%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET013-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 02:08:50 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 39
% Syntax : Number of formulae : 159 ( 19 unt; 25 def)
% Number of atoms : 347 ( 20 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 343 ( 155 ~; 163 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 29 ( 27 usr; 26 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 293 ( 293 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( little_set(X)
| ~ member(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( X = Y
| member(f1(X,Y),Y)
| member(f1(X,Y),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] :
( X = Y
| ~ member(f1(X,Y),Y)
| ~ member(f1(X,Y),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] : little_set(non_ordered_pair(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] : ordered_pair(X,Y) = non_ordered_pair(singleton_set(X),non_ordered_pair(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [Z,X,Y] :
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [Z,X,Y] :
( member(Z,Y)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [Z,X,Y] :
( ~ member(Z,Y)
| ~ member(Z,X)
| member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [Z] : ~ member(Z,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f61,axiom,
member(empty_set,infinity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f101,axiom,
! [X] :
( member(f26(X),X)
| X = empty_set
| ~ little_set(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f142,hypothesis,
intersection(as,bs) = cs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f143,hypothesis,
intersection(bs,as) = ds,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f144,negated_conjecture,
cs != ds,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f145,plain,
! [X] :
( little_set(X)
| ! [Y] : ~ member(X,Y) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f146,plain,
! [X0,X1] :
( little_set(X0)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f148,plain,
! [X0,X1] :
( X0 = X1
| member(f1(X0,X1),X1)
| member(f1(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f149,plain,
! [X0,X1] :
( X0 = X1
| ~ member(f1(X0,X1),X1)
| ~ member(f1(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f156,plain,
! [X0,X1] : little_set(non_ordered_pair(X0,X1)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f158,plain,
! [X0,X1] : ordered_pair(X0,X1) = non_ordered_pair(singleton_set(X0),non_ordered_pair(X0,X1)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f178,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f179,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f178]) ).
fof(f180,plain,
! [Z,Y] :
( member(Z,Y)
| ! [X] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f181,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f180]) ).
fof(f182,plain,
! [Z,Y] :
( ~ member(Z,Y)
| ! [X] :
( ~ member(Z,X)
| member(Z,intersection(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f30]) ).
fof(f183,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f182]) ).
fof(f219,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f222,plain,
member(empty_set,infinity),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f268,plain,
! [X0] :
( member(f26(X0),X0)
| X0 = empty_set
| ~ little_set(X0) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f322,plain,
intersection(as,bs) = cs,
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f323,plain,
intersection(bs,as) = ds,
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f324,plain,
cs != ds,
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f339,plain,
( ~ member(f1(cs,ds),ds)
| ~ member(f1(cs,ds),cs) ),
inference(resolution,[status(thm)],[f149,f324]) ).
fof(f340,plain,
( ~ member(f1(ds,cs),cs)
| ~ member(f1(ds,cs),ds) ),
inference(resolution,[status(thm)],[f149,f324]) ).
fof(f341,definition,
( sQ0_spl
<=> member(f1(cs,ds),cs) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f343,plain,
( sQ0_spl
| ~ member(f1(cs,ds),cs) ),
inference(component_clause,[status(thm)],[f341]) ).
fof(f344,definition,
( sQ1_spl
<=> member(f1(cs,ds),ds) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f346,plain,
( sQ1_spl
| ~ member(f1(cs,ds),ds) ),
inference(component_clause,[status(thm)],[f344]) ).
fof(f347,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f339,f341,f344]) ).
fof(f348,definition,
( sQ2_spl
<=> member(f1(ds,cs),ds) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f350,plain,
( sQ2_spl
| ~ member(f1(ds,cs),ds) ),
inference(component_clause,[status(thm)],[f348]) ).
fof(f351,definition,
( sQ3_spl
<=> member(f1(ds,cs),cs) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f352,plain,
( ~ sQ3_spl
| member(f1(ds,cs),cs) ),
inference(component_clause,[status(thm)],[f351]) ).
fof(f353,plain,
( sQ3_spl
| ~ member(f1(ds,cs),cs) ),
inference(component_clause,[status(thm)],[f351]) ).
