TSTP Solution File: KLE091+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : KLE091+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 : n003.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 05:35:51 EDT 2023
% Result : Theorem 2.65s 0.81s
% Output : Proof 3.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KLE091+1 : 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 : n003.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 12:16:26 EDT 2023
% 0.13/0.35 % CPUTime :
% 2.65/0.81 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 2.65/0.81
% 2.65/0.81 % SZS status Theorem
% 2.65/0.81
% 3.32/0.83 % SZS output start Proof
% 3.32/0.83 Take the following subset of the input axioms:
% 3.32/0.84 fof(additive_associativity, axiom, ![A, B, C]: addition(A, addition(B, C))=addition(addition(A, B), C)).
% 3.32/0.84 fof(additive_commutativity, axiom, ![A2, B2]: addition(A2, B2)=addition(B2, A2)).
% 3.32/0.84 fof(additive_idempotence, axiom, ![A2]: addition(A2, A2)=A2).
% 3.32/0.84 fof(additive_identity, axiom, ![A2]: addition(A2, zero)=A2).
% 3.32/0.84 fof(codomain1, axiom, ![X0]: multiplication(X0, coantidomain(X0))=zero).
% 3.32/0.84 fof(codomain2, axiom, ![X1, X0_2]: addition(coantidomain(multiplication(X0_2, X1)), coantidomain(multiplication(coantidomain(coantidomain(X0_2)), X1)))=coantidomain(multiplication(coantidomain(coantidomain(X0_2)), X1))).
% 3.32/0.84 fof(codomain3, axiom, ![X0_2]: addition(coantidomain(coantidomain(X0_2)), coantidomain(X0_2))=one).
% 3.32/0.84 fof(codomain4, axiom, ![X0_2]: codomain(X0_2)=coantidomain(coantidomain(X0_2))).
% 3.32/0.84 fof(domain1, axiom, ![X0_2]: multiplication(antidomain(X0_2), X0_2)=zero).
% 3.32/0.84 fof(domain2, axiom, ![X0_2, X1_2]: addition(antidomain(multiplication(X0_2, X1_2)), antidomain(multiplication(X0_2, antidomain(antidomain(X1_2)))))=antidomain(multiplication(X0_2, antidomain(antidomain(X1_2))))).
% 3.32/0.84 fof(domain3, axiom, ![X0_2]: addition(antidomain(antidomain(X0_2)), antidomain(X0_2))=one).
% 3.32/0.84 fof(domain4, axiom, ![X0_2]: domain(X0_2)=antidomain(antidomain(X0_2))).
% 3.32/0.84 fof(goals, conjecture, ![X0_2]: domain(codomain(X0_2))=codomain(X0_2)).
% 3.32/0.84 fof(left_distributivity, axiom, ![A2, B2, C2]: multiplication(addition(A2, B2), C2)=addition(multiplication(A2, C2), multiplication(B2, C2))).
% 3.32/0.84 fof(multiplicative_left_identity, axiom, ![A2]: multiplication(one, A2)=A2).
% 3.32/0.84 fof(multiplicative_right_identity, axiom, ![A2]: multiplication(A2, one)=A2).
% 3.32/0.84 fof(right_distributivity, axiom, ![A2, B2, C2]: multiplication(A2, addition(B2, C2))=addition(multiplication(A2, B2), multiplication(A2, C2))).
% 3.32/0.84
% 3.32/0.84 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.32/0.84 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.32/0.84 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.32/0.84 fresh(y, y, x1...xn) = u
% 3.32/0.84 C => fresh(s, t, x1...xn) = v
% 3.32/0.84 where fresh is a fresh function symbol and x1..xn are the free
% 3.32/0.84 variables of u and v.
% 3.32/0.84 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.32/0.84 input problem has no model of domain size 1).
% 3.32/0.84
% 3.32/0.84 The encoding turns the above axioms into the following unit equations and goals:
% 3.32/0.84
% 3.32/0.84 Axiom 1 (multiplicative_right_identity): multiplication(X, one) = X.
