%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET247-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 02:09:43 PM UTC 2026
% Result : Unsatisfiable 55.09s 7.57s
% Output : CNFRefutation 55.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 40
% Syntax : Number of formulae : 157 ( 40 unt; 17 def)
% Number of atoms : 287 ( 49 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 242 ( 112 ~; 113 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 18 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 7 con; 0-3 aty)
% Number of variables : 186 ( 186 !; 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(f2,axiom,
! [X,Y] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( subclass(X,Y)
| ~ member(not_subclass_element(X,Y),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] :
( X = Y
| ~ subclass(Y,X)
| ~ subclass(X,Y) ),
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(f15,axiom,
! [U,V,X,Y] :
( member(V,Y)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [Z,X,Y] :
( ordered_pair(first(Z),second(Z)) = Z
| ~ member(Z,cross_product(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [Z,X,Y] :
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [Z,X,Y] :
( member(Z,Y)
| ~ member(Z,intersection(X,Y)) ),
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(f28,axiom,
! [Xr,X,Y] : intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [X,Z] :
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [X] :
( member(null_class,X)
| ~ inductive(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,axiom,
! [X] :
( member(regular(X),X)
| X = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [X] :
( intersection(X,regular(X)) = null_class
| X = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f98,axiom,
subclass(domain_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f99,axiom,
! [X,Y] :
( domain_of(X) = Y
| ~ member(ordered_pair(X,Y),domain_relation) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f100,axiom,
! [X] :
( member(ordered_pair(X,domain_of(X)),domain_relation)
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f113,negated_conjecture,
restrict(xr,x,null_class) != null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f114,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f115,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f116,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f117,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f118,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f121,plain,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f128,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f130,plain,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f133,plain,
! [V,Y] :
( member(V,Y)
| ! [U,X] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f134,plain,
! [X0,X1,X2,X3] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f136,plain,
! [Z] :
( ordered_pair(first(Z),second(Z)) = Z
| ! [X,Y] : ~ member(Z,cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f137,plain,
! [X0,X1,X2] :
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f141,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f142,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f143,plain,
! [Z,Y] :
( member(Z,Y)
| ! [X] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f144,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f145,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f150,plain,
! [X0,X1,X2] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f152,plain,
! [X0,X1] :
( ~ member(X1,domain_of(X0))
| restrict(X0,singleton(X1),universal_class) != null_class ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f166,plain,
subclass(successor_relation,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f169,plain,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f172,plain,
inductive(omega),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f188,plain,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f189,plain,
! [X0] :
( intersection(X0,regular(X0)) = null_class
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f225,plain,
subclass(domain_relation,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f226,plain,
! [X0,X1] :
( domain_of(X0) = X1
| ~ member(ordered_pair(X0,X1),domain_relation) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f227,plain,
! [X0] :
( member(ordered_pair(X0,domain_of(X0)),domain_relation)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f245,plain,
restrict(xr,x,null_class) != null_class,
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f351,definition,
( sQ4_spl
<=> null_class = null_class ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f353,plain,
( sQ4_spl
| null_class != null_class ),
inference(component_clause,[status(thm)],[f351]) ).
fof(f381,plain,
! [X0,X1] : member(ordered_pair(X0,X1),universal_class),
inference(paramodulation,[status(thm)],[f130,f128]) ).
fof(f414,plain,
( sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f353]) ).
fof(f415,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f414]) ).
fof(f515,plain,
! [X0,X1,X2,X3] :
( member(X0,X1)
| ~ member(X0,restrict(X1,X2,X3)) ),
inference(paramodulation,[status(thm)],[f150,f142]) ).
fof(f600,plain,
! [X0,X1] :
( member(regular(intersection(X0,X1)),X1)
| intersection(X0,X1) = null_class ),
inference(resolution,[status(thm)],[f188,f144]) ).
fof(f911,definition,
! [X1] :
( sQ47_spl
<=> ~ member(null_class,X1) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f912,plain,
! [X0] :
( ~ sQ47_spl
| ~ member(null_class,X0) ),
inference(component_clause,[status(thm)],[f911]) ).
fof(f915,plain,
! [X0] :
( ~ sQ47_spl
| ~ inductive(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f169,f912]) ).
fof(f925,plain,
( ~ sQ47_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f172,f915]) ).
