%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU270+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 02:19:58 PM UTC 2026
% Result : Theorem 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 27
% Syntax : Number of formulae : 126 ( 18 unt; 14 def)
% Number of atoms : 422 ( 29 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 472 ( 176 ~; 187 |; 75 &)
% ( 24 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 29 ( 27 usr; 15 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 121 ( 108 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(B,A)
| ordinal_subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] :
( relation(A)
=> ( connected(A)
<=> is_connected_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B] :
( relation(B)
=> ( B = inclusion_relation(A)
<=> ( ! [C,D] :
( ( in(D,A)
& in(C,A) )
=> ( in(ordered_pair(C,D),B)
<=> subset(C,D) ) )
& relation_field(B) = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,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(f17,axiom,
! [A] : relation(inclusion_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,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(f33,axiom,
? [A] :
( function(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,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(f39,axiom,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [A,B] :
( ordinal(B)
=> ( in(A,B)
=> ordinal(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,conjecture,
! [A] :
( ordinal(A)
=> connected(inclusion_relation(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> connected(inclusion_relation(A)) ),
inference(negated_conjecture,[status(cth)],[f51]) ).
fof(f76,plain,
! [A,B] :
( ordinal_subset(B,A)
| ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f77,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f78,plain,
! [A] :
( ( connected(A)
<=> is_connected_in(A,relation_field(A)) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f79,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)],[f78]) ).
fof(f81,plain,
! [X0] :
( ~ is_connected_in(X0,relation_field(X0))
| connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f82,plain,
! [A,B] :
( ( B = inclusion_relation(A)
<=> ( ! [C,D] :
( ( in(ordered_pair(C,D),B)
<=> subset(C,D) )
| ~ in(D,A)
| ~ in(C,A) )
& relation_field(B) = A ) )
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f83,plain,
! [A,B] :
( ( ( ? [C,D] :
( ( subset(C,D)
| in(ordered_pair(C,D),B) )
& ( ~ subset(C,D)
| ~ in(ordered_pair(C,D),B) )
& in(D,A)
& in(C,A) )
| relation_field(B) != A
| B = inclusion_relation(A) )
& ( ( ! [C,D] :
( ( ( ~ subset(C,D)
| in(ordered_pair(C,D),B) )
& ( subset(C,D)
| ~ in(ordered_pair(C,D),B) ) )
| ~ in(D,A)
| ~ in(C,A) )
& relation_field(B) = A )
| B != inclusion_relation(A) ) )
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f82]) ).
fof(f84,plain,
! [B] :
( ( ! [A] :
( ? [C,D] :
( ( subset(C,D)
| in(ordered_pair(C,D),B) )
& ( ~ subset(C,D)
| ~ in(ordered_pair(C,D),B) )
& in(D,A)
& in(C,A) )
| relation_field(B) != A
| B = inclusion_relation(A) )
& ! [A] :
( ( ! [C,D] :
( ( ( ~ subset(C,D)
| in(ordered_pair(C,D),B) )
& ( subset(C,D)
| ~ in(ordered_pair(C,D),B) ) )
| ~ in(D,A)
| ~ in(C,A) )
& relation_field(B) = A )
| B != inclusion_relation(A) ) )
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f83]) ).
fof(f85,plain,
! [B] :
( ( ! [A] :
( ( ( subset(sK0_skl(A,B),sK1_skl(A,B))
| in(ordered_pair(sK0_skl(A,B),sK1_skl(A,B)),B) )
& ( ~ subset(sK0_skl(A,B),sK1_skl(A,B))
| ~ in(ordered_pair(sK0_skl(A,B),sK1_skl(A,B)),B) )
& in(sK1_skl(A,B),A)
& in(sK0_skl(A,B),A) )
| relation_field(B) != A
| B = inclusion_relation(A) )
& ! [A] :
( ( ! [C,D] :
( ( ( ~ subset(C,D)
| in(ordered_pair(C,D),B) )
& ( subset(C,D)
| ~ in(ordered_pair(C,D),B) ) )
| ~ in(D,A)
| ~ in(C,A) )
& relation_field(B) = A )
| B != inclusion_relation(A) ) )
| ~ relation(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(C,sK0_skl(A,B)),skolemize(D,sK1_skl(A,B))],[f84]) ).
