one, Y), X)
% 48.69/6.58 = { by axiom 4 (additive_commutativity) }
% 48.69/6.58 multiplication(addition(Y, one), X)
% 48.69/6.58
% 48.69/6.58 Lemma 20: addition(multiplication(X, Y), multiplication(X, Z)) = multiplication(X, addition(Z, Y)).
% 48.69/6.58 Proof:
% 48.69/6.58 addition(multiplication(X, Y), multiplication(X, Z))
% 48.69/6.58 = { by axiom 9 (right_distributivity) R->L }
% 48.69/6.58 multiplication(X, addition(Y, Z))
% 48.69/6.58 = { by axiom 4 (additive_commutativity) }
% 48.69/6.58 multiplication(X, addition(Z, Y))
% 48.69/6.58
% 48.69/6.58 Lemma 21: addition(multiplication(X, star(X)), star(X)) = star(X).
% 48.69/6.58 Proof:
% 48.69/6.58 addition(multiplication(X, star(X)), star(X))
% 48.69/6.58 = { by axiom 3 (additive_idempotence) R->L }
% 48.69/6.58 addition(multiplication(X, star(X)), addition(star(X), star(X)))
% 48.69/6.58 = { by axiom 5 (additive_associativity) }
% 48.69/6.58 addition(addition(multiplication(X, star(X)), star(X)), star(X))
% 48.69/6.58 = { by lemma 15 R->L }
% 48.69/6.58 addition(addition(multiplication(X, star(X)), star(X)), addition(one, addition(multiplication(X, star(X)), star(X))))
% 48.69/6.58 = { by lemma 16 R->L }
% 48.69/6.58 addition(addition(multiplication(X, star(X)), star(X)), addition(one, addition(one, addition(multiplication(X, star(X)), star(X)))))
% 48.69/6.58 = { by axiom 4 (additive_commutativity) R->L }
% 48.69/6.58 addition(addition(multiplication(X, star(X)), star(X)), addition(one, addition(addition(multiplication(X, star(X)), star(X)), one)))
% 48.69/6.58 = { by axiom 5 (additive_associativity) }
% 48.69/6.58 addition(addition(addition(multiplication(X, star(X)), star(X)), one), addition(addition(multiplication(X, star(X)), star(X)), one))
% 48.69/6.58 = { by axiom 3 (additive_idempotence) }
% 48.69/6.58 addition(addition(multiplication(X, star(X)), star(X)), one)
% 48.69/6.58 = { by axiom 4 (additive_commutativity) }
% 48.69/6.58 addition(one, addition(multiplication(X, star(X)), star(X)))
% 48.69/6.58 = { by lemma 15 }
% 48.69/6.58 star(X)
% 48.69/6.58
% 48.69/6.58 Lemma 22: fresh4(leq(addition(X, multiplication(Y, Z)), Z), true, Y, Z, X) = leq(multiplication(star(Y), X), Z).
% 48.69/6.58 Proof:
% 48.69/6.58 fresh4(leq(addition(X, multiplication(Y, Z)), Z), true, Y, Z, X)
% 48.69/6.58 = { by axiom 4 (additive_commutativity) R->L }
% 48.69/6.58 fresh4(leq(addition(multiplication(Y, Z), X), Z), true, Y, Z, X)
% 48.69/6.58 = { by axiom 14 (star_induction_left) }
% 48.69/6.58 leq(multiplication(star(Y), X), Z)
% 48.69/6.58
% 48.69/6.58 Goal 1 (goals): multiplication(star(x0), x1) = addition(x1, multiplication(multiplication(x0, star(x0)), x1)).
