%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU234+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 02:19:49 PM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 41
% Syntax : Number of formulae : 179 ( 35 unt; 24 def)
% Number of atoms : 455 ( 21 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 418 ( 142 ~; 152 |; 84 &)
% ( 28 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 36 ( 34 usr; 25 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-1 aty)
% Number of variables : 99 ( 87 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] :
( ( function(A)
& empty(A)
& relation(A) )
=> ( one_to_one(A)
& function(A)
& relation(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
=> ordinal(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] :
( empty(A)
=> ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] :
( epsilon_connected(A)
<=> ! [B,C] :
~ ( ~ in(C,B)
& B != C
& ~ in(B,C)
& in(C,A)
& in(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ in(B,A)
& A != B
& ~ in(A,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,conjecture,
! [A] :
( ! [B] :
( in(B,A)
=> ( subset(B,A)
& ordinal(B) ) )
=> ordinal(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
~ ! [A] :
( ! [B] :
( in(B,A)
=> ( subset(B,A)
& ordinal(B) ) )
=> ordinal(A) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f39,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,plain,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f47,plain,
! [X0] :
( epsilon_connected(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f48,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f49,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,plain,
! [A] :
( ( one_to_one(A)
& function(A)
& relation(A) )
| ~ function(A)
| ~ empty(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f53,plain,
! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f54,plain,
! [A] :
( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f55,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
! [A] :
( ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f59,plain,
! [X0] :
( ordinal(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f60,plain,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( subset(B,A)
| ~ in(B,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f61,plain,
! [A] :
( ( ? [B] :
( ~ subset(B,A)
& in(B,A) )
| epsilon_transitive(A) )
& ( ! [B] :
( subset(B,A)
| ~ in(B,A) )
| ~ epsilon_transitive(A) ) ),
inference(NNF_transformation,[status(thm)],[f60]) ).
fof(f62,plain,
( ! [A] :
( ? [B] :
( ~ subset(B,A)
& in(B,A) )
| epsilon_transitive(A) )
& ! [A] :
( ! [B] :
( subset(B,A)
| ~ in(B,A) )
| ~ epsilon_transitive(A) ) ),
inference(miniscoping,[status(thm)],[f61]) ).
fof(f63,plain,
( ! [A] :
( ( ~ subset(sK0_skl(A),A)
& in(sK0_skl(A),A) )
| epsilon_transitive(A) )
& ! [A] :
( ! [B] :
( subset(B,A)
| ~ in(B,A) )
| ~ epsilon_transitive(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B,sK0_skl(A))],[f62]) ).
fof(f65,plain,
! [X0] :
( in(sK0_skl(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f66,plain,
! [X0] :
( ~ subset(sK0_skl(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f67,plain,
! [A] :
( epsilon_connected(A)
<=> ! [B,C] :
( in(C,B)
| B = C
| in(B,C)
| ~ in(C,A)
| ~ in(B,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f68,plain,
! [A] :
( ( ? [B,C] :
( ~ in(C,B)
& B != C
& ~ in(B,C)
& in(C,A)
& in(B,A) )
| epsilon_connected(A) )
& ( ! [B,C] :
( in(C,B)
| B = C
| in(B,C)
| ~ in(C,A)
| ~ in(B,A) )
| ~ epsilon_connected(A) ) ),
inference(NNF_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
( ! [A] :
( ? [B,C] :
( ~ in(C,B)
& B != C
& ~ in(B,C)
& in(C,A)
& in(B,A) )
| epsilon_connected(A) )
& ! [A] :
( ! [B,C] :
( in(C,B)
| B = C
| in(B,C)
| ~ in(C,A)
| ~ in(B,A) )
| ~ epsilon_connected(A) ) ),
inference(miniscoping,[status(thm)],[f68]) ).
fof(f70,plain,
( ! [A] :
( ( ~ in(sK2_skl(A),sK1_skl(A))
& sK1_skl(A) != sK2_skl(A)
& ~ in(sK1_skl(A),sK2_skl(A))
& in(sK2_skl(A),A)
& in(sK1_skl(A),A) )
| epsilon_connected(A) )
& ! [A] :
( ! [B,C] :
( in(C,B)
| B = C
| in(B,C)
| ~ in(C,A)
| ~ in(B,A) )
| ~ epsilon_connected(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(B,sK1_skl(A)),skolemize(C,sK2_skl(A))],[f69]) ).
fof(f72,plain,
! [X0] :
( in(sK1_skl(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f73,plain,
! [X0] :
( in(sK2_skl(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f74,plain,
! [X0] :
( ~ in(sK1_skl(X0),sK2_skl(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f75,plain,
! [X0] :
( sK1_skl(X0) != sK2_skl(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f76,plain,
! [X0] :
( ~ in(sK2_skl(X0),sK1_skl(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f84,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f90,plain,
function(empty_set),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f93,plain,
epsilon_transitive(empty_set),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f95,plain,
ordinal(empty_set),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f101,plain,
( ordinal(sK5_skl)
& epsilon_connected(sK5_skl)
& epsilon_transitive(sK5_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(A,sK5_skl)],[f17]) ).