fof(f86,plain,
! [X0,X1] :
( relation_field(X0) = X1
| X0 != inclusion_relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f88,plain,
! [X0,X1,X2,X3] :
( ~ subset(X2,X3)
| in(ordered_pair(X2,X3),X0)
| ~ in(X3,X1)
| ~ in(X2,X1)
| X0 != inclusion_relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f96,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)],[f14]) ).
fof(f97,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)],[f96]) ).
fof(f98,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)],[f97]) ).
fof(f99,plain,
! [A] :
( ( ! [B] :
( ( ~ in(ordered_pair(sK3_skl(B,A),sK2_skl(B,A)),A)
& ~ in(ordered_pair(sK2_skl(B,A),sK3_skl(B,A)),A)
& sK2_skl(B,A) != sK3_skl(B,A)
& in(sK3_skl(B,A),B)
& in(sK2_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,[sK2_skl,sK3_skl]),skolemize(C,sK2_skl(B,A)),skolemize(D,sK3_skl(B,A))],[f98]) ).
fof(f101,plain,
! [X0,X1] :
( in(sK2_skl(X1,X0),X1)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f102,plain,
! [X0,X1] :
( in(sK3_skl(X1,X0),X1)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f104,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK2_skl(X1,X0),sK3_skl(X1,X0)),X0)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f105,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK3_skl(X1,X0),sK2_skl(X1,X0)),X0)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f106,plain,
! [X0] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f111,plain,
relation(empty_set),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f127,plain,
( function(sK5_skl)
& relation(sK5_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(A,sK5_skl)],[f33]) ).
fof(f128,plain,
relation(sK5_skl),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f136,plain,
( function(sK8_skl)
& empty(sK8_skl)
& relation(sK8_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(A,sK8_skl)],[f36]) ).
fof(f137,plain,
relation(sK8_skl),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f140,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)],[f37]) ).
fof(f141,plain,
relation(sK9_skl),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f150,plain,
( one_to_one(sK11_skl)
& function(sK11_skl)
& relation(sK11_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl]),skolemize(A,sK11_skl)],[f39]) ).
fof(f151,plain,
relation(sK11_skl),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f163,plain,
! [A,B] :
( ( ordinal_subset(A,B)
<=> subset(A,B) )
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f164,plain,
! [A,B] :
( ( ( ~ subset(A,B)
| ordinal_subset(A,B) )
& ( subset(A,B)
| ~ ordinal_subset(A,B) ) )
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(NNF_transformation,[status(thm)],[f163]) ).
fof(f165,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f175,plain,
! [A,B] :
( ordinal(A)
| ~ in(A,B)
| ~ ordinal(B) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f176,plain,
! [B] :
( ! [A] :
( ordinal(A)
| ~ in(A,B) )
| ~ ordinal(B) ),
inference(miniscoping,[status(thm)],[f175]) ).
fof(f177,plain,
! [X0,X1] :
( ordinal(X1)
| ~ in(X1,X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f187,plain,
? [A] :
( ~ connected(inclusion_relation(A))
& ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f52]) ).
fof(f188,plain,
( ~ connected(inclusion_relation(sK14_skl))
& ordinal(sK14_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl]),skolemize(A,sK14_skl)],[f187]) ).
fof(f189,plain,
ordinal(sK14_skl),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f190,plain,
~ connected(inclusion_relation(sK14_skl)),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f210,plain,
! [X0] :
( relation_field(inclusion_relation(X0)) = X0
| ~ relation(inclusion_relation(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f86]) ).
fof(f212,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| in(ordered_pair(X1,X2),inclusion_relation(X0))
| ~ in(X2,X0)
| ~ in(X1,X0)
| ~ relation(inclusion_relation(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f88]) ).
