TSTP Solution File: KLE023+2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : KLE023+2 : 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 : n002.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 05:35:32 EDT 2023
% Result : Theorem 0.19s 0.59s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE023+2 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % 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 : n002.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 11:12:05 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.59 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.59
% 0.19/0.59 % SZS status Theorem
% 0.19/0.59
% 0.19/0.60 % SZS output start Proof
% 0.19/0.60 Take the following subset of the input axioms:
% 0.19/0.61 fof(additive_associativity, axiom, ![A, B, C]: addition(A, addition(B, C))=addition(addition(A, B), C)).
% 0.19/0.61 fof(additive_commutativity, axiom, ![A2, B2]: addition(A2, B2)=addition(B2, A2)).
% 0.19/0.61 fof(additive_idempotence, axiom, ![A2]: addition(A2, A2)=A2).
% 0.19/0.61 fof(additive_identity, axiom, ![A2]: addition(A2, zero)=A2).
% 0.19/0.61 fof(goals, conjecture, ![X0, X1, X2]: ((test(X1) & test(X2)) => (addition(multiplication(X1, X0), multiplication(X0, X2))=multiplication(X0, X2) => addition(multiplication(X0, c(X2)), multiplication(c(X1), X0))=multiplication(c(X1), X0)))).
% 0.19/0.61 fof(left_distributivity, axiom, ![A2, B2, C2]: multiplication(addition(A2, B2), C2)=addition(multiplication(A2, C2), multiplication(B2, C2))).
% 0.19/0.61 fof(multiplicative_associativity, axiom, ![A2, B2, C2]: multiplication(A2, multiplication(B2, C2))=multiplication(multiplication(A2, B2), C2)).
% 0.19/0.61 fof(multiplicative_left_identity, axiom, ![A2]: multiplication(one, A2)=A2).
% 0.19/0.61 fof(multiplicative_right_identity, axiom, ![A2]: multiplication(A2, one)=A2).
% 0.19/0.61 fof(right_annihilation, axiom, ![A2]: multiplication(A2, zero)=zero).
% 0.19/0.61 fof(right_distributivity, axiom, ![A2, B2, C2]: multiplication(A2, addition(B2, C2))=addition(multiplication(A2, B2), multiplication(A2, C2))).
% 0.19/0.61 fof(test_1, axiom, ![X0_2]: (test(X0_2) <=> ?[X1_2]: complement(X1_2, X0_2))).
% 0.19/0.61 fof(test_2, axiom, ![X0_2, X1_2]: (complement(X1_2, X0_2) <=> (multiplication(X0_2, X1_2)=zero & (multiplication(X1_2, X0_2)=zero & addition(X0_2, X1_2)=one)))).
% 0.19/0.61 fof(test_3, axiom, ![X0_2, X1_2]: (test(X0_2) => (c(X0_2)=X1_2 <=> complement(X0_2, X1_2)))).
% 0.19/0.61
% 0.19/0.61 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.61 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.61 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.61 fresh(y, y, x1...xn) = u
% 0.19/0.61 C => fresh(s, t, x1...xn) = v
% 0.19/0.61 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.61 variables of u and v.
% 0.19/0.61 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.61 input problem has no model of domain size 1).
% 0.19/0.61
% 0.19/0.61 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.61
% 0.19/0.61 Axiom 1 (goals_1): test(x1) = true.
% 0.19/0.61 Axiom 2 (goals_2): test(x2) = true.
% 0.19/0.61 Axiom 3 (right_annihilation): multiplication(X, zero) = zero.
% 0.19/0.61 Axiom 4 (multiplicative_right_identity): multiplication(X, one) = X.
% 0.19/0.61 Axiom 5 (multiplicative_left_identity): multiplication(one, X) = X.
% 0.19/0.61 Axiom 6 (additive_idempotence): addition(X, X) = X.
% 0.19/0.61 Axiom 7 (additive_commutativity): addition(X, Y) = addition(Y, X).
