%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET603+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 02:10:12 PM UTC 2026
% Result : Theorem 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 63 ( 10 unt; 7 def)
% Number of atoms : 164 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 168 ( 67 ~; 73 |; 16 &)
% ( 11 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 65 ( 62 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : ~ member(X,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [B,A,E] :
( member(B,difference(E,A))
<=> ( ~ member(B,A)
& member(B,E) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [E] : equal_set(difference(E,empty_set),E),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [E] : equal_set(difference(E,empty_set),E),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,B)
| ~ member(X,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f15,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)],[f14]) ).
fof(f16,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)],[f15]) ).
fof(f17,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))],[f16]) ).
fof(f19,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f21,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(f22,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)],[f21]) ).
fof(f24,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f40,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
! [B,A,E] :
( ( member(B,A)
| ~ member(B,E)
| member(B,difference(E,A)) )
& ( ( ~ member(B,A)
& member(B,E) )
| ~ member(B,difference(E,A)) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( ! [B,A,E] :
( member(B,A)
| ~ member(B,E)
| member(B,difference(E,A)) )
& ! [B,A,E] :
( ( ~ member(B,A)
& member(B,E) )
| ~ member(B,difference(E,A)) ) ),
inference(miniscoping,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f45,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,X1)
| member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f68,plain,
? [E] : ~ equal_set(difference(E,empty_set),E),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f69,plain,
~ equal_set(difference(sK3_skl,empty_set),sK3_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(E,sK3_skl)],[f68]) ).
fof(f70,plain,
~ equal_set(difference(sK3_skl,empty_set),sK3_skl),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f78,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| equal_set(X0,X1)
| member(sK0_skl(X0,X1),X1) ),
inference(resolution,[status(thm)],[f19,f25]) ).
fof(f89,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| equal_set(X0,X1)
| member(sK0_skl(X0,X1),X1) ),
inference(resolution,[status(thm)],[f78,f19]) ).
fof(f90,plain,
( member(sK0_skl(sK3_skl,difference(sK3_skl,empty_set)),difference(sK3_skl,empty_set))
| member(sK0_skl(difference(sK3_skl,empty_set),sK3_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f89,f70]) ).
fof(f93,definition,
( sQ0_spl
<=> member(sK0_skl(difference(sK3_skl,empty_set),sK3_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ0_spl
| member(sK0_skl(difference(sK3_skl,empty_set),sK3_skl),sK3_skl) ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,definition,
( sQ1_spl
<=> member(sK0_skl(sK3_skl,difference(sK3_skl,empty_set)),difference(sK3_skl,empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f97,plain,
( ~ sQ1_spl
| member(sK0_skl(sK3_skl,difference(sK3_skl,empty_set)),difference(sK3_skl,empty_set)) ),
inference(component_clause,[status(thm)],[f96]) ).
fof(f99,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f90,f93,f96]) ).
fof(f109,plain,
! [X0] :
( ~ sQ0_spl
| member(sK0_skl(difference(sK3_skl,empty_set),sK3_skl),X0)
| member(sK0_skl(difference(sK3_skl,empty_set),sK3_skl),difference(sK3_skl,X0)) ),
inference(resolution,[status(thm)],[f94,f45]) ).
fof(f127,plain,
( ~ sQ0_spl
| subset(sK3_skl,difference(sK3_skl,empty_set))
| member(sK0_skl(difference(sK3_skl,empty_set),sK3_skl),empty_set) ),
inference(resolution,[status(thm)],[f109,f20]) ).
fof(f131,definition,
( sQ2_spl
<=> member(sK0_skl(difference(sK3_skl,empty_set),sK3_skl),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f132,plain,
( ~ sQ2_spl
| member(sK0_skl(difference(sK3_skl,empty_set),sK3_skl),empty_set) ),
inference(component_clause,[status(thm)],[f131]) ).
fof(f134,definition,
( sQ3_spl
<=> subset(sK3_skl,difference(sK3_skl,empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f135,plain,
( ~ sQ3_spl
| subset(sK3_skl,difference(sK3_skl,empty_set)) ),
inference(component_clause,[status(thm)],[f134]) ).
