TSTP Solution File: FLD065-1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : FLD065-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n022.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 May 31 12:07:07 EDT 2023
% Result : Unsatisfiable 9.28s 1.52s
% Output : CNFRefutation 9.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 26
% Syntax : Number of formulae : 98 ( 12 unt; 0 def)
% Number of atoms : 249 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 283 ( 132 ~; 141 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 11 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 97 (; 97 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] :
( equalish(add(X,Y),add(Y,X))
| ~ defined(X)
| ~ defined(Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] :
( defined(additive_inverse(X))
| ~ defined(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y] :
( equalish(X,Y)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,Z,Y] :
( less_or_equal(X,Z)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,Y] :
( less_or_equal(X,Y)
| less_or_equal(Y,X)
| ~ defined(X)
| ~ defined(Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,Z,Y] :
( less_or_equal(add(X,Z),add(Y,Z))
| ~ defined(Z)
| ~ less_or_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X] :
( equalish(X,X)
| ~ defined(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y] :
( equalish(X,Y)
| ~ equalish(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X,Z,Y] :
( equalish(X,Z)
| ~ equalish(X,Y)
| ~ equalish(Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [Y,Z,X] :
( less_or_equal(Y,Z)
| ~ less_or_equal(X,Z)
| ~ equalish(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
less_or_equal(additive_inverse(a),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ less_or_equal(additive_identity,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,plain,
! [X0] :
( equalish(add(additive_identity,X0),X0)
| ~ defined(X0) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f34,plain,
! [X0] :
( equalish(add(X0,additive_inverse(X0)),additive_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f35,plain,
! [Y] :
( ! [X] :
( equalish(add(X,Y),add(Y,X))
| ~ defined(X) )
| ~ defined(Y) ),
inference(miniscoping,[status(esa)],[f4]) ).
fof(f36,plain,
! [X0,X1] :
( equalish(add(X0,X1),add(X1,X0))
| ~ defined(X0)
| ~ defined(X1) ),
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f47,plain,
defined(additive_identity),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f48,plain,
! [X0] :
( defined(additive_inverse(X0))
| ~ defined(X0) ),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f53,plain,
! [X0,X1] :
( equalish(X0,X1)
| ~ less_or_equal(X0,X1)
| ~ less_or_equal(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f54,plain,
! [Z,Y] :
( ! [X] :
( less_or_equal(X,Z)
| ~ less_or_equal(X,Y) )
| ~ less_or_equal(Y,Z) ),
inference(miniscoping,[status(esa)],[f17]) ).
fof(f55,plain,
! [X0,X1,X2] :
( less_or_equal(X0,X1)
| ~ less_or_equal(X0,X2)
| ~ less_or_equal(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f56,plain,
! [Y] :
( ! [X] :
( less_or_equal(X,Y)
| less_or_equal(Y,X)
| ~ defined(X) )
| ~ defined(Y) ),
inference(miniscoping,[status(esa)],[f18]) ).
fof(f57,plain,
! [X0,X1] :
( less_or_equal(X0,X1)
| less_or_equal(X1,X0)
| ~ defined(X0)
| ~ defined(X1) ),
inference(cnf_transformation,[status(esa)],[f56]) ).
fof(f58,plain,
! [X,Y] :
( ! [Z] :
( less_or_equal(add(X,Z),add(Y,Z))
| ~ defined(Z) )
| ~ less_or_equal(X,Y) ),
inference(miniscoping,[status(esa)],[f19]) ).
fof(f59,plain,
! [X0,X1,X2] :
( less_or_equal(add(X0,X1),add(X2,X1))
| ~ defined(X1)
| ~ less_or_equal(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f58]) ).
fof(f62,plain,
! [X0] :
( equalish(X0,X0)
| ~ defined(X0) ),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f63,plain,
! [X0,X1] :
( equalish(X0,X1)
| ~ equalish(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f64,plain,
! [Z,Y] :
( ! [X] :
( equalish(X,Z)
| ~ equalish(X,Y) )
| ~ equalish(Y,Z) ),
inference(miniscoping,[status(esa)],[f23]) ).
fof(f65,plain,
! [X0,X1,X2] :
( equalish(X0,X1)
| ~ equalish(X0,X2)
| ~ equalish(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f64]) ).
fof(f70,plain,
! [Y,X] :
( ! [Z] :
( less_or_equal(Y,Z)
| ~ less_or_equal(X,Z) )
| ~ equalish(X,Y) ),
inference(miniscoping,[status(esa)],[f26]) ).
fof(f71,plain,
! [X0,X1,X2] :
( less_or_equal(X0,X1)
| ~ less_or_equal(X2,X1)
| ~ equalish(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f73,plain,
defined(a),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f74,plain,
less_or_equal(additive_inverse(a),additive_identity),
inference(cnf_transformation,[status(esa)],[f29]) ).
fof(f75,plain,
~ less_or_equal(additive_identity,a),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f85,plain,
! [X0] :
( less_or_equal(X0,additive_identity)
| ~ equalish(additive_inverse(a),X0) ),
inference(resolution,[status(thm)],[f71,f74]) ).