% 3.32/0.84 Axiom 2 (multiplicative_left_identity): multiplication(one, X) = X.
% 3.32/0.84 Axiom 3 (additive_idempotence): addition(X, X) = X.
% 3.32/0.84 Axiom 4 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 3.32/0.84 Axiom 5 (additive_identity): addition(X, zero) = X.
% 3.32/0.84 Axiom 6 (domain4): domain(X) = antidomain(antidomain(X)).
% 3.32/0.84 Axiom 7 (codomain4): codomain(X) = coantidomain(coantidomain(X)).
% 3.32/0.84 Axiom 8 (codomain1): multiplication(X, coantidomain(X)) = zero.
% 3.32/0.84 Axiom 9 (domain1): multiplication(antidomain(X), X) = zero.
% 3.32/0.84 Axiom 10 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 3.32/0.84 Axiom 11 (domain3): addition(antidomain(antidomain(X)), antidomain(X)) = one.
% 3.32/0.84 Axiom 12 (codomain3): addition(coantidomain(coantidomain(X)), coantidomain(X)) = one.
% 3.32/0.84 Axiom 13 (right_distributivity): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 3.32/0.84 Axiom 14 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 3.32/0.84 Axiom 15 (domain2): addition(antidomain(multiplication(X, Y)), antidomain(multiplication(X, antidomain(antidomain(Y))))) = antidomain(multiplication(X, antidomain(antidomain(Y)))).
% 3.32/0.84 Axiom 16 (codomain2): addition(coantidomain(multiplication(X, Y)), coantidomain(multiplication(coantidomain(coantidomain(X)), Y))) = coantidomain(multiplication(coantidomain(coantidomain(X)), Y)).
% 3.32/0.84
% 3.32/0.84 Lemma 17: antidomain(one) = zero.
% 3.32/0.84 Proof:
% 3.32/0.84 antidomain(one)
% 3.32/0.84 = { by axiom 1 (multiplicative_right_identity) R->L }
% 3.32/0.84 multiplication(antidomain(one), one)
% 3.32/0.84 = { by axiom 9 (domain1) }
% 3.32/0.84 zero
% 3.32/0.84
% 3.32/0.84 Lemma 18: addition(zero, X) = X.
% 3.32/0.84 Proof:
% 3.32/0.84 addition(zero, X)
% 3.32/0.84 = { by axiom 4 (additive_commutativity) R->L }
% 3.32/0.84 addition(X, zero)
% 3.32/0.84 = { by axiom 5 (additive_identity) }
% 3.32/0.84 X
% 3.32/0.84
% 3.32/0.84 Lemma 19: codomain(coantidomain(X)) = coantidomain(codomain(X)).
% 3.32/0.84 Proof:
% 3.32/0.84 codomain(coantidomain(X))
% 3.32/0.84 = { by axiom 7 (codomain4) }
% 3.32/0.84 coantidomain(coantidomain(coantidomain(X)))
% 3.32/0.84 = { by axiom 7 (codomain4) R->L }
% 3.32/0.84 coantidomain(codomain(X))
% 3.32/0.84
% 3.32/0.84 Lemma 20: addition(X, addition(X, Y)) = addition(X, Y).
% 3.32/0.84 Proof:
% 3.32/0.84 addition(X, addition(X, Y))
% 3.32/0.84 = { by axiom 10 (additive_associativity) }
% 3.32/0.84 addition(addition(X, X), Y)
% 3.32/0.84 = { by axiom 3 (additive_idempotence) }
% 3.32/0.84 addition(X, Y)
% 3.32/0.84
% 3.32/0.84 Lemma 21: addition(antidomain(X), domain(X)) = one.
