0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : twee %s --tstp --casc --quiet --conditional-encoding if --smaller --drop-non-horn 0.03/0.23 % Computer : n014.star.cs.uiowa.edu 0.03/0.23 % Model : x86_64 x86_64 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.23 % Memory : 32218.625MB 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.23 % CPULimit : 300 0.03/0.23 % DateTime : Sat Jul 14 05:49:25 CDT 2018 0.03/0.23 % CPUTime : 11.34/11.57 % SZS status Theorem 11.34/11.57 11.34/11.57 % SZS output start Proof 11.34/11.57 Take the following subset of the input axioms: 11.42/11.65 fof(additive_associativity, axiom, 11.42/11.65 ![A, B, C]: 11.42/11.65 addition(A, addition(B, C))=addition(addition(A, B), C)). 11.42/11.65 fof(additive_commutativity, axiom, 11.42/11.65 ![A, B]: addition(B, A)=addition(A, B)). 11.42/11.65 fof(additive_idempotence, axiom, ![A]: A=addition(A, A)). 11.42/11.65 fof(additive_identity, axiom, ![A]: addition(A, zero)=A). 11.42/11.65 fof(domain1, axiom, 11.42/11.65 ![X0]: zero=multiplication(antidomain(X0), X0)). 11.42/11.65 fof(domain2, axiom, 11.42/11.65 ![X0, X1]: 11.42/11.65 antidomain(multiplication(X0, 11.42/11.65 antidomain(antidomain(X1))))=addition(antidomain(multiplication(X0, 11.42/11.65 X1)), 11.42/11.65 antidomain(multiplication(X0, 11.42/11.65 antidomain(antidomain(X1)))))). 11.42/11.65 fof(domain3, axiom, 11.42/11.65 ![X0]: one=addition(antidomain(antidomain(X0)), antidomain(X0))). 11.42/11.65 fof(domain4, axiom, ![X0]: domain(X0)=antidomain(antidomain(X0))). 11.42/11.65 fof(goals, conjecture, 11.42/11.65 ![X0, X1]: 11.42/11.65 domain(multiplication(X0, domain(X1)))=domain(multiplication(X0, 11.42/11.65 X1))). 11.42/11.65 fof(left_annihilation, axiom, ![A]: zero=multiplication(zero, A)). 11.42/11.65 fof(left_distributivity, axiom, 11.42/11.65 ![A, B, C]: 11.42/11.65 addition(multiplication(A, C), 11.42/11.65 multiplication(B, C))=multiplication(addition(A, B), C)). 11.42/11.65 fof(multiplicative_associativity, axiom, 11.42/11.65 ![A, B, C]: 11.42/11.65 multiplication(multiplication(A, B), C)=multiplication(A, 11.42/11.65 multiplication(B, C))). 11.42/11.65 fof(multiplicative_left_identity, axiom, 11.42/11.65 ![A]: A=multiplication(one, A)). 11.42/11.65 fof(multiplicative_right_identity, axiom, 11.42/11.65 ![A]: A=multiplication(A, one)). 11.42/11.65 fof(right_distributivity, axiom, 11.42/11.65 ![A, B, C]: 11.42/11.65 addition(multiplication(A, B), 11.42/11.65 multiplication(A, C))=multiplication(A, addition(B, C))). 11.42/11.65 11.42/11.65 Now clausify the problem and encode Horn clauses using encoding 3 of 11.42/11.65 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 11.42/11.65 We repeatedly replace C & s=t => u=v by the two clauses: 11.42/11.65 $$fresh(y, y, x1...xn) = u 11.42/11.65 C => $$fresh(s, t, x1...xn) = v 11.42/11.65 where $$fresh is a fresh function symbol and x1..xn are the free 11.42/11.65 variables of u and v. 11.42/11.65 A predicate p(X) is encoded as p(X)=$$true (this is sound, because the 11.42/11.65 input problem has no model of domain size 1). 11.42/11.65 11.42/11.65 The encoding turns the above axioms into the following unit equations and goals: 11.42/11.65 11.42/11.65 Axiom 3 (right_distributivity): addition(multiplication(X, Y), multiplication(X, Z)) = multiplication(X, addition(Y, Z)). 11.42/11.65 Axiom 4 (left_distributivity): addition(multiplication(X, Y), multiplication(Z, Y)) = multiplication(addition(X, Z), Y). 11.42/11.65 Axiom 5 (additive_commutativity): addition(X, Y) = addition(Y, X). 11.42/11.65 Axiom 6 (multiplicative_left_identity): X = multiplication(one, X). 11.42/11.65 Axiom 7 (multiplicative_right_identity): X = multiplication(X, one). 11.42/11.65 Axiom 8 (left_annihilation): zero = multiplication(zero, X). 11.42/11.65 Axiom 9 (additive_identity): addition(X, zero) = X. 11.42/11.65 Axiom 11 (multiplicative_associativity): multiplication(multiplication(X, Y), Z) = multiplication(X, multiplication(Y, Z)). 11.42/11.65 Axiom 12 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z). 11.42/11.65 Axiom 15 (additive_idempotence): X = addition(X, X). 