fof(f86,plain,
( spl0_2
<=> less_or_equal(a,additive_identity) ),
introduced(split_symbol_definition) ).
fof(f87,plain,
( less_or_equal(a,additive_identity)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f86]) ).
fof(f89,plain,
( spl0_3
<=> defined(a) ),
introduced(split_symbol_definition) ).
fof(f91,plain,
( ~ defined(a)
| spl0_3 ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,plain,
( spl0_4
<=> defined(additive_identity) ),
introduced(split_symbol_definition) ).
fof(f94,plain,
( ~ defined(additive_identity)
| spl0_4 ),
inference(component_clause,[status(thm)],[f92]) ).
fof(f95,plain,
( less_or_equal(a,additive_identity)
| ~ defined(a)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[f57,f75]) ).
fof(f96,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f95,f86,f89,f92]) ).
fof(f100,plain,
( spl0_6
<=> defined(additive_inverse(a)) ),
introduced(split_symbol_definition) ).
fof(f102,plain,
( ~ defined(additive_inverse(a))
| spl0_6 ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f106,plain,
! [X0,X1,X2] :
( less_or_equal(X0,X1)
| ~ defined(X0)
| ~ defined(X1)
| less_or_equal(X2,X0)
| ~ less_or_equal(X2,X1) ),
inference(resolution,[status(thm)],[f57,f55]) ).
fof(f107,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f94,f47]) ).
fof(f108,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f107]) ).
fof(f109,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f91,f73]) ).
fof(f110,plain,
spl0_3,
inference(contradiction_clause,[status(thm)],[f109]) ).
fof(f119,plain,
! [X0,X1,X2] :
( less_or_equal(X0,X1)
| ~ defined(X0)
| ~ defined(X1)
| less_or_equal(X2,X0)
| less_or_equal(X1,X2)
| ~ defined(X1)
| ~ defined(X2) ),
inference(resolution,[status(thm)],[f106,f57]) ).
fof(f120,plain,
! [X0,X1,X2] :
( less_or_equal(X0,X1)
| ~ defined(X0)
| ~ defined(X1)
| less_or_equal(X2,X0)
| less_or_equal(X1,X2)
| ~ defined(X2) ),
inference(duplicate_literals_removal,[status(esa)],[f119]) ).
fof(f129,plain,
( spl0_7
<=> less_or_equal(additive_inverse(a),additive_identity) ),
introduced(split_symbol_definition) ).
fof(f132,plain,
( ~ defined(additive_inverse(a))
| less_or_equal(additive_inverse(a),additive_identity) ),
inference(resolution,[status(thm)],[f62,f85]) ).
fof(f133,plain,
( ~ spl0_6
| spl0_7 ),
inference(split_clause,[status(thm)],[f132,f100,f129]) ).
fof(f136,plain,
! [X0] :
( equalish(X0,add(additive_identity,X0))
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f63,f33]) ).
fof(f139,plain,
! [X0,X1] :
( equalish(X0,X1)
| ~ equalish(X0,add(additive_identity,X1))
| ~ defined(X1) ),
inference(resolution,[status(thm)],[f65,f33]) ).
fof(f140,plain,
! [X0,X1] :
( equalish(X0,additive_identity)
| ~ equalish(X0,add(X1,additive_inverse(X1)))
| ~ defined(X1) ),
inference(resolution,[status(thm)],[f65,f34]) ).
fof(f212,plain,
! [X0] :
( less_or_equal(X0,additive_identity)
| ~ equalish(a,X0)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f87,f71]) ).
fof(f214,plain,
( spl0_15
<=> equalish(additive_identity,a) ),
introduced(split_symbol_definition) ).
fof(f215,plain,
( equalish(additive_identity,a)
| ~ spl0_15 ),
inference(component_clause,[status(thm)],[f214]) ).
fof(f217,plain,
( spl0_16
<=> less_or_equal(additive_identity,a) ),
introduced(split_symbol_definition) ).
fof(f218,plain,
( less_or_equal(additive_identity,a)
| ~ spl0_16 ),
inference(component_clause,[status(thm)],[f217]) ).
fof(f222,plain,
( ~ defined(a)
| spl0_6 ),
inference(resolution,[status(thm)],[f102,f48]) ).
fof(f223,plain,
( ~ spl0_3
| spl0_6 ),
inference(split_clause,[status(thm)],[f222,f89,f100]) ).
fof(f232,plain,
( spl0_18
<=> less_or_equal(add(additive_identity,a),additive_identity) ),
introduced(split_symbol_definition) ).
fof(f233,plain,
( less_or_equal(add(additive_identity,a),additive_identity)
| ~ spl0_18 ),
inference(component_clause,[status(thm)],[f232]) ).
fof(f235,plain,
( less_or_equal(add(additive_identity,a),additive_identity)
| ~ defined(a)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f212,f136]) ).
fof(f236,plain,
( spl0_18
| ~ spl0_3
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f235,f232,f89,f86]) ).
fof(f288,plain,
( spl0_25
<=> equalish(additive_identity,add(additive_identity,a)) ),
introduced(split_symbol_definition) ).
