TSTP Solution File: FLD059-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : FLD059-1 : 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 : n019.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 22:37:07 EDT 2023
% Result : Unsatisfiable 0.20s 0.47s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : FLD059-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Aug 27 23:39:13 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.20/0.47 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.20/0.47
% 0.20/0.47 % SZS status Unsatisfiable
% 0.20/0.47
% 0.20/0.47 % SZS output start Proof
% 0.20/0.47 Take the following subset of the input axioms:
% 0.20/0.48 fof(a_is_defined, hypothesis, defined(a)).
% 0.20/0.48 fof(compatibility_of_equality_and_order_relation, axiom, ![X, Y, Z]: (less_or_equal(Y, Z) | (~less_or_equal(X, Z) | ~equalish(X, Y)))).
% 0.20/0.48 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)))).
% 0.20/0.48 fof(existence_of_identity_addition, axiom, ![X2]: (equalish(add(additive_identity, X2), X2) | ~defined(X2))).
% 0.20/0.48 fof(less_or_equal_2, negated_conjecture, less_or_equal(additive_identity, a)).
% 0.20/0.48 fof(not_less_or_equal_3, negated_conjecture, ~less_or_equal(additive_identity, add(a, a))).
% 0.20/0.48 fof(symmetry_of_equality, axiom, ![X2, Y2]: (equalish(X2, Y2) | ~equalish(Y2, X2))).
% 0.20/0.48 fof(transitivity_of_order_relation, axiom, ![X2, Y2, Z2]: (less_or_equal(X2, Z2) | (~less_or_equal(X2, Y2) | ~less_or_equal(Y2, Z2)))).
% 0.20/0.48 fof(well_definedness_of_additive_identity, axiom, defined(additive_identity)).
% 0.20/0.48
% 0.20/0.48 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.48 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.48 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.48 fresh(y, y, x1...xn) = u
% 0.20/0.48 C => fresh(s, t, x1...xn) = v
% 0.20/0.48 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.48 variables of u and v.
% 0.20/0.48 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.48 input problem has no model of domain size 1).
% 0.20/0.48
% 0.20/0.48 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.48
% 0.20/0.48 Axiom 1 (well_definedness_of_additive_identity): defined(additive_identity) = true.
% 0.20/0.48 Axiom 2 (a_is_defined): defined(a) = true.
% 0.20/0.48 Axiom 3 (less_or_equal_2): less_or_equal(additive_identity, a) = true.
% 0.20/0.48 Axiom 4 (existence_of_identity_addition): fresh14(X, X, Y) = true.
% 0.20/0.48 Axiom 5 (compatibility_of_equality_and_order_relation): fresh19(X, X, Y, Z) = true.
% 0.20/0.48 Axiom 6 (existence_of_identity_addition): fresh14(defined(X), true, X) = equalish(add(additive_identity, X), X).
% 0.20/0.48 Axiom 7 (symmetry_of_equality): fresh10(X, X, Y, Z) = true.
% 0.20/0.48 Axiom 8 (transitivity_of_order_relation): fresh6(X, X, Y, Z) = true.
% 0.20/0.48 Axiom 9 (compatibility_of_equality_and_order_relation): fresh20(X, X, Y, Z, W) = less_or_equal(Y, Z).
% 0.20/0.48 Axiom 10 (compatibility_of_order_relation_and_addition): fresh18(X, X, Y, Z, W) = less_or_equal(add(Y, Z), add(W, Z)).
% 0.20/0.48 Axiom 11 (compatibility_of_order_relation_and_addition): fresh17(X, X, Y, Z, W) = true.
% 0.20/0.48 Axiom 12 (symmetry_of_equality): fresh10(equalish(X, Y), true, Y, X) = equalish(Y, X).
% 0.20/0.48 Axiom 13 (transitivity_of_order_relation): fresh7(X, X, Y, Z, W) = less_or_equal(Y, Z).
% 0.20/0.48 Axiom 14 (compatibility_of_equality_and_order_relation): fresh20(less_or_equal(X, Y), true, Z, Y, X) = fresh19(equalish(X, Z), true, Z, Y).
% 0.20/0.48 Axiom 15 (compatibility_of_order_relation_and_addition): fresh18(less_or_equal(X, Y), true, X, Z, Y) = fresh17(defined(Z), true, X, Z, Y).
% 0.20/0.48 Axiom 16 (transitivity_of_order_relation): fresh7(less_or_equal(X, Y), true, Z, Y, X) = fresh6(less_or_equal(Z, X), true, Z, Y).
