TSTP Solution File: KLE039+2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : KLE039+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 : n014.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 05:35:37 EDT 2023
% Result : Theorem 13.38s 2.64s
% Output : Proof 13.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : KLE039+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.35 % Computer : n014.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Aug 29 11:16:45 EDT 2023
% 0.15/0.35 % CPUTime :
% 13.38/2.64 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 13.38/2.64
% 13.38/2.64 % SZS status Theorem
% 13.38/2.64
% 13.38/2.66 % SZS output start Proof
% 13.38/2.68 Take the following subset of the input axioms:
% 13.38/2.68 fof(additive_associativity, axiom, ![A, B, C]: addition(A, addition(B, C))=addition(addition(A, B), C)).
% 13.38/2.68 fof(additive_commutativity, axiom, ![A3, B2]: addition(A3, B2)=addition(B2, A3)).
% 13.38/2.68 fof(additive_idempotence, axiom, ![A3]: addition(A3, A3)=A3).
% 13.38/2.68 fof(goals, conjecture, ![X0]: (leq(star(star(X0)), star(X0)) & leq(star(X0), star(star(X0))))).
% 13.38/2.68 fof(left_distributivity, axiom, ![A3, B2, C2]: multiplication(addition(A3, B2), C2)=addition(multiplication(A3, C2), multiplication(B2, C2))).
% 13.38/2.68 fof(multiplicative_associativity, axiom, ![A3, B2, C2]: multiplication(A3, multiplication(B2, C2))=multiplication(multiplication(A3, B2), C2)).
% 13.38/2.68 fof(multiplicative_left_identity, axiom, ![A3]: multiplication(one, A3)=A3).
% 13.38/2.68 fof(multiplicative_right_identity, axiom, ![A3]: multiplication(A3, one)=A3).
% 13.38/2.68 fof(order, axiom, ![A2, B2]: (leq(A2, B2) <=> addition(A2, B2)=B2)).
% 13.38/2.68 fof(right_distributivity, axiom, ![A3, B2, C2]: multiplication(A3, addition(B2, C2))=addition(multiplication(A3, B2), multiplication(A3, C2))).
% 13.38/2.68 fof(star_induction_left, axiom, ![B2, C2, A2_2]: (leq(addition(multiplication(A2_2, B2), C2), B2) => leq(multiplication(star(A2_2), C2), B2))).
% 13.38/2.68 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))).
% 13.38/2.68 fof(star_unfold_right, axiom, ![A3]: leq(addition(one, multiplication(A3, star(A3))), star(A3))).
% 13.38/2.68
% 13.38/2.68 Now clausify the problem and encode Horn clauses using encoding 3 of
% 13.38/2.68 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 13.38/2.68 We repeatedly replace C & s=t => u=v by the two clauses:
% 13.38/2.68 fresh(y, y, x1...xn) = u
% 13.38/2.68 C => fresh(s, t, x1...xn) = v
% 13.38/2.68 where fresh is a fresh function symbol and x1..xn are the free
% 13.38/2.68 variables of u and v.
% 13.38/2.68 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 13.38/2.68 input problem has no model of domain size 1).
% 13.38/2.68
% 13.38/2.68 The encoding turns the above axioms into the following unit equations and goals:
% 13.38/2.68
% 13.38/2.68 Axiom 1 (multiplicative_right_identity): multiplication(X, one) = X.
% 13.38/2.68 Axiom 2 (multiplicative_left_identity): multiplication(one, X) = X.
% 13.38/2.68 Axiom 3 (additive_idempotence): addition(X, X) = X.
% 13.38/2.68 Axiom 4 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 13.38/2.68 Axiom 5 (multiplicative_associativity): multiplication(X, multiplication(Y, Z)) = multiplication(multiplication(X, Y), Z).
% 13.38/2.68 Axiom 6 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 13.38/2.68 Axiom 7 (order_1): fresh(X, X, Y, Z) = Z.
% 13.38/2.68 Axiom 8 (order): fresh3(X, X, Y, Z) = true.
