TSTP Solution File: FLD008-4 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : FLD008-4 : 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 : n025.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 22:36:46 EDT 2023
% Result : Unsatisfiable 268.73s 35.01s
% Output : Proof 269.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : FLD008-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.33 % Computer : n025.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Aug 28 00:50:09 EDT 2023
% 0.11/0.33 % CPUTime :
% 268.73/35.01 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 268.73/35.01
% 268.73/35.01 % SZS status Unsatisfiable
% 268.73/35.01
% 268.73/35.12 % SZS output start Proof
% 268.73/35.12 Take the following subset of the input axioms:
% 268.73/35.12 fof(a_is_defined, hypothesis, defined(a)).
% 268.73/35.12 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))))).
% 268.73/35.12 fof(associativity_addition_2, axiom, ![X2, Y2, Z2, V2, W2, U2]: (sum(U2, Z2, W2) | (~sum(X2, Y2, U2) | (~sum(Y2, Z2, V2) | ~sum(X2, V2, W2))))).
% 268.73/35.12 fof(b_is_defined, hypothesis, defined(b)).
% 268.73/35.12 fof(c_is_defined, hypothesis, defined(c)).
% 268.73/35.12 fof(commutativity_addition, axiom, ![X2, Y2, Z2]: (sum(Y2, X2, Z2) | ~sum(X2, Y2, Z2))).
% 268.73/35.12 fof(d_is_defined, hypothesis, defined(d)).
% 268.73/35.12 fof(existence_of_identity_addition, axiom, ![X2]: (sum(additive_identity, X2, X2) | ~defined(X2))).
% 268.73/35.12 fof(existence_of_inverse_addition, axiom, ![X2]: (sum(additive_inverse(X2), X2, additive_identity) | ~defined(X2))).
% 268.73/35.12 fof(not_sum_7, negated_conjecture, ~sum(additive_identity, additive_inverse(c), d)).
% 268.73/35.12 fof(sum_5, negated_conjecture, sum(a, b, c)).
% 268.73/35.12 fof(sum_6, negated_conjecture, sum(additive_inverse(a), additive_inverse(b), d)).
% 268.73/35.12 fof(well_definedness_of_additive_identity, axiom, defined(additive_identity)).
% 268.73/35.12 fof(well_definedness_of_additive_inverse, axiom, ![X2]: (defined(additive_inverse(X2)) | ~defined(X2))).
% 268.73/35.12
% 268.73/35.12 Now clausify the problem and encode Horn clauses using encoding 3 of
% 268.73/35.12 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 268.73/35.12 We repeatedly replace C & s=t => u=v by the two clauses:
% 268.73/35.12 fresh(y, y, x1...xn) = u
% 268.73/35.12 C => fresh(s, t, x1...xn) = v
% 268.73/35.12 where fresh is a fresh function symbol and x1..xn are the free
% 268.73/35.12 variables of u and v.
% 268.73/35.12 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 268.73/35.12 input problem has no model of domain size 1).
% 268.73/35.12
% 268.73/35.12 The encoding turns the above axioms into the following unit equations and goals:
% 268.73/35.12
% 268.73/35.12 Axiom 1 (well_definedness_of_additive_identity): defined(additive_identity) = true.
% 268.73/35.12 Axiom 2 (c_is_defined): defined(c) = true.
% 268.73/35.12 Axiom 3 (d_is_defined): defined(d) = true.
% 268.73/35.12 Axiom 4 (a_is_defined): defined(a) = true.
% 268.73/35.12 Axiom 5 (b_is_defined): defined(b) = true.
% 268.73/35.12 Axiom 6 (sum_5): sum(a, b, c) = true.
% 268.73/35.12 Axiom 7 (existence_of_identity_addition): fresh14(X, X, Y) = true.
% 268.73/35.12 Axiom 8 (existence_of_inverse_addition): fresh12(X, X, Y) = true.
% 268.73/35.12 Axiom 9 (well_definedness_of_additive_inverse): fresh3(X, X, Y) = true.
% 268.73/35.12 Axiom 10 (existence_of_identity_addition): fresh14(defined(X), true, X) = sum(additive_identity, X, X).
% 268.73/35.12 Axiom 11 (existence_of_inverse_addition): fresh12(defined(X), true, X) = sum(additive_inverse(X), X, additive_identity).
% 268.73/35.12 Axiom 12 (well_definedness_of_additive_inverse): fresh3(defined(X), true, X) = defined(additive_inverse(X)).
% 268.73/35.12 Axiom 13 (sum_6): sum(additive_inverse(a), additive_inverse(b), d) = true.
% 268.73/35.12 Axiom 14 (associativity_addition_1): fresh44(X, X, Y, Z, W) = true.
% 268.73/35.12 Axiom 15 (associativity_addition_2): fresh42(X, X, Y, Z, W) = true.
% 268.73/35.12 Axiom 16 (commutativity_addition): fresh18(X, X, Y, Z, W) = true.
% 268.73/35.12 Axiom 17 (associativity_addition_1): fresh22(X, X, Y, Z, W, V, U) = sum(Y, Z, W).
% 268.73/35.12 Axiom 18 (associativity_addition_2): fresh21(X, X, Y, Z, W, V, U) = sum(Y, Z, W).
% 268.73/35.12 Axiom 19 (commutativity_addition): fresh18(sum(X, Y, Z), true, Y, X, Z) = sum(Y, X, Z).
% 268.73/35.12 Axiom 20 (associativity_addition_1): fresh43(X, X, Y, Z, W, V, U, T) = fresh44(sum(Y, V, U), true, Y, Z, W).
% 268.73/35.12 Axiom 21 (associativity_addition_2): fresh41(X, X, Y, Z, W, V, U, T) = fresh42(sum(V, U, Y), true, Y, Z, W).
% 268.73/35.12 Axiom 22 (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).
