TSTP Solution File: RNG004-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG004-2 : 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 : 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 13:58:43 EDT 2023
% Result : Unsatisfiable 4.50s 1.01s
% Output : Proof 5.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG004-2 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 : Sun Aug 27 03:25:18 EDT 2023
% 0.13/0.35 % CPUTime :
% 4.50/1.01 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 4.50/1.01
% 4.50/1.01 % SZS status Unsatisfiable
% 4.50/1.01
% 5.19/1.05 % SZS output start Proof
% 5.19/1.05 Take the following subset of the input axioms:
% 5.19/1.05 fof(a_inverse_times_b_inverse, hypothesis, product(additive_inverse(a), additive_inverse(b), d)).
% 5.19/1.05 fof(a_times_b, hypothesis, product(a, b, c)).
% 5.19/1.05 fof(addition_is_well_defined, axiom, ![X, Y, U, V]: (~sum(X, Y, U) | (~sum(X, Y, V) | U=V))).
% 5.19/1.05 fof(additive_identity1, axiom, ![X2]: sum(additive_identity, X2, X2)).
% 5.19/1.05 fof(additive_identity2, axiom, ![X2]: sum(X2, additive_identity, X2)).
% 5.19/1.05 fof(associativity_of_addition2, axiom, ![Z, W, X2, Y2, U2, V5]: (~sum(X2, Y2, U2) | (~sum(Y2, Z, V5) | (~sum(X2, V5, W) | sum(U2, Z, W))))).
% 5.19/1.05 fof(cancellation1, axiom, ![X2, Y2, Z2, W2]: (~sum(X2, Y2, Z2) | (~sum(X2, W2, Z2) | Y2=W2))).
% 5.19/1.05 fof(cancellation2, axiom, ![X2, Y2, Z2, W2]: (~sum(X2, Y2, Z2) | (~sum(W2, Y2, Z2) | X2=W2))).
% 5.19/1.05 fof(closure_of_addition, axiom, ![X2, Y2]: sum(X2, Y2, add(X2, Y2))).
% 5.19/1.05 fof(closure_of_multiplication, axiom, ![X2, Y2]: product(X2, Y2, multiply(X2, Y2))).
% 5.19/1.05 fof(commutativity_of_addition, axiom, ![X2, Y2, Z2]: (~sum(X2, Y2, Z2) | sum(Y2, X2, Z2))).
% 5.19/1.05 fof(distributivity1, axiom, ![V1, V2, V3, V4, X2, Y2, Z2]: (~product(X2, Y2, V1) | (~product(X2, Z2, V2) | (~sum(Y2, Z2, V3) | (~product(X2, V3, V4) | sum(V1, V2, V4)))))).
% 5.19/1.05 fof(distributivity3, axiom, ![X2, Y2, Z2, V1_2, V2_2, V3_2, V4_2]: (~product(Y2, X2, V1_2) | (~product(Z2, X2, V2_2) | (~sum(Y2, Z2, V3_2) | (~product(V3_2, X2, V4_2) | sum(V1_2, V2_2, V4_2)))))).
% 5.19/1.05 fof(left_inverse, axiom, ![X2]: sum(additive_inverse(X2), X2, additive_identity)).
% 5.19/1.05 fof(prove_c_equals_d, negated_conjecture, c!=d).
% 5.19/1.05 fof(right_inverse, axiom, ![X2]: sum(X2, additive_inverse(X2), additive_identity)).
% 5.19/1.05
% 5.19/1.05 Now clausify the problem and encode Horn clauses using encoding 3 of
% 5.19/1.05 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 5.19/1.05 We repeatedly replace C & s=t => u=v by the two clauses:
% 5.19/1.05 fresh(y, y, x1...xn) = u
% 5.19/1.05 C => fresh(s, t, x1...xn) = v
% 5.19/1.05 where fresh is a fresh function symbol and x1..xn are the free
% 5.19/1.05 variables of u and v.
% 5.19/1.05 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 5.19/1.05 input problem has no model of domain size 1).
% 5.19/1.05
% 5.19/1.05 The encoding turns the above axioms into the following unit equations and goals:
% 5.19/1.05
% 5.19/1.05 Axiom 1 (additive_identity2): sum(X, additive_identity, X) = true.