fof(f354,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f340,f348,f351]) ).
fof(f371,plain,
( empty_set = empty_set
| ~ little_set(empty_set) ),
inference(resolution,[status(thm)],[f268,f219]) ).
fof(f372,definition,
( sQ4_spl
<=> little_set(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f374,plain,
( sQ4_spl
| ~ little_set(empty_set) ),
inference(component_clause,[status(thm)],[f372]) ).
fof(f375,definition,
( sQ5_spl
<=> empty_set = empty_set ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f378,plain,
( sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f371,f372,f375]) ).
fof(f383,plain,
( sQ2_spl
| ds = cs
| member(f1(ds,cs),cs) ),
inference(resolution,[status(thm)],[f350,f148]) ).
fof(f384,definition,
( sQ6_spl
<=> ds = cs ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f385,plain,
( ~ sQ6_spl
| ds = cs ),
inference(component_clause,[status(thm)],[f384]) ).
fof(f387,plain,
( sQ2_spl
| sQ6_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f383,f351,f384,f348]) ).
fof(f388,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f385,f324]) ).
fof(f389,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f388]) ).
fof(f390,plain,
( sQ0_spl
| cs = ds
| member(f1(cs,ds),ds) ),
inference(resolution,[status(thm)],[f343,f148]) ).
fof(f391,plain,
( sQ0_spl
| sQ6_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f390,f344,f384,f341]) ).
fof(f396,plain,
! [X0] :
( sQ4_spl
| ~ member(empty_set,X0) ),
inference(resolution,[status(thm)],[f374,f146]) ).
fof(f397,plain,
( sQ4_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f222,f396]) ).
fof(f398,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f397]) ).
fof(f404,plain,
! [X0,X1] : little_set(ordered_pair(X0,X1)),
inference(paramodulation,[status(thm)],[f158,f156]) ).
fof(f416,plain,
! [X0] :
( sQ2_spl
| ~ member(f1(ds,cs),intersection(ds,X0)) ),
inference(resolution,[status(thm)],[f179,f350]) ).
fof(f419,plain,
! [X0,X1] :
( sQ2_spl
| ~ member(f1(ds,cs),intersection(intersection(ds,X0),X1)) ),
inference(resolution,[status(thm)],[f416,f179]) ).
fof(f425,plain,
! [X0,X1,X2] :
( sQ2_spl
| ~ member(f1(ds,cs),intersection(intersection(intersection(ds,X0),X1),X2)) ),
inference(resolution,[status(thm)],[f419,f179]) ).
fof(f429,plain,
! [X0,X1,X2,X3] :
( sQ2_spl
| ~ member(f1(ds,cs),intersection(intersection(intersection(intersection(ds,X0),X1),X2),X3)) ),
inference(resolution,[status(thm)],[f425,f179]) ).
fof(f431,plain,
! [X0,X1,X2,X3,X4] :
( sQ2_spl
| ~ member(f1(ds,cs),intersection(intersection(intersection(intersection(intersection(ds,X0),X1),X2),X3),X4)) ),
inference(resolution,[status(thm)],[f429,f179]) ).
fof(f435,plain,
! [X0,X1,X2,X3,X4,X5] :
( sQ2_spl
| ~ member(f1(ds,cs),intersection(intersection(intersection(intersection(intersection(intersection(ds,X0),X1),X2),X3),X4),X5)) ),
inference(resolution,[status(thm)],[f431,f179]) ).
fof(f441,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( sQ2_spl
| ~ member(f1(ds,cs),intersection(intersection(intersection(intersection(intersection(intersection(intersection(ds,X0),X1),X2),X3),X4),X5),X6)) ),
inference(resolution,[status(thm)],[f435,f179]) ).
fof(f445,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( sQ2_spl
| ~ member(f1(ds,cs),intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(ds,X0),X1),X2),X3),X4),X5),X6),X7)) ),
inference(resolution,[status(thm)],[f441,f179]) ).
fof(f449,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( sQ2_spl
| ~ member(f1(ds,cs),intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(ds,X0),X1),X2),X3),X4),X5),X6),X7),X8)) ),
inference(resolution,[status(thm)],[f445,f179]) ).