% 268.73/35.12 Axiom 23 (associativity_addition_2): fresh41(sum(X, Y, Z), true, W, Y, V, U, X, Z) = fresh21(sum(U, Z, V), true, W, Y, V, U, X).
% 268.73/35.12
% 268.73/35.12 Lemma 24: defined(additive_inverse(c)) = true.
% 268.73/35.12 Proof:
% 268.73/35.12 defined(additive_inverse(c))
% 268.73/35.12 = { by axiom 12 (well_definedness_of_additive_inverse) R->L }
% 268.73/35.12 fresh3(defined(c), true, c)
% 268.73/35.12 = { by axiom 2 (c_is_defined) }
% 268.73/35.12 fresh3(true, true, c)
% 268.73/35.12 = { by axiom 9 (well_definedness_of_additive_inverse) }
% 268.73/35.12 true
% 268.73/35.12
% 268.73/35.12 Lemma 25: sum(additive_identity, additive_identity, additive_identity) = true.
% 268.73/35.12 Proof:
% 268.73/35.12 sum(additive_identity, additive_identity, additive_identity)
% 268.73/35.12 = { by axiom 10 (existence_of_identity_addition) R->L }
% 268.73/35.12 fresh14(defined(additive_identity), true, additive_identity)
% 268.73/35.12 = { by axiom 1 (well_definedness_of_additive_identity) }
% 268.73/35.12 fresh14(true, true, additive_identity)
% 268.73/35.12 = { by axiom 7 (existence_of_identity_addition) }
% 268.73/35.12 true
% 268.73/35.12
% 268.73/35.12 Lemma 26: sum(additive_identity, b, b) = true.
% 268.73/35.12 Proof:
% 268.73/35.12 sum(additive_identity, b, b)
% 268.73/35.12 = { by axiom 10 (existence_of_identity_addition) R->L }
% 268.73/35.12 fresh14(defined(b), true, b)
% 268.73/35.12 = { by axiom 5 (b_is_defined) }
% 268.73/35.12 fresh14(true, true, b)
% 268.73/35.12 = { by axiom 7 (existence_of_identity_addition) }
% 268.73/35.12 true
% 268.73/35.12
% 268.73/35.12 Lemma 27: sum(additive_identity, c, c) = true.
% 268.73/35.12 Proof:
% 268.73/35.12 sum(additive_identity, c, c)
% 268.73/35.12 = { by axiom 10 (existence_of_identity_addition) R->L }
% 268.73/35.12 fresh14(defined(c), true, c)
% 268.73/35.12 = { by axiom 2 (c_is_defined) }
% 268.73/35.12 fresh14(true, true, c)
% 268.73/35.12 = { by axiom 7 (existence_of_identity_addition) }
% 268.73/35.12 true
% 268.73/35.12
% 268.73/35.12 Lemma 28: sum(d, additive_identity, d) = true.
% 268.73/35.12 Proof:
% 268.73/35.12 sum(d, additive_identity, d)
% 268.73/35.12 = { by axiom 19 (commutativity_addition) R->L }
% 268.73/35.12 fresh18(sum(additive_identity, d, d), true, d, additive_identity, d)
% 268.73/35.12 = { by axiom 10 (existence_of_identity_addition) R->L }
% 268.73/35.12 fresh18(fresh14(defined(d), true, d), true, d, additive_identity, d)
% 268.73/35.12 = { by axiom 3 (d_is_defined) }
% 268.73/35.12 fresh18(fresh14(true, true, d), true, d, additive_identity, d)
% 268.73/35.12 = { by axiom 7 (existence_of_identity_addition) }
% 268.73/35.12 fresh18(true, true, d, additive_identity, d)
% 268.73/35.12 = { by axiom 16 (commutativity_addition) }
% 268.73/35.12 true
% 268.73/35.12
% 268.73/35.12 Lemma 29: sum(additive_inverse(additive_identity), additive_identity, additive_identity) = true.
% 268.73/35.12 Proof:
% 268.73/35.12 sum(additive_inverse(additive_identity), additive_identity, additive_identity)
% 268.73/35.12 = { by axiom 11 (existence_of_inverse_addition) R->L }
% 268.73/35.12 fresh12(defined(additive_identity), true, additive_identity)
% 268.73/35.12 = { by axiom 1 (well_definedness_of_additive_identity) }
% 268.73/35.12 fresh12(true, true, additive_identity)
% 268.73/35.12 = { by axiom 8 (existence_of_inverse_addition) }
% 268.73/35.12 true
% 268.73/35.12
% 268.73/35.12 Lemma 30: sum(additive_identity, additive_identity, additive_inverse(additive_identity)) = true.
