%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM404+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 01:40:27 PM UTC 2026
% Result : Theorem 0.15s 0.48s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 52
% Syntax : Number of formulae : 223 ( 45 unt; 31 def)
% Number of atoms : 543 ( 13 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 485 ( 165 ~; 181 |; 86 &)
% ( 40 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 43 ( 41 usr; 32 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 138 ( 121 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] :
( ( function(A)
& empty(A)
& relation(A) )
=> ( one_to_one(A)
& function(A)
& relation(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
=> ordinal(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] :
( empty(A)
=> ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,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/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [A,B] :
( ordinal(B)
=> ( in(A,B)
=> ordinal(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ in(B,A)
& A != B
& ~ in(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,conjecture,
! [A] :
~ ! [B] :
( in(B,A)
<=> ordinal(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
~ ! [A] :
~ ! [B] :
( in(B,A)
<=> ordinal(B) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f43,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f44,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f46,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f48,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [X0] :
( epsilon_connected(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f51,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [A] :
( ( one_to_one(A)
& function(A)
& relation(A) )
| ~ function(A)
| ~ empty(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f55,plain,
! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f56,plain,
! [A] :
( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f57,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
! [A] :
( ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f61,plain,
! [X0] :
( ordinal(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f62,plain,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( subset(B,A)
| ~ in(B,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f63,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)],[f62]) ).
fof(f64,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)],[f63]) ).
fof(f65,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))],[f64]) ).
fof(f67,plain,
! [X0] :
( in(sK0_skl(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f68,plain,
! [X0] :
( ~ subset(sK0_skl(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f69,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(f70,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)],[f69]) ).
fof(f71,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)],[f70]) ).
fof(f72,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))],[f71]) ).
fof(f74,plain,
! [X0] :
( in(sK1_skl(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f75,plain,
! [X0] :
( in(sK2_skl(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f76,plain,
! [X0] :
( ~ in(sK1_skl(X0),sK2_skl(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f77,plain,
! [X0] :
( sK1_skl(X0) != sK2_skl(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f78,plain,
! [X0] :
( ~ in(sK2_skl(X0),sK1_skl(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f79,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f80,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f79]) ).
fof(f81,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f80]) ).
fof(f82,plain,
( ! [A,B] :
( ( ~ in(sK3_skl(B,A),B)
& in(sK3_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(C,sK3_skl(B,A))],[f81]) ).
fof(f84,plain,
! [X0,X1] :
( in(sK3_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f85,plain,
! [X0,X1] :
( ~ in(sK3_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f93,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f99,plain,
function(empty_set),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f102,plain,
epsilon_transitive(empty_set),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f103,plain,
epsilon_connected(empty_set),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f110,plain,
( ordinal(sK6_skl)
& epsilon_connected(sK6_skl)
& epsilon_transitive(sK6_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(A,sK6_skl)],[f18]) ).
fof(f111,plain,
epsilon_transitive(sK6_skl),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f112,plain,
epsilon_connected(sK6_skl),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f114,plain,
( relation(sK7_skl)
& empty(sK7_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(A,sK7_skl)],[f19]) ).
fof(f115,plain,
empty(sK7_skl),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f117,plain,
empty(sK8_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(A,sK8_skl)],[f20]) ).
fof(f118,plain,
empty(sK8_skl),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f119,plain,
( function(sK9_skl)
& empty(sK9_skl)
& relation(sK9_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(A,sK9_skl)],[f21]) ).
fof(f121,plain,
empty(sK9_skl),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f122,plain,
function(sK9_skl),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f123,plain,
( ordinal(sK10_skl)
& epsilon_connected(sK10_skl)
& epsilon_transitive(sK10_skl)
& empty(sK10_skl)
& one_to_one(sK10_skl)
& function(sK10_skl)
& relation(sK10_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(A,sK10_skl)],[f22]) ).
fof(f125,plain,
function(sK10_skl),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f127,plain,
empty(sK10_skl),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f140,plain,
( ordinal(sK14_skl)
& epsilon_connected(sK14_skl)
& epsilon_transitive(sK14_skl)
& ~ empty(sK14_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl]),skolemize(A,sK14_skl)],[f26]) ).
