TSTP Solution File: NUM003-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM003-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n016.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 11:54:57 EDT 2023
% Result : Unsatisfiable 12.35s 1.99s
% Output : Proof 12.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM003-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 17:58:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 12.35/1.99 Command-line arguments: --no-flatten-goal
% 12.35/1.99
% 12.35/1.99 % SZS status Unsatisfiable
% 12.35/1.99
% 12.35/2.01 % SZS output start Proof
% 12.35/2.01 Take the following subset of the input axioms:
% 12.35/2.01 fof(add_substitution1, axiom, ![B, C, D, A2]: (~equalish(A2, B) | (~equalish(C, add(A2, D)) | equalish(C, add(B, D))))).
% 12.35/2.01 fof(add_substitution2, axiom, ![B2, C2, A2_2, D2]: (~equalish(A2_2, B2) | (~equalish(C2, add(D2, A2_2)) | equalish(C2, add(D2, B2))))).
% 12.35/2.01 fof(addition_inverts_subtraction1, axiom, ![A, B2]: equalish(subtract(add(A, B2), B2), A)).
% 12.35/2.01 fof(addition_inverts_subtraction2, axiom, ![B2, A3]: equalish(A3, subtract(add(A3, B2), B2))).
% 12.35/2.01 fof(commutativity1, axiom, ![B2, C2, A3]: equalish(add(subtract(A3, B2), C2), subtract(add(A3, C2), B2))).
% 12.35/2.01 fof(commutativity2, axiom, ![B2, C2, A3]: equalish(subtract(add(A3, B2), C2), add(subtract(A3, C2), B2))).
% 12.35/2.01 fof(commutativity_of_addition, axiom, ![B2, A3]: equalish(add(A3, B2), add(B2, A3))).
% 12.35/2.01 fof(prove_equation, negated_conjecture, ~equalish(add(a, subtract(b, c)), add(subtract(a, c), b))).
% 12.35/2.01 fof(reflexivity, axiom, ![A3]: equalish(A3, A3)).
% 12.35/2.01 fof(subtract_substitution1, axiom, ![B2, C2, A2_2, D2]: (~equalish(A2_2, B2) | (~equalish(C2, subtract(A2_2, D2)) | equalish(C2, subtract(B2, D2))))).
% 12.35/2.01 fof(subtract_substitution2, axiom, ![B2, C2, A2_2, D2]: (~equalish(A2_2, B2) | (~equalish(C2, subtract(D2, A2_2)) | equalish(C2, subtract(D2, B2))))).
% 12.35/2.01 fof(transitivity, axiom, ![B2, C2, A2_2]: (~equalish(A2_2, B2) | (~equalish(B2, C2) | equalish(A2_2, C2)))).
% 12.35/2.01
% 12.35/2.01 Now clausify the problem and encode Horn clauses using encoding 3 of
% 12.35/2.01 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 12.35/2.01 We repeatedly replace C & s=t => u=v by the two clauses:
% 12.35/2.01 fresh(y, y, x1...xn) = u
% 12.35/2.01 C => fresh(s, t, x1...xn) = v
% 12.35/2.01 where fresh is a fresh function symbol and x1..xn are the free
% 12.35/2.01 variables of u and v.
% 12.35/2.01 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 12.35/2.01 input problem has no model of domain size 1).
% 12.35/2.01
% 12.35/2.01 The encoding turns the above axioms into the following unit equations and goals:
% 12.35/2.01
% 12.35/2.01 Axiom 1 (reflexivity): equalish(X, X) = true.
% 12.35/2.01 Axiom 2 (transitivity): fresh(X, X, Y, Z) = true.
% 12.35/2.01 Axiom 3 (add_substitution1): fresh10(X, X, Y, Z, W) = true.
% 12.35/2.01 Axiom 4 (add_substitution2): fresh7(X, X, Y, Z, W) = true.
% 12.35/2.01 Axiom 5 (subtract_substitution1): fresh5(X, X, Y, Z, W) = true.
% 12.35/2.01 Axiom 6 (subtract_substitution2): fresh3(X, X, Y, Z, W) = true.
% 12.35/2.01 Axiom 7 (transitivity): fresh2(X, X, Y, Z, W) = equalish(Y, W).
% 12.35/2.01 Axiom 8 (add_substitution1): fresh9(X, X, Y, Z, W, V) = equalish(W, add(Z, V)).
