TSTP Solution File: SET120-7 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET120-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n022.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 12:34:04 EDT 2023
% Result : Unsatisfiable 42.72s 5.87s
% Output : CNFRefutation 43.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 19
% Syntax : Number of formulae : 65 ( 27 unt; 0 def)
% Number of atoms : 112 ( 41 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 91 ( 44 ~; 44 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 97 (; 97 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,U] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
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(f14,axiom,
! [U,V,X,Y] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U,X,V,Y] :
( ~ member(U,X)
| ~ member(V,Y)
| member(ordered_pair(U,V),cross_product(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f107,axiom,
member(null_class,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f116,axiom,
! [X,Y] :
( ~ member(X,universal_class)
| unordered_pair(X,Y) != null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f126,axiom,
! [X] :
( member(X,universal_class)
| singleton(X) = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f145,axiom,
! [X,Y] : member(ordered_pair(X,Y),universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f151,axiom,
! [W,X,Y,Z] :
( ordered_pair(W,X) != ordered_pair(Y,Z)
| ~ member(W,universal_class)
| W = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f155,axiom,
! [X] :
( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
| second(X) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f159,axiom,
! [U,V] :
( ~ member(ordered_pair(U,V),cross_product(universal_class,universal_class))
| second(ordered_pair(U,V)) = V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f163,axiom,
! [X] :
( ordered_pair(first(X),second(X)) = X
| second(X) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f166,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f167,negated_conjecture,
second(ordered_pair(x,y)) != ordered_pair(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f168,plain,
! [Y,U] :
( ! [X] :
( ~ subclass(X,Y)
| ~ member(U,X) )
| member(U,Y) ),
inference(miniscoping,[status(esa)],[f1]) ).
fof(f169,plain,
! [X0,X1,X2] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f168]) ).
fof(f172,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f182,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f183,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f185,plain,
! [U,X] :
( ! [V,Y] : ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) ),
inference(miniscoping,[status(esa)],[f14]) ).
fof(f186,plain,
! [X0,X1,X2,X3] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f185]) ).
fof(f189,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| member(ordered_pair(X0,X2),cross_product(X1,X3)) ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f293,plain,
member(null_class,universal_class),
inference(cnf_transformation,[status(esa)],[f107]) ).
fof(f307,plain,
! [X] :
( ~ member(X,universal_class)
| ! [Y] : unordered_pair(X,Y) != null_class ),
inference(miniscoping,[status(esa)],[f116]) ).
fof(f308,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| unordered_pair(X0,X1) != null_class ),
inference(cnf_transformation,[status(esa)],[f307]) ).
fof(f320,plain,
! [X0] :
( member(X0,universal_class)
| singleton(X0) = null_class ),
inference(cnf_transformation,[status(esa)],[f126]) ).
fof(f340,plain,
! [X0,X1] : member(ordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[status(esa)],[f145]) ).
fof(f349,plain,
! [W,Y] :
( ! [X,Z] : ordered_pair(W,X) != ordered_pair(Y,Z)
| ~ member(W,universal_class)
| W = Y ),
inference(miniscoping,[status(esa)],[f151]) ).
fof(f350,plain,
! [X0,X1,X2,X3] :
( ordered_pair(X0,X1) != ordered_pair(X2,X3)
| ~ member(X0,universal_class)
| X0 = X2 ),
inference(cnf_transformation,[status(esa)],[f349]) ).
fof(f355,plain,
! [X0] :
( member(ordered_pair(first(X0),second(X0)),cross_product(universal_class,universal_class))
| second(X0) = X0 ),
inference(cnf_transformation,[status(esa)],[f155]) ).
fof(f359,plain,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
| second(ordered_pair(X0,X1)) = X1 ),
inference(cnf_transformation,[status(esa)],[f159]) ).
fof(f363,plain,
! [X0] :
( ordered_pair(first(X0),second(X0)) = X0
| second(X0) = X0 ),
inference(cnf_transformation,[status(esa)],[f163]) ).
fof(f366,plain,
~ member(x,universal_class),
inference(cnf_transformation,[status(esa)],[f166]) ).
fof(f367,plain,
second(ordered_pair(x,y)) != ordered_pair(x,y),
inference(cnf_transformation,[status(esa)],[f167]) ).
fof(f374,plain,
! [X0] :
( ~ subclass(X0,universal_class)
| ~ member(x,X0) ),
inference(resolution,[status(thm)],[f169,f366]) ).
fof(f375,plain,
! [X0] : ~ member(x,X0),
inference(forward_subsumption_resolution,[status(thm)],[f374,f172]) ).
fof(f692,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,X1)
| member(ordered_pair(ordered_pair(X2,X3),X0),cross_product(universal_class,X1)) ),
inference(resolution,[status(thm)],[f189,f340]) ).
fof(f696,plain,
! [X0,X1] : member(ordered_pair(ordered_pair(X0,X1),null_class),cross_product(universal_class,universal_class)),
inference(resolution,[status(thm)],[f692,f293]) ).
