%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET811+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 02:10:40 PM UTC 2026
% Result : Theorem 0.15s 0.52s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 22
% Syntax : Number of formulae : 126 ( 7 unt; 16 def)
% Number of atoms : 348 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 360 ( 138 ~; 155 |; 38 &)
% ( 23 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 22 usr; 17 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 115 ( 109 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A] :
( member(A,on)
<=> ( ! [X] :
( member(X,A)
=> subset(X,A) )
& strict_well_order(member_predicate,A)
& set(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y] :
( apply(member_predicate,X,Y)
<=> member(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,R,A,Y] :
( member(Y,initial_segment(X,R,A))
<=> ( apply(R,Y,X)
& member(Y,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,conjecture,
! [A] :
( member(A,on)
=> ! [X] :
( member(X,A)
=> equal_set(X,initial_segment(X,member_predicate,A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
~ ! [A] :
( member(A,on)
=> ! [X] :
( member(X,A)
=> equal_set(X,initial_segment(X,member_predicate,A)) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f22,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,B)
| ~ member(X,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f23,plain,
! [A,B] :
( ( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
( ! [A,B] :
( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f25,plain,
( ! [A,B] :
( ( ~ member(sK0_skl(B,A),B)
& member(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(B,A))],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f28,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f29,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f30,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f33,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f76,plain,
! [A] :
( member(A,on)
<=> ( ! [X] :
( subset(X,A)
| ~ member(X,A) )
& strict_well_order(member_predicate,A)
& set(A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f77,plain,
! [A] :
( ( ? [X] :
( ~ subset(X,A)
& member(X,A) )
| ~ strict_well_order(member_predicate,A)
| ~ set(A)
| member(A,on) )
& ( ( ! [X] :
( subset(X,A)
| ~ member(X,A) )
& strict_well_order(member_predicate,A)
& set(A) )
| ~ member(A,on) ) ),
inference(NNF_transformation,[status(thm)],[f76]) ).
fof(f78,plain,
( ! [A] :
( ? [X] :
( ~ subset(X,A)
& member(X,A) )
| ~ strict_well_order(member_predicate,A)
| ~ set(A)
| member(A,on) )
& ! [A] :
( ( ! [X] :
( subset(X,A)
| ~ member(X,A) )
& strict_well_order(member_predicate,A)
& set(A) )
| ~ member(A,on) ) ),
inference(miniscoping,[status(thm)],[f77]) ).
fof(f79,plain,
( ! [A] :
( ( ~ subset(sK3_skl(A),A)
& member(sK3_skl(A),A) )
| ~ strict_well_order(member_predicate,A)
| ~ set(A)
| member(A,on) )
& ! [A] :
( ( ! [X] :
( subset(X,A)
| ~ member(X,A) )
& strict_well_order(member_predicate,A)
& set(A) )
| ~ member(A,on) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(X,sK3_skl(A))],[f78]) ).
fof(f82,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ member(X1,X0)
| ~ member(X0,on) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f103,plain,
! [X,Y] :
( ( ~ member(X,Y)
| apply(member_predicate,X,Y) )
& ( member(X,Y)
| ~ apply(member_predicate,X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f15]) ).
fof(f104,plain,
( ! [X,Y] :
( ~ member(X,Y)
| apply(member_predicate,X,Y) )
& ! [X,Y] :
( member(X,Y)
| ~ apply(member_predicate,X,Y) ) ),
inference(miniscoping,[status(thm)],[f103]) ).
fof(f105,plain,
! [X0,X1] :
( member(X0,X1)
| ~ apply(member_predicate,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f106,plain,
! [X0,X1] :
( ~ member(X0,X1)
| apply(member_predicate,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f123,plain,
! [X,R,A,Y] :
( ( ~ apply(R,Y,X)
| ~ member(Y,A)
| member(Y,initial_segment(X,R,A)) )
& ( ( apply(R,Y,X)
& member(Y,A) )
| ~ member(Y,initial_segment(X,R,A)) ) ),
inference(NNF_transformation,[status(thm)],[f18]) ).