fof(f102,plain,
epsilon_transitive(sK5_skl),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f103,plain,
epsilon_connected(sK5_skl),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f105,plain,
( relation(sK6_skl)
& empty(sK6_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(A,sK6_skl)],[f18]) ).
fof(f106,plain,
empty(sK6_skl),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f110,plain,
( function(sK8_skl)
& empty(sK8_skl)
& relation(sK8_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(A,sK8_skl)],[f20]) ).
fof(f112,plain,
empty(sK8_skl),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f113,plain,
function(sK8_skl),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f114,plain,
( ordinal(sK9_skl)
& epsilon_connected(sK9_skl)
& epsilon_transitive(sK9_skl)
& empty(sK9_skl)
& one_to_one(sK9_skl)
& function(sK9_skl)
& relation(sK9_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(A,sK9_skl)],[f21]) ).
fof(f116,plain,
function(sK9_skl),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f118,plain,
empty(sK9_skl),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f119,plain,
epsilon_transitive(sK9_skl),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f120,plain,
epsilon_connected(sK9_skl),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f131,plain,
( ordinal(sK13_skl)
& epsilon_connected(sK13_skl)
& epsilon_transitive(sK13_skl)
& ~ empty(sK13_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(A,sK13_skl)],[f25]) ).
fof(f133,plain,
epsilon_transitive(sK13_skl),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f134,plain,
epsilon_connected(sK13_skl),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f151,plain,
! [A] :
( ! [B] :
( in(B,A)
| A = B
| in(A,B)
| ~ ordinal(B) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f152,plain,
! [X0,X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f155,plain,
? [A] :
( ~ ordinal(A)
& ! [B] :
( ( subset(B,A)
& ordinal(B) )
| ~ in(B,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f156,plain,
( ~ ordinal(sK17_skl)
& ! [B] :
( ( subset(B,sK17_skl)
& ordinal(B) )
| ~ in(B,sK17_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl]),skolemize(A,sK17_skl)],[f155]) ).
fof(f157,plain,
! [X0] :
( ordinal(X0)
| ~ in(X0,sK17_skl) ),
inference(cnf_transformation,[status(thm)],[f156]) ).
fof(f158,plain,
! [X0] :
( subset(X0,sK17_skl)
| ~ in(X0,sK17_skl) ),
inference(cnf_transformation,[status(thm)],[f156]) ).
fof(f159,plain,
~ ordinal(sK17_skl),
inference(cnf_transformation,[status(thm)],[f156]) ).
fof(f172,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f173,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f172]) ).
fof(f174,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f173]) ).
fof(f178,plain,
epsilon_connected(empty_set),
inference(resolution,[status(thm)],[f47,f95]) ).
fof(f182,plain,
! [X0,X1] :
( ~ empty(X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f152,f174]) ).
fof(f184,definition,
( sQ0_spl
<=> ordinal(sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( ~ sQ0_spl
| ordinal(sK17_skl) ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f195,plain,
! [X0,X1] :
( ~ empty(X1)
| X1 = X0
| in(X1,X0)
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f182,f59]) ).
fof(f199,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| X1 = X0
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f195,f174]) ).
fof(f209,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| X0 = X1 ),
inference(forward_subsumption_resolution,[status(thm)],[f199,f59]) ).
fof(f212,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f84,f209]) ).
fof(f220,plain,
sK6_skl = empty_set,
inference(resolution,[status(thm)],[f106,f212]) ).
fof(f222,plain,
! [X0] :
( ~ empty(X0)
| X0 = sK6_skl ),
inference(resolution,[status(thm)],[f106,f209]) ).
fof(f232,plain,
! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f53,f49]) ).
fof(f234,plain,
( one_to_one(empty_set)
| ~ empty(empty_set) ),
inference(resolution,[status(thm)],[f232,f90]) ).
fof(f242,definition,
( sQ7_spl
<=> empty(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f244,plain,
( sQ7_spl
| ~ empty(empty_set) ),
inference(component_clause,[status(thm)],[f242]) ).
fof(f245,definition,
( sQ8_spl
<=> one_to_one(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f248,plain,
( sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f234,f242,f245]) ).
fof(f249,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f244,f84]) ).
fof(f250,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f249]) ).
fof(f251,plain,
epsilon_transitive(sK6_skl),
inference(backward_demodulation,[status(thm)],[f220,f93]) ).
fof(f253,plain,
function(sK6_skl),
inference(backward_demodulation,[status(thm)],[f220,f90]) ).