% 268.73/35.12 Proof:
% 268.73/35.12 sum(additive_identity, additive_identity, additive_inverse(additive_identity))
% 268.73/35.12 = { by axiom 18 (associativity_addition_2) R->L }
% 268.73/35.12 fresh21(true, true, additive_identity, additive_identity, additive_inverse(additive_identity), additive_inverse(additive_identity), additive_identity)
% 268.73/35.12 = { by axiom 16 (commutativity_addition) R->L }
% 268.73/35.12 fresh21(fresh18(true, true, additive_inverse(additive_identity), additive_identity, additive_inverse(additive_identity)), true, additive_identity, additive_identity, additive_inverse(additive_identity), additive_inverse(additive_identity), additive_identity)
% 268.73/35.12 = { by axiom 7 (existence_of_identity_addition) R->L }
% 268.73/35.12 fresh21(fresh18(fresh14(true, true, additive_inverse(additive_identity)), true, additive_inverse(additive_identity), additive_identity, additive_inverse(additive_identity)), true, additive_identity, additive_identity, additive_inverse(additive_identity), additive_inverse(additive_identity), additive_identity)
% 268.73/35.12 = { by axiom 9 (well_definedness_of_additive_inverse) R->L }
% 268.73/35.12 fresh21(fresh18(fresh14(fresh3(true, true, additive_identity), true, additive_inverse(additive_identity)), true, additive_inverse(additive_identity), additive_identity, additive_inverse(additive_identity)), true, additive_identity, additive_identity, additive_inverse(additive_identity), additive_inverse(additive_identity), additive_identity)
% 268.73/35.12 = { by axiom 1 (well_definedness_of_additive_identity) R->L }
% 268.73/35.12 fresh21(fresh18(fresh14(fresh3(defined(additive_identity), true, additive_identity), true, additive_inverse(additive_identity)), true, additive_inverse(additive_identity), additive_identity, additive_inverse(additive_identity)), true, additive_identity, additive_identity, additive_inverse(additive_identity), additive_inverse(additive_identity), additive_identity)
% 268.73/35.12 = { by axiom 12 (well_definedness_of_additive_inverse) }
% 268.73/35.12 fresh21(fresh18(fresh14(defined(additive_inverse(additive_identity)), true, additive_inverse(additive_identity)), true, additive_inverse(additive_identity), additive_identity, additive_inverse(additive_identity)), true, additive_identity, additive_identity, additive_inverse(additive_identity), additive_inverse(additive_identity), additive_identity)
% 268.73/35.12 = { by axiom 10 (existence_of_identity_addition) }
% 268.73/35.12 fresh21(fresh18(sum(additive_identity, additive_inverse(additive_identity), additive_inverse(additive_identity)), true, additive_inverse(additive_identity), additive_identity, additive_inverse(additive_identity)), true, additive_identity, additive_identity, additive_inverse(additive_identity), additive_inverse(additive_identity), additive_identity)
% 268.73/35.12 = { by axiom 19 (commutativity_addition) }
% 268.73/35.12 fresh21(sum(additive_inverse(additive_identity), additive_identity, additive_inverse(additive_identity)), true, additive_identity, additive_identity, additive_inverse(additive_identity), additive_inverse(additive_identity), additive_identity)
% 268.73/35.12 = { by axiom 23 (associativity_addition_2) R->L }
% 268.73/35.12 fresh41(sum(additive_identity, additive_identity, additive_identity), true, additive_identity, additive_identity, additive_inverse(additive_identity), additive_inverse(additive_identity), additive_identity, additive_identity)
% 268.73/35.12 = { by lemma 25 }
% 268.73/35.12 fresh41(true, true, additive_identity, additive_identity, additive_inverse(additive_identity), additive_inverse(additive_identity), additive_identity, additive_identity)
% 268.73/35.12 = { by axiom 21 (associativity_addition_2) }
% 268.73/35.12 fresh42(sum(additive_inverse(additive_identity), additive_identity, additive_identity), true, additive_identity, additive_identity, additive_inverse(additive_identity))
% 268.73/35.12 = { by lemma 29 }
% 268.73/35.12 fresh42(true, true, additive_identity, additive_identity, additive_inverse(additive_identity))
% 268.73/35.12 = { by axiom 15 (associativity_addition_2) }
% 268.73/35.12 true
% 268.73/35.12
% 268.73/35.12 Lemma 31: sum(additive_identity, additive_inverse(c), additive_inverse(c)) = true.
% 268.73/35.12 Proof:
% 268.73/35.12 sum(additive_identity, additive_inverse(c), additive_inverse(c))
% 268.73/35.12 = { by axiom 10 (existence_of_identity_addition) R->L }
% 268.73/35.12 fresh14(defined(additive_inverse(c)), true, additive_inverse(c))
% 268.73/35.12 = { by lemma 24 }
% 268.73/35.12 fresh14(true, true, additive_inverse(c))
% 268.73/35.12 = { by axiom 7 (existence_of_identity_addition) }
% 268.73/35.12 true
% 268.73/35.12
% 268.73/35.12 Lemma 32: sum(additive_inverse(c), c, additive_inverse(additive_identity)) = true.
% 268.73/35.12 Proof:
% 268.73/35.12 sum(additive_inverse(c), c, additive_inverse(additive_identity))
% 268.73/35.12 = { by axiom 18 (associativity_addition_2) R->L }
% 268.73/35.12 fresh21(true, true, additive_inverse(c), c, additive_inverse(additive_identity), additive_identity, additive_inverse(c))
% 268.73/35.12 = { by lemma 30 R->L }
% 268.73/35.12 fresh21(sum(additive_identity, additive_identity, additive_inverse(additive_identity)), true, additive_inverse(c), c, additive_inverse(additive_identity), additive_identity, additive_inverse(c))
% 268.73/35.12 = { by axiom 23 (associativity_addition_2) R->L }
% 268.73/35.12 fresh41(sum(additive_inverse(c), c, additive_identity), true, additive_inverse(c), c, additive_inverse(additive_identity), additive_identity, additive_inverse(c), additive_identity)
% 268.73/35.12 = { by axiom 11 (existence_of_inverse_addition) R->L }
% 268.73/35.12 fresh41(fresh12(defined(c), true, c), true, additive_inverse(c), c, additive_inverse(additive_identity), additive_identity, additive_inverse(c), additive_identity)
% 268.73/35.12 = { by axiom 2 (c_is_defined) }
% 268.73/35.12 fresh41(fresh12(true, true, c), true, additive_inverse(c), c, additive_inverse(additive_identity), additive_identity, additive_inverse(c), additive_identity)
% 268.73/35.12 = { by axiom 8 (existence_of_inverse_addition) }
% 268.73/35.12 fresh41(true, true, additive_inverse(c), c, additive_inverse(additive_identity), additive_identity, additive_inverse(c), additive_identity)
% 268.73/35.12 = { by axiom 21 (associativity_addition_2) }
% 268.73/35.12 fresh42(sum(additive_identity, additive_inverse(c), additive_inverse(c)), true, additive_inverse(c), c, additive_inverse(additive_identity))
% 268.73/35.12 = { by lemma 31 }
% 268.73/35.13 fresh42(true, true, additive_inverse(c), c, additive_inverse(additive_identity))
% 268.73/35.13 = { by axiom 15 (associativity_addition_2) }
% 268.73/35.13 true
% 268.73/35.13
% 268.73/35.13 Lemma 33: sum(additive_inverse(additive_inverse(c)), additive_identity, c) = true.
