TSTP Solution File: SET075-6 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET075-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n008.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 20:38:59 EDT 2024
% Result : Unsatisfiable 0.18s 0.44s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 18
% Syntax : Number of formulae : 70 ( 23 unt; 0 def)
% Number of atoms : 122 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 92 ( 40 ~; 45 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 59 ( 59 !; 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(f4,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Y,X] :
( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [U,V,X,Y] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U,V,X,Y] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [Z,X] :
( ~ member(Z,complement(X))
| ~ member(Z,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,axiom,
inductive(omega),
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(f92,negated_conjecture,
member(ordered_pair(x,y),cross_product(u,v)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f93,negated_conjecture,
unordered_pair(x,y) = null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f94,plain,
! [Y,U] :
( ! [X] :
( ~ subclass(X,Y)
| ~ member(U,X) )
| member(U,Y) ),
inference(miniscoping,[status(esa)],[f1]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f94]) ).
fof(f98,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f106,plain,
! [Y] :
( ~ member(Y,universal_class)
| ! [X] : member(Y,unordered_pair(X,Y)) ),
inference(miniscoping,[status(esa)],[f10]) ).
fof(f107,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f106]) ).
fof(f108,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f111,plain,
! [U,X] :
( ! [V,Y] : ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) ),
inference(miniscoping,[status(esa)],[f14]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f111]) ).
fof(f113,plain,
! [V,Y] :
( ! [U,X] : ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) ),
inference(miniscoping,[status(esa)],[f15]) ).
fof(f114,plain,
! [X0,X1,X2,X3] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f113]) ).
fof(f126,plain,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f152,plain,
inductive(omega),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f168,plain,
! [X0] :
( X0 = null_class
| member(regular(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f66]) ).
fof(f199,plain,
member(ordered_pair(x,y),cross_product(u,v)),
inference(cnf_transformation,[status(esa)],[f92]) ).
fof(f200,plain,
unordered_pair(x,y) = null_class,
inference(cnf_transformation,[status(esa)],[f93]) ).
fof(f204,plain,
member(null_class,universal_class),
inference(paramodulation,[status(thm)],[f200,f108]) ).
fof(f209,plain,
( spl0_0
<=> member(x,universal_class) ),
introduced(split_symbol_definition) ).
fof(f211,plain,
( ~ member(x,universal_class)
| spl0_0 ),
inference(component_clause,[status(thm)],[f209]) ).
fof(f218,plain,
( spl0_2
<=> member(y,universal_class) ),
introduced(split_symbol_definition) ).
fof(f220,plain,
( ~ member(y,universal_class)
| spl0_2 ),
inference(component_clause,[status(thm)],[f218]) ).
fof(f221,plain,
( spl0_3
<=> member(y,null_class) ),
introduced(split_symbol_definition) ).
fof(f222,plain,
( member(y,null_class)
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f221]) ).
fof(f224,plain,
( ~ member(y,universal_class)
| member(y,null_class) ),
inference(paramodulation,[status(thm)],[f200,f107]) ).
fof(f225,plain,
( ~ spl0_2
| spl0_3 ),
inference(split_clause,[status(thm)],[f224,f218,f221]) ).
fof(f227,plain,
member(x,u),
inference(resolution,[status(thm)],[f112,f199]) ).
fof(f228,plain,
member(y,v),
inference(resolution,[status(thm)],[f114,f199]) ).
fof(f261,plain,
! [X0] :
( ~ subclass(v,X0)
| member(y,X0) ),
inference(resolution,[status(thm)],[f95,f228]) ).
fof(f262,plain,
! [X0] :
( ~ subclass(u,X0)
| member(x,X0) ),
inference(resolution,[status(thm)],[f95,f227]) ).
fof(f281,plain,
member(y,universal_class),
inference(resolution,[status(thm)],[f261,f98]) ).
fof(f282,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f281,f220]) ).
fof(f283,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f282]) ).
fof(f285,plain,
member(x,universal_class),
inference(resolution,[status(thm)],[f262,f98]) ).
fof(f286,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f285,f211]) ).
