TSTP Solution File: FLD013-3 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : FLD013-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 : n011.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 22:36:48 EDT 2023
% Result : Unsatisfiable 41.46s 8.09s
% Output : Proof 42.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : FLD013-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.29 % Computer : n011.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Mon Aug 28 00:49:55 EDT 2023
% 0.10/0.29 % CPUTime :
% 41.46/8.09 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 41.46/8.09
% 41.46/8.09 % SZS status Unsatisfiable
% 41.46/8.09
% 42.02/8.15 % SZS output start Proof
% 42.02/8.15 Take the following subset of the input axioms:
% 42.02/8.15 fof(a_is_defined, hypothesis, defined(a)).
% 42.02/8.15 fof(associativity_addition_1, axiom, ![X, V, W, Y, U, Z]: (sum(X, V, W) | (~sum(X, Y, U) | (~sum(Y, Z, V) | ~sum(U, Z, W))))).
% 42.02/8.15 fof(b_is_defined, hypothesis, defined(b)).
% 42.02/8.15 fof(c_is_defined, hypothesis, defined(c)).
% 42.02/8.15 fof(commutativity_addition, axiom, ![X2, Y2, Z2]: (sum(Y2, X2, Z2) | ~sum(X2, Y2, Z2))).
% 42.02/8.15 fof(d_is_defined, hypothesis, defined(d)).
% 42.02/8.15 fof(existence_of_identity_addition, axiom, ![X2]: (sum(additive_identity, X2, X2) | ~defined(X2))).
% 42.02/8.15 fof(not_sum_7, negated_conjecture, ~sum(a, c, add(d, b))).
% 42.02/8.15 fof(sum_5, negated_conjecture, sum(additive_identity, a, b)).
% 42.02/8.15 fof(sum_6, negated_conjecture, sum(additive_identity, c, d)).
% 42.02/8.15 fof(totality_of_addition, axiom, ![X2, Y2]: (sum(X2, Y2, add(X2, Y2)) | (~defined(X2) | ~defined(Y2)))).
% 42.02/8.15 fof(well_definedness_of_additive_identity, axiom, defined(additive_identity)).
% 42.02/8.15
% 42.02/8.15 Now clausify the problem and encode Horn clauses using encoding 3 of
% 42.02/8.15 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 42.02/8.15 We repeatedly replace C & s=t => u=v by the two clauses:
% 42.02/8.15 fresh(y, y, x1...xn) = u
% 42.02/8.15 C => fresh(s, t, x1...xn) = v
% 42.02/8.15 where fresh is a fresh function symbol and x1..xn are the free
% 42.02/8.15 variables of u and v.
% 42.02/8.15 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 42.02/8.16 input problem has no model of domain size 1).
% 42.02/8.16
% 42.02/8.16 The encoding turns the above axioms into the following unit equations and goals:
% 42.02/8.16
% 42.02/8.16 Axiom 1 (well_definedness_of_additive_identity): defined(additive_identity) = true.
% 42.02/8.16 Axiom 2 (b_is_defined): defined(b) = true.
% 42.02/8.16 Axiom 3 (d_is_defined): defined(d) = true.
% 42.02/8.16 Axiom 4 (a_is_defined): defined(a) = true.
% 42.02/8.16 Axiom 5 (c_is_defined): defined(c) = true.
% 42.02/8.16 Axiom 6 (sum_5): sum(additive_identity, a, b) = true.
% 42.02/8.16 Axiom 7 (sum_6): sum(additive_identity, c, d) = true.
% 42.02/8.16 Axiom 8 (existence_of_identity_addition): fresh14(X, X, Y) = true.
% 42.02/8.16 Axiom 9 (existence_of_identity_addition): fresh14(defined(X), true, X) = sum(additive_identity, X, X).
% 42.02/8.16 Axiom 10 (totality_of_addition): fresh11(X, X, Y, Z) = sum(Y, Z, add(Y, Z)).
% 42.02/8.16 Axiom 11 (totality_of_addition): fresh10(X, X, Y, Z) = true.
% 42.02/8.16 Axiom 12 (associativity_addition_1): fresh44(X, X, Y, Z, W) = true.
% 42.02/8.16 Axiom 13 (commutativity_addition): fresh18(X, X, Y, Z, W) = true.
% 42.02/8.16 Axiom 14 (totality_of_addition): fresh11(defined(X), true, Y, X) = fresh10(defined(Y), true, Y, X).