fof(f142,plain,
epsilon_transitive(sK14_skl),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f143,plain,
epsilon_connected(sK14_skl),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f160,plain,
! [A,B] :
( ordinal(A)
| ~ in(A,B)
| ~ ordinal(B) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f161,plain,
! [B] :
( ! [A] :
( ordinal(A)
| ~ in(A,B) )
| ~ ordinal(B) ),
inference(miniscoping,[status(thm)],[f160]) ).
fof(f162,plain,
! [X0,X1] :
( ordinal(X1)
| ~ in(X1,X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f161]) ).
fof(f163,plain,
! [A] :
( ! [B] :
( in(B,A)
| A = B
| in(A,B)
| ~ ordinal(B) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f164,plain,
! [X0,X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f163]) ).
fof(f167,plain,
? [A] :
! [B] :
( in(B,A)
<=> ordinal(B) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f168,plain,
? [A] :
! [B] :
( ( ~ ordinal(B)
| in(B,A) )
& ( ordinal(B)
| ~ in(B,A) ) ),
inference(NNF_transformation,[status(thm)],[f167]) ).
fof(f169,plain,
? [A] :
( ! [B] :
( ~ ordinal(B)
| in(B,A) )
& ! [B] :
( ordinal(B)
| ~ in(B,A) ) ),
inference(miniscoping,[status(thm)],[f168]) ).
fof(f170,plain,
( ! [B] :
( ~ ordinal(B)
| in(B,sK18_skl) )
& ! [B] :
( ordinal(B)
| ~ in(B,sK18_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18_skl]),skolemize(A,sK18_skl)],[f169]) ).
fof(f171,plain,
! [X0] :
( ordinal(X0)
| ~ in(X0,sK18_skl) ),
inference(cnf_transformation,[status(thm)],[f170]) ).
fof(f172,plain,
! [X0] :
( ~ ordinal(X0)
| in(X0,sK18_skl) ),
inference(cnf_transformation,[status(thm)],[f170]) ).
fof(f192,plain,
! [X0] :
( ~ ordinal(X0)
| ~ in(sK18_skl,X0) ),
inference(resolution,[status(thm)],[f44,f172]) ).
fof(f193,plain,
( ~ ordinal(sK18_skl)
| ~ ordinal(sK18_skl) ),
inference(resolution,[status(thm)],[f192,f172]) ).
fof(f194,definition,
( sQ0_spl
<=> ordinal(sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f197,plain,
~ sQ0_spl,
inference(split_clause,[status(thm)],[f193,f194]) ).
fof(f219,plain,
function(sK7_skl),
inference(resolution,[status(thm)],[f115,f46]) ).
fof(f220,plain,
ordinal(sK7_skl),
inference(resolution,[status(thm)],[f115,f61]) ).
fof(f221,plain,
function(sK8_skl),
inference(resolution,[status(thm)],[f118,f46]) ).
fof(f222,plain,
ordinal(sK8_skl),
inference(resolution,[status(thm)],[f118,f61]) ).
fof(f224,plain,
ordinal(sK9_skl),
inference(resolution,[status(thm)],[f121,f61]) ).
fof(f231,plain,
! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f55,f51]) ).
fof(f232,plain,
( one_to_one(sK10_skl)
| ~ empty(sK10_skl) ),
inference(resolution,[status(thm)],[f231,f125]) ).
fof(f233,plain,
( one_to_one(sK9_skl)
| ~ empty(sK9_skl) ),
inference(resolution,[status(thm)],[f231,f122]) ).
fof(f235,plain,
( one_to_one(empty_set)
| ~ empty(empty_set) ),
inference(resolution,[status(thm)],[f231,f99]) ).
fof(f236,definition,
( sQ4_spl
<=> empty(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f238,plain,
( sQ4_spl
| ~ empty(sK10_skl) ),
inference(component_clause,[status(thm)],[f236]) ).
fof(f239,definition,
( sQ5_spl
<=> one_to_one(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f242,plain,
( sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f232,f236,f239]) ).
fof(f243,definition,
( sQ6_spl
<=> empty(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f245,plain,
( sQ6_spl
| ~ empty(sK9_skl) ),
inference(component_clause,[status(thm)],[f243]) ).
fof(f246,definition,
( sQ7_spl
<=> one_to_one(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f249,plain,
( sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f233,f243,f246]) ).
