TSTP Solution File: NUM001-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM001-1 : 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 : n020.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 11:54:56 EDT 2023
% Result : Unsatisfiable 6.35s 1.20s
% Output : Proof 6.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM001-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.35 % Computer : n020.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Fri Aug 25 11:16:45 EDT 2023
% 0.16/0.35 % CPUTime :
% 6.35/1.20 Command-line arguments: --no-flatten-goal
% 6.35/1.20
% 6.35/1.20 % SZS status Unsatisfiable
% 6.35/1.20
% 6.35/1.20 % SZS output start Proof
% 6.35/1.20 Take the following subset of the input axioms:
% 6.35/1.21 fof(addition_inverts_subtraction1, axiom, ![A, B]: equalish(subtract(add(A, B), B), A)).
% 6.35/1.21 fof(addition_inverts_subtraction2, axiom, ![B2, A3]: equalish(A3, subtract(add(A3, B2), B2))).
% 6.35/1.21 fof(associativity_of_addition, axiom, ![C, B2, A3]: equalish(add(A3, add(B2, C)), add(add(A3, B2), C))).
% 6.35/1.21 fof(commutativity_of_addition, axiom, ![B2, A3]: equalish(add(A3, B2), add(B2, A3))).
% 6.35/1.21 fof(prove_equation, negated_conjecture, ~equalish(add(add(a, b), c), add(a, add(b, c)))).
% 6.35/1.21 fof(reflexivity, axiom, ![A3]: equalish(A3, A3)).
% 6.35/1.21 fof(subtract_substitution1, axiom, ![D, A2, B2, C2]: (~equalish(A2, B2) | (~equalish(C2, subtract(A2, D)) | equalish(C2, subtract(B2, D))))).
% 6.35/1.21 fof(subtract_substitution2, axiom, ![B2, C2, A2_2, D2]: (~equalish(A2_2, B2) | (~equalish(C2, subtract(D2, A2_2)) | equalish(C2, subtract(D2, B2))))).
% 6.35/1.21 fof(transitivity, axiom, ![B2, C2, A2_2]: (~equalish(A2_2, B2) | (~equalish(B2, C2) | equalish(A2_2, C2)))).
% 6.35/1.21
% 6.35/1.21 Now clausify the problem and encode Horn clauses using encoding 3 of
% 6.35/1.21 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 6.35/1.21 We repeatedly replace C & s=t => u=v by the two clauses:
% 6.35/1.21 fresh(y, y, x1...xn) = u
% 6.35/1.21 C => fresh(s, t, x1...xn) = v
% 6.35/1.21 where fresh is a fresh function symbol and x1..xn are the free
% 6.35/1.21 variables of u and v.
% 6.35/1.21 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 6.35/1.21 input problem has no model of domain size 1).
% 6.35/1.21
% 6.35/1.21 The encoding turns the above axioms into the following unit equations and goals:
% 6.35/1.21
% 6.35/1.21 Axiom 1 (reflexivity): equalish(X, X) = true.
% 6.35/1.21 Axiom 2 (transitivity): fresh(X, X, Y, Z) = true.
% 6.35/1.21 Axiom 3 (subtract_substitution1): fresh5(X, X, Y, Z, W) = true.
% 6.35/1.21 Axiom 4 (subtract_substitution2): fresh3(X, X, Y, Z, W) = true.
% 6.35/1.21 Axiom 5 (transitivity): fresh2(X, X, Y, Z, W) = equalish(Y, W).
% 6.35/1.21 Axiom 6 (subtract_substitution1): fresh6(X, X, Y, Z, W, V) = equalish(W, subtract(Z, V)).
% 6.35/1.21 Axiom 7 (subtract_substitution2): fresh4(X, X, Y, Z, W, V) = equalish(W, subtract(V, Z)).
% 6.35/1.21 Axiom 8 (addition_inverts_subtraction2): equalish(X, subtract(add(X, Y), Y)) = true.
% 6.35/1.21 Axiom 9 (commutativity_of_addition): equalish(add(X, Y), add(Y, X)) = true.
% 6.35/1.21 Axiom 10 (addition_inverts_subtraction1): equalish(subtract(add(X, Y), Y), X) = true.
% 6.35/1.21 Axiom 11 (transitivity): fresh2(equalish(X, Y), true, Z, X, Y) = fresh(equalish(Z, X), true, Z, Y).