% 48.69/6.58 Proof:
% 48.69/6.58 multiplication(star(x0), x1)
% 48.69/6.58 = { by lemma 21 R->L }
% 48.69/6.58 multiplication(addition(multiplication(x0, star(x0)), star(x0)), x1)
% 48.69/6.58 = { by axiom 4 (additive_commutativity) R->L }
% 48.69/6.58 multiplication(addition(star(x0), multiplication(x0, star(x0))), x1)
% 48.69/6.58 = { by lemma 17 R->L }
% 48.69/6.58 multiplication(addition(addition(one, star(x0)), multiplication(x0, star(x0))), x1)
% 48.69/6.58 = { by axiom 5 (additive_associativity) R->L }
% 48.69/6.58 multiplication(addition(one, addition(star(x0), multiplication(x0, star(x0)))), x1)
% 48.69/6.58 = { by axiom 4 (additive_commutativity) R->L }
% 48.69/6.58 multiplication(addition(one, addition(multiplication(x0, star(x0)), star(x0))), x1)
% 48.69/6.58 = { by axiom 5 (additive_associativity) }
% 48.69/6.58 multiplication(addition(addition(one, multiplication(x0, star(x0))), star(x0)), x1)
% 48.69/6.58 = { by axiom 4 (additive_commutativity) }
% 48.69/6.58 multiplication(addition(star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.58 = { by axiom 11 (order_1) R->L }
% 48.69/6.58 multiplication(fresh(leq(star(x0), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.58 = { by axiom 6 (order_1) R->L }
% 48.69/6.58 multiplication(fresh(leq(fresh(true, true, multiplication(star(x0), multiplication(x0, star(x0))), star(x0)), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.58 = { by axiom 8 (star_induction_left) R->L }
% 48.69/6.58 multiplication(fresh(leq(fresh(fresh4(true, true, x0, star(x0), multiplication(x0, star(x0))), true, multiplication(star(x0), multiplication(x0, star(x0))), star(x0)), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.58 = { by axiom 7 (order) R->L }
% 48.69/6.59 multiplication(fresh(leq(fresh(fresh4(fresh3(star(x0), star(x0), multiplication(x0, star(x0)), star(x0)), true, x0, star(x0), multiplication(x0, star(x0))), true, multiplication(star(x0), multiplication(x0, star(x0))), star(x0)), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.59 = { by lemma 21 R->L }
% 48.69/6.59 multiplication(fresh(leq(fresh(fresh4(fresh3(addition(multiplication(x0, star(x0)), star(x0)), star(x0), multiplication(x0, star(x0)), star(x0)), true, x0, star(x0), multiplication(x0, star(x0))), true, multiplication(star(x0), multiplication(x0, star(x0))), star(x0)), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.59 = { by axiom 12 (order) }
% 48.69/6.59 multiplication(fresh(leq(fresh(fresh4(leq(multiplication(x0, star(x0)), star(x0)), true, x0, star(x0), multiplication(x0, star(x0))), true, multiplication(star(x0), multiplication(x0, star(x0))), star(x0)), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.59 = { by axiom 3 (additive_idempotence) R->L }
% 48.69/6.59 multiplication(fresh(leq(fresh(fresh4(leq(addition(multiplication(x0, star(x0)), multiplication(x0, star(x0))), star(x0)), true, x0, star(x0), multiplication(x0, star(x0))), true, multiplication(star(x0), multiplication(x0, star(x0))), star(x0)), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.59 = { by lemma 22 }
% 48.69/6.59 multiplication(fresh(leq(fresh(leq(multiplication(star(x0), multiplication(x0, star(x0))), star(x0)), true, multiplication(star(x0), multiplication(x0, star(x0))), star(x0)), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.59 = { by axiom 11 (order_1) }
% 48.69/6.59 multiplication(fresh(leq(addition(multiplication(star(x0), multiplication(x0, star(x0))), star(x0)), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.59 = { by axiom 4 (additive_commutativity) }
% 48.69/6.59 multiplication(fresh(leq(addition(star(x0), multiplication(star(x0), multiplication(x0, star(x0)))), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.59 = { by lemma 18 }
% 48.69/6.59 multiplication(fresh(leq(multiplication(star(x0), addition(multiplication(x0, star(x0)), one)), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.59 = { by axiom 4 (additive_commutativity) }
% 48.69/6.59 multiplication(fresh(leq(multiplication(star(x0), addition(one, multiplication(x0, star(x0)))), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.59 = { by lemma 22 R->L }
% 48.69/6.59 multiplication(fresh(fresh4(leq(addition(addition(one, multiplication(x0, star(x0))), multiplication(x0, addition(one, multiplication(x0, star(x0))))), addition(one, multiplication(x0, star(x0)))), true, x0, addition(one, multiplication(x0, star(x0))), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.59 = { by lemma 19 }
% 48.69/6.59 multiplication(fresh(fresh4(leq(multiplication(addition(x0, one), addition(one, multiplication(x0, star(x0)))), addition(one, multiplication(x0, star(x0)))), true, x0, addition(one, multiplication(x0, star(x0))), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.59 = { by axiom 4 (additive_commutativity) R->L }
% 48.69/6.59 multiplication(fresh(fresh4(leq(multiplication(addition(x0, one), addition(multiplication(x0, star(x0)), one)), addition(one, multiplication(x0, star(x0)))), true, x0, addition(one, multiplication(x0, star(x0))), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.59 = { by lemma 18 R->L }