% 5.19/1.05 Axiom 2 (additive_identity1): sum(additive_identity, X, X) = true.
% 5.19/1.05 Axiom 3 (a_times_b): product(a, b, c) = true.
% 5.19/1.05 Axiom 4 (right_inverse): sum(X, additive_inverse(X), additive_identity) = true.
% 5.19/1.05 Axiom 5 (left_inverse): sum(additive_inverse(X), X, additive_identity) = true.
% 5.19/1.05 Axiom 6 (cancellation2): fresh(X, X, Y, Z) = Z.
% 5.19/1.05 Axiom 7 (addition_is_well_defined): fresh7(X, X, Y, Z) = Z.
% 5.19/1.05 Axiom 8 (cancellation1): fresh3(X, X, Y, Z) = Z.
% 5.19/1.05 Axiom 9 (closure_of_addition): sum(X, Y, add(X, Y)) = true.
% 5.19/1.05 Axiom 10 (closure_of_multiplication): product(X, Y, multiply(X, Y)) = true.
% 5.19/1.05 Axiom 11 (a_inverse_times_b_inverse): product(additive_inverse(a), additive_inverse(b), d) = true.
% 5.19/1.05 Axiom 12 (associativity_of_addition2): fresh35(X, X, Y, Z, W) = true.
% 5.19/1.05 Axiom 13 (distributivity1): fresh29(X, X, Y, Z, W) = true.
% 5.19/1.05 Axiom 14 (distributivity3): fresh21(X, X, Y, Z, W) = true.
% 5.19/1.05 Axiom 15 (commutativity_of_addition): fresh9(X, X, Y, Z, W) = true.
% 5.19/1.05 Axiom 16 (addition_is_well_defined): fresh8(X, X, Y, Z, W, V) = W.
% 5.19/1.05 Axiom 17 (cancellation1): fresh4(X, X, Y, Z, W, V) = Z.
% 5.19/1.05 Axiom 18 (cancellation2): fresh2(X, X, Y, Z, W, V) = Y.
% 5.19/1.05 Axiom 19 (associativity_of_addition2): fresh12(X, X, Y, Z, W, V, U) = sum(W, V, U).
% 5.19/1.05 Axiom 20 (associativity_of_addition2): fresh34(X, X, Y, Z, W, V, U, T) = fresh35(sum(Y, Z, W), true, W, V, T).
% 5.19/1.05 Axiom 21 (distributivity1): fresh27(X, X, Y, Z, W, V, U, T) = sum(Z, V, T).
% 5.19/1.06 Axiom 22 (distributivity3): fresh19(X, X, Y, Z, W, V, U, T) = sum(Z, V, T).
% 5.19/1.06 Axiom 23 (commutativity_of_addition): fresh9(sum(X, Y, Z), true, X, Y, Z) = sum(Y, X, Z).
% 5.19/1.06 Axiom 24 (distributivity1): fresh28(X, X, Y, Z, W, V, U, T, S) = fresh29(sum(Z, V, T), true, W, U, S).
% 5.19/1.06 Axiom 25 (distributivity3): fresh20(X, X, Y, Z, W, V, U, T, S) = fresh21(sum(Y, V, T), true, W, U, S).
% 5.19/1.06 Axiom 26 (addition_is_well_defined): fresh8(sum(X, Y, Z), true, X, Y, W, Z) = fresh7(sum(X, Y, W), true, W, Z).
% 5.19/1.06 Axiom 27 (cancellation1): fresh4(sum(X, Y, Z), true, X, W, Z, Y) = fresh3(sum(X, W, Z), true, W, Y).
% 5.19/1.06 Axiom 28 (cancellation2): fresh2(sum(X, Y, Z), true, W, Y, Z, X) = fresh(sum(W, Y, Z), true, W, X).
% 5.19/1.06 Axiom 29 (associativity_of_addition2): fresh34(sum(X, Y, Z), true, W, X, V, Y, Z, U) = fresh12(sum(W, Z, U), true, W, X, V, Y, U).
