%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ITP004+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 : n026.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 12:50:00 PM UTC 2026
% Result : Theorem 14.28s 2.43s
% Output : CNFRefutation 15.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 70 ( 8 unt; 7 def)
% Number of atoms : 249 ( 9 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 307 ( 128 ~; 135 |; 14 &)
% ( 11 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 92 ( 89 !; 3 ?)
% 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(f17,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Epred__set_2ECHOICE(A_27a),arr(arr(A_27a,bool),A_27a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Epred__set_2EREST(A_27a),arr(arr(A_27a,bool),arr(A_27a,bool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1t] :
( mem(V1t,arr(A_27a,bool))
=> ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t))
<=> ! [V2x] :
( mem(V2x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s))
=> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V2y)))
<=> ( V1x != V2y
& p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ap(c_2Epred__set_2EREST(A_27a),V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),ap(c_2Epred__set_2ECHOICE(A_27a),V0s)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,conjecture,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Epred__set_2EREST(A_27a),V0s)),V0s)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ ! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Epred__set_2EREST(A_27a),V0s)),V0s)) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f33,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(f34,plain,
! [X0,X1,X2,X3] :
( mem(ap(X0,X3),X2)
| ~ mem(X3,X1)
| ~ mem(X0,arr(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f69,plain,
! [A_27a] :
( mem(c_2Epred__set_2ECHOICE(A_27a),arr(arr(A_27a,bool),A_27a))
| ~ ne(A_27a) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f70,plain,
! [X0] :
( mem(c_2Epred__set_2ECHOICE(X0),arr(arr(X0,bool),X0))
| ~ ne(X0) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f73,plain,
! [A_27a] :
( mem(c_2Epred__set_2EREST(A_27a),arr(arr(A_27a,bool),arr(A_27a,bool)))
| ~ ne(A_27a) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f74,plain,
! [X0] :
( mem(c_2Epred__set_2EREST(X0),arr(arr(X0,bool),arr(X0,bool)))
| ~ ne(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f89,plain,
! [A_27a] :
( ! [V0s] :
( ! [V1t] :
( ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t))
<=> ! [V2x] :
( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t))
| ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s))
| ~ mem(V2x,A_27a) ) )
| ~ mem(V1t,arr(A_27a,bool)) )
| ~ mem(V0s,arr(A_27a,bool)) )
| ~ ne(A_27a) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f90,plain,
! [A_27a] :
( ! [V0s] :
( ! [V1t] :
( ( ( ? [V2x] :
( ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s))
& mem(V2x,A_27a) )
| p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) )
& ( ! [V2x] :
( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t))
| ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s))
| ~ mem(V2x,A_27a) )
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) ) )
| ~ mem(V1t,arr(A_27a,bool)) )
| ~ mem(V0s,arr(A_27a,bool)) )
| ~ ne(A_27a) ),
inference(NNF_transformation,[status(thm)],[f89]) ).
fof(f91,plain,
! [A_27a] :
( ! [V0s] :
( ! [V1t] :
( ( ( ( ~ p(ap(ap(c_2Ebool_2EIN(A_27a),sK2_skl(V1t,V0s,A_27a)),V1t))
& p(ap(ap(c_2Ebool_2EIN(A_27a),sK2_skl(V1t,V0s,A_27a)),V0s))
& mem(sK2_skl(V1t,V0s,A_27a),A_27a) )
| p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) )
& ( ! [V2x] :
( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t))
| ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s))
| ~ mem(V2x,A_27a) )
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) ) )
| ~ mem(V1t,arr(A_27a,bool)) )
| ~ mem(V0s,arr(A_27a,bool)) )
| ~ ne(A_27a) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(V2x,sK2_skl(V1t,V0s,A_27a))],[f90]) ).