% 12.35/2.01 Axiom 9 (add_substitution2): fresh8(X, X, Y, Z, W, V) = equalish(W, add(V, Z)).
% 12.35/2.01 Axiom 10 (subtract_substitution1): fresh6(X, X, Y, Z, W, V) = equalish(W, subtract(Z, V)).
% 12.35/2.01 Axiom 11 (subtract_substitution2): fresh4(X, X, Y, Z, W, V) = equalish(W, subtract(V, Z)).
% 12.35/2.01 Axiom 12 (addition_inverts_subtraction2): equalish(X, subtract(add(X, Y), Y)) = true.
% 12.35/2.01 Axiom 13 (commutativity_of_addition): equalish(add(X, Y), add(Y, X)) = true.
% 12.35/2.01 Axiom 14 (addition_inverts_subtraction1): equalish(subtract(add(X, Y), Y), X) = true.
% 12.35/2.01 Axiom 15 (transitivity): fresh2(equalish(X, Y), true, Z, X, Y) = fresh(equalish(Z, X), true, Z, Y).
% 12.35/2.01 Axiom 16 (add_substitution1): fresh9(equalish(X, add(Y, Z)), true, Y, W, X, Z) = fresh10(equalish(Y, W), true, W, X, Z).
% 12.35/2.01 Axiom 17 (add_substitution2): fresh8(equalish(X, add(Y, Z)), true, Z, W, X, Y) = fresh7(equalish(Z, W), true, W, X, Y).
% 12.35/2.01 Axiom 18 (subtract_substitution1): fresh6(equalish(X, subtract(Y, Z)), true, Y, W, X, Z) = fresh5(equalish(Y, W), true, W, X, Z).
% 12.35/2.01 Axiom 19 (subtract_substitution2): fresh4(equalish(X, subtract(Y, Z)), true, Z, W, X, Y) = fresh3(equalish(Z, W), true, W, X, Y).
% 12.35/2.01 Axiom 20 (commutativity2): equalish(subtract(add(X, Y), Z), add(subtract(X, Z), Y)) = true.
% 12.35/2.01 Axiom 21 (commutativity1): equalish(add(subtract(X, Y), Z), subtract(add(X, Z), Y)) = true.
% 12.35/2.01
% 12.35/2.01 Lemma 22: equalish(X, subtract(add(Y, X), Y)) = true.
% 12.35/2.01 Proof:
% 12.35/2.01 equalish(X, subtract(add(Y, X), Y))
% 12.35/2.01 = { by axiom 10 (subtract_substitution1) R->L }
% 12.35/2.01 fresh6(true, true, add(X, Y), add(Y, X), X, Y)
% 12.35/2.01 = { by axiom 12 (addition_inverts_subtraction2) R->L }
% 12.35/2.02 fresh6(equalish(X, subtract(add(X, Y), Y)), true, add(X, Y), add(Y, X), X, Y)
% 12.35/2.02 = { by axiom 18 (subtract_substitution1) }
% 12.35/2.02 fresh5(equalish(add(X, Y), add(Y, X)), true, add(Y, X), X, Y)
% 12.35/2.02 = { by axiom 13 (commutativity_of_addition) }
% 12.35/2.02 fresh5(true, true, add(Y, X), X, Y)
% 12.35/2.02 = { by axiom 5 (subtract_substitution1) }
% 12.35/2.02 true
% 12.35/2.02
% 12.35/2.02 Lemma 23: fresh(equalish(X, subtract(add(Y, Z), Z)), true, X, Y) = equalish(X, Y).
% 12.35/2.02 Proof:
% 12.35/2.02 fresh(equalish(X, subtract(add(Y, Z), Z)), true, X, Y)
% 12.35/2.02 = { by axiom 15 (transitivity) R->L }
% 12.35/2.02 fresh2(equalish(subtract(add(Y, Z), Z), Y), true, X, subtract(add(Y, Z), Z), Y)
% 12.35/2.02 = { by axiom 14 (addition_inverts_subtraction1) }
% 12.35/2.02 fresh2(true, true, X, subtract(add(Y, Z), Z), Y)
% 12.35/2.02 = { by axiom 7 (transitivity) }
% 12.35/2.02 equalish(X, Y)
% 12.35/2.02
% 12.35/2.02 Lemma 24: equalish(add(subtract(X, Y), Y), X) = true.