% 6.35/1.21 Axiom 12 (subtract_substitution1): fresh6(equalish(X, subtract(Y, Z)), true, Y, W, X, Z) = fresh5(equalish(Y, W), true, W, X, Z).
% 6.35/1.21 Axiom 13 (subtract_substitution2): fresh4(equalish(X, subtract(Y, Z)), true, Z, W, X, Y) = fresh3(equalish(Z, W), true, W, X, Y).
% 6.35/1.21 Axiom 14 (associativity_of_addition): equalish(add(X, add(Y, Z)), add(add(X, Y), Z)) = true.
% 6.35/1.21
% 6.35/1.21 Goal 1 (prove_equation): equalish(add(add(a, b), c), add(a, add(b, c))) = true.
% 6.35/1.21 Proof:
% 6.35/1.21 equalish(add(add(a, b), c), add(a, add(b, c)))
% 6.35/1.21 = { by axiom 5 (transitivity) R->L }
% 6.35/1.21 fresh2(true, true, add(add(a, b), c), subtract(add(add(add(a, b), c), add(a, add(b, c))), add(add(a, b), c)), add(a, add(b, c)))
% 6.35/1.21 = { by axiom 2 (transitivity) R->L }
% 6.35/1.21 fresh2(fresh(true, true, subtract(add(add(add(a, b), c), add(a, add(b, c))), add(add(a, b), c)), add(a, add(b, c))), true, add(add(a, b), c), subtract(add(add(add(a, b), c), add(a, add(b, c))), add(add(a, b), c)), add(a, add(b, c)))
% 6.35/1.21 = { by axiom 3 (subtract_substitution1) R->L }
% 6.35/1.21 fresh2(fresh(fresh5(true, true, add(add(a, add(b, c)), add(add(a, b), c)), subtract(add(add(add(a, b), c), add(a, add(b, c))), add(add(a, b), c)), add(add(a, b), c)), true, subtract(add(add(add(a, b), c), add(a, add(b, c))), add(add(a, b), c)), add(a, add(b, c))), true, add(add(a, b), c), subtract(add(add(add(a, b), c), add(a, add(b, c))), add(add(a, b), c)), add(a, add(b, c)))
% 6.35/1.21 = { by axiom 9 (commutativity_of_addition) R->L }
% 6.35/1.21 fresh2(fresh(fresh5(equalish(add(add(add(a, b), c), add(a, add(b, c))), add(add(a, add(b, c)), add(add(a, b), c))), true, add(add(a, add(b, c)), add(add(a, b), c)), subtract(add(add(add(a, b), c), add(a, add(b, c))), add(add(a, b), c)), add(add(a, b), c)), true, subtract(add(add(add(a, b), c), add(a, add(b, c))), add(add(a, b), c)), add(a, add(b, c))), true, add(add(a, b), c), subtract(add(add(add(a, b), c), add(a, add(b, c))), add(add(a, b), c)), add(a, add(b, c)))
% 6.35/1.21 = { by axiom 12 (subtract_substitution1) R->L }
% 6.35/1.21 fresh2(fresh(fresh6(equalish(subtract(add(add(add(a, b), c), add(a, add(b, c))), add(add(a, b), c)), subtract(add(add(add(a, b), c), add(a, add(b, c))), add(add(a, b), c))), true, add(add(add(a, b), c), add(a, add(b, c))), add(add(a, add(b, c)), add(add(a, b), c)), subtract(add(add(add(a, b), c), add(a, add(b, c))), add(add(a, b), c)), add(add(a, b), c)), true, subtract(add(add(add(a, b), c), add(a, add(b, c))), add(add(a, b), c)), add(a, add(b, c))), true, add(add(a, b), c), subtract(add(add(add(a, b), c), add(a, add(b, c))), add(add(a, b), c)), add(a, add(b, c)))
% 6.35/1.21 = { by axiom 1 (reflexivity) }
% 6.35/1.21 fresh2(fresh(fresh6(true, true, add(add(add(a, b), c), add(a, add(b, c))), add(add(a, add(b, c)), add(add(a, b), c)), subtract(add(add(add(a, b), c), add(a, add(b, c))), add(add(a, b), c)), add(add(a, b), c)), true, subtract(add(add(add(a, b), c), add(a, add(b, c))), add(add(a, b), c)), add(a, add(b, c))), true, add(add(a, b), c), subtract(add(add(add(a, b), c), add(a, add(b, c))), add(add(a, b), c)), add(a, add(b, c)))
