TSTP Solution File: KLE084+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : KLE084+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 : n015.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 05:35:49 EDT 2023
% Result : Theorem 0.20s 0.77s
% Output : Proof 3.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : KLE084+1 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 12:11:56 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.77 Command-line arguments: --ground-connectedness --complete-subsets
% 0.20/0.77
% 0.20/0.77 % SZS status Theorem
% 0.20/0.77
% 3.12/0.79 % SZS output start Proof
% 3.12/0.79 Take the following subset of the input axioms:
% 3.12/0.79 fof(additive_associativity, axiom, ![A, B, C]: addition(A, addition(B, C))=addition(addition(A, B), C)).
% 3.12/0.79 fof(additive_commutativity, axiom, ![A3, B2]: addition(A3, B2)=addition(B2, A3)).
% 3.12/0.79 fof(additive_idempotence, axiom, ![A3]: addition(A3, A3)=A3).
% 3.12/0.79 fof(additive_identity, axiom, ![A3]: addition(A3, zero)=A3).
% 3.12/0.79 fof(domain1, axiom, ![X0]: multiplication(antidomain(X0), X0)=zero).
% 3.12/0.79 fof(domain2, axiom, ![X1, X0_2]: addition(antidomain(multiplication(X0_2, X1)), antidomain(multiplication(X0_2, antidomain(antidomain(X1)))))=antidomain(multiplication(X0_2, antidomain(antidomain(X1))))).
% 3.12/0.79 fof(domain3, axiom, ![X0_2]: addition(antidomain(antidomain(X0_2)), antidomain(X0_2))=one).
% 3.12/0.79 fof(domain4, axiom, ![X0_2]: domain(X0_2)=antidomain(antidomain(X0_2))).
% 3.12/0.79 fof(goals, conjecture, ![X0_2, X1_2]: domain(multiplication(X0_2, X1_2))=domain(multiplication(X0_2, domain(X1_2)))).
% 3.12/0.79 fof(left_annihilation, axiom, ![A3]: multiplication(zero, A3)=zero).
% 3.12/0.79 fof(left_distributivity, axiom, ![A3, B2, C2]: multiplication(addition(A3, B2), C2)=addition(multiplication(A3, C2), multiplication(B2, C2))).
% 3.12/0.79 fof(multiplicative_associativity, axiom, ![A3, B2, C2]: multiplication(A3, multiplication(B2, C2))=multiplication(multiplication(A3, B2), C2)).
% 3.12/0.79 fof(multiplicative_left_identity, axiom, ![A3]: multiplication(one, A3)=A3).
% 3.12/0.79 fof(multiplicative_right_identity, axiom, ![A3]: multiplication(A3, one)=A3).
% 3.12/0.79 fof(order, axiom, ![A2, B2]: (leq(A2, B2) <=> addition(A2, B2)=B2)).
% 3.12/0.79 fof(right_distributivity, axiom, ![A3, B2, C2]: multiplication(A3, addition(B2, C2))=addition(multiplication(A3, B2), multiplication(A3, C2))).
% 3.12/0.79
% 3.12/0.79 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.12/0.79 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.12/0.79 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.12/0.79 fresh(y, y, x1...xn) = u
% 3.12/0.79 C => fresh(s, t, x1...xn) = v
% 3.12/0.79 where fresh is a fresh function symbol and x1..xn are the free
% 3.12/0.79 variables of u and v.
% 3.12/0.79 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.12/0.80 input problem has no model of domain size 1).
% 3.12/0.80
% 3.12/0.80 The encoding turns the above axioms into the following unit equations and goals:
% 3.12/0.80
% 3.12/0.80 Axiom 1 (domain4): domain(X) = antidomain(antidomain(X)).
% 3.12/0.80 Axiom 2 (additive_idempotence): addition(X, X) = X.
% 3.12/0.80 Axiom 3 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 3.12/0.80 Axiom 4 (additive_identity): addition(X, zero) = X.