fof(f451,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( sQ2_spl
| ~ member(f1(ds,cs),intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(ds,X0),X1),X2),X3),X4),X5),X6),X7),X8),X9)) ),
inference(resolution,[status(thm)],[f449,f179]) ).
fof(f455,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] :
( sQ2_spl
| ~ member(f1(ds,cs),intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(ds,X0),X1),X2),X3),X4),X5),X6),X7),X8),X9),X10)) ),
inference(resolution,[status(thm)],[f451,f179]) ).
fof(f459,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( sQ2_spl
| ~ member(f1(ds,cs),intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(ds,X0),X1),X2),X3),X4),X5),X6),X7),X8),X9),X10),X11)) ),
inference(resolution,[status(thm)],[f455,f179]) ).
fof(f555,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( sQ2_spl
| ~ member(f1(ds,cs),X11)
| ~ member(f1(ds,cs),intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(ds,X0),X1),X2),X3),X4),X5),X6),X7),X8),X9),X10)) ),
inference(resolution,[status(thm)],[f183,f459]) ).
fof(f556,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] :
( sQ2_spl
| ~ member(f1(ds,cs),X10)
| ~ member(f1(ds,cs),intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(ds,X0),X1),X2),X3),X4),X5),X6),X7),X8),X9)) ),
inference(resolution,[status(thm)],[f183,f455]) ).
fof(f557,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( sQ2_spl
| ~ member(f1(ds,cs),X9)
| ~ member(f1(ds,cs),intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(ds,X0),X1),X2),X3),X4),X5),X6),X7),X8)) ),
inference(resolution,[status(thm)],[f183,f451]) ).
fof(f558,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( sQ2_spl
| ~ member(f1(ds,cs),X8)
| ~ member(f1(ds,cs),intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(ds,X0),X1),X2),X3),X4),X5),X6),X7)) ),
inference(resolution,[status(thm)],[f183,f449]) ).
fof(f559,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( sQ2_spl
| ~ member(f1(ds,cs),X7)
| ~ member(f1(ds,cs),intersection(intersection(intersection(intersection(intersection(intersection(intersection(ds,X0),X1),X2),X3),X4),X5),X6)) ),
inference(resolution,[status(thm)],[f183,f445]) ).
fof(f560,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( sQ2_spl
| ~ member(f1(ds,cs),X6)
| ~ member(f1(ds,cs),intersection(intersection(intersection(intersection(intersection(intersection(ds,X0),X1),X2),X3),X4),X5)) ),
inference(resolution,[status(thm)],[f183,f441]) ).
fof(f561,plain,
! [X0,X1,X2,X3,X4,X5] :
( sQ2_spl
| ~ member(f1(ds,cs),X5)
| ~ member(f1(ds,cs),intersection(intersection(intersection(intersection(intersection(ds,X0),X1),X2),X3),X4)) ),
inference(resolution,[status(thm)],[f183,f435]) ).
fof(f562,plain,
! [X0,X1,X2,X3,X4] :
( sQ2_spl
| ~ member(f1(ds,cs),X4)
| ~ member(f1(ds,cs),intersection(intersection(intersection(intersection(ds,X0),X1),X2),X3)) ),
inference(resolution,[status(thm)],[f183,f431]) ).
fof(f563,plain,
! [X0,X1,X2,X3] :
( sQ2_spl
| ~ member(f1(ds,cs),X3)
| ~ member(f1(ds,cs),intersection(intersection(intersection(ds,X0),X1),X2)) ),
inference(resolution,[status(thm)],[f183,f429]) ).
fof(f564,plain,
! [X0,X1,X2] :
( sQ2_spl
| ~ member(f1(ds,cs),X2)
| ~ member(f1(ds,cs),intersection(intersection(ds,X0),X1)) ),
inference(resolution,[status(thm)],[f183,f425]) ).
fof(f565,plain,
! [X0,X1] :
( sQ2_spl
| ~ member(f1(ds,cs),X1)
| ~ member(f1(ds,cs),intersection(ds,X0)) ),
inference(resolution,[status(thm)],[f183,f419]) ).