fof(f926,plain,
~ sQ47_spl,
inference(contradiction_clause,[status(thm)],[f925]) ).
fof(f1135,definition,
! [X0] :
( sQ54_spl
<=> ~ member(X0,domain_of(null_class)) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f1136,plain,
! [X0] :
( ~ sQ54_spl
| ~ member(X0,domain_of(null_class)) ),
inference(component_clause,[status(thm)],[f1135]) ).
fof(f1146,plain,
( ~ sQ54_spl
| domain_of(null_class) = null_class ),
inference(resolution,[status(thm)],[f1136,f188]) ).
fof(f1254,definition,
( sQ63_spl
<=> member(null_class,universal_class) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f1256,plain,
( sQ63_spl
| ~ member(null_class,universal_class) ),
inference(component_clause,[status(thm)],[f1254]) ).
fof(f1891,plain,
( ~ sQ54_spl
| member(ordered_pair(null_class,null_class),domain_relation)
| ~ member(null_class,universal_class) ),
inference(paramodulation,[status(thm)],[f1146,f227]) ).
fof(f1895,definition,
( sQ98_spl
<=> member(ordered_pair(null_class,null_class),domain_relation) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f1896,plain,
( ~ sQ98_spl
| member(ordered_pair(null_class,null_class),domain_relation) ),
inference(component_clause,[status(thm)],[f1895]) ).
fof(f1898,plain,
( ~ sQ54_spl
| sQ98_spl
| ~ sQ63_spl ),
inference(split_clause,[status(thm)],[f1891,f1254,f1895,f1135]) ).
fof(f2369,plain,
! [X0] :
( sQ63_spl
| ~ member(null_class,X0)
| ~ subclass(X0,universal_class) ),
inference(resolution,[status(thm)],[f115,f1256]) ).
fof(f2415,plain,
! [X0] :
( sQ63_spl
| ~ member(null_class,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2369,f118]) ).
fof(f2432,plain,
! [X0,X1,X2,X3] :
( member(not_subclass_element(restrict(X0,X1,X2),X3),X0)
| subclass(restrict(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f116,f515]) ).
fof(f2433,plain,
! [X0,X1,X2] :
( member(not_subclass_element(intersection(X0,X1),X2),X1)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[f116,f144]) ).
fof(f2434,plain,
! [X0,X1,X2] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[f116,f142]) ).
fof(f2445,plain,
! [X0,X1] :
( sQ63_spl
| ~ member(null_class,X1)
| ~ member(null_class,X0) ),
inference(resolution,[status(thm)],[f2415,f145]) ).
fof(f2449,plain,
( sQ63_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f2445,f911,f1254]) ).
fof(f3240,plain,
( ~ sQ98_spl
| domain_of(null_class) = null_class ),
inference(resolution,[status(thm)],[f226,f1896]) ).
fof(f4060,definition,
( sQ174_spl
<=> subclass(null_class,domain_relation) ),
introduced(definition,[new_symbols(definition,[sQ174_spl])],[split_symbol_definition]) ).
fof(f4062,plain,
( sQ174_spl
| ~ subclass(null_class,domain_relation) ),
inference(component_clause,[status(thm)],[f4060]) ).
fof(f9838,plain,
! [X0,X1,X2] :
( ordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),second(regular(intersection(X0,cross_product(X1,X2))))) = regular(intersection(X0,cross_product(X1,X2)))
| intersection(X0,cross_product(X1,X2)) = null_class ),
inference(resolution,[status(thm)],[f600,f137]) ).
fof(f9861,plain,
! [X0,X1,X2] :
( member(regular(restrict(X0,X1,X2)),cross_product(X1,X2))
| intersection(X0,cross_product(X1,X2)) = null_class ),
inference(paramodulation,[status(thm)],[f150,f600]) ).
fof(f9863,plain,
! [X0,X1,X2] :
( ordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),second(regular(intersection(X0,cross_product(X1,X2))))) = regular(intersection(X0,cross_product(X1,X2)))
| restrict(X0,X1,X2) = null_class ),
inference(forward_demodulation,[status(thm)],[f150,f9838]) ).