fof(f218,plain,
! [X0,X1,X2] :
( ~ subset(X0,X2)
| in(ordered_pair(X0,X2),inclusion_relation(X1))
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f212,f106]) ).
fof(f220,plain,
! [X0] : relation_field(inclusion_relation(X0)) = X0,
inference(backward_subsumption_resolution,[status(thm)],[f210,f106]) ).
fof(f221,plain,
! [X0] :
( ~ is_connected_in(inclusion_relation(X0),relation_field(inclusion_relation(X0)))
| connected(inclusion_relation(X0)) ),
inference(resolution,[status(thm)],[f81,f106]) ).
fof(f222,plain,
! [X0] :
( ~ is_connected_in(inclusion_relation(X0),X0)
| connected(inclusion_relation(X0)) ),
inference(forward_demodulation,[status(thm)],[f220,f221]) ).
fof(f251,plain,
~ is_connected_in(inclusion_relation(sK14_skl),sK14_skl),
inference(resolution,[status(thm)],[f222,f190]) ).
fof(f253,plain,
( in(sK3_skl(sK14_skl,inclusion_relation(sK14_skl)),sK14_skl)
| ~ relation(inclusion_relation(sK14_skl)) ),
inference(resolution,[status(thm)],[f251,f102]) ).
fof(f254,plain,
( in(sK2_skl(sK14_skl,inclusion_relation(sK14_skl)),sK14_skl)
| ~ relation(inclusion_relation(sK14_skl)) ),
inference(resolution,[status(thm)],[f251,f101]) ).
fof(f255,definition,
( sQ7_spl
<=> relation(inclusion_relation(sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f257,plain,
( sQ7_spl
| ~ relation(inclusion_relation(sK14_skl)) ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f258,definition,
( sQ8_spl
<=> in(sK3_skl(sK14_skl,inclusion_relation(sK14_skl)),sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f259,plain,
( ~ sQ8_spl
| in(sK3_skl(sK14_skl,inclusion_relation(sK14_skl)),sK14_skl) ),
inference(component_clause,[status(thm)],[f258]) ).
fof(f261,plain,
( sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f253,f255,f258]) ).
fof(f262,definition,
( sQ9_spl
<=> in(sK2_skl(sK14_skl,inclusion_relation(sK14_skl)),sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f263,plain,
( ~ sQ9_spl
| in(sK2_skl(sK14_skl,inclusion_relation(sK14_skl)),sK14_skl) ),
inference(component_clause,[status(thm)],[f262]) ).
fof(f265,plain,
( sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f254,f255,f262]) ).
fof(f266,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f257,f106]) ).
fof(f267,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f266]) ).
fof(f271,definition,
( sQ10_spl
<=> relation(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f273,plain,
( sQ10_spl
| ~ relation(empty_set) ),
inference(component_clause,[status(thm)],[f271]) ).
fof(f275,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f273,f111]) ).
fof(f276,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f275]) ).
fof(f305,plain,
( ~ in(ordered_pair(sK2_skl(sK14_skl,inclusion_relation(sK14_skl)),sK3_skl(sK14_skl,inclusion_relation(sK14_skl))),inclusion_relation(sK14_skl))
| ~ relation(inclusion_relation(sK14_skl)) ),
inference(resolution,[status(thm)],[f104,f251]) ).
fof(f306,definition,
( sQ14_spl
<=> in(ordered_pair(sK2_skl(sK14_skl,inclusion_relation(sK14_skl)),sK3_skl(sK14_skl,inclusion_relation(sK14_skl))),inclusion_relation(sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f308,plain,
( sQ14_spl
| ~ in(ordered_pair(sK2_skl(sK14_skl,inclusion_relation(sK14_skl)),sK3_skl(sK14_skl,inclusion_relation(sK14_skl))),inclusion_relation(sK14_skl)) ),
inference(component_clause,[status(thm)],[f306]) ).
fof(f309,plain,
( ~ sQ14_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f305,f255,f306]) ).