fof(f567,plain,
! [X0] :
( ~ member(X0,as)
| ~ member(X0,bs)
| member(X0,ds) ),
inference(paramodulation,[status(thm)],[f323,f183]) ).
fof(f568,plain,
! [X0] :
( ~ member(X0,bs)
| ~ member(X0,as)
| member(X0,cs) ),
inference(paramodulation,[status(thm)],[f322,f183]) ).
fof(f719,definition,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] :
( sQ45_spl
<=> ~ member(f1(ds,cs),intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(ds,X0),X1),X2),X3),X4),X5),X6),X7),X8),X9),X10)) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f722,definition,
! [X11] :
( sQ46_spl
<=> ~ member(f1(ds,cs),X11) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f723,plain,
! [X0] :
( ~ sQ46_spl
| ~ member(f1(ds,cs),X0) ),
inference(component_clause,[status(thm)],[f722]) ).
fof(f725,plain,
( sQ2_spl
| sQ46_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f555,f719,f722,f348]) ).
fof(f726,definition,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( sQ47_spl
<=> ~ member(f1(ds,cs),intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(ds,X0),X1),X2),X3),X4),X5),X6),X7),X8),X9)) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f729,plain,
( sQ2_spl
| sQ46_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f556,f726,f722,f348]) ).
fof(f730,definition,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( sQ48_spl
<=> ~ member(f1(ds,cs),intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(ds,X0),X1),X2),X3),X4),X5),X6),X7),X8)) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f733,plain,
( sQ2_spl
| sQ46_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f557,f730,f722,f348]) ).
fof(f734,definition,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( sQ49_spl
<=> ~ member(f1(ds,cs),intersection(intersection(intersection(intersection(intersection(intersection(intersection(intersection(ds,X0),X1),X2),X3),X4),X5),X6),X7)) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f737,plain,
( sQ2_spl
| sQ46_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f558,f734,f722,f348]) ).
fof(f738,definition,
! [X0,X1,X2,X3,X4,X5,X6] :
( sQ50_spl
<=> ~ member(f1(ds,cs),intersection(intersection(intersection(intersection(intersection(intersection(intersection(ds,X0),X1),X2),X3),X4),X5),X6)) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f741,plain,
( sQ2_spl
| sQ46_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f559,f738,f722,f348]) ).
fof(f742,definition,
! [X0,X1,X2,X3,X4,X5] :
( sQ51_spl
<=> ~ member(f1(ds,cs),intersection(intersection(intersection(intersection(intersection(intersection(ds,X0),X1),X2),X3),X4),X5)) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f745,plain,
( sQ2_spl
| sQ46_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f560,f742,f722,f348]) ).
fof(f746,definition,
! [X0,X1,X2,X3,X4] :
( sQ52_spl
<=> ~ member(f1(ds,cs),intersection(intersection(intersection(intersection(intersection(ds,X0),X1),X2),X3),X4)) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f749,plain,
( sQ2_spl
| sQ46_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f561,f746,f722,f348]) ).
fof(f750,definition,
! [X0,X1,X2,X3] :
( sQ53_spl
<=> ~ member(f1(ds,cs),intersection(intersection(intersection(intersection(ds,X0),X1),X2),X3)) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f753,plain,
( sQ2_spl
| sQ46_spl
| sQ53_spl ),
inference(split_clause,[status(thm)],[f562,f750,f722,f348]) ).
fof(f754,definition,
! [X0,X1,X2] :
( sQ54_spl
<=> ~ member(f1(ds,cs),intersection(intersection(intersection(ds,X0),X1),X2)) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f757,plain,
( sQ2_spl
| sQ46_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f563,f754,f722,f348]) ).
fof(f758,definition,
! [X0,X1] :
( sQ55_spl
<=> ~ member(f1(ds,cs),intersection(intersection(ds,X0),X1)) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f761,plain,
( sQ2_spl
| sQ46_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f564,f758,f722,f348]) ).
