%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET593+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 : n010.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 02:10:10 PM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 63 ( 3 unt; 7 def)
% Number of atoms : 168 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 163 ( 58 ~; 72 |; 19 &)
% ( 11 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 8 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 78 ( 73 !; 5 ?)
% 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,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [B,C,D] :
( subset(B,union(C,D))
=> ( subset(difference(B,D),C)
& subset(difference(B,C),D) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [B,C,D] :
( subset(B,union(C,D))
=> ( subset(difference(B,D),C)
& subset(difference(B,C),D) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,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(f10,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)],[f9]) ).
fof(f11,plain,
! [X0,X1,X2] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f14,plain,
! [B,C,D] :
( ( member(D,C)
| ~ member(D,B)
| member(D,difference(B,C)) )
& ( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f15,plain,
( ! [B,C,D] :
( member(D,C)
| ~ member(D,B)
| member(D,difference(B,C)) )
& ! [B,C,D] :
( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f19,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,C)
| ~ member(D,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f20,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)],[f19]) ).
fof(f21,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)],[f20]) ).
fof(f22,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))],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f35,plain,
? [B,C,D] :
( ( ~ subset(difference(B,D),C)
| ~ subset(difference(B,C),D) )
& subset(B,union(C,D)) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f36,plain,
( ( ~ subset(difference(sK2_skl,sK4_skl),sK3_skl)
| ~ subset(difference(sK2_skl,sK3_skl),sK4_skl) )
& subset(sK2_skl,union(sK3_skl,sK4_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(B,sK2_skl),skolemize(C,sK3_skl),skolemize(D,sK4_skl)],[f35]) ).
fof(f37,plain,
subset(sK2_skl,union(sK3_skl,sK4_skl)),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
( ~ subset(difference(sK2_skl,sK4_skl),sK3_skl)
| ~ subset(difference(sK2_skl,sK3_skl),sK4_skl) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f39,definition,
( sQ0_spl
<=> subset(difference(sK2_skl,sK3_skl),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f41,plain,
( sQ0_spl
| ~ subset(difference(sK2_skl,sK3_skl),sK4_skl) ),
inference(component_clause,[status(thm)],[f39]) ).
fof(f42,definition,
( sQ1_spl
<=> subset(difference(sK2_skl,sK4_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f44,plain,
( sQ1_spl
| ~ subset(difference(sK2_skl,sK4_skl),sK3_skl) ),
inference(component_clause,[status(thm)],[f42]) ).
fof(f45,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f38,f39,f42]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ~ member(sK0_skl(X2,difference(X0,X1)),X1)
| subset(difference(X0,X1),X2) ),
inference(resolution,[status(thm)],[f24,f17]) ).
fof(f59,plain,
! [X0,X1,X2] :
( member(sK0_skl(X2,difference(X0,X1)),X0)
| subset(difference(X0,X1),X2) ),
inference(resolution,[status(thm)],[f24,f16]) ).
fof(f65,plain,
! [X0] :
( member(X0,union(sK3_skl,sK4_skl))
| ~ member(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f23,f37]) ).
fof(f67,plain,
! [X0] :
( subset(sK2_skl,X0)
| member(sK0_skl(X0,sK2_skl),union(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f65,f24]) ).
fof(f79,plain,
( subset(sK2_skl,union(sK3_skl,sK4_skl))
| subset(sK2_skl,union(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f67,f25]) ).
fof(f81,definition,
( sQ2_spl
<=> subset(sK2_skl,union(sK3_skl,sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f84,plain,
sQ2_spl,
inference(split_clause,[status(thm)],[f79,f81]) ).
fof(f99,plain,
( sQ0_spl
| ~ member(sK0_skl(sK4_skl,difference(sK2_skl,sK3_skl)),sK3_skl) ),
inference(resolution,[status(thm)],[f58,f41]) ).
fof(f101,plain,
( sQ0_spl
| member(sK0_skl(sK4_skl,difference(sK2_skl,sK3_skl)),sK2_skl) ),
inference(resolution,[status(thm)],[f59,f41]) ).
