%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET134-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 02:09:27 PM UTC 2026
% Result : Unsatisfiable 1.26s 0.68s
% Output : CNFRefutation 0.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of formulae : 67 ( 17 unt; 4 def)
% Number of atoms : 129 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 113 ( 51 ~; 58 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 91 ( 91 !; 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(f10,axiom,
! [Y,X] :
( member(Y,unordered_pair(X,Y))
| ~ member(Y,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [Z,X,Y] :
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [Z,X] :
( member(Z,X)
| member(Z,complement(X))
| ~ member(Z,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X,Y] : complement(intersection(complement(X),complement(Y))) = union(X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [X] : union(X,singleton(X)) = successor(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [X] :
( intersection(X,regular(X)) = null_class
| X = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f92,axiom,
! [X,Y] : union(singleton(X),Y) = set_builder(X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f93,negated_conjecture,
member(u,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f94,negated_conjecture,
set_builder(u,set_builder(y,set_builder(z,null_class))) = null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f95,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f96,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f99,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f107,plain,
! [Y] :
( ! [X] : member(Y,unordered_pair(X,Y))
| ~ member(Y,universal_class) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f108,plain,
! [X0,X1] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f110,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f122,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f123,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f127,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f128,plain,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f129,plain,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f146,plain,
! [X0] : union(X0,singleton(X0)) = successor(X0),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f170,plain,
! [X0] :
( intersection(X0,regular(X0)) = null_class
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f200,plain,
! [X0,X1] : union(singleton(X0),X1) = set_builder(X0,X1),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f201,plain,
member(u,universal_class),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f202,plain,
set_builder(u,set_builder(y,set_builder(z,null_class))) = null_class,
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f210,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f99,f96]) ).
fof(f225,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| member(X0,unordered_pair(X1,X0)) ),
inference(resolution,[status(thm)],[f108,f210]) ).
fof(f282,plain,
! [X0,X1,X2] : complement(intersection(union(X0,X1),complement(X2))) = union(intersection(complement(X0),complement(X1)),X2),
inference(paramodulation,[status(thm)],[f129,f129]) ).
fof(f300,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(X0,singleton(X0)) ),
inference(paramodulation,[status(thm)],[f110,f225]) ).
fof(f349,plain,
! [X0,X1] :
( X1 = null_class
| member(X0,X1)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f170,f123]) ).
fof(f368,plain,
! [X0] :
( member(u,X0)
| member(u,complement(X0)) ),
inference(resolution,[status(thm)],[f128,f201]) ).
fof(f420,plain,
! [X0,X1] :
( member(u,intersection(complement(X0),complement(X1)))
| member(u,union(X0,X1)) ),
inference(paramodulation,[status(thm)],[f129,f368]) ).
fof(f429,plain,
! [X0,X1] :
( member(u,complement(X0))
| member(u,union(X0,X1)) ),
inference(resolution,[status(thm)],[f420,f123]) ).
fof(f449,plain,
! [X0,X1] :
( ~ member(u,X0)
| member(u,union(X0,X1)) ),
inference(resolution,[status(thm)],[f429,f127]) ).
fof(f452,plain,
! [X0,X1,X2] :
( member(u,union(X0,X1))
| member(u,union(intersection(complement(X0),complement(X1)),X2)) ),
inference(paramodulation,[status(thm)],[f129,f429]) ).
fof(f455,plain,
! [X0,X1,X2] :
( member(u,union(X0,X1))
| member(u,complement(intersection(union(X0,X1),complement(X2)))) ),
inference(forward_demodulation,[status(thm)],[f282,f452]) ).
fof(f662,definition,
( sQ16_spl
<=> member(u,null_class) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f663,plain,
( ~ sQ16_spl
| member(u,null_class) ),
inference(component_clause,[status(thm)],[f662]) ).
fof(f670,plain,
! [X0] :
( ~ sQ16_spl
| X0 = null_class
| member(u,X0) ),
inference(resolution,[status(thm)],[f663,f349]) ).