% 5.19/1.06 Axiom 30 (distributivity1): fresh26(X, X, Y, Z, W, V, U, T, S) = fresh27(product(Y, Z, W), true, Z, W, V, U, T, S).
% 5.19/1.06 Axiom 31 (distributivity3): fresh18(X, X, Y, Z, W, V, U, T, S) = fresh19(product(Y, Z, W), true, Y, W, V, U, T, S).
% 5.19/1.06 Axiom 32 (distributivity1): fresh26(product(X, Y, Z), true, X, W, V, U, T, Y, Z) = fresh28(product(X, U, T), true, X, W, V, U, T, Y, Z).
% 5.19/1.06 Axiom 33 (distributivity3): fresh18(product(X, Y, Z), true, W, Y, V, U, T, X, Z) = fresh20(product(U, Y, T), true, W, Y, V, U, T, X, Z).
% 5.19/1.06
% 5.19/1.06 Lemma 34: additive_inverse(additive_inverse(X)) = X.
% 5.19/1.06 Proof:
% 5.19/1.06 additive_inverse(additive_inverse(X))
% 5.19/1.06 = { by axiom 8 (cancellation1) R->L }
% 5.19/1.06 fresh3(true, true, X, additive_inverse(additive_inverse(X)))
% 5.19/1.06 = { by axiom 5 (left_inverse) R->L }
% 5.19/1.06 fresh3(sum(additive_inverse(X), X, additive_identity), true, X, additive_inverse(additive_inverse(X)))
% 5.19/1.06 = { by axiom 27 (cancellation1) R->L }
% 5.19/1.06 fresh4(sum(additive_inverse(X), additive_inverse(additive_inverse(X)), additive_identity), true, additive_inverse(X), X, additive_identity, additive_inverse(additive_inverse(X)))
% 5.19/1.06 = { by axiom 4 (right_inverse) }
% 5.19/1.06 fresh4(true, true, additive_inverse(X), X, additive_identity, additive_inverse(additive_inverse(X)))
% 5.19/1.06 = { by axiom 17 (cancellation1) }
% 5.19/1.06 X
% 5.19/1.06
% 5.19/1.06 Lemma 35: fresh(sum(X, Y, Y), true, X, additive_identity) = X.
% 5.19/1.06 Proof:
% 5.19/1.06 fresh(sum(X, Y, Y), true, X, additive_identity)
% 5.19/1.06 = { by axiom 28 (cancellation2) R->L }
% 5.19/1.06 fresh2(sum(additive_identity, Y, Y), true, X, Y, Y, additive_identity)
% 5.19/1.06 = { by axiom 2 (additive_identity1) }
% 5.19/1.06 fresh2(true, true, X, Y, Y, additive_identity)
% 5.19/1.06 = { by axiom 18 (cancellation2) }
% 5.19/1.06 X
% 5.19/1.06
% 5.19/1.06 Lemma 36: fresh18(X, X, Y, Z, multiply(Y, Z), W, V, U, T) = sum(multiply(Y, Z), V, T).
% 5.19/1.06 Proof:
% 5.19/1.06 fresh18(X, X, Y, Z, multiply(Y, Z), W, V, U, T)
% 5.19/1.06 = { by axiom 31 (distributivity3) }
% 5.19/1.06 fresh19(product(Y, Z, multiply(Y, Z)), true, Y, multiply(Y, Z), W, V, U, T)
% 5.19/1.06 = { by axiom 10 (closure_of_multiplication) }
% 5.19/1.06 fresh19(true, true, Y, multiply(Y, Z), W, V, U, T)
% 5.19/1.06 = { by axiom 22 (distributivity3) }
% 5.19/1.06 sum(multiply(Y, Z), V, T)
% 5.19/1.06
% 5.19/1.06 Goal 1 (prove_c_equals_d): c = d.