fof(f9864,plain,
! [X0,X1,X2] :
( ordered_pair(first(regular(restrict(X0,X1,X2))),second(regular(intersection(X0,cross_product(X1,X2))))) = regular(intersection(X0,cross_product(X1,X2)))
| restrict(X0,X1,X2) = null_class ),
inference(forward_demodulation,[status(thm)],[f150,f9863]) ).
fof(f9865,plain,
! [X0,X1,X2] :
( ordered_pair(first(regular(restrict(X0,X1,X2))),second(regular(restrict(X0,X1,X2)))) = regular(intersection(X0,cross_product(X1,X2)))
| restrict(X0,X1,X2) = null_class ),
inference(forward_demodulation,[status(thm)],[f150,f9864]) ).
fof(f9866,plain,
! [X0,X1,X2] :
( ordered_pair(first(regular(restrict(X0,X1,X2))),second(regular(restrict(X0,X1,X2)))) = regular(restrict(X0,X1,X2))
| restrict(X0,X1,X2) = null_class ),
inference(forward_demodulation,[status(thm)],[f150,f9865]) ).
fof(f9890,plain,
! [X0,X1,X2] :
( member(regular(restrict(X0,X1,X2)),cross_product(X1,X2))
| restrict(X0,X1,X2) = null_class ),
inference(forward_demodulation,[status(thm)],[f150,f9861]) ).
fof(f11312,plain,
! [X0,X1,X2] :
( subclass(restrict(X0,X1,X2),X0)
| subclass(restrict(X0,X1,X2),X0) ),
inference(resolution,[status(thm)],[f2432,f117]) ).
fof(f11335,plain,
! [X0,X1,X2] : subclass(restrict(X0,X1,X2),X0),
inference(duplicate_literals_removal,[status(thm)],[f11312]) ).
fof(f18270,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X1)
| subclass(intersection(X0,X1),X1) ),
inference(resolution,[status(thm)],[f2433,f117]) ).
fof(f18316,plain,
! [X0,X1] : subclass(intersection(X0,X1),X1),
inference(duplicate_literals_removal,[status(thm)],[f18270]) ).
fof(f18338,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[f2434,f117]) ).
fof(f18384,plain,
! [X0,X1] : subclass(intersection(X0,X1),X0),
inference(duplicate_literals_removal,[status(thm)],[f18338]) ).
fof(f19467,plain,
! [X0] :
( X0 = null_class
| subclass(null_class,X0) ),
inference(paramodulation,[status(thm)],[f189,f18384]) ).
fof(f19598,plain,
! [X0] :
( X0 = null_class
| X0 = null_class
| ~ subclass(X0,null_class) ),
inference(resolution,[status(thm)],[f121,f19467]) ).
fof(f19635,plain,
! [X0] :
( X0 = null_class
| ~ subclass(X0,null_class) ),
inference(duplicate_literals_removal,[status(thm)],[f19598]) ).
fof(f21112,plain,
! [X0] : intersection(null_class,X0) = null_class,
inference(resolution,[status(thm)],[f19635,f18384]) ).
fof(f21114,plain,
! [X0,X1] : restrict(null_class,X0,X1) = null_class,
inference(resolution,[status(thm)],[f19635,f11335]) ).
fof(f21184,plain,
! [X0] : subclass(null_class,X0),
inference(paramodulation,[status(thm)],[f21112,f18316]) ).
fof(f22533,plain,
! [X0] : ~ member(X0,domain_of(null_class)),
inference(resolution,[status(thm)],[f21114,f152]) ).
fof(f22536,plain,
! [X0] :
( ~ member(X0,domain_of(null_class))
| null_class != null_class ),
inference(paramodulation,[status(thm)],[f21114,f152]) ).
fof(f22554,plain,
( sQ54_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f22536,f351,f1135]) ).
fof(f22694,plain,
! [X0] :
( ~ sQ98_spl
| ~ member(X0,null_class) ),
inference(forward_demodulation,[status(thm)],[f3240,f22533]) ).
fof(f30910,plain,
ordered_pair(first(regular(restrict(xr,x,null_class))),second(regular(restrict(xr,x,null_class)))) = regular(restrict(xr,x,null_class)),
inference(resolution,[status(thm)],[f9866,f245]) ).
fof(f31267,plain,
member(regular(restrict(xr,x,null_class)),universal_class),
inference(paramodulation,[status(thm)],[f30910,f381]) ).