fof(f258,plain,
epsilon_connected(sK6_skl),
inference(backward_demodulation,[status(thm)],[f220,f178]) ).
fof(f262,plain,
( one_to_one(sK6_skl)
| ~ empty(sK6_skl) ),
inference(resolution,[status(thm)],[f253,f232]) ).
fof(f263,definition,
( sQ9_spl
<=> empty(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f265,plain,
( sQ9_spl
| ~ empty(sK6_skl) ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f266,definition,
( sQ10_spl
<=> one_to_one(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f269,plain,
( sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f262,f263,f266]) ).
fof(f270,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f265,f106]) ).
fof(f271,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f270]) ).
fof(f284,plain,
sK8_skl = sK6_skl,
inference(resolution,[status(thm)],[f112,f222]) ).
fof(f292,plain,
( one_to_one(sK8_skl)
| ~ empty(sK8_skl) ),
inference(resolution,[status(thm)],[f113,f232]) ).
fof(f293,definition,
( sQ11_spl
<=> empty(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f295,plain,
( sQ11_spl
| ~ empty(sK8_skl) ),
inference(component_clause,[status(thm)],[f293]) ).
fof(f296,definition,
( sQ12_spl
<=> one_to_one(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f299,plain,
( sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f292,f293,f296]) ).
fof(f300,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f295,f112]) ).
fof(f301,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f300]) ).
fof(f302,plain,
( one_to_one(sK9_skl)
| ~ empty(sK9_skl) ),
inference(resolution,[status(thm)],[f116,f232]) ).
fof(f303,definition,
( sQ13_spl
<=> empty(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f305,plain,
( sQ13_spl
| ~ empty(sK9_skl) ),
inference(component_clause,[status(thm)],[f303]) ).
fof(f306,definition,
( sQ14_spl
<=> one_to_one(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f309,plain,
( sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f302,f303,f306]) ).
fof(f328,plain,
( ordinal(sK13_skl)
| ~ epsilon_connected(sK13_skl) ),
inference(resolution,[status(thm)],[f55,f133]) ).
fof(f329,plain,
( ordinal(sK9_skl)
| ~ epsilon_connected(sK9_skl) ),
inference(resolution,[status(thm)],[f55,f119]) ).
fof(f330,plain,
( ordinal(sK6_skl)
| ~ epsilon_connected(sK6_skl) ),
inference(resolution,[status(thm)],[f55,f251]) ).
fof(f331,plain,
( ordinal(sK5_skl)
| ~ epsilon_connected(sK5_skl) ),
inference(resolution,[status(thm)],[f55,f102]) ).
fof(f332,definition,
( sQ17_spl
<=> epsilon_connected(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f334,plain,
( sQ17_spl
| ~ epsilon_connected(sK13_skl) ),
inference(component_clause,[status(thm)],[f332]) ).
fof(f335,definition,
( sQ18_spl
<=> ordinal(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f338,plain,
( sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f328,f332,f335]) ).
fof(f339,definition,
( sQ19_spl
<=> epsilon_connected(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f341,plain,
( sQ19_spl
| ~ epsilon_connected(sK9_skl) ),
inference(component_clause,[status(thm)],[f339]) ).
fof(f342,definition,
( sQ20_spl
<=> ordinal(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f345,plain,
( sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f329,f339,f342]) ).
fof(f346,definition,
( sQ21_spl
<=> epsilon_connected(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f348,plain,
( sQ21_spl
| ~ epsilon_connected(sK6_skl) ),
inference(component_clause,[status(thm)],[f346]) ).
fof(f349,definition,
( sQ22_spl
<=> ordinal(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f352,plain,
( sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f330,f346,f349]) ).
fof(f353,definition,
( sQ23_spl
<=> epsilon_connected(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f355,plain,
( sQ23_spl
| ~ epsilon_connected(sK5_skl) ),
inference(component_clause,[status(thm)],[f353]) ).
fof(f356,definition,
( sQ24_spl
<=> ordinal(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f359,plain,
( sQ24_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f331,f353,f356]) ).
fof(f360,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f355,f103]) ).
fof(f361,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f360]) ).
fof(f362,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f348,f258]) ).
fof(f363,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f362]) ).
fof(f364,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f341,f120]) ).
fof(f365,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f364]) ).
fof(f374,plain,
epsilon_connected(sK8_skl),
inference(backward_demodulation,[status(thm)],[f284,f258]) ).
fof(f379,plain,
epsilon_transitive(sK8_skl),
inference(backward_demodulation,[status(thm)],[f284,f251]) ).
fof(f386,plain,
( ordinal(sK8_skl)
| ~ epsilon_connected(sK8_skl) ),
inference(resolution,[status(thm)],[f379,f55]) ).