fof(f124,plain,
( ! [X,R,A,Y] :
( ~ apply(R,Y,X)
| ~ member(Y,A)
| member(Y,initial_segment(X,R,A)) )
& ! [X,R,A,Y] :
( ( apply(R,Y,X)
& member(Y,A) )
| ~ member(Y,initial_segment(X,R,A)) ) ),
inference(miniscoping,[status(thm)],[f123]) ).
fof(f125,plain,
! [X0,X1,X2,X3] :
( member(X0,X3)
| ~ member(X0,initial_segment(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f126,plain,
! [X0,X1,X2,X3] :
( apply(X2,X0,X1)
| ~ member(X0,initial_segment(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f127,plain,
! [X0,X1,X2,X3] :
( ~ apply(X2,X0,X1)
| ~ member(X0,X3)
| member(X0,initial_segment(X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f132,plain,
? [A] :
( ? [X] :
( ~ equal_set(X,initial_segment(X,member_predicate,A))
& member(X,A) )
& member(A,on) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f133,plain,
( ~ equal_set(sK14_skl,initial_segment(sK14_skl,member_predicate,sK13_skl))
& member(sK14_skl,sK13_skl)
& member(sK13_skl,on) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(A,sK13_skl),skolemize(X,sK14_skl)],[f132]) ).
fof(f134,plain,
member(sK13_skl,on),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f135,plain,
member(sK14_skl,sK13_skl),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f136,plain,
~ equal_set(sK14_skl,initial_segment(sK14_skl,member_predicate,sK13_skl)),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f148,plain,
! [X0] :
( subset(X0,sK13_skl)
| ~ member(X0,sK13_skl) ),
inference(resolution,[status(thm)],[f82,f134]) ).
fof(f151,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| equal_set(X0,X1)
| member(sK0_skl(X0,X1),X1) ),
inference(resolution,[status(thm)],[f27,f33]) ).
fof(f152,plain,
subset(sK14_skl,sK13_skl),
inference(resolution,[status(thm)],[f148,f135]) ).
fof(f153,plain,
! [X0] :
( member(X0,sK13_skl)
| ~ member(X0,sK14_skl) ),
inference(resolution,[status(thm)],[f152,f26]) ).
fof(f154,plain,
( ~ subset(sK13_skl,sK14_skl)
| equal_set(sK13_skl,sK14_skl) ),
inference(resolution,[status(thm)],[f152,f33]) ).
fof(f155,definition,
( sQ0_spl
<=> equal_set(sK13_skl,sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( ~ sQ0_spl
| equal_set(sK13_skl,sK14_skl) ),
inference(component_clause,[status(thm)],[f155]) ).
fof(f158,definition,
( sQ1_spl
<=> subset(sK13_skl,sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f160,plain,
( sQ1_spl
| ~ subset(sK13_skl,sK14_skl) ),
inference(component_clause,[status(thm)],[f158]) ).
fof(f161,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f154,f155,f158]) ).
fof(f163,plain,
( ~ sQ0_spl
| subset(sK13_skl,sK14_skl) ),
inference(resolution,[status(thm)],[f156,f31]) ).
fof(f164,plain,
! [X0] :
( ~ sQ0_spl
| member(X0,sK14_skl)
| ~ member(X0,sK13_skl) ),
inference(resolution,[status(thm)],[f163,f26]) ).
fof(f165,plain,
( ~ sQ0_spl
| ~ subset(sK14_skl,sK13_skl)
| equal_set(sK14_skl,sK13_skl) ),
inference(resolution,[status(thm)],[f163,f33]) ).
fof(f166,definition,
( sQ2_spl
<=> equal_set(sK14_skl,sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f167,plain,
( ~ sQ2_spl
| equal_set(sK14_skl,sK13_skl) ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f168,plain,
( sQ2_spl
| ~ equal_set(sK14_skl,sK13_skl) ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f169,definition,
( sQ3_spl
<=> subset(sK14_skl,sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f171,plain,
( sQ3_spl
| ~ subset(sK14_skl,sK13_skl) ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f172,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f165,f166,f169,f155]) ).
fof(f173,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f171,f152]) ).
fof(f174,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f173]) ).
