TSTP Solution File: BOO009-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : BOO009-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n014.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 : Wed Aug 30 18:11:19 EDT 2023
% Result : Unsatisfiable 5.25s 1.11s
% Output : Proof 5.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO009-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Aug 27 08:22:02 EDT 2023
% 0.12/0.33 % CPUTime :
% 5.25/1.11 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 5.25/1.11
% 5.25/1.11 % SZS status Unsatisfiable
% 5.25/1.11
% 5.89/1.16 % SZS output start Proof
% 5.89/1.16 Take the following subset of the input axioms:
% 5.89/1.16 fof(addition_is_well_defined, axiom, ![X, Y, U, V]: (~sum(X, Y, U) | (~sum(X, Y, V) | U=V))).
% 5.89/1.17 fof(additive_identity2, axiom, ![X2]: sum(X2, additive_identity, X2)).
% 5.89/1.17 fof(additive_inverse2, axiom, ![X2]: sum(X2, inverse(X2), multiplicative_identity)).
% 5.89/1.17 fof(closure_of_addition, axiom, ![X2, Y2]: sum(X2, Y2, add(X2, Y2))).
% 5.89/1.17 fof(closure_of_multiplication, axiom, ![X2, Y2]: product(X2, Y2, multiply(X2, Y2))).
% 5.89/1.17 fof(commutativity_of_multiplication, axiom, ![Z, X2, Y2]: (~product(X2, Y2, Z) | product(Y2, X2, Z))).
% 5.89/1.17 fof(distributivity2, axiom, ![V1, V2, V3, V4, X2, Y2, Z2]: (~product(X2, Y2, V1) | (~product(X2, Z2, V2) | (~sum(Y2, Z2, V3) | (~sum(V1, V2, V4) | product(X2, V3, V4)))))).
% 5.89/1.17 fof(distributivity5, axiom, ![X2, Y2, Z2, V1_2, V2_2, V3_2, V4_2]: (~sum(X2, Y2, V1_2) | (~sum(X2, Z2, V2_2) | (~product(Y2, Z2, V3_2) | (~sum(X2, V3_2, V4_2) | product(V1_2, V2_2, V4_2)))))).
% 5.89/1.17 fof(distributivity6, axiom, ![X2, Y2, Z2, V1_2, V2_2, V3_2, V4_2]: (~sum(X2, Y2, V1_2) | (~sum(X2, Z2, V2_2) | (~product(Y2, Z2, V3_2) | (~product(V1_2, V2_2, V4_2) | sum(X2, V3_2, V4_2)))))).
% 5.89/1.17 fof(multiplication_is_well_defined, axiom, ![X2, Y2, U2, V5]: (~product(X2, Y2, U2) | (~product(X2, Y2, V5) | U2=V5))).
% 5.89/1.17 fof(multiplicative_identity1, axiom, ![X2]: product(multiplicative_identity, X2, X2)).
% 5.89/1.17 fof(multiplicative_identity2, axiom, ![X2]: product(X2, multiplicative_identity, X2)).
% 5.89/1.17 fof(prove_equations, negated_conjecture, ~product(x, add(x, y), x)).
% 5.89/1.17
% 5.89/1.17 Now clausify the problem and encode Horn clauses using encoding 3 of
% 5.89/1.17 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 5.89/1.17 We repeatedly replace C & s=t => u=v by the two clauses:
% 5.89/1.17 fresh(y, y, x1...xn) = u
% 5.89/1.17 C => fresh(s, t, x1...xn) = v
% 5.89/1.17 where fresh is a fresh function symbol and x1..xn are the free
% 5.89/1.17 variables of u and v.
% 5.89/1.17 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 5.89/1.17 input problem has no model of domain size 1).
% 5.89/1.17
% 5.89/1.17 The encoding turns the above axioms into the following unit equations and goals:
% 5.89/1.17
% 5.89/1.17 Axiom 1 (additive_identity2): sum(X, additive_identity, X) = true.
% 5.89/1.17 Axiom 2 (multiplicative_identity2): product(X, multiplicative_identity, X) = true.
