TSTP Solution File: SET084-6 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET084-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 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 : Tue Apr 30 20:39:03 EDT 2024
% Result : Unsatisfiable 0.15s 0.32s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 20
% Syntax : Number of formulae : 67 ( 14 unt; 0 def)
% Number of atoms : 137 ( 40 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 122 ( 52 ~; 61 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 10 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 36 ( 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X,Y] :
( ~ subclass(X,Y)
| ~ subclass(Y,X)
| X = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [U,X,Y] :
( ~ member(U,unordered_pair(X,Y))
| U = X
| U = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [X] :
( ~ inductive(X)
| subclass(image(successor_relation,X),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [Y] :
( ~ inductive(Y)
| subclass(omega,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,axiom,
! [X] :
( X = null_class
| member(regular(X),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f92,negated_conjecture,
singleton(x) = singleton(y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f93,negated_conjecture,
member(y,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f94,negated_conjecture,
x != y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f102,plain,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f103,plain,
! [U,Y] :
( ! [X] :
( ~ member(U,unordered_pair(X,Y))
| U = X )
| U = Y ),
inference(miniscoping,[status(esa)],[f8]) ).
fof(f104,plain,
! [X0,X1,X2] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[status(esa)],[f103]) ).
fof(f105,plain,
! [X] :
( ~ member(X,universal_class)
| ! [Y] : member(X,unordered_pair(X,Y)) ),
inference(miniscoping,[status(esa)],[f9]) ).
fof(f106,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f105]) ).
fof(f110,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f151,plain,
! [X0] :
( ~ inductive(X0)
| subclass(image(successor_relation,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f153,plain,
inductive(omega),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f154,plain,
! [X0] :
( ~ inductive(X0)
| subclass(omega,X0) ),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f169,plain,
! [X0] :
( X0 = null_class
| member(regular(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f66]) ).
fof(f200,plain,
singleton(x) = singleton(y),
inference(cnf_transformation,[status(esa)],[f92]) ).
fof(f201,plain,
member(y,universal_class),
inference(cnf_transformation,[status(esa)],[f93]) ).
fof(f202,plain,
x != y,
inference(cnf_transformation,[status(esa)],[f94]) ).
fof(f220,plain,
! [X0] :
( ~ subclass(X0,omega)
| X0 = omega
| ~ inductive(X0) ),
inference(resolution,[status(thm)],[f102,f154]) ).
fof(f244,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f110,f104]) ).
fof(f245,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(duplicate_literals_removal,[status(esa)],[f244]) ).
fof(f247,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(X0,singleton(X0)) ),
inference(paramodulation,[status(thm)],[f110,f106]) ).
fof(f250,plain,
! [X0] :
( regular(singleton(X0)) = X0
| singleton(X0) = null_class ),
inference(resolution,[status(thm)],[f245,f169]) ).
fof(f253,plain,
! [X0] :
( ~ member(X0,singleton(x))
| X0 = y ),
inference(paramodulation,[status(thm)],[f200,f245]) ).
fof(f254,plain,
( spl0_4
<=> regular(singleton(x)) = y ),
introduced(split_symbol_definition) ).
fof(f255,plain,
( regular(singleton(x)) = y
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f254]) ).
fof(f257,plain,
( spl0_5
<=> singleton(x) = null_class ),
introduced(split_symbol_definition) ).
fof(f258,plain,
( singleton(x) = null_class
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f260,plain,
( regular(singleton(x)) = y
| singleton(x) = null_class ),
inference(resolution,[status(thm)],[f253,f169]) ).
fof(f261,plain,
( spl0_4
| spl0_5 ),
inference(split_clause,[status(thm)],[f260,f254,f257]) ).
fof(f279,plain,
( null_class = singleton(y)
| ~ spl0_5 ),
inference(backward_demodulation,[status(thm)],[f258,f200]) ).
fof(f280,plain,
! [X0] :
( ~ member(X0,null_class)
| X0 = x
| ~ spl0_5 ),
inference(paramodulation,[status(thm)],[f258,f245]) ).
fof(f311,plain,
( spl0_12
<=> member(y,null_class) ),
introduced(split_symbol_definition) ).
fof(f312,plain,
( member(y,null_class)
| ~ spl0_12 ),
inference(component_clause,[status(thm)],[f311]) ).