% 0.19/0.61 Axiom 8 (additive_identity): addition(X, zero) = X.
% 0.19/0.61 Axiom 9 (test_1): fresh16(X, X, Y) = true.
% 0.19/0.61 Axiom 10 (multiplicative_associativity): multiplication(X, multiplication(Y, Z)) = multiplication(multiplication(X, Y), Z).
% 0.19/0.61 Axiom 11 (additive_associativity): addition(X, addition(Y, Z)) = addition(addition(X, Y), Z).
% 0.19/0.61 Axiom 12 (test_3_1): fresh(X, X, Y, Z) = Z.
% 0.19/0.61 Axiom 13 (test_2): fresh18(X, X, Y, Z) = true.
% 0.19/0.61 Axiom 14 (test_1): fresh16(test(X), true, X) = complement(x1_2(X), X).
% 0.19/0.61 Axiom 15 (test_2): fresh13(X, X, Y, Z) = complement(Z, Y).
% 0.19/0.61 Axiom 16 (test_2_1): fresh12(X, X, Y, Z) = one.
% 0.19/0.61 Axiom 17 (test_2_2): fresh11(X, X, Y, Z) = zero.
% 0.19/0.61 Axiom 18 (test_2_3): fresh10(X, X, Y, Z) = zero.
% 0.19/0.61 Axiom 19 (test_3): fresh9(X, X, Y, Z) = complement(Y, Z).
% 0.19/0.61 Axiom 20 (test_3): fresh8(X, X, Y, Z) = true.
% 0.19/0.61 Axiom 21 (test_3_1): fresh7(X, X, Y, Z) = c(Y).
% 0.19/0.61 Axiom 22 (test_3): fresh9(test(X), true, X, Y) = fresh8(c(X), Y, X, Y).
% 0.19/0.61 Axiom 23 (right_distributivity): multiplication(X, addition(Y, Z)) = addition(multiplication(X, Y), multiplication(X, Z)).
% 0.19/0.61 Axiom 24 (left_distributivity): multiplication(addition(X, Y), Z) = addition(multiplication(X, Z), multiplication(Y, Z)).
% 0.19/0.61 Axiom 25 (goals): addition(multiplication(x1, x0), multiplication(x0, x2)) = multiplication(x0, x2).
% 0.19/0.61 Axiom 26 (test_2): fresh17(X, X, Y, Z) = fresh18(addition(Y, Z), one, Y, Z).
% 0.19/0.61 Axiom 27 (test_2): fresh17(multiplication(X, Y), zero, Y, X) = fresh13(multiplication(Y, X), zero, Y, X).
% 0.19/0.61 Axiom 28 (test_2_1): fresh12(complement(X, Y), true, Y, X) = addition(Y, X).
% 0.19/0.61 Axiom 29 (test_2_2): fresh11(complement(X, Y), true, Y, X) = multiplication(Y, X).
% 0.19/0.61 Axiom 30 (test_2_3): fresh10(complement(X, Y), true, Y, X) = multiplication(X, Y).
% 0.19/0.61 Axiom 31 (test_3_1): fresh7(complement(X, Y), true, X, Y) = fresh(test(X), true, X, Y).
% 0.19/0.61
% 0.19/0.61 Lemma 32: complement(x1_2(x2), x2) = true.
% 0.19/0.61 Proof:
% 0.19/0.61 complement(x1_2(x2), x2)
% 0.19/0.61 = { by axiom 14 (test_1) R->L }
% 0.19/0.61 fresh16(test(x2), true, x2)
% 0.19/0.61 = { by axiom 2 (goals_2) }
% 0.19/0.61 fresh16(true, true, x2)
% 0.19/0.61 = { by axiom 9 (test_1) }
% 0.19/0.61 true
% 0.19/0.61
% 0.19/0.61 Lemma 33: multiplication(x2, x1_2(x2)) = zero.
