TSTP Solution File: SET024-3 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET024-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n007.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 12:33:37 EDT 2023
% Result : Unsatisfiable 0.21s 0.38s
% Output : CNFRefutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 49 ( 18 unt; 0 def)
% Number of atoms : 93 ( 27 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 69 ( 25 ~; 40 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 44 (; 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X,Y] :
( member(f1(X,Y),X)
| member(f1(X,Y),Y)
| X = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [U,X,Y] :
( ~ member(U,non_ordered_pair(X,Y))
| U = X
| U = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [U,X,Y] :
( member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| U != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] : little_set(non_ordered_pair(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] : singleton_set(X) = non_ordered_pair(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [Z] : ~ member(Z,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f150,hypothesis,
little_set(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f151,negated_conjecture,
~ member(a,singleton_set(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f155,plain,
! [X0,X1] :
( member(f1(X0,X1),X0)
| member(f1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f157,plain,
! [U,Y] :
( ! [X] :
( ~ member(U,non_ordered_pair(X,Y))
| U = X )
| U = Y ),
inference(miniscoping,[status(esa)],[f5]) ).
fof(f158,plain,
! [X0,X1,X2] :
( ~ member(X0,non_ordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[status(esa)],[f157]) ).
fof(f159,plain,
! [U,X] :
( ! [Y] : member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| U != X ),
inference(miniscoping,[status(esa)],[f6]) ).
fof(f160,plain,
! [X0,X1,X2] :
( member(X0,non_ordered_pair(X1,X2))
| ~ little_set(X0)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f159]) ).
fof(f163,plain,
! [X0,X1] : little_set(non_ordered_pair(X0,X1)),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f164,plain,
! [X0] : singleton_set(X0) = non_ordered_pair(X0,X0),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f226,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(esa)],[f58]) ).
fof(f340,plain,
little_set(a),
inference(cnf_transformation,[status(esa)],[f150]) ).
fof(f341,plain,
~ member(a,singleton_set(a)),
inference(cnf_transformation,[status(esa)],[f151]) ).
fof(f342,plain,
! [X0,X1] :
( member(X0,non_ordered_pair(X0,X1))
| ~ little_set(X0) ),
inference(destructive_equality_resolution,[status(esa)],[f160]) ).
fof(f366,plain,
! [X0] : little_set(singleton_set(X0)),
inference(paramodulation,[status(thm)],[f164,f163]) ).
fof(f379,plain,
! [X0,X1] :
( ~ member(X0,singleton_set(X1))
| X0 = X1
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f164,f158]) ).
fof(f380,plain,
! [X0,X1] :
( ~ member(X0,singleton_set(X1))
| X0 = X1 ),
inference(duplicate_literals_removal,[status(esa)],[f379]) ).
fof(f381,plain,
! [X0,X1] :
( f1(X0,singleton_set(X1)) = X1
| member(f1(X0,singleton_set(X1)),X0)
| X0 = singleton_set(X1) ),
inference(resolution,[status(thm)],[f380,f155]) ).
fof(f390,plain,
! [X0] :
( f1(empty_set,singleton_set(X0)) = X0
| empty_set = singleton_set(X0) ),
inference(resolution,[status(thm)],[f381,f226]) ).
fof(f396,plain,
! [X0] :
( member(f1(empty_set,singleton_set(X0)),empty_set)
| member(X0,singleton_set(X0))
| empty_set = singleton_set(X0)
| empty_set = singleton_set(X0) ),
inference(paramodulation,[status(thm)],[f390,f155]) ).
fof(f397,plain,
! [X0] :
( member(f1(empty_set,singleton_set(X0)),empty_set)
| member(X0,singleton_set(X0))
| empty_set = singleton_set(X0) ),
inference(duplicate_literals_removal,[status(esa)],[f396]) ).
fof(f398,plain,
! [X0] :
( member(X0,singleton_set(X0))
| empty_set = singleton_set(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f397,f226]) ).
fof(f402,plain,
( spl0_0
<=> member(a,empty_set) ),
introduced(split_symbol_definition) ).
fof(f403,plain,
( member(a,empty_set)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f402]) ).
fof(f405,plain,
( spl0_1
<=> little_set(a) ),
introduced(split_symbol_definition) ).
fof(f407,plain,
( ~ little_set(a)
| spl0_1 ),
inference(component_clause,[status(thm)],[f405]) ).
fof(f413,plain,
( spl0_2
<=> little_set(empty_set) ),
introduced(split_symbol_definition) ).
fof(f415,plain,
( ~ little_set(empty_set)
| spl0_2 ),
inference(component_clause,[status(thm)],[f413]) ).
fof(f432,plain,
empty_set = singleton_set(a),
inference(resolution,[status(thm)],[f398,f341]) ).
fof(f554,plain,
( spl0_15
<=> singleton_set(empty_set) = singleton_set(empty_set) ),
introduced(split_symbol_definition) ).
fof(f556,plain,
( singleton_set(empty_set) != singleton_set(empty_set)
| spl0_15 ),
inference(component_clause,[status(thm)],[f554]) ).
fof(f743,plain,
little_set(empty_set),
inference(paramodulation,[status(thm)],[f432,f366]) ).
fof(f859,plain,
! [X0] :
( member(X0,singleton_set(X0))
| ~ little_set(X0) ),
inference(paramodulation,[status(thm)],[f164,f342]) ).
fof(f906,plain,
( $false
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f403,f226]) ).
fof(f907,plain,
~ spl0_0,
inference(contradiction_clause,[status(thm)],[f906]) ).
fof(f908,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f407,f340]) ).
fof(f909,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f908]) ).
fof(f910,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f415,f743]) ).
fof(f911,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f910]) ).
fof(f939,plain,
( $false
| spl0_15 ),
inference(trivial_equality_resolution,[status(esa)],[f556]) ).
fof(f940,plain,
spl0_15,
inference(contradiction_clause,[status(thm)],[f939]) ).
fof(f1261,plain,
( member(a,empty_set)
| ~ little_set(a) ),
inference(paramodulation,[status(thm)],[f432,f859]) ).
fof(f1262,plain,
( spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f1261,f402,f405]) ).
fof(f1263,plain,
$false,
inference(sat_refutation,[status(thm)],[f907,f909,f911,f940,f1262]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET024-3 : TPTP v8.1.2. Released v1.0.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue May 30 10:06:02 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % Drodi V3.5.1
% 0.21/0.38 % Refutation found
% 0.21/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.21/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.39/0.61 % Elapsed time: 0.037606 seconds
% 0.39/0.61 % CPU time: 0.134210 seconds
% 0.39/0.61 % Memory used: 18.813 MB
%------------------------------------------------------------------------------