% 3.12/0.80 Axiom 5 (multiplicative_right_identity): multiplication(X, one) = X.
% 3.12/0.80 Axiom 6 (multiplicative_left_identity): multiplication(one, X) = X.
% 3.12/0.80 Axiom 7 (left_annihilation): multiplication(zero, X) = zero.
% 3.12/0.80 Axiom 8 (domain1): multiplication(antidomain(X), X) = zero.
% 3.12/0.80 Axiom 9 (order): fresh(X, X, Y, Z) = true.
% 3.12/0.80 Axiom 10 (order_1): fresh2(X, X, Y, Z) = Z.
% 3.12/0.80 Axiom 11 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 3.12/0.80 Axiom 12 (multiplicative_associativity): multiplication(X, multiplication(Y, Z)) = multiplication(multiplication(X, Y), Z).
% 3.12/0.80 Axiom 13 (domain3): addition(antidomain(antidomain(X)), antidomain(X)) = one.
% 3.12/0.80 Axiom 14 (order): fresh(addition(X, Y), Y, X, Y) = leq(X, Y).
% 3.12/0.80 Axiom 15 (order_1): fresh2(leq(X, Y), true, X, Y) = addition(X, Y).
% 3.12/0.80 Axiom 16 (right_distributivity): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 3.12/0.80 Axiom 17 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 3.12/0.80 Axiom 18 (domain2): addition(antidomain(multiplication(X, Y)), antidomain(multiplication(X, antidomain(antidomain(Y))))) = antidomain(multiplication(X, antidomain(antidomain(Y)))).
% 3.12/0.80
% 3.12/0.80 Lemma 19: antidomain(one) = zero.
% 3.12/0.80 Proof:
% 3.12/0.80 antidomain(one)
% 3.12/0.80 = { by axiom 5 (multiplicative_right_identity) R->L }
% 3.41/0.80 multiplication(antidomain(one), one)
% 3.41/0.80 = { by axiom 8 (domain1) }
% 3.41/0.80 zero
% 3.41/0.80
% 3.41/0.80 Lemma 20: addition(domain(X), antidomain(X)) = one.
% 3.41/0.80 Proof:
% 3.41/0.80 addition(domain(X), antidomain(X))
% 3.41/0.80 = { by axiom 1 (domain4) }
% 3.41/0.80 addition(antidomain(antidomain(X)), antidomain(X))
% 3.41/0.80 = { by axiom 13 (domain3) }
% 3.41/0.80 one
% 3.41/0.80
% 3.41/0.80 Lemma 21: multiplication(antidomain(X), addition(X, Y)) = multiplication(antidomain(X), Y).
% 3.41/0.80 Proof:
% 3.41/0.80 multiplication(antidomain(X), addition(X, Y))
% 3.41/0.80 = { by axiom 3 (additive_commutativity) R->L }
% 3.41/0.80 multiplication(antidomain(X), addition(Y, X))
% 3.41/0.80 = { by axiom 16 (right_distributivity) }
% 3.41/0.80 addition(multiplication(antidomain(X), Y), multiplication(antidomain(X), X))
% 3.41/0.80 = { by axiom 8 (domain1) }
% 3.41/0.80 addition(multiplication(antidomain(X), Y), zero)
% 3.41/0.80 = { by axiom 4 (additive_identity) }
% 3.41/0.80 multiplication(antidomain(X), Y)
% 3.41/0.80
% 3.41/0.80 Lemma 22: multiplication(domain(X), X) = X.