% 12.35/2.02 Proof:
% 12.35/2.02 equalish(add(subtract(X, Y), Y), X)
% 12.35/2.02 = { by lemma 23 R->L }
% 12.35/2.02 fresh(equalish(add(subtract(X, Y), Y), subtract(add(X, Y), Y)), true, add(subtract(X, Y), Y), X)
% 12.35/2.02 = { by axiom 21 (commutativity1) }
% 12.35/2.02 fresh(true, true, add(subtract(X, Y), Y), X)
% 12.35/2.02 = { by axiom 2 (transitivity) }
% 12.35/2.02 true
% 12.35/2.02
% 12.35/2.02 Goal 1 (prove_equation): equalish(add(a, subtract(b, c)), add(subtract(a, c), b)) = true.
% 12.35/2.02 Proof:
% 12.35/2.02 equalish(add(a, subtract(b, c)), add(subtract(a, c), b))
% 12.35/2.02 = { by axiom 9 (add_substitution2) R->L }
% 12.35/2.02 fresh8(true, true, subtract(add(a, subtract(b, c)), subtract(a, c)), b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.02 = { by axiom 2 (transitivity) R->L }
% 12.35/2.02 fresh8(fresh(true, true, add(a, subtract(b, c)), add(subtract(a, c), subtract(add(a, subtract(b, c)), subtract(a, c)))), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.02 = { by axiom 2 (transitivity) R->L }
% 12.35/2.02 fresh8(fresh(fresh(true, true, add(a, subtract(b, c)), add(subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(a, c))), true, add(a, subtract(b, c)), add(subtract(a, c), subtract(add(a, subtract(b, c)), subtract(a, c)))), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.02 = { by axiom 6 (subtract_substitution2) R->L }
% 12.35/2.02 fresh8(fresh(fresh(fresh3(true, true, add(a, subtract(b, c)), add(a, subtract(b, c)), add(add(subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(a, c)), add(a, subtract(b, c)))), true, add(a, subtract(b, c)), add(subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(a, c))), true, add(a, subtract(b, c)), add(subtract(a, c), subtract(add(a, subtract(b, c)), subtract(a, c)))), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.02 = { by lemma 24 R->L }
% 12.35/2.02 fresh8(fresh(fresh(fresh3(equalish(add(subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(a, c)), add(a, subtract(b, c))), true, add(a, subtract(b, c)), add(a, subtract(b, c)), add(add(subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(a, c)), add(a, subtract(b, c)))), true, add(a, subtract(b, c)), add(subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(a, c))), true, add(a, subtract(b, c)), add(subtract(a, c), subtract(add(a, subtract(b, c)), subtract(a, c)))), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.02 = { by axiom 19 (subtract_substitution2) R->L }
% 12.35/2.02 fresh8(fresh(fresh(fresh4(equalish(add(a, subtract(b, c)), subtract(add(add(subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(a, c)), add(a, subtract(b, c))), add(subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(a, c)))), true, add(subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(a, c)), add(a, subtract(b, c)), add(a, subtract(b, c)), add(add(subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(a, c)), add(a, subtract(b, c)))), true, add(a, subtract(b, c)), add(subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(a, c))), true, add(a, subtract(b, c)), add(subtract(a, c), subtract(add(a, subtract(b, c)), subtract(a, c)))), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.02 = { by lemma 22 }
% 12.35/2.02 fresh8(fresh(fresh(fresh4(true, true, add(subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(a, c)), add(a, subtract(b, c)), add(a, subtract(b, c)), add(add(subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(a, c)), add(a, subtract(b, c)))), true, add(a, subtract(b, c)), add(subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(a, c))), true, add(a, subtract(b, c)), add(subtract(a, c), subtract(add(a, subtract(b, c)), subtract(a, c)))), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.02 = { by axiom 11 (subtract_substitution2) }
% 12.35/2.02 fresh8(fresh(fresh(equalish(add(a, subtract(b, c)), subtract(add(add(subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(a, c)), add(a, subtract(b, c))), add(a, subtract(b, c)))), true, add(a, subtract(b, c)), add(subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(a, c))), true, add(a, subtract(b, c)), add(subtract(a, c), subtract(add(a, subtract(b, c)), subtract(a, c)))), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.02 = { by lemma 23 }
