TSTP Solution File: KLE097+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : KLE097+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 : n006.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 05:35:52 EDT 2023
% Result : Theorem 21.47s 3.13s
% Output : Proof 21.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : KLE097+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13 % 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 : n006.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 12:25:36 EDT 2023
% 0.13/0.35 % CPUTime :
% 21.47/3.13 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 21.47/3.13
% 21.47/3.13 % SZS status Theorem
% 21.47/3.13
% 21.93/3.14 % SZS output start Proof
% 21.93/3.14 Take the following subset of the input axioms:
% 21.93/3.14 fof(additive_associativity, axiom, ![A, B, C]: addition(A, addition(B, C))=addition(addition(A, B), C)).
% 21.93/3.14 fof(additive_commutativity, axiom, ![A2, B2]: addition(A2, B2)=addition(B2, A2)).
% 21.93/3.14 fof(additive_idempotence, axiom, ![A2]: addition(A2, A2)=A2).
% 21.93/3.14 fof(additive_identity, axiom, ![A2]: addition(A2, zero)=A2).
% 21.93/3.14 fof(complement, axiom, ![X0]: c(X0)=antidomain(domain(X0))).
% 21.93/3.14 fof(domain1, axiom, ![X0_2]: multiplication(antidomain(X0_2), X0_2)=zero).
% 21.93/3.14 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))))).
% 21.93/3.14 fof(domain3, axiom, ![X0_2]: addition(antidomain(antidomain(X0_2)), antidomain(X0_2))=one).
% 21.93/3.14 fof(domain4, axiom, ![X0_2]: domain(X0_2)=antidomain(antidomain(X0_2))).
% 21.93/3.14 fof(forward_diamond, axiom, ![X0_2, X1_2]: forward_diamond(X0_2, X1_2)=domain(multiplication(X0_2, domain(X1_2)))).
% 21.93/3.14 fof(goals, conjecture, ![X2, X0_2, X1_2]: (addition(forward_diamond(X0_2, domain(X1_2)), domain(X2))=domain(X2) <= addition(multiplication(X0_2, domain(X1_2)), multiplication(domain(X2), X0_2))=multiplication(domain(X2), X0_2))).
% 21.93/3.14 fof(left_annihilation, axiom, ![A2]: multiplication(zero, A2)=zero).
% 21.93/3.14 fof(left_distributivity, axiom, ![A2, B2, C2]: multiplication(addition(A2, B2), C2)=addition(multiplication(A2, C2), multiplication(B2, C2))).
% 21.93/3.14 fof(multiplicative_associativity, axiom, ![A2, B2, C2]: multiplication(A2, multiplication(B2, C2))=multiplication(multiplication(A2, B2), C2)).
% 21.93/3.14 fof(multiplicative_left_identity, axiom, ![A2]: multiplication(one, A2)=A2).
% 21.93/3.14 fof(multiplicative_right_identity, axiom, ![A2]: multiplication(A2, one)=A2).
% 21.93/3.14 fof(right_distributivity, axiom, ![A2, B2, C2]: multiplication(A2, addition(B2, C2))=addition(multiplication(A2, B2), multiplication(A2, C2))).
% 21.93/3.14
% 21.93/3.14 Now clausify the problem and encode Horn clauses using encoding 3 of
% 21.93/3.14 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 21.93/3.14 We repeatedly replace C & s=t => u=v by the two clauses:
% 21.93/3.14 fresh(y, y, x1...xn) = u
% 21.93/3.14 C => fresh(s, t, x1...xn) = v
% 21.93/3.14 where fresh is a fresh function symbol and x1..xn are the free
% 21.93/3.14 variables of u and v.
% 21.93/3.14 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 21.93/3.14 input problem has no model of domain size 1).
% 21.93/3.14
% 21.93/3.14 The encoding turns the above axioms into the following unit equations and goals:
% 21.93/3.14
% 21.93/3.14 Axiom 1 (multiplicative_right_identity): multiplication(X, one) = X.
% 21.93/3.14 Axiom 2 (left_annihilation): multiplication(zero, X) = zero.
% 21.93/3.14 Axiom 3 (multiplicative_left_identity): multiplication(one, X) = X.
% 21.93/3.14 Axiom 4 (additive_idempotence): addition(X, X) = X.
% 21.93/3.14 Axiom 5 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 21.93/3.14 Axiom 6 (additive_identity): addition(X, zero) = X.
% 21.93/3.14 Axiom 7 (complement): c(X) = antidomain(domain(X)).
% 21.93/3.14 Axiom 8 (domain4): domain(X) = antidomain(antidomain(X)).
