%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET102-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 02:09:21 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.48s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 10 unt; 2 def)
% Number of atoms : 49 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 47 ( 26 ~; 19 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,U] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] :
( subclass(X,Y)
| X != Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Y,X] :
( member(Y,unordered_pair(X,Y))
| ~ member(Y,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(f13,axiom,
! [X,Y] : unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f146,negated_conjecture,
~ member(unordered_pair(x,singleton(y)),ordered_pair(x,y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f147,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f148,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f152,plain,
! [X0,X1] :
( subclass(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f159,plain,
! [Y] :
( ! [X] : member(Y,unordered_pair(X,Y))
| ~ member(Y,universal_class) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f160,plain,
! [X0,X1] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f161,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f163,plain,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f320,plain,
~ member(unordered_pair(x,singleton(y)),ordered_pair(x,y)),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f321,plain,
! [X0] : subclass(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f152]) ).
fof(f333,plain,
! [X0] :
( ~ member(unordered_pair(x,singleton(y)),X0)
| ~ subclass(X0,ordered_pair(x,y)) ),
inference(resolution,[status(thm)],[f148,f320]) ).
fof(f341,plain,
! [X0] :
( ~ member(unordered_pair(x,singleton(y)),universal_class)
| ~ subclass(unordered_pair(X0,unordered_pair(x,singleton(y))),ordered_pair(x,y)) ),
inference(resolution,[status(thm)],[f333,f160]) ).
fof(f344,definition,
! [X0] :
( sQ0_spl
<=> ~ subclass(unordered_pair(X0,unordered_pair(x,singleton(y))),ordered_pair(x,y)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f345,plain,
! [X0] :
( ~ sQ0_spl
| ~ subclass(unordered_pair(X0,unordered_pair(x,singleton(y))),ordered_pair(x,y)) ),
inference(component_clause,[status(thm)],[f344]) ).
fof(f347,definition,
( sQ1_spl
<=> member(unordered_pair(x,singleton(y)),universal_class) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f349,plain,
( sQ1_spl
| ~ member(unordered_pair(x,singleton(y)),universal_class) ),
inference(component_clause,[status(thm)],[f347]) ).
fof(f350,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f341,f344,f347]) ).
fof(f397,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f349,f161]) ).
fof(f398,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f397]) ).
fof(f434,plain,
( ~ sQ0_spl
| ~ subclass(ordered_pair(x,y),ordered_pair(x,y)) ),
inference(paramodulation,[status(thm)],[f163,f345]) ).
fof(f438,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f434,f321]) ).
fof(f439,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f438]) ).
fof(f440,plain,
$false,
inference(sat_refutation,[status(thm)],[f350,f398,f439]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET102-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n019.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Mon Sep 21 04:53:04 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.45 % Drodi V4.1.1
% 0.15/0.48 % Refutation found
% 0.15/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.53 % Elapsed time: 0.077881 seconds
% 0.21/0.53 % CPU time: 0.220052 seconds
% 0.21/0.53 % Total memory used: 107.397 MB
% 0.21/0.53 % Net memory used: 107.256 MB
%------------------------------------------------------------------------------