% 42.02/8.16 Axiom 15 (associativity_addition_1): fresh22(X, X, Y, Z, W, V, U) = sum(Y, Z, W).
% 42.02/8.16 Axiom 16 (commutativity_addition): fresh18(sum(X, Y, Z), true, Y, X, Z) = sum(Y, X, Z).
% 42.02/8.16 Axiom 17 (associativity_addition_1): fresh43(X, X, Y, Z, W, V, U, T) = fresh44(sum(Y, V, U), true, Y, Z, W).
% 42.02/8.16 Axiom 18 (associativity_addition_1): fresh43(sum(X, Y, Z), true, W, V, Z, U, X, Y) = fresh22(sum(U, Y, V), true, W, V, Z, U, X).
% 42.02/8.16
% 42.02/8.16 Lemma 19: sum(additive_identity, additive_identity, additive_identity) = true.
% 42.02/8.16 Proof:
% 42.02/8.16 sum(additive_identity, additive_identity, additive_identity)
% 42.02/8.16 = { by axiom 9 (existence_of_identity_addition) R->L }
% 42.02/8.16 fresh14(defined(additive_identity), true, additive_identity)
% 42.02/8.16 = { by axiom 1 (well_definedness_of_additive_identity) }
% 42.02/8.16 fresh14(true, true, additive_identity)
% 42.02/8.16 = { by axiom 8 (existence_of_identity_addition) }
% 42.02/8.16 true
% 42.02/8.16
% 42.02/8.16 Lemma 20: sum(additive_identity, a, a) = true.
% 42.02/8.16 Proof:
% 42.02/8.16 sum(additive_identity, a, a)
% 42.02/8.16 = { by axiom 9 (existence_of_identity_addition) R->L }
% 42.02/8.16 fresh14(defined(a), true, a)
% 42.02/8.16 = { by axiom 4 (a_is_defined) }
% 42.02/8.16 fresh14(true, true, a)
% 42.02/8.16 = { by axiom 8 (existence_of_identity_addition) }
% 42.02/8.16 true
% 42.02/8.16
% 42.02/8.16 Lemma 21: fresh43(sum(X, additive_identity, Y), true, Z, add(additive_identity, additive_identity), Y, additive_identity, X, additive_identity) = sum(Z, add(additive_identity, additive_identity), Y).
% 42.02/8.16 Proof:
% 42.02/8.16 fresh43(sum(X, additive_identity, Y), true, Z, add(additive_identity, additive_identity), Y, additive_identity, X, additive_identity)
% 42.02/8.16 = { by axiom 18 (associativity_addition_1) }
% 42.02/8.16 fresh22(sum(additive_identity, additive_identity, add(additive_identity, additive_identity)), true, Z, add(additive_identity, additive_identity), Y, additive_identity, X)
% 42.02/8.16 = { by axiom 10 (totality_of_addition) R->L }
% 42.02/8.16 fresh22(fresh11(true, true, additive_identity, additive_identity), true, Z, add(additive_identity, additive_identity), Y, additive_identity, X)
% 42.02/8.16 = { by axiom 1 (well_definedness_of_additive_identity) R->L }
% 42.02/8.16 fresh22(fresh11(defined(additive_identity), true, additive_identity, additive_identity), true, Z, add(additive_identity, additive_identity), Y, additive_identity, X)
% 42.02/8.16 = { by axiom 14 (totality_of_addition) }
% 42.02/8.16 fresh22(fresh10(defined(additive_identity), true, additive_identity, additive_identity), true, Z, add(additive_identity, additive_identity), Y, additive_identity, X)
% 42.02/8.16 = { by axiom 1 (well_definedness_of_additive_identity) }
% 42.02/8.16 fresh22(fresh10(true, true, additive_identity, additive_identity), true, Z, add(additive_identity, additive_identity), Y, additive_identity, X)
% 42.02/8.16 = { by axiom 11 (totality_of_addition) }
% 42.02/8.16 fresh22(true, true, Z, add(additive_identity, additive_identity), Y, additive_identity, X)
% 42.02/8.16 = { by axiom 15 (associativity_addition_1) }
% 42.02/8.16 sum(Z, add(additive_identity, additive_identity), Y)
% 42.02/8.16
% 42.02/8.16 Lemma 22: fresh44(sum(X, additive_identity, additive_identity), true, X, add(additive_identity, additive_identity), additive_identity) = sum(X, add(additive_identity, additive_identity), additive_identity).
