%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU240+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:19:51 PM UTC 2026
% Result : Theorem 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 33
% Syntax : Number of formulae : 140 ( 14 unt; 22 def)
% Number of atoms : 462 ( 6 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 542 ( 220 ~; 229 |; 52 &)
% ( 28 <=>; 12 =>; 0 <=; 1 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 31 ( 29 usr; 23 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 149 ( 132 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,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] :
( relation(A)
=> ( transitive(A)
<=> is_transitive_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_transitive_in(A,B)
<=> ! [C,D,E] :
( ( in(ordered_pair(D,E),A)
& in(ordered_pair(C,D),A)
& in(E,B)
& in(D,B)
& in(C,B) )
=> in(ordered_pair(C,E),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,conjecture,
! [A] :
( relation(A)
=> ( transitive(A)
<=> ! [B,C,D] :
( ( in(ordered_pair(C,D),A)
& in(ordered_pair(B,C),A) )
=> in(ordered_pair(B,D),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( transitive(A)
<=> ! [B,C,D] :
( ( in(ordered_pair(C,D),A)
& in(ordered_pair(B,C),A) )
=> in(ordered_pair(B,D),A) ) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f28,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_field(C))
& in(A,relation_field(C)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f42,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
! [A] :
( ( one_to_one(A)
& function(A)
& relation(A) )
| ~ function(A)
| ~ empty(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f46,plain,
! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f49,plain,
! [A] :
( ( transitive(A)
<=> is_transitive_in(A,relation_field(A)) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f50,plain,
! [A] :
( ( ( ~ is_transitive_in(A,relation_field(A))
| transitive(A) )
& ( is_transitive_in(A,relation_field(A))
| ~ transitive(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
! [X0] :
( is_transitive_in(X0,relation_field(X0))
| ~ transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [X0] :
( ~ is_transitive_in(X0,relation_field(X0))
| transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f56,plain,
! [A] :
( ! [B] :
( is_transitive_in(A,B)
<=> ! [C,D,E] :
( in(ordered_pair(C,E),A)
| ~ in(ordered_pair(D,E),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(E,B)
| ~ in(D,B)
| ~ in(C,B) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f57,plain,
! [A] :
( ! [B] :
( ( ? [C,D,E] :
( ~ in(ordered_pair(C,E),A)
& in(ordered_pair(D,E),A)
& in(ordered_pair(C,D),A)
& in(E,B)
& in(D,B)
& in(C,B) )
| is_transitive_in(A,B) )
& ( ! [C,D,E] :
( in(ordered_pair(C,E),A)
| ~ in(ordered_pair(D,E),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(E,B)
| ~ in(D,B)
| ~ in(C,B) )
| ~ is_transitive_in(A,B) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
! [A] :
( ( ! [B] :
( ? [C,E] :
( ~ in(ordered_pair(C,E),A)
& ? [D] :
( in(ordered_pair(D,E),A)
& in(ordered_pair(C,D),A)
& in(E,B)
& in(D,B)
& in(C,B) ) )
| is_transitive_in(A,B) )
& ! [B] :
( ! [C,E] :
( in(ordered_pair(C,E),A)
| ! [D] :
( ~ in(ordered_pair(D,E),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(E,B)
| ~ in(D,B)
| ~ in(C,B) ) )
| ~ is_transitive_in(A,B) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f57]) ).
fof(f59,plain,
! [A] :
( ( ! [B] :
( ( ~ in(ordered_pair(sK0_skl(B,A),sK1_skl(B,A)),A)
& in(ordered_pair(sK2_skl(B,A),sK1_skl(B,A)),A)
& in(ordered_pair(sK0_skl(B,A),sK2_skl(B,A)),A)
& in(sK1_skl(B,A),B)
& in(sK2_skl(B,A),B)
& in(sK0_skl(B,A),B) )
| is_transitive_in(A,B) )
& ! [B] :
( ! [C,E] :
( in(ordered_pair(C,E),A)
| ! [D] :
( ~ in(ordered_pair(D,E),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(E,B)
| ~ in(D,B)
| ~ in(C,B) ) )
| ~ is_transitive_in(A,B) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(C,sK0_skl(B,A)),skolemize(E,sK1_skl(B,A)),skolemize(D,sK2_skl(B,A))],[f58]) ).