% 5.19/1.06 Proof:
% 5.19/1.06 c
% 5.19/1.06 = { by lemma 34 R->L }
% 5.19/1.06 additive_inverse(additive_inverse(c))
% 5.19/1.06 = { by axiom 7 (addition_is_well_defined) R->L }
% 5.19/1.06 additive_inverse(fresh7(true, true, add(additive_identity, additive_inverse(c)), additive_inverse(c)))
% 5.19/1.06 = { by axiom 15 (commutativity_of_addition) R->L }
% 5.19/1.06 additive_inverse(fresh7(fresh9(true, true, additive_identity, additive_inverse(c), add(additive_identity, additive_inverse(c))), true, add(additive_identity, additive_inverse(c)), additive_inverse(c)))
% 5.19/1.06 = { by axiom 9 (closure_of_addition) R->L }
% 5.19/1.06 additive_inverse(fresh7(fresh9(sum(additive_identity, additive_inverse(c), add(additive_identity, additive_inverse(c))), true, additive_identity, additive_inverse(c), add(additive_identity, additive_inverse(c))), true, add(additive_identity, additive_inverse(c)), additive_inverse(c)))
% 5.19/1.06 = { by axiom 23 (commutativity_of_addition) }
% 5.19/1.06 additive_inverse(fresh7(sum(additive_inverse(c), additive_identity, add(additive_identity, additive_inverse(c))), true, add(additive_identity, additive_inverse(c)), additive_inverse(c)))
% 5.19/1.06 = { by axiom 26 (addition_is_well_defined) R->L }
% 5.19/1.06 additive_inverse(fresh8(sum(additive_inverse(c), additive_identity, additive_inverse(c)), true, additive_inverse(c), additive_identity, add(additive_identity, additive_inverse(c)), additive_inverse(c)))
% 5.19/1.06 = { by axiom 1 (additive_identity2) }
% 5.19/1.06 additive_inverse(fresh8(true, true, additive_inverse(c), additive_identity, add(additive_identity, additive_inverse(c)), additive_inverse(c)))
% 5.19/1.06 = { by axiom 16 (addition_is_well_defined) }
% 5.19/1.06 additive_inverse(add(additive_identity, additive_inverse(c)))
% 5.19/1.06 = { by axiom 6 (cancellation2) R->L }
% 5.19/1.06 additive_inverse(add(fresh(true, true, multiply(additive_identity, b), additive_identity), additive_inverse(c)))
% 5.19/1.06 = { by axiom 14 (distributivity3) R->L }
% 5.19/1.06 additive_inverse(add(fresh(fresh21(true, true, multiply(additive_identity, b), c, c), true, multiply(additive_identity, b), additive_identity), additive_inverse(c)))
% 5.19/1.06 = { by axiom 2 (additive_identity1) R->L }
% 5.19/1.06 additive_inverse(add(fresh(fresh21(sum(additive_identity, a, a), true, multiply(additive_identity, b), c, c), true, multiply(additive_identity, b), additive_identity), additive_inverse(c)))
% 5.19/1.06 = { by axiom 25 (distributivity3) R->L }
% 5.19/1.06 additive_inverse(add(fresh(fresh20(true, true, additive_identity, b, multiply(additive_identity, b), a, c, a, c), true, multiply(additive_identity, b), additive_identity), additive_inverse(c)))
% 5.19/1.06 = { by axiom 3 (a_times_b) R->L }
% 5.19/1.06 additive_inverse(add(fresh(fresh20(product(a, b, c), true, additive_identity, b, multiply(additive_identity, b), a, c, a, c), true, multiply(additive_identity, b), additive_identity), additive_inverse(c)))
% 5.19/1.06 = { by axiom 33 (distributivity3) R->L }
% 5.19/1.06 additive_inverse(add(fresh(fresh18(product(a, b, c), true, additive_identity, b, multiply(additive_identity, b), a, c, a, c), true, multiply(additive_identity, b), additive_identity), additive_inverse(c)))
% 5.19/1.06 = { by axiom 3 (a_times_b) }
% 5.19/1.06 additive_inverse(add(fresh(fresh18(true, true, additive_identity, b, multiply(additive_identity, b), a, c, a, c), true, multiply(additive_identity, b), additive_identity), additive_inverse(c)))
% 5.19/1.06 = { by lemma 36 }