% 13.38/2.68 Axiom 9 (star_induction_left): fresh4(X, X, Y, Z, W) = true.
% 13.38/2.68 Axiom 10 (star_induction_right): fresh2(X, X, Y, Z, W) = true.
% 13.38/2.68 Axiom 11 (right_distributivity): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 13.38/2.68 Axiom 12 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 13.38/2.68 Axiom 13 (order_1): fresh(leq(X, Y), true, X, Y) = addition(X, Y).
% 13.38/2.68 Axiom 14 (order): fresh3(addition(X, Y), Y, X, Y) = leq(X, Y).
% 13.38/2.68 Axiom 15 (star_unfold_right): leq(addition(one, multiplication(X, star(X))), star(X)) = true.
% 13.38/2.68 Axiom 16 (star_induction_left): fresh4(leq(addition(multiplication(X, Y), Z), Y), true, X, Y, Z) = leq(multiplication(star(X), Z), Y).
% 13.38/2.68 Axiom 17 (star_induction_right): fresh2(leq(addition(multiplication(X, Y), Z), X), true, X, Y, Z) = leq(multiplication(Z, star(Y)), X).
% 13.38/2.68
% 13.38/2.68 Lemma 18: addition(multiplication(X, Y), Y) = multiplication(addition(X, one), Y).
% 13.38/2.68 Proof:
% 13.38/2.68 addition(multiplication(X, Y), Y)
% 13.38/2.68 = { by axiom 2 (multiplicative_left_identity) R->L }
% 13.38/2.68 addition(multiplication(X, Y), multiplication(one, Y))
% 13.38/2.68 = { by axiom 12 (left_distributivity) R->L }
% 13.38/2.68 multiplication(addition(X, one), Y)
% 13.38/2.68
% 13.38/2.68 Lemma 19: addition(multiplication(addition(X, one), star(X)), one) = star(X).
% 13.38/2.68 Proof:
% 13.38/2.68 addition(multiplication(addition(X, one), star(X)), one)
% 13.38/2.68 = { by axiom 4 (additive_commutativity) }
% 13.38/2.68 addition(one, multiplication(addition(X, one), star(X)))
% 13.38/2.68 = { by lemma 18 R->L }
% 13.38/2.68 addition(one, addition(multiplication(X, star(X)), star(X)))
% 13.38/2.68 = { by axiom 6 (additive_associativity) }
% 13.38/2.68 addition(addition(one, multiplication(X, star(X))), star(X))
% 13.38/2.68 = { by axiom 13 (order_1) R->L }
% 13.38/2.68 fresh(leq(addition(one, multiplication(X, star(X))), star(X)), true, addition(one, multiplication(X, star(X))), star(X))
% 13.38/2.68 = { by axiom 15 (star_unfold_right) }
% 13.38/2.68 fresh(true, true, addition(one, multiplication(X, star(X))), star(X))
% 13.38/2.68 = { by axiom 7 (order_1) }
% 13.38/2.68 star(X)
% 13.38/2.68
% 13.38/2.68 Lemma 20: addition(X, addition(X, Y)) = addition(X, Y).
% 13.38/2.68 Proof:
% 13.38/2.68 addition(X, addition(X, Y))
% 13.38/2.68 = { by axiom 6 (additive_associativity) }
% 13.38/2.68 addition(addition(X, X), Y)
% 13.38/2.68 = { by axiom 3 (additive_idempotence) }
% 13.38/2.68 addition(X, Y)
% 13.38/2.68
% 13.38/2.68 Lemma 21: addition(X, addition(Y, X)) = addition(Y, X).
% 13.38/2.68 Proof:
% 13.38/2.68 addition(X, addition(Y, X))
% 13.38/2.68 = { by axiom 4 (additive_commutativity) }
% 13.38/2.68 addition(X, addition(X, Y))
% 13.38/2.68 = { by lemma 20 }
% 13.38/2.68 addition(X, Y)
% 13.38/2.68 = { by axiom 4 (additive_commutativity) R->L }
% 13.38/2.68 addition(Y, X)
% 13.38/2.68
% 13.38/2.68 Lemma 22: addition(one, star(X)) = star(X).