% 21.93/3.14 Axiom 9 (domain1): multiplication(antidomain(X), X) = zero.
% 21.93/3.14 Axiom 10 (multiplicative_associativity): multiplication(X, multiplication(Y, Z)) = multiplication(multiplication(X, Y), Z).
% 21.93/3.14 Axiom 11 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 21.93/3.14 Axiom 12 (forward_diamond): forward_diamond(X, Y) = domain(multiplication(X, domain(Y))).
% 21.93/3.15 Axiom 13 (domain3): addition(antidomain(antidomain(X)), antidomain(X)) = one.
% 21.93/3.15 Axiom 14 (right_distributivity): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 21.93/3.15 Axiom 15 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 21.93/3.15 Axiom 16 (goals): addition(multiplication(x0, domain(x1)), multiplication(domain(x2), x0)) = multiplication(domain(x2), x0).
% 21.93/3.15 Axiom 17 (domain2): addition(antidomain(multiplication(X, Y)), antidomain(multiplication(X, antidomain(antidomain(Y))))) = antidomain(multiplication(X, antidomain(antidomain(Y)))).
% 21.93/3.15
% 21.93/3.15 Lemma 18: antidomain(one) = zero.
% 21.93/3.15 Proof:
% 21.93/3.15 antidomain(one)
% 21.93/3.15 = { by axiom 1 (multiplicative_right_identity) R->L }
% 21.93/3.15 multiplication(antidomain(one), one)
% 21.93/3.15 = { by axiom 9 (domain1) }
% 21.93/3.15 zero
% 21.93/3.15
% 21.93/3.15 Lemma 19: addition(domain(X), antidomain(X)) = one.
% 21.93/3.15 Proof:
% 21.93/3.15 addition(domain(X), antidomain(X))
% 21.93/3.15 = { by axiom 8 (domain4) }
% 21.93/3.15 addition(antidomain(antidomain(X)), antidomain(X))
% 21.93/3.15 = { by axiom 13 (domain3) }
% 21.93/3.15 one
% 21.93/3.15
% 21.93/3.15 Lemma 20: multiplication(antidomain(X), addition(X, Y)) = multiplication(antidomain(X), Y).
% 21.93/3.15 Proof:
% 21.93/3.15 multiplication(antidomain(X), addition(X, Y))
% 21.93/3.15 = { by axiom 5 (additive_commutativity) R->L }
% 21.93/3.15 multiplication(antidomain(X), addition(Y, X))
% 21.93/3.15 = { by axiom 14 (right_distributivity) }
% 21.93/3.15 addition(multiplication(antidomain(X), Y), multiplication(antidomain(X), X))
% 21.93/3.15 = { by axiom 9 (domain1) }
% 21.93/3.15 addition(multiplication(antidomain(X), Y), zero)
% 21.93/3.15 = { by axiom 6 (additive_identity) }
% 21.93/3.15 multiplication(antidomain(X), Y)
% 21.93/3.15
% 21.93/3.15 Lemma 21: domain(antidomain(X)) = c(X).
% 21.93/3.15 Proof:
% 21.93/3.15 domain(antidomain(X))
% 21.93/3.15 = { by axiom 8 (domain4) }
% 21.93/3.15 antidomain(antidomain(antidomain(X)))
% 21.93/3.15 = { by axiom 8 (domain4) R->L }
% 21.93/3.15 antidomain(domain(X))
% 21.93/3.15 = { by axiom 7 (complement) R->L }
% 21.93/3.15 c(X)
% 21.93/3.15
% 21.93/3.15 Lemma 22: multiplication(addition(X, antidomain(Y)), Y) = multiplication(X, Y).
% 21.93/3.15 Proof:
% 21.93/3.15 multiplication(addition(X, antidomain(Y)), Y)
% 21.93/3.15 = { by axiom 15 (left_distributivity) }
% 21.93/3.15 addition(multiplication(X, Y), multiplication(antidomain(Y), Y))
% 21.93/3.15 = { by axiom 9 (domain1) }
% 21.93/3.15 addition(multiplication(X, Y), zero)
% 21.93/3.15 = { by axiom 6 (additive_identity) }
% 21.93/3.15 multiplication(X, Y)
% 21.93/3.15
% 21.93/3.15 Lemma 23: c(X) = antidomain(X).