% 5.19/1.06 additive_inverse(add(fresh(sum(multiply(additive_identity, b), c, c), true, multiply(additive_identity, b), additive_identity), additive_inverse(c)))
% 5.19/1.06 = { by lemma 35 }
% 5.19/1.06 additive_inverse(add(multiply(additive_identity, b), additive_inverse(c)))
% 5.19/1.06 = { by axiom 18 (cancellation2) R->L }
% 5.19/1.06 additive_inverse(fresh2(true, true, add(multiply(additive_identity, b), additive_inverse(c)), c, multiply(additive_identity, b), multiply(additive_inverse(a), b)))
% 5.19/1.06 = { by axiom 14 (distributivity3) R->L }
% 5.19/1.06 additive_inverse(fresh2(fresh21(true, true, multiply(additive_inverse(a), b), c, multiply(additive_identity, b)), true, add(multiply(additive_identity, b), additive_inverse(c)), c, multiply(additive_identity, b), multiply(additive_inverse(a), b)))
% 5.19/1.06 = { by axiom 5 (left_inverse) R->L }
% 5.19/1.06 additive_inverse(fresh2(fresh21(sum(additive_inverse(a), a, additive_identity), true, multiply(additive_inverse(a), b), c, multiply(additive_identity, b)), true, add(multiply(additive_identity, b), additive_inverse(c)), c, multiply(additive_identity, b), multiply(additive_inverse(a), b)))
% 5.19/1.06 = { by axiom 25 (distributivity3) R->L }
% 5.19/1.06 additive_inverse(fresh2(fresh20(true, true, additive_inverse(a), b, multiply(additive_inverse(a), b), a, c, additive_identity, multiply(additive_identity, b)), true, add(multiply(additive_identity, b), additive_inverse(c)), c, multiply(additive_identity, b), multiply(additive_inverse(a), b)))
% 5.19/1.06 = { by axiom 3 (a_times_b) R->L }
% 5.19/1.06 additive_inverse(fresh2(fresh20(product(a, b, c), true, additive_inverse(a), b, multiply(additive_inverse(a), b), a, c, additive_identity, multiply(additive_identity, b)), true, add(multiply(additive_identity, b), additive_inverse(c)), c, multiply(additive_identity, b), multiply(additive_inverse(a), b)))
% 5.19/1.06 = { by axiom 33 (distributivity3) R->L }
% 5.19/1.06 additive_inverse(fresh2(fresh18(product(additive_identity, b, multiply(additive_identity, b)), true, additive_inverse(a), b, multiply(additive_inverse(a), b), a, c, additive_identity, multiply(additive_identity, b)), true, add(multiply(additive_identity, b), additive_inverse(c)), c, multiply(additive_identity, b), multiply(additive_inverse(a), b)))
% 5.19/1.06 = { by axiom 10 (closure_of_multiplication) }
% 5.19/1.06 additive_inverse(fresh2(fresh18(true, true, additive_inverse(a), b, multiply(additive_inverse(a), b), a, c, additive_identity, multiply(additive_identity, b)), true, add(multiply(additive_identity, b), additive_inverse(c)), c, multiply(additive_identity, b), multiply(additive_inverse(a), b)))
% 5.19/1.06 = { by lemma 36 }
% 5.19/1.06 additive_inverse(fresh2(sum(multiply(additive_inverse(a), b), c, multiply(additive_identity, b)), true, add(multiply(additive_identity, b), additive_inverse(c)), c, multiply(additive_identity, b), multiply(additive_inverse(a), b)))
% 5.19/1.06 = { by axiom 28 (cancellation2) }
% 5.19/1.06 additive_inverse(fresh(sum(add(multiply(additive_identity, b), additive_inverse(c)), c, multiply(additive_identity, b)), true, add(multiply(additive_identity, b), additive_inverse(c)), multiply(additive_inverse(a), b)))
% 5.19/1.06 = { by axiom 19 (associativity_of_addition2) R->L }
% 5.19/1.06 additive_inverse(fresh(fresh12(true, true, multiply(additive_identity, b), additive_inverse(c), add(multiply(additive_identity, b), additive_inverse(c)), c, multiply(additive_identity, b)), true, add(multiply(additive_identity, b), additive_inverse(c)), multiply(additive_inverse(a), b)))