fof(f441,plain,
( spl0_26
<=> image(successor_relation,omega) = omega ),
introduced(split_symbol_definition) ).
fof(f444,plain,
( spl0_27
<=> inductive(image(successor_relation,omega)) ),
introduced(split_symbol_definition) ).
fof(f447,plain,
( spl0_28
<=> inductive(omega) ),
introduced(split_symbol_definition) ).
fof(f449,plain,
( ~ inductive(omega)
| spl0_28 ),
inference(component_clause,[status(thm)],[f447]) ).
fof(f450,plain,
( image(successor_relation,omega) = omega
| ~ inductive(image(successor_relation,omega))
| ~ inductive(omega) ),
inference(resolution,[status(thm)],[f220,f151]) ).
fof(f451,plain,
( spl0_26
| ~ spl0_27
| ~ spl0_28 ),
inference(split_clause,[status(thm)],[f450,f441,f444,f447]) ).
fof(f452,plain,
( spl0_29
<=> omega = omega ),
introduced(split_symbol_definition) ).
fof(f455,plain,
( omega = omega
| ~ inductive(omega)
| ~ inductive(omega) ),
inference(resolution,[status(thm)],[f220,f154]) ).
fof(f456,plain,
( spl0_29
| ~ spl0_28 ),
inference(split_clause,[status(thm)],[f455,f452,f447]) ).
fof(f459,plain,
( $false
| spl0_28 ),
inference(forward_subsumption_resolution,[status(thm)],[f449,f153]) ).
fof(f460,plain,
spl0_28,
inference(contradiction_clause,[status(thm)],[f459]) ).
fof(f462,plain,
( spl0_30
<=> member(y,universal_class) ),
introduced(split_symbol_definition) ).
fof(f464,plain,
( ~ member(y,universal_class)
| spl0_30 ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f465,plain,
( ~ member(y,universal_class)
| member(y,null_class)
| ~ spl0_5 ),
inference(paramodulation,[status(thm)],[f279,f247]) ).
fof(f466,plain,
( ~ spl0_30
| spl0_12
| ~ spl0_5 ),
inference(split_clause,[status(thm)],[f465,f462,f311,f257]) ).
fof(f527,plain,
( y = x
| ~ spl0_12
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f312,f280]) ).
fof(f528,plain,
( $false
| ~ spl0_12
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f527,f202]) ).
fof(f529,plain,
( ~ spl0_12
| ~ spl0_5 ),
inference(contradiction_clause,[status(thm)],[f528]) ).
fof(f530,plain,
( $false
| spl0_30 ),
inference(forward_subsumption_resolution,[status(thm)],[f464,f201]) ).
fof(f531,plain,
spl0_30,
inference(contradiction_clause,[status(thm)],[f530]) ).
fof(f532,plain,
( spl0_39
<=> x = y ),
introduced(split_symbol_definition) ).
fof(f533,plain,
( x = y
| ~ spl0_39 ),
inference(component_clause,[status(thm)],[f532]) ).
fof(f535,plain,
( x = y
| singleton(x) = null_class
| ~ spl0_4 ),
inference(paramodulation,[status(thm)],[f250,f255]) ).
fof(f536,plain,
( spl0_39
| spl0_5
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f535,f532,f257,f254]) ).
fof(f546,plain,
( $false
| ~ spl0_39 ),
inference(forward_subsumption_resolution,[status(thm)],[f533,f202]) ).
fof(f547,plain,
~ spl0_39,
inference(contradiction_clause,[status(thm)],[f546]) ).
fof(f548,plain,
$false,
inference(sat_refutation,[status(thm)],[f261,f451,f456,f460,f466,f529,f531,f536,f547]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.09 % Problem : SET084-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.30 % Computer : n026.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon Apr 29 22:01:04 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.15/0.31 % Drodi V3.6.0
% 0.15/0.32 % Refutation found
% 0.15/0.32 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.33 % Elapsed time: 0.020758 seconds
% 0.15/0.33 % CPU time: 0.045309 seconds
% 0.15/0.33 % Total memory used: 15.832 MB
% 0.15/0.33 % Net memory used: 15.806 MB
%------------------------------------------------------------------------------