% 3.32/0.84 Proof:
% 3.32/0.84 addition(antidomain(X), domain(X))
% 3.32/0.84 = { by axiom 4 (additive_commutativity) R->L }
% 3.32/0.84 addition(domain(X), antidomain(X))
% 3.32/0.84 = { by axiom 6 (domain4) }
% 3.32/0.84 addition(antidomain(antidomain(X)), antidomain(X))
% 3.32/0.84 = { by axiom 11 (domain3) }
% 3.32/0.84 one
% 3.32/0.84
% 3.32/0.84 Lemma 22: addition(domain(X), antidomain(X)) = one.
% 3.32/0.84 Proof:
% 3.32/0.84 addition(domain(X), antidomain(X))
% 3.32/0.84 = { by axiom 4 (additive_commutativity) R->L }
% 3.32/0.84 addition(antidomain(X), domain(X))
% 3.32/0.84 = { by lemma 21 }
% 3.32/0.84 one
% 3.32/0.84
% 3.32/0.84 Lemma 23: addition(coantidomain(X), codomain(X)) = one.
% 3.32/0.84 Proof:
% 3.32/0.84 addition(coantidomain(X), codomain(X))
% 3.32/0.84 = { by axiom 4 (additive_commutativity) R->L }
% 3.32/0.84 addition(codomain(X), coantidomain(X))
% 3.32/0.84 = { by axiom 7 (codomain4) }
% 3.32/0.84 addition(coantidomain(coantidomain(X)), coantidomain(X))
% 3.32/0.84 = { by axiom 12 (codomain3) }
% 3.32/0.84 one
% 3.32/0.84
% 3.32/0.84 Lemma 24: addition(codomain(X), coantidomain(X)) = one.
% 3.32/0.84 Proof:
% 3.32/0.84 addition(codomain(X), coantidomain(X))
% 3.32/0.84 = { by axiom 4 (additive_commutativity) R->L }
% 3.32/0.84 addition(coantidomain(X), codomain(X))
% 3.32/0.84 = { by lemma 23 }
% 3.32/0.84 one
% 3.32/0.84
% 3.32/0.84 Lemma 25: multiplication(X, addition(Y, coantidomain(X))) = multiplication(X, Y).
% 3.32/0.84 Proof:
% 3.32/0.84 multiplication(X, addition(Y, coantidomain(X)))
% 3.32/0.84 = { by axiom 13 (right_distributivity) }
% 3.32/0.84 addition(multiplication(X, Y), multiplication(X, coantidomain(X)))
% 3.32/0.84 = { by axiom 8 (codomain1) }
% 3.32/0.84 addition(multiplication(X, Y), zero)
% 3.32/0.84 = { by axiom 5 (additive_identity) }
% 3.32/0.84 multiplication(X, Y)
% 3.32/0.84
% 3.32/0.84 Goal 1 (goals): domain(codomain(x0)) = codomain(x0).
% 3.32/0.84 Proof:
% 3.32/0.84 domain(codomain(x0))
% 3.32/0.84 = { by axiom 2 (multiplicative_left_identity) R->L }
% 3.32/0.84 multiplication(one, domain(codomain(x0)))
% 3.32/0.84 = { by lemma 24 R->L }
% 3.32/0.84 multiplication(addition(codomain(x0), coantidomain(x0)), domain(codomain(x0)))
% 3.32/0.84 = { by axiom 4 (additive_commutativity) R->L }
% 3.32/0.84 multiplication(addition(coantidomain(x0), codomain(x0)), domain(codomain(x0)))
% 3.32/0.84 = { by axiom 1 (multiplicative_right_identity) R->L }
% 3.32/0.84 multiplication(addition(multiplication(coantidomain(x0), one), codomain(x0)), domain(codomain(x0)))
% 3.32/0.84 = { by lemma 23 R->L }
% 3.32/0.84 multiplication(addition(multiplication(coantidomain(x0), addition(coantidomain(coantidomain(x0)), codomain(coantidomain(x0)))), codomain(x0)), domain(codomain(x0)))
% 3.32/0.84 = { by axiom 4 (additive_commutativity) R->L }
% 3.32/0.84 multiplication(addition(multiplication(coantidomain(x0), addition(codomain(coantidomain(x0)), coantidomain(coantidomain(x0)))), codomain(x0)), domain(codomain(x0)))
% 3.32/0.84 = { by lemma 25 }
% 3.32/0.84 multiplication(addition(multiplication(coantidomain(x0), codomain(coantidomain(x0))), codomain(x0)), domain(codomain(x0)))
% 3.32/0.84 = { by lemma 19 }
% 3.32/0.84 multiplication(addition(multiplication(coantidomain(x0), coantidomain(codomain(x0))), codomain(x0)), domain(codomain(x0)))
% 3.32/0.84 = { by axiom 5 (additive_identity) R->L }