fof(f257,definition,
( sQ10_spl
<=> empty(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f259,plain,
( sQ10_spl
| ~ empty(empty_set) ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f260,definition,
( sQ11_spl
<=> one_to_one(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f263,plain,
( sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f235,f257,f260]) ).
fof(f264,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f259,f93]) ).
fof(f265,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f264]) ).
fof(f266,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f245,f121]) ).
fof(f267,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f266]) ).
fof(f268,plain,
epsilon_connected(sK7_skl),
inference(resolution,[status(thm)],[f220,f49]) ).
fof(f269,plain,
epsilon_transitive(sK7_skl),
inference(resolution,[status(thm)],[f220,f48]) ).
fof(f270,plain,
epsilon_connected(sK8_skl),
inference(resolution,[status(thm)],[f222,f49]) ).
fof(f271,plain,
epsilon_transitive(sK8_skl),
inference(resolution,[status(thm)],[f222,f48]) ).
fof(f272,plain,
epsilon_connected(sK9_skl),
inference(resolution,[status(thm)],[f224,f49]) ).
fof(f273,plain,
epsilon_transitive(sK9_skl),
inference(resolution,[status(thm)],[f224,f48]) ).
fof(f276,plain,
ordinal(sK10_skl),
inference(resolution,[status(thm)],[f127,f61]) ).
fof(f277,plain,
epsilon_connected(sK10_skl),
inference(resolution,[status(thm)],[f276,f49]) ).
fof(f278,plain,
epsilon_transitive(sK10_skl),
inference(resolution,[status(thm)],[f276,f48]) ).
fof(f279,plain,
( ordinal(sK10_skl)
| ~ epsilon_connected(sK10_skl) ),
inference(resolution,[status(thm)],[f57,f278]) ).
fof(f280,plain,
( ordinal(sK9_skl)
| ~ epsilon_connected(sK9_skl) ),
inference(resolution,[status(thm)],[f57,f273]) ).
fof(f281,plain,
( ordinal(sK8_skl)
| ~ epsilon_connected(sK8_skl) ),
inference(resolution,[status(thm)],[f57,f271]) ).
fof(f282,plain,
( ordinal(sK7_skl)
| ~ epsilon_connected(sK7_skl) ),
inference(resolution,[status(thm)],[f57,f269]) ).
fof(f283,plain,
( ordinal(sK6_skl)
| ~ epsilon_connected(sK6_skl) ),
inference(resolution,[status(thm)],[f57,f111]) ).
fof(f284,plain,
( ordinal(empty_set)
| ~ epsilon_connected(empty_set) ),
inference(resolution,[status(thm)],[f57,f102]) ).
fof(f285,definition,
( sQ12_spl
<=> epsilon_connected(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f287,plain,
( sQ12_spl
| ~ epsilon_connected(sK10_skl) ),
inference(component_clause,[status(thm)],[f285]) ).
fof(f288,definition,
( sQ13_spl
<=> ordinal(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f291,plain,
( sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f279,f285,f288]) ).
fof(f292,definition,
( sQ14_spl
<=> epsilon_connected(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f294,plain,
( sQ14_spl
| ~ epsilon_connected(sK9_skl) ),
inference(component_clause,[status(thm)],[f292]) ).
fof(f295,definition,
( sQ15_spl
<=> ordinal(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f298,plain,
( sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f280,f292,f295]) ).
fof(f299,definition,
( sQ16_spl
<=> epsilon_connected(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f301,plain,
( sQ16_spl
| ~ epsilon_connected(sK8_skl) ),
inference(component_clause,[status(thm)],[f299]) ).
fof(f302,definition,
( sQ17_spl
<=> ordinal(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f305,plain,
( sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f281,f299,f302]) ).
fof(f306,definition,
( sQ18_spl
<=> epsilon_connected(sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f308,plain,
( sQ18_spl
| ~ epsilon_connected(sK7_skl) ),
inference(component_clause,[status(thm)],[f306]) ).
fof(f309,definition,
( sQ19_spl
<=> ordinal(sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f312,plain,
( sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f282,f306,f309]) ).