fof(f60,plain,
! [X0,X1,X2,X3,X4] :
( in(ordered_pair(X2,X4),X0)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1)
| ~ is_transitive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f64,plain,
! [X0,X1] :
( in(ordered_pair(sK0_skl(X1,X0),sK2_skl(X1,X0)),X0)
| is_transitive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f65,plain,
! [X0,X1] :
( in(ordered_pair(sK2_skl(X1,X0),sK1_skl(X1,X0)),X0)
| is_transitive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f66,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0)),X0)
| is_transitive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f69,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f79,plain,
? [A] :
( ( transitive(A)
<~> ! [B,C,D] :
( in(ordered_pair(B,D),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(ordered_pair(B,C),A) ) )
& relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f80,plain,
? [A] :
( ( ? [B,C,D] :
( ~ in(ordered_pair(B,D),A)
& in(ordered_pair(C,D),A)
& in(ordered_pair(B,C),A) )
| ~ transitive(A) )
& ( ! [B,C,D] :
( in(ordered_pair(B,D),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(ordered_pair(B,C),A) )
| transitive(A) )
& relation(A) ),
inference(NNF_transformation,[status(thm)],[f79]) ).
fof(f81,plain,
? [A] :
( ( ? [B,D] :
( ~ in(ordered_pair(B,D),A)
& ? [C] :
( in(ordered_pair(C,D),A)
& in(ordered_pair(B,C),A) ) )
| ~ transitive(A) )
& ( ! [B,D] :
( in(ordered_pair(B,D),A)
| ! [C] :
( ~ in(ordered_pair(C,D),A)
| ~ in(ordered_pair(B,C),A) ) )
| transitive(A) )
& relation(A) ),
inference(miniscoping,[status(thm)],[f80]) ).
fof(f82,plain,
( ( ( ~ in(ordered_pair(sK5_skl,sK6_skl),sK4_skl)
& in(ordered_pair(sK7_skl,sK6_skl),sK4_skl)
& in(ordered_pair(sK5_skl,sK7_skl),sK4_skl) )
| ~ transitive(sK4_skl) )
& ( ! [B,D] :
( in(ordered_pair(B,D),sK4_skl)
| ! [C] :
( ~ in(ordered_pair(C,D),sK4_skl)
| ~ in(ordered_pair(B,C),sK4_skl) ) )
| transitive(sK4_skl) )
& relation(sK4_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl,sK7_skl]),skolemize(A,sK4_skl),skolemize(B,sK5_skl),skolemize(D,sK6_skl),skolemize(C,sK7_skl)],[f81]) ).
fof(f83,plain,
relation(sK4_skl),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f84,plain,
! [X0,X1,X2] :
( in(ordered_pair(X0,X2),sK4_skl)
| ~ in(ordered_pair(X1,X2),sK4_skl)
| ~ in(ordered_pair(X0,X1),sK4_skl)
| transitive(sK4_skl) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f85,plain,
( in(ordered_pair(sK5_skl,sK7_skl),sK4_skl)
| ~ transitive(sK4_skl) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f86,plain,
( in(ordered_pair(sK7_skl,sK6_skl),sK4_skl)
| ~ transitive(sK4_skl) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f87,plain,
( ~ in(ordered_pair(sK5_skl,sK6_skl),sK4_skl)
| ~ transitive(sK4_skl) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f91,plain,
empty(sK9_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(A,sK9_skl)],[f28]) ).
fof(f92,plain,
empty(sK9_skl),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f93,plain,
( function(sK10_skl)
& empty(sK10_skl)
& relation(sK10_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(A,sK10_skl)],[f29]) ).
fof(f94,plain,
relation(sK10_skl),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f95,plain,
empty(sK10_skl),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f108,plain,
! [A,B,C] :
( ( in(B,relation_field(C))
& in(A,relation_field(C)) )
| ~ in(ordered_pair(A,B),C)
| ~ relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f109,plain,
! [C] :
( ! [A,B] :
( ( in(B,relation_field(C))
& in(A,relation_field(C)) )
| ~ in(ordered_pair(A,B),C) )
| ~ relation(C) ),
inference(miniscoping,[status(thm)],[f108]) ).
fof(f110,plain,
! [X0,X1,X2] :
( in(X1,relation_field(X0))
| ~ in(ordered_pair(X1,X2),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f111,plain,
! [X0,X1,X2] :
( in(X2,relation_field(X0))
| ~ in(ordered_pair(X1,X2),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f112,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f113,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f114,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f115,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f114]) ).
fof(f116,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f120,definition,
( sQ0_spl
<=> transitive(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f123,definition,
! [X0,X1,X2] :
( sQ1_spl
<=> ( in(ordered_pair(X0,X2),sK4_skl)
| ~ in(ordered_pair(X1,X2),sK4_skl)
| ~ in(ordered_pair(X0,X1),sK4_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f124,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| in(ordered_pair(X0,X2),sK4_skl)
| ~ in(ordered_pair(X1,X2),sK4_skl)
| ~ in(ordered_pair(X0,X1),sK4_skl) ),
inference(component_clause,[status(thm)],[f123]) ).