% 3.32/0.84 multiplication(addition(addition(multiplication(coantidomain(x0), coantidomain(codomain(x0))), zero), codomain(x0)), domain(codomain(x0)))
% 3.32/0.84 = { by axiom 8 (codomain1) R->L }
% 3.32/0.84 multiplication(addition(addition(multiplication(coantidomain(x0), coantidomain(codomain(x0))), multiplication(codomain(x0), coantidomain(codomain(x0)))), codomain(x0)), domain(codomain(x0)))
% 3.32/0.84 = { by axiom 14 (left_distributivity) R->L }
% 3.32/0.84 multiplication(addition(multiplication(addition(coantidomain(x0), codomain(x0)), coantidomain(codomain(x0))), codomain(x0)), domain(codomain(x0)))
% 3.32/0.84 = { by axiom 4 (additive_commutativity) }
% 3.32/0.84 multiplication(addition(multiplication(addition(codomain(x0), coantidomain(x0)), coantidomain(codomain(x0))), codomain(x0)), domain(codomain(x0)))
% 3.32/0.84 = { by lemma 24 }
% 3.32/0.84 multiplication(addition(multiplication(one, coantidomain(codomain(x0))), codomain(x0)), domain(codomain(x0)))
% 3.32/0.84 = { by axiom 2 (multiplicative_left_identity) }
% 3.32/0.84 multiplication(addition(coantidomain(codomain(x0)), codomain(x0)), domain(codomain(x0)))
% 3.32/0.84 = { by axiom 14 (left_distributivity) }
% 3.32/0.84 addition(multiplication(coantidomain(codomain(x0)), domain(codomain(x0))), multiplication(codomain(x0), domain(codomain(x0))))
% 3.32/0.84 = { by axiom 2 (multiplicative_left_identity) R->L }
% 3.32/0.84 addition(multiplication(one, multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))), multiplication(codomain(x0), domain(codomain(x0))))
% 3.32/0.84 = { by lemma 21 R->L }
% 3.32/0.84 addition(multiplication(addition(antidomain(multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))), domain(multiplication(coantidomain(codomain(x0)), domain(codomain(x0))))), multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))), multiplication(codomain(x0), domain(codomain(x0))))
% 3.32/0.84 = { by lemma 20 R->L }
% 3.32/0.84 addition(multiplication(addition(antidomain(multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))), addition(antidomain(multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))), domain(multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))))), multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))), multiplication(codomain(x0), domain(codomain(x0))))
% 3.32/0.84 = { by lemma 21 }
% 3.32/0.84 addition(multiplication(addition(antidomain(multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))), one), multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))), multiplication(codomain(x0), domain(codomain(x0))))
% 3.32/0.84 = { by axiom 4 (additive_commutativity) }
% 3.32/0.84 addition(multiplication(addition(one, antidomain(multiplication(coantidomain(codomain(x0)), domain(codomain(x0))))), multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))), multiplication(codomain(x0), domain(codomain(x0))))
% 3.32/0.84 = { by lemma 21 R->L }
% 3.32/0.84 addition(multiplication(addition(addition(antidomain(one), domain(one)), antidomain(multiplication(coantidomain(codomain(x0)), domain(codomain(x0))))), multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))), multiplication(codomain(x0), domain(codomain(x0))))
% 3.32/0.84 = { by lemma 17 }
% 3.32/0.84 addition(multiplication(addition(addition(zero, domain(one)), antidomain(multiplication(coantidomain(codomain(x0)), domain(codomain(x0))))), multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))), multiplication(codomain(x0), domain(codomain(x0))))