fof(f175,plain,
( sQ1_spl
| member(sK0_skl(sK14_skl,sK13_skl),sK13_skl) ),
inference(resolution,[status(thm)],[f160,f27]) ).
fof(f176,plain,
( ~ sQ2_spl
| subset(sK13_skl,sK14_skl) ),
inference(resolution,[status(thm)],[f167,f32]) ).
fof(f178,plain,
( ~ sQ2_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f176,f160]) ).
fof(f179,plain,
( ~ sQ2_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f178]) ).
fof(f185,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,initial_segment(X1,member_predicate,X2)) ),
inference(resolution,[status(thm)],[f127,f106]) ).
fof(f186,plain,
( ~ subset(sK14_skl,initial_segment(sK14_skl,member_predicate,sK13_skl))
| member(sK0_skl(sK14_skl,initial_segment(sK14_skl,member_predicate,sK13_skl)),initial_segment(sK14_skl,member_predicate,sK13_skl)) ),
inference(resolution,[status(thm)],[f151,f136]) ).
fof(f189,definition,
( sQ4_spl
<=> member(sK0_skl(sK14_skl,initial_segment(sK14_skl,member_predicate,sK13_skl)),initial_segment(sK14_skl,member_predicate,sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f190,plain,
( ~ sQ4_spl
| member(sK0_skl(sK14_skl,initial_segment(sK14_skl,member_predicate,sK13_skl)),initial_segment(sK14_skl,member_predicate,sK13_skl)) ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,definition,
( sQ5_spl
<=> subset(sK14_skl,initial_segment(sK14_skl,member_predicate,sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f193,plain,
( ~ sQ5_spl
| subset(sK14_skl,initial_segment(sK14_skl,member_predicate,sK13_skl)) ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f194,plain,
( sQ5_spl
| ~ subset(sK14_skl,initial_segment(sK14_skl,member_predicate,sK13_skl)) ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f195,plain,
( ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f186,f189,f192]) ).
fof(f203,plain,
( ~ sQ4_spl
| apply(member_predicate,sK0_skl(sK14_skl,initial_segment(sK14_skl,member_predicate,sK13_skl)),sK14_skl) ),
inference(resolution,[status(thm)],[f190,f126]) ).
fof(f204,plain,
( ~ sQ4_spl
| member(sK0_skl(sK14_skl,initial_segment(sK14_skl,member_predicate,sK13_skl)),sK13_skl) ),
inference(resolution,[status(thm)],[f190,f125]) ).
fof(f205,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| member(sK0_skl(sK14_skl,initial_segment(sK14_skl,member_predicate,sK13_skl)),sK14_skl) ),
inference(resolution,[status(thm)],[f204,f164]) ).
fof(f207,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| subset(initial_segment(sK14_skl,member_predicate,sK13_skl),sK14_skl) ),
inference(resolution,[status(thm)],[f205,f28]) ).
fof(f209,plain,
( ~ sQ4_spl
| member(sK0_skl(sK14_skl,initial_segment(sK14_skl,member_predicate,sK13_skl)),sK14_skl) ),
inference(resolution,[status(thm)],[f203,f105]) ).
fof(f212,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| ~ subset(sK14_skl,initial_segment(sK14_skl,member_predicate,sK13_skl))
| equal_set(sK14_skl,initial_segment(sK14_skl,member_predicate,sK13_skl)) ),
inference(resolution,[status(thm)],[f207,f33]) ).
fof(f213,definition,
( sQ6_spl
<=> equal_set(sK14_skl,initial_segment(sK14_skl,member_predicate,sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f214,plain,
( ~ sQ6_spl
| equal_set(sK14_skl,initial_segment(sK14_skl,member_predicate,sK13_skl)) ),
inference(component_clause,[status(thm)],[f213]) ).
fof(f216,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f212,f213,f192,f189,f155]) ).
fof(f229,plain,
! [X0,X1,X2] :
( subset(X2,initial_segment(X0,member_predicate,X1))
| ~ member(sK0_skl(initial_segment(X0,member_predicate,X1),X2),X0)
| ~ member(sK0_skl(initial_segment(X0,member_predicate,X1),X2),X1) ),
inference(resolution,[status(thm)],[f185,f28]) ).