fof(f310,plain,
( sQ14_spl
| ~ subset(sK2_skl(sK14_skl,inclusion_relation(sK14_skl)),sK3_skl(sK14_skl,inclusion_relation(sK14_skl)))
| ~ in(sK3_skl(sK14_skl,inclusion_relation(sK14_skl)),sK14_skl)
| ~ in(sK2_skl(sK14_skl,inclusion_relation(sK14_skl)),sK14_skl) ),
inference(resolution,[status(thm)],[f308,f218]) ).
fof(f313,definition,
( sQ15_spl
<=> subset(sK2_skl(sK14_skl,inclusion_relation(sK14_skl)),sK3_skl(sK14_skl,inclusion_relation(sK14_skl))) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f316,plain,
( sQ14_spl
| ~ sQ15_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f310,f262,f258,f313,f306]) ).
fof(f324,definition,
( sQ18_spl
<=> in(ordered_pair(sK3_skl(sK14_skl,inclusion_relation(sK14_skl)),sK2_skl(sK14_skl,inclusion_relation(sK14_skl))),inclusion_relation(sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f326,plain,
( sQ18_spl
| ~ in(ordered_pair(sK3_skl(sK14_skl,inclusion_relation(sK14_skl)),sK2_skl(sK14_skl,inclusion_relation(sK14_skl))),inclusion_relation(sK14_skl)) ),
inference(component_clause,[status(thm)],[f324]) ).
fof(f336,plain,
( ~ in(ordered_pair(sK3_skl(sK14_skl,inclusion_relation(sK14_skl)),sK2_skl(sK14_skl,inclusion_relation(sK14_skl))),inclusion_relation(sK14_skl))
| ~ relation(inclusion_relation(sK14_skl)) ),
inference(resolution,[status(thm)],[f105,f251]) ).
fof(f337,plain,
( ~ sQ18_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f336,f255,f324]) ).
fof(f338,plain,
( sQ18_spl
| ~ subset(sK3_skl(sK14_skl,inclusion_relation(sK14_skl)),sK2_skl(sK14_skl,inclusion_relation(sK14_skl)))
| ~ in(sK2_skl(sK14_skl,inclusion_relation(sK14_skl)),sK14_skl)
| ~ in(sK3_skl(sK14_skl,inclusion_relation(sK14_skl)),sK14_skl) ),
inference(resolution,[status(thm)],[f326,f218]) ).
fof(f341,definition,
( sQ20_spl
<=> subset(sK3_skl(sK14_skl,inclusion_relation(sK14_skl)),sK2_skl(sK14_skl,inclusion_relation(sK14_skl))) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f343,plain,
( sQ20_spl
| ~ subset(sK3_skl(sK14_skl,inclusion_relation(sK14_skl)),sK2_skl(sK14_skl,inclusion_relation(sK14_skl))) ),
inference(component_clause,[status(thm)],[f341]) ).
fof(f344,plain,
( sQ18_spl
| ~ sQ20_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f338,f258,f262,f341,f324]) ).
fof(f384,definition,
( sQ29_spl
<=> relation(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f386,plain,
( sQ29_spl
| ~ relation(sK5_skl) ),
inference(component_clause,[status(thm)],[f384]) ).
fof(f388,plain,
( sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f386,f128]) ).
fof(f389,plain,
sQ29_spl,
inference(contradiction_clause,[status(thm)],[f388]) ).
fof(f424,definition,
( sQ37_spl
<=> relation(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f426,plain,
( sQ37_spl
| ~ relation(sK8_skl) ),
inference(component_clause,[status(thm)],[f424]) ).
fof(f428,plain,
( sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f426,f137]) ).
fof(f429,plain,
sQ37_spl,
inference(contradiction_clause,[status(thm)],[f428]) ).
fof(f461,definition,
( sQ45_spl
<=> relation(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f463,plain,
( sQ45_spl
| ~ relation(sK9_skl) ),
inference(component_clause,[status(thm)],[f461]) ).
fof(f465,plain,
( sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f463,f141]) ).
