%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET120-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:09:25 PM UTC 2026
% Result : Unsatisfiable 4.52s 1.02s
% Output : CNFRefutation 4.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 39 ( 11 unt; 3 def)
% Number of atoms : 70 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 60 ( 29 ~; 28 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,U] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [U,V,X,Y] :
( member(U,X)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f153,axiom,
! [Y,Z] :
( member(ordered_pair(first(ordered_pair(Y,Z)),second(ordered_pair(Y,Z))),cross_product(universal_class,universal_class))
| ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f155,axiom,
! [X] :
( second(X) = X
| member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f157,axiom,
! [X] :
( second(X) = X
| ordered_pair(first(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(f168,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f169,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f168]) ).
fof(f172,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f185,plain,
! [U,X] :
( member(U,X)
| ! [V,Y] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f186,plain,
! [X0,X1,X2,X3] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f185]) ).
fof(f353,plain,
! [X0,X1] :
( member(ordered_pair(first(ordered_pair(X0,X1)),second(ordered_pair(X0,X1))),cross_product(universal_class,universal_class))
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f355,plain,
! [X0] :
( second(X0) = X0
| member(ordered_pair(first(X0),second(X0)),cross_product(universal_class,universal_class)) ),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f357,plain,
! [X0] :
( second(X0) = X0
| ordered_pair(first(X0),second(X0)) = X0 ),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f366,plain,
~ member(x,universal_class),
inference(cnf_transformation,[status(thm)],[f166]) ).
fof(f367,plain,
second(ordered_pair(x,y)) != ordered_pair(x,y),
inference(cnf_transformation,[status(thm)],[f167]) ).
fof(f377,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f172,f169]) ).
fof(f770,plain,
! [X0] : ~ member(x,X0),
inference(resolution,[status(thm)],[f377,f366]) ).
fof(f6113,plain,
ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))) = ordered_pair(x,y),
inference(resolution,[status(thm)],[f357,f367]) ).
fof(f6139,plain,
( second(ordered_pair(x,y)) = ordered_pair(x,y)
| member(ordered_pair(x,y),cross_product(universal_class,universal_class)) ),
inference(paramodulation,[status(thm)],[f6113,f355]) ).
fof(f6142,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))
| ~ member(ordered_pair(x,y),cross_product(universal_class,universal_class)) ),
inference(paramodulation,[status(thm)],[f6113,f353]) ).
fof(f6153,definition,
( sQ181_spl
<=> member(ordered_pair(x,y),cross_product(universal_class,universal_class)) ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f6156,definition,
( sQ182_spl
<=> second(ordered_pair(x,y)) = ordered_pair(x,y) ),
introduced(definition,[new_symbols(definition,[sQ182_spl])],[split_symbol_definition]) ).
fof(f6157,plain,
( ~ sQ182_spl
| second(ordered_pair(x,y)) = ordered_pair(x,y) ),
inference(component_clause,[status(thm)],[f6156]) ).
fof(f6159,plain,
( sQ182_spl
| sQ181_spl ),
inference(split_clause,[status(thm)],[f6139,f6153,f6156]) ).
fof(f6164,definition,
( sQ184_spl
<=> 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(definition,[new_symbols(definition,[sQ184_spl])],[split_symbol_definition]) ).
fof(f6165,plain,
( ~ sQ184_spl
| 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(component_clause,[status(thm)],[f6164]) ).
fof(f6167,plain,
( sQ184_spl
| ~ sQ181_spl ),
inference(split_clause,[status(thm)],[f6142,f6153,f6164]) ).
fof(f6172,plain,
( ~ sQ184_spl
| 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)) ),
inference(forward_demodulation,[status(thm)],[f6113,f6165]) ).
fof(f6173,plain,
( ~ sQ184_spl
| member(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))),cross_product(universal_class,universal_class)) ),
inference(forward_demodulation,[status(thm)],[f6113,f6172]) ).
fof(f6174,plain,
( ~ sQ184_spl
| member(ordered_pair(x,y),cross_product(universal_class,universal_class)) ),
inference(forward_demodulation,[status(thm)],[f6113,f6173]) ).
fof(f6175,plain,
( ~ sQ182_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6157,f367]) ).
fof(f6176,plain,
~ sQ182_spl,
inference(contradiction_clause,[status(thm)],[f6175]) ).
fof(f6595,plain,
( ~ sQ184_spl
| member(x,universal_class) ),
inference(resolution,[status(thm)],[f186,f6174]) ).
fof(f6599,plain,
( ~ sQ184_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6595,f770]) ).
fof(f6600,plain,
~ sQ184_spl,
inference(contradiction_clause,[status(thm)],[f6599]) ).
fof(f6601,plain,
$false,
inference(sat_refutation,[status(thm)],[f6159,f6167,f6176,f6600]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET120-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n016.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Mon Sep 21 04:59:52 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.13/0.39 % Drodi V4.1.1
% 4.52/1.02 % Refutation found
% 4.52/1.02 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.52/1.02 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.52/1.08 % Elapsed time: 0.690765 seconds
% 4.52/1.08 % CPU time: 4.986079 seconds
% 4.52/1.08 % Total memory used: 164.827 MB
% 4.52/1.08 % Net memory used: 158.608 MB
%------------------------------------------------------------------------------