11.42/11.65 Axiom 18 (domain2): antidomain(multiplication(X, antidomain(antidomain(Y)))) = addition(antidomain(multiplication(X, Y)), antidomain(multiplication(X, antidomain(antidomain(Y))))). 11.42/11.65 Axiom 21 (domain1): zero = multiplication(antidomain(X), X). 11.42/11.65 Axiom 22 (domain3): one = addition(antidomain(antidomain(X)), antidomain(X)). 11.42/11.65 Axiom 23 (domain4): domain(X) = antidomain(antidomain(X)). 11.42/11.65 11.42/11.65 Lemma 24: addition(antidomain(X), antidomain(antidomain(X))) = one. 11.42/11.65 Proof: 11.42/11.65 addition(antidomain(X), antidomain(antidomain(X))) 11.42/11.65 = { by axiom 5 (additive_commutativity) } 11.42/11.65 addition(antidomain(antidomain(X)), antidomain(X)) 11.42/11.65 = { by axiom 22 (domain3) } 11.42/11.65 one 11.42/11.65 11.42/11.65 Lemma 25: antidomain(one) = zero. 11.42/11.65 Proof: 11.42/11.65 antidomain(one) 11.42/11.65 = { by axiom 7 (multiplicative_right_identity) } 11.42/11.65 multiplication(antidomain(one), one) 11.42/11.65 = { by axiom 21 (domain1) } 11.42/11.65 zero 11.42/11.65 11.42/11.65 Lemma 26: addition(antidomain(X), domain(X)) = one. 11.42/11.65 Proof: 11.42/11.65 addition(antidomain(X), domain(X)) 11.42/11.65 = { by axiom 23 (domain4) } 11.42/11.65 addition(antidomain(X), antidomain(antidomain(X))) 11.42/11.65 = { by lemma 24 } 11.42/11.65 one 11.42/11.65 11.42/11.65 Lemma 27: multiplication(addition(X, antidomain(Y)), Y) = multiplication(X, Y). 11.42/11.65 Proof: 11.42/11.65 multiplication(addition(X, antidomain(Y)), Y) 11.42/11.65 = { by axiom 4 (left_distributivity) } 11.42/11.65 addition(multiplication(X, Y), multiplication(antidomain(Y), Y)) 11.42/11.65 = { by axiom 21 (domain1) } 11.42/11.65 addition(multiplication(X, Y), zero) 11.42/11.65 = { by axiom 9 (additive_identity) } 11.55/11.73 multiplication(X, Y) 11.55/11.73 11.55/11.73 Goal 1 (goals): domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))) = domain(multiplication(sK2_goals_X0, sK1_goals_X1)). 11.55/11.73 Proof: 11.55/11.73 domain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))) 11.55/11.73 = { by axiom 23 (domain4) } 11.55/11.73 antidomain(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))) 11.55/11.73 = { by axiom 23 (domain4) } 11.55/11.73 antidomain(antidomain(multiplication(sK2_goals_X0, antidomain(antidomain(sK1_goals_X1))))) 11.55/11.73 = { by axiom 18 (domain2) } 11.55/11.73 antidomain(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), antidomain(multiplication(sK2_goals_X0, antidomain(antidomain(sK1_goals_X1)))))) 11.55/11.73 = { by axiom 23 (domain4) } 11.55/11.73 antidomain(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))))) 11.55/11.73 = { by axiom 7 (multiplicative_right_identity) } 11.55/11.73 antidomain(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), one))) 11.55/11.73 = { by lemma 26 } 11.55/11.73 antidomain(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), domain(multiplication(sK2_goals_X0, sK1_goals_X1)))))) 11.55/11.73 = { by axiom 5 (additive_commutativity) } 11.55/11.73 antidomain(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), addition(domain(multiplication(sK2_goals_X0, sK1_goals_X1)), antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)))))) 11.55/11.73 = { by axiom 3 (right_distributivity) } 11.55/11.73 antidomain(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), addition(multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)))))) 11.55/11.73 = { by axiom 5 (additive_commutativity) } 11.55/11.73 antidomain(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), addition(multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), antidomain(multiplication(sK2_goals_X0, sK1_goals_X1))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, sK1_goals_X1)))))) 11.55/11.73 = { by axiom 12 (additive_associativity) } 11.55/11.73 antidomain(addition(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))) 11.55/11.73 = { by axiom 6 (multiplicative_left_identity) } 11.55/11.73 antidomain(addition(addition(multiplication(one, antidomain(multiplication(sK2_goals_X0, sK1_goals_X1))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))) 11.55/11.73 = { by axiom 4 (left_distributivity) } 11.55/11.73 