fof(f107,plain,
( sQ0_spl
| member(sK0_skl(sK4_skl,difference(sK2_skl,sK3_skl)),union(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f101,f65]) ).
fof(f110,plain,
( sQ1_spl
| member(sK0_skl(sK3_skl,difference(sK2_skl,sK4_skl)),sK2_skl) ),
inference(resolution,[status(thm)],[f44,f59]) ).
fof(f111,plain,
( sQ1_spl
| ~ member(sK0_skl(sK3_skl,difference(sK2_skl,sK4_skl)),sK4_skl) ),
inference(resolution,[status(thm)],[f44,f58]) ).
fof(f113,plain,
( sQ1_spl
| member(sK0_skl(sK3_skl,difference(sK2_skl,sK4_skl)),union(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f110,f65]) ).
fof(f151,plain,
( sQ1_spl
| member(sK0_skl(sK3_skl,difference(sK2_skl,sK4_skl)),sK4_skl)
| member(sK0_skl(sK3_skl,difference(sK2_skl,sK4_skl)),sK3_skl) ),
inference(resolution,[status(thm)],[f113,f11]) ).
fof(f152,definition,
( sQ5_spl
<=> member(sK0_skl(sK3_skl,difference(sK2_skl,sK4_skl)),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f153,plain,
( ~ sQ5_spl
| member(sK0_skl(sK3_skl,difference(sK2_skl,sK4_skl)),sK3_skl) ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f155,definition,
( sQ6_spl
<=> member(sK0_skl(sK3_skl,difference(sK2_skl,sK4_skl)),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( ~ sQ6_spl
| member(sK0_skl(sK3_skl,difference(sK2_skl,sK4_skl)),sK4_skl) ),
inference(component_clause,[status(thm)],[f155]) ).
fof(f158,plain,
( sQ1_spl
| sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f151,f152,f155,f42]) ).
fof(f189,plain,
( sQ0_spl
| member(sK0_skl(sK4_skl,difference(sK2_skl,sK3_skl)),sK4_skl)
| member(sK0_skl(sK4_skl,difference(sK2_skl,sK3_skl)),sK3_skl) ),
inference(resolution,[status(thm)],[f107,f11]) ).
fof(f190,definition,
( sQ7_spl
<=> member(sK0_skl(sK4_skl,difference(sK2_skl,sK3_skl)),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f191,plain,
( ~ sQ7_spl
| member(sK0_skl(sK4_skl,difference(sK2_skl,sK3_skl)),sK3_skl) ),
inference(component_clause,[status(thm)],[f190]) ).
fof(f193,definition,
( sQ8_spl
<=> member(sK0_skl(sK4_skl,difference(sK2_skl,sK3_skl)),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f194,plain,
( ~ sQ8_spl
| member(sK0_skl(sK4_skl,difference(sK2_skl,sK3_skl)),sK4_skl) ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,plain,
( sQ0_spl
| sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f189,f190,f193,f39]) ).
fof(f197,plain,
( ~ sQ7_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f191,f99]) ).
fof(f198,plain,
( ~ sQ7_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f197]) ).
fof(f230,plain,
( ~ sQ5_spl
| subset(difference(sK2_skl,sK4_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f153,f25]) ).
fof(f231,plain,
( ~ sQ5_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f230,f44]) ).
fof(f232,plain,
( ~ sQ5_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f231]) ).
fof(f236,plain,
( ~ sQ8_spl
| subset(difference(sK2_skl,sK3_skl),sK4_skl) ),
inference(resolution,[status(thm)],[f194,f25]) ).
fof(f237,plain,
( ~ sQ8_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f236,f39,f193]) ).
fof(f248,plain,
( sQ1_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f111,f156]) ).
fof(f249,plain,
( sQ1_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f248]) ).
fof(f250,plain,
$false,
inference(sat_refutation,[status(thm)],[f45,f84,f158,f196,f198,f232,f237,f249]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET593+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:28:11 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.42 % Elapsed time: 0.050391 seconds
% 0.09/0.42 % CPU time: 0.214735 seconds
% 0.09/0.42 % Total memory used: 103.557 MB
% 0.09/0.42 % Net memory used: 102.882 MB
%------------------------------------------------------------------------------