% 5.19/1.06 = { by axiom 1 (additive_identity2) R->L }
% 5.19/1.06 additive_inverse(fresh(fresh12(sum(multiply(additive_identity, b), additive_identity, multiply(additive_identity, b)), true, multiply(additive_identity, b), additive_inverse(c), add(multiply(additive_identity, b), additive_inverse(c)), c, multiply(additive_identity, b)), true, add(multiply(additive_identity, b), additive_inverse(c)), multiply(additive_inverse(a), b)))
% 5.19/1.06 = { by axiom 29 (associativity_of_addition2) R->L }
% 5.19/1.06 additive_inverse(fresh(fresh34(sum(additive_inverse(c), c, additive_identity), true, multiply(additive_identity, b), additive_inverse(c), add(multiply(additive_identity, b), additive_inverse(c)), c, additive_identity, multiply(additive_identity, b)), true, add(multiply(additive_identity, b), additive_inverse(c)), multiply(additive_inverse(a), b)))
% 5.19/1.06 = { by axiom 5 (left_inverse) }
% 5.19/1.06 additive_inverse(fresh(fresh34(true, true, multiply(additive_identity, b), additive_inverse(c), add(multiply(additive_identity, b), additive_inverse(c)), c, additive_identity, multiply(additive_identity, b)), true, add(multiply(additive_identity, b), additive_inverse(c)), multiply(additive_inverse(a), b)))
% 5.19/1.06 = { by axiom 20 (associativity_of_addition2) }
% 5.19/1.06 additive_inverse(fresh(fresh35(sum(multiply(additive_identity, b), additive_inverse(c), add(multiply(additive_identity, b), additive_inverse(c))), true, add(multiply(additive_identity, b), additive_inverse(c)), c, multiply(additive_identity, b)), true, add(multiply(additive_identity, b), additive_inverse(c)), multiply(additive_inverse(a), b)))
% 5.19/1.06 = { by axiom 9 (closure_of_addition) }
% 5.19/1.06 additive_inverse(fresh(fresh35(true, true, add(multiply(additive_identity, b), additive_inverse(c)), c, multiply(additive_identity, b)), true, add(multiply(additive_identity, b), additive_inverse(c)), multiply(additive_inverse(a), b)))
% 5.19/1.06 = { by axiom 12 (associativity_of_addition2) }
% 5.19/1.06 additive_inverse(fresh(true, true, add(multiply(additive_identity, b), additive_inverse(c)), multiply(additive_inverse(a), b)))
% 5.19/1.07 = { by axiom 6 (cancellation2) }
% 5.19/1.07 additive_inverse(multiply(additive_inverse(a), b))
% 5.19/1.07 = { by axiom 6 (cancellation2) R->L }
% 5.19/1.07 fresh(true, true, d, additive_inverse(multiply(additive_inverse(a), b)))
% 5.19/1.07 = { by axiom 13 (distributivity1) R->L }
% 5.19/1.07 fresh(fresh29(true, true, d, multiply(additive_inverse(a), additive_inverse(additive_inverse(b))), multiply(additive_inverse(a), additive_identity)), true, d, additive_inverse(multiply(additive_inverse(a), b)))
% 5.19/1.07 = { by axiom 4 (right_inverse) R->L }
% 5.19/1.07 fresh(fresh29(sum(additive_inverse(b), additive_inverse(additive_inverse(b)), additive_identity), true, d, multiply(additive_inverse(a), additive_inverse(additive_inverse(b))), multiply(additive_inverse(a), additive_identity)), true, d, additive_inverse(multiply(additive_inverse(a), b)))
% 5.19/1.07 = { by axiom 24 (distributivity1) R->L }
% 5.19/1.07 fresh(fresh28(true, true, additive_inverse(a), additive_inverse(b), d, additive_inverse(additive_inverse(b)), multiply(additive_inverse(a), additive_inverse(additive_inverse(b))), additive_identity, multiply(additive_inverse(a), additive_identity)), true, d, additive_inverse(multiply(additive_inverse(a), b)))
% 5.19/1.07 = { by axiom 10 (closure_of_multiplication) R->L }