fof(f762,definition,
! [X0] :
( sQ56_spl
<=> ~ member(f1(ds,cs),intersection(ds,X0)) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f765,plain,
( sQ2_spl
| sQ46_spl
| sQ56_spl ),
inference(split_clause,[status(thm)],[f565,f762,f722,f348]) ).
fof(f807,definition,
! [X0] :
( sQ60_spl
<=> ~ little_set(X0) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f808,plain,
! [X0] :
( ~ sQ60_spl
| ~ little_set(X0) ),
inference(component_clause,[status(thm)],[f807]) ).
fof(f819,plain,
( ~ sQ60_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f404,f808]) ).
fof(f846,plain,
~ sQ60_spl,
inference(contradiction_clause,[status(thm)],[f819]) ).
fof(f896,definition,
! [X1] :
( sQ65_spl
<=> ~ member(f1(ds,cs),intersection(X1,cs)) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f897,plain,
! [X0] :
( ~ sQ65_spl
| ~ member(f1(ds,cs),intersection(X0,cs)) ),
inference(component_clause,[status(thm)],[f896]) ).
fof(f908,plain,
! [X0] :
( ~ sQ65_spl
| ~ member(f1(ds,cs),cs)
| ~ member(f1(ds,cs),X0) ),
inference(resolution,[status(thm)],[f897,f183]) ).
fof(f911,plain,
( ~ sQ65_spl
| ~ sQ3_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f908,f722,f351,f896]) ).
fof(f1018,plain,
( sQ1_spl
| ~ member(f1(cs,ds),as)
| ~ member(f1(cs,ds),bs) ),
inference(resolution,[status(thm)],[f567,f346]) ).
fof(f1020,definition,
( sQ72_spl
<=> member(f1(cs,ds),bs) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1022,plain,
( sQ72_spl
| ~ member(f1(cs,ds),bs) ),
inference(component_clause,[status(thm)],[f1020]) ).
fof(f1023,definition,
( sQ73_spl
<=> member(f1(cs,ds),as) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f1025,plain,
( sQ73_spl
| ~ member(f1(cs,ds),as) ),
inference(component_clause,[status(thm)],[f1023]) ).
fof(f1026,plain,
( sQ1_spl
| ~ sQ73_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f1018,f1020,f1023,f344]) ).
fof(f1034,plain,
! [X0] :
( sQ72_spl
| ~ member(f1(cs,ds),intersection(X0,bs)) ),
inference(resolution,[status(thm)],[f1022,f181]) ).
fof(f1035,plain,
! [X0] :
( sQ72_spl
| ~ member(f1(cs,ds),intersection(bs,X0)) ),
inference(resolution,[status(thm)],[f1022,f179]) ).
fof(f1036,plain,
( sQ3_spl
| ~ member(f1(ds,cs),bs)
| ~ member(f1(ds,cs),as) ),
inference(resolution,[status(thm)],[f568,f353]) ).
fof(f1038,definition,
( sQ76_spl
<=> member(f1(ds,cs),as) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f1040,plain,
( sQ76_spl
| ~ member(f1(ds,cs),as) ),
inference(component_clause,[status(thm)],[f1038]) ).
fof(f1041,definition,
( sQ77_spl
<=> member(f1(ds,cs),bs) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1043,plain,
( sQ77_spl
| ~ member(f1(ds,cs),bs) ),
inference(component_clause,[status(thm)],[f1041]) ).
fof(f1044,plain,
( sQ3_spl
| ~ sQ77_spl
| ~ sQ76_spl ),
inference(split_clause,[status(thm)],[f1036,f1038,f1041,f351]) ).
fof(f1046,plain,
! [X0] :
( sQ76_spl
| ~ member(f1(ds,cs),intersection(X0,as)) ),
inference(resolution,[status(thm)],[f1040,f181]) ).
fof(f1071,plain,
( sQ72_spl
| ~ member(f1(cs,ds),cs) ),
inference(paramodulation,[status(thm)],[f322,f1034]) ).
fof(f1073,plain,
( sQ72_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f1071,f341,f1020]) ).
fof(f1074,plain,
! [X0] :
( sQ73_spl
| ~ member(f1(cs,ds),intersection(X0,as)) ),
inference(resolution,[status(thm)],[f1025,f181]) ).
