TSTP Solution File: FLD070-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : FLD070-1 : 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 : n032.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 22:37:12 EDT 2023
% Result : Unsatisfiable 0.14s 0.42s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : FLD070-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Mon Aug 28 00:34:45 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.14/0.42 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.14/0.42
% 0.14/0.42 % SZS status Unsatisfiable
% 0.14/0.42
% 0.14/0.43 % SZS output start Proof
% 0.14/0.43 Take the following subset of the input axioms:
% 0.14/0.43 fof(b_is_defined, hypothesis, defined(b)).
% 0.14/0.43 fof(compatibility_of_equality_and_order_relation, axiom, ![X, Y, Z]: (less_or_equal(Y, Z) | (~less_or_equal(X, Z) | ~equalish(X, Y)))).
% 0.14/0.43 fof(compatibility_of_order_relation_and_addition, axiom, ![X2, Y2, Z2]: (less_or_equal(add(X2, Z2), add(Y2, Z2)) | (~defined(Z2) | ~less_or_equal(X2, Y2)))).
% 0.14/0.43 fof(existence_of_identity_addition, axiom, ![X2]: (equalish(add(additive_identity, X2), X2) | ~defined(X2))).
% 0.14/0.43 fof(less_or_equal_3, negated_conjecture, less_or_equal(additive_identity, a)).
% 0.14/0.43 fof(less_or_equal_4, negated_conjecture, less_or_equal(additive_identity, b)).
% 0.14/0.43 fof(not_less_or_equal_5, negated_conjecture, ~less_or_equal(additive_identity, add(a, b))).
% 0.14/0.43 fof(symmetry_of_equality, axiom, ![X2, Y2]: (equalish(X2, Y2) | ~equalish(Y2, X2))).
% 0.14/0.43 fof(transitivity_of_order_relation, axiom, ![X2, Y2, Z2]: (less_or_equal(X2, Z2) | (~less_or_equal(X2, Y2) | ~less_or_equal(Y2, Z2)))).
% 0.14/0.43 fof(well_definedness_of_additive_identity, axiom, defined(additive_identity)).
% 0.14/0.43
% 0.14/0.43 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.14/0.43 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.14/0.43 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.14/0.43 fresh(y, y, x1...xn) = u
% 0.14/0.43 C => fresh(s, t, x1...xn) = v
% 0.14/0.43 where fresh is a fresh function symbol and x1..xn are the free
% 0.14/0.43 variables of u and v.
% 0.14/0.43 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.14/0.43 input problem has no model of domain size 1).
% 0.14/0.43
% 0.14/0.43 The encoding turns the above axioms into the following unit equations and goals:
% 0.14/0.43
% 0.14/0.43 Axiom 1 (well_definedness_of_additive_identity): defined(additive_identity) = true.
% 0.14/0.43 Axiom 2 (b_is_defined): defined(b) = true.
% 0.14/0.43 Axiom 3 (less_or_equal_3): less_or_equal(additive_identity, a) = true.
% 0.14/0.43 Axiom 4 (less_or_equal_4): less_or_equal(additive_identity, b) = true.
% 0.14/0.43 Axiom 5 (existence_of_identity_addition): fresh14(X, X, Y) = true.
% 0.14/0.43 Axiom 6 (compatibility_of_equality_and_order_relation): fresh19(X, X, Y, Z) = true.
% 0.14/0.43 Axiom 7 (existence_of_identity_addition): fresh14(defined(X), true, X) = equalish(add(additive_identity, X), X).
% 0.14/0.43 Axiom 8 (symmetry_of_equality): fresh10(X, X, Y, Z) = true.
% 0.14/0.43 Axiom 9 (transitivity_of_order_relation): fresh6(X, X, Y, Z) = true.
% 0.14/0.43 Axiom 10 (compatibility_of_equality_and_order_relation): fresh20(X, X, Y, Z, W) = less_or_equal(Y, Z).
% 0.14/0.43 Axiom 11 (compatibility_of_order_relation_and_addition): fresh18(X, X, Y, Z, W) = less_or_equal(add(Y, Z), add(W, Z)).
% 0.14/0.43 Axiom 12 (compatibility_of_order_relation_and_addition): fresh17(X, X, Y, Z, W) = true.
% 0.14/0.43 Axiom 13 (symmetry_of_equality): fresh10(equalish(X, Y), true, Y, X) = equalish(Y, X).
% 0.14/0.43 Axiom 14 (transitivity_of_order_relation): fresh7(X, X, Y, Z, W) = less_or_equal(Y, Z).
% 0.14/0.43 Axiom 15 (compatibility_of_equality_and_order_relation): fresh20(less_or_equal(X, Y), true, Z, Y, X) = fresh19(equalish(X, Z), true, Z, Y).