% 0.20/0.48
% 0.20/0.48 Lemma 17: equalish(add(additive_identity, additive_identity), additive_identity) = true.
% 0.20/0.48 Proof:
% 0.20/0.48 equalish(add(additive_identity, additive_identity), additive_identity)
% 0.20/0.48 = { by axiom 6 (existence_of_identity_addition) R->L }
% 0.20/0.48 fresh14(defined(additive_identity), true, additive_identity)
% 0.20/0.48 = { by axiom 1 (well_definedness_of_additive_identity) }
% 0.20/0.48 fresh14(true, true, additive_identity)
% 0.20/0.48 = { by axiom 4 (existence_of_identity_addition) }
% 0.20/0.48 true
% 0.20/0.48
% 0.20/0.48 Goal 1 (not_less_or_equal_3): less_or_equal(additive_identity, add(a, a)) = true.
% 0.20/0.48 Proof:
% 0.20/0.48 less_or_equal(additive_identity, add(a, a))
% 0.20/0.48 = { by axiom 9 (compatibility_of_equality_and_order_relation) R->L }
% 0.20/0.48 fresh20(true, true, additive_identity, add(a, a), add(additive_identity, additive_identity))
% 0.20/0.48 = { by axiom 8 (transitivity_of_order_relation) R->L }
% 0.20/0.48 fresh20(fresh6(true, true, add(additive_identity, additive_identity), add(a, a)), true, additive_identity, add(a, a), add(additive_identity, additive_identity))
% 0.20/0.48 = { by axiom 5 (compatibility_of_equality_and_order_relation) R->L }
% 0.20/0.48 fresh20(fresh6(fresh19(true, true, add(additive_identity, additive_identity), a), true, add(additive_identity, additive_identity), add(a, a)), true, additive_identity, add(a, a), add(additive_identity, additive_identity))
% 0.20/0.48 = { by axiom 7 (symmetry_of_equality) R->L }
% 0.20/0.48 fresh20(fresh6(fresh19(fresh10(true, true, additive_identity, add(additive_identity, additive_identity)), true, add(additive_identity, additive_identity), a), true, add(additive_identity, additive_identity), add(a, a)), true, additive_identity, add(a, a), add(additive_identity, additive_identity))
% 0.20/0.48 = { by lemma 17 R->L }
% 0.20/0.48 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), a), true, add(additive_identity, additive_identity), add(a, a)), true, additive_identity, add(a, a), add(additive_identity, additive_identity))
% 0.20/0.48 = { by axiom 12 (symmetry_of_equality) }
% 0.20/0.48 fresh20(fresh6(fresh19(equalish(additive_identity, add(additive_identity, additive_identity)), true, add(additive_identity, additive_identity), a), true, add(additive_identity, additive_identity), add(a, a)), true, additive_identity, add(a, a), add(additive_identity, additive_identity))
% 0.20/0.48 = { by axiom 14 (compatibility_of_equality_and_order_relation) R->L }
% 0.20/0.48 fresh20(fresh6(fresh20(less_or_equal(additive_identity, a), true, add(additive_identity, additive_identity), a, additive_identity), true, add(additive_identity, additive_identity), add(a, a)), true, additive_identity, add(a, a), add(additive_identity, additive_identity))
% 0.20/0.48 = { by axiom 3 (less_or_equal_2) }
% 0.20/0.48 fresh20(fresh6(fresh20(true, true, add(additive_identity, additive_identity), a, additive_identity), true, add(additive_identity, additive_identity), add(a, a)), true, additive_identity, add(a, a), add(additive_identity, additive_identity))
% 0.20/0.48 = { by axiom 9 (compatibility_of_equality_and_order_relation) }
% 0.20/0.48 fresh20(fresh6(less_or_equal(add(additive_identity, additive_identity), a), true, add(additive_identity, additive_identity), add(a, a)), true, additive_identity, add(a, a), add(additive_identity, additive_identity))
% 0.20/0.48 = { by axiom 16 (transitivity_of_order_relation) R->L }
% 0.20/0.48 fresh20(fresh7(less_or_equal(a, add(a, a)), true, add(additive_identity, additive_identity), add(a, a), a), true, additive_identity, add(a, a), add(additive_identity, additive_identity))
% 0.20/0.48 = { by axiom 9 (compatibility_of_equality_and_order_relation) R->L }
% 0.20/0.48 fresh20(fresh7(fresh20(true, true, a, add(a, a), add(additive_identity, a)), true, add(additive_identity, additive_identity), add(a, a), a), true, additive_identity, add(a, a), add(additive_identity, additive_identity))
