TSTP Solution File: SET012-3 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET012-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n013.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 12:33:30 EDT 2023
% Result : Unsatisfiable 6.52s 1.26s
% Output : CNFRefutation 6.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 19
% Syntax : Number of formulae : 66 ( 15 unt; 0 def)
% Number of atoms : 128 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 112 ( 50 ~; 56 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 7 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 42 (; 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( ~ member(X,Y)
| little_set(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( little_set(f1(X,Y))
| X = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( member(f1(X,Y),X)
| member(f1(X,Y),Y)
| X = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] :
( ~ member(f1(X,Y),X)
| ~ member(f1(X,Y),Y)
| X = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [Z,X] :
( ~ member(Z,complement(X))
| ~ member(Z,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [Z,X] :
( member(Z,complement(X))
| ~ little_set(Z)
| member(Z,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f86,axiom,
! [Xf] :
( ~ function(Xf)
| relation(Xf) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f87,axiom,
! [Xf] :
( ~ function(Xf)
| single_valued_set(Xf) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f88,axiom,
! [Xf] :
( function(Xf)
| ~ relation(Xf)
| ~ single_valued_set(Xf) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f100,axiom,
function(f25),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f142,hypothesis,
complement(as) = bs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f143,hypothesis,
complement(bs) = cs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f144,negated_conjecture,
as != cs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f145,plain,
! [X] :
( ! [Y] : ~ member(X,Y)
| little_set(X) ),
inference(miniscoping,[status(esa)],[f1]) ).
fof(f146,plain,
! [X0,X1] :
( ~ member(X0,X1)
| little_set(X0) ),
inference(cnf_transformation,[status(esa)],[f145]) ).
fof(f147,plain,
! [X0,X1] :
( little_set(f1(X0,X1))
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f148,plain,
! [X0,X1] :
( member(f1(X0,X1),X0)
| member(f1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f149,plain,
! [X0,X1] :
( ~ member(f1(X0,X1),X0)
| ~ member(f1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f184,plain,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f185,plain,
! [X0,X1] :
( member(X0,complement(X1))
| ~ little_set(X0)
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f251,plain,
! [X0] :
( ~ function(X0)
| relation(X0) ),
inference(cnf_transformation,[status(esa)],[f86]) ).
fof(f252,plain,
! [X0] :
( ~ function(X0)
| single_valued_set(X0) ),
inference(cnf_transformation,[status(esa)],[f87]) ).
fof(f253,plain,
! [X0] :
( function(X0)
| ~ relation(X0)
| ~ single_valued_set(X0) ),
inference(cnf_transformation,[status(esa)],[f88]) ).
fof(f267,plain,
function(f25),
inference(cnf_transformation,[status(esa)],[f100]) ).
fof(f322,plain,
complement(as) = bs,
inference(cnf_transformation,[status(esa)],[f142]) ).
fof(f323,plain,
complement(bs) = cs,
inference(cnf_transformation,[status(esa)],[f143]) ).
fof(f324,plain,
as != cs,
inference(cnf_transformation,[status(esa)],[f144]) ).
fof(f328,plain,
relation(f25),
inference(resolution,[status(thm)],[f251,f267]) ).
fof(f329,plain,
single_valued_set(f25),
inference(resolution,[status(thm)],[f252,f267]) ).
fof(f336,plain,
little_set(f1(as,cs)),
inference(resolution,[status(thm)],[f147,f324]) ).
fof(f354,plain,
( spl0_0
<=> function(f25) ),
introduced(split_symbol_definition) ).
fof(f357,plain,
( spl0_1
<=> single_valued_set(f25) ),
introduced(split_symbol_definition) ).
fof(f359,plain,
( ~ single_valued_set(f25)
| spl0_1 ),
inference(component_clause,[status(thm)],[f357]) ).
fof(f366,plain,
( spl0_2
<=> relation(f25) ),
introduced(split_symbol_definition) ).
fof(f368,plain,
( ~ relation(f25)
| spl0_2 ),
inference(component_clause,[status(thm)],[f366]) ).
fof(f369,plain,
( function(f25)
| ~ relation(f25) ),
inference(resolution,[status(thm)],[f253,f329]) ).
fof(f370,plain,
( spl0_0
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f369,f354,f366]) ).
