%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET173+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 02:09:33 PM UTC 2026
% Result : Theorem 0.15s 10.48s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 59 ( 6 unt; 6 def)
% Number of atoms : 161 ( 11 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 170 ( 68 ~; 70 |; 20 &)
% ( 11 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 82 ( 78 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [B,C] : intersection(B,union(B,C)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [B,C] : intersection(B,union(B,C)) = B,
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [B,C,D] :
( ( ( ~ member(D,C)
& ~ member(D,B) )
| member(D,union(B,C)) )
& ( member(D,C)
| member(D,B)
| ~ member(D,union(B,C)) ) ),
inference(NNF_transformation,[status(thm)],[f1]) ).
fof(f12,plain,
( ! [B,C,D] :
( ( ~ member(D,C)
& ~ member(D,B) )
| member(D,union(B,C)) )
& ! [B,C,D] :
( member(D,C)
| member(D,B)
| ~ member(D,union(B,C)) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f16,plain,
! [B,C,D] :
( ( ~ member(D,C)
| ~ member(D,B)
| member(D,intersection(B,C)) )
& ( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f17,plain,
( ! [B,C,D] :
( ~ member(D,C)
| ~ member(D,B)
| member(D,intersection(B,C)) )
& ! [B,C,D] :
( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f21,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f22,plain,
( ! [B,C] :
( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ! [B,C] :
( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f25,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f28,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,C)
| ~ member(D,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f29,plain,
! [B,C] :
( ( ? [D] :
( ~ member(D,C)
& member(D,B) )
| subset(B,C) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(NNF_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
( ! [B,C] :
( ? [D] :
( ~ member(D,C)
& member(D,B) )
| subset(B,C) )
& ! [B,C] :
( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f31,plain,
( ! [B,C] :
( ( ~ member(sK0_skl(C,B),C)
& member(sK0_skl(C,B),B) )
| subset(B,C) )
& ! [B,C] :
( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f30]) ).
fof(f33,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f34,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f43,plain,
? [B,C] : intersection(B,union(B,C)) != B,
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f44,plain,
intersection(sK2_skl,union(sK2_skl,sK3_skl)) != sK2_skl,
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(B,sK2_skl),skolemize(C,sK3_skl)],[f43]) ).
fof(f45,plain,
intersection(sK2_skl,union(sK2_skl,sK3_skl)) != sK2_skl,
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f60,plain,
( ~ subset(sK2_skl,intersection(sK2_skl,union(sK2_skl,sK3_skl)))
| ~ subset(intersection(sK2_skl,union(sK2_skl,sK3_skl)),sK2_skl) ),
inference(resolution,[status(thm)],[f25,f45]) ).
fof(f62,definition,
( sQ0_spl
<=> subset(intersection(sK2_skl,union(sK2_skl,sK3_skl)),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( sQ0_spl
| ~ subset(intersection(sK2_skl,union(sK2_skl,sK3_skl)),sK2_skl) ),
inference(component_clause,[status(thm)],[f62]) ).
fof(f65,definition,
( sQ1_spl
<=> subset(sK2_skl,intersection(sK2_skl,union(sK2_skl,sK3_skl))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f67,plain,
( sQ1_spl
| ~ subset(sK2_skl,intersection(sK2_skl,union(sK2_skl,sK3_skl))) ),
inference(component_clause,[status(thm)],[f65]) ).
fof(f68,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f60,f62,f65]) ).
fof(f72,plain,
( sQ0_spl
| ~ member(sK0_skl(sK2_skl,intersection(sK2_skl,union(sK2_skl,sK3_skl))),sK2_skl) ),
inference(resolution,[status(thm)],[f64,f34]) ).
fof(f75,plain,
! [X0] :
( sQ0_spl
| ~ member(sK0_skl(sK2_skl,intersection(sK2_skl,union(sK2_skl,sK3_skl))),intersection(X0,sK2_skl)) ),
inference(resolution,[status(thm)],[f72,f19]) ).
fof(f89,plain,
! [X0] :
( sQ0_spl
| ~ member(sK0_skl(sK2_skl,intersection(sK2_skl,union(sK2_skl,sK3_skl))),sK2_skl)
| ~ member(sK0_skl(sK2_skl,intersection(sK2_skl,union(sK2_skl,sK3_skl))),X0) ),
inference(resolution,[status(thm)],[f75,f20]) ).
fof(f96,definition,
! [X0] :
( sQ2_spl
<=> ~ member(sK0_skl(sK2_skl,intersection(sK2_skl,union(sK2_skl,sK3_skl))),X0) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f97,plain,
! [X0] :
( ~ sQ2_spl
| ~ member(sK0_skl(sK2_skl,intersection(sK2_skl,union(sK2_skl,sK3_skl))),X0) ),
inference(component_clause,[status(thm)],[f96]) ).