fof(f466,plain,
sQ45_spl,
inference(contradiction_clause,[status(thm)],[f465]) ).
fof(f501,definition,
( sQ53_spl
<=> relation(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f503,plain,
( sQ53_spl
| ~ relation(sK11_skl) ),
inference(component_clause,[status(thm)],[f501]) ).
fof(f505,plain,
( sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f503,f151]) ).
fof(f506,plain,
sQ53_spl,
inference(contradiction_clause,[status(thm)],[f505]) ).
fof(f540,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1)
| subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f165,f77]) ).
fof(f541,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f540]) ).
fof(f552,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1)
| subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f541,f165]) ).
fof(f553,plain,
! [X0,X1] :
( subset(X1,X0)
| subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f552]) ).
fof(f554,plain,
( sQ20_spl
| subset(sK2_skl(sK14_skl,inclusion_relation(sK14_skl)),sK3_skl(sK14_skl,inclusion_relation(sK14_skl)))
| ~ ordinal(sK3_skl(sK14_skl,inclusion_relation(sK14_skl)))
| ~ ordinal(sK2_skl(sK14_skl,inclusion_relation(sK14_skl))) ),
inference(resolution,[status(thm)],[f553,f343]) ).
fof(f556,definition,
( sQ61_spl
<=> ordinal(sK2_skl(sK14_skl,inclusion_relation(sK14_skl))) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f558,plain,
( sQ61_spl
| ~ ordinal(sK2_skl(sK14_skl,inclusion_relation(sK14_skl))) ),
inference(component_clause,[status(thm)],[f556]) ).
fof(f559,definition,
( sQ62_spl
<=> ordinal(sK3_skl(sK14_skl,inclusion_relation(sK14_skl))) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f561,plain,
( sQ62_spl
| ~ ordinal(sK3_skl(sK14_skl,inclusion_relation(sK14_skl))) ),
inference(component_clause,[status(thm)],[f559]) ).
fof(f562,plain,
( sQ20_spl
| sQ15_spl
| ~ sQ62_spl
| ~ sQ61_spl ),
inference(split_clause,[status(thm)],[f554,f556,f559,f313,f341]) ).
fof(f565,plain,
! [X0] :
( sQ61_spl
| ~ in(sK2_skl(sK14_skl,inclusion_relation(sK14_skl)),X0)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f558,f177]) ).
fof(f575,plain,
! [X0] :
( sQ62_spl
| ~ in(sK3_skl(sK14_skl,inclusion_relation(sK14_skl)),X0)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f561,f177]) ).
fof(f592,plain,
( ~ sQ9_spl
| sQ61_spl
| ~ ordinal(sK14_skl) ),
inference(resolution,[status(thm)],[f565,f263]) ).
fof(f593,plain,
( ~ sQ9_spl
| sQ61_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f592,f189]) ).
fof(f594,plain,
( ~ sQ9_spl
| sQ61_spl ),
inference(contradiction_clause,[status(thm)],[f593]) ).
fof(f601,plain,
( ~ sQ8_spl
| sQ62_spl
| ~ ordinal(sK14_skl) ),
inference(resolution,[status(thm)],[f575,f259]) ).
fof(f602,plain,
( ~ sQ8_spl
| sQ62_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f601,f189]) ).
fof(f603,plain,
( ~ sQ8_spl
| sQ62_spl ),
inference(contradiction_clause,[status(thm)],[f602]) ).
fof(f604,plain,
$false,
inference(sat_refutation,[status(thm)],[f261,f265,f267,f276,f309,f316,f337,f344,f389,f429,f466,f506,f562,f594,f603]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU270+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n018.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Mon Sep 21 06:07:28 UTC 2026
% 0.10/0.34 % CPUTime :
% 0.10/0.36 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.081420 seconds
% 0.13/0.43 % CPU time: 0.371256 seconds
% 0.13/0.43 % Total memory used: 110.334 MB
% 0.13/0.43 % Net memory used: 109.832 MB
%------------------------------------------------------------------------------