%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU242+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 : n018.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 02:19:52 PM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 25
% Syntax : Number of formulae : 106 ( 11 unt; 16 def)
% Number of atoms : 357 ( 41 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 419 ( 168 ~; 180 |; 41 &)
% ( 22 <=>; 7 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 17 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 104 ( 96 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] :
( relation(A)
=> ( connected(A)
<=> is_connected_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_connected_in(A,B)
<=> ! [C,D] :
~ ( ~ in(ordered_pair(D,C),A)
& ~ in(ordered_pair(C,D),A)
& C != D
& in(D,B)
& in(C,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(B,A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,conjecture,
! [A] :
( relation(A)
=> ( connected(A)
<=> ! [B,C] :
~ ( ~ in(ordered_pair(C,B),A)
& ~ in(ordered_pair(B,C),A)
& B != C
& in(C,relation_field(A))
& in(B,relation_field(A)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( connected(A)
<=> ! [B,C] :
~ ( ~ in(ordered_pair(C,B),A)
& ~ in(ordered_pair(B,C),A)
& B != C
& in(C,relation_field(A))
& in(B,relation_field(A)) ) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f32,axiom,
! [A] : set_union2(A,empty_set) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f48,plain,
! [A] :
( ( connected(A)
<=> is_connected_in(A,relation_field(A)) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f49,plain,
! [A] :
( ( ( ~ is_connected_in(A,relation_field(A))
| connected(A) )
& ( is_connected_in(A,relation_field(A))
| ~ connected(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f48]) ).
fof(f50,plain,
! [X0] :
( is_connected_in(X0,relation_field(X0))
| ~ connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
! [X0] :
( ~ is_connected_in(X0,relation_field(X0))
| connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f55,plain,
! [A] :
( ! [B] :
( is_connected_in(A,B)
<=> ! [C,D] :
( in(ordered_pair(D,C),A)
| in(ordered_pair(C,D),A)
| C = D
| ~ in(D,B)
| ~ in(C,B) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f56,plain,
! [A] :
( ! [B] :
( ( ? [C,D] :
( ~ in(ordered_pair(D,C),A)
& ~ in(ordered_pair(C,D),A)
& C != D
& in(D,B)
& in(C,B) )
| is_connected_in(A,B) )
& ( ! [C,D] :
( in(ordered_pair(D,C),A)
| in(ordered_pair(C,D),A)
| C = D
| ~ in(D,B)
| ~ in(C,B) )
| ~ is_connected_in(A,B) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
! [A] :
( ( ! [B] :
( ? [C,D] :
( ~ in(ordered_pair(D,C),A)
& ~ in(ordered_pair(C,D),A)
& C != D
& in(D,B)
& in(C,B) )
| is_connected_in(A,B) )
& ! [B] :
( ! [C,D] :
( in(ordered_pair(D,C),A)
| in(ordered_pair(C,D),A)
| C = D
| ~ in(D,B)
| ~ in(C,B) )
| ~ is_connected_in(A,B) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f56]) ).
fof(f58,plain,
! [A] :
( ( ! [B] :
( ( ~ in(ordered_pair(sK1_skl(B,A),sK0_skl(B,A)),A)
& ~ in(ordered_pair(sK0_skl(B,A),sK1_skl(B,A)),A)
& sK0_skl(B,A) != sK1_skl(B,A)
& in(sK1_skl(B,A),B)
& in(sK0_skl(B,A),B) )
| is_connected_in(A,B) )
& ! [B] :
( ! [C,D] :
( in(ordered_pair(D,C),A)
| in(ordered_pair(C,D),A)
| C = D
| ~ in(D,B)
| ~ in(C,B) )
| ~ is_connected_in(A,B) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(C,sK0_skl(B,A)),skolemize(D,sK1_skl(B,A))],[f57]) ).