fof(f679,plain,
! [X0,X1] :
( member(u,successor(X0))
| member(u,complement(intersection(union(X0,singleton(X0)),complement(X1)))) ),
inference(paramodulation,[status(thm)],[f146,f455]) ).
fof(f681,plain,
! [X0,X1] :
( member(u,successor(X0))
| member(u,complement(intersection(successor(X0),complement(X1)))) ),
inference(forward_demodulation,[status(thm)],[f146,f679]) ).
fof(f704,plain,
! [X0] :
( ~ sQ16_spl
| ~ member(u,X0)
| complement(X0) = null_class ),
inference(resolution,[status(thm)],[f670,f127]) ).
fof(f923,plain,
! [X0,X1] :
( ~ member(u,singleton(X0))
| member(u,set_builder(X0,X1)) ),
inference(paramodulation,[status(thm)],[f200,f449]) ).
fof(f966,plain,
! [X0] :
( ~ sQ16_spl
| ~ member(u,X0)
| complement(universal_class) = null_class ),
inference(resolution,[status(thm)],[f704,f210]) ).
fof(f974,definition,
! [X1] :
( sQ31_spl
<=> ~ member(u,X1) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f975,plain,
! [X0] :
( ~ sQ31_spl
| ~ member(u,X0) ),
inference(component_clause,[status(thm)],[f974]) ).
fof(f990,definition,
( sQ35_spl
<=> complement(universal_class) = null_class ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f991,plain,
( ~ sQ35_spl
| complement(universal_class) = null_class ),
inference(component_clause,[status(thm)],[f990]) ).
fof(f993,plain,
( ~ sQ16_spl
| sQ31_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f966,f990,f974,f662]) ).
fof(f1058,plain,
! [X0,X1] :
( ~ member(u,X1)
| member(u,set_builder(u,X0)) ),
inference(resolution,[status(thm)],[f923,f300]) ).
fof(f1059,definition,
! [X0] :
( sQ46_spl
<=> member(u,set_builder(u,X0)) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f1060,plain,
! [X0] :
( ~ sQ46_spl
| member(u,set_builder(u,X0)) ),
inference(component_clause,[status(thm)],[f1059]) ).
fof(f1062,plain,
( sQ31_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f1058,f1059,f974]) ).
fof(f1063,plain,
! [X0] :
( ~ sQ31_spl
| member(u,successor(X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[f681,f975]) ).
fof(f1088,plain,
( ~ sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1063,f975]) ).
fof(f1089,plain,
~ sQ31_spl,
inference(contradiction_clause,[status(thm)],[f1088]) ).
fof(f1090,plain,
( ~ sQ46_spl
| member(u,null_class) ),
inference(paramodulation,[status(thm)],[f202,f1060]) ).
fof(f1092,plain,
( ~ sQ46_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f1090,f662,f1059]) ).
fof(f1316,plain,
! [X0] :
( ~ sQ35_spl
| ~ member(X0,universal_class)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f991,f127]) ).
fof(f1319,plain,
( ~ sQ16_spl
| ~ sQ35_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f663,f1328]) ).
fof(f1328,plain,
! [X0] :
( ~ sQ35_spl
| ~ member(X0,null_class) ),
inference(forward_subsumption_resolution,[status(thm)],[f1316,f210]) ).
fof(f1329,plain,
( ~ sQ16_spl
| ~ sQ35_spl ),
inference(contradiction_clause,[status(thm)],[f1319]) ).
fof(f1330,plain,
$false,
inference(sat_refutation,[status(thm)],[f993,f1062,f1089,f1092,f1329]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET134-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n003.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 04:57:16 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 1.26/0.68 % Refutation found
% 1.26/0.68 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.26/0.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.93/0.71 % Elapsed time: 0.323673 seconds
% 0.93/0.71 % CPU time: 2.245876 seconds
% 0.93/0.71 % Total memory used: 151.364 MB
% 0.93/0.71 % Net memory used: 146.562 MB
%------------------------------------------------------------------------------