%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ITP020+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 12:50:18 PM UTC 2026
% Result : Theorem 11.10s 1.89s
% Output : CNFRefutation 11.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 15
% Syntax : Number of formulae : 60 ( 7 unt; 7 def)
% Number of atoms : 193 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 238 ( 105 ~; 99 |; 14 &)
% ( 9 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 11 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-4 aty)
% Number of variables : 78 ( 69 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B,F] :
( mem(F,arr(A,B))
=> ! [X] :
( mem(X,A)
=> mem(ap(F,X),B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Epred__set_2EUNIV(A_27a),arr(A_27a,bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A0] :
( ne(A0)
=> ! [A1] :
( ne(A1)
=> ne(ty_2Epair_2Eprod(A0,A1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Epred__set_2ECROSS(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
ne(ty_2Enum_2Enum),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1t] :
( mem(V1t,arr(A_27b,bool))
=> ( ? [V2f] :
( p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V2f),V0s),V1t))
& mem(V2f,arr(A_27a,A_27b)) )
<=> ? [V3g] :
( p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27b,A_27a),V3g),V1t),V0s))
& mem(V3g,arr(A_27b,A_27a)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f62,axiom,
? [V0f] :
( p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),V0f),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))
& mem(V0f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f63,conjecture,
? [V0f] :
( p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0f),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))))
& mem(V0f,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f64,negated_conjecture,
~ ? [V0f] :
( p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0f),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))))
& mem(V0f,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) ),
inference(negated_conjecture,[status(cth)],[f63]) ).
fof(f69,plain,
! [A,B,F] :
( ! [X] :
( mem(ap(F,X),B)
| ~ mem(X,A) )
| ~ mem(F,arr(A,B)) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f70,plain,
! [X0,X1,X2,X3] :
( mem(ap(X0,X3),X2)
| ~ mem(X3,X1)
| ~ mem(X0,arr(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f125,plain,
! [A_27a] :
( mem(c_2Epred__set_2EUNIV(A_27a),arr(A_27a,bool))
| ~ ne(A_27a) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f126,plain,
! [X0] :
( mem(c_2Epred__set_2EUNIV(X0),arr(X0,bool))
| ~ ne(X0) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f127,plain,
! [A0] :
( ! [A1] :
( ne(ty_2Epair_2Eprod(A0,A1))
| ~ ne(A1) )
| ~ ne(A0) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f128,plain,
! [X0,X1] :
( ne(ty_2Epair_2Eprod(X0,X1))
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f129,plain,
! [A_27a] :
( ! [A_27b] :
( mem(c_2Epred__set_2ECROSS(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))))
| ~ ne(A_27b) )
| ~ ne(A_27a) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f130,plain,
! [X0,X1] :
( mem(c_2Epred__set_2ECROSS(X0,X1),arr(arr(X0,bool),arr(arr(X1,bool),arr(ty_2Epair_2Eprod(X0,X1),bool))))
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f133,plain,
ne(ty_2Enum_2Enum),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f285,plain,
! [A_27a] :
( ! [A_27b] :
( ! [V0s] :
( ! [V1t] :
( ( ? [V2f] :
( p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V2f),V0s),V1t))
& mem(V2f,arr(A_27a,A_27b)) )
<=> ? [V3g] :
( p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27b,A_27a),V3g),V1t),V0s))
& mem(V3g,arr(A_27b,A_27a)) ) )
| ~ mem(V1t,arr(A_27b,bool)) )
| ~ mem(V0s,arr(A_27a,bool)) )
| ~ ne(A_27b) )
| ~ ne(A_27a) ),
inference(pre_NNF_transformation,[status(thm)],[f51]) ).
fof(f286,plain,
! [A_27a] :
( ! [A_27b] :
( ! [V0s] :
( ! [V1t] :
( ( ( ! [V3g] :
( ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27b,A_27a),V3g),V1t),V0s))
| ~ mem(V3g,arr(A_27b,A_27a)) )
| ? [V2f] :
( p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V2f),V0s),V1t))
& mem(V2f,arr(A_27a,A_27b)) ) )
& ( ? [V3g] :
( p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27b,A_27a),V3g),V1t),V0s))
& mem(V3g,arr(A_27b,A_27a)) )
| ! [V2f] :
( ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V2f),V0s),V1t))
| ~ mem(V2f,arr(A_27a,A_27b)) ) ) )
| ~ mem(V1t,arr(A_27b,bool)) )
| ~ mem(V0s,arr(A_27a,bool)) )
| ~ ne(A_27b) )
| ~ ne(A_27a) ),
inference(NNF_transformation,[status(thm)],[f285]) ).