% 3.41/0.80 Proof:
% 3.41/0.80 multiplication(domain(X), X)
% 3.41/0.80 = { by axiom 4 (additive_identity) R->L }
% 3.41/0.80 addition(multiplication(domain(X), X), zero)
% 3.41/0.80 = { by axiom 8 (domain1) R->L }
% 3.41/0.80 addition(multiplication(domain(X), X), multiplication(antidomain(X), X))
% 3.41/0.80 = { by axiom 17 (left_distributivity) R->L }
% 3.41/0.80 multiplication(addition(domain(X), antidomain(X)), X)
% 3.41/0.80 = { by lemma 20 }
% 3.41/0.80 multiplication(one, X)
% 3.41/0.80 = { by axiom 6 (multiplicative_left_identity) }
% 3.41/0.80 X
% 3.41/0.80
% 3.41/0.80 Lemma 23: antidomain(domain(X)) = antidomain(X).
% 3.41/0.80 Proof:
% 3.41/0.80 antidomain(domain(X))
% 3.41/0.80 = { by axiom 5 (multiplicative_right_identity) R->L }
% 3.41/0.80 multiplication(antidomain(domain(X)), one)
% 3.41/0.80 = { by lemma 20 R->L }
% 3.41/0.80 multiplication(antidomain(domain(X)), addition(domain(X), antidomain(X)))
% 3.41/0.80 = { by lemma 21 }
% 3.41/0.80 multiplication(antidomain(domain(X)), antidomain(X))
% 3.41/0.80 = { by axiom 1 (domain4) }
% 3.41/0.80 multiplication(antidomain(antidomain(antidomain(X))), antidomain(X))
% 3.41/0.80 = { by axiom 1 (domain4) R->L }
% 3.41/0.80 multiplication(domain(antidomain(X)), antidomain(X))
% 3.41/0.80 = { by lemma 22 }
% 3.41/0.80 antidomain(X)
% 3.41/0.80
% 3.41/0.80 Lemma 24: domain(domain(X)) = domain(X).
% 3.41/0.80 Proof:
% 3.41/0.80 domain(domain(X))
% 3.41/0.80 = { by axiom 1 (domain4) }
% 3.41/0.80 antidomain(antidomain(domain(X)))
% 3.41/0.80 = { by lemma 23 }
% 3.41/0.80 antidomain(antidomain(X))
% 3.41/0.80 = { by axiom 1 (domain4) R->L }
% 3.41/0.80 domain(X)
% 3.41/0.80
% 3.41/0.80 Lemma 25: addition(one, antidomain(X)) = one.
% 3.41/0.80 Proof:
% 3.41/0.80 addition(one, antidomain(X))
% 3.41/0.80 = { by axiom 3 (additive_commutativity) R->L }
% 3.41/0.80 addition(antidomain(X), one)
% 3.41/0.80 = { by axiom 15 (order_1) R->L }
% 3.41/0.80 fresh2(leq(antidomain(X), one), true, antidomain(X), one)
% 3.41/0.80 = { by lemma 20 R->L }
% 3.41/0.80 fresh2(leq(antidomain(X), addition(domain(X), antidomain(X))), true, antidomain(X), one)
% 3.41/0.80 = { by axiom 3 (additive_commutativity) R->L }
% 3.41/0.80 fresh2(leq(antidomain(X), addition(antidomain(X), domain(X))), true, antidomain(X), one)
% 3.41/0.80 = { by axiom 14 (order) R->L }
% 3.41/0.80 fresh2(fresh(addition(antidomain(X), addition(antidomain(X), domain(X))), addition(antidomain(X), domain(X)), antidomain(X), addition(antidomain(X), domain(X))), true, antidomain(X), one)
% 3.41/0.80 = { by axiom 11 (additive_associativity) }
% 3.41/0.80 fresh2(fresh(addition(addition(antidomain(X), antidomain(X)), domain(X)), addition(antidomain(X), domain(X)), antidomain(X), addition(antidomain(X), domain(X))), true, antidomain(X), one)
% 3.41/0.80 = { by axiom 2 (additive_idempotence) }
% 3.41/0.80 fresh2(fresh(addition(antidomain(X), domain(X)), addition(antidomain(X), domain(X)), antidomain(X), addition(antidomain(X), domain(X))), true, antidomain(X), one)
% 3.41/0.80 = { by axiom 9 (order) }
% 3.41/0.80 fresh2(true, true, antidomain(X), one)
% 3.41/0.80 = { by axiom 10 (order_1) }
% 3.41/0.80 one
% 3.41/0.80
% 3.41/0.80 Lemma 26: addition(antidomain(multiplication(X, Y)), antidomain(multiplication(X, domain(Y)))) = antidomain(multiplication(X, domain(Y))).