fof(f287,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f286]) ).
fof(f336,plain,
( spl0_12
<=> member(unordered_pair(x,null_class),universal_class) ),
introduced(split_symbol_definition) ).
fof(f338,plain,
( ~ member(unordered_pair(x,null_class),universal_class)
| spl0_12 ),
inference(component_clause,[status(thm)],[f336]) ).
fof(f351,plain,
( $false
| spl0_12 ),
inference(forward_subsumption_resolution,[status(thm)],[f338,f108]) ).
fof(f352,plain,
spl0_12,
inference(contradiction_clause,[status(thm)],[f351]) ).
fof(f405,plain,
! [X0] :
( ~ member(regular(complement(X0)),X0)
| complement(X0) = null_class ),
inference(resolution,[status(thm)],[f126,f168]) ).
fof(f712,plain,
( spl0_50
<=> inductive(omega) ),
introduced(split_symbol_definition) ).
fof(f714,plain,
( ~ inductive(omega)
| spl0_50 ),
inference(component_clause,[status(thm)],[f712]) ).
fof(f724,plain,
( $false
| spl0_50 ),
inference(forward_subsumption_resolution,[status(thm)],[f714,f152]) ).
fof(f725,plain,
spl0_50,
inference(contradiction_clause,[status(thm)],[f724]) ).
fof(f787,plain,
( spl0_56
<=> member(null_class,universal_class) ),
introduced(split_symbol_definition) ).
fof(f789,plain,
( ~ member(null_class,universal_class)
| spl0_56 ),
inference(component_clause,[status(thm)],[f787]) ).
fof(f796,plain,
( $false
| spl0_56 ),
inference(forward_subsumption_resolution,[status(thm)],[f789,f204]) ).
fof(f797,plain,
spl0_56,
inference(contradiction_clause,[status(thm)],[f796]) ).
fof(f1239,plain,
! [X0,X1] :
( ~ subclass(X0,X1)
| member(regular(X0),X1)
| X0 = null_class ),
inference(resolution,[status(thm)],[f95,f168]) ).
fof(f1630,plain,
! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class
| complement(X0) = null_class ),
inference(resolution,[status(thm)],[f1239,f405]) ).
fof(f1631,plain,
! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class ),
inference(duplicate_literals_removal,[status(esa)],[f1630]) ).
fof(f2154,plain,
complement(universal_class) = null_class,
inference(resolution,[status(thm)],[f1631,f98]) ).
fof(f2166,plain,
! [X0] :
( ~ member(X0,null_class)
| ~ member(X0,universal_class) ),
inference(paramodulation,[status(thm)],[f2154,f126]) ).
fof(f2167,plain,
( spl0_172
<=> subclass(universal_class,universal_class) ),
introduced(split_symbol_definition) ).
fof(f2169,plain,
( ~ subclass(universal_class,universal_class)
| spl0_172 ),
inference(component_clause,[status(thm)],[f2167]) ).
fof(f2174,plain,
( $false
| spl0_172 ),
inference(forward_subsumption_resolution,[status(thm)],[f2169,f98]) ).
fof(f2175,plain,
spl0_172,
inference(contradiction_clause,[status(thm)],[f2174]) ).
fof(f2192,plain,
( ~ member(y,universal_class)
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f2166,f222]) ).
fof(f2193,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f2192,f218,f221]) ).
fof(f2194,plain,
$false,
inference(sat_refutation,[status(thm)],[f225,f283,f287,f352,f725,f797,f2175,f2193]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET075-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.34 % Computer : n008.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Mon Apr 29 21:41:27 EDT 2024
% 0.11/0.35 % CPUTime :
% 0.11/0.36 % Drodi V3.6.0
% 0.18/0.44 % Refutation found
% 0.18/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.18/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.46 % Elapsed time: 0.099346 seconds
% 0.18/0.46 % CPU time: 0.676175 seconds
% 0.18/0.46 % Total memory used: 73.306 MB
% 0.18/0.46 % Net memory used: 72.469 MB
%------------------------------------------------------------------------------