fof(f31270,plain,
! [X0,X1] :
( member(second(regular(restrict(xr,x,null_class))),X1)
| ~ member(regular(restrict(xr,x,null_class)),cross_product(X0,X1)) ),
inference(paramodulation,[status(thm)],[f30910,f134]) ).
fof(f31942,definition,
( sQ1286_spl
<=> restrict(xr,x,null_class) = null_class ),
introduced(definition,[new_symbols(definition,[sQ1286_spl])],[split_symbol_definition]) ).
fof(f31943,plain,
( ~ sQ1286_spl
| restrict(xr,x,null_class) = null_class ),
inference(component_clause,[status(thm)],[f31942]) ).
fof(f31968,definition,
! [X3] :
( sQ1293_spl
<=> ~ member(regular(restrict(xr,x,null_class)),X3) ),
introduced(definition,[new_symbols(definition,[sQ1293_spl])],[split_symbol_definition]) ).
fof(f31969,plain,
! [X0] :
( ~ sQ1293_spl
| ~ member(regular(restrict(xr,x,null_class)),X0) ),
inference(component_clause,[status(thm)],[f31968]) ).
fof(f32003,plain,
( ~ sQ1286_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f31943,f245]) ).
fof(f32004,plain,
~ sQ1286_spl,
inference(contradiction_clause,[status(thm)],[f32003]) ).
fof(f32796,plain,
( ~ sQ1293_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f31267,f31969]) ).
fof(f32819,plain,
~ sQ1293_spl,
inference(contradiction_clause,[status(thm)],[f32796]) ).
fof(f33050,definition,
( sQ1357_spl
<=> subclass(null_class,range_of(inverse(null_class))) ),
introduced(definition,[new_symbols(definition,[sQ1357_spl])],[split_symbol_definition]) ).
fof(f33052,plain,
( sQ1357_spl
| ~ subclass(null_class,range_of(inverse(null_class))) ),
inference(component_clause,[status(thm)],[f33050]) ).
fof(f33058,plain,
( sQ1357_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f33052,f21184]) ).
fof(f33059,plain,
sQ1357_spl,
inference(contradiction_clause,[status(thm)],[f33058]) ).
fof(f33320,plain,
( sQ174_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4062,f21184]) ).
fof(f33321,plain,
sQ174_spl,
inference(contradiction_clause,[status(thm)],[f33320]) ).
fof(f33629,definition,
! [X0,X1] :
( sQ1392_spl
<=> ~ subclass(successor_relation,cross_product(X0,X1)) ),
introduced(definition,[new_symbols(definition,[sQ1392_spl])],[split_symbol_definition]) ).
fof(f33630,plain,
! [X0,X1] :
( ~ sQ1392_spl
| ~ subclass(successor_relation,cross_product(X0,X1)) ),
inference(component_clause,[status(thm)],[f33629]) ).
fof(f33633,definition,
( sQ1393_spl
<=> subclass(successor_relation,universal_class) ),
introduced(definition,[new_symbols(definition,[sQ1393_spl])],[split_symbol_definition]) ).
fof(f33635,plain,
( sQ1393_spl
| ~ subclass(successor_relation,universal_class) ),
inference(component_clause,[status(thm)],[f33633]) ).
fof(f33640,definition,
! [X0] :
( sQ1394_spl
<=> ~ subclass(successor_relation,X0) ),
introduced(definition,[new_symbols(definition,[sQ1394_spl])],[split_symbol_definition]) ).
fof(f33641,plain,
! [X0] :
( ~ sQ1394_spl
| ~ subclass(successor_relation,X0) ),
inference(component_clause,[status(thm)],[f33640]) ).
fof(f33644,plain,
( sQ1393_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f33635,f118]) ).
fof(f33645,plain,
sQ1393_spl,
inference(contradiction_clause,[status(thm)],[f33644]) ).
fof(f33646,plain,
( ~ sQ1394_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f166,f33641]) ).
fof(f33650,plain,
~ sQ1394_spl,
inference(contradiction_clause,[status(thm)],[f33646]) ).
fof(f34269,plain,
( ~ sQ1392_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f166,f33630]) ).
fof(f34273,plain,
~ sQ1392_spl,
inference(contradiction_clause,[status(thm)],[f34269]) ).