% 268.73/35.13 Proof:
% 268.73/35.13 sum(additive_inverse(additive_inverse(c)), additive_identity, c)
% 268.73/35.13 = { by axiom 17 (associativity_addition_1) R->L }
% 268.73/35.13 fresh22(true, true, additive_inverse(additive_inverse(c)), additive_identity, c, additive_inverse(additive_identity), c)
% 268.73/35.13 = { by lemma 29 R->L }
% 268.73/35.13 fresh22(sum(additive_inverse(additive_identity), additive_identity, additive_identity), true, additive_inverse(additive_inverse(c)), additive_identity, c, additive_inverse(additive_identity), c)
% 268.73/35.13 = { by axiom 22 (associativity_addition_1) R->L }
% 268.73/35.13 fresh43(sum(c, additive_identity, c), true, additive_inverse(additive_inverse(c)), additive_identity, c, additive_inverse(additive_identity), c, additive_identity)
% 268.73/35.13 = { by axiom 19 (commutativity_addition) R->L }
% 268.73/35.13 fresh43(fresh18(sum(additive_identity, c, c), true, c, additive_identity, c), true, additive_inverse(additive_inverse(c)), additive_identity, c, additive_inverse(additive_identity), c, additive_identity)
% 268.73/35.13 = { by lemma 27 }
% 268.73/35.13 fresh43(fresh18(true, true, c, additive_identity, c), true, additive_inverse(additive_inverse(c)), additive_identity, c, additive_inverse(additive_identity), c, additive_identity)
% 268.73/35.13 = { by axiom 16 (commutativity_addition) }
% 268.73/35.13 fresh43(true, true, additive_inverse(additive_inverse(c)), additive_identity, c, additive_inverse(additive_identity), c, additive_identity)
% 268.73/35.13 = { by axiom 20 (associativity_addition_1) }
% 268.73/35.13 fresh44(sum(additive_inverse(additive_inverse(c)), additive_inverse(additive_identity), c), true, additive_inverse(additive_inverse(c)), additive_identity, c)
% 268.73/35.13 = { by axiom 17 (associativity_addition_1) R->L }
% 268.73/35.13 fresh44(fresh22(true, true, additive_inverse(additive_inverse(c)), additive_inverse(additive_identity), c, additive_inverse(c), additive_identity), true, additive_inverse(additive_inverse(c)), additive_identity, c)
% 268.73/35.13 = { by lemma 32 R->L }
% 268.73/35.13 fresh44(fresh22(sum(additive_inverse(c), c, additive_inverse(additive_identity)), true, additive_inverse(additive_inverse(c)), additive_inverse(additive_identity), c, additive_inverse(c), additive_identity), true, additive_inverse(additive_inverse(c)), additive_identity, c)
% 268.73/35.13 = { by axiom 22 (associativity_addition_1) R->L }
% 268.73/35.13 fresh44(fresh43(sum(additive_identity, c, c), true, additive_inverse(additive_inverse(c)), additive_inverse(additive_identity), c, additive_inverse(c), additive_identity, c), true, additive_inverse(additive_inverse(c)), additive_identity, c)
% 268.73/35.13 = { by lemma 27 }
% 268.73/35.13 fresh44(fresh43(true, true, additive_inverse(additive_inverse(c)), additive_inverse(additive_identity), c, additive_inverse(c), additive_identity, c), true, additive_inverse(additive_inverse(c)), additive_identity, c)
% 268.73/35.13 = { by axiom 20 (associativity_addition_1) }
% 268.73/35.13 fresh44(fresh44(sum(additive_inverse(additive_inverse(c)), additive_inverse(c), additive_identity), true, additive_inverse(additive_inverse(c)), additive_inverse(additive_identity), c), true, additive_inverse(additive_inverse(c)), additive_identity, c)
% 268.73/35.13 = { by axiom 11 (existence_of_inverse_addition) R->L }
% 268.73/35.13 fresh44(fresh44(fresh12(defined(additive_inverse(c)), true, additive_inverse(c)), true, additive_inverse(additive_inverse(c)), additive_inverse(additive_identity), c), true, additive_inverse(additive_inverse(c)), additive_identity, c)
% 268.73/35.13 = { by lemma 24 }
% 268.73/35.13 fresh44(fresh44(fresh12(true, true, additive_inverse(c)), true, additive_inverse(additive_inverse(c)), additive_inverse(additive_identity), c), true, additive_inverse(additive_inverse(c)), additive_identity, c)
% 268.73/35.13 = { by axiom 8 (existence_of_inverse_addition) }
% 268.73/35.13 fresh44(fresh44(true, true, additive_inverse(additive_inverse(c)), additive_inverse(additive_identity), c), true, additive_inverse(additive_inverse(c)), additive_identity, c)
% 268.73/35.13 = { by axiom 14 (associativity_addition_1) }
% 268.73/35.13 fresh44(true, true, additive_inverse(additive_inverse(c)), additive_identity, c)
% 268.73/35.13 = { by axiom 14 (associativity_addition_1) }
% 268.73/35.13 true
% 268.73/35.13
% 268.73/35.13 Goal 1 (not_sum_7): sum(additive_identity, additive_inverse(c), d) = true.