% 48.69/6.59 multiplication(fresh(fresh4(leq(addition(addition(x0, one), multiplication(addition(x0, one), multiplication(x0, star(x0)))), addition(one, multiplication(x0, star(x0)))), true, x0, addition(one, multiplication(x0, star(x0))), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.59 = { by lemma 19 R->L }
% 48.69/6.59 multiplication(fresh(fresh4(leq(addition(addition(x0, one), addition(multiplication(x0, star(x0)), multiplication(x0, multiplication(x0, star(x0))))), addition(one, multiplication(x0, star(x0)))), true, x0, addition(one, multiplication(x0, star(x0))), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.59 = { by lemma 20 }
% 48.69/6.59 multiplication(fresh(fresh4(leq(addition(addition(x0, one), multiplication(x0, addition(multiplication(x0, star(x0)), star(x0)))), addition(one, multiplication(x0, star(x0)))), true, x0, addition(one, multiplication(x0, star(x0))), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.59 = { by lemma 21 }
% 48.69/6.59 multiplication(fresh(fresh4(leq(addition(addition(x0, one), multiplication(x0, star(x0))), addition(one, multiplication(x0, star(x0)))), true, x0, addition(one, multiplication(x0, star(x0))), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.59 = { by axiom 5 (additive_associativity) R->L }
% 48.69/6.59 multiplication(fresh(fresh4(leq(addition(x0, addition(one, multiplication(x0, star(x0)))), addition(one, multiplication(x0, star(x0)))), true, x0, addition(one, multiplication(x0, star(x0))), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.59 = { by axiom 4 (additive_commutativity) R->L }
% 48.69/6.59 multiplication(fresh(fresh4(leq(addition(x0, addition(multiplication(x0, star(x0)), one)), addition(one, multiplication(x0, star(x0)))), true, x0, addition(one, multiplication(x0, star(x0))), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.59 = { by axiom 5 (additive_associativity) }
% 48.69/6.59 multiplication(fresh(fresh4(leq(addition(addition(x0, multiplication(x0, star(x0))), one), addition(one, multiplication(x0, star(x0)))), true, x0, addition(one, multiplication(x0, star(x0))), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.59 = { by axiom 4 (additive_commutativity) R->L }
% 48.69/6.59 multiplication(fresh(fresh4(leq(addition(addition(multiplication(x0, star(x0)), x0), one), addition(one, multiplication(x0, star(x0)))), true, x0, addition(one, multiplication(x0, star(x0))), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.59 = { by axiom 1 (multiplicative_right_identity) R->L }
% 48.69/6.59 multiplication(fresh(fresh4(leq(addition(addition(multiplication(x0, star(x0)), multiplication(x0, one)), one), addition(one, multiplication(x0, star(x0)))), true, x0, addition(one, multiplication(x0, star(x0))), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.59 = { by lemma 20 }
% 48.69/6.59 multiplication(fresh(fresh4(leq(addition(multiplication(x0, addition(one, star(x0))), one), addition(one, multiplication(x0, star(x0)))), true, x0, addition(one, multiplication(x0, star(x0))), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.59 = { by lemma 17 }
% 48.69/6.59 multiplication(fresh(fresh4(leq(addition(multiplication(x0, star(x0)), one), addition(one, multiplication(x0, star(x0)))), true, x0, addition(one, multiplication(x0, star(x0))), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.59 = { by axiom 4 (additive_commutativity) }
% 48.69/6.59 multiplication(fresh(fresh4(leq(addition(one, multiplication(x0, star(x0))), addition(one, multiplication(x0, star(x0)))), true, x0, addition(one, multiplication(x0, star(x0))), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.59 = { by axiom 12 (order) R->L }
% 48.69/6.59 multiplication(fresh(fresh4(fresh3(addition(addition(one, multiplication(x0, star(x0))), addition(one, multiplication(x0, star(x0)))), addition(one, multiplication(x0, star(x0))), addition(one, multiplication(x0, star(x0))), addition(one, multiplication(x0, star(x0)))), true, x0, addition(one, multiplication(x0, star(x0))), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.59 = { by axiom 3 (additive_idempotence) }
% 48.69/6.59 multiplication(fresh(fresh4(fresh3(addition(one, multiplication(x0, star(x0))), addition(one, multiplication(x0, star(x0))), addition(one, multiplication(x0, star(x0))), addition(one, multiplication(x0, star(x0)))), true, x0, addition(one, multiplication(x0, star(x0))), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.59 = { by axiom 7 (order) }
% 48.69/6.59 multiplication(fresh(fresh4(true, true, x0, addition(one, multiplication(x0, star(x0))), addition(one, multiplication(x0, star(x0)))), true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.59 = { by axiom 8 (star_induction_left) }
% 48.69/6.59 multiplication(fresh(true, true, star(x0), addition(one, multiplication(x0, star(x0)))), x1)
% 48.69/6.59 = { by axiom 6 (order_1) }
% 48.69/6.59 multiplication(addition(one, multiplication(x0, star(x0))), x1)
% 48.69/6.59 = { by axiom 4 (additive_commutativity) R->L }
% 48.69/6.59 multiplication(addition(multiplication(x0, star(x0)), one), x1)
% 48.69/6.59 = { by lemma 19 R->L }
% 48.69/6.59 addition(x1, multiplication(multiplication(x0, star(x0)), x1))
% 48.69/6.59 % SZS output end Proof
% 48.69/6.59
% 48.69/6.59 RESULT: Theorem (the conjecture is true).
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