% 13.38/2.68 Proof:
% 13.38/2.68 addition(one, star(X))
% 13.38/2.68 = { by lemma 19 R->L }
% 13.38/2.68 addition(one, addition(multiplication(addition(X, one), star(X)), one))
% 13.38/2.68 = { by lemma 21 }
% 13.38/2.68 addition(multiplication(addition(X, one), star(X)), one)
% 13.38/2.68 = { by lemma 19 }
% 13.38/2.68 star(X)
% 13.38/2.68
% 13.38/2.68 Lemma 23: addition(Z, addition(X, Y)) = addition(X, addition(Y, Z)).
% 13.38/2.68 Proof:
% 13.38/2.68 addition(Z, addition(X, Y))
% 13.38/2.68 = { by axiom 4 (additive_commutativity) R->L }
% 13.38/2.68 addition(addition(X, Y), Z)
% 13.38/2.68 = { by axiom 6 (additive_associativity) R->L }
% 13.38/2.68 addition(X, addition(Y, Z))
% 13.38/2.68
% 13.38/2.68 Lemma 24: addition(one, addition(multiplication(X, star(X)), star(X))) = star(X).
% 13.38/2.68 Proof:
% 13.38/2.68 addition(one, addition(multiplication(X, star(X)), star(X)))
% 13.38/2.68 = { by axiom 6 (additive_associativity) }
% 13.38/2.68 addition(addition(one, multiplication(X, star(X))), star(X))
% 13.38/2.68 = { by axiom 13 (order_1) R->L }
% 13.38/2.68 fresh(leq(addition(one, multiplication(X, star(X))), star(X)), true, addition(one, multiplication(X, star(X))), star(X))
% 13.38/2.68 = { by axiom 15 (star_unfold_right) }
% 13.38/2.68 fresh(true, true, addition(one, multiplication(X, star(X))), star(X))
% 13.38/2.68 = { by axiom 7 (order_1) }
% 13.38/2.68 star(X)
% 13.38/2.68
% 13.38/2.68 Lemma 25: addition(multiplication(X, star(X)), star(X)) = star(X).
% 13.38/2.68 Proof:
% 13.38/2.68 addition(multiplication(X, star(X)), star(X))
% 13.38/2.68 = { by lemma 21 R->L }
% 13.38/2.68 addition(star(X), addition(multiplication(X, star(X)), star(X)))
% 13.38/2.68 = { by axiom 4 (additive_commutativity) R->L }
% 13.38/2.68 addition(addition(multiplication(X, star(X)), star(X)), star(X))
% 13.38/2.68 = { by lemma 24 R->L }
% 13.38/2.68 addition(addition(multiplication(X, star(X)), star(X)), addition(one, addition(multiplication(X, star(X)), star(X))))
% 13.38/2.68 = { by lemma 21 }
% 13.38/2.68 addition(one, addition(multiplication(X, star(X)), star(X)))
% 13.38/2.68 = { by lemma 24 }
% 13.38/2.68 star(X)
% 13.38/2.68
% 13.38/2.68 Goal 1 (goals): tuple(leq(star(star(x0_2)), star(x0_2)), leq(star(x0), star(star(x0)))) = tuple(true, true).