fof(f373,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f368,f328]) ).
fof(f374,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f373]) ).
fof(f382,plain,
! [X0] :
( ~ member(X0,bs)
| ~ member(X0,as) ),
inference(paramodulation,[status(thm)],[f322,f184]) ).
fof(f437,plain,
( spl0_3
<=> member(f1(as,cs),as) ),
introduced(split_symbol_definition) ).
fof(f440,plain,
( spl0_4
<=> member(f1(as,cs),cs) ),
introduced(split_symbol_definition) ).
fof(f441,plain,
( member(f1(as,cs),cs)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f442,plain,
( ~ member(f1(as,cs),cs)
| spl0_4 ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f443,plain,
( member(f1(as,cs),as)
| member(f1(as,cs),cs) ),
inference(resolution,[status(thm)],[f148,f324]) ).
fof(f444,plain,
( spl0_3
| spl0_4 ),
inference(split_clause,[status(thm)],[f443,f437,f440]) ).
fof(f463,plain,
( ~ member(f1(as,cs),as)
| ~ member(f1(as,cs),cs) ),
inference(resolution,[status(thm)],[f149,f324]) ).
fof(f464,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f463,f437,f440]) ).
fof(f1432,plain,
! [X0,X1] :
( ~ little_set(X0)
| member(X0,X1)
| ~ member(X0,complement(complement(X1))) ),
inference(resolution,[status(thm)],[f185,f184]) ).
fof(f1433,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(X0,complement(complement(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[f1432,f146]) ).
fof(f1499,plain,
( spl0_67
<=> little_set(f1(as,cs)) ),
introduced(split_symbol_definition) ).
fof(f1501,plain,
( ~ little_set(f1(as,cs))
| spl0_67 ),
inference(component_clause,[status(thm)],[f1499]) ).
fof(f1529,plain,
! [X0] :
( member(X0,complement(bs))
| ~ little_set(X0)
| ~ member(X0,as) ),
inference(resolution,[status(thm)],[f185,f382]) ).
fof(f1530,plain,
! [X0] :
( member(X0,cs)
| ~ little_set(X0)
| ~ member(X0,as) ),
inference(forward_demodulation,[status(thm)],[f323,f1529]) ).
fof(f1531,plain,
! [X0] :
( member(X0,cs)
| ~ member(X0,as) ),
inference(forward_subsumption_resolution,[status(thm)],[f1530,f146]) ).
fof(f1558,plain,
( $false
| spl0_67 ),
inference(forward_subsumption_resolution,[status(thm)],[f1501,f336]) ).
fof(f1559,plain,
spl0_67,
inference(contradiction_clause,[status(thm)],[f1558]) ).
fof(f1567,plain,
( ~ member(f1(as,cs),as)
| spl0_4 ),
inference(resolution,[status(thm)],[f1531,f442]) ).
fof(f1568,plain,
( ~ spl0_3
| spl0_4 ),
inference(split_clause,[status(thm)],[f1567,f437,f440]) ).
fof(f1688,plain,
! [X0] :
( member(X0,as)
| ~ member(X0,complement(bs)) ),
inference(paramodulation,[status(thm)],[f322,f1433]) ).
fof(f1689,plain,
! [X0] :
( member(X0,as)
| ~ member(X0,cs) ),
inference(forward_demodulation,[status(thm)],[f323,f1688]) ).
fof(f2974,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f359,f329]) ).
fof(f2975,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f2974]) ).
fof(f3114,plain,
( member(f1(as,cs),as)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f1689,f441]) ).
fof(f3115,plain,
( spl0_3
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f3114,f437,f440]) ).
fof(f3142,plain,
$false,
inference(sat_refutation,[status(thm)],[f370,f374,f444,f464,f1559,f1568,f2975,f3115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET012-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32 % Computer : n013.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Tue May 30 10:12:50 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.10/0.33 % Drodi V3.5.1
% 6.52/1.26 % Refutation found
% 6.52/1.26 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 6.52/1.26 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 6.52/1.29 % Elapsed time: 0.954165 seconds
% 6.52/1.29 % CPU time: 6.668384 seconds
% 6.52/1.29 % Memory used: 139.059 MB
%------------------------------------------------------------------------------