0.00/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.10 % Command : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn 0.08/0.30 % Computer : n016.cluster.edu 0.08/0.30 % Model : x86_64 x86_64 0.08/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.08/0.30 % Memory : 8042.1875MB 0.08/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.08/0.30 % CPULimit : 960 0.08/0.30 % WCLimit : 120 0.08/0.30 % DateTime : Thu Jul 2 08:30:21 EDT 2020 0.08/0.30 % CPUTime : 4.45/0.97 % SZS status Theorem 4.45/0.97 4.45/0.97 % SZS output start Proof 4.45/0.97 Take the following subset of the input axioms: 4.45/0.97 fof(additive_commutativity, axiom, ![A, B]: addition(B, A)=addition(A, B)). 4.45/0.97 fof(additive_idempotence, axiom, ![A]: A=addition(A, A)). 4.45/0.97 fof(additive_identity, axiom, ![A]: addition(A, zero)=A). 4.45/0.97 fof(goals, conjecture, ![X0, X1, X2, X3, X4]: ((test(X3) & test(X4)) => (leq(addition(multiplication(X3, addition(multiplication(X3, X0), multiplication(c(X3), X1))), multiplication(c(X3), X2)), addition(multiplication(X3, X0), multiplication(c(X3), X2))) & leq(addition(multiplication(X3, X0), multiplication(c(X3), X2)), addition(multiplication(X3, addition(multiplication(X3, X0), multiplication(c(X3), X1))), multiplication(c(X3), X2)))))). 4.45/0.97 fof(left_annihilation, axiom, ![A]: zero=multiplication(zero, A)). 4.45/0.97 fof(left_distributivity, axiom, ![A, B, C]: addition(multiplication(A, C), multiplication(B, C))=multiplication(addition(A, B), C)). 4.45/0.97 fof(multiplicative_associativity, axiom, ![A, B, C]: multiplication(A, multiplication(B, C))=multiplication(multiplication(A, B), C)). 4.45/0.97 fof(multiplicative_left_identity, axiom, ![A]: multiplication(one, A)=A). 4.45/0.97 fof(multiplicative_right_identity, axiom, ![A]: multiplication(A, one)=A). 4.45/0.97 fof(order, axiom, ![A, B]: (leq(A, B) <=> B=addition(A, B))). 4.45/0.97 fof(right_distributivity, axiom, ![A, B, C]: addition(multiplication(A, B), multiplication(A, C))=multiplication(A, addition(B, C))). 4.45/0.97 fof(test_1, axiom, ![X0]: (test(X0) <=> ?[X1]: complement(X1, X0))). 4.45/0.97 fof(test_2, axiom, ![X0, X1]: (complement(X1, X0) <=> (zero=multiplication(X0, X1) & (zero=multiplication(X1, X0) & addition(X0, X1)=one)))). 4.45/0.97 fof(test_3, axiom, ![X0, X1]: ((complement(X0, X1) <=> X1=c(X0)) <= test(X0))). 4.45/0.97 4.45/0.97 Now clausify the problem and encode Horn clauses using encoding 3 of 4.45/0.97 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 4.45/0.97 We repeatedly replace C & s=t => u=v by the two clauses: 4.45/0.97 fresh(y, y, x1...xn) = u 4.45/0.97 C => fresh(s, t, x1...xn) = v 4.45/0.97 where fresh is a fresh function symbol and x1..xn are the free 4.45/0.97 variables of u and v. 4.45/0.97 A predicate p(X) is encoded as p(X)=true (this is sound, because the 4.45/0.97 input problem has no model of domain size 1). 4.45/0.97 4.45/0.97 The encoding turns the above axioms into the following unit equations and goals: 4.45/0.97 4.45/0.97 Axiom 1 (order): fresh11(X, X, Y, Z) = true. 4.45/0.97 Axiom 2 (test_1): fresh12(X, X, Y) = true. 4.45/0.97 Axiom 3 (test_2_1): fresh8(X, X, Y, Z) = one. 4.45/0.97 Axiom 4 (test_2_2): fresh7(X, X, Y, Z) = zero. 4.45/0.97 Axiom 5 (test_2_3): fresh6(X, X, Y, Z) = zero. 4.45/0.97 Axiom 6 (test_3): fresh5(X, X, Y, Z) = complement(Y, Z). 