% 13.38/2.68 Proof:
% 13.38/2.68 tuple(leq(star(star(x0_2)), star(x0_2)), leq(star(x0), star(star(x0))))
% 13.38/2.68 = { by axiom 14 (order) R->L }
% 13.38/2.68 tuple(leq(star(star(x0_2)), star(x0_2)), fresh3(addition(star(x0), star(star(x0))), star(star(x0)), star(x0), star(star(x0))))
% 13.38/2.68 = { by lemma 19 R->L }
% 13.38/2.68 tuple(leq(star(star(x0_2)), star(x0_2)), fresh3(addition(star(x0), addition(multiplication(addition(star(x0), one), star(star(x0))), one)), star(star(x0)), star(x0), star(star(x0))))
% 13.38/2.68 = { by axiom 4 (additive_commutativity) }
% 13.38/2.68 tuple(leq(star(star(x0_2)), star(x0_2)), fresh3(addition(star(x0), addition(multiplication(addition(one, star(x0)), star(star(x0))), one)), star(star(x0)), star(x0), star(star(x0))))
% 13.38/2.68 = { by lemma 23 }
% 13.38/2.68 tuple(leq(star(star(x0_2)), star(x0_2)), fresh3(addition(multiplication(addition(one, star(x0)), star(star(x0))), addition(one, star(x0))), star(star(x0)), star(x0), star(star(x0))))
% 13.38/2.68 = { by axiom 1 (multiplicative_right_identity) R->L }
% 13.38/2.68 tuple(leq(star(star(x0_2)), star(x0_2)), fresh3(addition(multiplication(addition(one, star(x0)), star(star(x0))), multiplication(addition(one, star(x0)), one)), star(star(x0)), star(x0), star(star(x0))))
% 13.38/2.68 = { by axiom 11 (right_distributivity) R->L }
% 13.38/2.68 tuple(leq(star(star(x0_2)), star(x0_2)), fresh3(multiplication(addition(one, star(x0)), addition(star(star(x0)), one)), star(star(x0)), star(x0), star(star(x0))))
% 13.38/2.68 = { by axiom 4 (additive_commutativity) }
% 13.38/2.68 tuple(leq(star(star(x0_2)), star(x0_2)), fresh3(multiplication(addition(star(x0), one), addition(star(star(x0)), one)), star(star(x0)), star(x0), star(star(x0))))
% 13.38/2.68 = { by axiom 4 (additive_commutativity) }
% 13.38/2.68 tuple(leq(star(star(x0_2)), star(x0_2)), fresh3(multiplication(addition(star(x0), one), addition(one, star(star(x0)))), star(star(x0)), star(x0), star(star(x0))))
% 13.38/2.68 = { by lemma 22 }
% 13.38/2.68 tuple(leq(star(star(x0_2)), star(x0_2)), fresh3(multiplication(addition(star(x0), one), star(star(x0))), star(star(x0)), star(x0), star(star(x0))))
% 13.38/2.68 = { by axiom 3 (additive_idempotence) R->L }
% 13.38/2.68 tuple(leq(star(star(x0_2)), star(x0_2)), fresh3(multiplication(addition(star(x0), addition(one, one)), star(star(x0))), star(star(x0)), star(x0), star(star(x0))))
% 13.38/2.68 = { by axiom 6 (additive_associativity) }
% 13.38/2.68 tuple(leq(star(star(x0_2)), star(x0_2)), fresh3(multiplication(addition(addition(star(x0), one), one), star(star(x0))), star(star(x0)), star(x0), star(star(x0))))
% 13.38/2.68 = { by lemma 18 R->L }
% 13.38/2.68 tuple(leq(star(star(x0_2)), star(x0_2)), fresh3(addition(multiplication(addition(star(x0), one), star(star(x0))), star(star(x0))), star(star(x0)), star(x0), star(star(x0))))
% 13.38/2.68 = { by lemma 19 R->L }
% 13.38/2.68 tuple(leq(star(star(x0_2)), star(x0_2)), fresh3(addition(multiplication(addition(star(x0), one), star(star(x0))), addition(multiplication(addition(star(x0), one), star(star(x0))), one)), star(star(x0)), star(x0), star(star(x0))))