% 3.32/0.84 = { by lemma 18 }
% 3.32/0.84 addition(multiplication(addition(domain(one), antidomain(multiplication(coantidomain(codomain(x0)), domain(codomain(x0))))), multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))), multiplication(codomain(x0), domain(codomain(x0))))
% 3.32/0.84 = { by axiom 6 (domain4) }
% 3.32/0.84 addition(multiplication(addition(antidomain(antidomain(one)), antidomain(multiplication(coantidomain(codomain(x0)), domain(codomain(x0))))), multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))), multiplication(codomain(x0), domain(codomain(x0))))
% 3.32/0.84 = { by lemma 17 }
% 3.32/0.84 addition(multiplication(addition(antidomain(zero), antidomain(multiplication(coantidomain(codomain(x0)), domain(codomain(x0))))), multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))), multiplication(codomain(x0), domain(codomain(x0))))
% 3.32/0.84 = { by axiom 8 (codomain1) R->L }
% 3.32/0.84 addition(multiplication(addition(antidomain(multiplication(codomain(coantidomain(x0)), coantidomain(codomain(coantidomain(x0))))), antidomain(multiplication(coantidomain(codomain(x0)), domain(codomain(x0))))), multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))), multiplication(codomain(x0), domain(codomain(x0))))
% 3.32/0.84 = { by axiom 1 (multiplicative_right_identity) R->L }
% 3.32/0.84 addition(multiplication(addition(antidomain(multiplication(codomain(coantidomain(x0)), coantidomain(multiplication(codomain(coantidomain(x0)), one)))), antidomain(multiplication(coantidomain(codomain(x0)), domain(codomain(x0))))), multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))), multiplication(codomain(x0), domain(codomain(x0))))
% 3.32/0.84 = { by axiom 7 (codomain4) }
% 3.32/0.84 addition(multiplication(addition(antidomain(multiplication(codomain(coantidomain(x0)), coantidomain(multiplication(coantidomain(coantidomain(coantidomain(x0))), one)))), antidomain(multiplication(coantidomain(codomain(x0)), domain(codomain(x0))))), multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))), multiplication(codomain(x0), domain(codomain(x0))))
% 3.32/0.84 = { by axiom 16 (codomain2) R->L }
% 3.32/0.84 addition(multiplication(addition(antidomain(multiplication(codomain(coantidomain(x0)), addition(coantidomain(multiplication(coantidomain(x0), one)), coantidomain(multiplication(coantidomain(coantidomain(coantidomain(x0))), one))))), antidomain(multiplication(coantidomain(codomain(x0)), domain(codomain(x0))))), multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))), multiplication(codomain(x0), domain(codomain(x0))))
% 3.32/0.84 = { by axiom 7 (codomain4) R->L }
% 3.32/0.84 addition(multiplication(addition(antidomain(multiplication(codomain(coantidomain(x0)), addition(coantidomain(multiplication(coantidomain(x0), one)), coantidomain(multiplication(codomain(coantidomain(x0)), one))))), antidomain(multiplication(coantidomain(codomain(x0)), domain(codomain(x0))))), multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))), multiplication(codomain(x0), domain(codomain(x0))))
% 3.32/0.84 = { by axiom 1 (multiplicative_right_identity) }