fof(f287,plain,
! [A_27a] :
( ! [A_27b] :
( ! [V0s] :
( ! [V1t] :
( ( ( ! [V3g] :
( ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27b,A_27a),V3g),V1t),V0s))
| ~ mem(V3g,arr(A_27b,A_27a)) )
| ( p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),sK24_skl(V1t,V0s,A_27b,A_27a)),V0s),V1t))
& mem(sK24_skl(V1t,V0s,A_27b,A_27a),arr(A_27a,A_27b)) ) )
& ( ( p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27b,A_27a),sK23_skl(V1t,V0s,A_27b,A_27a)),V1t),V0s))
& mem(sK23_skl(V1t,V0s,A_27b,A_27a),arr(A_27b,A_27a)) )
| ! [V2f] :
( ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V2f),V0s),V1t))
| ~ mem(V2f,arr(A_27a,A_27b)) ) ) )
| ~ mem(V1t,arr(A_27b,bool)) )
| ~ mem(V0s,arr(A_27a,bool)) )
| ~ ne(A_27b) )
| ~ ne(A_27a) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl,sK24_skl]),skolemize(V3g,sK23_skl(V1t,V0s,A_27b,A_27a)),skolemize(V2f,sK24_skl(V1t,V0s,A_27b,A_27a))],[f286]) ).
fof(f290,plain,
! [X0,X1,X2,X3,X4] :
( ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),X4),X3),X2))
| ~ mem(X4,arr(X1,X0))
| mem(sK24_skl(X3,X2,X1,X0),arr(X0,X1))
| ~ mem(X3,arr(X1,bool))
| ~ mem(X2,arr(X0,bool))
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[status(thm)],[f287]) ).
fof(f291,plain,
! [X0,X1,X2,X3,X4] :
( ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),X4),X3),X2))
| ~ mem(X4,arr(X1,X0))
| p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),sK24_skl(X3,X2,X1,X0)),X2),X3))
| ~ mem(X3,arr(X1,bool))
| ~ mem(X2,arr(X0,bool))
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[status(thm)],[f287]) ).
fof(f372,plain,
( p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),sK25_skl),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))
& mem(sK25_skl,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25_skl]),skolemize(V0f,sK25_skl)],[f62]) ).
fof(f373,plain,
mem(sK25_skl,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum)),
inference(cnf_transformation,[status(thm)],[f372]) ).
fof(f374,plain,
p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),sK25_skl),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),
inference(cnf_transformation,[status(thm)],[f372]) ).
fof(f375,plain,
! [V0f] :
( ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0f),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))))
| ~ mem(V0f,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) ),
inference(pre_NNF_transformation,[status(thm)],[f64]) ).
fof(f376,plain,
! [X0] :
( ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))))
| ~ mem(X0,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) ),
inference(cnf_transformation,[status(thm)],[f375]) ).
fof(f556,plain,
! [X0,X1,X2] :
( mem(ap(c_2Epred__set_2ECROSS(X0,X1),X2),arr(arr(X1,bool),arr(ty_2Epair_2Eprod(X0,X1),bool)))
| ~ mem(X2,arr(X0,bool))
| ~ ne(X1)
| ~ ne(X0) ),
inference(resolution,[status(thm)],[f130,f70]) ).
fof(f558,plain,
! [X0,X1,X2,X3] :
( mem(ap(ap(c_2Epred__set_2ECROSS(X0,X1),X2),X3),arr(ty_2Epair_2Eprod(X0,X1),bool))
| ~ mem(X3,arr(X1,bool))
| ~ mem(X2,arr(X0,bool))
| ~ ne(X1)
| ~ ne(X0) ),
inference(resolution,[status(thm)],[f556,f70]) ).
fof(f2779,definition,
( sQ176_spl
<=> ne(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)) ),
introduced(definition,[new_symbols(definition,[sQ176_spl])],[split_symbol_definition]) ).
fof(f2781,plain,
( sQ176_spl
| ~ ne(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)) ),
inference(component_clause,[status(thm)],[f2779]) ).
fof(f2782,definition,
( sQ177_spl
<=> ne(ty_2Enum_2Enum) ),
introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition]) ).
fof(f2784,plain,
( sQ177_spl
| ~ ne(ty_2Enum_2Enum) ),
inference(component_clause,[status(thm)],[f2782]) ).
fof(f2785,definition,
( sQ178_spl
<=> mem(ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),bool)) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f2787,plain,
( sQ178_spl
| ~ mem(ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),bool)) ),
inference(component_clause,[status(thm)],[f2785]) ).
fof(f2788,definition,
( sQ179_spl
<=> mem(c_2Epred__set_2EUNIV(ty_2Enum_2Enum),arr(ty_2Enum_2Enum,bool)) ),
introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition]) ).
fof(f2790,plain,
( sQ179_spl
| ~ mem(c_2Epred__set_2EUNIV(ty_2Enum_2Enum),arr(ty_2Enum_2Enum,bool)) ),
inference(component_clause,[status(thm)],[f2788]) ).
fof(f2791,definition,
! [X0] :
( sQ180_spl
<=> ( ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),X0),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))
| ~ mem(X0,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum)) ) ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f2792,plain,
! [X0] :
( ~ sQ180_spl
| ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),X0),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))
| ~ mem(X0,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum)) ),
inference(component_clause,[status(thm)],[f2791]) ).