% 42.02/8.16 Proof:
% 42.02/8.16 fresh44(sum(X, additive_identity, additive_identity), true, X, add(additive_identity, additive_identity), additive_identity)
% 42.02/8.16 = { by axiom 17 (associativity_addition_1) R->L }
% 42.02/8.16 fresh43(true, true, X, add(additive_identity, additive_identity), additive_identity, additive_identity, additive_identity, additive_identity)
% 42.02/8.16 = { by lemma 19 R->L }
% 42.02/8.16 fresh43(sum(additive_identity, additive_identity, additive_identity), true, X, add(additive_identity, additive_identity), additive_identity, additive_identity, additive_identity, additive_identity)
% 42.02/8.16 = { by lemma 21 }
% 42.02/8.16 sum(X, add(additive_identity, additive_identity), additive_identity)
% 42.02/8.16
% 42.02/8.16 Goal 1 (not_sum_7): sum(a, c, add(d, b)) = true.
% 42.02/8.16 Proof:
% 42.02/8.16 sum(a, c, add(d, b))
% 42.02/8.16 = { by axiom 16 (commutativity_addition) R->L }
% 42.02/8.16 fresh18(sum(c, a, add(d, b)), true, a, c, add(d, b))
% 42.02/8.16 = { by axiom 15 (associativity_addition_1) R->L }
% 42.02/8.16 fresh18(fresh22(true, true, c, a, add(d, b), add(additive_identity, additive_identity), d), true, a, c, add(d, b))
% 42.02/8.16 = { by axiom 12 (associativity_addition_1) R->L }
% 42.02/8.16 fresh18(fresh22(fresh44(true, true, add(additive_identity, additive_identity), b, a), true, c, a, add(d, b), add(additive_identity, additive_identity), d), true, a, c, add(d, b))
% 42.02/8.16 = { by axiom 12 (associativity_addition_1) R->L }
% 42.02/8.16 fresh18(fresh22(fresh44(fresh44(true, true, add(additive_identity, additive_identity), add(additive_identity, additive_identity), additive_identity), true, add(additive_identity, additive_identity), b, a), true, c, a, add(d, b), add(additive_identity, additive_identity), d), true, a, c, add(d, b))
% 42.02/8.16 = { by axiom 13 (commutativity_addition) R->L }
% 42.02/8.16 fresh18(fresh22(fresh44(fresh44(fresh18(true, true, add(additive_identity, additive_identity), additive_identity, additive_identity), true, add(additive_identity, additive_identity), add(additive_identity, additive_identity), additive_identity), true, add(additive_identity, additive_identity), b, a), true, c, a, add(d, b), add(additive_identity, additive_identity), d), true, a, c, add(d, b))
% 42.02/8.16 = { by axiom 12 (associativity_addition_1) R->L }
% 42.02/8.16 fresh18(fresh22(fresh44(fresh44(fresh18(fresh44(true, true, additive_identity, add(additive_identity, additive_identity), additive_identity), true, add(additive_identity, additive_identity), additive_identity, additive_identity), true, add(additive_identity, additive_identity), add(additive_identity, additive_identity), additive_identity), true, add(additive_identity, additive_identity), b, a), true, c, a, add(d, b), add(additive_identity, additive_identity), d), true, a, c, add(d, b))
% 42.02/8.16 = { by lemma 19 R->L }
% 42.02/8.16 fresh18(fresh22(fresh44(fresh44(fresh18(fresh44(sum(additive_identity, additive_identity, additive_identity), true, additive_identity, add(additive_identity, additive_identity), additive_identity), true, add(additive_identity, additive_identity), additive_identity, additive_identity), true, add(additive_identity, additive_identity), add(additive_identity, additive_identity), additive_identity), true, add(additive_identity, additive_identity), b, a), true, c, a, add(d, b), add(additive_identity, additive_identity), d), true, a, c, add(d, b))
% 42.02/8.16 = { by lemma 22 }
% 42.02/8.16 fresh18(fresh22(fresh44(fresh44(fresh18(sum(additive_identity, add(additive_identity, additive_identity), additive_identity), true, add(additive_identity, additive_identity), additive_identity, additive_identity), true, add(additive_identity, additive_identity), add(additive_identity, additive_identity), additive_identity), true, add(additive_identity, additive_identity), b, a), true, c, a, add(d, b), add(additive_identity, additive_identity), d), true, a, c, add(d, b))