% 268.73/35.13 Proof:
% 268.73/35.13 sum(additive_identity, additive_inverse(c), d)
% 268.73/35.13 = { by axiom 19 (commutativity_addition) R->L }
% 268.73/35.13 fresh18(sum(additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.13 = { by axiom 18 (associativity_addition_2) R->L }
% 268.73/35.13 fresh18(fresh21(true, true, additive_inverse(c), additive_identity, d, additive_inverse(additive_identity), d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.13 = { by axiom 16 (commutativity_addition) R->L }
% 268.73/35.13 fresh18(fresh21(fresh18(true, true, additive_inverse(additive_identity), d, d), true, additive_inverse(c), additive_identity, d, additive_inverse(additive_identity), d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.13 = { by axiom 14 (associativity_addition_1) R->L }
% 268.73/35.13 fresh18(fresh21(fresh18(fresh44(true, true, d, additive_inverse(additive_identity), d), true, additive_inverse(additive_identity), d, d), true, additive_inverse(c), additive_identity, d, additive_inverse(additive_identity), d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.13 = { by lemma 28 R->L }
% 268.73/35.13 fresh18(fresh21(fresh18(fresh44(sum(d, additive_identity, d), true, d, additive_inverse(additive_identity), d), true, additive_inverse(additive_identity), d, d), true, additive_inverse(c), additive_identity, d, additive_inverse(additive_identity), d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.13 = { by axiom 20 (associativity_addition_1) R->L }
% 268.73/35.13 fresh18(fresh21(fresh18(fresh43(true, true, d, additive_inverse(additive_identity), d, additive_identity, d, additive_identity), true, additive_inverse(additive_identity), d, d), true, additive_inverse(c), additive_identity, d, additive_inverse(additive_identity), d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.13 = { by lemma 28 R->L }
% 268.73/35.13 fresh18(fresh21(fresh18(fresh43(sum(d, additive_identity, d), true, d, additive_inverse(additive_identity), d, additive_identity, d, additive_identity), true, additive_inverse(additive_identity), d, d), true, additive_inverse(c), additive_identity, d, additive_inverse(additive_identity), d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.13 = { by axiom 22 (associativity_addition_1) }
% 268.73/35.13 fresh18(fresh21(fresh18(fresh22(sum(additive_identity, additive_identity, additive_inverse(additive_identity)), true, d, additive_inverse(additive_identity), d, additive_identity, d), true, additive_inverse(additive_identity), d, d), true, additive_inverse(c), additive_identity, d, additive_inverse(additive_identity), d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.13 = { by lemma 30 }
% 268.73/35.13 fresh18(fresh21(fresh18(fresh22(true, true, d, additive_inverse(additive_identity), d, additive_identity, d), true, additive_inverse(additive_identity), d, d), true, additive_inverse(c), additive_identity, d, additive_inverse(additive_identity), d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.13 = { by axiom 17 (associativity_addition_1) }
% 268.73/35.13 fresh18(fresh21(fresh18(sum(d, additive_inverse(additive_identity), d), true, additive_inverse(additive_identity), d, d), true, additive_inverse(c), additive_identity, d, additive_inverse(additive_identity), d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.13 = { by axiom 19 (commutativity_addition) }
% 268.73/35.13 fresh18(fresh21(sum(additive_inverse(additive_identity), d, d), true, additive_inverse(c), additive_identity, d, additive_inverse(additive_identity), d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.13 = { by axiom 23 (associativity_addition_2) R->L }
% 268.73/35.13 fresh18(fresh41(sum(d, additive_identity, d), true, additive_inverse(c), additive_identity, d, additive_inverse(additive_identity), d, d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.13 = { by lemma 28 }
% 268.73/35.13 fresh18(fresh41(true, true, additive_inverse(c), additive_identity, d, additive_inverse(additive_identity), d, d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.13 = { by axiom 21 (associativity_addition_2) }
% 268.73/35.13 fresh18(fresh42(sum(additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.13 = { by axiom 19 (commutativity_addition) R->L }
% 268.73/35.13 fresh18(fresh42(fresh18(sum(d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.13 = { by axiom 17 (associativity_addition_1) R->L }
% 268.73/35.13 fresh18(fresh42(fresh18(fresh22(true, true, d, additive_inverse(additive_identity), additive_inverse(c), c, additive_identity), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.13 = { by axiom 16 (commutativity_addition) R->L }
% 268.73/35.13 fresh18(fresh42(fresh18(fresh22(fresh18(true, true, c, additive_inverse(c), additive_inverse(additive_identity)), true, d, additive_inverse(additive_identity), additive_inverse(c), c, additive_identity), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.13 = { by lemma 32 R->L }
% 268.73/35.13 fresh18(fresh42(fresh18(fresh22(fresh18(sum(additive_inverse(c), c, additive_inverse(additive_identity)), true, c, additive_inverse(c), additive_inverse(additive_identity)), true, d, additive_inverse(additive_identity), additive_inverse(c), c, additive_identity), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.13 = { by axiom 19 (commutativity_addition) }
% 268.73/35.13 fresh18(fresh42(fresh18(fresh22(sum(c, additive_inverse(c), additive_inverse(additive_identity)), true, d, additive_inverse(additive_identity), additive_inverse(c), c, additive_identity), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.13 = { by axiom 22 (associativity_addition_1) R->L }
% 268.73/35.13 fresh18(fresh42(fresh18(fresh43(sum(additive_identity, additive_inverse(c), additive_inverse(c)), true, d, additive_inverse(additive_identity), additive_inverse(c), c, additive_identity, additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.13 = { by lemma 31 }
% 268.73/35.13 fresh18(fresh42(fresh18(fresh43(true, true, d, additive_inverse(additive_identity), additive_inverse(c), c, additive_identity, additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.13 = { by axiom 20 (associativity_addition_1) }
% 268.73/35.13 fresh18(fresh42(fresh18(fresh44(sum(d, c, additive_identity), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.13 = { by axiom 18 (associativity_addition_2) R->L }