4.45/0.97 Axiom 7 (test_3): fresh4(X, X, Y, Z) = true. 4.45/0.97 Axiom 8 (left_distributivity): addition(multiplication(X, Y), multiplication(Z, Y)) = multiplication(addition(X, Z), Y). 4.45/0.97 Axiom 9 (multiplicative_right_identity): multiplication(X, one) = X. 4.45/0.97 Axiom 10 (additive_commutativity): addition(X, Y) = addition(Y, X). 4.45/0.97 Axiom 11 (multiplicative_left_identity): multiplication(one, X) = X. 4.45/0.97 Axiom 12 (right_distributivity): addition(multiplication(X, Y), multiplication(X, Z)) = multiplication(X, addition(Y, Z)). 4.45/0.97 Axiom 13 (additive_idempotence): X = addition(X, X). 4.45/0.97 Axiom 14 (additive_identity): addition(X, zero) = X. 4.45/0.97 Axiom 15 (order): fresh11(X, addition(Y, X), Y, X) = leq(Y, X). 4.45/0.97 Axiom 16 (left_annihilation): zero = multiplication(zero, X). 4.45/0.97 Axiom 17 (multiplicative_associativity): multiplication(X, multiplication(Y, Z)) = multiplication(multiplication(X, Y), Z). 4.45/0.97 Axiom 18 (test_1): fresh12(test(X), true, X) = complement(sK8_test_1_X1(X), X). 4.45/0.97 Axiom 19 (test_2_3): fresh6(complement(X, Y), true, Y, X) = multiplication(X, Y). 4.45/0.97 Axiom 20 (test_2_2): fresh7(complement(X, Y), true, Y, X) = multiplication(Y, X). 4.45/0.97 Axiom 21 (test_2_1): fresh8(complement(X, Y), true, Y, X) = addition(Y, X). 4.45/0.97 Axiom 22 (test_3): fresh5(test(X), true, X, Y) = fresh4(Y, c(X), X, Y). 4.45/0.98 Axiom 23 (goals): test(sK7_goals_X3) = true. 4.45/0.98 4.45/0.98 Lemma 24: complement(sK8_test_1_X1(sK7_goals_X3), sK7_goals_X3) = true. 4.45/0.98 Proof: 4.45/0.98 complement(sK8_test_1_X1(sK7_goals_X3), sK7_goals_X3) 4.45/0.98 = { by axiom 18 (test_1) } 4.45/0.98 fresh12(test(sK7_goals_X3), true, sK7_goals_X3) 4.45/0.98 = { by axiom 23 (goals) } 4.45/0.98 fresh12(true, true, sK7_goals_X3) 4.45/0.98 = { by axiom 2 (test_1) } 4.45/0.98 true 4.45/0.98 4.45/0.98 Lemma 25: multiplication(sK8_test_1_X1(sK7_goals_X3), sK7_goals_X3) = zero. 4.45/0.98 Proof: 4.45/0.98 multiplication(sK8_test_1_X1(sK7_goals_X3), sK7_goals_X3) 4.45/0.98 = { by axiom 19 (test_2_3) } 4.45/0.98 fresh6(complement(sK8_test_1_X1(sK7_goals_X3), sK7_goals_X3), true, sK7_goals_X3, sK8_test_1_X1(sK7_goals_X3)) 4.45/0.98 = { by lemma 24 } 4.45/0.98 fresh6(true, true, sK7_goals_X3, sK8_test_1_X1(sK7_goals_X3)) 4.45/0.98 = { by axiom 5 (test_2_3) } 4.45/0.98 zero 4.45/0.98 4.45/0.98 Lemma 26: addition(zero, X) = X. 4.45/0.98 Proof: 4.45/0.98 addition(zero, X) 4.45/0.98 = { by axiom 10 (additive_commutativity) } 4.45/0.98 addition(X, zero) 4.45/0.98 = { by axiom 14 (additive_identity) } 4.45/0.98 X 4.45/0.98 4.45/0.98 Lemma 27: complement(sK7_goals_X3, c(sK7_goals_X3)) = true. 4.45/0.98 Proof: 4.45/0.98 complement(sK7_goals_X3, c(sK7_goals_X3)) 4.45/0.98 = { by axiom 6 (test_3) } 4.45/0.98 fresh5(true, true, sK7_goals_X3, c(sK7_goals_X3)) 4.45/0.98 = { by axiom 23 (goals) } 4.45/0.98 fresh5(test(sK7_goals_X3), true, sK7_goals_X3, c(sK7_goals_X3)) 4.45/0.98 = { by axiom 22 (test_3) } 4.45/0.98 fresh4(c(sK7_goals_X3), c(sK7_goals_X3), sK7_goals_X3, c(sK7_goals_X3)) 4.45/0.98 = { by axiom 7 (test_3) } 4.45/0.98 true 4.45/0.98 4.45/0.98 Lemma 28: addition(sK7_goals_X3, sK8_test_1_X1(sK7_goals_X3)) = one. 4.45/0.98 Proof: 4.45/0.98 addition(sK7_goals_X3, sK8_test_1_X1(sK7_goals_X3)) 4.45/0.98 = { by axiom 21 (test_2_1) } 4.45/0.98 fresh8(complement(sK8_test_1_X1(sK7_goals_X3), sK7_goals_X3), true, sK7_goals_X3, sK8_test_1_X1(sK7_goals_X3)) 4.45/0.98 = { by lemma 24 } 4.45/0.98 fresh8(true, true, sK7_goals_X3, sK8_test_1_X1(sK7_goals_X3)) 4.45/0.98 = { by axiom 3 (test_2_1) } 4.45/0.99 one 4.45/0.99 4.45/0.99 Lemma 29: multiplication(sK7_goals_X3, addition(X, multiplication(c(sK7_goals_X3), Y))) = multiplication(sK7_goals_X3, X). 