% 21.93/3.15 Proof:
% 21.93/3.15 c(X)
% 21.93/3.15 = { by axiom 7 (complement) }
% 21.93/3.15 antidomain(domain(X))
% 21.93/3.15 = { by axiom 1 (multiplicative_right_identity) R->L }
% 21.93/3.15 multiplication(antidomain(domain(X)), one)
% 21.93/3.15 = { by lemma 19 R->L }
% 21.93/3.15 multiplication(antidomain(domain(X)), addition(domain(X), antidomain(X)))
% 21.93/3.15 = { by lemma 20 }
% 21.93/3.15 multiplication(antidomain(domain(X)), antidomain(X))
% 21.93/3.15 = { by axiom 7 (complement) R->L }
% 21.93/3.15 multiplication(c(X), antidomain(X))
% 21.93/3.15 = { by lemma 21 R->L }
% 21.93/3.15 multiplication(domain(antidomain(X)), antidomain(X))
% 21.93/3.15 = { by lemma 22 R->L }
% 21.93/3.15 multiplication(addition(domain(antidomain(X)), antidomain(antidomain(X))), antidomain(X))
% 21.93/3.15 = { by lemma 19 }
% 21.93/3.15 multiplication(one, antidomain(X))
% 21.93/3.15 = { by axiom 3 (multiplicative_left_identity) }
% 21.93/3.15 antidomain(X)
% 21.93/3.15
% 21.93/3.15 Lemma 24: addition(zero, X) = X.
% 21.93/3.15 Proof:
% 21.93/3.15 addition(zero, X)
% 21.93/3.15 = { by axiom 5 (additive_commutativity) R->L }
% 21.93/3.15 addition(X, zero)
% 21.93/3.15 = { by axiom 6 (additive_identity) }
% 21.93/3.15 X
% 21.93/3.15
% 21.93/3.15 Lemma 25: antidomain(domain(X)) = antidomain(X).
% 21.93/3.15 Proof:
% 21.93/3.15 antidomain(domain(X))
% 21.93/3.15 = { by axiom 7 (complement) R->L }
% 21.93/3.15 c(X)
% 21.93/3.15 = { by lemma 23 }
% 21.93/3.15 antidomain(X)
% 21.93/3.15
% 21.93/3.15 Lemma 26: addition(Y, addition(Z, X)) = addition(X, addition(Y, Z)).
% 21.93/3.15 Proof:
% 21.93/3.15 addition(Y, addition(Z, X))
% 21.93/3.15 = { by axiom 5 (additive_commutativity) R->L }
% 21.93/3.15 addition(addition(Z, X), Y)
% 21.93/3.15 = { by axiom 5 (additive_commutativity) }
% 21.93/3.15 addition(addition(X, Z), Y)
% 21.93/3.15 = { by axiom 11 (additive_associativity) R->L }
% 21.93/3.15 addition(X, addition(Z, Y))
% 21.93/3.15 = { by axiom 5 (additive_commutativity) }
% 21.93/3.15 addition(X, addition(Y, Z))
% 21.93/3.15
% 21.93/3.15 Lemma 27: multiplication(antidomain(X), multiplication(X, Y)) = zero.
% 21.93/3.15 Proof:
% 21.93/3.15 multiplication(antidomain(X), multiplication(X, Y))
% 21.93/3.15 = { by axiom 10 (multiplicative_associativity) }
% 21.93/3.15 multiplication(multiplication(antidomain(X), X), Y)
% 21.93/3.15 = { by axiom 9 (domain1) }
% 21.93/3.15 multiplication(zero, Y)
% 21.93/3.15 = { by axiom 2 (left_annihilation) }
% 21.93/3.15 zero
% 21.93/3.15
% 21.93/3.15 Lemma 28: addition(forward_diamond(X, Y), antidomain(multiplication(X, domain(Y)))) = one.
% 21.93/3.15 Proof:
% 21.93/3.15 addition(forward_diamond(X, Y), antidomain(multiplication(X, domain(Y))))
% 21.93/3.15 = { by axiom 12 (forward_diamond) }
% 21.93/3.15 addition(domain(multiplication(X, domain(Y))), antidomain(multiplication(X, domain(Y))))
% 21.93/3.15 = { by lemma 19 }
% 21.93/3.15 one
% 21.93/3.15
% 21.93/3.15 Goal 1 (goals_1): addition(forward_diamond(x0, domain(x1)), domain(x2)) = domain(x2).