% 6.35/1.21 = { by axiom 6 (subtract_substitution1) }
% 6.35/1.21 fresh2(fresh(equalish(subtract(add(add(add(a, b), c), add(a, add(b, c))), add(add(a, b), c)), subtract(add(add(a, add(b, c)), add(add(a, b), c)), add(add(a, b), c))), true, subtract(add(add(add(a, b), c), add(a, add(b, c))), add(add(a, b), c)), add(a, add(b, c))), true, add(add(a, b), c), subtract(add(add(add(a, b), c), add(a, add(b, c))), add(add(a, b), c)), add(a, add(b, c)))
% 6.35/1.21 = { by axiom 11 (transitivity) R->L }
% 6.35/1.21 fresh2(fresh2(equalish(subtract(add(add(a, add(b, c)), add(add(a, b), c)), add(add(a, b), c)), add(a, add(b, c))), true, subtract(add(add(add(a, b), c), add(a, add(b, c))), add(add(a, b), c)), subtract(add(add(a, add(b, c)), add(add(a, b), c)), add(add(a, b), c)), add(a, add(b, c))), true, add(add(a, b), c), subtract(add(add(add(a, b), c), add(a, add(b, c))), add(add(a, b), c)), add(a, add(b, c)))
% 6.35/1.21 = { by axiom 10 (addition_inverts_subtraction1) }
% 6.35/1.21 fresh2(fresh2(true, true, subtract(add(add(add(a, b), c), add(a, add(b, c))), add(add(a, b), c)), subtract(add(add(a, add(b, c)), add(add(a, b), c)), add(add(a, b), c)), add(a, add(b, c))), true, add(add(a, b), c), subtract(add(add(add(a, b), c), add(a, add(b, c))), add(add(a, b), c)), add(a, add(b, c)))
% 6.35/1.21 = { by axiom 5 (transitivity) }
% 6.35/1.21 fresh2(equalish(subtract(add(add(add(a, b), c), add(a, add(b, c))), add(add(a, b), c)), add(a, add(b, c))), true, add(add(a, b), c), subtract(add(add(add(a, b), c), add(a, add(b, c))), add(add(a, b), c)), add(a, add(b, c)))
% 6.35/1.21 = { by axiom 11 (transitivity) }
% 6.35/1.21 fresh(equalish(add(add(a, b), c), subtract(add(add(add(a, b), c), add(a, add(b, c))), add(add(a, b), c))), true, add(add(a, b), c), add(a, add(b, c)))
% 6.35/1.21 = { by axiom 7 (subtract_substitution2) R->L }
% 6.35/1.21 fresh(fresh4(true, true, add(a, add(b, c)), add(add(a, b), c), add(add(a, b), c), add(add(add(a, b), c), add(a, add(b, c)))), true, add(add(a, b), c), add(a, add(b, c)))
% 6.35/1.21 = { by axiom 8 (addition_inverts_subtraction2) R->L }
% 6.35/1.21 fresh(fresh4(equalish(add(add(a, b), c), subtract(add(add(add(a, b), c), add(a, add(b, c))), add(a, add(b, c)))), true, add(a, add(b, c)), add(add(a, b), c), add(add(a, b), c), add(add(add(a, b), c), add(a, add(b, c)))), true, add(add(a, b), c), add(a, add(b, c)))
% 6.35/1.21 = { by axiom 13 (subtract_substitution2) }
% 6.35/1.21 fresh(fresh3(equalish(add(a, add(b, c)), add(add(a, b), c)), true, add(add(a, b), c), add(add(a, b), c), add(add(add(a, b), c), add(a, add(b, c)))), true, add(add(a, b), c), add(a, add(b, c)))
% 6.35/1.21 = { by axiom 14 (associativity_of_addition) }
% 6.35/1.21 fresh(fresh3(true, true, add(add(a, b), c), add(add(a, b), c), add(add(add(a, b), c), add(a, add(b, c)))), true, add(add(a, b), c), add(a, add(b, c)))
% 6.35/1.21 = { by axiom 4 (subtract_substitution2) }
% 6.35/1.21 fresh(true, true, add(add(a, b), c), add(a, add(b, c)))
% 6.35/1.21 = { by axiom 2 (transitivity) }
% 6.35/1.21 true
% 6.35/1.21 % SZS output end Proof
% 6.35/1.21
% 6.35/1.21 RESULT: Unsatisfiable (the axioms are contradictory).
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