fof(f232,plain,
( sQ5_spl
| member(sK0_skl(initial_segment(sK14_skl,member_predicate,sK13_skl),sK14_skl),sK14_skl) ),
inference(resolution,[status(thm)],[f194,f27]) ).
fof(f242,plain,
( sQ5_spl
| member(sK0_skl(initial_segment(sK14_skl,member_predicate,sK13_skl),sK14_skl),sK13_skl) ),
inference(resolution,[status(thm)],[f232,f153]) ).
fof(f267,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f214,f136]) ).
fof(f268,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f267]) ).
fof(f276,plain,
( sQ5_spl
| ~ member(sK0_skl(initial_segment(sK14_skl,member_predicate,sK13_skl),sK14_skl),sK14_skl)
| ~ member(sK0_skl(initial_segment(sK14_skl,member_predicate,sK13_skl),sK14_skl),sK13_skl) ),
inference(resolution,[status(thm)],[f229,f194]) ).
fof(f279,definition,
( sQ12_spl
<=> member(sK0_skl(initial_segment(sK14_skl,member_predicate,sK13_skl),sK14_skl),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f281,plain,
( sQ12_spl
| ~ member(sK0_skl(initial_segment(sK14_skl,member_predicate,sK13_skl),sK14_skl),sK13_skl) ),
inference(component_clause,[status(thm)],[f279]) ).
fof(f282,definition,
( sQ13_spl
<=> member(sK0_skl(initial_segment(sK14_skl,member_predicate,sK13_skl),sK14_skl),sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f284,plain,
( sQ13_spl
| ~ member(sK0_skl(initial_segment(sK14_skl,member_predicate,sK13_skl),sK14_skl),sK14_skl) ),
inference(component_clause,[status(thm)],[f282]) ).
fof(f285,plain,
( sQ5_spl
| ~ sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f276,f279,f282,f192]) ).
fof(f301,plain,
( sQ12_spl
| sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f281,f242]) ).
fof(f302,plain,
( sQ12_spl
| sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f301]) ).
fof(f303,plain,
( sQ13_spl
| sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f284,f232]) ).
fof(f304,plain,
( sQ13_spl
| sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f303]) ).
fof(f306,plain,
( sQ2_spl
| ~ subset(sK14_skl,sK13_skl)
| member(sK0_skl(sK14_skl,sK13_skl),sK13_skl) ),
inference(resolution,[status(thm)],[f168,f151]) ).
fof(f307,definition,
( sQ14_spl
<=> member(sK0_skl(sK14_skl,sK13_skl),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f310,plain,
( sQ2_spl
| ~ sQ3_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f306,f307,f169,f166]) ).
fof(f314,plain,
( sQ1_spl
| subset(sK0_skl(sK14_skl,sK13_skl),sK13_skl) ),
inference(resolution,[status(thm)],[f175,f148]) ).
fof(f317,plain,
( ~ sQ5_spl
| ~ subset(initial_segment(sK14_skl,member_predicate,sK13_skl),sK14_skl)
| equal_set(initial_segment(sK14_skl,member_predicate,sK13_skl),sK14_skl) ),
inference(resolution,[status(thm)],[f193,f33]) ).
fof(f318,definition,
( sQ15_spl
<=> equal_set(initial_segment(sK14_skl,member_predicate,sK13_skl),sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f319,plain,
( ~ sQ15_spl
| equal_set(initial_segment(sK14_skl,member_predicate,sK13_skl),sK14_skl) ),
inference(component_clause,[status(thm)],[f318]) ).
fof(f321,definition,
( sQ16_spl
<=> subset(initial_segment(sK14_skl,member_predicate,sK13_skl),sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f324,plain,
( ~ sQ5_spl
| ~ sQ16_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f317,f318,f321,f192]) ).
fof(f328,plain,
( sQ1_spl
| ~ subset(sK13_skl,sK0_skl(sK14_skl,sK13_skl))
| equal_set(sK13_skl,sK0_skl(sK14_skl,sK13_skl)) ),
inference(resolution,[status(thm)],[f314,f33]) ).