% 0.19/0.61 Proof:
% 0.19/0.61 multiplication(x2, x1_2(x2))
% 0.19/0.61 = { by axiom 29 (test_2_2) R->L }
% 0.19/0.61 fresh11(complement(x1_2(x2), x2), true, x2, x1_2(x2))
% 0.19/0.61 = { by lemma 32 }
% 0.19/0.61 fresh11(true, true, x2, x1_2(x2))
% 0.19/0.61 = { by axiom 17 (test_2_2) }
% 0.19/0.61 zero
% 0.19/0.61
% 0.19/0.61 Lemma 34: addition(x2, x1_2(x2)) = one.
% 0.19/0.61 Proof:
% 0.19/0.61 addition(x2, x1_2(x2))
% 0.19/0.61 = { by axiom 28 (test_2_1) R->L }
% 0.19/0.61 fresh12(complement(x1_2(x2), x2), true, x2, x1_2(x2))
% 0.19/0.61 = { by lemma 32 }
% 0.19/0.61 fresh12(true, true, x2, x1_2(x2))
% 0.19/0.61 = { by axiom 16 (test_2_1) }
% 0.19/0.61 one
% 0.19/0.61
% 0.19/0.61 Lemma 35: x1_2(x2) = c(x2).
% 0.19/0.61 Proof:
% 0.19/0.61 x1_2(x2)
% 0.19/0.61 = { by axiom 12 (test_3_1) R->L }
% 0.19/0.61 fresh(true, true, x2, x1_2(x2))
% 0.19/0.61 = { by axiom 2 (goals_2) R->L }
% 0.19/0.61 fresh(test(x2), true, x2, x1_2(x2))
% 0.19/0.61 = { by axiom 31 (test_3_1) R->L }
% 0.19/0.61 fresh7(complement(x2, x1_2(x2)), true, x2, x1_2(x2))
% 0.19/0.61 = { by axiom 15 (test_2) R->L }
% 0.19/0.61 fresh7(fresh13(zero, zero, x1_2(x2), x2), true, x2, x1_2(x2))
% 0.19/0.61 = { by axiom 18 (test_2_3) R->L }
% 0.19/0.61 fresh7(fresh13(fresh10(true, true, x2, x1_2(x2)), zero, x1_2(x2), x2), true, x2, x1_2(x2))
% 0.19/0.61 = { by lemma 32 R->L }
% 0.19/0.61 fresh7(fresh13(fresh10(complement(x1_2(x2), x2), true, x2, x1_2(x2)), zero, x1_2(x2), x2), true, x2, x1_2(x2))
% 0.19/0.61 = { by axiom 30 (test_2_3) }
% 0.19/0.61 fresh7(fresh13(multiplication(x1_2(x2), x2), zero, x1_2(x2), x2), true, x2, x1_2(x2))
% 0.19/0.61 = { by axiom 27 (test_2) R->L }
% 0.19/0.61 fresh7(fresh17(multiplication(x2, x1_2(x2)), zero, x1_2(x2), x2), true, x2, x1_2(x2))
% 0.19/0.61 = { by lemma 33 }
% 0.19/0.61 fresh7(fresh17(zero, zero, x1_2(x2), x2), true, x2, x1_2(x2))
% 0.19/0.61 = { by axiom 26 (test_2) }
% 0.19/0.61 fresh7(fresh18(addition(x1_2(x2), x2), one, x1_2(x2), x2), true, x2, x1_2(x2))
% 0.19/0.61 = { by axiom 7 (additive_commutativity) }
% 0.19/0.61 fresh7(fresh18(addition(x2, x1_2(x2)), one, x1_2(x2), x2), true, x2, x1_2(x2))
% 0.19/0.61 = { by lemma 34 }
% 0.19/0.61 fresh7(fresh18(one, one, x1_2(x2), x2), true, x2, x1_2(x2))
% 0.19/0.61 = { by axiom 13 (test_2) }
% 0.19/0.61 fresh7(true, true, x2, x1_2(x2))
% 0.19/0.61 = { by axiom 21 (test_3_1) }
% 0.19/0.61 c(x2)
% 0.19/0.61
% 0.19/0.61 Lemma 36: addition(x2, c(x2)) = one.