% 0.20/0.48 = { by axiom 11 (compatibility_of_order_relation_and_addition) R->L }
% 0.20/0.48 fresh20(fresh7(fresh20(fresh17(true, true, additive_identity, a, a), true, a, add(a, a), add(additive_identity, a)), true, add(additive_identity, additive_identity), add(a, a), a), true, additive_identity, add(a, a), add(additive_identity, additive_identity))
% 0.20/0.48 = { by axiom 2 (a_is_defined) R->L }
% 0.20/0.48 fresh20(fresh7(fresh20(fresh17(defined(a), true, additive_identity, a, a), true, a, add(a, a), add(additive_identity, a)), true, add(additive_identity, additive_identity), add(a, a), a), true, additive_identity, add(a, a), add(additive_identity, additive_identity))
% 0.20/0.48 = { by axiom 15 (compatibility_of_order_relation_and_addition) R->L }
% 0.20/0.48 fresh20(fresh7(fresh20(fresh18(less_or_equal(additive_identity, a), true, additive_identity, a, a), true, a, add(a, a), add(additive_identity, a)), true, add(additive_identity, additive_identity), add(a, a), a), true, additive_identity, add(a, a), add(additive_identity, additive_identity))
% 0.20/0.48 = { by axiom 3 (less_or_equal_2) }
% 0.20/0.48 fresh20(fresh7(fresh20(fresh18(true, true, additive_identity, a, a), true, a, add(a, a), add(additive_identity, a)), true, add(additive_identity, additive_identity), add(a, a), a), true, additive_identity, add(a, a), add(additive_identity, additive_identity))
% 0.20/0.48 = { by axiom 10 (compatibility_of_order_relation_and_addition) }
% 0.20/0.48 fresh20(fresh7(fresh20(less_or_equal(add(additive_identity, a), add(a, a)), true, a, add(a, a), add(additive_identity, a)), true, add(additive_identity, additive_identity), add(a, a), a), true, additive_identity, add(a, a), add(additive_identity, additive_identity))
% 0.20/0.48 = { by axiom 14 (compatibility_of_equality_and_order_relation) }
% 0.20/0.48 fresh20(fresh7(fresh19(equalish(add(additive_identity, a), a), true, a, add(a, a)), true, add(additive_identity, additive_identity), add(a, a), a), true, additive_identity, add(a, a), add(additive_identity, additive_identity))
% 0.20/0.48 = { by axiom 6 (existence_of_identity_addition) R->L }
% 0.20/0.48 fresh20(fresh7(fresh19(fresh14(defined(a), true, a), true, a, add(a, a)), true, add(additive_identity, additive_identity), add(a, a), a), true, additive_identity, add(a, a), add(additive_identity, additive_identity))
% 0.20/0.48 = { by axiom 2 (a_is_defined) }
% 0.20/0.48 fresh20(fresh7(fresh19(fresh14(true, true, a), true, a, add(a, a)), true, add(additive_identity, additive_identity), add(a, a), a), true, additive_identity, add(a, a), add(additive_identity, additive_identity))
% 0.20/0.48 = { by axiom 4 (existence_of_identity_addition) }
% 0.20/0.48 fresh20(fresh7(fresh19(true, true, a, add(a, a)), true, add(additive_identity, additive_identity), add(a, a), a), true, additive_identity, add(a, a), add(additive_identity, additive_identity))
% 0.20/0.48 = { by axiom 5 (compatibility_of_equality_and_order_relation) }
% 0.20/0.48 fresh20(fresh7(true, true, add(additive_identity, additive_identity), add(a, a), a), true, additive_identity, add(a, a), add(additive_identity, additive_identity))
% 0.20/0.48 = { by axiom 13 (transitivity_of_order_relation) }
% 0.20/0.48 fresh20(less_or_equal(add(additive_identity, additive_identity), add(a, a)), true, additive_identity, add(a, a), add(additive_identity, additive_identity))
% 0.20/0.48 = { by axiom 14 (compatibility_of_equality_and_order_relation) }
% 0.20/0.48 fresh19(equalish(add(additive_identity, additive_identity), additive_identity), true, additive_identity, add(a, a))
% 0.20/0.48 = { by lemma 17 }
% 0.20/0.48 fresh19(true, true, additive_identity, add(a, a))
% 0.20/0.48 = { by axiom 5 (compatibility_of_equality_and_order_relation) }
% 0.20/0.48 true
% 0.20/0.48 % SZS output end Proof
% 0.20/0.48
% 0.20/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
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