TSTP Solution File: FLD018-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : FLD018-1 : 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 : n026.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 22:36:51 EDT 2023
% Result : Unsatisfiable 12.03s 1.98s
% Output : Proof 12.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD018-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.37 % Computer : n026.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8042.1875MB
% 0.13/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Aug 28 00:37:49 EDT 2023
% 0.21/0.37 % CPUTime :
% 12.03/1.98 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 12.03/1.98
% 12.03/1.98 % SZS status Unsatisfiable
% 12.03/1.98
% 12.03/1.99 % SZS output start Proof
% 12.03/1.99 Take the following subset of the input axioms:
% 12.03/1.99 fof(a_equals_additive_identity_2, negated_conjecture, equalish(a, additive_identity)).
% 12.03/1.99 fof(a_is_defined, hypothesis, defined(a)).
% 12.03/1.99 fof(additive_inverse_not_equal_to_additive_identity_3, negated_conjecture, ~equalish(additive_inverse(a), additive_identity)).
% 12.03/1.99 fof(compatibility_of_equality_and_addition, axiom, ![X, Y, Z]: (equalish(add(X, Z), add(Y, Z)) | (~defined(Z) | ~equalish(X, Y)))).
% 12.03/1.99 fof(existence_of_identity_addition, axiom, ![X2]: (equalish(add(additive_identity, X2), X2) | ~defined(X2))).
% 12.03/1.99 fof(existence_of_inverse_addition, axiom, ![X2]: (equalish(add(X2, additive_inverse(X2)), additive_identity) | ~defined(X2))).
% 12.03/1.99 fof(symmetry_of_equality, axiom, ![X2, Y2]: (equalish(X2, Y2) | ~equalish(Y2, X2))).
% 12.03/1.99 fof(transitivity_of_equality, axiom, ![X2, Y2, Z2]: (equalish(X2, Z2) | (~equalish(X2, Y2) | ~equalish(Y2, Z2)))).
% 12.03/1.99 fof(well_definedness_of_additive_inverse, axiom, ![X2]: (defined(additive_inverse(X2)) | ~defined(X2))).
% 12.03/1.99
% 12.03/1.99 Now clausify the problem and encode Horn clauses using encoding 3 of
% 12.03/1.99 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 12.03/1.99 We repeatedly replace C & s=t => u=v by the two clauses:
% 12.03/1.99 fresh(y, y, x1...xn) = u
% 12.03/1.99 C => fresh(s, t, x1...xn) = v
% 12.03/1.99 where fresh is a fresh function symbol and x1..xn are the free
% 12.03/1.99 variables of u and v.
% 12.03/1.99 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 12.03/1.99 input problem has no model of domain size 1).
% 12.03/1.99
% 12.03/1.99 The encoding turns the above axioms into the following unit equations and goals:
% 12.03/1.99
% 12.03/2.00 Axiom 1 (a_is_defined): defined(a) = true.
% 12.03/2.00 Axiom 2 (a_equals_additive_identity_2): equalish(a, additive_identity) = true.
% 12.03/2.00 Axiom 3 (existence_of_identity_addition): fresh14(X, X, Y) = true.
% 12.03/2.00 Axiom 4 (existence_of_inverse_addition): fresh12(X, X, Y) = true.
% 12.03/2.00 Axiom 5 (well_definedness_of_additive_inverse): fresh3(X, X, Y) = true.
% 12.03/2.00 Axiom 6 (existence_of_identity_addition): fresh14(defined(X), true, X) = equalish(add(additive_identity, X), X).
% 12.03/2.00 Axiom 7 (existence_of_inverse_addition): fresh12(defined(X), true, X) = equalish(add(X, additive_inverse(X)), additive_identity).
% 12.03/2.00 Axiom 8 (symmetry_of_equality): fresh10(X, X, Y, Z) = true.
% 12.03/2.00 Axiom 9 (transitivity_of_equality): fresh8(X, X, Y, Z) = true.
% 12.03/2.00 Axiom 10 (well_definedness_of_additive_inverse): fresh3(defined(X), true, X) = defined(additive_inverse(X)).
% 12.03/2.00 Axiom 11 (compatibility_of_equality_and_addition): fresh24(X, X, Y, Z, W) = equalish(add(Y, Z), add(W, Z)).
% 12.03/2.00 Axiom 12 (compatibility_of_equality_and_addition): fresh23(X, X, Y, Z, W) = true.
% 12.03/2.00 Axiom 13 (symmetry_of_equality): fresh10(equalish(X, Y), true, Y, X) = equalish(Y, X).
% 12.03/2.00 Axiom 14 (transitivity_of_equality): fresh9(X, X, Y, Z, W) = equalish(Y, Z).
% 12.03/2.00 Axiom 15 (compatibility_of_equality_and_addition): fresh24(defined(X), true, Y, X, Z) = fresh23(equalish(Y, Z), true, Y, X, Z).
% 12.03/2.00 Axiom 16 (transitivity_of_equality): fresh9(equalish(X, Y), true, Z, Y, X) = fresh8(equalish(Z, X), true, Z, Y).