% 0.19/0.61 Proof:
% 0.19/0.61 addition(x2, c(x2))
% 0.19/0.61 = { by axiom 7 (additive_commutativity) R->L }
% 0.19/0.61 addition(c(x2), x2)
% 0.19/0.61 = { by axiom 28 (test_2_1) R->L }
% 0.19/0.61 fresh12(complement(x2, c(x2)), true, c(x2), x2)
% 0.19/0.61 = { by axiom 19 (test_3) R->L }
% 0.19/0.61 fresh12(fresh9(true, true, x2, c(x2)), true, c(x2), x2)
% 0.19/0.61 = { by axiom 2 (goals_2) R->L }
% 0.19/0.61 fresh12(fresh9(test(x2), true, x2, c(x2)), true, c(x2), x2)
% 0.19/0.61 = { by axiom 22 (test_3) }
% 0.19/0.61 fresh12(fresh8(c(x2), c(x2), x2, c(x2)), true, c(x2), x2)
% 0.19/0.61 = { by axiom 20 (test_3) }
% 0.19/0.61 fresh12(true, true, c(x2), x2)
% 0.19/0.61 = { by axiom 16 (test_2_1) }
% 0.19/0.61 one
% 0.19/0.61
% 0.19/0.61 Lemma 37: addition(X, addition(X, Y)) = addition(X, Y).
% 0.19/0.61 Proof:
% 0.19/0.61 addition(X, addition(X, Y))
% 0.19/0.61 = { by axiom 11 (additive_associativity) }
% 0.19/0.61 addition(addition(X, X), Y)
% 0.19/0.61 = { by axiom 6 (additive_idempotence) }
% 0.19/0.61 addition(X, Y)
% 0.19/0.61
% 0.19/0.61 Lemma 38: addition(X, multiplication(X, Y)) = multiplication(X, addition(Y, one)).
% 0.19/0.61 Proof:
% 0.19/0.61 addition(X, multiplication(X, Y))
% 0.19/0.61 = { by axiom 4 (multiplicative_right_identity) R->L }
% 0.19/0.61 addition(multiplication(X, one), multiplication(X, Y))
% 0.19/0.61 = { by axiom 23 (right_distributivity) R->L }
% 0.19/0.61 multiplication(X, addition(one, Y))
% 0.19/0.61 = { by axiom 7 (additive_commutativity) }
% 0.19/0.61 multiplication(X, addition(Y, one))
% 0.19/0.61
% 0.19/0.61 Goal 1 (goals_3): addition(multiplication(x0, c(x2)), multiplication(c(x1), x0)) = multiplication(c(x1), x0).