% 3.32/0.84 addition(multiplication(addition(antidomain(multiplication(codomain(coantidomain(x0)), addition(coantidomain(coantidomain(x0)), coantidomain(multiplication(codomain(coantidomain(x0)), one))))), antidomain(multiplication(coantidomain(codomain(x0)), domain(codomain(x0))))), multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))), multiplication(codomain(x0), domain(codomain(x0))))
% 3.32/0.84 = { by axiom 1 (multiplicative_right_identity) }
% 3.32/0.84 addition(multiplication(addition(antidomain(multiplication(codomain(coantidomain(x0)), addition(coantidomain(coantidomain(x0)), coantidomain(codomain(coantidomain(x0)))))), antidomain(multiplication(coantidomain(codomain(x0)), domain(codomain(x0))))), multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))), multiplication(codomain(x0), domain(codomain(x0))))
% 3.32/0.84 = { by lemma 25 }
% 3.32/0.84 addition(multiplication(addition(antidomain(multiplication(codomain(coantidomain(x0)), coantidomain(coantidomain(x0)))), antidomain(multiplication(coantidomain(codomain(x0)), domain(codomain(x0))))), multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))), multiplication(codomain(x0), domain(codomain(x0))))
% 3.32/0.84 = { by axiom 7 (codomain4) R->L }
% 3.32/0.85 addition(multiplication(addition(antidomain(multiplication(codomain(coantidomain(x0)), codomain(x0))), antidomain(multiplication(coantidomain(codomain(x0)), domain(codomain(x0))))), multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))), multiplication(codomain(x0), domain(codomain(x0))))
% 3.32/0.85 = { by lemma 19 }
% 3.32/0.85 addition(multiplication(addition(antidomain(multiplication(coantidomain(codomain(x0)), codomain(x0))), antidomain(multiplication(coantidomain(codomain(x0)), domain(codomain(x0))))), multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))), multiplication(codomain(x0), domain(codomain(x0))))
% 3.32/0.85 = { by axiom 6 (domain4) }
% 3.32/0.85 addition(multiplication(addition(antidomain(multiplication(coantidomain(codomain(x0)), codomain(x0))), antidomain(multiplication(coantidomain(codomain(x0)), antidomain(antidomain(codomain(x0)))))), multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))), multiplication(codomain(x0), domain(codomain(x0))))
% 3.32/0.85 = { by axiom 15 (domain2) }
% 3.32/0.85 addition(multiplication(antidomain(multiplication(coantidomain(codomain(x0)), antidomain(antidomain(codomain(x0))))), multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))), multiplication(codomain(x0), domain(codomain(x0))))
% 3.32/0.85 = { by axiom 6 (domain4) R->L }
% 3.32/0.85 addition(multiplication(antidomain(multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))), multiplication(coantidomain(codomain(x0)), domain(codomain(x0)))), multiplication(codomain(x0), domain(codomain(x0))))
% 3.32/0.85 = { by axiom 9 (domain1) }
% 3.32/0.85 addition(zero, multiplication(codomain(x0), domain(codomain(x0))))
% 3.32/0.85 = { by lemma 18 }
% 3.32/0.85 multiplication(codomain(x0), domain(codomain(x0)))
% 3.32/0.85 = { by lemma 25 R->L }
% 3.32/0.85 multiplication(codomain(x0), addition(domain(codomain(x0)), coantidomain(codomain(x0))))
% 3.32/0.85 = { by axiom 1 (multiplicative_right_identity) R->L }
% 3.32/0.85 multiplication(codomain(x0), addition(multiplication(domain(codomain(x0)), one), coantidomain(codomain(x0))))
% 3.32/0.85 = { by lemma 24 R->L }
% 3.32/0.85 multiplication(codomain(x0), addition(multiplication(domain(codomain(x0)), addition(codomain(x0), coantidomain(x0))), coantidomain(codomain(x0))))
% 3.32/0.85 = { by lemma 20 R->L }