% 12.35/2.02 fresh8(fresh(equalish(add(a, subtract(b, c)), add(subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(a, c))), true, add(a, subtract(b, c)), add(subtract(a, c), subtract(add(a, subtract(b, c)), subtract(a, c)))), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.02 = { by axiom 15 (transitivity) R->L }
% 12.35/2.02 fresh8(fresh2(equalish(add(subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(a, c)), add(subtract(a, c), subtract(add(a, subtract(b, c)), subtract(a, c)))), true, add(a, subtract(b, c)), add(subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(a, c)), add(subtract(a, c), subtract(add(a, subtract(b, c)), subtract(a, c)))), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.02 = { by axiom 13 (commutativity_of_addition) }
% 12.35/2.02 fresh8(fresh2(true, true, add(a, subtract(b, c)), add(subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(a, c)), add(subtract(a, c), subtract(add(a, subtract(b, c)), subtract(a, c)))), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.02 = { by axiom 7 (transitivity) }
% 12.35/2.02 fresh8(equalish(add(a, subtract(b, c)), add(subtract(a, c), subtract(add(a, subtract(b, c)), subtract(a, c)))), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.02 = { by axiom 17 (add_substitution2) }
% 12.35/2.02 fresh7(equalish(subtract(add(a, subtract(b, c)), subtract(a, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.02 = { by axiom 7 (transitivity) R->L }
% 12.35/2.02 fresh7(fresh2(true, true, subtract(add(a, subtract(b, c)), subtract(a, c)), add(c, subtract(b, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.02 = { by axiom 2 (transitivity) R->L }
% 12.35/2.02 fresh7(fresh2(fresh(true, true, add(c, subtract(b, c)), b), true, subtract(add(a, subtract(b, c)), subtract(a, c)), add(c, subtract(b, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.02 = { by axiom 13 (commutativity_of_addition) R->L }
% 12.35/2.02 fresh7(fresh2(fresh(equalish(add(c, subtract(b, c)), add(subtract(b, c), c)), true, add(c, subtract(b, c)), b), true, subtract(add(a, subtract(b, c)), subtract(a, c)), add(c, subtract(b, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.02 = { by axiom 15 (transitivity) R->L }
% 12.35/2.02 fresh7(fresh2(fresh2(equalish(add(subtract(b, c), c), b), true, add(c, subtract(b, c)), add(subtract(b, c), c), b), true, subtract(add(a, subtract(b, c)), subtract(a, c)), add(c, subtract(b, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.02 = { by lemma 24 }
% 12.35/2.02 fresh7(fresh2(fresh2(true, true, add(c, subtract(b, c)), add(subtract(b, c), c), b), true, subtract(add(a, subtract(b, c)), subtract(a, c)), add(c, subtract(b, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.02 = { by axiom 7 (transitivity) }
% 12.35/2.02 fresh7(fresh2(equalish(add(c, subtract(b, c)), b), true, subtract(add(a, subtract(b, c)), subtract(a, c)), add(c, subtract(b, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.02 = { by axiom 15 (transitivity) }
% 12.35/2.02 fresh7(fresh(equalish(subtract(add(a, subtract(b, c)), subtract(a, c)), add(c, subtract(b, c))), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.02 = { by axiom 8 (add_substitution1) R->L }
% 12.35/2.02 fresh7(fresh(fresh9(true, true, subtract(a, subtract(a, c)), c, subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(b, c)), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.02 = { by axiom 20 (commutativity2) R->L }
% 12.35/2.02 fresh7(fresh(fresh9(equalish(subtract(add(a, subtract(b, c)), subtract(a, c)), add(subtract(a, subtract(a, c)), subtract(b, c))), true, subtract(a, subtract(a, c)), c, subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(b, c)), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.02 = { by axiom 16 (add_substitution1) }
% 12.35/2.02 fresh7(fresh(fresh10(equalish(subtract(a, subtract(a, c)), c), true, c, subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(b, c)), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.02 = { by axiom 7 (transitivity) R->L }
% 12.35/2.02 fresh7(fresh(fresh10(fresh2(true, true, subtract(a, subtract(a, c)), subtract(add(subtract(a, subtract(a, c)), c), subtract(a, subtract(a, c))), c), true, c, subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(b, c)), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.02 = { by axiom 2 (transitivity) R->L }
