TSTP Solution File: FLD023-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : FLD023-1 : 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 : n004.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 22:36:52 EDT 2023
% Result : Unsatisfiable 65.73s 8.78s
% Output : Proof 65.73s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD023-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 00:10:07 EDT 2023
% 0.14/0.34 % CPUTime :
% 65.73/8.78 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 65.73/8.78
% 65.73/8.78 % SZS status Unsatisfiable
% 65.73/8.78
% 65.73/8.78 % SZS output start Proof
% 65.73/8.78 Take the following subset of the input axioms:
% 65.73/8.78 fof(a_equals_b_3, negated_conjecture, equalish(a, b)).
% 65.73/8.78 fof(a_is_defined, hypothesis, defined(a)).
% 65.73/8.78 fof(additive_identity_not_equal_to_add_4, negated_conjecture, ~equalish(additive_identity, add(b, additive_inverse(a)))).
% 65.73/8.78 fof(compatibility_of_equality_and_addition, axiom, ![X, Y, Z]: (equalish(add(X, Z), add(Y, Z)) | (~defined(Z) | ~equalish(X, Y)))).
% 65.73/8.78 fof(existence_of_inverse_addition, axiom, ![X2]: (equalish(add(X2, additive_inverse(X2)), additive_identity) | ~defined(X2))).
% 65.73/8.78 fof(symmetry_of_equality, axiom, ![X2, Y2]: (equalish(X2, Y2) | ~equalish(Y2, X2))).
% 65.73/8.78 fof(transitivity_of_equality, axiom, ![X2, Y2, Z2]: (equalish(X2, Z2) | (~equalish(X2, Y2) | ~equalish(Y2, Z2)))).
% 65.73/8.78 fof(well_definedness_of_additive_inverse, axiom, ![X2]: (defined(additive_inverse(X2)) | ~defined(X2))).
% 65.73/8.78
% 65.73/8.78 Now clausify the problem and encode Horn clauses using encoding 3 of
% 65.73/8.78 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 65.73/8.78 We repeatedly replace C & s=t => u=v by the two clauses:
% 65.73/8.78 fresh(y, y, x1...xn) = u
% 65.73/8.78 C => fresh(s, t, x1...xn) = v
% 65.73/8.78 where fresh is a fresh function symbol and x1..xn are the free
% 65.73/8.78 variables of u and v.
% 65.73/8.78 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 65.73/8.78 input problem has no model of domain size 1).
% 65.73/8.78
% 65.73/8.78 The encoding turns the above axioms into the following unit equations and goals:
% 65.73/8.78
% 65.73/8.78 Axiom 1 (a_is_defined): defined(a) = true.
% 65.73/8.78 Axiom 2 (a_equals_b_3): equalish(a, b) = true.
% 65.73/8.78 Axiom 3 (existence_of_inverse_addition): fresh12(X, X, Y) = true.
% 65.73/8.78 Axiom 4 (well_definedness_of_additive_inverse): fresh3(X, X, Y) = true.
% 65.73/8.78 Axiom 5 (symmetry_of_equality): fresh10(X, X, Y, Z) = true.
% 65.73/8.78 Axiom 6 (transitivity_of_equality): fresh8(X, X, Y, Z) = true.
% 65.73/8.78 Axiom 7 (well_definedness_of_additive_inverse): fresh3(defined(X), true, X) = defined(additive_inverse(X)).
% 65.73/8.78 Axiom 8 (existence_of_inverse_addition): fresh12(defined(X), true, X) = equalish(add(X, additive_inverse(X)), additive_identity).
% 65.73/8.78 Axiom 9 (compatibility_of_equality_and_addition): fresh23(X, X, Y, Z, W) = true.
% 65.73/8.78 Axiom 10 (transitivity_of_equality): fresh9(X, X, Y, Z, W) = equalish(Y, Z).
% 65.73/8.78 Axiom 11 (compatibility_of_equality_and_addition): fresh24(X, X, Y, Z, W) = equalish(add(Y, Z), add(W, Z)).
% 65.73/8.78 Axiom 12 (symmetry_of_equality): fresh10(equalish(X, Y), true, Y, X) = equalish(Y, X).
% 65.73/8.78 Axiom 13 (compatibility_of_equality_and_addition): fresh24(defined(X), true, Y, X, Z) = fresh23(equalish(Y, Z), true, Y, X, Z).
% 65.73/8.78 Axiom 14 (transitivity_of_equality): fresh9(equalish(X, Y), true, Z, Y, X) = fresh8(equalish(Z, X), true, Z, Y).
% 65.73/8.78
% 65.73/8.78 Goal 1 (additive_identity_not_equal_to_add_4): equalish(additive_identity, add(b, additive_inverse(a))) = true.