fof(f387,definition,
( sQ25_spl
<=> epsilon_connected(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f389,plain,
( sQ25_spl
| ~ epsilon_connected(sK8_skl) ),
inference(component_clause,[status(thm)],[f387]) ).
fof(f390,definition,
( sQ26_spl
<=> ordinal(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f393,plain,
( sQ26_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f386,f387,f390]) ).
fof(f394,plain,
( sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f389,f374]) ).
fof(f395,plain,
sQ25_spl,
inference(contradiction_clause,[status(thm)],[f394]) ).
fof(f435,plain,
( subset(sK0_skl(sK17_skl),sK17_skl)
| epsilon_transitive(sK17_skl) ),
inference(resolution,[status(thm)],[f65,f158]) ).
fof(f440,definition,
( sQ31_spl
<=> epsilon_transitive(sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f441,plain,
( ~ sQ31_spl
| epsilon_transitive(sK17_skl) ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f443,definition,
( sQ32_spl
<=> subset(sK0_skl(sK17_skl),sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f444,plain,
( ~ sQ32_spl
| subset(sK0_skl(sK17_skl),sK17_skl) ),
inference(component_clause,[status(thm)],[f443]) ).
fof(f446,plain,
( sQ32_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f435,f440,f443]) ).
fof(f458,plain,
( ~ sQ31_spl
| ordinal(sK17_skl)
| ~ epsilon_connected(sK17_skl) ),
inference(resolution,[status(thm)],[f441,f55]) ).
fof(f459,definition,
( sQ34_spl
<=> epsilon_connected(sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f462,plain,
( ~ sQ31_spl
| sQ0_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f458,f459,f184,f440]) ).
fof(f463,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f185,f159]) ).
fof(f464,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f463]) ).
fof(f479,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f305,f118]) ).
fof(f480,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f479]) ).
fof(f481,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f334,f134]) ).
fof(f482,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f481]) ).
fof(f490,plain,
( ordinal(sK1_skl(sK17_skl))
| epsilon_connected(sK17_skl) ),
inference(resolution,[status(thm)],[f72,f157]) ).
fof(f502,definition,
( sQ36_spl
<=> ordinal(sK1_skl(sK17_skl)) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f505,plain,
( sQ36_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f490,f459,f502]) ).
fof(f514,plain,
( ordinal(sK2_skl(sK17_skl))
| epsilon_connected(sK17_skl) ),
inference(resolution,[status(thm)],[f73,f157]) ).
fof(f526,definition,
( sQ39_spl
<=> ordinal(sK2_skl(sK17_skl)) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f527,plain,
( ~ sQ39_spl
| ordinal(sK2_skl(sK17_skl)) ),
inference(component_clause,[status(thm)],[f526]) ).
fof(f529,plain,
( sQ39_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f514,f459,f526]) ).
fof(f548,plain,
! [X0] :
( sK2_skl(X0) = sK1_skl(X0)
| in(sK2_skl(X0),sK1_skl(X0))
| ~ ordinal(sK1_skl(X0))
| ~ ordinal(sK2_skl(X0))
| epsilon_connected(X0) ),
inference(resolution,[status(thm)],[f74,f152]) ).
fof(f550,plain,
! [X0] :
( in(sK2_skl(X0),sK1_skl(X0))
| ~ ordinal(sK1_skl(X0))
| ~ ordinal(sK2_skl(X0))
| epsilon_connected(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f548,f75]) ).
fof(f571,plain,
! [X0] :
( ~ ordinal(sK1_skl(X0))
| ~ ordinal(sK2_skl(X0))
| epsilon_connected(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f550,f76]) ).
fof(f572,plain,
( ~ sQ39_spl
| ~ ordinal(sK1_skl(sK17_skl))
| epsilon_connected(sK17_skl) ),
inference(resolution,[status(thm)],[f571,f527]) ).
fof(f573,plain,
( ~ sQ39_spl
| ~ sQ36_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f572,f459,f502,f526]) ).
fof(f581,plain,
( ~ sQ32_spl
| epsilon_transitive(sK17_skl) ),
inference(resolution,[status(thm)],[f444,f66]) ).
fof(f582,plain,
( ~ sQ32_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f581,f440,f443]) ).
fof(f583,plain,
$false,
inference(sat_refutation,[status(thm)],[f248,f250,f269,f271,f299,f301,f309,f338,f345,f352,f359,f361,f363,f365,f393,f395,f446,f462,f464,f480,f482,f505,f529,f573,f582]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU234+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 06:01:36 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.43 % Elapsed time: 0.051783 seconds
% 0.10/0.43 % CPU time: 0.181027 seconds
% 0.10/0.43 % Total memory used: 83.494 MB
% 0.10/0.43 % Net memory used: 83.337 MB
%------------------------------------------------------------------------------