% 268.73/35.13 fresh18(fresh42(fresh18(fresh44(fresh21(true, true, d, c, additive_identity, additive_inverse(b), additive_inverse(a)), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.13 = { by axiom 8 (existence_of_inverse_addition) R->L }
% 268.73/35.14 fresh18(fresh42(fresh18(fresh44(fresh21(fresh12(true, true, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a)), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.14 = { by axiom 5 (b_is_defined) R->L }
% 268.73/35.14 fresh18(fresh42(fresh18(fresh44(fresh21(fresh12(defined(b), true, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a)), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.14 = { by axiom 11 (existence_of_inverse_addition) }
% 268.73/35.14 fresh18(fresh42(fresh18(fresh44(fresh21(sum(additive_inverse(b), b, additive_identity), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a)), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.14 = { by axiom 23 (associativity_addition_2) R->L }
% 268.73/35.14 fresh18(fresh42(fresh18(fresh44(fresh41(sum(additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.14 = { by axiom 17 (associativity_addition_1) R->L }
% 268.73/35.14 fresh18(fresh42(fresh18(fresh44(fresh41(fresh22(true, true, additive_inverse(a), c, b, additive_inverse(additive_inverse(c)), b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.14 = { by lemma 33 R->L }
% 268.73/35.14 fresh18(fresh42(fresh18(fresh44(fresh41(fresh22(sum(additive_inverse(additive_inverse(c)), additive_identity, c), true, additive_inverse(a), c, b, additive_inverse(additive_inverse(c)), b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.14 = { by axiom 22 (associativity_addition_1) R->L }
% 268.73/35.14 fresh18(fresh42(fresh18(fresh44(fresh41(fresh43(sum(b, additive_identity, b), true, additive_inverse(a), c, b, additive_inverse(additive_inverse(c)), b, additive_identity), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.14 = { by axiom 19 (commutativity_addition) R->L }
% 268.73/35.14 fresh18(fresh42(fresh18(fresh44(fresh41(fresh43(fresh18(sum(additive_identity, b, b), true, b, additive_identity, b), true, additive_inverse(a), c, b, additive_inverse(additive_inverse(c)), b, additive_identity), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.14 = { by lemma 26 }
% 268.73/35.14 fresh18(fresh42(fresh18(fresh44(fresh41(fresh43(fresh18(true, true, b, additive_identity, b), true, additive_inverse(a), c, b, additive_inverse(additive_inverse(c)), b, additive_identity), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 268.73/35.14 = { by axiom 16 (commutativity_addition) }
% 268.73/35.14 fresh18(fresh42(fresh18(fresh44(fresh41(fresh43(true, true, additive_inverse(a), c, b, additive_inverse(additive_inverse(c)), b, additive_identity), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.14 = { by axiom 20 (associativity_addition_1) }
% 269.40/35.14 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(sum(additive_inverse(a), additive_inverse(additive_inverse(c)), b), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.14 = { by axiom 17 (associativity_addition_1) R->L }
% 269.40/35.14 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh22(true, true, additive_inverse(a), additive_inverse(additive_inverse(c)), b, a, additive_identity), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.14 = { by axiom 15 (associativity_addition_2) R->L }
% 269.40/35.14 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh22(fresh42(true, true, a, b, additive_inverse(additive_inverse(c))), true, additive_inverse(a), additive_inverse(additive_inverse(c)), b, a, additive_identity), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.14 = { by axiom 7 (existence_of_identity_addition) R->L }
% 269.40/35.14 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh22(fresh42(fresh14(true, true, a), true, a, b, additive_inverse(additive_inverse(c))), true, additive_inverse(a), additive_inverse(additive_inverse(c)), b, a, additive_identity), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.14 = { by axiom 4 (a_is_defined) R->L }
% 269.40/35.14 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh22(fresh42(fresh14(defined(a), true, a), true, a, b, additive_inverse(additive_inverse(c))), true, additive_inverse(a), additive_inverse(additive_inverse(c)), b, a, additive_identity), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.14 = { by axiom 10 (existence_of_identity_addition) }
% 269.40/35.14 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh22(fresh42(sum(additive_identity, a, a), true, a, b, additive_inverse(additive_inverse(c))), true, additive_inverse(a), additive_inverse(additive_inverse(c)), b, a, additive_identity), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.14 = { by axiom 21 (associativity_addition_2) R->L }
% 269.40/35.14 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh22(fresh41(true, true, a, b, additive_inverse(additive_inverse(c)), additive_identity, a, c), true, additive_inverse(a), additive_inverse(additive_inverse(c)), b, a, additive_identity), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.14 = { by axiom 6 (sum_5) R->L }
% 269.40/35.14 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh22(fresh41(sum(a, b, c), true, a, b, additive_inverse(additive_inverse(c)), additive_identity, a, c), true, additive_inverse(a), additive_inverse(additive_inverse(c)), b, a, additive_identity), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.14 = { by axiom 23 (associativity_addition_2) }
% 269.40/35.14 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh22(fresh21(sum(additive_identity, c, additive_inverse(additive_inverse(c))), true, a, b, additive_inverse(additive_inverse(c)), additive_identity, a), true, additive_inverse(a), additive_inverse(additive_inverse(c)), b, a, additive_identity), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.14 = { by axiom 19 (commutativity_addition) R->L }
% 269.40/35.14 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh22(fresh21(fresh18(sum(c, additive_identity, additive_inverse(additive_inverse(c))), true, additive_identity, c, additive_inverse(additive_inverse(c))), true, a, b, additive_inverse(additive_inverse(c)), additive_identity, a), true, additive_inverse(a), additive_inverse(additive_inverse(c)), b, a, additive_identity), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.14 = { by axiom 18 (associativity_addition_2) R->L }