% 13.38/2.68 = { by lemma 20 }
% 13.38/2.68 tuple(leq(star(star(x0_2)), star(x0_2)), fresh3(addition(multiplication(addition(star(x0), one), star(star(x0))), one), star(star(x0)), star(x0), star(star(x0))))
% 13.38/2.68 = { by lemma 19 }
% 13.38/2.68 tuple(leq(star(star(x0_2)), star(x0_2)), fresh3(star(star(x0)), star(star(x0)), star(x0), star(star(x0))))
% 13.38/2.68 = { by axiom 8 (order) }
% 13.38/2.68 tuple(leq(star(star(x0_2)), star(x0_2)), true)
% 13.38/2.68 = { by lemma 25 R->L }
% 13.38/2.68 tuple(leq(addition(multiplication(star(x0_2), star(star(x0_2))), star(star(x0_2))), star(x0_2)), true)
% 13.38/2.68 = { by lemma 18 }
% 13.38/2.68 tuple(leq(multiplication(addition(star(x0_2), one), star(star(x0_2))), star(x0_2)), true)
% 13.38/2.68 = { by axiom 4 (additive_commutativity) }
% 13.38/2.68 tuple(leq(multiplication(addition(one, star(x0_2)), star(star(x0_2))), star(x0_2)), true)
% 13.38/2.68 = { by lemma 22 }
% 13.38/2.68 tuple(leq(multiplication(star(x0_2), star(star(x0_2))), star(x0_2)), true)
% 13.38/2.68 = { by lemma 25 R->L }
% 13.38/2.68 tuple(leq(multiplication(star(x0_2), star(addition(multiplication(x0_2, star(x0_2)), star(x0_2)))), star(x0_2)), true)
% 13.38/2.68 = { by axiom 2 (multiplicative_left_identity) R->L }
% 13.38/2.69 tuple(leq(multiplication(star(x0_2), multiplication(one, star(addition(multiplication(x0_2, star(x0_2)), star(x0_2))))), star(x0_2)), true)
% 13.38/2.69 = { by axiom 5 (multiplicative_associativity) }
% 13.38/2.69 tuple(leq(multiplication(multiplication(star(x0_2), one), star(addition(multiplication(x0_2, star(x0_2)), star(x0_2)))), star(x0_2)), true)
% 13.38/2.69 = { by axiom 17 (star_induction_right) R->L }
% 13.38/2.69 tuple(fresh2(leq(addition(multiplication(star(x0_2), addition(multiplication(x0_2, star(x0_2)), star(x0_2))), multiplication(star(x0_2), one)), star(x0_2)), true, star(x0_2), addition(multiplication(x0_2, star(x0_2)), star(x0_2)), multiplication(star(x0_2), one)), true)
% 13.38/2.69 = { by axiom 11 (right_distributivity) R->L }
% 13.38/2.69 tuple(fresh2(leq(multiplication(star(x0_2), addition(addition(multiplication(x0_2, star(x0_2)), star(x0_2)), one)), star(x0_2)), true, star(x0_2), addition(multiplication(x0_2, star(x0_2)), star(x0_2)), multiplication(star(x0_2), one)), true)
% 13.38/2.69 = { by axiom 4 (additive_commutativity) }
% 13.38/2.69 tuple(fresh2(leq(multiplication(star(x0_2), addition(one, addition(multiplication(x0_2, star(x0_2)), star(x0_2)))), star(x0_2)), true, star(x0_2), addition(multiplication(x0_2, star(x0_2)), star(x0_2)), multiplication(star(x0_2), one)), true)
% 13.38/2.69 = { by axiom 1 (multiplicative_right_identity) }
% 13.38/2.69 tuple(fresh2(leq(multiplication(star(x0_2), addition(one, addition(multiplication(x0_2, star(x0_2)), star(x0_2)))), star(x0_2)), true, star(x0_2), addition(multiplication(x0_2, star(x0_2)), star(x0_2)), star(x0_2)), true)
% 13.38/2.69 = { by lemma 24 }
% 13.38/2.69 tuple(fresh2(leq(multiplication(star(x0_2), star(x0_2)), star(x0_2)), true, star(x0_2), addition(multiplication(x0_2, star(x0_2)), star(x0_2)), star(x0_2)), true)
% 13.38/2.69 = { by lemma 25 }