fof(f93,plain,
! [X0,X1,X2] :
( mem(sK2_skl(X2,X1,X0),X0)
| p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ~ mem(X2,arr(X0,bool))
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f94,plain,
! [X0,X1,X2] :
( p(ap(ap(c_2Ebool_2EIN(X0),sK2_skl(X2,X1,X0)),X1))
| p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ~ mem(X2,arr(X0,bool))
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ~ p(ap(ap(c_2Ebool_2EIN(X0),sK2_skl(X2,X1,X0)),X2))
| p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ~ mem(X2,arr(X0,bool))
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f96,plain,
! [A_27a] :
( ! [V0s] :
( ! [V1x] :
( ! [V2y] :
( ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V2y)))
<=> ( V1x != V2y
& p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) ) )
| ~ mem(V2y,A_27a) )
| ~ mem(V1x,A_27a) )
| ~ mem(V0s,arr(A_27a,bool)) )
| ~ ne(A_27a) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f97,plain,
! [A_27a] :
( ! [V0s] :
( ! [V1x] :
( ! [V2y] :
( ( ( V1x = V2y
| ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s))
| p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V2y))) )
& ( ( V1x != V2y
& p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) )
| ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V2y))) ) )
| ~ mem(V2y,A_27a) )
| ~ mem(V1x,A_27a) )
| ~ mem(V0s,arr(A_27a,bool)) )
| ~ ne(A_27a) ),
inference(NNF_transformation,[status(thm)],[f96]) ).
fof(f98,plain,
! [X0,X1,X2,X3] :
( p(ap(ap(c_2Ebool_2EIN(X0),X2),X1))
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
| ~ mem(X3,X0)
| ~ mem(X2,X0)
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f101,plain,
! [A_27a] :
( ! [V0s] :
( ap(c_2Epred__set_2EREST(A_27a),V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),ap(c_2Epred__set_2ECHOICE(A_27a),V0s))
| ~ mem(V0s,arr(A_27a,bool)) )
| ~ ne(A_27a) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f102,plain,
! [X0,X1] :
( ap(c_2Epred__set_2EREST(X0),X1) = ap(ap(c_2Epred__set_2EDELETE(X0),X1),ap(c_2Epred__set_2ECHOICE(X0),X1))
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f103,plain,
? [A_27a] :
( ? [V0s] :
( ~ p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Epred__set_2EREST(A_27a),V0s)),V0s))
& mem(V0s,arr(A_27a,bool)) )
& ne(A_27a) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f104,plain,
( ~ p(ap(ap(c_2Epred__set_2ESUBSET(sK3_skl),ap(c_2Epred__set_2EREST(sK3_skl),sK4_skl)),sK4_skl))
& mem(sK4_skl,arr(sK3_skl,bool))
& ne(sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(A_27a,sK3_skl),skolemize(V0s,sK4_skl)],[f103]) ).
fof(f105,plain,
ne(sK3_skl),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f106,plain,
mem(sK4_skl,arr(sK3_skl,bool)),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f107,plain,
~ p(ap(ap(c_2Epred__set_2ESUBSET(sK3_skl),ap(c_2Epred__set_2EREST(sK3_skl),sK4_skl)),sK4_skl)),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f215,definition,
( sQ4_spl
<=> ne(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f217,plain,
( sQ4_spl
| ~ ne(sK3_skl) ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f313,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f217,f105]) ).
fof(f314,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f313]) ).
fof(f414,plain,
! [X0,X1,X2,X3] :
( p(ap(ap(c_2Epred__set_2ESUBSET(X0),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)),X2))
| ~ mem(X2,arr(X0,bool))
| ~ mem(ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3),arr(X0,bool))
| ~ ne(X0)
| p(ap(ap(c_2Ebool_2EIN(X0),sK2_skl(X2,ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3),X0)),X1))
| ~ mem(X3,X0)
| ~ mem(sK2_skl(X2,ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3),X0),X0)
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(resolution,[status(thm)],[f98,f94]) ).