% 42.02/8.16 = { by axiom 16 (commutativity_addition) }
% 42.02/8.16 fresh18(fresh22(fresh44(fresh44(sum(add(additive_identity, additive_identity), additive_identity, additive_identity), true, add(additive_identity, additive_identity), add(additive_identity, additive_identity), additive_identity), true, add(additive_identity, additive_identity), b, a), true, c, a, add(d, b), add(additive_identity, additive_identity), d), true, a, c, add(d, b))
% 42.02/8.16 = { by lemma 22 }
% 42.02/8.16 fresh18(fresh22(fresh44(sum(add(additive_identity, additive_identity), add(additive_identity, additive_identity), additive_identity), true, add(additive_identity, additive_identity), b, a), true, c, a, add(d, b), add(additive_identity, additive_identity), d), true, a, c, add(d, b))
% 42.02/8.16 = { by axiom 17 (associativity_addition_1) R->L }
% 42.02/8.16 fresh18(fresh22(fresh43(true, true, add(additive_identity, additive_identity), b, a, add(additive_identity, additive_identity), additive_identity, a), true, c, a, add(d, b), add(additive_identity, additive_identity), d), true, a, c, add(d, b))
% 42.02/8.16 = { by lemma 20 R->L }
% 42.02/8.16 fresh18(fresh22(fresh43(sum(additive_identity, a, a), true, add(additive_identity, additive_identity), b, a, add(additive_identity, additive_identity), additive_identity, a), true, c, a, add(d, b), add(additive_identity, additive_identity), d), true, a, c, add(d, b))
% 42.02/8.16 = { by axiom 18 (associativity_addition_1) }
% 42.02/8.16 fresh18(fresh22(fresh22(sum(add(additive_identity, additive_identity), a, b), true, add(additive_identity, additive_identity), b, a, add(additive_identity, additive_identity), additive_identity), true, c, a, add(d, b), add(additive_identity, additive_identity), d), true, a, c, add(d, b))
% 42.02/8.16 = { by axiom 16 (commutativity_addition) R->L }
% 42.02/8.16 fresh18(fresh22(fresh22(fresh18(sum(a, add(additive_identity, additive_identity), b), true, add(additive_identity, additive_identity), a, b), true, add(additive_identity, additive_identity), b, a, add(additive_identity, additive_identity), additive_identity), true, c, a, add(d, b), add(additive_identity, additive_identity), d), true, a, c, add(d, b))
% 42.02/8.16 = { by lemma 21 R->L }
% 42.02/8.16 fresh18(fresh22(fresh22(fresh18(fresh43(sum(a, additive_identity, b), true, a, add(additive_identity, additive_identity), b, additive_identity, a, additive_identity), true, add(additive_identity, additive_identity), a, b), true, add(additive_identity, additive_identity), b, a, add(additive_identity, additive_identity), additive_identity), true, c, a, add(d, b), add(additive_identity, additive_identity), d), true, a, c, add(d, b))
% 42.02/8.16 = { by axiom 16 (commutativity_addition) R->L }
% 42.02/8.16 fresh18(fresh22(fresh22(fresh18(fresh43(fresh18(sum(additive_identity, a, b), true, a, additive_identity, b), true, a, add(additive_identity, additive_identity), b, additive_identity, a, additive_identity), true, add(additive_identity, additive_identity), a, b), true, add(additive_identity, additive_identity), b, a, add(additive_identity, additive_identity), additive_identity), true, c, a, add(d, b), add(additive_identity, additive_identity), d), true, a, c, add(d, b))
% 42.02/8.16 = { by axiom 6 (sum_5) }
% 42.02/8.16 fresh18(fresh22(fresh22(fresh18(fresh43(fresh18(true, true, a, additive_identity, b), true, a, add(additive_identity, additive_identity), b, additive_identity, a, additive_identity), true, add(additive_identity, additive_identity), a, b), true, add(additive_identity, additive_identity), b, a, add(additive_identity, additive_identity), additive_identity), true, c, a, add(d, b), add(additive_identity, additive_identity), d), true, a, c, add(d, b))