% 12.03/2.00
% 12.03/2.00 Lemma 17: defined(additive_inverse(a)) = true.
% 12.03/2.00 Proof:
% 12.03/2.00 defined(additive_inverse(a))
% 12.03/2.00 = { by axiom 10 (well_definedness_of_additive_inverse) R->L }
% 12.03/2.00 fresh3(defined(a), true, a)
% 12.03/2.00 = { by axiom 1 (a_is_defined) }
% 12.03/2.00 fresh3(true, true, a)
% 12.03/2.00 = { by axiom 5 (well_definedness_of_additive_inverse) }
% 12.03/2.00 true
% 12.03/2.00
% 12.03/2.00 Goal 1 (additive_inverse_not_equal_to_additive_identity_3): equalish(additive_inverse(a), additive_identity) = true.
% 12.03/2.00 Proof:
% 12.03/2.00 equalish(additive_inverse(a), additive_identity)
% 12.03/2.00 = { by axiom 13 (symmetry_of_equality) R->L }
% 12.03/2.00 fresh10(equalish(additive_identity, additive_inverse(a)), true, additive_inverse(a), additive_identity)
% 12.03/2.00 = { by axiom 14 (transitivity_of_equality) R->L }
% 12.03/2.00 fresh10(fresh9(true, true, additive_identity, additive_inverse(a), add(additive_identity, additive_inverse(a))), true, additive_inverse(a), additive_identity)
% 12.03/2.00 = { by axiom 3 (existence_of_identity_addition) R->L }
% 12.03/2.00 fresh10(fresh9(fresh14(true, true, additive_inverse(a)), true, additive_identity, additive_inverse(a), add(additive_identity, additive_inverse(a))), true, additive_inverse(a), additive_identity)
% 12.03/2.00 = { by lemma 17 R->L }
% 12.03/2.00 fresh10(fresh9(fresh14(defined(additive_inverse(a)), true, additive_inverse(a)), true, additive_identity, additive_inverse(a), add(additive_identity, additive_inverse(a))), true, additive_inverse(a), additive_identity)
% 12.03/2.00 = { by axiom 6 (existence_of_identity_addition) }
% 12.03/2.00 fresh10(fresh9(equalish(add(additive_identity, additive_inverse(a)), additive_inverse(a)), true, additive_identity, additive_inverse(a), add(additive_identity, additive_inverse(a))), true, additive_inverse(a), additive_identity)
% 12.03/2.00 = { by axiom 16 (transitivity_of_equality) }
% 12.03/2.00 fresh10(fresh8(equalish(additive_identity, add(additive_identity, additive_inverse(a))), true, additive_identity, additive_inverse(a)), true, additive_inverse(a), additive_identity)
% 12.03/2.00 = { by axiom 13 (symmetry_of_equality) R->L }
% 12.03/2.00 fresh10(fresh8(fresh10(equalish(add(additive_identity, additive_inverse(a)), additive_identity), true, additive_identity, add(additive_identity, additive_inverse(a))), true, additive_identity, additive_inverse(a)), true, additive_inverse(a), additive_identity)
% 12.03/2.00 = { by axiom 14 (transitivity_of_equality) R->L }
% 12.03/2.00 fresh10(fresh8(fresh10(fresh9(true, true, add(additive_identity, additive_inverse(a)), additive_identity, add(a, additive_inverse(a))), true, additive_identity, add(additive_identity, additive_inverse(a))), true, additive_identity, additive_inverse(a)), true, additive_inverse(a), additive_identity)
% 12.03/2.00 = { by axiom 4 (existence_of_inverse_addition) R->L }
% 12.03/2.00 fresh10(fresh8(fresh10(fresh9(fresh12(true, true, a), true, add(additive_identity, additive_inverse(a)), additive_identity, add(a, additive_inverse(a))), true, additive_identity, add(additive_identity, additive_inverse(a))), true, additive_identity, additive_inverse(a)), true, additive_inverse(a), additive_identity)
% 12.03/2.00 = { by axiom 1 (a_is_defined) R->L }
% 12.03/2.00 fresh10(fresh8(fresh10(fresh9(fresh12(defined(a), true, a), true, add(additive_identity, additive_inverse(a)), additive_identity, add(a, additive_inverse(a))), true, additive_identity, add(additive_identity, additive_inverse(a))), true, additive_identity, additive_inverse(a)), true, additive_inverse(a), additive_identity)
% 12.03/2.00 = { by axiom 7 (existence_of_inverse_addition) }
% 12.03/2.00 fresh10(fresh8(fresh10(fresh9(equalish(add(a, additive_inverse(a)), additive_identity), true, add(additive_identity, additive_inverse(a)), additive_identity, add(a, additive_inverse(a))), true, additive_identity, add(additive_identity, additive_inverse(a))), true, additive_identity, additive_inverse(a)), true, additive_inverse(a), additive_identity)
% 12.03/2.00 = { by axiom 16 (transitivity_of_equality) }