fof(f126,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f84,f120,f123]) ).
fof(f127,definition,
( sQ2_spl
<=> in(ordered_pair(sK5_skl,sK7_skl),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( ~ sQ2_spl
| in(ordered_pair(sK5_skl,sK7_skl),sK4_skl) ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,plain,
( sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f85,f120,f127]) ).
fof(f131,definition,
( sQ3_spl
<=> in(ordered_pair(sK7_skl,sK6_skl),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f132,plain,
( ~ sQ3_spl
| in(ordered_pair(sK7_skl,sK6_skl),sK4_skl) ),
inference(component_clause,[status(thm)],[f131]) ).
fof(f134,plain,
( sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f86,f120,f131]) ).
fof(f135,definition,
( sQ4_spl
<=> in(ordered_pair(sK5_skl,sK6_skl),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( ~ sQ4_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f87,f120,f135]) ).
fof(f142,plain,
! [X0] :
( one_to_one(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f46,f42]) ).
fof(f143,plain,
( one_to_one(sK10_skl)
| ~ relation(sK10_skl) ),
inference(resolution,[status(thm)],[f142,f95]) ).
fof(f144,plain,
( one_to_one(sK9_skl)
| ~ relation(sK9_skl) ),
inference(resolution,[status(thm)],[f142,f92]) ).
fof(f145,plain,
( one_to_one(empty_set)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f142,f69]) ).
fof(f146,definition,
( sQ5_spl
<=> relation(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f148,plain,
( sQ5_spl
| ~ relation(sK10_skl) ),
inference(component_clause,[status(thm)],[f146]) ).
fof(f149,definition,
( sQ6_spl
<=> one_to_one(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f152,plain,
( sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f143,f146,f149]) ).
fof(f153,definition,
( sQ7_spl
<=> relation(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f155,plain,
( sQ7_spl
| ~ relation(sK9_skl) ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,definition,
( sQ8_spl
<=> one_to_one(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f159,plain,
( sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f144,f153,f156]) ).
fof(f160,definition,
( sQ9_spl
<=> relation(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f162,plain,
( sQ9_spl
| ~ relation(empty_set) ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f163,definition,
( sQ10_spl
<=> one_to_one(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f145,f160,f163]) ).
fof(f167,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f148,f94]) ).
fof(f168,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f167]) ).
fof(f172,plain,
sK10_skl = empty_set,
inference(resolution,[status(thm)],[f113,f95]) ).
fof(f173,plain,
sK9_skl = empty_set,
inference(resolution,[status(thm)],[f113,f92]) ).
fof(f177,plain,
( sQ9_spl
| ~ relation(sK10_skl) ),
inference(backward_demodulation,[status(thm)],[f172,f162]) ).
fof(f180,plain,
( sQ9_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f177,f146,f160]) ).
fof(f183,plain,
( sQ7_spl
| ~ relation(sK10_skl) ),
inference(backward_demodulation,[status(thm)],[f186,f155]) ).
fof(f186,plain,
sK9_skl = sK10_skl,
inference(forward_demodulation,[status(thm)],[f172,f173]) ).
fof(f187,plain,
( sQ7_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f183,f146,f153]) ).
fof(f287,plain,
! [X0,X1] :
( ~ sQ3_spl
| in(ordered_pair(X1,sK6_skl),sK4_skl)
| ~ in(ordered_pair(X1,sK7_skl),sK4_skl)
| ~ in(sK6_skl,X0)
| ~ in(sK7_skl,X0)
| ~ in(X1,X0)
| ~ is_transitive_in(sK4_skl,X0)
| ~ relation(sK4_skl) ),
inference(resolution,[status(thm)],[f60,f132]) ).
fof(f289,definition,
( sQ14_spl
<=> relation(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f291,plain,
( sQ14_spl
| ~ relation(sK4_skl) ),
inference(component_clause,[status(thm)],[f289]) ).
fof(f292,definition,
! [X0,X1] :
( sQ15_spl
<=> ( in(ordered_pair(X1,sK6_skl),sK4_skl)
| ~ in(ordered_pair(X1,sK7_skl),sK4_skl)
| ~ in(sK6_skl,X0)
| ~ in(sK7_skl,X0)
| ~ in(X1,X0)
| ~ is_transitive_in(sK4_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f293,plain,
! [X0,X1] :
( ~ sQ15_spl
| in(ordered_pair(X1,sK6_skl),sK4_skl)
| ~ in(ordered_pair(X1,sK7_skl),sK4_skl)
| ~ in(sK6_skl,X0)
| ~ in(sK7_skl,X0)
| ~ in(X1,X0)
| ~ is_transitive_in(sK4_skl,X0) ),
inference(component_clause,[status(thm)],[f292]) ).