% 12.35/2.02 fresh7(fresh(fresh10(fresh2(fresh(true, true, subtract(add(subtract(a, subtract(a, c)), c), subtract(a, subtract(a, c))), c), true, subtract(a, subtract(a, c)), subtract(add(subtract(a, subtract(a, c)), c), subtract(a, subtract(a, c))), c), true, c, subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(b, c)), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.02 = { by axiom 5 (subtract_substitution1) R->L }
% 12.35/2.02 fresh7(fresh(fresh10(fresh2(fresh(fresh5(true, true, add(c, subtract(a, subtract(a, c))), subtract(add(subtract(a, subtract(a, c)), c), subtract(a, subtract(a, c))), subtract(a, subtract(a, c))), true, subtract(add(subtract(a, subtract(a, c)), c), subtract(a, subtract(a, c))), c), true, subtract(a, subtract(a, c)), subtract(add(subtract(a, subtract(a, c)), c), subtract(a, subtract(a, c))), c), true, c, subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(b, c)), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.02 = { by axiom 13 (commutativity_of_addition) R->L }
% 12.35/2.02 fresh7(fresh(fresh10(fresh2(fresh(fresh5(equalish(add(subtract(a, subtract(a, c)), c), add(c, subtract(a, subtract(a, c)))), true, add(c, subtract(a, subtract(a, c))), subtract(add(subtract(a, subtract(a, c)), c), subtract(a, subtract(a, c))), subtract(a, subtract(a, c))), true, subtract(add(subtract(a, subtract(a, c)), c), subtract(a, subtract(a, c))), c), true, subtract(a, subtract(a, c)), subtract(add(subtract(a, subtract(a, c)), c), subtract(a, subtract(a, c))), c), true, c, subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(b, c)), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.02 = { by axiom 18 (subtract_substitution1) R->L }
% 12.35/2.02 fresh7(fresh(fresh10(fresh2(fresh(fresh6(equalish(subtract(add(subtract(a, subtract(a, c)), c), subtract(a, subtract(a, c))), subtract(add(subtract(a, subtract(a, c)), c), subtract(a, subtract(a, c)))), true, add(subtract(a, subtract(a, c)), c), add(c, subtract(a, subtract(a, c))), subtract(add(subtract(a, subtract(a, c)), c), subtract(a, subtract(a, c))), subtract(a, subtract(a, c))), true, subtract(add(subtract(a, subtract(a, c)), c), subtract(a, subtract(a, c))), c), true, subtract(a, subtract(a, c)), subtract(add(subtract(a, subtract(a, c)), c), subtract(a, subtract(a, c))), c), true, c, subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(b, c)), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.02 = { by axiom 1 (reflexivity) }
% 12.35/2.03 fresh7(fresh(fresh10(fresh2(fresh(fresh6(true, true, add(subtract(a, subtract(a, c)), c), add(c, subtract(a, subtract(a, c))), subtract(add(subtract(a, subtract(a, c)), c), subtract(a, subtract(a, c))), subtract(a, subtract(a, c))), true, subtract(add(subtract(a, subtract(a, c)), c), subtract(a, subtract(a, c))), c), true, subtract(a, subtract(a, c)), subtract(add(subtract(a, subtract(a, c)), c), subtract(a, subtract(a, c))), c), true, c, subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(b, c)), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.03 = { by axiom 10 (subtract_substitution1) }
% 12.35/2.03 fresh7(fresh(fresh10(fresh2(fresh(equalish(subtract(add(subtract(a, subtract(a, c)), c), subtract(a, subtract(a, c))), subtract(add(c, subtract(a, subtract(a, c))), subtract(a, subtract(a, c)))), true, subtract(add(subtract(a, subtract(a, c)), c), subtract(a, subtract(a, c))), c), true, subtract(a, subtract(a, c)), subtract(add(subtract(a, subtract(a, c)), c), subtract(a, subtract(a, c))), c), true, c, subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(b, c)), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.03 = { by lemma 23 }
% 12.35/2.03 fresh7(fresh(fresh10(fresh2(equalish(subtract(add(subtract(a, subtract(a, c)), c), subtract(a, subtract(a, c))), c), true, subtract(a, subtract(a, c)), subtract(add(subtract(a, subtract(a, c)), c), subtract(a, subtract(a, c))), c), true, c, subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(b, c)), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.03 = { by axiom 15 (transitivity) }
% 12.35/2.03 fresh7(fresh(fresh10(fresh(equalish(subtract(a, subtract(a, c)), subtract(add(subtract(a, subtract(a, c)), c), subtract(a, subtract(a, c)))), true, subtract(a, subtract(a, c)), c), true, c, subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(b, c)), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.03 = { by axiom 11 (subtract_substitution2) R->L }