% 3.41/0.80 Proof:
% 3.41/0.80 addition(antidomain(multiplication(X, Y)), antidomain(multiplication(X, domain(Y))))
% 3.41/0.80 = { by axiom 1 (domain4) }
% 3.41/0.80 addition(antidomain(multiplication(X, Y)), antidomain(multiplication(X, antidomain(antidomain(Y)))))
% 3.41/0.80 = { by axiom 18 (domain2) }
% 3.41/0.80 antidomain(multiplication(X, antidomain(antidomain(Y))))
% 3.41/0.80 = { by axiom 1 (domain4) R->L }
% 3.41/0.80 antidomain(multiplication(X, domain(Y)))
% 3.41/0.80
% 3.41/0.80 Goal 1 (goals): domain(multiplication(x0, x1)) = domain(multiplication(x0, domain(x1))).
% 3.41/0.80 Proof:
% 3.41/0.80 domain(multiplication(x0, x1))
% 3.41/0.80 = { by axiom 6 (multiplicative_left_identity) R->L }
% 3.41/0.80 multiplication(one, domain(multiplication(x0, x1)))
% 3.41/0.80 = { by lemma 20 R->L }
% 3.41/0.80 multiplication(addition(domain(multiplication(x0, domain(x1))), antidomain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1)))
% 3.41/0.80 = { by axiom 17 (left_distributivity) }
% 3.41/0.80 addition(multiplication(domain(multiplication(x0, domain(x1))), domain(multiplication(x0, x1))), multiplication(antidomain(multiplication(x0, domain(x1))), domain(multiplication(x0, x1))))
% 3.41/0.80 = { by lemma 24 R->L }
% 3.41/0.80 addition(multiplication(domain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1))), multiplication(antidomain(multiplication(x0, domain(x1))), domain(multiplication(x0, x1))))
% 3.41/0.80 = { by axiom 1 (domain4) }
% 3.41/0.80 addition(multiplication(antidomain(antidomain(domain(multiplication(x0, domain(x1))))), domain(multiplication(x0, x1))), multiplication(antidomain(multiplication(x0, domain(x1))), domain(multiplication(x0, x1))))
% 3.41/0.80 = { by lemma 21 R->L }
% 3.41/0.80 addition(multiplication(antidomain(antidomain(domain(multiplication(x0, domain(x1))))), addition(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1)))), multiplication(antidomain(multiplication(x0, domain(x1))), domain(multiplication(x0, x1))))
% 3.41/0.80 = { by axiom 3 (additive_commutativity) }
% 3.41/0.80 addition(multiplication(antidomain(antidomain(domain(multiplication(x0, domain(x1))))), addition(domain(multiplication(x0, x1)), antidomain(domain(multiplication(x0, domain(x1)))))), multiplication(antidomain(multiplication(x0, domain(x1))), domain(multiplication(x0, x1))))
% 3.41/0.80 = { by lemma 23 }
% 3.41/0.80 addition(multiplication(antidomain(antidomain(domain(multiplication(x0, domain(x1))))), addition(domain(multiplication(x0, x1)), antidomain(multiplication(x0, domain(x1))))), multiplication(antidomain(multiplication(x0, domain(x1))), domain(multiplication(x0, x1))))
% 3.41/0.80 = { by lemma 26 R->L }
% 3.41/0.80 addition(multiplication(antidomain(antidomain(domain(multiplication(x0, domain(x1))))), addition(domain(multiplication(x0, x1)), addition(antidomain(multiplication(x0, x1)), antidomain(multiplication(x0, domain(x1)))))), multiplication(antidomain(multiplication(x0, domain(x1))), domain(multiplication(x0, x1))))
% 3.41/0.80 = { by axiom 11 (additive_associativity) }
% 3.41/0.80 addition(multiplication(antidomain(antidomain(domain(multiplication(x0, domain(x1))))), addition(addition(domain(multiplication(x0, x1)), antidomain(multiplication(x0, x1))), antidomain(multiplication(x0, domain(x1))))), multiplication(antidomain(multiplication(x0, domain(x1))), domain(multiplication(x0, x1))))
% 3.41/0.80 = { by lemma 20 }
% 3.41/0.80 addition(multiplication(antidomain(antidomain(domain(multiplication(x0, domain(x1))))), addition(one, antidomain(multiplication(x0, domain(x1))))), multiplication(antidomain(multiplication(x0, domain(x1))), domain(multiplication(x0, x1))))