fof(f295,plain,
( ~ sQ3_spl
| sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f287,f289,f292,f131]) ).
fof(f300,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f291,f83]) ).
fof(f301,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f300]) ).
fof(f308,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ15_spl
| in(ordered_pair(sK5_skl,sK6_skl),sK4_skl)
| ~ in(sK6_skl,X0)
| ~ in(sK7_skl,X0)
| ~ in(sK5_skl,X0)
| ~ is_transitive_in(sK4_skl,X0) ),
inference(resolution,[status(thm)],[f293,f128]) ).
fof(f309,definition,
! [X0] :
( sQ17_spl
<=> ( ~ in(sK6_skl,X0)
| ~ in(sK7_skl,X0)
| ~ in(sK5_skl,X0)
| ~ is_transitive_in(sK4_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f310,plain,
! [X0] :
( ~ sQ17_spl
| ~ in(sK6_skl,X0)
| ~ in(sK7_skl,X0)
| ~ in(sK5_skl,X0)
| ~ is_transitive_in(sK4_skl,X0) ),
inference(component_clause,[status(thm)],[f309]) ).
fof(f312,plain,
( ~ sQ2_spl
| ~ sQ15_spl
| sQ4_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f308,f309,f135,f292,f127]) ).
fof(f320,plain,
! [X0,X1] :
( ~ empty(X0)
| is_transitive_in(X0,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f64,f116]) ).
fof(f323,plain,
! [X0] :
( transitive(X0)
| ~ relation(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f320,f52]) ).
fof(f324,plain,
! [X0] :
( transitive(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f323]) ).
fof(f325,plain,
( transitive(sK10_skl)
| ~ relation(sK10_skl) ),
inference(resolution,[status(thm)],[f324,f95]) ).
fof(f326,definition,
( sQ18_spl
<=> transitive(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f329,plain,
( sQ18_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f325,f146,f326]) ).
fof(f334,plain,
( ~ sQ3_spl
| in(sK7_skl,relation_field(sK4_skl))
| ~ relation(sK4_skl) ),
inference(resolution,[status(thm)],[f110,f132]) ).
fof(f335,plain,
( ~ sQ2_spl
| in(sK5_skl,relation_field(sK4_skl))
| ~ relation(sK4_skl) ),
inference(resolution,[status(thm)],[f110,f128]) ).
fof(f337,definition,
( sQ19_spl
<=> in(sK7_skl,relation_field(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f340,plain,
( ~ sQ3_spl
| sQ19_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f334,f289,f337,f131]) ).
fof(f341,definition,
( sQ20_spl
<=> in(sK5_skl,relation_field(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f342,plain,
( ~ sQ20_spl
| in(sK5_skl,relation_field(sK4_skl)) ),
inference(component_clause,[status(thm)],[f341]) ).
fof(f344,plain,
( ~ sQ2_spl
| sQ20_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f335,f289,f341,f127]) ).
fof(f359,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_transitive_in(sK4_skl,X1)
| ~ relation(sK4_skl)
| in(ordered_pair(X0,sK1_skl(X1,sK4_skl)),sK4_skl)
| ~ in(ordered_pair(X0,sK2_skl(X1,sK4_skl)),sK4_skl) ),
inference(resolution,[status(thm)],[f124,f65]) ).
fof(f361,definition,
! [X0,X1] :
( sQ21_spl
<=> ( is_transitive_in(sK4_skl,X1)
| in(ordered_pair(X0,sK1_skl(X1,sK4_skl)),sK4_skl)
| ~ in(ordered_pair(X0,sK2_skl(X1,sK4_skl)),sK4_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f362,plain,
! [X0,X1] :
( ~ sQ21_spl
| is_transitive_in(sK4_skl,X1)
| in(ordered_pair(X0,sK1_skl(X1,sK4_skl)),sK4_skl)
| ~ in(ordered_pair(X0,sK2_skl(X1,sK4_skl)),sK4_skl) ),
inference(component_clause,[status(thm)],[f361]) ).
fof(f364,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f359,f361,f289,f123]) ).
fof(f369,plain,
! [X0] :
( ~ sQ21_spl
| is_transitive_in(sK4_skl,X0)
| ~ relation(sK4_skl)
| is_transitive_in(sK4_skl,X0)
| in(ordered_pair(sK0_skl(X0,sK4_skl),sK1_skl(X0,sK4_skl)),sK4_skl) ),
inference(resolution,[status(thm)],[f362,f64]) ).