fof(f1075,plain,
! [X0] :
( sQ73_spl
| ~ member(f1(cs,ds),intersection(as,X0)) ),
inference(resolution,[status(thm)],[f1025,f179]) ).
fof(f1079,plain,
( sQ76_spl
| ~ member(f1(ds,cs),ds) ),
inference(paramodulation,[status(thm)],[f323,f1046]) ).
fof(f1081,plain,
( sQ76_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f1079,f348,f1038]) ).
fof(f1082,plain,
! [X0] :
( sQ77_spl
| ~ member(f1(ds,cs),intersection(X0,bs)) ),
inference(resolution,[status(thm)],[f1043,f181]) ).
fof(f1083,plain,
! [X0] :
( sQ77_spl
| ~ member(f1(ds,cs),intersection(bs,X0)) ),
inference(resolution,[status(thm)],[f1043,f179]) ).
fof(f1087,plain,
( sQ73_spl
| ~ member(f1(cs,ds),ds) ),
inference(paramodulation,[status(thm)],[f323,f1074]) ).
fof(f1092,plain,
( sQ73_spl
| ~ member(f1(cs,ds),cs) ),
inference(paramodulation,[status(thm)],[f322,f1075]) ).
fof(f1094,plain,
( sQ73_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f1092,f341,f1023]) ).
fof(f1098,plain,
( sQ0_spl
| ~ member(f1(cs,ds),bs)
| ~ member(f1(cs,ds),as) ),
inference(resolution,[status(thm)],[f343,f568]) ).
fof(f1102,plain,
( sQ0_spl
| ~ sQ72_spl
| ~ sQ73_spl ),
inference(split_clause,[status(thm)],[f1098,f1023,f1020,f341]) ).
fof(f1103,plain,
( sQ73_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f1087,f344,f1023]) ).
fof(f1109,plain,
( sQ77_spl
| ~ member(f1(ds,cs),cs) ),
inference(paramodulation,[status(thm)],[f322,f1082]) ).
fof(f1114,plain,
( sQ77_spl
| ~ member(f1(ds,cs),ds) ),
inference(paramodulation,[status(thm)],[f323,f1083]) ).
fof(f1116,plain,
( sQ77_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f1114,f348,f1041]) ).
fof(f1117,plain,
( ~ sQ3_spl
| ~ sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f352,f723]) ).
fof(f1118,plain,
( ~ sQ3_spl
| ~ sQ46_spl ),
inference(contradiction_clause,[status(thm)],[f1117]) ).
fof(f1120,plain,
( sQ2_spl
| ~ member(f1(ds,cs),as)
| ~ member(f1(ds,cs),bs) ),
inference(resolution,[status(thm)],[f350,f567]) ).
fof(f1124,plain,
( sQ2_spl
| ~ sQ76_spl
| ~ sQ77_spl ),
inference(split_clause,[status(thm)],[f1120,f1041,f1038,f348]) ).
fof(f1125,plain,
( sQ77_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1109,f351,f1041]) ).
fof(f1143,plain,
( sQ72_spl
| ~ member(f1(cs,ds),ds) ),
inference(paramodulation,[status(thm)],[f323,f1035]) ).
fof(f1145,plain,
( sQ72_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f1143,f344,f1020]) ).
fof(f1146,plain,
$false,
inference(sat_refutation,[status(thm)],[f347,f354,f378,f387,f389,f391,f398,f725,f729,f733,f737,f741,f745,f749,f753,f757,f761,f765,f846,f911,f1026,f1044,f1073,f1081,f1094,f1102,f1103,f1116,f1118,f1124,f1125,f1145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET013-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Mon Sep 21 04:41:23 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.30 % Drodi V4.1.1
% 0.08/0.38 % Refutation found
% 0.08/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.39 % Elapsed time: 0.091914 seconds
% 0.08/0.39 % CPU time: 0.348470 seconds
% 0.08/0.39 % Total memory used: 116.986 MB
% 0.08/0.39 % Net memory used: 116.399 MB
%------------------------------------------------------------------------------