4.45/0.99 Proof: 4.45/0.99 multiplication(sK7_goals_X3, addition(X, multiplication(c(sK7_goals_X3), Y))) 4.45/0.99 = { by axiom 10 (additive_commutativity) } 4.45/0.99 multiplication(sK7_goals_X3, addition(multiplication(c(sK7_goals_X3), Y), X)) 4.45/0.99 = { by axiom 11 (multiplicative_left_identity) } 4.45/0.99 multiplication(sK7_goals_X3, addition(multiplication(multiplication(one, c(sK7_goals_X3)), Y), X)) 4.45/0.99 = { by lemma 28 } 4.45/0.99 multiplication(sK7_goals_X3, addition(multiplication(multiplication(addition(sK7_goals_X3, sK8_test_1_X1(sK7_goals_X3)), c(sK7_goals_X3)), Y), X)) 4.45/0.99 = { by axiom 8 (left_distributivity) } 4.45/0.99 multiplication(sK7_goals_X3, addition(multiplication(addition(multiplication(sK7_goals_X3, c(sK7_goals_X3)), multiplication(sK8_test_1_X1(sK7_goals_X3), c(sK7_goals_X3))), Y), X)) 4.45/0.99 = { by axiom 19 (test_2_3) } 4.45/0.99 multiplication(sK7_goals_X3, addition(multiplication(addition(fresh6(complement(sK7_goals_X3, c(sK7_goals_X3)), true, c(sK7_goals_X3), sK7_goals_X3), multiplication(sK8_test_1_X1(sK7_goals_X3), c(sK7_goals_X3))), Y), X)) 4.45/0.99 = { by lemma 27 } 4.45/0.99 multiplication(sK7_goals_X3, addition(multiplication(addition(fresh6(true, true, c(sK7_goals_X3), sK7_goals_X3), multiplication(sK8_test_1_X1(sK7_goals_X3), c(sK7_goals_X3))), Y), X)) 4.45/0.99 = { by axiom 5 (test_2_3) } 4.45/0.99 multiplication(sK7_goals_X3, addition(multiplication(addition(zero, multiplication(sK8_test_1_X1(sK7_goals_X3), c(sK7_goals_X3))), Y), X)) 4.45/0.99 = { by lemma 25 } 4.45/0.99 multiplication(sK7_goals_X3, addition(multiplication(addition(multiplication(sK8_test_1_X1(sK7_goals_X3), sK7_goals_X3), multiplication(sK8_test_1_X1(sK7_goals_X3), c(sK7_goals_X3))), Y), X)) 4.45/0.99 = { by axiom 12 (right_distributivity) } 4.45/0.99 multiplication(sK7_goals_X3, addition(multiplication(multiplication(sK8_test_1_X1(sK7_goals_X3), addition(sK7_goals_X3, c(sK7_goals_X3))), Y), X)) 4.45/0.99 = { by axiom 10 (additive_commutativity) } 4.45/0.99 multiplication(sK7_goals_X3, addition(multiplication(multiplication(sK8_test_1_X1(sK7_goals_X3), addition(c(sK7_goals_X3), sK7_goals_X3)), Y), X)) 4.45/0.99 = { by axiom 21 (test_2_1) } 4.45/0.99 multiplication(sK7_goals_X3, addition(multiplication(multiplication(sK8_test_1_X1(sK7_goals_X3), fresh8(complement(sK7_goals_X3, c(sK7_goals_X3)), true, c(sK7_goals_X3), sK7_goals_X3)), Y), X)) 4.45/0.99 = { by lemma 27 } 4.45/0.99 multiplication(sK7_goals_X3, addition(multiplication(multiplication(sK8_test_1_X1(sK7_goals_X3), fresh8(true, true, c(sK7_goals_X3), sK7_goals_X3)), Y), X)) 4.45/0.99 = { by axiom 3 (test_2_1) } 4.45/0.99 multiplication(sK7_goals_X3, addition(multiplication(multiplication(sK8_test_1_X1(sK7_goals_X3), one), Y), X)) 4.45/0.99 = { by axiom 9 (multiplicative_right_identity) } 4.45/0.99 multiplication(sK7_goals_X3, addition(multiplication(sK8_test_1_X1(sK7_goals_X3), Y), X)) 4.45/0.99 = { by axiom 12 (right_distributivity) } 4.45/0.99 addition(multiplication(sK7_goals_X3, multiplication(sK8_test_1_X1(sK7_goals_X3), Y)), multiplication(sK7_goals_X3, X)) 