% 3.41/0.80 = { by axiom 3 (additive_commutativity) }
% 3.41/0.80 addition(multiplication(antidomain(antidomain(domain(multiplication(x0, domain(x1))))), addition(antidomain(multiplication(x0, domain(x1))), one)), multiplication(antidomain(multiplication(x0, domain(x1))), domain(multiplication(x0, x1))))
% 3.41/0.80 = { by lemma 23 R->L }
% 3.41/0.80 addition(multiplication(antidomain(antidomain(domain(multiplication(x0, domain(x1))))), addition(antidomain(domain(multiplication(x0, domain(x1)))), one)), multiplication(antidomain(multiplication(x0, domain(x1))), domain(multiplication(x0, x1))))
% 3.41/0.80 = { by axiom 3 (additive_commutativity) }
% 3.41/0.80 addition(multiplication(antidomain(antidomain(domain(multiplication(x0, domain(x1))))), addition(one, antidomain(domain(multiplication(x0, domain(x1)))))), multiplication(antidomain(multiplication(x0, domain(x1))), domain(multiplication(x0, x1))))
% 3.41/0.81 = { by lemma 25 }
% 3.41/0.81 addition(multiplication(antidomain(antidomain(domain(multiplication(x0, domain(x1))))), one), multiplication(antidomain(multiplication(x0, domain(x1))), domain(multiplication(x0, x1))))
% 3.41/0.81 = { by axiom 5 (multiplicative_right_identity) }
% 3.41/0.81 addition(antidomain(antidomain(domain(multiplication(x0, domain(x1))))), multiplication(antidomain(multiplication(x0, domain(x1))), domain(multiplication(x0, x1))))
% 3.41/0.81 = { by axiom 1 (domain4) R->L }
% 3.41/0.81 addition(domain(domain(multiplication(x0, domain(x1)))), multiplication(antidomain(multiplication(x0, domain(x1))), domain(multiplication(x0, x1))))
% 3.41/0.81 = { by lemma 24 }
% 3.41/0.81 addition(domain(multiplication(x0, domain(x1))), multiplication(antidomain(multiplication(x0, domain(x1))), domain(multiplication(x0, x1))))
% 3.41/0.81 = { by lemma 23 R->L }
% 3.41/0.81 addition(domain(multiplication(x0, domain(x1))), multiplication(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1))))
% 3.41/0.81 = { by axiom 6 (multiplicative_left_identity) R->L }
% 3.41/0.81 addition(domain(multiplication(x0, domain(x1))), multiplication(one, multiplication(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1)))))
% 3.41/0.81 = { by lemma 25 R->L }
% 3.41/0.81 addition(domain(multiplication(x0, domain(x1))), multiplication(addition(one, antidomain(multiplication(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1))))), multiplication(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1)))))
% 3.41/0.81 = { by lemma 20 R->L }
% 3.41/0.81 addition(domain(multiplication(x0, domain(x1))), multiplication(addition(addition(domain(one), antidomain(one)), antidomain(multiplication(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1))))), multiplication(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1)))))
% 3.41/0.81 = { by lemma 19 }
% 3.41/0.81 addition(domain(multiplication(x0, domain(x1))), multiplication(addition(addition(domain(one), zero), antidomain(multiplication(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1))))), multiplication(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1)))))
% 3.41/0.81 = { by axiom 4 (additive_identity) }
% 3.41/0.81 addition(domain(multiplication(x0, domain(x1))), multiplication(addition(domain(one), antidomain(multiplication(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1))))), multiplication(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1)))))
% 3.41/0.81 = { by axiom 1 (domain4) }