antidomain(addition(multiplication(addition(one, antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), antidomain(multiplication(sK2_goals_X0, sK1_goals_X1))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))) 11.55/11.73 = { by axiom 5 (additive_commutativity) } 11.55/11.73 antidomain(addition(multiplication(addition(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), one), antidomain(multiplication(sK2_goals_X0, sK1_goals_X1))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))) 11.55/11.73 = { by lemma 24 } 11.55/11.73 antidomain(addition(multiplication(addition(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), addition(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), antidomain(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))))), antidomain(multiplication(sK2_goals_X0, sK1_goals_X1))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))) 11.55/11.73 = { by axiom 12 (additive_associativity) } 11.55/11.73 antidomain(addition(multiplication(addition(addition(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1)))), antidomain(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))))), antidomain(multiplication(sK2_goals_X0, sK1_goals_X1))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))) 11.55/11.73 = { by axiom 15 (additive_idempotence) } 11.55/11.73 antidomain(addition(multiplication(addition(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), antidomain(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))))), antidomain(multiplication(sK2_goals_X0, sK1_goals_X1))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))) 11.55/11.73 = { by lemma 24 } 11.55/11.73 antidomain(addition(multiplication(one, antidomain(multiplication(sK2_goals_X0, sK1_goals_X1))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))) 11.55/11.73 = { by axiom 6 (multiplicative_left_identity) } 11.55/11.73 antidomain(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, sK1_goals_X1))))) 11.55/11.73 = { by axiom 6 (multiplicative_left_identity) } 11.55/11.73 antidomain(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, multiplication(one, sK1_goals_X1)))))) 11.55/11.73 = { by lemma 24 } 11.55/11.73 antidomain(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, multiplication(addition(antidomain(sK1_goals_X1), antidomain(antidomain(sK1_goals_X1))), sK1_goals_X1)))))) 11.55/11.73 = { by axiom 5 (additive_commutativity) } 11.55/11.73 antidomain(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, multiplication(addition(antidomain(antidomain(sK1_goals_X1)), antidomain(sK1_goals_X1)), sK1_goals_X1)))))) 11.55/11.73 = { by lemma 27 } 11.55/11.73 antidomain(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, multiplication(antidomain(antidomain(sK1_goals_X1)), sK1_goals_X1)))))) 11.55/11.73 = { by axiom 23 (domain4) } 11.55/11.73 antidomain(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, multiplication(domain(sK1_goals_X1), sK1_goals_X1)))))) 11.55/11.73 = { by axiom 6 (multiplicative_left_identity) } 11.55/11.73 antidomain(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), multiplication(one, multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, multiplication(domain(sK1_goals_X1), sK1_goals_X1))))))) 11.55/11.73 = { by lemma 26 } 11.55/11.73 antidomain(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), multiplication(addition(antidomain(one), domain(one)), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, multiplication(domain(sK1_goals_X1), sK1_goals_X1))))))) 11.55/11.73 = { by lemma 25 } 11.55/11.73 antidomain(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), multiplication(addition(zero, domain(one)), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, multiplication(domain(sK1_goals_X1), sK1_goals_X1))))))) 11.55/11.73 = { by axiom 5 (additive_commutativity) } 11.55/11.73 antidomain(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), multiplication(addition(domain(one), zero), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, multiplication(domain(sK1_goals_X1), sK1_goals_X1))))))) 11.55/11.73 = { by axiom 9 (additive_identity) } 11.55/11.73 antidomain(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), multiplication(domain(one), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, multiplication(domain(sK1_goals_X1), sK1_goals_X1))))))) 