% 5.89/1.17 Axiom 3 (multiplicative_identity1): product(multiplicative_identity, X, X) = true.
% 5.89/1.17 Axiom 4 (multiplication_is_well_defined): fresh(X, X, Y, Z) = Z.
% 5.89/1.17 Axiom 5 (addition_is_well_defined): fresh3(X, X, Y, Z) = Z.
% 5.89/1.17 Axiom 6 (additive_inverse2): sum(X, inverse(X), multiplicative_identity) = true.
% 5.89/1.17 Axiom 7 (distributivity2): fresh34(X, X, Y, Z, W) = true.
% 5.89/1.17 Axiom 8 (distributivity5): fresh22(X, X, Y, Z, W) = true.
% 5.89/1.17 Axiom 9 (distributivity6): fresh18(X, X, Y, Z, W) = true.
% 5.89/1.17 Axiom 10 (commutativity_of_multiplication): fresh6(X, X, Y, Z, W) = true.
% 5.89/1.17 Axiom 11 (closure_of_addition): sum(X, Y, add(X, Y)) = true.
% 5.89/1.17 Axiom 12 (closure_of_multiplication): product(X, Y, multiply(X, Y)) = true.
% 5.89/1.17 Axiom 13 (addition_is_well_defined): fresh4(X, X, Y, Z, W, V) = W.
% 5.89/1.17 Axiom 14 (multiplication_is_well_defined): fresh2(X, X, Y, Z, W, V) = W.
% 5.89/1.17 Axiom 15 (distributivity2): fresh32(X, X, Y, Z, W, V, U) = product(Y, V, U).
% 5.89/1.17 Axiom 16 (distributivity5): fresh20(X, X, Y, Z, W, V, U) = product(W, V, U).
% 5.89/1.17 Axiom 17 (distributivity6): fresh16(X, X, Y, Z, W, V, U) = sum(Y, V, U).
% 5.89/1.17 Axiom 18 (distributivity5): fresh21(X, X, Y, Z, W, V, U, T) = fresh22(sum(Y, Z, W), true, W, U, T).
% 5.89/1.17 Axiom 19 (commutativity_of_multiplication): fresh6(product(X, Y, Z), true, X, Y, Z) = product(Y, X, Z).
% 5.89/1.17 Axiom 20 (distributivity2): fresh33(X, X, Y, Z, W, V, U, T, S) = fresh34(sum(Z, V, T), true, Y, T, S).
% 5.89/1.17 Axiom 21 (distributivity6): fresh17(X, X, Y, Z, W, V, U, T, S) = fresh18(sum(Y, Z, W), true, Y, T, S).
% 5.89/1.17 Axiom 22 (addition_is_well_defined): fresh4(sum(X, Y, Z), true, X, Y, W, Z) = fresh3(sum(X, Y, W), true, W, Z).
% 5.89/1.17 Axiom 23 (multiplication_is_well_defined): fresh2(product(X, Y, Z), true, X, Y, W, Z) = fresh(product(X, Y, W), true, W, Z).
% 5.89/1.17 Axiom 24 (distributivity2): fresh31(X, X, Y, Z, W, V, U, T, S) = fresh32(sum(W, U, S), true, Y, Z, V, T, S).
% 5.89/1.17 Axiom 25 (distributivity5): fresh19(X, X, Y, Z, W, V, U, T, S) = fresh20(sum(Y, V, U), true, Y, Z, W, U, S).
% 5.89/1.17 Axiom 26 (distributivity6): fresh15(X, X, Y, Z, W, V, U, T, S) = fresh16(sum(Y, V, U), true, Y, Z, W, T, S).
% 5.89/1.17 Axiom 27 (distributivity2): fresh31(product(X, Y, Z), true, X, W, V, Y, Z, U, T) = fresh33(product(X, W, V), true, X, W, V, Y, Z, U, T).
% 5.89/1.17 Axiom 28 (distributivity5): fresh19(product(X, Y, Z), true, W, X, V, Y, U, Z, T) = fresh21(sum(W, Z, T), true, W, X, V, Y, U, T).