fof(f59,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X0)
| X2 = X3
| ~ in(X3,X1)
| ~ in(X2,X1)
| ~ is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f60,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0),X1)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f61,plain,
! [X0,X1] :
( in(sK1_skl(X1,X0),X1)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f62,plain,
! [X0,X1] :
( sK0_skl(X1,X0) != sK1_skl(X1,X0)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f63,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0)),X0)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f64,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK1_skl(X1,X0),sK0_skl(X1,X0)),X0)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f67,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f69,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f70,plain,
! [A] :
( ! [B] : ~ empty(set_union2(A,B))
| empty(A) ),
inference(miniscoping,[status(thm)],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f73,plain,
! [A] :
( ! [B] : ~ empty(set_union2(B,A))
| empty(A) ),
inference(miniscoping,[status(thm)],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f77,plain,
? [A] :
( ( connected(A)
<~> ! [B,C] :
( in(ordered_pair(C,B),A)
| in(ordered_pair(B,C),A)
| B = C
| ~ in(C,relation_field(A))
| ~ in(B,relation_field(A)) ) )
& relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f78,plain,
? [A] :
( ( ? [B,C] :
( ~ in(ordered_pair(C,B),A)
& ~ in(ordered_pair(B,C),A)
& B != C
& in(C,relation_field(A))
& in(B,relation_field(A)) )
| ~ connected(A) )
& ( ! [B,C] :
( in(ordered_pair(C,B),A)
| in(ordered_pair(B,C),A)
| B = C
| ~ in(C,relation_field(A))
| ~ in(B,relation_field(A)) )
| connected(A) )
& relation(A) ),
inference(NNF_transformation,[status(thm)],[f77]) ).
fof(f79,plain,
( ( ( ~ in(ordered_pair(sK5_skl,sK4_skl),sK3_skl)
& ~ in(ordered_pair(sK4_skl,sK5_skl),sK3_skl)
& sK4_skl != sK5_skl
& in(sK5_skl,relation_field(sK3_skl))
& in(sK4_skl,relation_field(sK3_skl)) )
| ~ connected(sK3_skl) )
& ( ! [B,C] :
( in(ordered_pair(C,B),sK3_skl)
| in(ordered_pair(B,C),sK3_skl)
| B = C
| ~ in(C,relation_field(sK3_skl))
| ~ in(B,relation_field(sK3_skl)) )
| connected(sK3_skl) )
& relation(sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl),skolemize(C,sK5_skl)],[f78]) ).
fof(f80,plain,
relation(sK3_skl),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f81,plain,
! [X0,X1] :
( in(ordered_pair(X1,X0),sK3_skl)
| in(ordered_pair(X0,X1),sK3_skl)
| X0 = X1
| ~ in(X1,relation_field(sK3_skl))
| ~ in(X0,relation_field(sK3_skl))
| connected(sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f82,plain,
( in(sK4_skl,relation_field(sK3_skl))
| ~ connected(sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f83,plain,
( in(sK5_skl,relation_field(sK3_skl))
| ~ connected(sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f84,plain,
( sK4_skl != sK5_skl
| ~ connected(sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f85,plain,
( ~ in(ordered_pair(sK4_skl,sK5_skl),sK3_skl)
| ~ connected(sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f86,plain,
( ~ in(ordered_pair(sK5_skl,sK4_skl),sK3_skl)
| ~ connected(sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f102,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f107,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f108,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f115,definition,
( sQ0_spl
<=> connected(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( ~ sQ0_spl
| connected(sK3_skl) ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,definition,
! [X0,X1] :
( sQ1_spl
<=> ( in(ordered_pair(X1,X0),sK3_skl)
| in(ordered_pair(X0,X1),sK3_skl)
| X0 = X1
| ~ in(X1,relation_field(sK3_skl))
| ~ in(X0,relation_field(sK3_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f119,plain,
! [X0,X1] :
( ~ sQ1_spl
| in(ordered_pair(X1,X0),sK3_skl)
| in(ordered_pair(X0,X1),sK3_skl)
| X0 = X1
| ~ in(X1,relation_field(sK3_skl))
| ~ in(X0,relation_field(sK3_skl)) ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f81,f115,f118]) ).
fof(f122,definition,
( sQ2_spl
<=> in(sK4_skl,relation_field(sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f125,plain,
( sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f82,f115,f122]) ).
fof(f126,definition,
( sQ3_spl
<=> in(sK5_skl,relation_field(sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f129,plain,
( sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f83,f115,f126]) ).
fof(f130,definition,
( sQ4_spl
<=> sK4_skl = sK5_skl ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f133,plain,
( ~ sQ4_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f84,f115,f130]) ).
fof(f134,definition,
( sQ5_spl
<=> in(ordered_pair(sK4_skl,sK5_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f136,plain,
( sQ5_spl
| ~ in(ordered_pair(sK4_skl,sK5_skl),sK3_skl) ),
inference(component_clause,[status(thm)],[f134]) ).
fof(f137,plain,
( ~ sQ5_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f85,f115,f134]) ).
fof(f138,definition,
( sQ6_spl
<=> in(ordered_pair(sK5_skl,sK4_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f141,plain,
( ~ sQ6_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f86,f115,f138]) ).
fof(f157,plain,
! [X0] : X0 = set_union2(empty_set,X0),
inference(paramodulation,[status(thm)],[f102,f47]) ).