fof(f2800,plain,
( sQ177_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2784,f133]) ).
fof(f2801,plain,
sQ177_spl,
inference(contradiction_clause,[status(thm)],[f2800]) ).
fof(f2808,plain,
( sQ176_spl
| ~ ne(ty_2Enum_2Enum)
| ~ ne(ty_2Enum_2Enum) ),
inference(resolution,[status(thm)],[f2781,f128]) ).
fof(f2809,plain,
( sQ176_spl
| ~ sQ177_spl ),
inference(split_clause,[status(thm)],[f2808,f2782,f2779]) ).
fof(f2940,plain,
! [X0] :
( ~ mem(sK24_skl(ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
| ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),X0),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))
| ~ mem(X0,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum))
| ~ mem(ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),bool))
| ~ mem(c_2Epred__set_2EUNIV(ty_2Enum_2Enum),arr(ty_2Enum_2Enum,bool))
| ~ ne(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
| ~ ne(ty_2Enum_2Enum) ),
inference(resolution,[status(thm)],[f291,f376]) ).
fof(f2943,definition,
( sQ184_spl
<=> mem(sK24_skl(ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) ),
introduced(definition,[new_symbols(definition,[sQ184_spl])],[split_symbol_definition]) ).
fof(f2946,plain,
( ~ sQ184_spl
| sQ180_spl
| ~ sQ178_spl
| ~ sQ179_spl
| ~ sQ176_spl
| ~ sQ177_spl ),
inference(split_clause,[status(thm)],[f2940,f2782,f2779,f2788,f2785,f2791,f2943]) ).
fof(f3029,plain,
( sQ179_spl
| ~ ne(ty_2Enum_2Enum) ),
inference(resolution,[status(thm)],[f2790,f126]) ).
fof(f3030,plain,
( sQ179_spl
| ~ sQ177_spl ),
inference(split_clause,[status(thm)],[f3029,f2782,f2788]) ).
fof(f3059,plain,
( sQ178_spl
| ~ mem(c_2Epred__set_2EUNIV(ty_2Enum_2Enum),arr(ty_2Enum_2Enum,bool))
| ~ mem(c_2Epred__set_2EUNIV(ty_2Enum_2Enum),arr(ty_2Enum_2Enum,bool))
| ~ ne(ty_2Enum_2Enum)
| ~ ne(ty_2Enum_2Enum) ),
inference(resolution,[status(thm)],[f2787,f558]) ).
fof(f3060,plain,
( sQ178_spl
| ~ sQ179_spl
| ~ sQ177_spl ),
inference(split_clause,[status(thm)],[f3059,f2782,f2788,f2785]) ).
fof(f3778,plain,
( ~ mem(sK25_skl,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum))
| mem(sK24_skl(ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
| ~ mem(ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),bool))
| ~ mem(c_2Epred__set_2EUNIV(ty_2Enum_2Enum),arr(ty_2Enum_2Enum,bool))
| ~ ne(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))
| ~ ne(ty_2Enum_2Enum) ),
inference(resolution,[status(thm)],[f374,f290]) ).
fof(f3781,definition,
( sQ234_spl
<=> mem(sK25_skl,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum)) ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f3783,plain,
( sQ234_spl
| ~ mem(sK25_skl,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum)) ),
inference(component_clause,[status(thm)],[f3781]) ).
fof(f3784,plain,
( ~ sQ234_spl
| sQ184_spl
| ~ sQ178_spl
| ~ sQ179_spl
| ~ sQ176_spl
| ~ sQ177_spl ),
inference(split_clause,[status(thm)],[f3778,f2782,f2779,f2788,f2785,f2943,f3781]) ).
fof(f3786,plain,
( sQ234_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3783,f373]) ).
fof(f3787,plain,
sQ234_spl,
inference(contradiction_clause,[status(thm)],[f3786]) ).
fof(f3795,plain,
( ~ sQ180_spl
| ~ mem(sK25_skl,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum)) ),
inference(resolution,[status(thm)],[f2792,f374]) ).
fof(f3798,plain,
( ~ sQ180_spl
| ~ sQ234_spl ),
inference(split_clause,[status(thm)],[f3795,f3781,f2791]) ).
fof(f3801,plain,
$false,
inference(sat_refutation,[status(thm)],[f2801,f2809,f2946,f3030,f3060,f3784,f3787,f3798]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP020+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 21:52:28 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 11.10/1.89 % Refutation found
% 11.10/1.89 % SZS status Theorem for theBenchmark: Theorem is valid
% 11.10/1.89 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 11.03/1.94 % Elapsed time: 1.569755 seconds
% 11.03/1.94 % CPU time: 12.058426 seconds
% 11.03/1.94 % Total memory used: 249.041 MB
% 11.03/1.94 % Net memory used: 235.359 MB
%------------------------------------------------------------------------------