fof(f99,definition,
( sQ3_spl
<=> member(sK0_skl(sK2_skl,intersection(sK2_skl,union(sK2_skl,sK3_skl))),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f101,plain,
( sQ3_spl
| ~ member(sK0_skl(sK2_skl,intersection(sK2_skl,union(sK2_skl,sK3_skl))),sK2_skl) ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,plain,
( sQ0_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f89,f96,f99,f62]) ).
fof(f103,plain,
( sQ1_spl
| ~ member(sK0_skl(intersection(sK2_skl,union(sK2_skl,sK3_skl)),sK2_skl),intersection(sK2_skl,union(sK2_skl,sK3_skl))) ),
inference(resolution,[status(thm)],[f67,f34]) ).
fof(f107,plain,
! [X0] :
( sQ3_spl
| ~ member(sK0_skl(sK2_skl,intersection(sK2_skl,union(sK2_skl,sK3_skl))),intersection(sK2_skl,X0)) ),
inference(resolution,[status(thm)],[f101,f18]) ).
fof(f116,plain,
( sQ3_spl
| subset(intersection(sK2_skl,union(sK2_skl,sK3_skl)),sK2_skl) ),
inference(resolution,[status(thm)],[f107,f33]) ).
fof(f147,plain,
( ~ sQ2_spl
| subset(intersection(sK2_skl,union(sK2_skl,sK3_skl)),sK2_skl) ),
inference(resolution,[status(thm)],[f97,f33]) ).
fof(f156,plain,
( sQ1_spl
| ~ member(sK0_skl(intersection(sK2_skl,union(sK2_skl,sK3_skl)),sK2_skl),union(sK2_skl,sK3_skl))
| ~ member(sK0_skl(intersection(sK2_skl,union(sK2_skl,sK3_skl)),sK2_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f103,f20]) ).
fof(f161,definition,
( sQ5_spl
<=> member(sK0_skl(intersection(sK2_skl,union(sK2_skl,sK3_skl)),sK2_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f163,plain,
( sQ5_spl
| ~ member(sK0_skl(intersection(sK2_skl,union(sK2_skl,sK3_skl)),sK2_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f164,definition,
( sQ6_spl
<=> member(sK0_skl(intersection(sK2_skl,union(sK2_skl,sK3_skl)),sK2_skl),union(sK2_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( sQ6_spl
| ~ member(sK0_skl(intersection(sK2_skl,union(sK2_skl,sK3_skl)),sK2_skl),union(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f164]) ).
fof(f167,plain,
( sQ1_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f156,f161,f164,f65]) ).
fof(f168,plain,
( sQ0_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f64,f147]) ).
fof(f169,plain,
( sQ0_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f168]) ).
fof(f177,plain,
( sQ5_spl
| subset(sK2_skl,intersection(sK2_skl,union(sK2_skl,sK3_skl))) ),
inference(resolution,[status(thm)],[f163,f33]) ).
fof(f182,plain,
( sQ5_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f177,f67]) ).
fof(f183,plain,
( sQ5_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f182]) ).
fof(f184,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f116,f62,f99]) ).
fof(f210,plain,
( sQ6_spl
| ~ member(sK0_skl(intersection(sK2_skl,union(sK2_skl,sK3_skl)),sK2_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f166,f14]) ).
fof(f215,plain,
( sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f210,f161,f164]) ).
fof(f216,plain,
$false,
inference(sat_refutation,[status(thm)],[f68,f102,f167,f169,f183,f184,f215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET173+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/10.44 % Computer : n013.cluster.edu
% 0.15/10.44 % Model : x86_64 x86_64
% 0.15/10.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/10.44 % Memory : 8046.5625MB
% 0.15/10.44 % OS : Linux 6.8.0-71-generic
% 0.15/10.44 % CPULimit : 300
% 0.15/10.44 % WCLimit : 300
% 0.15/10.44 % DateTime : Mon Sep 21 04:58:31 UTC 2026
% 0.15/10.44 % CPUTime :
% 0.15/10.46 % Drodi V4.1.1
% 0.15/10.48 % Refutation found
% 0.15/10.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/10.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/10.50 % Elapsed time: 0.053873 seconds
% 0.21/10.50 % CPU time: 0.196494 seconds
% 0.21/10.50 % Total memory used: 102.682 MB
% 0.21/10.50 % Net memory used: 102.203 MB
%------------------------------------------------------------------------------