% 21.93/3.15 Proof:
% 21.93/3.15 addition(forward_diamond(x0, domain(x1)), domain(x2))
% 21.93/3.15 = { by axiom 3 (multiplicative_left_identity) R->L }
% 21.93/3.15 multiplication(one, addition(forward_diamond(x0, domain(x1)), domain(x2)))
% 21.93/3.15 = { by lemma 19 R->L }
% 21.93/3.15 multiplication(addition(domain(x2), antidomain(x2)), addition(forward_diamond(x0, domain(x1)), domain(x2)))
% 21.93/3.15 = { by axiom 5 (additive_commutativity) R->L }
% 21.93/3.15 multiplication(addition(antidomain(x2), domain(x2)), addition(forward_diamond(x0, domain(x1)), domain(x2)))
% 21.93/3.15 = { by axiom 15 (left_distributivity) }
% 21.93/3.15 addition(multiplication(antidomain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by lemma 24 R->L }
% 21.93/3.15 addition(multiplication(antidomain(x2), addition(zero, addition(forward_diamond(x0, domain(x1)), domain(x2)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by lemma 25 R->L }
% 21.93/3.15 addition(multiplication(antidomain(domain(x2)), addition(zero, addition(forward_diamond(x0, domain(x1)), domain(x2)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by lemma 26 }
% 21.93/3.15 addition(multiplication(antidomain(domain(x2)), addition(domain(x2), addition(zero, forward_diamond(x0, domain(x1))))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by lemma 20 }
% 21.93/3.15 addition(multiplication(antidomain(domain(x2)), addition(zero, forward_diamond(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by lemma 25 }
% 21.93/3.15 addition(multiplication(antidomain(x2), addition(zero, forward_diamond(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by lemma 24 }
% 21.93/3.15 addition(multiplication(antidomain(x2), forward_diamond(x0, domain(x1))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by axiom 8 (domain4) }
% 21.93/3.15 addition(multiplication(antidomain(x2), forward_diamond(x0, antidomain(antidomain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by axiom 12 (forward_diamond) }
% 21.93/3.15 addition(multiplication(antidomain(x2), domain(multiplication(x0, domain(antidomain(antidomain(x1)))))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by lemma 21 }
% 21.93/3.15 addition(multiplication(antidomain(x2), domain(multiplication(x0, c(antidomain(x1))))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by lemma 23 }
% 21.93/3.15 addition(multiplication(antidomain(x2), domain(multiplication(x0, antidomain(antidomain(x1))))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by axiom 8 (domain4) R->L }
% 21.93/3.15 addition(multiplication(antidomain(x2), domain(multiplication(x0, domain(x1)))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by axiom 3 (multiplicative_left_identity) R->L }
% 21.93/3.15 addition(multiplication(one, multiplication(antidomain(x2), domain(multiplication(x0, domain(x1))))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by lemma 19 R->L }
% 21.93/3.15 addition(multiplication(addition(domain(one), antidomain(one)), multiplication(antidomain(x2), domain(multiplication(x0, domain(x1))))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by lemma 18 }
% 21.93/3.15 addition(multiplication(addition(domain(one), zero), multiplication(antidomain(x2), domain(multiplication(x0, domain(x1))))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by axiom 6 (additive_identity) }
% 21.93/3.15 addition(multiplication(domain(one), multiplication(antidomain(x2), domain(multiplication(x0, domain(x1))))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by axiom 8 (domain4) }
% 21.93/3.15 addition(multiplication(antidomain(antidomain(one)), multiplication(antidomain(x2), domain(multiplication(x0, domain(x1))))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by lemma 18 }
% 21.93/3.15 addition(multiplication(antidomain(zero), multiplication(antidomain(x2), domain(multiplication(x0, domain(x1))))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by lemma 27 R->L }
% 21.93/3.15 addition(multiplication(antidomain(multiplication(antidomain(domain(x2)), multiplication(domain(x2), x0))), multiplication(antidomain(x2), domain(multiplication(x0, domain(x1))))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by axiom 16 (goals) R->L }
% 21.93/3.15 addition(multiplication(antidomain(multiplication(antidomain(domain(x2)), addition(multiplication(x0, domain(x1)), multiplication(domain(x2), x0)))), multiplication(antidomain(x2), domain(multiplication(x0, domain(x1))))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by axiom 5 (additive_commutativity) R->L }
% 21.93/3.15 addition(multiplication(antidomain(multiplication(antidomain(domain(x2)), addition(multiplication(domain(x2), x0), multiplication(x0, domain(x1))))), multiplication(antidomain(x2), domain(multiplication(x0, domain(x1))))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by axiom 14 (right_distributivity) }