4.45/0.99 = { by axiom 17 (multiplicative_associativity) } 4.45/0.99 addition(multiplication(multiplication(sK7_goals_X3, sK8_test_1_X1(sK7_goals_X3)), Y), multiplication(sK7_goals_X3, X)) 4.45/0.99 = { by axiom 20 (test_2_2) } 4.45/0.99 addition(multiplication(fresh7(complement(sK8_test_1_X1(sK7_goals_X3), sK7_goals_X3), true, sK7_goals_X3, sK8_test_1_X1(sK7_goals_X3)), Y), multiplication(sK7_goals_X3, X)) 4.45/0.99 = { by lemma 24 } 4.45/0.99 addition(multiplication(fresh7(true, true, sK7_goals_X3, sK8_test_1_X1(sK7_goals_X3)), Y), multiplication(sK7_goals_X3, X)) 4.45/0.99 = { by axiom 4 (test_2_2) } 4.45/0.99 addition(multiplication(zero, Y), multiplication(sK7_goals_X3, X)) 4.45/0.99 = { by axiom 16 (left_annihilation) } 4.45/0.99 addition(zero, multiplication(sK7_goals_X3, X)) 4.45/0.99 = { by lemma 26 } 4.45/1.00 multiplication(sK7_goals_X3, X) 4.45/1.00 4.45/1.00 Lemma 30: multiplication(sK7_goals_X3, multiplication(sK7_goals_X3, X)) = multiplication(sK7_goals_X3, X). 4.45/1.00 Proof: 4.45/1.00 multiplication(sK7_goals_X3, multiplication(sK7_goals_X3, X)) 4.45/1.00 = { by axiom 17 (multiplicative_associativity) } 4.45/1.00 multiplication(multiplication(sK7_goals_X3, sK7_goals_X3), X) 4.45/1.00 = { by lemma 26 } 4.45/1.00 multiplication(addition(zero, multiplication(sK7_goals_X3, sK7_goals_X3)), X) 4.45/1.00 = { by lemma 25 } 4.45/1.00 multiplication(addition(multiplication(sK8_test_1_X1(sK7_goals_X3), sK7_goals_X3), multiplication(sK7_goals_X3, sK7_goals_X3)), X) 4.45/1.00 = { by axiom 8 (left_distributivity) } 4.45/1.00 multiplication(multiplication(addition(sK8_test_1_X1(sK7_goals_X3), sK7_goals_X3), sK7_goals_X3), X) 4.45/1.00 = { by axiom 10 (additive_commutativity) } 4.45/1.00 multiplication(multiplication(addition(sK7_goals_X3, sK8_test_1_X1(sK7_goals_X3)), sK7_goals_X3), X) 4.45/1.00 = { by lemma 28 } 4.45/1.00 multiplication(multiplication(one, sK7_goals_X3), X) 4.45/1.00 = { by axiom 11 (multiplicative_left_identity) } 4.45/1.00 multiplication(sK7_goals_X3, X) 4.45/1.00 4.45/1.00 Lemma 31: leq(X, X) = true. 4.45/1.00 Proof: 4.45/1.00 leq(X, X) 4.45/1.00 = { by axiom 15 (order) } 4.45/1.00 fresh11(X, addition(X, X), X, X) 4.45/1.00 = { by axiom 13 (additive_idempotence) } 4.45/1.00 fresh11(X, X, X, X) 4.45/1.00 = { by axiom 1 (order) } 4.97/1.00 true 4.97/1.00 4.97/1.00 Goal 1 (goals_2): tuple(leq(addition(multiplication(sK7_goals_X3, addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK5_goals_X1))), multiplication(c(sK7_goals_X3), sK4_goals_X2)), addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK4_goals_X2))), leq(addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK2_goals_X2)), addition(multiplication(sK7_goals_X3, addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK3_goals_X1))), multiplication(c(sK7_goals_X3), sK2_goals_X2)))) = tuple(true, true). 4.97/1.00 Proof: 4.97/1.00 tuple(leq(addition(multiplication(sK7_goals_X3, addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK5_goals_X1))), multiplication(c(sK7_goals_X3), sK4_goals_X2)), addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK4_goals_X2))), leq(addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK2_goals_X2)), addition(multiplication(sK7_goals_X3, addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK3_goals_X1))), multiplication(c(sK7_goals_X3), sK2_goals_X2)))) 4.97/1.00 = { by axiom 10 (additive_commutativity) } 4.97/1.00 tuple(leq(addition(multiplication(c(sK7_goals_X3), sK4_goals_X2), multiplication(sK7_goals_X3, addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK5_goals_X1)))), addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK4_goals_X2))), leq(addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK2_goals_X2)), addition(multiplication(sK7_goals_X3, addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK3_goals_X1))), multiplication(c(sK7_goals_X3), sK2_goals_X2)))) 4.97/1.00 = { by lemma 29 } 4.97/1.00 tuple(leq(addition(multiplication(c(sK7_goals_X3), sK4_goals_X2), multiplication(sK7_goals_X3, multiplication(sK7_goals_X3, sK6_goals_X0))), addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK4_goals_X2))), leq(addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK2_goals_X2)), addition(multiplication(sK7_goals_X3, addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK3_goals_X1))), multiplication(c(sK7_goals_X3), sK2_goals_X2)))) 4.97/1.00 = { by lemma 30 } 4.97/1.00 tuple(leq(addition(multiplication(c(sK7_goals_X3), sK4_goals_X2), multiplication(sK7_goals_X3, sK6_goals_X0)), addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK4_goals_X2))), leq(addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK2_goals_X2)), addition(multiplication(sK7_goals_X3, addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK3_goals_X1))), multiplication(c(sK7_goals_X3), sK2_goals_X2)))) 4.97/1.00 = { by axiom 10 (additive_commutativity) } 4.97/1.00 tuple(leq(addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK4_goals_X2)), addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK4_goals_X2))), leq(addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK2_goals_X2)), addition(multiplication(sK7_goals_X3, addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK3_goals_X1))), multiplication(c(sK7_goals_X3), sK2_goals_X2)))) 4.97/1.00 = { by lemma 31 } 4.97/1.00 tuple(true, leq(addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK2_goals_X2)), addition(multiplication(sK7_goals_X3, addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK3_goals_X1))), multiplication(c(sK7_goals_X3), sK2_goals_X2)))) 4.97/1.00 = { by axiom 10 (additive_commutativity) } 4.97/1.00 tuple(true, leq(addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK2_goals_X2)), addition(multiplication(c(sK7_goals_X3), sK2_goals_X2), multiplication(sK7_goals_X3, addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK3_goals_X1)))))) 4.97/1.00 = { by lemma 29 } 4.97/1.00 tuple(true, leq(addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK2_goals_X2)), addition(multiplication(c(sK7_goals_X3), sK2_goals_X2), multiplication(sK7_goals_X3, multiplication(sK7_goals_X3, sK6_goals_X0))))) 4.97/1.00 = { by lemma 30 } 4.97/1.00 tuple(true, leq(addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK2_goals_X2)), addition(multiplication(c(sK7_goals_X3), sK2_goals_X2), multiplication(sK7_goals_X3, sK6_goals_X0)))) 4.97/1.00 = { by axiom 10 (additive_commutativity) } 4.97/1.00 tuple(true, leq(addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK2_goals_X2)), addition(multiplication(sK7_goals_X3, sK6_goals_X0), multiplication(c(sK7_goals_X3), sK2_goals_X2)))) 4.97/1.00 = { by lemma 31 } 4.97/1.00 tuple(true, true) 4.97/1.00 % SZS output end Proof 4.97/1.00 4.97/1.00 RESULT: Theorem (the conjecture is true). 4.97/1.01 EOF