% 13.38/2.69 tuple(fresh2(leq(multiplication(star(x0_2), star(x0_2)), star(x0_2)), true, star(x0_2), star(x0_2), star(x0_2)), true)
% 13.38/2.69 = { by lemma 22 R->L }
% 13.38/2.69 tuple(fresh2(leq(multiplication(star(x0_2), addition(one, star(x0_2))), star(x0_2)), true, star(x0_2), star(x0_2), star(x0_2)), true)
% 13.38/2.69 = { by axiom 16 (star_induction_left) R->L }
% 13.38/2.69 tuple(fresh2(fresh4(leq(addition(multiplication(x0_2, star(x0_2)), addition(one, star(x0_2))), star(x0_2)), true, x0_2, star(x0_2), addition(one, star(x0_2))), true, star(x0_2), star(x0_2), star(x0_2)), true)
% 13.38/2.69 = { by lemma 23 R->L }
% 13.38/2.69 tuple(fresh2(fresh4(leq(addition(star(x0_2), addition(multiplication(x0_2, star(x0_2)), one)), star(x0_2)), true, x0_2, star(x0_2), addition(one, star(x0_2))), true, star(x0_2), star(x0_2), star(x0_2)), true)
% 13.38/2.69 = { by axiom 4 (additive_commutativity) }
% 13.38/2.69 tuple(fresh2(fresh4(leq(addition(star(x0_2), addition(one, multiplication(x0_2, star(x0_2)))), star(x0_2)), true, x0_2, star(x0_2), addition(one, star(x0_2))), true, star(x0_2), star(x0_2), star(x0_2)), true)
% 13.38/2.69 = { by axiom 6 (additive_associativity) }
% 13.38/2.69 tuple(fresh2(fresh4(leq(addition(addition(star(x0_2), one), multiplication(x0_2, star(x0_2))), star(x0_2)), true, x0_2, star(x0_2), addition(one, star(x0_2))), true, star(x0_2), star(x0_2), star(x0_2)), true)
% 13.38/2.69 = { by axiom 4 (additive_commutativity) R->L }
% 13.38/2.69 tuple(fresh2(fresh4(leq(addition(multiplication(x0_2, star(x0_2)), addition(star(x0_2), one)), star(x0_2)), true, x0_2, star(x0_2), addition(one, star(x0_2))), true, star(x0_2), star(x0_2), star(x0_2)), true)
% 13.38/2.69 = { by lemma 23 R->L }
% 13.38/2.69 tuple(fresh2(fresh4(leq(addition(one, addition(multiplication(x0_2, star(x0_2)), star(x0_2))), star(x0_2)), true, x0_2, star(x0_2), addition(one, star(x0_2))), true, star(x0_2), star(x0_2), star(x0_2)), true)
% 13.38/2.69 = { by lemma 24 }
% 13.38/2.69 tuple(fresh2(fresh4(leq(star(x0_2), star(x0_2)), true, x0_2, star(x0_2), addition(one, star(x0_2))), true, star(x0_2), star(x0_2), star(x0_2)), true)
% 13.38/2.69 = { by axiom 14 (order) R->L }
% 13.38/2.69 tuple(fresh2(fresh4(fresh3(addition(star(x0_2), star(x0_2)), star(x0_2), star(x0_2), star(x0_2)), true, x0_2, star(x0_2), addition(one, star(x0_2))), true, star(x0_2), star(x0_2), star(x0_2)), true)
% 13.38/2.69 = { by axiom 3 (additive_idempotence) }
% 13.38/2.69 tuple(fresh2(fresh4(fresh3(star(x0_2), star(x0_2), star(x0_2), star(x0_2)), true, x0_2, star(x0_2), addition(one, star(x0_2))), true, star(x0_2), star(x0_2), star(x0_2)), true)
% 13.38/2.69 = { by axiom 8 (order) }
% 13.38/2.69 tuple(fresh2(fresh4(true, true, x0_2, star(x0_2), addition(one, star(x0_2))), true, star(x0_2), star(x0_2), star(x0_2)), true)
% 13.38/2.69 = { by axiom 9 (star_induction_left) }
% 13.38/2.69 tuple(fresh2(true, true, star(x0_2), star(x0_2), star(x0_2)), true)
% 13.38/2.69 = { by axiom 10 (star_induction_right) }
% 13.38/2.69 tuple(true, true)
% 13.38/2.69 % SZS output end Proof
% 13.38/2.69
% 13.38/2.69 RESULT: Theorem (the conjecture is true).
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