% 0.14/0.43 Axiom 16 (compatibility_of_order_relation_and_addition): fresh18(less_or_equal(X, Y), true, X, Z, Y) = fresh17(defined(Z), true, X, Z, Y).
% 0.14/0.43 Axiom 17 (transitivity_of_order_relation): fresh7(less_or_equal(X, Y), true, Z, Y, X) = fresh6(less_or_equal(Z, X), true, Z, Y).
% 0.14/0.43
% 0.14/0.43 Lemma 18: equalish(add(additive_identity, additive_identity), additive_identity) = true.
% 0.14/0.43 Proof:
% 0.14/0.43 equalish(add(additive_identity, additive_identity), additive_identity)
% 0.14/0.43 = { by axiom 7 (existence_of_identity_addition) R->L }
% 0.14/0.43 fresh14(defined(additive_identity), true, additive_identity)
% 0.14/0.43 = { by axiom 1 (well_definedness_of_additive_identity) }
% 0.14/0.43 fresh14(true, true, additive_identity)
% 0.14/0.43 = { by axiom 5 (existence_of_identity_addition) }
% 0.14/0.43 true
% 0.14/0.43
% 0.14/0.43 Goal 1 (not_less_or_equal_5): less_or_equal(additive_identity, add(a, b)) = true.
% 0.14/0.43 Proof:
% 0.14/0.43 less_or_equal(additive_identity, add(a, b))
% 0.14/0.43 = { by axiom 10 (compatibility_of_equality_and_order_relation) R->L }
% 0.14/0.43 fresh20(true, true, additive_identity, add(a, b), add(additive_identity, additive_identity))
% 0.14/0.43 = { by axiom 9 (transitivity_of_order_relation) R->L }
% 0.14/0.43 fresh20(fresh6(true, true, add(additive_identity, additive_identity), add(a, b)), true, additive_identity, add(a, b), add(additive_identity, additive_identity))
% 0.14/0.44 = { by axiom 6 (compatibility_of_equality_and_order_relation) R->L }
% 0.14/0.44 fresh20(fresh6(fresh19(true, true, add(additive_identity, additive_identity), b), true, add(additive_identity, additive_identity), add(a, b)), true, additive_identity, add(a, b), add(additive_identity, additive_identity))
% 0.14/0.44 = { by axiom 8 (symmetry_of_equality) R->L }
% 0.14/0.44 fresh20(fresh6(fresh19(fresh10(true, true, additive_identity, add(additive_identity, additive_identity)), true, add(additive_identity, additive_identity), b), true, add(additive_identity, additive_identity), add(a, b)), true, additive_identity, add(a, b), add(additive_identity, additive_identity))
% 0.14/0.44 = { by lemma 18 R->L }
% 0.14/0.44 fresh20(fresh6(fresh19(fresh10(equalish(add(additive_identity, additive_identity), additive_identity), true, additive_identity, add(additive_identity, additive_identity)), true, add(additive_identity, additive_identity), b), true, add(additive_identity, additive_identity), add(a, b)), true, additive_identity, add(a, b), add(additive_identity, additive_identity))
% 0.14/0.44 = { by axiom 13 (symmetry_of_equality) }
% 0.14/0.44 fresh20(fresh6(fresh19(equalish(additive_identity, add(additive_identity, additive_identity)), true, add(additive_identity, additive_identity), b), true, add(additive_identity, additive_identity), add(a, b)), true, additive_identity, add(a, b), add(additive_identity, additive_identity))
% 0.14/0.44 = { by axiom 15 (compatibility_of_equality_and_order_relation) R->L }
% 0.14/0.44 fresh20(fresh6(fresh20(less_or_equal(additive_identity, b), true, add(additive_identity, additive_identity), b, additive_identity), true, add(additive_identity, additive_identity), add(a, b)), true, additive_identity, add(a, b), add(additive_identity, additive_identity))
% 0.14/0.44 = { by axiom 4 (less_or_equal_4) }
% 0.14/0.44 fresh20(fresh6(fresh20(true, true, add(additive_identity, additive_identity), b, additive_identity), true, add(additive_identity, additive_identity), add(a, b)), true, additive_identity, add(a, b), add(additive_identity, additive_identity))
% 0.14/0.44 = { by axiom 10 (compatibility_of_equality_and_order_relation) }
% 0.14/0.44 fresh20(fresh6(less_or_equal(add(additive_identity, additive_identity), b), true, add(additive_identity, additive_identity), add(a, b)), true, additive_identity, add(a, b), add(additive_identity, additive_identity))
% 0.14/0.44 = { by axiom 17 (transitivity_of_order_relation) R->L }
% 0.14/0.44 fresh20(fresh7(less_or_equal(b, add(a, b)), true, add(additive_identity, additive_identity), add(a, b), b), true, additive_identity, add(a, b), add(additive_identity, additive_identity))