% 5.89/1.17 Axiom 29 (distributivity6): fresh15(product(X, Y, Z), true, W, V, X, U, Y, T, Z) = fresh17(product(V, U, T), true, W, V, X, U, Y, T, Z).
% 5.89/1.17
% 5.89/1.17 Lemma 30: fresh3(sum(X, Y, Z), true, Z, add(X, Y)) = Z.
% 5.89/1.17 Proof:
% 5.89/1.17 fresh3(sum(X, Y, Z), true, Z, add(X, Y))
% 5.89/1.17 = { by axiom 22 (addition_is_well_defined) R->L }
% 5.89/1.17 fresh4(sum(X, Y, add(X, Y)), true, X, Y, Z, add(X, Y))
% 5.89/1.17 = { by axiom 11 (closure_of_addition) }
% 5.89/1.17 fresh4(true, true, X, Y, Z, add(X, Y))
% 5.89/1.17 = { by axiom 13 (addition_is_well_defined) }
% 5.89/1.17 Z
% 5.89/1.17
% 5.89/1.17 Goal 1 (prove_equations): product(x, add(x, y), x) = true.
% 5.89/1.17 Proof:
% 5.89/1.17 product(x, add(x, y), x)
% 5.89/1.17 = { by axiom 19 (commutativity_of_multiplication) R->L }
% 5.89/1.17 fresh6(product(add(x, y), x, x), true, add(x, y), x, x)
% 5.89/1.17 = { by axiom 16 (distributivity5) R->L }
% 5.89/1.17 fresh6(fresh20(true, true, x, y, add(x, y), x, x), true, add(x, y), x, x)
% 5.89/1.17 = { by axiom 1 (additive_identity2) R->L }
% 5.89/1.17 fresh6(fresh20(sum(x, additive_identity, x), true, x, y, add(x, y), x, x), true, add(x, y), x, x)
% 5.89/1.17 = { by axiom 25 (distributivity5) R->L }
% 5.89/1.17 fresh6(fresh19(true, true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.17 = { by axiom 12 (closure_of_multiplication) R->L }
% 5.89/1.17 fresh6(fresh19(product(y, additive_identity, multiply(y, additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.17 = { by axiom 14 (multiplication_is_well_defined) R->L }
% 5.89/1.17 fresh6(fresh19(product(y, additive_identity, fresh2(true, true, additive_identity, multiplicative_identity, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.17 = { by axiom 2 (multiplicative_identity2) R->L }
% 5.89/1.17 fresh6(fresh19(product(y, additive_identity, fresh2(product(additive_identity, multiplicative_identity, additive_identity), true, additive_identity, multiplicative_identity, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.17 = { by axiom 23 (multiplication_is_well_defined) }
% 5.89/1.17 fresh6(fresh19(product(y, additive_identity, fresh(product(additive_identity, multiplicative_identity, multiply(y, additive_identity)), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.17 = { by lemma 30 R->L }
% 5.89/1.17 fresh6(fresh19(product(y, additive_identity, fresh(product(additive_identity, fresh3(sum(y, inverse(y), multiplicative_identity), true, multiplicative_identity, add(y, inverse(y))), multiply(y, additive_identity)), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.17 = { by axiom 6 (additive_inverse2) }
% 5.89/1.17 fresh6(fresh19(product(y, additive_identity, fresh(product(additive_identity, fresh3(true, true, multiplicative_identity, add(y, inverse(y))), multiply(y, additive_identity)), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 5 (addition_is_well_defined) }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, fresh(product(additive_identity, add(y, inverse(y)), multiply(y, additive_identity)), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 5 (addition_is_well_defined) R->L }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, fresh(product(additive_identity, fresh3(true, true, add(y, multiplicative_identity), add(y, inverse(y))), multiply(y, additive_identity)), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 9 (distributivity6) R->L }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, fresh(product(additive_identity, fresh3(fresh18(true, true, y, inverse(y), add(y, multiplicative_identity)), true, add(y, multiplicative_identity), add(y, inverse(y))), multiply(y, additive_identity)), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 6 (additive_inverse2) R->L }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, fresh(product(additive_identity, fresh3(fresh18(sum(y, inverse(y), multiplicative_identity), true, y, inverse(y), add(y, multiplicative_identity)), true, add(y, multiplicative_identity), add(y, inverse(y))), multiply(y, additive_identity)), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 21 (distributivity6) R->L }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, fresh(product(additive_identity, fresh3(fresh17(true, true, y, inverse(y), multiplicative_identity, multiplicative_identity, add(y, multiplicative_identity), inverse(y), add(y, multiplicative_identity)), true, add(y, multiplicative_identity), add(y, inverse(y))), multiply(y, additive_identity)), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 2 (multiplicative_identity2) R->L }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, fresh(product(additive_identity, fresh3(fresh17(product(inverse(y), multiplicative_identity, inverse(y)), true, y, inverse(y), multiplicative_identity, multiplicative_identity, add(y, multiplicative_identity), inverse(y), add(y, multiplicative_identity)), true, add(y, multiplicative_identity), add(y, inverse(y))), multiply(y, additive_identity)), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 29 (distributivity6) R->L }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, fresh(product(additive_identity, fresh3(fresh15(product(multiplicative_identity, add(y, multiplicative_identity), add(y, multiplicative_identity)), true, y, inverse(y), multiplicative_identity, multiplicative_identity, add(y, multiplicative_identity), inverse(y), add(y, multiplicative_identity)), true, add(y, multiplicative_identity), add(y, inverse(y))), multiply(y, additive_identity)), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 3 (multiplicative_identity1) }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, fresh(product(additive_identity, fresh3(fresh15(true, true, y, inverse(y), multiplicative_identity, multiplicative_identity, add(y, multiplicative_identity), inverse(y), add(y, multiplicative_identity)), true, add(y, multiplicative_identity), add(y, inverse(y))), multiply(y, additive_identity)), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 26 (distributivity6) }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, fresh(product(additive_identity, fresh3(fresh16(sum(y, multiplicative_identity, add(y, multiplicative_identity)), true, y, inverse(y), multiplicative_identity, inverse(y), add(y, multiplicative_identity)), true, add(y, multiplicative_identity), add(y, inverse(y))), multiply(y, additive_identity)), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 11 (closure_of_addition) }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, fresh(product(additive_identity, fresh3(fresh16(true, true, y, inverse(y), multiplicative_identity, inverse(y), add(y, multiplicative_identity)), true, add(y, multiplicative_identity), add(y, inverse(y))), multiply(y, additive_identity)), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 17 (distributivity6) }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, fresh(product(additive_identity, fresh3(sum(y, inverse(y), add(y, multiplicative_identity)), true, add(y, multiplicative_identity), add(y, inverse(y))), multiply(y, additive_identity)), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by lemma 30 }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, fresh(product(additive_identity, add(y, multiplicative_identity), multiply(y, additive_identity)), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 4 (multiplication_is_well_defined) R->L }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, fresh(product(additive_identity, add(y, multiplicative_identity), fresh(true, true, multiply(additive_identity, y), multiply(y, additive_identity))), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 10 (commutativity_of_multiplication) R->L }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, fresh(product(additive_identity, add(y, multiplicative_identity), fresh(fresh6(true, true, additive_identity, y, multiply(additive_identity, y)), true, multiply(additive_identity, y), multiply(y, additive_identity))), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 12 (closure_of_multiplication) R->L }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, fresh(product(additive_identity, add(y, multiplicative_identity), fresh(fresh6(product(additive_identity, y, multiply(additive_identity, y)), true, additive_identity, y, multiply(additive_identity, y)), true, multiply(additive_identity, y), multiply(y, additive_identity))), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 19 (commutativity_of_multiplication) }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, fresh(product(additive_identity, add(y, multiplicative_identity), fresh(product(y, additive_identity, multiply(additive_identity, y)), true, multiply(additive_identity, y), multiply(y, additive_identity))), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 23 (multiplication_is_well_defined) R->L }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, fresh(product(additive_identity, add(y, multiplicative_identity), fresh2(product(y, additive_identity, multiply(y, additive_identity)), true, y, additive_identity, multiply(additive_identity, y), multiply(y, additive_identity))), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 