% 269.40/35.14 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh22(fresh21(fresh18(fresh21(true, true, c, additive_identity, additive_inverse(additive_inverse(c)), additive_inverse(additive_inverse(c)), additive_identity), true, additive_identity, c, additive_inverse(additive_inverse(c))), true, a, b, additive_inverse(additive_inverse(c)), additive_identity, a), true, additive_inverse(a), additive_inverse(additive_inverse(c)), b, a, additive_identity), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.14 = { by axiom 16 (commutativity_addition) R->L }
% 269.40/35.14 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh22(fresh21(fresh18(fresh21(fresh18(true, true, additive_inverse(additive_inverse(c)), additive_identity, additive_inverse(additive_inverse(c))), true, c, additive_identity, additive_inverse(additive_inverse(c)), additive_inverse(additive_inverse(c)), additive_identity), true, additive_identity, c, additive_inverse(additive_inverse(c))), true, a, b, additive_inverse(additive_inverse(c)), additive_identity, a), true, additive_inverse(a), additive_inverse(additive_inverse(c)), b, a, additive_identity), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.14 = { by axiom 7 (existence_of_identity_addition) R->L }
% 269.40/35.14 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh22(fresh21(fresh18(fresh21(fresh18(fresh14(true, true, additive_inverse(additive_inverse(c))), true, additive_inverse(additive_inverse(c)), additive_identity, additive_inverse(additive_inverse(c))), true, c, additive_identity, additive_inverse(additive_inverse(c)), additive_inverse(additive_inverse(c)), additive_identity), true, additive_identity, c, additive_inverse(additive_inverse(c))), true, a, b, additive_inverse(additive_inverse(c)), additive_identity, a), true, additive_inverse(a), additive_inverse(additive_inverse(c)), b, a, additive_identity), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.14 = { by axiom 9 (well_definedness_of_additive_inverse) R->L }
% 269.40/35.14 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh22(fresh21(fresh18(fresh21(fresh18(fresh14(fresh3(true, true, additive_inverse(c)), true, additive_inverse(additive_inverse(c))), true, additive_inverse(additive_inverse(c)), additive_identity, additive_inverse(additive_inverse(c))), true, c, additive_identity, additive_inverse(additive_inverse(c)), additive_inverse(additive_inverse(c)), additive_identity), true, additive_identity, c, additive_inverse(additive_inverse(c))), true, a, b, additive_inverse(additive_inverse(c)), additive_identity, a), true, additive_inverse(a), additive_inverse(additive_inverse(c)), b, a, additive_identity), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.14 = { by lemma 24 R->L }
% 269.40/35.15 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh22(fresh21(fresh18(fresh21(fresh18(fresh14(fresh3(defined(additive_inverse(c)), true, additive_inverse(c)), true, additive_inverse(additive_inverse(c))), true, additive_inverse(additive_inverse(c)), additive_identity, additive_inverse(additive_inverse(c))), true, c, additive_identity, additive_inverse(additive_inverse(c)), additive_inverse(additive_inverse(c)), additive_identity), true, additive_identity, c, additive_inverse(additive_inverse(c))), true, a, b, additive_inverse(additive_inverse(c)), additive_identity, a), true, additive_inverse(a), additive_inverse(additive_inverse(c)), b, a, additive_identity), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.15 = { by axiom 12 (well_definedness_of_additive_inverse) }
% 269.40/35.15 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh22(fresh21(fresh18(fresh21(fresh18(fresh14(defined(additive_inverse(additive_inverse(c))), true, additive_inverse(additive_inverse(c))), true, additive_inverse(additive_inverse(c)), additive_identity, additive_inverse(additive_inverse(c))), true, c, additive_identity, additive_inverse(additive_inverse(c)), additive_inverse(additive_inverse(c)), additive_identity), true, additive_identity, c, additive_inverse(additive_inverse(c))), true, a, b, additive_inverse(additive_inverse(c)), additive_identity, a), true, additive_inverse(a), additive_inverse(additive_inverse(c)), b, a, additive_identity), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.15 = { by axiom 10 (existence_of_identity_addition) }
% 269.40/35.15 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh22(fresh21(fresh18(fresh21(fresh18(sum(additive_identity, additive_inverse(additive_inverse(c)), additive_inverse(additive_inverse(c))), true, additive_inverse(additive_inverse(c)), additive_identity, additive_inverse(additive_inverse(c))), true, c, additive_identity, additive_inverse(additive_inverse(c)), additive_inverse(additive_inverse(c)), additive_identity), true, additive_identity, c, additive_inverse(additive_inverse(c))), true, a, b, additive_inverse(additive_inverse(c)), additive_identity, a), true, additive_inverse(a), additive_inverse(additive_inverse(c)), b, a, additive_identity), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.15 = { by axiom 19 (commutativity_addition) }
% 269.40/35.15 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh22(fresh21(fresh18(fresh21(sum(additive_inverse(additive_inverse(c)), additive_identity, additive_inverse(additive_inverse(c))), true, c, additive_identity, additive_inverse(additive_inverse(c)), additive_inverse(additive_inverse(c)), additive_identity), true, additive_identity, c, additive_inverse(additive_inverse(c))), true, a, b, additive_inverse(additive_inverse(c)), additive_identity, a), true, additive_inverse(a), additive_inverse(additive_inverse(c)), b, a, additive_identity), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.15 = { by axiom 23 (associativity_addition_2) R->L }
% 269.40/35.15 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh22(fresh21(fresh18(fresh41(sum(additive_identity, additive_identity, additive_identity), true, c, additive_identity, additive_inverse(additive_inverse(c)), additive_inverse(additive_inverse(c)), additive_identity, additive_identity), true, additive_identity, c, additive_inverse(additive_inverse(c))), true, a, b, additive_inverse(additive_inverse(c)), additive_identity, a), true, additive_inverse(a), additive_inverse(additive_inverse(c)), b, a, additive_identity), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.15 = { by lemma 25 }