% 42.02/8.16 = { by axiom 13 (commutativity_addition) }
% 42.02/8.16 fresh18(fresh22(fresh22(fresh18(fresh43(true, true, a, add(additive_identity, additive_identity), b, additive_identity, a, additive_identity), true, add(additive_identity, additive_identity), a, b), true, add(additive_identity, additive_identity), b, a, add(additive_identity, additive_identity), additive_identity), true, c, a, add(d, b), add(additive_identity, additive_identity), d), true, a, c, add(d, b))
% 42.02/8.16 = { by axiom 17 (associativity_addition_1) }
% 42.02/8.16 fresh18(fresh22(fresh22(fresh18(fresh44(sum(a, additive_identity, a), true, a, add(additive_identity, additive_identity), b), true, add(additive_identity, additive_identity), a, b), true, add(additive_identity, additive_identity), b, a, add(additive_identity, additive_identity), additive_identity), true, c, a, add(d, b), add(additive_identity, additive_identity), d), true, a, c, add(d, b))
% 42.02/8.16 = { by axiom 16 (commutativity_addition) R->L }
% 42.02/8.16 fresh18(fresh22(fresh22(fresh18(fresh44(fresh18(sum(additive_identity, a, a), true, a, additive_identity, a), true, a, add(additive_identity, additive_identity), b), true, add(additive_identity, additive_identity), a, b), true, add(additive_identity, additive_identity), b, a, add(additive_identity, additive_identity), additive_identity), true, c, a, add(d, b), add(additive_identity, additive_identity), d), true, a, c, add(d, b))
% 42.02/8.17 = { by lemma 20 }
% 42.02/8.17 fresh18(fresh22(fresh22(fresh18(fresh44(fresh18(true, true, a, additive_identity, a), true, a, add(additive_identity, additive_identity), b), true, add(additive_identity, additive_identity), a, b), true, add(additive_identity, additive_identity), b, a, add(additive_identity, additive_identity), additive_identity), true, c, a, add(d, b), add(additive_identity, additive_identity), d), true, a, c, add(d, b))
% 42.02/8.17 = { by axiom 13 (commutativity_addition) }
% 42.02/8.17 fresh18(fresh22(fresh22(fresh18(fresh44(true, true, a, add(additive_identity, additive_identity), b), true, add(additive_identity, additive_identity), a, b), true, add(additive_identity, additive_identity), b, a, add(additive_identity, additive_identity), additive_identity), true, c, a, add(d, b), add(additive_identity, additive_identity), d), true, a, c, add(d, b))
% 42.02/8.17 = { by axiom 12 (associativity_addition_1) }
% 42.02/8.17 fresh18(fresh22(fresh22(fresh18(true, true, add(additive_identity, additive_identity), a, b), true, add(additive_identity, additive_identity), b, a, add(additive_identity, additive_identity), additive_identity), true, c, a, add(d, b), add(additive_identity, additive_identity), d), true, a, c, add(d, b))
% 42.02/8.17 = { by axiom 13 (commutativity_addition) }
% 42.02/8.17 fresh18(fresh22(fresh22(true, true, add(additive_identity, additive_identity), b, a, add(additive_identity, additive_identity), additive_identity), true, c, a, add(d, b), add(additive_identity, additive_identity), d), true, a, c, add(d, b))
% 42.02/8.17 = { by axiom 15 (associativity_addition_1) }
% 42.02/8.17 fresh18(fresh22(sum(add(additive_identity, additive_identity), b, a), true, c, a, add(d, b), add(additive_identity, additive_identity), d), true, a, c, add(d, b))
% 42.02/8.17 = { by axiom 18 (associativity_addition_1) R->L }
% 42.02/8.17 fresh18(fresh43(sum(d, b, add(d, b)), true, c, a, add(d, b), add(additive_identity, additive_identity), d, b), true, a, c, add(d, b))
% 42.02/8.17 = { by axiom 10 (totality_of_addition) R->L }
% 42.02/8.17 fresh18(fresh43(fresh11(true, true, d, b), true, c, a, add(d, b), add(additive_identity, additive_identity), d, b), true, a, c, add(d, b))
% 42.02/8.17 = { by axiom 2 (b_is_defined) R->L }
% 42.02/8.17 fresh18(fresh43(fresh11(defined(b), true, d, b), true, c, a, add(d, b), add(additive_identity, additive_identity), d, b), true, a, c, add(d, b))
