TSTP Solution File: NUM004-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM004-1 : 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 : n007.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 9.28s 1.54s
% Output : Proof 9.28s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM004-1 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.13 % 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 : n007.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 10:24:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 9.28/1.54 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 9.28/1.54
% 9.28/1.54 % SZS status Unsatisfiable
% 9.28/1.54
% 9.28/1.54 % SZS output start Proof
% 9.28/1.54 Take the following subset of the input axioms:
% 9.28/1.54 fof(commutativity2, axiom, ![A, B, C]: equalish(subtract(add(A, B), C), add(subtract(A, C), B))).
% 9.28/1.54 fof(commutativity_of_addition, axiom, ![B2, A3]: equalish(add(A3, B2), add(B2, A3))).
% 9.28/1.54 fof(prove_equation, negated_conjecture, ~equalish(subtract(add(a, b), c), add(a, subtract(b, c)))).
% 9.28/1.54 fof(reflexivity, axiom, ![A3]: equalish(A3, A3)).
% 9.28/1.54 fof(subtract_substitution1, axiom, ![D, A2, B2, C2]: (~equalish(A2, B2) | (~equalish(C2, subtract(A2, D)) | equalish(C2, subtract(B2, D))))).
% 9.28/1.54 fof(transitivity, axiom, ![B2, C2, A2_2]: (~equalish(A2_2, B2) | (~equalish(B2, C2) | equalish(A2_2, C2)))).
% 9.28/1.54
% 9.28/1.54 Now clausify the problem and encode Horn clauses using encoding 3 of
% 9.28/1.54 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 9.28/1.54 We repeatedly replace C & s=t => u=v by the two clauses:
% 9.28/1.54 fresh(y, y, x1...xn) = u
% 9.28/1.54 C => fresh(s, t, x1...xn) = v
% 9.28/1.54 where fresh is a fresh function symbol and x1..xn are the free
% 9.28/1.54 variables of u and v.
% 9.28/1.54 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 9.28/1.54 input problem has no model of domain size 1).
% 9.28/1.54
% 9.28/1.54 The encoding turns the above axioms into the following unit equations and goals:
% 9.28/1.54
% 9.28/1.54 Axiom 1 (reflexivity): equalish(X, X) = true.
% 9.28/1.54 Axiom 2 (transitivity): fresh(X, X, Y, Z) = true.
% 9.28/1.54 Axiom 3 (subtract_substitution1): fresh5(X, X, Y, Z, W) = true.
% 9.28/1.54 Axiom 4 (transitivity): fresh2(X, X, Y, Z, W) = equalish(Y, W).
% 9.28/1.54 Axiom 5 (commutativity_of_addition): equalish(add(X, Y), add(Y, X)) = true.
% 9.28/1.54 Axiom 6 (subtract_substitution1): fresh6(X, X, Y, Z, W, V) = equalish(W, subtract(Z, V)).
% 9.28/1.54 Axiom 7 (transitivity): fresh2(equalish(X, Y), true, Z, X, Y) = fresh(equalish(Z, X), true, Z, Y).
% 9.28/1.54 Axiom 8 (commutativity2): equalish(subtract(add(X, Y), Z), add(subtract(X, Z), Y)) = true.
% 9.28/1.54 Axiom 9 (subtract_substitution1): fresh6(equalish(X, subtract(Y, Z)), true, Y, W, X, Z) = fresh5(equalish(Y, W), true, W, X, Z).
% 9.28/1.54
% 9.28/1.54 Goal 1 (prove_equation): equalish(subtract(add(a, b), c), add(a, subtract(b, c))) = true.
% 9.28/1.54 Proof:
% 9.28/1.54 equalish(subtract(add(a, b), c), add(a, subtract(b, c)))
% 9.28/1.54 = { by axiom 4 (transitivity) R->L }
% 9.28/1.54 fresh2(true, true, subtract(add(a, b), c), add(subtract(b, c), a), add(a, subtract(b, c)))
% 9.28/1.54 = { by axiom 5 (commutativity_of_addition) R->L }
% 9.28/1.54 fresh2(equalish(add(subtract(b, c), a), add(a, subtract(b, c))), true, subtract(add(a, b), c), add(subtract(b, c), a), add(a, subtract(b, c)))
% 9.28/1.54 = { by axiom 7 (transitivity) }
% 9.28/1.54 fresh(equalish(subtract(add(a, b), c), add(subtract(b, c), a)), true, subtract(add(a, b), c), add(a, subtract(b, c)))
% 9.28/1.54 = { by axiom 4 (transitivity) R->L }
% 9.28/1.54 fresh(fresh2(true, true, subtract(add(a, b), c), subtract(add(b, a), c), add(subtract(b, c), a)), true, subtract(add(a, b), c), add(a, subtract(b, c)))
% 9.28/1.54 = { by axiom 8 (commutativity2) R->L }
% 9.28/1.54 fresh(fresh2(equalish(subtract(add(b, a), c), add(subtract(b, c), a)), true, subtract(add(a, b), c), subtract(add(b, a), c), add(subtract(b, c), a)), true, subtract(add(a, b), c), add(a, subtract(b, c)))
% 9.28/1.54 = { by axiom 7 (transitivity) }
% 9.28/1.54 fresh(fresh(equalish(subtract(add(a, b), c), subtract(add(b, a), c)), true, subtract(add(a, b), c), add(subtract(b, c), a)), true, subtract(add(a, b), c), add(a, subtract(b, c)))
% 9.28/1.54 = { by axiom 6 (subtract_substitution1) R->L }
% 9.28/1.54 fresh(fresh(fresh6(true, true, add(a, b), add(b, a), subtract(add(a, b), c), c), true, subtract(add(a, b), c), add(subtract(b, c), a)), true, subtract(add(a, b), c), add(a, subtract(b, c)))
% 9.28/1.54 = { by axiom 1 (reflexivity) R->L }
% 9.28/1.54 fresh(fresh(fresh6(equalish(subtract(add(a, b), c), subtract(add(a, b), c)), true, add(a, b), add(b, a), subtract(add(a, b), c), c), true, subtract(add(a, b), c), add(subtract(b, c), a)), true, subtract(add(a, b), c), add(a, subtract(b, c)))
% 9.28/1.54 = { by axiom 9 (subtract_substitution1) }
% 9.28/1.54 fresh(fresh(fresh5(equalish(add(a, b), add(b, a)), true, add(b, a), subtract(add(a, b), c), c), true, subtract(add(a, b), c), add(subtract(b, c), a)), true, subtract(add(a, b), c), add(a, subtract(b, c)))
% 9.28/1.54 = { by axiom 5 (commutativity_of_addition) }
% 9.28/1.54 fresh(fresh(fresh5(true, true, add(b, a), subtract(add(a, b), c), c), true, subtract(add(a, b), c), add(subtract(b, c), a)), true, subtract(add(a, b), c), add(a, subtract(b, c)))
% 9.28/1.54 = { by axiom 3 (subtract_substitution1) }
% 9.28/1.54 fresh(fresh(true, true, subtract(add(a, b), c), add(subtract(b, c), a)), true, subtract(add(a, b), c), add(a, subtract(b, c)))
% 9.28/1.54 = { by axiom 2 (transitivity) }
% 9.28/1.54 fresh(true, true, subtract(add(a, b), c), add(a, subtract(b, c)))
% 9.28/1.54 = { by axiom 2 (transitivity) }
% 9.28/1.54 true
% 9.28/1.54 % SZS output end Proof
% 9.28/1.54
% 9.28/1.54 RESULT: Unsatisfiable (the axioms are contradictory).
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