% 5.19/1.07 fresh(fresh28(product(additive_inverse(a), additive_inverse(additive_inverse(b)), multiply(additive_inverse(a), additive_inverse(additive_inverse(b)))), true, additive_inverse(a), additive_inverse(b), d, additive_inverse(additive_inverse(b)), multiply(additive_inverse(a), additive_inverse(additive_inverse(b))), additive_identity, multiply(additive_inverse(a), additive_identity)), true, d, additive_inverse(multiply(additive_inverse(a), b)))
% 5.19/1.07 = { by axiom 32 (distributivity1) R->L }
% 5.19/1.07 fresh(fresh26(product(additive_inverse(a), additive_identity, multiply(additive_inverse(a), additive_identity)), true, additive_inverse(a), additive_inverse(b), d, additive_inverse(additive_inverse(b)), multiply(additive_inverse(a), additive_inverse(additive_inverse(b))), additive_identity, multiply(additive_inverse(a), additive_identity)), true, d, additive_inverse(multiply(additive_inverse(a), b)))
% 5.19/1.07 = { by axiom 10 (closure_of_multiplication) }
% 5.19/1.07 fresh(fresh26(true, true, additive_inverse(a), additive_inverse(b), d, additive_inverse(additive_inverse(b)), multiply(additive_inverse(a), additive_inverse(additive_inverse(b))), additive_identity, multiply(additive_inverse(a), additive_identity)), true, d, additive_inverse(multiply(additive_inverse(a), b)))
% 5.19/1.07 = { by axiom 30 (distributivity1) }
% 5.19/1.07 fresh(fresh27(product(additive_inverse(a), additive_inverse(b), d), true, additive_inverse(b), d, additive_inverse(additive_inverse(b)), multiply(additive_inverse(a), additive_inverse(additive_inverse(b))), additive_identity, multiply(additive_inverse(a), additive_identity)), true, d, additive_inverse(multiply(additive_inverse(a), b)))
% 5.19/1.07 = { by axiom 11 (a_inverse_times_b_inverse) }
% 5.19/1.07 fresh(fresh27(true, true, additive_inverse(b), d, additive_inverse(additive_inverse(b)), multiply(additive_inverse(a), additive_inverse(additive_inverse(b))), additive_identity, multiply(additive_inverse(a), additive_identity)), true, d, additive_inverse(multiply(additive_inverse(a), b)))
% 5.19/1.07 = { by axiom 21 (distributivity1) }
% 5.19/1.07 fresh(sum(d, multiply(additive_inverse(a), additive_inverse(additive_inverse(b))), multiply(additive_inverse(a), additive_identity)), true, d, additive_inverse(multiply(additive_inverse(a), b)))
% 5.19/1.07 = { by lemma 34 }
% 5.19/1.07 fresh(sum(d, multiply(additive_inverse(a), b), multiply(additive_inverse(a), additive_identity)), true, d, additive_inverse(multiply(additive_inverse(a), b)))
% 5.19/1.07 = { by lemma 35 R->L }
% 5.19/1.07 fresh(sum(d, multiply(additive_inverse(a), b), fresh(sum(multiply(additive_inverse(a), additive_identity), d, d), true, multiply(additive_inverse(a), additive_identity), additive_identity)), true, d, additive_inverse(multiply(additive_inverse(a), b)))
% 5.19/1.07 = { by axiom 21 (distributivity1) R->L }
% 5.19/1.07 fresh(sum(d, multiply(additive_inverse(a), b), fresh(fresh27(true, true, additive_identity, multiply(additive_inverse(a), additive_identity), additive_inverse(b), d, additive_inverse(b), d), true, multiply(additive_inverse(a), additive_identity), additive_identity)), true, d, additive_inverse(multiply(additive_inverse(a), b)))
% 5.19/1.07 = { by axiom 10 (closure_of_multiplication) R->L }
% 5.19/1.07 fresh(sum(d, multiply(additive_inverse(a), b), fresh(fresh27(product(additive_inverse(a), additive_identity, multiply(additive_inverse(a), additive_identity)), true, additive_identity, multiply(additive_inverse(a), additive_identity), additive_inverse(b), d, additive_inverse(b), d), true, multiply(additive_inverse(a), additive_identity), additive_identity)), true, d, additive_inverse(multiply(additive_inverse(a), b)))