% 3.41/0.81 addition(domain(multiplication(x0, domain(x1))), multiplication(addition(antidomain(antidomain(one)), antidomain(multiplication(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1))))), multiplication(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1)))))
% 3.41/0.81 = { by lemma 19 }
% 3.41/0.81 addition(domain(multiplication(x0, domain(x1))), multiplication(addition(antidomain(zero), antidomain(multiplication(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1))))), multiplication(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1)))))
% 3.41/0.81 = { by axiom 7 (left_annihilation) R->L }
% 3.41/0.81 addition(domain(multiplication(x0, domain(x1))), multiplication(addition(antidomain(multiplication(zero, x1)), antidomain(multiplication(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1))))), multiplication(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1)))))
% 3.41/0.81 = { by axiom 8 (domain1) R->L }
% 3.41/0.81 addition(domain(multiplication(x0, domain(x1))), multiplication(addition(antidomain(multiplication(multiplication(antidomain(multiplication(x0, domain(x1))), multiplication(x0, domain(x1))), x1)), antidomain(multiplication(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1))))), multiplication(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1)))))
% 3.41/0.81 = { by axiom 12 (multiplicative_associativity) R->L }
% 3.41/0.81 addition(domain(multiplication(x0, domain(x1))), multiplication(addition(antidomain(multiplication(antidomain(multiplication(x0, domain(x1))), multiplication(multiplication(x0, domain(x1)), x1))), antidomain(multiplication(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1))))), multiplication(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1)))))
% 3.41/0.81 = { by axiom 12 (multiplicative_associativity) R->L }
% 3.41/0.81 addition(domain(multiplication(x0, domain(x1))), multiplication(addition(antidomain(multiplication(antidomain(multiplication(x0, domain(x1))), multiplication(x0, multiplication(domain(x1), x1)))), antidomain(multiplication(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1))))), multiplication(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1)))))
% 3.41/0.81 = { by lemma 22 }
% 3.41/0.81 addition(domain(multiplication(x0, domain(x1))), multiplication(addition(antidomain(multiplication(antidomain(multiplication(x0, domain(x1))), multiplication(x0, x1))), antidomain(multiplication(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1))))), multiplication(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1)))))
% 3.41/0.81 = { by lemma 23 R->L }
% 3.41/0.81 addition(domain(multiplication(x0, domain(x1))), multiplication(addition(antidomain(multiplication(antidomain(domain(multiplication(x0, domain(x1)))), multiplication(x0, x1))), antidomain(multiplication(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1))))), multiplication(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1)))))
% 3.41/0.81 = { by lemma 26 }
% 3.41/0.81 addition(domain(multiplication(x0, domain(x1))), multiplication(antidomain(multiplication(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1)))), multiplication(antidomain(domain(multiplication(x0, domain(x1)))), domain(multiplication(x0, x1)))))
% 3.41/0.81 = { by axiom 8 (domain1) }
% 3.41/0.81 addition(domain(multiplication(x0, domain(x1))), zero)
% 3.41/0.81 = { by axiom 4 (additive_identity) }
% 3.41/0.81 domain(multiplication(x0, domain(x1)))
% 3.41/0.81 % SZS output end Proof
% 3.41/0.81
% 3.41/0.81 RESULT: Theorem (the conjecture is true).
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