fof(f415,plain,
! [X0,X1,X2,X3] :
( p(ap(ap(c_2Epred__set_2ESUBSET(X0),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)),X2))
| ~ mem(X2,arr(X0,bool))
| ~ mem(ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3),arr(X0,bool))
| p(ap(ap(c_2Ebool_2EIN(X0),sK2_skl(X2,ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3),X0)),X1))
| ~ mem(X3,X0)
| ~ mem(sK2_skl(X2,ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3),X0),X0)
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f414]) ).
fof(f416,plain,
! [X0,X1,X2,X3] :
( p(ap(ap(c_2Epred__set_2ESUBSET(X0),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X2)),X3))
| ~ mem(X3,arr(X0,bool))
| ~ mem(ap(ap(c_2Epred__set_2EDELETE(X0),X1),X2),arr(X0,bool))
| p(ap(ap(c_2Ebool_2EIN(X0),sK2_skl(X3,ap(ap(c_2Epred__set_2EDELETE(X0),X1),X2),X0)),X1))
| ~ mem(X2,X0)
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f415,f93]) ).
fof(f467,plain,
! [X0] :
( ap(c_2Epred__set_2EREST(sK3_skl),X0) = ap(ap(c_2Epred__set_2EDELETE(sK3_skl),X0),ap(c_2Epred__set_2ECHOICE(sK3_skl),X0))
| ~ mem(X0,arr(sK3_skl,bool)) ),
inference(resolution,[status(thm)],[f102,f105]) ).
fof(f489,plain,
ap(c_2Epred__set_2EREST(sK3_skl),sK4_skl) = ap(ap(c_2Epred__set_2EDELETE(sK3_skl),sK4_skl),ap(c_2Epred__set_2ECHOICE(sK3_skl),sK4_skl)),
inference(resolution,[status(thm)],[f467,f106]) ).
fof(f493,definition,
( sQ10_spl
<=> mem(sK4_skl,arr(sK3_skl,bool)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f495,plain,
( sQ10_spl
| ~ mem(sK4_skl,arr(sK3_skl,bool)) ),
inference(component_clause,[status(thm)],[f493]) ).
fof(f496,definition,
( sQ11_spl
<=> mem(ap(c_2Epred__set_2ECHOICE(sK3_skl),sK4_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f498,plain,
( sQ11_spl
| ~ mem(ap(c_2Epred__set_2ECHOICE(sK3_skl),sK4_skl),sK3_skl) ),
inference(component_clause,[status(thm)],[f496]) ).
fof(f507,plain,
! [X0] :
( sQ11_spl
| ~ mem(sK4_skl,X0)
| ~ mem(c_2Epred__set_2ECHOICE(sK3_skl),arr(X0,sK3_skl)) ),
inference(resolution,[status(thm)],[f498,f34]) ).
fof(f508,plain,
( sQ11_spl
| ~ ne(sK3_skl)
| ~ mem(sK4_skl,arr(sK3_skl,bool)) ),
inference(resolution,[status(thm)],[f507,f70]) ).
fof(f509,plain,
( sQ11_spl
| ~ sQ4_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f508,f493,f215,f496]) ).
fof(f510,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f495,f106]) ).
fof(f511,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f510]) ).
fof(f840,plain,
! [X0] :
( p(ap(ap(c_2Epred__set_2ESUBSET(sK3_skl),ap(ap(c_2Epred__set_2EDELETE(sK3_skl),sK4_skl),ap(c_2Epred__set_2ECHOICE(sK3_skl),sK4_skl))),X0))
| ~ mem(X0,arr(sK3_skl,bool))
| ~ mem(ap(c_2Epred__set_2EREST(sK3_skl),sK4_skl),arr(sK3_skl,bool))
| p(ap(ap(c_2Ebool_2EIN(sK3_skl),sK2_skl(X0,ap(ap(c_2Epred__set_2EDELETE(sK3_skl),sK4_skl),ap(c_2Epred__set_2ECHOICE(sK3_skl),sK4_skl)),sK3_skl)),sK4_skl))
| ~ mem(ap(c_2Epred__set_2ECHOICE(sK3_skl),sK4_skl),sK3_skl)
| ~ mem(sK4_skl,arr(sK3_skl,bool))
| ~ ne(sK3_skl) ),
inference(paramodulation,[status(thm)],[f489,f416]) ).