fof(f137,plain,
( ~ sQ0_spl
| sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f127,f131,f134,f93]) ).
fof(f143,plain,
( ~ sQ1_spl
| member(sK0_skl(sK3_skl,difference(sK3_skl,empty_set)),sK3_skl) ),
inference(resolution,[status(thm)],[f97,f43]) ).
fof(f145,plain,
( ~ sQ1_spl
| subset(difference(sK3_skl,empty_set),sK3_skl) ),
inference(resolution,[status(thm)],[f143,f20]) ).
fof(f147,plain,
( ~ sQ3_spl
| equal_set(sK3_skl,difference(sK3_skl,empty_set))
| member(sK0_skl(sK3_skl,difference(sK3_skl,empty_set)),difference(sK3_skl,empty_set)) ),
inference(resolution,[status(thm)],[f135,f78]) ).
fof(f150,plain,
( ~ sQ3_spl
| ~ subset(difference(sK3_skl,empty_set),sK3_skl)
| equal_set(difference(sK3_skl,empty_set),sK3_skl) ),
inference(resolution,[status(thm)],[f135,f25]) ).
fof(f151,definition,
( sQ5_spl
<=> equal_set(sK3_skl,difference(sK3_skl,empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f152,plain,
( ~ sQ5_spl
| equal_set(sK3_skl,difference(sK3_skl,empty_set)) ),
inference(component_clause,[status(thm)],[f151]) ).
fof(f154,plain,
( ~ sQ3_spl
| sQ5_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f147,f96,f151,f134]) ).
fof(f155,definition,
( sQ6_spl
<=> equal_set(difference(sK3_skl,empty_set),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( ~ sQ6_spl
| equal_set(difference(sK3_skl,empty_set),sK3_skl) ),
inference(component_clause,[status(thm)],[f155]) ).
fof(f158,definition,
( sQ7_spl
<=> subset(difference(sK3_skl,empty_set),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f160,plain,
( sQ7_spl
| ~ subset(difference(sK3_skl,empty_set),sK3_skl) ),
inference(component_clause,[status(thm)],[f158]) ).
fof(f161,plain,
( ~ sQ3_spl
| ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f150,f155,f158,f134]) ).
fof(f162,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f156,f70]) ).
fof(f163,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f162]) ).
fof(f164,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f132,f40]) ).
fof(f165,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f164]) ).
fof(f166,plain,
( ~ sQ1_spl
| equal_set(difference(sK3_skl,empty_set),sK3_skl)
| member(sK0_skl(difference(sK3_skl,empty_set),sK3_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f145,f78]) ).
fof(f169,plain,
( ~ sQ1_spl
| ~ subset(sK3_skl,difference(sK3_skl,empty_set))
| equal_set(sK3_skl,difference(sK3_skl,empty_set)) ),
inference(resolution,[status(thm)],[f145,f25]) ).
fof(f170,plain,
( ~ sQ1_spl
| sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f166,f93,f155,f96]) ).
fof(f171,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f169,f151,f134,f96]) ).
fof(f195,plain,
( ~ sQ5_spl
| subset(difference(sK3_skl,empty_set),sK3_skl) ),
inference(resolution,[status(thm)],[f152,f24]) ).
fof(f197,plain,
( ~ sQ5_spl
| sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f195,f160]) ).
fof(f198,plain,
( ~ sQ5_spl
| sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f197]) ).
fof(f199,plain,
$false,
inference(sat_refutation,[status(thm)],[f99,f137,f154,f161,f163,f165,f170,f171,f198]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET603+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:28:34 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.41 % Refutation found
% 0.10/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.44 % Elapsed time: 0.062903 seconds
% 0.10/0.44 % CPU time: 0.184328 seconds
% 0.10/0.44 % Total memory used: 81.785 MB
% 0.10/0.44 % Net memory used: 81.332 MB
%------------------------------------------------------------------------------