TSTP Solution File: SET120-7 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% 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 : n025.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 20:39:12 EDT 2024
% Result : Unsatisfiable 18.05s 2.72s
% Output : CNFRefutation 18.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 9 unt; 0 def)
% Number of atoms : 55 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 44 ( 21 ~; 20 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f153,axiom,
! [Y,Z] :
( ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| member(ordered_pair(first(ordered_pair(Y,Z)),second(ordered_pair(Y,Z))),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f157,axiom,
! [X] :
( ordered_pair(first(X),second(X)) = X
| second(X) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f166,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f167,negated_conjecture,
second(ordered_pair(x,y)) != ordered_pair(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(f353,plain,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
| member(ordered_pair(first(ordered_pair(X0,X1)),second(ordered_pair(X0,X1))),cross_product(universal_class,universal_class)) ),
inference(cnf_transformation,[status(esa)],[f153]) ).
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(f357,plain,
! [X0] :
( ordered_pair(first(X0),second(X0)) = X0
| second(X0) = X0 ),
inference(cnf_transformation,[status(esa)],[f157]) ).
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(f1110,plain,
! [X0,X1] : ~ member(ordered_pair(x,X0),cross_product(universal_class,X1)),
inference(resolution,[status(thm)],[f186,f366]) ).
fof(f11854,plain,
ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))) = ordered_pair(x,y),
inference(resolution,[status(thm)],[f357,f367]) ).
fof(f12765,plain,
( spl0_558
<=> member(ordered_pair(x,y),cross_product(universal_class,universal_class)) ),
introduced(split_symbol_definition) ).
fof(f12768,plain,
( spl0_559
<=> second(ordered_pair(x,y)) = ordered_pair(x,y) ),
introduced(split_symbol_definition) ).
fof(f12769,plain,
( second(ordered_pair(x,y)) = ordered_pair(x,y)
| ~ spl0_559 ),
inference(component_clause,[status(thm)],[f12768]) ).
fof(f12771,plain,
( member(ordered_pair(x,y),cross_product(universal_class,universal_class))
| second(ordered_pair(x,y)) = ordered_pair(x,y) ),
inference(paramodulation,[status(thm)],[f11854,f355]) ).
fof(f12772,plain,
( spl0_558
| spl0_559 ),
inference(split_clause,[status(thm)],[f12771,f12765,f12768]) ).
fof(f12783,plain,
( spl0_562
<=> member(ordered_pair(first(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y)))),second(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))))),cross_product(universal_class,universal_class)) ),
introduced(split_symbol_definition) ).
fof(f12784,plain,
( member(ordered_pair(first(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y)))),second(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))))),cross_product(universal_class,universal_class))
| ~ spl0_562 ),
inference(component_clause,[status(thm)],[f12783]) ).
fof(f12786,plain,
( ~ member(ordered_pair(x,y),cross_product(universal_class,universal_class))
| member(ordered_pair(first(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y)))),second(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))))),cross_product(universal_class,universal_class)) ),
inference(paramodulation,[status(thm)],[f11854,f353]) ).
fof(f12787,plain,
( ~ spl0_558
| spl0_562 ),
inference(split_clause,[status(thm)],[f12786,f12765,f12783]) ).
fof(f12817,plain,
( $false
| ~ spl0_559 ),
inference(forward_subsumption_resolution,[status(thm)],[f12769,f367]) ).
fof(f12818,plain,
~ spl0_559,
inference(contradiction_clause,[status(thm)],[f12817]) ).
fof(f12819,plain,
( member(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))))),cross_product(universal_class,universal_class))
| ~ spl0_562 ),
inference(forward_demodulation,[status(thm)],[f11854,f12784]) ).
fof(f12820,plain,
( member(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))),cross_product(universal_class,universal_class))
| ~ spl0_562 ),
inference(forward_demodulation,[status(thm)],[f11854,f12819]) ).
fof(f12821,plain,
( member(ordered_pair(x,y),cross_product(universal_class,universal_class))
| ~ spl0_562 ),
inference(forward_demodulation,[status(thm)],[f11854,f12820]) ).
fof(f12822,plain,
( $false
| ~ spl0_562 ),
inference(forward_subsumption_resolution,[status(thm)],[f12821,f1110]) ).
fof(f12823,plain,
~ spl0_562,
inference(contradiction_clause,[status(thm)],[f12822]) ).
fof(f12824,plain,
$false,
inference(sat_refutation,[status(thm)],[f12772,f12787,f12818,f12823]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET120-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% 0.08/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 22:05:41 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.37 % Drodi V3.6.0
% 18.05/2.72 % Refutation found
% 18.05/2.72 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 18.05/2.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 18.65/2.76 % Elapsed time: 2.393670 seconds
% 18.65/2.76 % CPU time: 18.835971 seconds
% 18.65/2.76 % Total memory used: 216.262 MB
% 18.65/2.76 % Net memory used: 210.884 MB
%------------------------------------------------------------------------------