fof(f313,definition,
( sQ20_spl
<=> epsilon_connected(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f315,plain,
( sQ20_spl
| ~ epsilon_connected(sK6_skl) ),
inference(component_clause,[status(thm)],[f313]) ).
fof(f316,definition,
( sQ21_spl
<=> ordinal(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f319,plain,
( sQ21_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f283,f313,f316]) ).
fof(f320,definition,
( sQ22_spl
<=> epsilon_connected(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f322,plain,
( sQ22_spl
| ~ epsilon_connected(empty_set) ),
inference(component_clause,[status(thm)],[f320]) ).
fof(f323,definition,
( sQ23_spl
<=> ordinal(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f326,plain,
( sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f284,f320,f323]) ).
fof(f327,plain,
( sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f322,f103]) ).
fof(f328,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f327]) ).
fof(f329,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f315,f112]) ).
fof(f330,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f329]) ).
fof(f331,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f308,f268]) ).
fof(f332,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f331]) ).
fof(f333,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f301,f270]) ).
fof(f334,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f333]) ).
fof(f335,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f294,f272]) ).
fof(f336,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f335]) ).
fof(f337,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f287,f277]) ).
fof(f338,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f337]) ).
fof(f352,plain,
( ordinal(sK14_skl)
| ~ epsilon_connected(sK14_skl) ),
inference(resolution,[status(thm)],[f142,f57]) ).
fof(f353,definition,
( sQ26_spl
<=> epsilon_connected(sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f355,plain,
( sQ26_spl
| ~ epsilon_connected(sK14_skl) ),
inference(component_clause,[status(thm)],[f353]) ).
fof(f356,definition,
( sQ27_spl
<=> ordinal(sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f359,plain,
( sQ27_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f352,f353,f356]) ).
fof(f378,plain,
( one_to_one(sK7_skl)
| ~ empty(sK7_skl) ),
inference(resolution,[status(thm)],[f219,f231]) ).
fof(f379,definition,
( sQ32_spl
<=> empty(sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f381,plain,
( sQ32_spl
| ~ empty(sK7_skl) ),
inference(component_clause,[status(thm)],[f379]) ).
fof(f382,definition,
( sQ33_spl
<=> one_to_one(sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f385,plain,
( sQ33_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f378,f379,f382]) ).
fof(f386,plain,
( sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f381,f115]) ).
fof(f387,plain,
sQ32_spl,
inference(contradiction_clause,[status(thm)],[f386]) ).
fof(f388,plain,
( one_to_one(sK8_skl)
| ~ empty(sK8_skl) ),
inference(resolution,[status(thm)],[f221,f231]) ).
fof(f389,definition,
( sQ34_spl
<=> empty(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f391,plain,
( sQ34_spl
| ~ empty(sK8_skl) ),
inference(component_clause,[status(thm)],[f389]) ).
fof(f392,definition,
( sQ35_spl
<=> one_to_one(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f395,plain,
( sQ35_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f388,f389,f392]) ).
fof(f396,plain,
( sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f391,f118]) ).
fof(f397,plain,
sQ34_spl,
inference(contradiction_clause,[status(thm)],[f396]) ).
fof(f405,definition,
( sQ36_spl
<=> epsilon_transitive(sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f406,plain,
( ~ sQ36_spl
| epsilon_transitive(sK18_skl) ),
inference(component_clause,[status(thm)],[f405]) ).
fof(f413,plain,
( ordinal(sK0_skl(sK18_skl))
| epsilon_transitive(sK18_skl) ),
inference(resolution,[status(thm)],[f67,f171]) ).
fof(f417,definition,
( sQ38_spl
<=> ordinal(sK0_skl(sK18_skl)) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f420,plain,
( sQ38_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f413,f405,f417]) ).
fof(f432,plain,
( ~ sQ36_spl
| ordinal(sK18_skl)
| ~ epsilon_connected(sK18_skl) ),
inference(resolution,[status(thm)],[f406,f57]) ).
fof(f433,definition,
( sQ40_spl
<=> epsilon_connected(sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f436,plain,
( ~ sQ36_spl
| sQ0_spl
| ~ sQ40_spl ),
inference(split_clause,[status(thm)],[f432,f433,f194,f405]) ).
fof(f441,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f238,f127]) ).
fof(f442,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f441]) ).
fof(f459,plain,
( sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f355,f143]) ).