fof(f34478,definition,
! [X0,X1] :
( sQ1410_spl
<=> ~ subclass(domain_relation,cross_product(X0,X1)) ),
introduced(definition,[new_symbols(definition,[sQ1410_spl])],[split_symbol_definition]) ).
fof(f34479,plain,
! [X0,X1] :
( ~ sQ1410_spl
| ~ subclass(domain_relation,cross_product(X0,X1)) ),
inference(component_clause,[status(thm)],[f34478]) ).
fof(f34485,definition,
( sQ1412_spl
<=> subclass(domain_relation,universal_class) ),
introduced(definition,[new_symbols(definition,[sQ1412_spl])],[split_symbol_definition]) ).
fof(f34487,plain,
( sQ1412_spl
| ~ subclass(domain_relation,universal_class) ),
inference(component_clause,[status(thm)],[f34485]) ).
fof(f34504,definition,
! [X0] :
( sQ1417_spl
<=> ~ subclass(domain_relation,X0) ),
introduced(definition,[new_symbols(definition,[sQ1417_spl])],[split_symbol_definition]) ).
fof(f34505,plain,
! [X0] :
( ~ sQ1417_spl
| ~ subclass(domain_relation,X0) ),
inference(component_clause,[status(thm)],[f34504]) ).
fof(f34515,plain,
( sQ1412_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f34487,f118]) ).
fof(f34516,plain,
sQ1412_spl,
inference(contradiction_clause,[status(thm)],[f34515]) ).
fof(f34517,plain,
( ~ sQ1417_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f225,f34505]) ).
fof(f34521,plain,
~ sQ1417_spl,
inference(contradiction_clause,[status(thm)],[f34517]) ).
fof(f34653,plain,
( ~ sQ1410_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f225,f34479]) ).
fof(f34657,plain,
~ sQ1410_spl,
inference(contradiction_clause,[status(thm)],[f34653]) ).
fof(f34898,definition,
( sQ1438_spl
<=> subclass(range_of(null_class),universal_class) ),
introduced(definition,[new_symbols(definition,[sQ1438_spl])],[split_symbol_definition]) ).
fof(f34900,plain,
( sQ1438_spl
| ~ subclass(range_of(null_class),universal_class) ),
inference(component_clause,[status(thm)],[f34898]) ).
fof(f34938,plain,
( sQ1438_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f34900,f118]) ).
fof(f34939,plain,
sQ1438_spl,
inference(contradiction_clause,[status(thm)],[f34938]) ).
fof(f35204,definition,
( sQ1459_spl
<=> member(second(regular(restrict(xr,x,null_class))),null_class) ),
introduced(definition,[new_symbols(definition,[sQ1459_spl])],[split_symbol_definition]) ).
fof(f35205,plain,
( ~ sQ1459_spl
| member(second(regular(restrict(xr,x,null_class))),null_class) ),
inference(component_clause,[status(thm)],[f35204]) ).
fof(f35408,plain,
( restrict(xr,x,null_class) = null_class
| member(second(regular(restrict(xr,x,null_class))),null_class) ),
inference(resolution,[status(thm)],[f31270,f9890]) ).
fof(f35419,plain,
( sQ1286_spl
| sQ1459_spl ),
inference(split_clause,[status(thm)],[f35408,f35204,f31942]) ).
fof(f35429,plain,
( ~ sQ1459_spl
| ~ sQ98_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f35205,f22694]) ).
fof(f35430,plain,
( ~ sQ1459_spl
| ~ sQ98_spl ),
inference(contradiction_clause,[status(thm)],[f35429]) ).
fof(f35431,plain,
$false,
inference(sat_refutation,[status(thm)],[f415,f926,f1898,f2449,f22554,f32004,f32819,f33059,f33321,f33645,f33650,f34273,f34516,f34521,f34657,f34939,f35419,f35430]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET247-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n007.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 21 05:00:51 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.45 % Drodi V4.1.1
% 55.09/7.57 % Refutation found
% 55.09/7.57 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 55.09/7.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 55.09/7.69 % Elapsed time: 7.240312 seconds
% 55.09/7.69 % CPU time: 56.698554 seconds
% 55.09/7.69 % Total memory used: 433.711 MB
% 55.09/7.69 % Net memory used: 395.677 MB
%------------------------------------------------------------------------------