fof(f848,definition,
! [X0] :
( sQ38_spl
<=> ( p(ap(ap(c_2Epred__set_2ESUBSET(sK3_skl),ap(ap(c_2Epred__set_2EDELETE(sK3_skl),sK4_skl),ap(c_2Epred__set_2ECHOICE(sK3_skl),sK4_skl))),X0))
| ~ mem(X0,arr(sK3_skl,bool))
| p(ap(ap(c_2Ebool_2EIN(sK3_skl),sK2_skl(X0,ap(ap(c_2Epred__set_2EDELETE(sK3_skl),sK4_skl),ap(c_2Epred__set_2ECHOICE(sK3_skl),sK4_skl)),sK3_skl)),sK4_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f849,plain,
! [X0] :
( ~ sQ38_spl
| p(ap(ap(c_2Epred__set_2ESUBSET(sK3_skl),ap(ap(c_2Epred__set_2EDELETE(sK3_skl),sK4_skl),ap(c_2Epred__set_2ECHOICE(sK3_skl),sK4_skl))),X0))
| ~ mem(X0,arr(sK3_skl,bool))
| p(ap(ap(c_2Ebool_2EIN(sK3_skl),sK2_skl(X0,ap(ap(c_2Epred__set_2EDELETE(sK3_skl),sK4_skl),ap(c_2Epred__set_2ECHOICE(sK3_skl),sK4_skl)),sK3_skl)),sK4_skl)) ),
inference(component_clause,[status(thm)],[f848]) ).
fof(f851,definition,
( sQ39_spl
<=> mem(ap(c_2Epred__set_2EREST(sK3_skl),sK4_skl),arr(sK3_skl,bool)) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f853,plain,
( sQ39_spl
| ~ mem(ap(c_2Epred__set_2EREST(sK3_skl),sK4_skl),arr(sK3_skl,bool)) ),
inference(component_clause,[status(thm)],[f851]) ).
fof(f854,plain,
( ~ sQ39_spl
| sQ38_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f840,f215,f493,f496,f848,f851]) ).
fof(f857,plain,
! [X0] :
( ~ sQ38_spl
| p(ap(ap(c_2Epred__set_2ESUBSET(sK3_skl),ap(ap(c_2Epred__set_2EDELETE(sK3_skl),sK4_skl),ap(c_2Epred__set_2ECHOICE(sK3_skl),sK4_skl))),X0))
| ~ mem(X0,arr(sK3_skl,bool))
| p(ap(ap(c_2Ebool_2EIN(sK3_skl),sK2_skl(X0,ap(c_2Epred__set_2EREST(sK3_skl),sK4_skl),sK3_skl)),sK4_skl)) ),
inference(forward_demodulation,[status(thm)],[f489,f849]) ).
fof(f858,plain,
! [X0] :
( ~ sQ38_spl
| p(ap(ap(c_2Epred__set_2ESUBSET(sK3_skl),ap(c_2Epred__set_2EREST(sK3_skl),sK4_skl)),X0))
| ~ mem(X0,arr(sK3_skl,bool))
| p(ap(ap(c_2Ebool_2EIN(sK3_skl),sK2_skl(X0,ap(c_2Epred__set_2EREST(sK3_skl),sK4_skl),sK3_skl)),sK4_skl)) ),
inference(forward_demodulation,[status(thm)],[f489,f857]) ).
fof(f878,plain,
! [X0] :
( sQ39_spl
| ~ mem(sK4_skl,X0)
| ~ mem(c_2Epred__set_2EREST(sK3_skl),arr(X0,arr(sK3_skl,bool))) ),
inference(resolution,[status(thm)],[f853,f34]) ).