% 65.73/8.78 Proof:
% 65.73/8.78 equalish(additive_identity, add(b, additive_inverse(a)))
% 65.73/8.78 = { by axiom 12 (symmetry_of_equality) R->L }
% 65.73/8.78 fresh10(equalish(add(b, additive_inverse(a)), additive_identity), true, additive_identity, add(b, additive_inverse(a)))
% 65.73/8.78 = { by axiom 10 (transitivity_of_equality) R->L }
% 65.73/8.78 fresh10(fresh9(true, true, add(b, additive_inverse(a)), additive_identity, add(a, additive_inverse(a))), true, additive_identity, add(b, additive_inverse(a)))
% 65.73/8.78 = { by axiom 3 (existence_of_inverse_addition) R->L }
% 65.73/8.78 fresh10(fresh9(fresh12(true, true, a), true, add(b, additive_inverse(a)), additive_identity, add(a, additive_inverse(a))), true, additive_identity, add(b, additive_inverse(a)))
% 65.73/8.78 = { by axiom 1 (a_is_defined) R->L }
% 65.73/8.78 fresh10(fresh9(fresh12(defined(a), true, a), true, add(b, additive_inverse(a)), additive_identity, add(a, additive_inverse(a))), true, additive_identity, add(b, additive_inverse(a)))
% 65.73/8.78 = { by axiom 8 (existence_of_inverse_addition) }
% 65.73/8.78 fresh10(fresh9(equalish(add(a, additive_inverse(a)), additive_identity), true, add(b, additive_inverse(a)), additive_identity, add(a, additive_inverse(a))), true, additive_identity, add(b, additive_inverse(a)))
% 65.73/8.78 = { by axiom 14 (transitivity_of_equality) }
% 65.73/8.78 fresh10(fresh8(equalish(add(b, additive_inverse(a)), add(a, additive_inverse(a))), true, add(b, additive_inverse(a)), additive_identity), true, additive_identity, add(b, additive_inverse(a)))
% 65.73/8.78 = { by axiom 11 (compatibility_of_equality_and_addition) R->L }
% 65.73/8.78 fresh10(fresh8(fresh24(true, true, b, additive_inverse(a), a), true, add(b, additive_inverse(a)), additive_identity), true, additive_identity, add(b, additive_inverse(a)))
% 65.73/8.78 = { by axiom 4 (well_definedness_of_additive_inverse) R->L }
% 65.73/8.78 fresh10(fresh8(fresh24(fresh3(true, true, a), true, b, additive_inverse(a), a), true, add(b, additive_inverse(a)), additive_identity), true, additive_identity, add(b, additive_inverse(a)))
% 65.73/8.78 = { by axiom 1 (a_is_defined) R->L }
% 65.73/8.78 fresh10(fresh8(fresh24(fresh3(defined(a), true, a), true, b, additive_inverse(a), a), true, add(b, additive_inverse(a)), additive_identity), true, additive_identity, add(b, additive_inverse(a)))
% 65.73/8.78 = { by axiom 7 (well_definedness_of_additive_inverse) }
% 65.73/8.78 fresh10(fresh8(fresh24(defined(additive_inverse(a)), true, b, additive_inverse(a), a), true, add(b, additive_inverse(a)), additive_identity), true, additive_identity, add(b, additive_inverse(a)))
% 65.73/8.78 = { by axiom 13 (compatibility_of_equality_and_addition) }
% 65.73/8.78 fresh10(fresh8(fresh23(equalish(b, a), true, b, additive_inverse(a), a), true, add(b, additive_inverse(a)), additive_identity), true, additive_identity, add(b, additive_inverse(a)))
% 65.73/8.78 = { by axiom 12 (symmetry_of_equality) R->L }
% 65.73/8.78 fresh10(fresh8(fresh23(fresh10(equalish(a, b), true, b, a), true, b, additive_inverse(a), a), true, add(b, additive_inverse(a)), additive_identity), true, additive_identity, add(b, additive_inverse(a)))
% 65.73/8.78 = { by axiom 2 (a_equals_b_3) }
% 65.73/8.78 fresh10(fresh8(fresh23(fresh10(true, true, b, a), true, b, additive_inverse(a), a), true, add(b, additive_inverse(a)), additive_identity), true, additive_identity, add(b, additive_inverse(a)))
% 65.73/8.78 = { by axiom 5 (symmetry_of_equality) }
% 65.73/8.78 fresh10(fresh8(fresh23(true, true, b, additive_inverse(a), a), true, add(b, additive_inverse(a)), additive_identity), true, additive_identity, add(b, additive_inverse(a)))
% 65.73/8.78 = { by axiom 9 (compatibility_of_equality_and_addition) }
% 65.73/8.78 fresh10(fresh8(true, true, add(b, additive_inverse(a)), additive_identity), true, additive_identity, add(b, additive_inverse(a)))
% 65.73/8.78 = { by axiom 6 (transitivity_of_equality) }
% 65.73/8.78 fresh10(true, true, additive_identity, add(b, additive_inverse(a)))
% 65.73/8.78 = { by axiom 5 (symmetry_of_equality) }
% 65.73/8.78 true
% 65.73/8.78 % SZS output end Proof
% 65.73/8.78
% 65.73/8.78 RESULT: Unsatisfiable (the axioms are contradictory).
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