% 269.40/35.15 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh22(fresh21(fresh18(fresh41(true, true, c, additive_identity, additive_inverse(additive_inverse(c)), additive_inverse(additive_inverse(c)), additive_identity, additive_identity), true, additive_identity, c, additive_inverse(additive_inverse(c))), true, a, b, additive_inverse(additive_inverse(c)), additive_identity, a), true, additive_inverse(a), additive_inverse(additive_inverse(c)), b, a, additive_identity), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.15 = { by axiom 21 (associativity_addition_2) }
% 269.40/35.15 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh22(fresh21(fresh18(fresh42(sum(additive_inverse(additive_inverse(c)), additive_identity, c), true, c, additive_identity, additive_inverse(additive_inverse(c))), true, additive_identity, c, additive_inverse(additive_inverse(c))), true, a, b, additive_inverse(additive_inverse(c)), additive_identity, a), true, additive_inverse(a), additive_inverse(additive_inverse(c)), b, a, additive_identity), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.15 = { by lemma 33 }
% 269.40/35.15 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh22(fresh21(fresh18(fresh42(true, true, c, additive_identity, additive_inverse(additive_inverse(c))), true, additive_identity, c, additive_inverse(additive_inverse(c))), true, a, b, additive_inverse(additive_inverse(c)), additive_identity, a), true, additive_inverse(a), additive_inverse(additive_inverse(c)), b, a, additive_identity), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.15 = { by axiom 15 (associativity_addition_2) }
% 269.40/35.15 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh22(fresh21(fresh18(true, true, additive_identity, c, additive_inverse(additive_inverse(c))), true, a, b, additive_inverse(additive_inverse(c)), additive_identity, a), true, additive_inverse(a), additive_inverse(additive_inverse(c)), b, a, additive_identity), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.15 = { by axiom 16 (commutativity_addition) }
% 269.40/35.15 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh22(fresh21(true, true, a, b, additive_inverse(additive_inverse(c)), additive_identity, a), true, additive_inverse(a), additive_inverse(additive_inverse(c)), b, a, additive_identity), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.15 = { by axiom 18 (associativity_addition_2) }
% 269.40/35.15 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh22(sum(a, b, additive_inverse(additive_inverse(c))), true, additive_inverse(a), additive_inverse(additive_inverse(c)), b, a, additive_identity), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.15 = { by axiom 22 (associativity_addition_1) R->L }
% 269.40/35.15 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh43(sum(additive_identity, b, b), true, additive_inverse(a), additive_inverse(additive_inverse(c)), b, a, additive_identity, b), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.15 = { by lemma 26 }
% 269.40/35.15 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh43(true, true, additive_inverse(a), additive_inverse(additive_inverse(c)), b, a, additive_identity, b), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.15 = { by axiom 20 (associativity_addition_1) }
% 269.40/35.15 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh44(sum(additive_inverse(a), a, additive_identity), true, additive_inverse(a), additive_inverse(additive_inverse(c)), b), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.15 = { by axiom 11 (existence_of_inverse_addition) R->L }
% 269.40/35.15 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh44(fresh12(defined(a), true, a), true, additive_inverse(a), additive_inverse(additive_inverse(c)), b), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.15 = { by axiom 4 (a_is_defined) }
% 269.40/35.15 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh44(fresh12(true, true, a), true, additive_inverse(a), additive_inverse(additive_inverse(c)), b), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.15 = { by axiom 8 (existence_of_inverse_addition) }
% 269.40/35.15 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(fresh44(true, true, additive_inverse(a), additive_inverse(additive_inverse(c)), b), true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.15 = { by axiom 14 (associativity_addition_1) }
% 269.40/35.15 fresh18(fresh42(fresh18(fresh44(fresh41(fresh44(true, true, additive_inverse(a), c, b), true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.15 = { by axiom 14 (associativity_addition_1) }
% 269.40/35.15 fresh18(fresh42(fresh18(fresh44(fresh41(true, true, d, c, additive_identity, additive_inverse(b), additive_inverse(a), b), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.15 = { by axiom 21 (associativity_addition_2) }
% 269.40/35.15 fresh18(fresh42(fresh18(fresh44(fresh42(sum(additive_inverse(b), additive_inverse(a), d), true, d, c, additive_identity), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.15 = { by axiom 19 (commutativity_addition) R->L }
% 269.40/35.15 fresh18(fresh42(fresh18(fresh44(fresh42(fresh18(sum(additive_inverse(a), additive_inverse(b), d), true, additive_inverse(b), additive_inverse(a), d), true, d, c, additive_identity), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.15 = { by axiom 13 (sum_6) }
% 269.40/35.15 fresh18(fresh42(fresh18(fresh44(fresh42(fresh18(true, true, additive_inverse(b), additive_inverse(a), d), true, d, c, additive_identity), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.15 = { by axiom 16 (commutativity_addition) }
% 269.40/35.15 fresh18(fresh42(fresh18(fresh44(fresh42(true, true, d, c, additive_identity), true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.15 = { by axiom 15 (associativity_addition_2) }
% 269.40/35.15 fresh18(fresh42(fresh18(fresh44(true, true, d, additive_inverse(additive_identity), additive_inverse(c)), true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.15 = { by axiom 14 (associativity_addition_1) }
% 269.40/35.15 fresh18(fresh42(fresh18(true, true, additive_inverse(additive_identity), d, additive_inverse(c)), true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.15 = { by axiom 16 (commutativity_addition) }
% 269.40/35.15 fresh18(fresh42(true, true, additive_inverse(c), additive_identity, d), true, additive_identity, additive_inverse(c), d)
% 269.40/35.15 = { by axiom 15 (associativity_addition_2) }
% 269.40/35.15 fresh18(true, true, additive_identity, additive_inverse(c), d)
% 269.40/35.15 = { by axiom 16 (commutativity_addition) }
% 269.40/35.15 true
% 269.40/35.15 % SZS output end Proof
% 269.40/35.15
% 269.40/35.15 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------