fof(f289,plain,
( equalish(additive_identity,add(additive_identity,a))
| ~ spl0_25 ),
inference(component_clause,[status(thm)],[f288]) ).
fof(f291,plain,
( spl0_26
<=> less_or_equal(additive_identity,add(additive_identity,a)) ),
introduced(split_symbol_definition) ).
fof(f293,plain,
( ~ less_or_equal(additive_identity,add(additive_identity,a))
| spl0_26 ),
inference(component_clause,[status(thm)],[f291]) ).
fof(f294,plain,
( equalish(additive_identity,add(additive_identity,a))
| ~ less_or_equal(additive_identity,add(additive_identity,a))
| ~ spl0_18 ),
inference(resolution,[status(thm)],[f233,f53]) ).
fof(f295,plain,
( spl0_25
| ~ spl0_26
| ~ spl0_18 ),
inference(split_clause,[status(thm)],[f294,f288,f291,f232]) ).
fof(f355,plain,
( equalish(a,additive_identity)
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f215,f63]) ).
fof(f393,plain,
( equalish(additive_identity,a)
| ~ defined(a)
| ~ spl0_25 ),
inference(resolution,[status(thm)],[f289,f139]) ).
fof(f394,plain,
( spl0_15
| ~ spl0_3
| ~ spl0_25 ),
inference(split_clause,[status(thm)],[f393,f214,f89,f288]) ).
fof(f583,plain,
! [X0] :
( equalish(add(additive_inverse(X0),X0),additive_identity)
| ~ defined(X0)
| ~ defined(additive_inverse(X0))
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f140,f36]) ).
fof(f584,plain,
! [X0] :
( equalish(add(additive_inverse(X0),X0),additive_identity)
| ~ defined(X0)
| ~ defined(additive_inverse(X0)) ),
inference(duplicate_literals_removal,[status(esa)],[f583]) ).
fof(f585,plain,
! [X0] :
( equalish(add(additive_inverse(X0),X0),additive_identity)
| ~ defined(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f584,f48]) ).
fof(f782,plain,
! [X0,X1,X2,X3] :
( ~ defined(X0)
| ~ less_or_equal(X1,X2)
| less_or_equal(X3,add(X2,X0))
| ~ equalish(add(X1,X0),X3) ),
inference(resolution,[status(thm)],[f59,f71]) ).
fof(f1186,plain,
! [X0,X1] :
( ~ defined(X0)
| ~ less_or_equal(additive_inverse(X0),X1)
| less_or_equal(additive_identity,add(X1,X0))
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f782,f585]) ).
fof(f1187,plain,
! [X0,X1] :
( ~ defined(X0)
| ~ less_or_equal(additive_inverse(X0),X1)
| less_or_equal(additive_identity,add(X1,X0)) ),
inference(duplicate_literals_removal,[status(esa)],[f1186]) ).
fof(f2429,plain,
( ~ defined(a)
| ~ less_or_equal(additive_inverse(a),additive_identity)
| spl0_26 ),
inference(resolution,[status(thm)],[f1187,f293]) ).
fof(f2430,plain,
( ~ spl0_3
| ~ spl0_7
| spl0_26 ),
inference(split_clause,[status(thm)],[f2429,f89,f129,f291]) ).
fof(f5597,plain,
! [X0,X1] :
( less_or_equal(X0,X0)
| ~ defined(X0)
| ~ defined(X0)
| ~ defined(X0)
| less_or_equal(X1,X0)
| ~ equalish(X0,X1) ),
inference(resolution,[status(thm)],[f120,f71]) ).
fof(f5598,plain,
! [X0,X1] :
( less_or_equal(X0,X0)
| ~ defined(X0)
| less_or_equal(X1,X0)
| ~ equalish(X0,X1) ),
inference(duplicate_literals_removal,[status(esa)],[f5597]) ).
fof(f5599,plain,
! [X0,X1] :
( ~ defined(X0)
| less_or_equal(X1,X0)
| ~ equalish(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f5598,f71]) ).
fof(f5699,plain,
( ~ defined(a)
| less_or_equal(additive_identity,a)
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f5599,f355]) ).
fof(f5700,plain,
( ~ spl0_3
| spl0_16
| ~ spl0_15 ),
inference(split_clause,[status(thm)],[f5699,f89,f217,f214]) ).
fof(f5839,plain,
( $false
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[status(thm)],[f218,f75]) ).
fof(f5840,plain,
~ spl0_16,
inference(contradiction_clause,[status(thm)],[f5839]) ).
fof(f5841,plain,
$false,
inference(sat_refutation,[status(thm)],[f96,f108,f110,f133,f223,f236,f295,f394,f2430,f5700,f5840]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : FLD065-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.06/0.25 % Computer : n022.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Tue May 30 11:00:42 EDT 2023
% 0.06/0.25 % CPUTime :
% 0.06/0.25 % Drodi V3.5.1
% 9.28/1.52 % Refutation found
% 9.28/1.52 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 9.28/1.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.50/1.55 % Elapsed time: 1.290752 seconds
% 9.50/1.55 % CPU time: 9.482514 seconds
% 9.50/1.55 % Memory used: 48.635 MB
%------------------------------------------------------------------------------