fof(f879,plain,
( sQ39_spl
| ~ ne(sK3_skl)
| ~ mem(sK4_skl,arr(sK3_skl,bool)) ),
inference(resolution,[status(thm)],[f878,f74]) ).
fof(f880,plain,
( sQ39_spl
| ~ sQ4_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f879,f493,f215,f851]) ).
fof(f4766,plain,
( ~ sQ38_spl
| p(ap(ap(c_2Epred__set_2ESUBSET(sK3_skl),ap(c_2Epred__set_2EREST(sK3_skl),sK4_skl)),sK4_skl))
| p(ap(ap(c_2Ebool_2EIN(sK3_skl),sK2_skl(sK4_skl,ap(c_2Epred__set_2EREST(sK3_skl),sK4_skl),sK3_skl)),sK4_skl)) ),
inference(resolution,[status(thm)],[f858,f106]) ).
fof(f4774,definition,
( sQ223_spl
<=> p(ap(ap(c_2Ebool_2EIN(sK3_skl),sK2_skl(sK4_skl,ap(c_2Epred__set_2EREST(sK3_skl),sK4_skl),sK3_skl)),sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ223_spl])],[split_symbol_definition]) ).
fof(f4775,plain,
( ~ sQ223_spl
| p(ap(ap(c_2Ebool_2EIN(sK3_skl),sK2_skl(sK4_skl,ap(c_2Epred__set_2EREST(sK3_skl),sK4_skl),sK3_skl)),sK4_skl)) ),
inference(component_clause,[status(thm)],[f4774]) ).
fof(f4777,definition,
( sQ224_spl
<=> p(ap(ap(c_2Epred__set_2ESUBSET(sK3_skl),ap(c_2Epred__set_2EREST(sK3_skl),sK4_skl)),sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ224_spl])],[split_symbol_definition]) ).
fof(f4778,plain,
( ~ sQ224_spl
| p(ap(ap(c_2Epred__set_2ESUBSET(sK3_skl),ap(c_2Epred__set_2EREST(sK3_skl),sK4_skl)),sK4_skl)) ),
inference(component_clause,[status(thm)],[f4777]) ).
fof(f4780,plain,
( ~ sQ38_spl
| sQ224_spl
| sQ223_spl ),
inference(split_clause,[status(thm)],[f4766,f4774,f4777,f848]) ).
fof(f4784,plain,
( ~ sQ223_spl
| p(ap(ap(c_2Epred__set_2ESUBSET(sK3_skl),ap(c_2Epred__set_2EREST(sK3_skl),sK4_skl)),sK4_skl))
| ~ mem(sK4_skl,arr(sK3_skl,bool))
| ~ mem(ap(c_2Epred__set_2EREST(sK3_skl),sK4_skl),arr(sK3_skl,bool))
| ~ ne(sK3_skl) ),
inference(resolution,[status(thm)],[f4775,f95]) ).
fof(f4795,plain,
( ~ sQ223_spl
| sQ224_spl
| ~ sQ10_spl
| ~ sQ39_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f4784,f215,f851,f493,f4777,f4774]) ).
fof(f4800,plain,
( ~ sQ224_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4778,f107]) ).
fof(f4801,plain,
~ sQ224_spl,
inference(contradiction_clause,[status(thm)],[f4800]) ).
fof(f4802,plain,
$false,
inference(sat_refutation,[status(thm)],[f314,f509,f511,f854,f880,f4780,f4795,f4801]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP004+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n026.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 20 21:43:22 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 14.28/2.43 % Refutation found
% 14.28/2.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 14.28/2.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 15.93/2.49 % Elapsed time: 2.113882 seconds
% 15.93/2.49 % CPU time: 16.407896 seconds
% 15.93/2.49 % Total memory used: 358.868 MB
% 15.93/2.49 % Net memory used: 320.160 MB
%------------------------------------------------------------------------------