% 21.93/3.15 addition(multiplication(antidomain(addition(multiplication(antidomain(domain(x2)), multiplication(domain(x2), x0)), multiplication(antidomain(domain(x2)), multiplication(x0, domain(x1))))), multiplication(antidomain(x2), domain(multiplication(x0, domain(x1))))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by lemma 27 }
% 21.93/3.15 addition(multiplication(antidomain(addition(zero, multiplication(antidomain(domain(x2)), multiplication(x0, domain(x1))))), multiplication(antidomain(x2), domain(multiplication(x0, domain(x1))))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by lemma 24 }
% 21.93/3.15 addition(multiplication(antidomain(multiplication(antidomain(domain(x2)), multiplication(x0, domain(x1)))), multiplication(antidomain(x2), domain(multiplication(x0, domain(x1))))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by lemma 25 }
% 21.93/3.15 addition(multiplication(antidomain(multiplication(antidomain(x2), multiplication(x0, domain(x1)))), multiplication(antidomain(x2), domain(multiplication(x0, domain(x1))))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by lemma 22 R->L }
% 21.93/3.15 addition(multiplication(addition(antidomain(multiplication(antidomain(x2), multiplication(x0, domain(x1)))), antidomain(multiplication(antidomain(x2), domain(multiplication(x0, domain(x1)))))), multiplication(antidomain(x2), domain(multiplication(x0, domain(x1))))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by axiom 8 (domain4) }
% 21.93/3.15 addition(multiplication(addition(antidomain(multiplication(antidomain(x2), multiplication(x0, domain(x1)))), antidomain(multiplication(antidomain(x2), antidomain(antidomain(multiplication(x0, domain(x1))))))), multiplication(antidomain(x2), domain(multiplication(x0, domain(x1))))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by axiom 17 (domain2) }
% 21.93/3.15 addition(multiplication(antidomain(multiplication(antidomain(x2), antidomain(antidomain(multiplication(x0, domain(x1)))))), multiplication(antidomain(x2), domain(multiplication(x0, domain(x1))))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by axiom 8 (domain4) R->L }
% 21.93/3.15 addition(multiplication(antidomain(multiplication(antidomain(x2), domain(multiplication(x0, domain(x1))))), multiplication(antidomain(x2), domain(multiplication(x0, domain(x1))))), multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by axiom 9 (domain1) }
% 21.93/3.15 addition(zero, multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by lemma 24 }
% 21.93/3.15 multiplication(domain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2)))
% 21.93/3.15 = { by axiom 8 (domain4) }
% 21.93/3.15 multiplication(antidomain(antidomain(x2)), addition(forward_diamond(x0, domain(x1)), domain(x2)))
% 21.93/3.15 = { by lemma 20 R->L }
% 21.93/3.15 multiplication(antidomain(antidomain(x2)), addition(antidomain(x2), addition(forward_diamond(x0, domain(x1)), domain(x2))))
% 21.93/3.15 = { by lemma 26 }
% 21.93/3.15 multiplication(antidomain(antidomain(x2)), addition(domain(x2), addition(antidomain(x2), forward_diamond(x0, domain(x1)))))
% 21.93/3.15 = { by axiom 11 (additive_associativity) }
% 21.93/3.15 multiplication(antidomain(antidomain(x2)), addition(addition(domain(x2), antidomain(x2)), forward_diamond(x0, domain(x1))))
% 21.93/3.15 = { by lemma 19 }
% 21.93/3.15 multiplication(antidomain(antidomain(x2)), addition(one, forward_diamond(x0, domain(x1))))
% 21.93/3.15 = { by axiom 5 (additive_commutativity) R->L }
% 21.93/3.15 multiplication(antidomain(antidomain(x2)), addition(forward_diamond(x0, domain(x1)), one))
% 21.93/3.15 = { by lemma 28 R->L }
% 21.93/3.15 multiplication(antidomain(antidomain(x2)), addition(forward_diamond(x0, domain(x1)), addition(forward_diamond(x0, domain(x1)), antidomain(multiplication(x0, domain(domain(x1)))))))
% 21.93/3.15 = { by axiom 11 (additive_associativity) }
% 21.93/3.15 multiplication(antidomain(antidomain(x2)), addition(addition(forward_diamond(x0, domain(x1)), forward_diamond(x0, domain(x1))), antidomain(multiplication(x0, domain(domain(x1))))))
% 21.93/3.15 = { by axiom 4 (additive_idempotence) }
% 21.93/3.15 multiplication(antidomain(antidomain(x2)), addition(forward_diamond(x0, domain(x1)), antidomain(multiplication(x0, domain(domain(x1))))))
% 21.93/3.15 = { by lemma 28 }
% 21.93/3.15 multiplication(antidomain(antidomain(x2)), one)
% 21.93/3.15 = { by axiom 1 (multiplicative_right_identity) }
% 21.93/3.15 antidomain(antidomain(x2))
% 21.93/3.15 = { by axiom 8 (domain4) R->L }
% 21.93/3.15 domain(x2)
% 21.93/3.15 % SZS output end Proof
% 21.93/3.15
% 21.93/3.15 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------