fof(f198,plain,
! [X0,X1] :
( X0 = empty_set
| ~ empty(set_union2(X0,X1)) ),
inference(resolution,[status(thm)],[f71,f108]) ).
fof(f226,plain,
! [X0] :
( empty_set = empty_set
| ~ empty(X0) ),
inference(paramodulation,[status(thm)],[f157,f198]) ).
fof(f242,definition,
! [X0] :
( sQ10_spl
<=> ~ empty(X0) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f243,plain,
! [X0] :
( ~ sQ10_spl
| ~ empty(X0) ),
inference(component_clause,[status(thm)],[f242]) ).
fof(f245,definition,
( sQ11_spl
<=> empty_set = empty_set ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f248,plain,
( sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f226,f242,f245]) ).
fof(f249,plain,
( ~ sQ10_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f67,f243]) ).
fof(f250,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f249]) ).
fof(f253,plain,
( ~ sQ0_spl
| is_connected_in(sK3_skl,relation_field(sK3_skl))
| ~ relation(sK3_skl) ),
inference(resolution,[status(thm)],[f116,f50]) ).
fof(f254,definition,
( sQ12_spl
<=> relation(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f256,plain,
( sQ12_spl
| ~ relation(sK3_skl) ),
inference(component_clause,[status(thm)],[f254]) ).
fof(f257,definition,
( sQ13_spl
<=> is_connected_in(sK3_skl,relation_field(sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f258,plain,
( ~ sQ13_spl
| is_connected_in(sK3_skl,relation_field(sK3_skl)) ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f260,plain,
( ~ sQ0_spl
| sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f253,f254,f257,f115]) ).
fof(f261,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f256,f80]) ).
fof(f262,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f261]) ).
fof(f263,plain,
! [X0] :
( ~ sQ1_spl
| is_connected_in(sK3_skl,X0)
| ~ relation(sK3_skl)
| in(ordered_pair(sK1_skl(X0,sK3_skl),sK0_skl(X0,sK3_skl)),sK3_skl)
| sK1_skl(X0,sK3_skl) = sK0_skl(X0,sK3_skl)
| ~ in(sK0_skl(X0,sK3_skl),relation_field(sK3_skl))
| ~ in(sK1_skl(X0,sK3_skl),relation_field(sK3_skl)) ),
inference(resolution,[status(thm)],[f119,f63]) ).
fof(f265,definition,
! [X0] :
( sQ14_spl
<=> ( is_connected_in(sK3_skl,X0)
| in(ordered_pair(sK1_skl(X0,sK3_skl),sK0_skl(X0,sK3_skl)),sK3_skl)
| sK1_skl(X0,sK3_skl) = sK0_skl(X0,sK3_skl)
| ~ in(sK0_skl(X0,sK3_skl),relation_field(sK3_skl))
| ~ in(sK1_skl(X0,sK3_skl),relation_field(sK3_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f266,plain,
! [X0] :
( ~ sQ14_spl
| is_connected_in(sK3_skl,X0)
| in(ordered_pair(sK1_skl(X0,sK3_skl),sK0_skl(X0,sK3_skl)),sK3_skl)
| sK1_skl(X0,sK3_skl) = sK0_skl(X0,sK3_skl)
| ~ in(sK0_skl(X0,sK3_skl),relation_field(sK3_skl))
| ~ in(sK1_skl(X0,sK3_skl),relation_field(sK3_skl)) ),
inference(component_clause,[status(thm)],[f265]) ).
fof(f268,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f263,f265,f254,f118]) ).
fof(f316,plain,
! [X0] :
( ~ empty(X0)
| empty(empty_set) ),
inference(paramodulation,[status(thm)],[f102,f74]) ).
fof(f328,definition,
( sQ18_spl
<=> empty(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f331,plain,
( sQ10_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f316,f328,f242]) ).
fof(f332,plain,
( ~ sQ14_spl
| is_connected_in(sK3_skl,relation_field(sK3_skl))
| ~ relation(sK3_skl)
| is_connected_in(sK3_skl,relation_field(sK3_skl))
| in(ordered_pair(sK1_skl(relation_field(sK3_skl),sK3_skl),sK0_skl(relation_field(sK3_skl),sK3_skl)),sK3_skl)
| sK1_skl(relation_field(sK3_skl),sK3_skl) = sK0_skl(relation_field(sK3_skl),sK3_skl)
| ~ in(sK1_skl(relation_field(sK3_skl),sK3_skl),relation_field(sK3_skl)) ),
inference(resolution,[status(thm)],[f266,f60]) ).