11.55/11.73 = { by axiom 23 (domain4) } 11.55/11.73 antidomain(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), multiplication(antidomain(antidomain(one)), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, multiplication(domain(sK1_goals_X1), sK1_goals_X1))))))) 11.55/11.73 = { by lemma 25 } 11.55/11.73 antidomain(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), multiplication(antidomain(zero), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, multiplication(domain(sK1_goals_X1), sK1_goals_X1))))))) 11.55/11.73 = { by axiom 8 (left_annihilation) } 11.55/11.73 antidomain(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), multiplication(antidomain(multiplication(zero, sK1_goals_X1)), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, multiplication(domain(sK1_goals_X1), sK1_goals_X1))))))) 11.55/11.73 = { by axiom 21 (domain1) } 11.55/11.73 antidomain(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), multiplication(antidomain(multiplication(multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), multiplication(sK2_goals_X0, domain(sK1_goals_X1))), sK1_goals_X1)), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, multiplication(domain(sK1_goals_X1), sK1_goals_X1))))))) 11.55/11.73 = { by axiom 11 (multiplicative_associativity) } 11.55/11.73 antidomain(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), multiplication(antidomain(multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), multiplication(multiplication(sK2_goals_X0, domain(sK1_goals_X1)), sK1_goals_X1))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, multiplication(domain(sK1_goals_X1), sK1_goals_X1))))))) 11.55/11.73 = { by axiom 11 (multiplicative_associativity) } 11.55/11.73 antidomain(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), multiplication(antidomain(multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), multiplication(sK2_goals_X0, multiplication(domain(sK1_goals_X1), sK1_goals_X1)))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), domain(multiplication(sK2_goals_X0, multiplication(domain(sK1_goals_X1), sK1_goals_X1))))))) 11.55/11.73 = { by axiom 23 (domain4) } 11.55/11.73 antidomain(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), multiplication(antidomain(multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), multiplication(sK2_goals_X0, multiplication(domain(sK1_goals_X1), sK1_goals_X1)))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), antidomain(antidomain(multiplication(sK2_goals_X0, multiplication(domain(sK1_goals_X1), sK1_goals_X1)))))))) 11.55/11.73 = { by lemma 27 } 11.55/11.73 antidomain(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), multiplication(addition(antidomain(multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), multiplication(sK2_goals_X0, multiplication(domain(sK1_goals_X1), sK1_goals_X1)))), antidomain(multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), antidomain(antidomain(multiplication(sK2_goals_X0, multiplication(domain(sK1_goals_X1), sK1_goals_X1))))))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), antidomain(antidomain(multiplication(sK2_goals_X0, multiplication(domain(sK1_goals_X1), sK1_goals_X1)))))))) 11.55/11.73 = { by axiom 18 (domain2) } 11.55/11.73 antidomain(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), multiplication(antidomain(multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), antidomain(antidomain(multiplication(sK2_goals_X0, multiplication(domain(sK1_goals_X1), sK1_goals_X1)))))), multiplication(antidomain(multiplication(sK2_goals_X0, domain(sK1_goals_X1))), antidomain(antidomain(multiplication(sK2_goals_X0, multiplication(domain(sK1_goals_X1), sK1_goals_X1)))))))) 11.55/11.73 = { by axiom 21 (domain1) } 11.55/11.73 antidomain(addition(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1)), zero)) 11.55/11.73 = { by axiom 9 (additive_identity) } 11.55/11.73 antidomain(antidomain(multiplication(sK2_goals_X0, sK1_goals_X1))) 11.55/11.73 = { by axiom 23 (domain4) } 11.55/11.73 domain(multiplication(sK2_goals_X0, sK1_goals_X1)) 11.55/11.73 % SZS output end Proof 11.55/11.73 11.55/11.73 RESULT: Theorem (the conjecture is true). 11.55/11.74 EOF