12 (closure_of_multiplication) }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, fresh(product(additive_identity, add(y, multiplicative_identity), fresh2(true, true, y, additive_identity, multiply(additive_identity, y), multiply(y, additive_identity))), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 14 (multiplication_is_well_defined) }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, fresh(product(additive_identity, add(y, multiplicative_identity), multiply(additive_identity, y)), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 15 (distributivity2) R->L }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, fresh(fresh32(true, true, additive_identity, y, multiplicative_identity, add(y, multiplicative_identity), multiply(additive_identity, y)), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 1 (additive_identity2) R->L }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, fresh(fresh32(sum(multiply(additive_identity, y), additive_identity, multiply(additive_identity, y)), true, additive_identity, y, multiplicative_identity, add(y, multiplicative_identity), multiply(additive_identity, y)), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 24 (distributivity2) R->L }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, fresh(fresh31(true, true, additive_identity, y, multiply(additive_identity, y), multiplicative_identity, additive_identity, add(y, multiplicative_identity), multiply(additive_identity, y)), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 2 (multiplicative_identity2) R->L }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, fresh(fresh31(product(additive_identity, multiplicative_identity, additive_identity), true, additive_identity, y, multiply(additive_identity, y), multiplicative_identity, additive_identity, add(y, multiplicative_identity), multiply(additive_identity, y)), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 27 (distributivity2) }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, fresh(fresh33(product(additive_identity, y, multiply(additive_identity, y)), true, additive_identity, y, multiply(additive_identity, y), multiplicative_identity, additive_identity, add(y, multiplicative_identity), multiply(additive_identity, y)), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 12 (closure_of_multiplication) }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, fresh(fresh33(true, true, additive_identity, y, multiply(additive_identity, y), multiplicative_identity, additive_identity, add(y, multiplicative_identity), multiply(additive_identity, y)), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 20 (distributivity2) }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, fresh(fresh34(sum(y, multiplicative_identity, add(y, multiplicative_identity)), true, additive_identity, add(y, multiplicative_identity), multiply(additive_identity, y)), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 11 (closure_of_addition) }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, fresh(fresh34(true, true, additive_identity, add(y, multiplicative_identity), multiply(additive_identity, y)), true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 7 (distributivity2) }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, fresh(true, true, multiply(y, additive_identity), additive_identity)), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 4 (multiplication_is_well_defined) }
% 5.89/1.18 fresh6(fresh19(product(y, additive_identity, additive_identity), true, x, y, add(x, y), additive_identity, x, additive_identity, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 28 (distributivity5) }
% 5.89/1.18 fresh6(fresh21(sum(x, additive_identity, x), true, x, y, add(x, y), additive_identity, x, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 1 (additive_identity2) }
% 5.89/1.18 fresh6(fresh21(true, true, x, y, add(x, y), additive_identity, x, x), true, add(x, y), x, x)
% 5.89/1.18 = { by axiom 18 (distributivity5) }
% 5.89/1.19 fresh6(fresh22(sum(x, y, add(x, y)), true, add(x, y), x, x), true, add(x, y), x, x)
% 5.89/1.19 = { by axiom 11 (closure_of_addition) }
% 5.89/1.19 fresh6(fresh22(true, true, add(x, y), x, x), true, add(x, y), x, x)
% 5.89/1.19 = { by axiom 8 (distributivity5) }
% 5.89/1.19 fresh6(true, true, add(x, y), x, x)
% 5.89/1.19 = { by axiom 10 (commutativity_of_multiplication) }
% 5.89/1.19 true
% 5.89/1.19 % SZS output end Proof
% 5.89/1.19
% 5.89/1.19 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------