fof(f333,definition,
( sQ19_spl
<=> in(sK1_skl(relation_field(sK3_skl),sK3_skl),relation_field(sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f335,plain,
( sQ19_spl
| ~ in(sK1_skl(relation_field(sK3_skl),sK3_skl),relation_field(sK3_skl)) ),
inference(component_clause,[status(thm)],[f333]) ).
fof(f336,definition,
( sQ20_spl
<=> sK1_skl(relation_field(sK3_skl),sK3_skl) = sK0_skl(relation_field(sK3_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f337,plain,
( ~ sQ20_spl
| sK1_skl(relation_field(sK3_skl),sK3_skl) = sK0_skl(relation_field(sK3_skl),sK3_skl) ),
inference(component_clause,[status(thm)],[f336]) ).
fof(f339,definition,
( sQ21_spl
<=> in(ordered_pair(sK1_skl(relation_field(sK3_skl),sK3_skl),sK0_skl(relation_field(sK3_skl),sK3_skl)),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f340,plain,
( ~ sQ21_spl
| in(ordered_pair(sK1_skl(relation_field(sK3_skl),sK3_skl),sK0_skl(relation_field(sK3_skl),sK3_skl)),sK3_skl) ),
inference(component_clause,[status(thm)],[f339]) ).
fof(f342,plain,
( ~ sQ14_spl
| ~ sQ12_spl
| sQ13_spl
| sQ21_spl
| sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f332,f333,f336,f339,f257,f254,f265]) ).
fof(f343,plain,
( ~ sQ13_spl
| connected(sK3_skl)
| ~ relation(sK3_skl) ),
inference(resolution,[status(thm)],[f258,f51]) ).
fof(f344,plain,
! [X0,X1] :
( ~ sQ13_spl
| in(ordered_pair(X1,X0),sK3_skl)
| in(ordered_pair(X0,X1),sK3_skl)
| X0 = X1
| ~ in(X1,relation_field(sK3_skl))
| ~ in(X0,relation_field(sK3_skl))
| ~ relation(sK3_skl) ),
inference(resolution,[status(thm)],[f258,f59]) ).
fof(f345,plain,
( ~ sQ13_spl
| sQ0_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f343,f254,f115,f257]) ).
fof(f346,plain,
( ~ sQ13_spl
| sQ1_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f344,f254,f118,f257]) ).
fof(f376,plain,
( ~ sQ20_spl
| is_connected_in(sK3_skl,relation_field(sK3_skl))
| ~ relation(sK3_skl) ),
inference(resolution,[status(thm)],[f337,f62]) ).
fof(f384,plain,
( ~ sQ20_spl
| sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f376,f254,f257,f336]) ).
fof(f401,plain,
( sQ19_spl
| is_connected_in(sK3_skl,relation_field(sK3_skl))
| ~ relation(sK3_skl) ),
inference(resolution,[status(thm)],[f335,f61]) ).
fof(f402,plain,
( sQ19_spl
| sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f401,f254,f257,f333]) ).
fof(f469,plain,
( ~ sQ21_spl
| is_connected_in(sK3_skl,relation_field(sK3_skl))
| ~ relation(sK3_skl) ),
inference(resolution,[status(thm)],[f340,f64]) ).
fof(f472,plain,
( ~ sQ21_spl
| sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f469,f254,f257,f339]) ).
fof(f515,plain,
( ~ sQ1_spl
| sQ5_spl
| in(ordered_pair(sK5_skl,sK4_skl),sK3_skl)
| sK5_skl = sK4_skl
| ~ in(sK4_skl,relation_field(sK3_skl))
| ~ in(sK5_skl,relation_field(sK3_skl)) ),
inference(resolution,[status(thm)],[f136,f119]) ).
fof(f516,plain,
( ~ sQ1_spl
| sQ5_spl
| sQ6_spl
| sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f515,f126,f122,f130,f138,f134,f118]) ).
fof(f517,plain,
$false,
inference(sat_refutation,[status(thm)],[f121,f125,f129,f133,f137,f141,f248,f250,f260,f262,f268,f331,f342,f345,f346,f384,f402,f472,f516]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU242+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n018.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Mon Sep 21 06:04:28 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.44 % Drodi V4.1.1
% 0.17/0.47 % Refutation found
% 0.17/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.50 % Elapsed time: 0.064613 seconds
% 0.17/0.50 % CPU time: 0.217986 seconds
% 0.17/0.50 % Total memory used: 65.687 MB
% 0.17/0.50 % Net memory used: 65.562 MB
%------------------------------------------------------------------------------