% 0.19/0.61 Proof:
% 0.19/0.61 addition(multiplication(x0, c(x2)), multiplication(c(x1), x0))
% 0.19/0.61 = { by axiom 7 (additive_commutativity) }
% 0.19/0.61 addition(multiplication(c(x1), x0), multiplication(x0, c(x2)))
% 0.19/0.61 = { by axiom 4 (multiplicative_right_identity) R->L }
% 0.19/0.61 addition(multiplication(c(x1), x0), multiplication(multiplication(x0, one), c(x2)))
% 0.19/0.61 = { by lemma 34 R->L }
% 0.19/0.61 addition(multiplication(c(x1), x0), multiplication(multiplication(x0, addition(x2, x1_2(x2))), c(x2)))
% 0.19/0.61 = { by lemma 37 R->L }
% 0.19/0.61 addition(multiplication(c(x1), x0), multiplication(multiplication(x0, addition(x2, addition(x2, x1_2(x2)))), c(x2)))
% 0.19/0.61 = { by lemma 34 }
% 0.19/0.61 addition(multiplication(c(x1), x0), multiplication(multiplication(x0, addition(x2, one)), c(x2)))
% 0.19/0.61 = { by lemma 38 R->L }
% 0.19/0.61 addition(multiplication(c(x1), x0), multiplication(addition(x0, multiplication(x0, x2)), c(x2)))
% 0.19/0.61 = { by axiom 7 (additive_commutativity) R->L }
% 0.19/0.61 addition(multiplication(c(x1), x0), multiplication(addition(multiplication(x0, x2), x0), c(x2)))
% 0.19/0.61 = { by axiom 5 (multiplicative_left_identity) R->L }
% 0.19/0.61 addition(multiplication(c(x1), x0), multiplication(addition(multiplication(x0, x2), multiplication(one, x0)), c(x2)))
% 0.19/0.61 = { by axiom 16 (test_2_1) R->L }
% 0.19/0.61 addition(multiplication(c(x1), x0), multiplication(addition(multiplication(x0, x2), multiplication(fresh12(true, true, c(x1), x1), x0)), c(x2)))
% 0.19/0.62 = { by axiom 20 (test_3) R->L }
% 0.19/0.62 addition(multiplication(c(x1), x0), multiplication(addition(multiplication(x0, x2), multiplication(fresh12(fresh8(c(x1), c(x1), x1, c(x1)), true, c(x1), x1), x0)), c(x2)))
% 0.19/0.62 = { by axiom 22 (test_3) R->L }
% 0.19/0.62 addition(multiplication(c(x1), x0), multiplication(addition(multiplication(x0, x2), multiplication(fresh12(fresh9(test(x1), true, x1, c(x1)), true, c(x1), x1), x0)), c(x2)))
% 0.19/0.62 = { by axiom 1 (goals_1) }
% 0.19/0.62 addition(multiplication(c(x1), x0), multiplication(addition(multiplication(x0, x2), multiplication(fresh12(fresh9(true, true, x1, c(x1)), true, c(x1), x1), x0)), c(x2)))
% 0.19/0.62 = { by axiom 19 (test_3) }
% 0.19/0.62 addition(multiplication(c(x1), x0), multiplication(addition(multiplication(x0, x2), multiplication(fresh12(complement(x1, c(x1)), true, c(x1), x1), x0)), c(x2)))
% 0.19/0.62 = { by axiom 28 (test_2_1) }
% 0.19/0.62 addition(multiplication(c(x1), x0), multiplication(addition(multiplication(x0, x2), multiplication(addition(c(x1), x1), x0)), c(x2)))
% 0.19/0.62 = { by axiom 24 (left_distributivity) }
% 0.19/0.62 addition(multiplication(c(x1), x0), multiplication(addition(multiplication(x0, x2), addition(multiplication(c(x1), x0), multiplication(x1, x0))), c(x2)))
% 0.19/0.62 = { by axiom 7 (additive_commutativity) R->L }
% 0.19/0.62 addition(multiplication(c(x1), x0), multiplication(addition(multiplication(x0, x2), addition(multiplication(x1, x0), multiplication(c(x1), x0))), c(x2)))
% 0.19/0.62 = { by axiom 11 (additive_associativity) }
% 0.19/0.62 addition(multiplication(c(x1), x0), multiplication(addition(addition(multiplication(x0, x2), multiplication(x1, x0)), multiplication(c(x1), x0)), c(x2)))
% 0.19/0.62 = { by axiom 7 (additive_commutativity) R->L }
