TSTP Solution File: FLD067-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : FLD067-1 : 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 22:37:10 EDT 2023
% Result : Unsatisfiable 0.20s 0.52s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD067-1 : 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
% 0.15/0.34 % Computer : n026.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Mon Aug 28 00:58:49 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.20/0.52 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.20/0.52
% 0.20/0.52 % SZS status Unsatisfiable
% 0.20/0.52
% 0.20/0.52 % SZS output start Proof
% 0.20/0.52 Take the following subset of the input axioms:
% 0.20/0.52 fof(a_is_defined, hypothesis, defined(a)).
% 0.20/0.52 fof(compatibility_of_equality_and_order_relation, axiom, ![X, Y, Z]: (less_or_equal(Y, Z) | (~less_or_equal(X, Z) | ~equalish(X, Y)))).
% 0.20/0.52 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)))).
% 0.20/0.52 fof(existence_of_inverse_addition, axiom, ![X2]: (equalish(add(X2, additive_inverse(X2)), additive_identity) | ~defined(X2))).
% 0.20/0.52 fof(less_or_equal_3, negated_conjecture, less_or_equal(a, b)).
% 0.20/0.52 fof(not_less_or_equal_4, negated_conjecture, ~less_or_equal(additive_identity, add(b, additive_inverse(a)))).
% 0.20/0.52 fof(well_definedness_of_additive_inverse, axiom, ![X2]: (defined(additive_inverse(X2)) | ~defined(X2))).
% 0.20/0.52
% 0.20/0.52 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.52 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.52 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.52 fresh(y, y, x1...xn) = u
% 0.20/0.52 C => fresh(s, t, x1...xn) = v
% 0.20/0.52 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.52 variables of u and v.
% 0.20/0.52 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.52 input problem has no model of domain size 1).
% 0.20/0.52
% 0.20/0.52 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.52
% 0.20/0.52 Axiom 1 (a_is_defined): defined(a) = true.
% 0.20/0.52 Axiom 2 (less_or_equal_3): less_or_equal(a, b) = true.
% 0.20/0.52 Axiom 3 (existence_of_inverse_addition): fresh12(X, X, Y) = true.
% 0.20/0.52 Axiom 4 (well_definedness_of_additive_inverse): fresh3(X, X, Y) = true.
% 0.20/0.52 Axiom 5 (compatibility_of_equality_and_order_relation): fresh19(X, X, Y, Z) = true.
% 0.20/0.52 Axiom 6 (existence_of_inverse_addition): fresh12(defined(X), true, X) = equalish(add(X, additive_inverse(X)), additive_identity).
% 0.20/0.52 Axiom 7 (well_definedness_of_additive_inverse): fresh3(defined(X), true, X) = defined(additive_inverse(X)).
% 0.20/0.52 Axiom 8 (compatibility_of_equality_and_order_relation): fresh20(X, X, Y, Z, W) = less_or_equal(Y, Z).
% 0.20/0.52 Axiom 9 (compatibility_of_order_relation_and_addition): fresh18(X, X, Y, Z, W) = less_or_equal(add(Y, Z), add(W, Z)).
% 0.20/0.52 Axiom 10 (compatibility_of_order_relation_and_addition): fresh17(X, X, Y, Z, W) = true.
% 0.20/0.52 Axiom 11 (compatibility_of_equality_and_order_relation): fresh20(less_or_equal(X, Y), true, Z, Y, X) = fresh19(equalish(X, Z), true, Z, Y).
% 0.20/0.52 Axiom 12 (compatibility_of_order_relation_and_addition): fresh18(less_or_equal(X, Y), true, X, Z, Y) = fresh17(defined(Z), true, X, Z, Y).
% 0.20/0.52
% 0.20/0.52 Goal 1 (not_less_or_equal_4): less_or_equal(additive_identity, add(b, additive_inverse(a))) = true.
% 0.20/0.52 Proof:
% 0.20/0.52 less_or_equal(additive_identity, add(b, additive_inverse(a)))
% 0.20/0.52 = { by axiom 8 (compatibility_of_equality_and_order_relation) R->L }
% 0.20/0.52 fresh20(true, true, additive_identity, add(b, additive_inverse(a)), add(a, additive_inverse(a)))
% 0.20/0.52 = { by axiom 10 (compatibility_of_order_relation_and_addition) R->L }
% 0.20/0.52 fresh20(fresh17(true, true, a, additive_inverse(a), b), true, additive_identity, add(b, additive_inverse(a)), add(a, additive_inverse(a)))
% 0.20/0.52 = { by axiom 4 (well_definedness_of_additive_inverse) R->L }
% 0.20/0.52 fresh20(fresh17(fresh3(true, true, a), true, a, additive_inverse(a), b), true, additive_identity, add(b, additive_inverse(a)), add(a, additive_inverse(a)))
% 0.20/0.52 = { by axiom 1 (a_is_defined) R->L }
% 0.20/0.52 fresh20(fresh17(fresh3(defined(a), true, a), true, a, additive_inverse(a), b), true, additive_identity, add(b, additive_inverse(a)), add(a, additive_inverse(a)))
% 0.20/0.52 = { by axiom 7 (well_definedness_of_additive_inverse) }
% 0.20/0.52 fresh20(fresh17(defined(additive_inverse(a)), true, a, additive_inverse(a), b), true, additive_identity, add(b, additive_inverse(a)), add(a, additive_inverse(a)))
% 0.20/0.52 = { by axiom 12 (compatibility_of_order_relation_and_addition) R->L }
% 0.20/0.52 fresh20(fresh18(less_or_equal(a, b), true, a, additive_inverse(a), b), true, additive_identity, add(b, additive_inverse(a)), add(a, additive_inverse(a)))
% 0.20/0.52 = { by axiom 2 (less_or_equal_3) }
% 0.20/0.52 fresh20(fresh18(true, true, a, additive_inverse(a), b), true, additive_identity, add(b, additive_inverse(a)), add(a, additive_inverse(a)))
% 0.20/0.52 = { by axiom 9 (compatibility_of_order_relation_and_addition) }
% 0.20/0.53 fresh20(less_or_equal(add(a, additive_inverse(a)), add(b, additive_inverse(a))), true, additive_identity, add(b, additive_inverse(a)), add(a, additive_inverse(a)))
% 0.20/0.53 = { by axiom 11 (compatibility_of_equality_and_order_relation) }
% 0.20/0.53 fresh19(equalish(add(a, additive_inverse(a)), additive_identity), true, additive_identity, add(b, additive_inverse(a)))
% 0.20/0.53 = { by axiom 6 (existence_of_inverse_addition) R->L }
% 0.20/0.53 fresh19(fresh12(defined(a), true, a), true, additive_identity, add(b, additive_inverse(a)))
% 0.20/0.53 = { by axiom 1 (a_is_defined) }
% 0.20/0.53 fresh19(fresh12(true, true, a), true, additive_identity, add(b, additive_inverse(a)))
% 0.20/0.53 = { by axiom 3 (existence_of_inverse_addition) }
% 0.20/0.53 fresh19(true, true, additive_identity, add(b, additive_inverse(a)))
% 0.20/0.53 = { by axiom 5 (compatibility_of_equality_and_order_relation) }
% 0.20/0.53 true
% 0.20/0.53 % SZS output end Proof
% 0.20/0.53
% 0.20/0.53 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------