fof(f329,definition,
( sQ17_spl
<=> equal_set(sK13_skl,sK0_skl(sK14_skl,sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f330,plain,
( ~ sQ17_spl
| equal_set(sK13_skl,sK0_skl(sK14_skl,sK13_skl)) ),
inference(component_clause,[status(thm)],[f329]) ).
fof(f332,definition,
( sQ18_spl
<=> subset(sK13_skl,sK0_skl(sK14_skl,sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f334,plain,
( sQ18_spl
| ~ subset(sK13_skl,sK0_skl(sK14_skl,sK13_skl)) ),
inference(component_clause,[status(thm)],[f332]) ).
fof(f335,plain,
( sQ1_spl
| ~ sQ18_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f328,f329,f332,f158]) ).
fof(f346,plain,
( ~ sQ17_spl
| subset(sK13_skl,sK0_skl(sK14_skl,sK13_skl)) ),
inference(resolution,[status(thm)],[f330,f31]) ).
fof(f353,plain,
( ~ sQ17_spl
| sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f346,f334]) ).
fof(f354,plain,
( ~ sQ17_spl
| sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f353]) ).
fof(f369,plain,
( ~ sQ17_spl
| ~ subset(sK0_skl(sK14_skl,sK13_skl),sK13_skl)
| equal_set(sK0_skl(sK14_skl,sK13_skl),sK13_skl) ),
inference(resolution,[status(thm)],[f346,f33]) ).
fof(f370,definition,
( sQ23_spl
<=> equal_set(sK0_skl(sK14_skl,sK13_skl),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f373,definition,
( sQ24_spl
<=> subset(sK0_skl(sK14_skl,sK13_skl),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f375,plain,
( sQ24_spl
| ~ subset(sK0_skl(sK14_skl,sK13_skl),sK13_skl) ),
inference(component_clause,[status(thm)],[f373]) ).
fof(f376,plain,
( ~ sQ17_spl
| ~ sQ24_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f369,f370,f373,f329]) ).
fof(f377,plain,
( sQ24_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f375,f314]) ).
fof(f378,plain,
( sQ24_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f377]) ).
fof(f425,plain,
( ~ sQ15_spl
| subset(initial_segment(sK14_skl,member_predicate,sK13_skl),sK14_skl) ),
inference(resolution,[status(thm)],[f319,f31]) ).
fof(f431,plain,
( ~ sQ15_spl
| ~ subset(sK14_skl,initial_segment(sK14_skl,member_predicate,sK13_skl))
| equal_set(sK14_skl,initial_segment(sK14_skl,member_predicate,sK13_skl)) ),
inference(resolution,[status(thm)],[f425,f33]) ).
fof(f432,plain,
( ~ sQ15_spl
| ~ sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f431,f213,f192,f318]) ).
fof(f822,plain,
( ~ sQ4_spl
| subset(initial_segment(sK14_skl,member_predicate,sK13_skl),sK14_skl) ),
inference(resolution,[status(thm)],[f209,f28]) ).
fof(f826,plain,
( ~ sQ4_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f822,f321,f189]) ).
fof(f827,plain,
$false,
inference(sat_refutation,[status(thm)],[f161,f172,f174,f179,f195,f216,f268,f285,f302,f304,f310,f324,f335,f354,f376,f378,f432,f826]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET811+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.44 % Computer : n003.cluster.edu
% 0.15/0.44 % Model : x86_64 x86_64
% 0.15/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.44 % Memory : 8046.5625MB
% 0.15/0.44 % OS : Linux 6.8.0-71-generic
% 0.15/0.44 % CPULimit : 300
% 0.15/0.44 % WCLimit : 300
% 0.15/0.44 % DateTime : Mon Sep 21 05:40:46 UTC 2026
% 0.15/0.45 % CPUTime :
% 0.15/0.46 % Drodi V4.1.1
% 0.15/0.52 % Refutation found
% 0.15/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.56 % Elapsed time: 0.108128 seconds
% 0.24/0.56 % CPU time: 0.385986 seconds
% 0.24/0.56 % Total memory used: 63.396 MB
% 0.24/0.56 % Net memory used: 63.045 MB
%------------------------------------------------------------------------------