% 0.19/0.62 addition(multiplication(c(x1), x0), multiplication(addition(addition(multiplication(x1, x0), multiplication(x0, x2)), multiplication(c(x1), x0)), c(x2)))
% 0.19/0.62 = { by axiom 25 (goals) }
% 0.19/0.62 addition(multiplication(c(x1), x0), multiplication(addition(multiplication(x0, x2), multiplication(c(x1), x0)), c(x2)))
% 0.19/0.62 = { by axiom 7 (additive_commutativity) }
% 0.19/0.62 addition(multiplication(c(x1), x0), multiplication(addition(multiplication(c(x1), x0), multiplication(x0, x2)), c(x2)))
% 0.19/0.62 = { by lemma 35 R->L }
% 0.19/0.62 addition(multiplication(c(x1), x0), multiplication(addition(multiplication(c(x1), x0), multiplication(x0, x2)), x1_2(x2)))
% 0.19/0.62 = { by axiom 7 (additive_commutativity) R->L }
% 0.19/0.62 addition(multiplication(c(x1), x0), multiplication(addition(multiplication(x0, x2), multiplication(c(x1), x0)), x1_2(x2)))
% 0.19/0.62 = { by axiom 24 (left_distributivity) }
% 0.19/0.62 addition(multiplication(c(x1), x0), addition(multiplication(multiplication(x0, x2), x1_2(x2)), multiplication(multiplication(c(x1), x0), x1_2(x2))))
% 0.19/0.62 = { by axiom 10 (multiplicative_associativity) R->L }
% 0.19/0.62 addition(multiplication(c(x1), x0), addition(multiplication(x0, multiplication(x2, x1_2(x2))), multiplication(multiplication(c(x1), x0), x1_2(x2))))
% 0.19/0.62 = { by lemma 33 }
% 0.19/0.62 addition(multiplication(c(x1), x0), addition(multiplication(x0, zero), multiplication(multiplication(c(x1), x0), x1_2(x2))))
% 0.19/0.62 = { by axiom 3 (right_annihilation) }
% 0.19/0.62 addition(multiplication(c(x1), x0), addition(zero, multiplication(multiplication(c(x1), x0), x1_2(x2))))
% 0.19/0.62 = { by axiom 7 (additive_commutativity) R->L }
% 0.19/0.62 addition(multiplication(c(x1), x0), addition(multiplication(multiplication(c(x1), x0), x1_2(x2)), zero))
% 0.19/0.62 = { by axiom 8 (additive_identity) }
% 0.19/0.62 addition(multiplication(c(x1), x0), multiplication(multiplication(c(x1), x0), x1_2(x2)))
% 0.19/0.62 = { by lemma 35 }
% 0.19/0.62 addition(multiplication(c(x1), x0), multiplication(multiplication(c(x1), x0), c(x2)))
% 0.19/0.62 = { by lemma 38 }
% 0.19/0.62 multiplication(multiplication(c(x1), x0), addition(c(x2), one))
% 0.19/0.62 = { by lemma 36 R->L }
% 0.19/0.62 multiplication(multiplication(c(x1), x0), addition(c(x2), addition(x2, c(x2))))
% 0.19/0.62 = { by lemma 37 R->L }
% 0.19/0.62 multiplication(multiplication(c(x1), x0), addition(c(x2), addition(x2, addition(x2, c(x2)))))
% 0.19/0.62 = { by axiom 7 (additive_commutativity) R->L }
% 0.19/0.62 multiplication(multiplication(c(x1), x0), addition(c(x2), addition(x2, addition(c(x2), x2))))
% 0.19/0.62 = { by axiom 11 (additive_associativity) }
% 0.19/0.62 multiplication(multiplication(c(x1), x0), addition(addition(c(x2), x2), addition(c(x2), x2)))
% 0.19/0.62 = { by axiom 6 (additive_idempotence) }
% 0.19/0.62 multiplication(multiplication(c(x1), x0), addition(c(x2), x2))
% 0.19/0.62 = { by axiom 7 (additive_commutativity) }
% 0.19/0.62 multiplication(multiplication(c(x1), x0), addition(x2, c(x2)))
% 0.19/0.62 = { by lemma 36 }
% 0.19/0.62 multiplication(multiplication(c(x1), x0), one)
% 0.19/0.62 = { by axiom 4 (multiplicative_right_identity) }
% 0.19/0.62 multiplication(c(x1), x0)
% 0.19/0.62 % SZS output end Proof
% 0.19/0.62
% 0.19/0.62 RESULT: Theorem (the conjecture is true).
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