% 42.02/8.17 = { by axiom 14 (totality_of_addition) }
% 42.02/8.17 fresh18(fresh43(fresh10(defined(d), true, d, b), true, c, a, add(d, b), add(additive_identity, additive_identity), d, b), true, a, c, add(d, b))
% 42.02/8.17 = { by axiom 3 (d_is_defined) }
% 42.02/8.17 fresh18(fresh43(fresh10(true, true, d, b), true, c, a, add(d, b), add(additive_identity, additive_identity), d, b), true, a, c, add(d, b))
% 42.02/8.17 = { by axiom 11 (totality_of_addition) }
% 42.02/8.17 fresh18(fresh43(true, true, c, a, add(d, b), add(additive_identity, additive_identity), d, b), true, a, c, add(d, b))
% 42.02/8.17 = { by axiom 17 (associativity_addition_1) }
% 42.02/8.17 fresh18(fresh44(sum(c, add(additive_identity, additive_identity), d), true, c, a, add(d, b)), true, a, c, add(d, b))
% 42.02/8.17 = { by lemma 21 R->L }
% 42.02/8.17 fresh18(fresh44(fresh43(sum(c, additive_identity, d), true, c, add(additive_identity, additive_identity), d, additive_identity, c, additive_identity), true, c, a, add(d, b)), true, a, c, add(d, b))
% 42.02/8.17 = { by axiom 16 (commutativity_addition) R->L }
% 42.02/8.17 fresh18(fresh44(fresh43(fresh18(sum(additive_identity, c, d), true, c, additive_identity, d), true, c, add(additive_identity, additive_identity), d, additive_identity, c, additive_identity), true, c, a, add(d, b)), true, a, c, add(d, b))
% 42.02/8.17 = { by axiom 7 (sum_6) }
% 42.02/8.17 fresh18(fresh44(fresh43(fresh18(true, true, c, additive_identity, d), true, c, add(additive_identity, additive_identity), d, additive_identity, c, additive_identity), true, c, a, add(d, b)), true, a, c, add(d, b))
% 42.02/8.17 = { by axiom 13 (commutativity_addition) }
% 42.02/8.17 fresh18(fresh44(fresh43(true, true, c, add(additive_identity, additive_identity), d, additive_identity, c, additive_identity), true, c, a, add(d, b)), true, a, c, add(d, b))
% 42.02/8.17 = { by axiom 17 (associativity_addition_1) }
% 42.02/8.17 fresh18(fresh44(fresh44(sum(c, additive_identity, c), true, c, add(additive_identity, additive_identity), d), true, c, a, add(d, b)), true, a, c, add(d, b))
% 42.02/8.17 = { by axiom 16 (commutativity_addition) R->L }
% 42.02/8.17 fresh18(fresh44(fresh44(fresh18(sum(additive_identity, c, c), true, c, additive_identity, c), true, c, add(additive_identity, additive_identity), d), true, c, a, add(d, b)), true, a, c, add(d, b))
% 42.02/8.17 = { by axiom 9 (existence_of_identity_addition) R->L }
% 42.02/8.17 fresh18(fresh44(fresh44(fresh18(fresh14(defined(c), true, c), true, c, additive_identity, c), true, c, add(additive_identity, additive_identity), d), true, c, a, add(d, b)), true, a, c, add(d, b))
% 42.02/8.17 = { by axiom 5 (c_is_defined) }
% 42.02/8.17 fresh18(fresh44(fresh44(fresh18(fresh14(true, true, c), true, c, additive_identity, c), true, c, add(additive_identity, additive_identity), d), true, c, a, add(d, b)), true, a, c, add(d, b))
% 42.02/8.17 = { by axiom 8 (existence_of_identity_addition) }
% 42.02/8.17 fresh18(fresh44(fresh44(fresh18(true, true, c, additive_identity, c), true, c, add(additive_identity, additive_identity), d), true, c, a, add(d, b)), true, a, c, add(d, b))
% 42.02/8.17 = { by axiom 13 (commutativity_addition) }
% 42.02/8.17 fresh18(fresh44(fresh44(true, true, c, add(additive_identity, additive_identity), d), true, c, a, add(d, b)), true, a, c, add(d, b))
% 42.02/8.17 = { by axiom 12 (associativity_addition_1) }
% 42.02/8.17 fresh18(fresh44(true, true, c, a, add(d, b)), true, a, c, add(d, b))
% 42.02/8.17 = { by axiom 12 (associativity_addition_1) }
% 42.02/8.17 fresh18(true, true, a, c, add(d, b))
% 42.02/8.17 = { by axiom 13 (commutativity_addition) }
% 42.02/8.17 true
% 42.02/8.17 % SZS output end Proof
% 42.02/8.18
% 42.02/8.18 RESULT: Unsatisfiable (the axioms are contradictory).
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