fof(f370,definition,
! [X0] :
( sQ23_spl
<=> ( is_transitive_in(sK4_skl,X0)
| is_transitive_in(sK4_skl,X0)
| in(ordered_pair(sK0_skl(X0,sK4_skl),sK1_skl(X0,sK4_skl)),sK4_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f371,plain,
! [X0] :
( ~ sQ23_spl
| is_transitive_in(sK4_skl,X0)
| is_transitive_in(sK4_skl,X0)
| in(ordered_pair(sK0_skl(X0,sK4_skl),sK1_skl(X0,sK4_skl)),sK4_skl) ),
inference(component_clause,[status(thm)],[f370]) ).
fof(f373,plain,
( ~ sQ21_spl
| ~ sQ14_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f369,f370,f289,f361]) ).
fof(f374,plain,
! [X0] :
( ~ sQ23_spl
| is_transitive_in(sK4_skl,X0)
| in(ordered_pair(sK0_skl(X0,sK4_skl),sK1_skl(X0,sK4_skl)),sK4_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f371]) ).
fof(f375,plain,
! [X0] :
( ~ sQ23_spl
| is_transitive_in(sK4_skl,X0)
| ~ relation(sK4_skl)
| is_transitive_in(sK4_skl,X0) ),
inference(resolution,[status(thm)],[f374,f66]) ).
fof(f383,definition,
! [X0] :
( sQ24_spl
<=> ( is_transitive_in(sK4_skl,X0)
| is_transitive_in(sK4_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f384,plain,
! [X0] :
( ~ sQ24_spl
| is_transitive_in(sK4_skl,X0)
| is_transitive_in(sK4_skl,X0) ),
inference(component_clause,[status(thm)],[f383]) ).
fof(f386,plain,
( ~ sQ23_spl
| ~ sQ14_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f375,f383,f289,f370]) ).
fof(f403,plain,
! [X0] :
( ~ sQ24_spl
| is_transitive_in(sK4_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f384]) ).
fof(f404,plain,
( ~ sQ24_spl
| transitive(sK4_skl)
| ~ relation(sK4_skl) ),
inference(resolution,[status(thm)],[f403,f52]) ).
fof(f405,plain,
( ~ sQ24_spl
| sQ0_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f404,f289,f120,f383]) ).
fof(f431,plain,
( ~ sQ3_spl
| in(sK6_skl,relation_field(sK4_skl))
| ~ relation(sK4_skl) ),
inference(resolution,[status(thm)],[f132,f111]) ).
fof(f437,definition,
( sQ30_spl
<=> in(sK6_skl,relation_field(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f440,plain,
( ~ sQ3_spl
| sQ30_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f431,f289,f437,f131]) ).
fof(f478,plain,
( ~ sQ20_spl
| ~ sQ17_spl
| ~ in(sK6_skl,relation_field(sK4_skl))
| ~ in(sK7_skl,relation_field(sK4_skl))
| ~ is_transitive_in(sK4_skl,relation_field(sK4_skl)) ),
inference(resolution,[status(thm)],[f310,f342]) ).
fof(f481,definition,
( sQ31_spl
<=> is_transitive_in(sK4_skl,relation_field(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f483,plain,
( sQ31_spl
| ~ is_transitive_in(sK4_skl,relation_field(sK4_skl)) ),
inference(component_clause,[status(thm)],[f481]) ).
fof(f484,plain,
( ~ sQ20_spl
| ~ sQ17_spl
| ~ sQ30_spl
| ~ sQ19_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f478,f481,f337,f437,f309,f341]) ).
fof(f487,plain,
( sQ31_spl
| ~ transitive(sK4_skl)
| ~ relation(sK4_skl) ),
inference(resolution,[status(thm)],[f483,f51]) ).
fof(f490,plain,
( sQ31_spl
| ~ sQ0_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f487,f289,f120,f481]) ).
fof(f493,plain,
$false,
inference(sat_refutation,[status(thm)],[f126,f130,f134,f138,f152,f159,f166,f168,f180,f187,f295,f301,f312,f329,f340,f344,f364,f373,f386,f405,f440,f484,f490]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU240+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 06:04:16 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.41 % Refutation found
% 0.14/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.45 % Elapsed time: 0.062536 seconds
% 0.14/0.45 % CPU time: 0.191723 seconds
% 0.14/0.45 % Total memory used: 103.974 MB
% 0.14/0.45 % Net memory used: 103.857 MB
%------------------------------------------------------------------------------