TSTP Solution File: SET068-7 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET068-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n027.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 : Tue Apr 30 20:38:57 EDT 2024
% Result : Unsatisfiable 0.20s 0.37s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 54 ( 16 unt; 0 def)
% Number of atoms : 102 ( 25 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 83 ( 35 ~; 46 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 70 ( 70 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,U] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( member(not_subclass_element(X,Y),X)
| subclass(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] :
( X != Y
| subclass(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [U,X,Y] :
( ~ member(U,unordered_pair(X,Y))
| U = X
| U = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66,axiom,
! [X] :
( X = null_class
| member(regular(X),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f104,axiom,
! [X] : subclass(null_class,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f108,axiom,
! [X,Y] : unordered_pair(X,Y) = unordered_pair(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f109,negated_conjecture,
~ subclass(singleton(y),unordered_pair(x,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f110,plain,
! [Y,U] :
( ! [X] :
( ~ subclass(X,Y)
| ~ member(U,X) )
| member(U,Y) ),
inference(miniscoping,[status(esa)],[f1]) ).
fof(f111,plain,
! [X0,X1,X2] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f110]) ).
fof(f112,plain,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f113,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f114,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f115,plain,
! [X0,X1] :
( X0 != X1
| subclass(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f118,plain,
! [U,Y] :
( ! [X] :
( ~ member(U,unordered_pair(X,Y))
| U = X )
| U = Y ),
inference(miniscoping,[status(esa)],[f8]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[status(esa)],[f118]) ).
fof(f120,plain,
! [X] :
( ~ member(X,universal_class)
| ! [Y] : member(X,unordered_pair(X,Y)) ),
inference(miniscoping,[status(esa)],[f9]) ).
fof(f121,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f120]) ).
fof(f125,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f184,plain,
! [X0] :
( X0 = null_class
| member(regular(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f66]) ).
fof(f232,plain,
! [X0] : subclass(null_class,X0),
inference(cnf_transformation,[status(esa)],[f104]) ).
fof(f236,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(esa)],[f108]) ).
fof(f237,plain,
~ subclass(singleton(y),unordered_pair(x,y)),
inference(cnf_transformation,[status(esa)],[f109]) ).
fof(f238,plain,
! [X0] : subclass(X0,X0),
inference(destructive_equality_resolution,[status(esa)],[f115]) ).
fof(f242,plain,
~ subclass(singleton(y),unordered_pair(y,x)),
inference(paramodulation,[status(thm)],[f236,f237]) ).
fof(f250,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f125,f119]) ).
fof(f251,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(duplicate_literals_removal,[status(esa)],[f250]) ).
fof(f255,plain,
! [X0,X1,X2] :
( member(X0,unordered_pair(X0,X1))
| ~ subclass(X2,universal_class)
| ~ member(X0,X2) ),
inference(resolution,[status(thm)],[f121,f111]) ).
fof(f256,plain,
! [X0,X1,X2] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f255,f114]) ).
fof(f282,plain,
! [X0,X1] :
( subclass(singleton(X0),X1)
| not_subclass_element(singleton(X0),X1) = X0 ),
inference(resolution,[status(thm)],[f112,f251]) ).
fof(f286,plain,
! [X0,X1,X2] :
( subclass(X0,X1)
| ~ subclass(X2,X1)
| ~ member(not_subclass_element(X0,X1),X2) ),
inference(resolution,[status(thm)],[f113,f111]) ).
fof(f447,plain,
! [X0] :
( singleton(X0) = null_class
| regular(singleton(X0)) = X0 ),
inference(resolution,[status(thm)],[f184,f251]) ).
fof(f638,plain,
! [X0] :
( singleton(X0) = null_class
| member(X0,singleton(X0))
| singleton(X0) = null_class ),
inference(paramodulation,[status(thm)],[f447,f184]) ).
fof(f639,plain,
! [X0] :
( singleton(X0) = null_class
| member(X0,singleton(X0)) ),
inference(duplicate_literals_removal,[status(esa)],[f638]) ).
fof(f682,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(resolution,[status(thm)],[f286,f238]) ).
fof(f686,plain,
not_subclass_element(singleton(y),unordered_pair(y,x)) = y,
inference(resolution,[status(thm)],[f282,f242]) ).
fof(f696,plain,
( spl0_12
<=> subclass(singleton(y),unordered_pair(y,x)) ),
introduced(split_symbol_definition) ).
fof(f697,plain,
( subclass(singleton(y),unordered_pair(y,x))
| ~ spl0_12 ),
inference(component_clause,[status(thm)],[f696]) ).
fof(f699,plain,
( spl0_13
<=> member(y,unordered_pair(y,x)) ),
introduced(split_symbol_definition) ).
fof(f701,plain,
( ~ member(y,unordered_pair(y,x))
| spl0_13 ),
inference(component_clause,[status(thm)],[f699]) ).
fof(f702,plain,
( subclass(singleton(y),unordered_pair(y,x))
| ~ member(y,unordered_pair(y,x)) ),
inference(paramodulation,[status(thm)],[f686,f682]) ).
fof(f703,plain,
( spl0_12
| ~ spl0_13 ),
inference(split_clause,[status(thm)],[f702,f696,f699]) ).
fof(f704,plain,
! [X0] :
( ~ member(y,X0)
| spl0_13 ),
inference(resolution,[status(thm)],[f701,f256]) ).
fof(f714,plain,
( singleton(y) = null_class
| spl0_13 ),
inference(resolution,[status(thm)],[f704,f639]) ).
fof(f717,plain,
( $false
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[status(thm)],[f697,f242]) ).
fof(f718,plain,
~ spl0_12,
inference(contradiction_clause,[status(thm)],[f717]) ).
fof(f728,plain,
( ~ subclass(null_class,unordered_pair(y,x))
| spl0_13 ),
inference(backward_demodulation,[status(thm)],[f714,f242]) ).
fof(f729,plain,
( $false
| spl0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[f728,f232]) ).
fof(f730,plain,
spl0_13,
inference(contradiction_clause,[status(thm)],[f729]) ).
fof(f731,plain,
$false,
inference(sat_refutation,[status(thm)],[f703,f718,f730]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET068-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.13/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 29 22:05:47 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.36 % Drodi V3.6.0
% 0.20/0.37 % Refutation found
% 0.20/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.20/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.38 % Elapsed time: 0.032122 seconds
% 0.20/0.38 % CPU time: 0.106226 seconds
% 0.20/0.38 % Total memory used: 22.336 MB
% 0.20/0.38 % Net memory used: 22.237 MB
%------------------------------------------------------------------------------