% 12.35/2.03 fresh7(fresh(fresh10(fresh(fresh4(true, true, c, subtract(a, subtract(a, c)), subtract(a, subtract(a, c)), add(subtract(a, subtract(a, c)), c)), true, subtract(a, subtract(a, c)), c), true, c, subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(b, c)), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.03 = { by axiom 12 (addition_inverts_subtraction2) R->L }
% 12.35/2.03 fresh7(fresh(fresh10(fresh(fresh4(equalish(subtract(a, subtract(a, c)), subtract(add(subtract(a, subtract(a, c)), c), c)), true, c, subtract(a, subtract(a, c)), subtract(a, subtract(a, c)), add(subtract(a, subtract(a, c)), c)), true, subtract(a, subtract(a, c)), c), true, c, subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(b, c)), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.03 = { by axiom 19 (subtract_substitution2) }
% 12.35/2.03 fresh7(fresh(fresh10(fresh(fresh3(equalish(c, subtract(a, subtract(a, c))), true, subtract(a, subtract(a, c)), subtract(a, subtract(a, c)), add(subtract(a, subtract(a, c)), c)), true, subtract(a, subtract(a, c)), c), true, c, subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(b, c)), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.03 = { by axiom 10 (subtract_substitution1) R->L }
% 12.35/2.03 fresh7(fresh(fresh10(fresh(fresh3(fresh6(true, true, add(subtract(a, c), c), a, c, subtract(a, c)), true, subtract(a, subtract(a, c)), subtract(a, subtract(a, c)), add(subtract(a, subtract(a, c)), c)), true, subtract(a, subtract(a, c)), c), true, c, subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(b, c)), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.03 = { by lemma 22 R->L }
% 12.35/2.03 fresh7(fresh(fresh10(fresh(fresh3(fresh6(equalish(c, subtract(add(subtract(a, c), c), subtract(a, c))), true, add(subtract(a, c), c), a, c, subtract(a, c)), true, subtract(a, subtract(a, c)), subtract(a, subtract(a, c)), add(subtract(a, subtract(a, c)), c)), true, subtract(a, subtract(a, c)), c), true, c, subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(b, c)), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.03 = { by axiom 18 (subtract_substitution1) }
% 12.35/2.03 fresh7(fresh(fresh10(fresh(fresh3(fresh5(equalish(add(subtract(a, c), c), a), true, a, c, subtract(a, c)), true, subtract(a, subtract(a, c)), subtract(a, subtract(a, c)), add(subtract(a, subtract(a, c)), c)), true, subtract(a, subtract(a, c)), c), true, c, subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(b, c)), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.03 = { by lemma 24 }
% 12.35/2.03 fresh7(fresh(fresh10(fresh(fresh3(fresh5(true, true, a, c, subtract(a, c)), true, subtract(a, subtract(a, c)), subtract(a, subtract(a, c)), add(subtract(a, subtract(a, c)), c)), true, subtract(a, subtract(a, c)), c), true, c, subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(b, c)), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.03 = { by axiom 5 (subtract_substitution1) }
% 12.35/2.03 fresh7(fresh(fresh10(fresh(fresh3(true, true, subtract(a, subtract(a, c)), subtract(a, subtract(a, c)), add(subtract(a, subtract(a, c)), c)), true, subtract(a, subtract(a, c)), c), true, c, subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(b, c)), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.03 = { by axiom 6 (subtract_substitution2) }
% 12.35/2.03 fresh7(fresh(fresh10(fresh(true, true, subtract(a, subtract(a, c)), c), true, c, subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(b, c)), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.03 = { by axiom 2 (transitivity) }
% 12.35/2.03 fresh7(fresh(fresh10(true, true, c, subtract(add(a, subtract(b, c)), subtract(a, c)), subtract(b, c)), true, subtract(add(a, subtract(b, c)), subtract(a, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.03 = { by axiom 3 (add_substitution1) }
% 12.35/2.03 fresh7(fresh(true, true, subtract(add(a, subtract(b, c)), subtract(a, c)), b), true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.03 = { by axiom 2 (transitivity) }
% 12.35/2.03 fresh7(true, true, b, add(a, subtract(b, c)), subtract(a, c))
% 12.35/2.03 = { by axiom 4 (add_substitution2) }
% 12.35/2.03 true
% 12.35/2.03 % SZS output end Proof
% 12.35/2.03
% 12.35/2.03 RESULT: Unsatisfiable (the axioms are contradictory).
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