% 0.14/0.44 = { by axiom 10 (compatibility_of_equality_and_order_relation) R->L }
% 0.14/0.44 fresh20(fresh7(fresh20(true, true, b, add(a, b), add(additive_identity, b)), true, add(additive_identity, additive_identity), add(a, b), b), true, additive_identity, add(a, b), add(additive_identity, additive_identity))
% 0.14/0.44 = { by axiom 12 (compatibility_of_order_relation_and_addition) R->L }
% 0.14/0.44 fresh20(fresh7(fresh20(fresh17(true, true, additive_identity, b, a), true, b, add(a, b), add(additive_identity, b)), true, add(additive_identity, additive_identity), add(a, b), b), true, additive_identity, add(a, b), add(additive_identity, additive_identity))
% 0.14/0.44 = { by axiom 2 (b_is_defined) R->L }
% 0.14/0.44 fresh20(fresh7(fresh20(fresh17(defined(b), true, additive_identity, b, a), true, b, add(a, b), add(additive_identity, b)), true, add(additive_identity, additive_identity), add(a, b), b), true, additive_identity, add(a, b), add(additive_identity, additive_identity))
% 0.14/0.44 = { by axiom 16 (compatibility_of_order_relation_and_addition) R->L }
% 0.14/0.44 fresh20(fresh7(fresh20(fresh18(less_or_equal(additive_identity, a), true, additive_identity, b, a), true, b, add(a, b), add(additive_identity, b)), true, add(additive_identity, additive_identity), add(a, b), b), true, additive_identity, add(a, b), add(additive_identity, additive_identity))
% 0.14/0.44 = { by axiom 3 (less_or_equal_3) }
% 0.14/0.44 fresh20(fresh7(fresh20(fresh18(true, true, additive_identity, b, a), true, b, add(a, b), add(additive_identity, b)), true, add(additive_identity, additive_identity), add(a, b), b), true, additive_identity, add(a, b), add(additive_identity, additive_identity))
% 0.14/0.44 = { by axiom 11 (compatibility_of_order_relation_and_addition) }
% 0.14/0.44 fresh20(fresh7(fresh20(less_or_equal(add(additive_identity, b), add(a, b)), true, b, add(a, b), add(additive_identity, b)), true, add(additive_identity, additive_identity), add(a, b), b), true, additive_identity, add(a, b), add(additive_identity, additive_identity))
% 0.14/0.44 = { by axiom 15 (compatibility_of_equality_and_order_relation) }
% 0.14/0.44 fresh20(fresh7(fresh19(equalish(add(additive_identity, b), b), true, b, add(a, b)), true, add(additive_identity, additive_identity), add(a, b), b), true, additive_identity, add(a, b), add(additive_identity, additive_identity))
% 0.14/0.44 = { by axiom 7 (existence_of_identity_addition) R->L }
% 0.14/0.44 fresh20(fresh7(fresh19(fresh14(defined(b), true, b), true, b, add(a, b)), true, add(additive_identity, additive_identity), add(a, b), b), true, additive_identity, add(a, b), add(additive_identity, additive_identity))
% 0.14/0.44 = { by axiom 2 (b_is_defined) }
% 0.14/0.44 fresh20(fresh7(fresh19(fresh14(true, true, b), true, b, add(a, b)), true, add(additive_identity, additive_identity), add(a, b), b), true, additive_identity, add(a, b), add(additive_identity, additive_identity))
% 0.14/0.44 = { by axiom 5 (existence_of_identity_addition) }
% 0.14/0.44 fresh20(fresh7(fresh19(true, true, b, add(a, b)), true, add(additive_identity, additive_identity), add(a, b), b), true, additive_identity, add(a, b), add(additive_identity, additive_identity))
% 0.14/0.44 = { by axiom 6 (compatibility_of_equality_and_order_relation) }
% 0.14/0.44 fresh20(fresh7(true, true, add(additive_identity, additive_identity), add(a, b), b), true, additive_identity, add(a, b), add(additive_identity, additive_identity))
% 0.14/0.44 = { by axiom 14 (transitivity_of_order_relation) }
% 0.14/0.44 fresh20(less_or_equal(add(additive_identity, additive_identity), add(a, b)), true, additive_identity, add(a, b), add(additive_identity, additive_identity))
% 0.14/0.44 = { by axiom 15 (compatibility_of_equality_and_order_relation) }
% 0.14/0.44 fresh19(equalish(add(additive_identity, additive_identity), additive_identity), true, additive_identity, add(a, b))
% 0.14/0.44 = { by lemma 18 }
% 0.14/0.44 fresh19(true, true, additive_identity, add(a, b))
% 0.14/0.44 = { by axiom 6 (compatibility_of_equality_and_order_relation) }
% 0.14/0.44 true
% 0.14/0.44 % SZS output end Proof
% 0.14/0.44
% 0.14/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------