% 12.03/2.00 fresh10(fresh8(fresh10(fresh8(equalish(add(additive_identity, additive_inverse(a)), add(a, additive_inverse(a))), true, add(additive_identity, additive_inverse(a)), additive_identity), true, additive_identity, add(additive_identity, additive_inverse(a))), true, additive_identity, additive_inverse(a)), true, additive_inverse(a), additive_identity)
% 12.03/2.00 = { by axiom 13 (symmetry_of_equality) R->L }
% 12.03/2.00 fresh10(fresh8(fresh10(fresh8(fresh10(equalish(add(a, additive_inverse(a)), add(additive_identity, additive_inverse(a))), true, add(additive_identity, additive_inverse(a)), add(a, additive_inverse(a))), true, add(additive_identity, additive_inverse(a)), additive_identity), true, additive_identity, add(additive_identity, additive_inverse(a))), true, additive_identity, additive_inverse(a)), true, additive_inverse(a), additive_identity)
% 12.03/2.00 = { by axiom 11 (compatibility_of_equality_and_addition) R->L }
% 12.03/2.00 fresh10(fresh8(fresh10(fresh8(fresh10(fresh24(true, true, a, additive_inverse(a), additive_identity), true, add(additive_identity, additive_inverse(a)), add(a, additive_inverse(a))), true, add(additive_identity, additive_inverse(a)), additive_identity), true, additive_identity, add(additive_identity, additive_inverse(a))), true, additive_identity, additive_inverse(a)), true, additive_inverse(a), additive_identity)
% 12.03/2.00 = { by lemma 17 R->L }
% 12.03/2.00 fresh10(fresh8(fresh10(fresh8(fresh10(fresh24(defined(additive_inverse(a)), true, a, additive_inverse(a), additive_identity), true, add(additive_identity, additive_inverse(a)), add(a, additive_inverse(a))), true, add(additive_identity, additive_inverse(a)), additive_identity), true, additive_identity, add(additive_identity, additive_inverse(a))), true, additive_identity, additive_inverse(a)), true, additive_inverse(a), additive_identity)
% 12.03/2.00 = { by axiom 15 (compatibility_of_equality_and_addition) }
% 12.03/2.00 fresh10(fresh8(fresh10(fresh8(fresh10(fresh23(equalish(a, additive_identity), true, a, additive_inverse(a), additive_identity), true, add(additive_identity, additive_inverse(a)), add(a, additive_inverse(a))), true, add(additive_identity, additive_inverse(a)), additive_identity), true, additive_identity, add(additive_identity, additive_inverse(a))), true, additive_identity, additive_inverse(a)), true, additive_inverse(a), additive_identity)
% 12.03/2.00 = { by axiom 2 (a_equals_additive_identity_2) }
% 12.03/2.00 fresh10(fresh8(fresh10(fresh8(fresh10(fresh23(true, true, a, additive_inverse(a), additive_identity), true, add(additive_identity, additive_inverse(a)), add(a, additive_inverse(a))), true, add(additive_identity, additive_inverse(a)), additive_identity), true, additive_identity, add(additive_identity, additive_inverse(a))), true, additive_identity, additive_inverse(a)), true, additive_inverse(a), additive_identity)
% 12.03/2.00 = { by axiom 12 (compatibility_of_equality_and_addition) }
% 12.03/2.00 fresh10(fresh8(fresh10(fresh8(fresh10(true, true, add(additive_identity, additive_inverse(a)), add(a, additive_inverse(a))), true, add(additive_identity, additive_inverse(a)), additive_identity), true, additive_identity, add(additive_identity, additive_inverse(a))), true, additive_identity, additive_inverse(a)), true, additive_inverse(a), additive_identity)
% 12.03/2.00 = { by axiom 8 (symmetry_of_equality) }
% 12.03/2.00 fresh10(fresh8(fresh10(fresh8(true, true, add(additive_identity, additive_inverse(a)), additive_identity), true, additive_identity, add(additive_identity, additive_inverse(a))), true, additive_identity, additive_inverse(a)), true, additive_inverse(a), additive_identity)
% 12.03/2.00 = { by axiom 9 (transitivity_of_equality) }
% 12.03/2.00 fresh10(fresh8(fresh10(true, true, additive_identity, add(additive_identity, additive_inverse(a))), true, additive_identity, additive_inverse(a)), true, additive_inverse(a), additive_identity)
% 12.03/2.02 = { by axiom 8 (symmetry_of_equality) }
% 12.03/2.02 fresh10(fresh8(true, true, additive_identity, additive_inverse(a)), true, additive_inverse(a), additive_identity)
% 12.03/2.02 = { by axiom 9 (transitivity_of_equality) }
% 12.03/2.02 fresh10(true, true, additive_inverse(a), additive_identity)
% 12.03/2.02 = { by axiom 8 (symmetry_of_equality) }
% 12.03/2.02 true
% 12.03/2.02 % SZS output end Proof
% 12.03/2.02
% 12.03/2.02 RESULT: Unsatisfiable (the axioms are contradictory).
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