% 5.19/1.07 = { by axiom 30 (distributivity1) R->L }
% 5.19/1.07 fresh(sum(d, multiply(additive_inverse(a), b), fresh(fresh26(true, true, additive_inverse(a), additive_identity, multiply(additive_inverse(a), additive_identity), additive_inverse(b), d, additive_inverse(b), d), true, multiply(additive_inverse(a), additive_identity), additive_identity)), true, d, additive_inverse(multiply(additive_inverse(a), b)))
% 5.19/1.07 = { by axiom 11 (a_inverse_times_b_inverse) R->L }
% 5.19/1.07 fresh(sum(d, multiply(additive_inverse(a), b), fresh(fresh26(product(additive_inverse(a), additive_inverse(b), d), true, additive_inverse(a), additive_identity, multiply(additive_inverse(a), additive_identity), additive_inverse(b), d, additive_inverse(b), d), true, multiply(additive_inverse(a), additive_identity), additive_identity)), true, d, additive_inverse(multiply(additive_inverse(a), b)))
% 5.19/1.07 = { by axiom 32 (distributivity1) }
% 5.19/1.07 fresh(sum(d, multiply(additive_inverse(a), b), fresh(fresh28(product(additive_inverse(a), additive_inverse(b), d), true, additive_inverse(a), additive_identity, multiply(additive_inverse(a), additive_identity), additive_inverse(b), d, additive_inverse(b), d), true, multiply(additive_inverse(a), additive_identity), additive_identity)), true, d, additive_inverse(multiply(additive_inverse(a), b)))
% 5.19/1.07 = { by axiom 11 (a_inverse_times_b_inverse) }
% 5.19/1.07 fresh(sum(d, multiply(additive_inverse(a), b), fresh(fresh28(true, true, additive_inverse(a), additive_identity, multiply(additive_inverse(a), additive_identity), additive_inverse(b), d, additive_inverse(b), d), true, multiply(additive_inverse(a), additive_identity), additive_identity)), true, d, additive_inverse(multiply(additive_inverse(a), b)))
% 5.19/1.07 = { by axiom 24 (distributivity1) }
% 5.19/1.07 fresh(sum(d, multiply(additive_inverse(a), b), fresh(fresh29(sum(additive_identity, additive_inverse(b), additive_inverse(b)), true, multiply(additive_inverse(a), additive_identity), d, d), true, multiply(additive_inverse(a), additive_identity), additive_identity)), true, d, additive_inverse(multiply(additive_inverse(a), b)))
% 5.19/1.07 = { by axiom 2 (additive_identity1) }
% 5.19/1.07 fresh(sum(d, multiply(additive_inverse(a), b), fresh(fresh29(true, true, multiply(additive_inverse(a), additive_identity), d, d), true, multiply(additive_inverse(a), additive_identity), additive_identity)), true, d, additive_inverse(multiply(additive_inverse(a), b)))
% 5.19/1.07 = { by axiom 13 (distributivity1) }
% 5.19/1.07 fresh(sum(d, multiply(additive_inverse(a), b), fresh(true, true, multiply(additive_inverse(a), additive_identity), additive_identity)), true, d, additive_inverse(multiply(additive_inverse(a), b)))
% 5.19/1.07 = { by axiom 6 (cancellation2) }
% 5.19/1.07 fresh(sum(d, multiply(additive_inverse(a), b), additive_identity), true, d, additive_inverse(multiply(additive_inverse(a), b)))
% 5.19/1.07 = { by axiom 28 (cancellation2) R->L }
% 5.19/1.07 fresh2(sum(additive_inverse(multiply(additive_inverse(a), b)), multiply(additive_inverse(a), b), additive_identity), true, d, multiply(additive_inverse(a), b), additive_identity, additive_inverse(multiply(additive_inverse(a), b)))
% 5.19/1.07 = { by axiom 5 (left_inverse) }
% 5.19/1.07 fresh2(true, true, d, multiply(additive_inverse(a), b), additive_identity, additive_inverse(multiply(additive_inverse(a), b)))
% 5.19/1.07 = { by axiom 18 (cancellation2) }
% 5.19/1.07 d
% 5.19/1.07 % SZS output end Proof
% 5.19/1.07
% 5.19/1.07 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------