% 3.32/0.85 multiplication(codomain(x0), addition(multiplication(domain(codomain(x0)), addition(codomain(x0), addition(codomain(x0), coantidomain(x0)))), coantidomain(codomain(x0))))
% 3.32/0.85 = { by lemma 24 }
% 3.32/0.85 multiplication(codomain(x0), addition(multiplication(domain(codomain(x0)), addition(codomain(x0), one)), coantidomain(codomain(x0))))
% 3.32/0.85 = { by axiom 4 (additive_commutativity) R->L }
% 3.32/0.85 multiplication(codomain(x0), addition(multiplication(domain(codomain(x0)), addition(one, codomain(x0))), coantidomain(codomain(x0))))
% 3.32/0.85 = { by axiom 13 (right_distributivity) }
% 3.32/0.85 multiplication(codomain(x0), addition(addition(multiplication(domain(codomain(x0)), one), multiplication(domain(codomain(x0)), codomain(x0))), coantidomain(codomain(x0))))
% 3.32/0.85 = { by axiom 1 (multiplicative_right_identity) }
% 3.32/0.85 multiplication(codomain(x0), addition(addition(domain(codomain(x0)), multiplication(domain(codomain(x0)), codomain(x0))), coantidomain(codomain(x0))))
% 3.32/0.85 = { by axiom 5 (additive_identity) R->L }
% 3.32/0.85 multiplication(codomain(x0), addition(addition(domain(codomain(x0)), addition(multiplication(domain(codomain(x0)), codomain(x0)), zero)), coantidomain(codomain(x0))))
% 3.32/0.85 = { by axiom 9 (domain1) R->L }
% 3.32/0.85 multiplication(codomain(x0), addition(addition(domain(codomain(x0)), addition(multiplication(domain(codomain(x0)), codomain(x0)), multiplication(antidomain(codomain(x0)), codomain(x0)))), coantidomain(codomain(x0))))
% 3.32/0.85 = { by axiom 14 (left_distributivity) R->L }
% 3.32/0.85 multiplication(codomain(x0), addition(addition(domain(codomain(x0)), multiplication(addition(domain(codomain(x0)), antidomain(codomain(x0))), codomain(x0))), coantidomain(codomain(x0))))
% 3.32/0.85 = { by lemma 22 }
% 3.32/0.85 multiplication(codomain(x0), addition(addition(domain(codomain(x0)), multiplication(one, codomain(x0))), coantidomain(codomain(x0))))
% 3.32/0.85 = { by axiom 2 (multiplicative_left_identity) }
% 3.32/0.85 multiplication(codomain(x0), addition(addition(domain(codomain(x0)), codomain(x0)), coantidomain(codomain(x0))))
% 3.32/0.85 = { by axiom 10 (additive_associativity) R->L }
% 3.32/0.85 multiplication(codomain(x0), addition(domain(codomain(x0)), addition(codomain(x0), coantidomain(codomain(x0)))))
% 3.32/0.85 = { by axiom 7 (codomain4) }
% 3.32/0.85 multiplication(codomain(x0), addition(domain(codomain(x0)), addition(coantidomain(coantidomain(x0)), coantidomain(codomain(x0)))))
% 3.32/0.85 = { by lemma 19 R->L }
% 3.32/0.85 multiplication(codomain(x0), addition(domain(codomain(x0)), addition(coantidomain(coantidomain(x0)), codomain(coantidomain(x0)))))
% 3.32/0.85 = { by lemma 23 }
% 3.32/0.85 multiplication(codomain(x0), addition(domain(codomain(x0)), one))
% 3.32/0.85 = { by lemma 22 R->L }
% 3.32/0.85 multiplication(codomain(x0), addition(domain(codomain(x0)), addition(domain(codomain(x0)), antidomain(codomain(x0)))))
% 3.32/0.85 = { by lemma 20 }
% 3.32/0.85 multiplication(codomain(x0), addition(domain(codomain(x0)), antidomain(codomain(x0))))
% 3.32/0.85 = { by lemma 22 }
% 3.32/0.85 multiplication(codomain(x0), one)
% 3.32/0.85 = { by axiom 1 (multiplicative_right_identity) }
% 3.32/0.85 codomain(x0)
% 3.32/0.85 % SZS output end Proof
% 3.32/0.85
% 3.32/0.85 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------