%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET123-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 02:09:26 PM UTC 2026
% Result : Unsatisfiable 0.24s 5.77s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 17
% Syntax : Number of formulae : 57 ( 19 unt; 5 def)
% Number of atoms : 110 ( 18 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 103 ( 50 ~; 48 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 57 ( 57 !; 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(f4,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [U,X,Y] :
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
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(f23,axiom,
! [Z,X,Y] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [Z,X] :
( member(Z,X)
| member(Z,complement(X))
| ~ member(Z,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X,Y] : complement(intersection(complement(X),complement(Y))) = union(X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f92,axiom,
! [X,Y] : union(singleton(X),Y) = set_builder(X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f93,negated_conjecture,
member(x,set_builder(y,z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f94,negated_conjecture,
x != y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,negated_conjecture,
~ member(x,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f97,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f100,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f104,plain,
! [U,Y] :
( U = Y
| ! [X] :
( U = X
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f105,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f111,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f127,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f128,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f129,plain,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f130,plain,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f201,plain,
! [X0,X1] : union(singleton(X0),X1) = set_builder(X0,X1),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f202,plain,
member(x,set_builder(y,z)),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f203,plain,
x != y,
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f204,plain,
~ member(x,z),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f211,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f100,f97]) ).
fof(f219,plain,
! [X0,X1] :
( X0 = X1
| X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f111,f105]) ).
fof(f220,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f219]) ).
fof(f261,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(complement(X1),complement(X2)))
| ~ member(X0,union(X1,X2)) ),
inference(paramodulation,[status(thm)],[f130,f128]) ).
fof(f302,definition,
( sQ6_spl
<=> member(x,universal_class) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f304,plain,
( sQ6_spl
| ~ member(x,universal_class) ),
inference(component_clause,[status(thm)],[f302]) ).
fof(f336,definition,
( sQ8_spl
<=> member(x,singleton(y)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f337,plain,
( ~ sQ8_spl
| member(x,singleton(y)) ),
inference(component_clause,[status(thm)],[f336]) ).
fof(f339,definition,
( sQ9_spl
<=> member(x,z) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f340,plain,
( ~ sQ9_spl
| member(x,z) ),
inference(component_clause,[status(thm)],[f339]) ).
fof(f352,plain,
! [X0] :
( sQ6_spl
| ~ member(x,X0) ),
inference(resolution,[status(thm)],[f211,f304]) ).
fof(f355,plain,
( sQ6_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f202,f352]) ).
fof(f362,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f355]) ).
fof(f4608,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(complement(singleton(X1)),complement(X2)))
| ~ member(X0,set_builder(X1,X2)) ),
inference(paramodulation,[status(thm)],[f201,f261]) ).
fof(f5013,definition,
( sQ126_spl
<=> member(x,complement(z)) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f5015,plain,
( sQ126_spl
| ~ member(x,complement(z)) ),
inference(component_clause,[status(thm)],[f5013]) ).
fof(f5047,plain,
( sQ126_spl
| member(x,z)
| ~ member(x,universal_class) ),
inference(resolution,[status(thm)],[f5015,f129]) ).
fof(f5048,plain,
( sQ126_spl
| sQ9_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f5047,f302,f339,f5013]) ).
fof(f5049,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f340,f204]) ).
fof(f5050,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f5049]) ).
fof(f5055,plain,
~ member(x,intersection(complement(singleton(y)),complement(z))),
inference(resolution,[status(thm)],[f202,f4608]) ).
fof(f5812,plain,
( ~ member(x,complement(z))
| ~ member(x,complement(singleton(y))) ),
inference(resolution,[status(thm)],[f5055,f127]) ).
fof(f5814,definition,
( sQ131_spl
<=> member(x,complement(singleton(y))) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f5816,plain,
( sQ131_spl
| ~ member(x,complement(singleton(y))) ),
inference(component_clause,[status(thm)],[f5814]) ).
fof(f5817,plain,
( ~ sQ126_spl
| ~ sQ131_spl ),
inference(split_clause,[status(thm)],[f5812,f5814,f5013]) ).
fof(f5999,plain,
( sQ131_spl
| member(x,singleton(y))
| ~ member(x,universal_class) ),
inference(resolution,[status(thm)],[f5816,f129]) ).
fof(f6001,plain,
( sQ131_spl
| sQ8_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f5999,f302,f336,f5814]) ).
fof(f6160,plain,
( ~ sQ8_spl
| x = y ),
inference(resolution,[status(thm)],[f337,f220]) ).
fof(f6162,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6160,f203]) ).
fof(f6163,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f6162]) ).
fof(f6164,plain,
$false,
inference(sat_refutation,[status(thm)],[f362,f5048,f5050,f5817,f6001,f6163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET123-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/5.45 % Computer : n018.cluster.edu
% 0.18/5.45 % Model : x86_64 x86_64
% 0.18/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.45 % Memory : 8046.5625MB
% 0.18/5.45 % OS : Linux 6.8.0-71-generic
% 0.18/5.45 % CPULimit : 300
% 0.18/5.45 % WCLimit : 300
% 0.18/5.46 % DateTime : Mon Sep 21 04:57:03 UTC 2026
% 0.18/5.46 % CPUTime :
% 0.18/5.48 % Drodi V4.1.1
% 0.24/5.77 % Refutation found
% 0.24/5.77 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.24/5.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/5.82 % Elapsed time: 0.339669 seconds
% 0.24/5.82 % CPU time: 2.215244 seconds
% 0.24/5.82 % Total memory used: 140.146 MB
% 0.24/5.82 % Net memory used: 136.303 MB
%------------------------------------------------------------------------------