fof(f703,plain,
! [X0,X1,X2,X3] : member(ordered_pair(ordered_pair(X0,X1),unordered_pair(X2,X3)),cross_product(universal_class,universal_class)),
inference(resolution,[status(thm)],[f692,f182]) ).
fof(f1411,plain,
! [X0,X1,X2,X3] : second(ordered_pair(ordered_pair(X0,X1),unordered_pair(X2,X3))) = unordered_pair(X2,X3),
inference(resolution,[status(thm)],[f359,f703]) ).
fof(f1414,plain,
! [X0,X1] : second(ordered_pair(ordered_pair(X0,X1),null_class)) = null_class,
inference(resolution,[status(thm)],[f359,f696]) ).
fof(f1423,plain,
! [X0,X1,X2] : second(ordered_pair(ordered_pair(X0,X1),singleton(X2))) = unordered_pair(X2,X2),
inference(paramodulation,[status(thm)],[f183,f1411]) ).
fof(f1644,plain,
singleton(x) = null_class,
inference(resolution,[status(thm)],[f320,f375]) ).
fof(f1665,plain,
! [X0,X1] : second(ordered_pair(ordered_pair(X0,X1),null_class)) = unordered_pair(x,x),
inference(paramodulation,[status(thm)],[f1644,f1423]) ).
fof(f1716,plain,
( spl0_46
<=> null_class = null_class ),
introduced(split_symbol_definition) ).
fof(f1718,plain,
( null_class != null_class
| spl0_46 ),
inference(component_clause,[status(thm)],[f1716]) ).
fof(f1724,plain,
( $false
| spl0_46 ),
inference(trivial_equality_resolution,[status(esa)],[f1718]) ).
fof(f1725,plain,
spl0_46,
inference(contradiction_clause,[status(thm)],[f1724]) ).
fof(f2016,plain,
null_class = unordered_pair(x,x),
inference(paramodulation,[status(thm)],[f1414,f1665]) ).
fof(f2667,plain,
( spl0_92
<=> member(x,universal_class) ),
introduced(split_symbol_definition) ).
fof(f2878,plain,
( ~ member(x,universal_class)
| null_class != null_class ),
inference(paramodulation,[status(thm)],[f2016,f308]) ).
fof(f2879,plain,
( ~ spl0_92
| ~ spl0_46 ),
inference(split_clause,[status(thm)],[f2878,f2667,f1716]) ).
fof(f22647,plain,
! [X0,X1] :
( second(ordered_pair(X0,X1)) = ordered_pair(X0,X1)
| ~ member(first(ordered_pair(X0,X1)),universal_class)
| first(ordered_pair(X0,X1)) = X0 ),
inference(resolution,[status(thm)],[f363,f350]) ).
fof(f38201,plain,
! [X0] :
( second(X0) = X0
| member(first(X0),universal_class) ),
inference(resolution,[status(thm)],[f355,f186]) ).
fof(f40156,plain,
! [X0,X1] :
( second(ordered_pair(X0,X1)) = ordered_pair(X0,X1)
| first(ordered_pair(X0,X1)) = X0 ),
inference(forward_subsumption_resolution,[status(thm)],[f22647,f38201]) ).
fof(f40157,plain,
first(ordered_pair(x,y)) = x,
inference(resolution,[status(thm)],[f40156,f367]) ).
fof(f40222,plain,
( spl0_1538
<=> second(ordered_pair(x,y)) = ordered_pair(x,y) ),
introduced(split_symbol_definition) ).
fof(f40223,plain,
( second(ordered_pair(x,y)) = ordered_pair(x,y)
| ~ spl0_1538 ),
inference(component_clause,[status(thm)],[f40222]) ).
fof(f40227,plain,
( second(ordered_pair(x,y)) = ordered_pair(x,y)
| member(x,universal_class) ),
inference(paramodulation,[status(thm)],[f40157,f38201]) ).
fof(f40228,plain,
( spl0_1538
| spl0_92 ),
inference(split_clause,[status(thm)],[f40227,f40222,f2667]) ).
fof(f40262,plain,
( $false
| ~ spl0_1538 ),
inference(forward_subsumption_resolution,[status(thm)],[f40223,f367]) ).
fof(f40263,plain,
~ spl0_1538,
inference(contradiction_clause,[status(thm)],[f40262]) ).
fof(f40264,plain,
$false,
inference(sat_refutation,[status(thm)],[f1725,f2879,f40228,f40263]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SET120-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% 0.09/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.33 % Computer : n022.cluster.edu
% 0.10/0.33 % Model : x86_64 x86_64
% 0.10/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.33 % Memory : 8042.1875MB
% 0.10/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.33 % CPULimit : 300
% 0.10/0.33 % WCLimit : 300
% 0.10/0.33 % DateTime : Tue May 30 10:19:57 EDT 2023
% 0.10/0.33 % CPUTime :
% 0.10/0.34 % Drodi V3.5.1
% 42.72/5.87 % Refutation found
% 42.72/5.87 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 42.72/5.87 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 43.35/5.95 % Elapsed time: 5.607353 seconds
% 43.35/5.95 % CPU time: 43.654600 seconds
% 43.35/5.95 % Memory used: 278.685 MB
%------------------------------------------------------------------------------