fof(f460,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f459]) ).
fof(f511,plain,
( ordinal(sK1_skl(sK18_skl))
| epsilon_connected(sK18_skl) ),
inference(resolution,[status(thm)],[f74,f171]) ).
fof(f518,definition,
( sQ45_spl
<=> ordinal(sK1_skl(sK18_skl)) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f521,plain,
( sQ45_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f511,f433,f518]) ).
fof(f522,plain,
( ordinal(sK2_skl(sK18_skl))
| epsilon_connected(sK18_skl) ),
inference(resolution,[status(thm)],[f75,f171]) ).
fof(f529,definition,
( sQ46_spl
<=> ordinal(sK2_skl(sK18_skl)) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f530,plain,
( ~ sQ46_spl
| ordinal(sK2_skl(sK18_skl)) ),
inference(component_clause,[status(thm)],[f529]) ).
fof(f532,plain,
( sQ46_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f522,f433,f529]) ).
fof(f533,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)],[f76,f164]) ).
fof(f620,plain,
! [X0] :
( in(sK2_skl(X0),sK1_skl(X0))
| ~ ordinal(sK1_skl(X0))
| ~ ordinal(sK2_skl(X0))
| epsilon_connected(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f533,f77]) ).
fof(f631,plain,
! [X0] :
( ordinal(sK3_skl(X0,sK18_skl))
| subset(sK18_skl,X0) ),
inference(resolution,[status(thm)],[f84,f171]) ).
fof(f638,plain,
! [X0,X1] :
( ordinal(sK3_skl(X1,X0))
| ~ ordinal(X0)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f84,f162]) ).
fof(f642,plain,
! [X0] :
( ~ ordinal(sK3_skl(sK18_skl,X0))
| subset(X0,sK18_skl) ),
inference(resolution,[status(thm)],[f85,f172]) ).
fof(f734,plain,
! [X0] :
( ~ ordinal(sK1_skl(X0))
| ~ ordinal(sK2_skl(X0))
| epsilon_connected(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f620,f78]) ).
fof(f735,plain,
( ~ sQ46_spl
| ~ ordinal(sK1_skl(sK18_skl))
| epsilon_connected(sK18_skl) ),
inference(resolution,[status(thm)],[f734,f530]) ).
fof(f737,plain,
( ~ sQ46_spl
| ~ sQ45_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f735,f433,f518,f529]) ).
fof(f811,plain,
( subset(sK18_skl,sK18_skl)
| subset(sK18_skl,sK18_skl) ),
inference(resolution,[status(thm)],[f642,f631]) ).
fof(f812,definition,
( sQ55_spl
<=> subset(sK18_skl,sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f815,plain,
sQ55_spl,
inference(split_clause,[status(thm)],[f811,f812]) ).
fof(f868,plain,
! [X0] :
( subset(X0,sK18_skl)
| ~ ordinal(X0)
| subset(X0,sK18_skl) ),
inference(resolution,[status(thm)],[f638,f642]) ).
fof(f871,plain,
! [X0] :
( ~ ordinal(X0)
| subset(X0,sK18_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f868]) ).
fof(f872,plain,
( epsilon_transitive(sK18_skl)
| ~ ordinal(sK0_skl(sK18_skl)) ),
inference(resolution,[status(thm)],[f871,f68]) ).
fof(f874,plain,
( sQ36_spl
| ~ sQ38_spl ),
inference(split_clause,[status(thm)],[f872,f417,f405]) ).
fof(f875,plain,
$false,
inference(sat_refutation,[status(thm)],[f197,f242,f249,f263,f265,f267,f291,f298,f305,f312,f319,f326,f328,f330,f332,f334,f336,f338,f359,f385,f387,f395,f397,f420,f436,f442,f460,f521,f532,f737,f815,f874]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM404+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n015.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Mon Sep 21 02:30:35 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.44 % Drodi V4.1.1
% 0.15/0.48 % Refutation found
% 0.15/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.54 % Elapsed time: 0.109754 seconds
% 0.15/0.54 % CPU time: 0.226732 seconds
% 0.15/0.54 % Total memory used: 24.760 MB
% 0.15/0.54 % Net memory used: 24.583 MB
%------------------------------------------------------------------------------