%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET577+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 : n006.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 02:10:07 PM UTC 2026
% Result : Theorem 0.17s 0.53s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 57 ( 5 unt; 5 def)
% Number of atoms : 183 ( 25 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 199 ( 73 ~; 84 |; 28 &)
% ( 12 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 83 ( 72 !; 11 ?)
% 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] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [B,C,D] :
( ! [E] :
( member(E,B)
<=> ( member(E,D)
| member(E,C) ) )
=> B = union(C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [B,C,D] :
( ! [E] :
( member(E,B)
<=> ( member(E,D)
| member(E,C) ) )
=> B = union(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(f12,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f14,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f15,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)],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f28,plain,
! [B,C] :
( ( ? [D] :
( ( member(D,C)
| member(D,B) )
& ( ~ member(D,C)
| ~ member(D,B) ) )
| B = C )
& ( ! [D] :
( ( ~ member(D,C)
| member(D,B) )
& ( member(D,C)
| ~ member(D,B) ) )
| B != C ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f29,plain,
( ! [B,C] :
( ? [D] :
( ( member(D,C)
| member(D,B) )
& ( ~ member(D,C)
| ~ member(D,B) ) )
| B = C )
& ! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| member(D,B) )
& ! [D] :
( member(D,C)
| ~ member(D,B) ) )
| B != C ) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f30,plain,
( ! [B,C] :
( ( ( member(sK1_skl(C,B),C)
| member(sK1_skl(C,B),B) )
& ( ~ member(sK1_skl(C,B),C)
| ~ member(sK1_skl(C,B),B) ) )
| B = C )
& ! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| member(D,B) )
& ! [D] :
( member(D,C)
| ~ member(D,B) ) )
| B != C ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B))],[f29]) ).
fof(f33,plain,
! [X0,X1] :
( ~ member(sK1_skl(X1,X0),X1)
| ~ member(sK1_skl(X1,X0),X0)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f34,plain,
! [X0,X1] :
( member(sK1_skl(X1,X0),X1)
| member(sK1_skl(X1,X0),X0)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f35,plain,
? [B,C,D] :
( B != union(C,D)
& ! [E] :
( member(E,B)
<=> ( member(E,D)
| member(E,C) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f36,plain,
? [B,C,D] :
( B != union(C,D)
& ! [E] :
( ( ( ~ member(E,D)
& ~ member(E,C) )
| member(E,B) )
& ( member(E,D)
| member(E,C)
| ~ member(E,B) ) ) ),
inference(NNF_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
? [B,C,D] :
( B != union(C,D)
& ! [E] :
( ( ~ member(E,D)
& ~ member(E,C) )
| member(E,B) )
& ! [E] :
( member(E,D)
| member(E,C)
| ~ member(E,B) ) ),
inference(miniscoping,[status(thm)],[f36]) ).
fof(f38,plain,
( sK2_skl != union(sK3_skl,sK4_skl)
& ! [E] :
( ( ~ member(E,sK4_skl)
& ~ member(E,sK3_skl) )
| member(E,sK2_skl) )
& ! [E] :
( member(E,sK4_skl)
| member(E,sK3_skl)
| ~ member(E,sK2_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)],[f37]) ).
fof(f39,plain,
! [X0] :
( member(X0,sK4_skl)
| member(X0,sK3_skl)
| ~ member(X0,sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [X0] :
( ~ member(X0,sK3_skl)
| member(X0,sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f41,plain,
! [X0] :
( ~ member(X0,sK4_skl)
| member(X0,sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f42,plain,
sK2_skl != union(sK3_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f43,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f16]) ).
fof(f65,plain,
( ~ member(sK1_skl(sK2_skl,union(sK3_skl,sK4_skl)),sK2_skl)
| ~ member(sK1_skl(sK2_skl,union(sK3_skl,sK4_skl)),union(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f33,f42]) ).
fof(f73,definition,
( sQ4_spl
<=> member(sK1_skl(sK2_skl,union(sK3_skl,sK4_skl)),union(sK3_skl,sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( sQ4_spl
| ~ member(sK1_skl(sK2_skl,union(sK3_skl,sK4_skl)),union(sK3_skl,sK4_skl)) ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,definition,
( sQ5_spl
<=> member(sK1_skl(sK2_skl,union(sK3_skl,sK4_skl)),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( sQ5_spl
| ~ member(sK1_skl(sK2_skl,union(sK3_skl,sK4_skl)),sK2_skl) ),
inference(component_clause,[status(thm)],[f76]) ).
fof(f79,plain,
( ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f65,f73,f76]) ).
fof(f80,plain,
( sQ4_spl
| member(sK1_skl(sK2_skl,union(sK3_skl,sK4_skl)),sK2_skl)
| union(sK3_skl,sK4_skl) = sK2_skl ),
inference(resolution,[status(thm)],[f75,f34]) ).
fof(f81,plain,
( sQ4_spl
| ~ member(sK1_skl(sK2_skl,union(sK3_skl,sK4_skl)),sK4_skl) ),
inference(resolution,[status(thm)],[f75,f13]) ).
fof(f82,plain,
( sQ4_spl
| ~ member(sK1_skl(sK2_skl,union(sK3_skl,sK4_skl)),sK3_skl) ),
inference(resolution,[status(thm)],[f75,f12]) ).
fof(f85,definition,
( sQ6_spl
<=> union(sK3_skl,sK4_skl) = sK2_skl ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ6_spl
| union(sK3_skl,sK4_skl) = sK2_skl ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ4_spl
| sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f80,f85,f76,f73]) ).
fof(f89,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f86,f42]) ).
fof(f90,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f89]) ).
fof(f97,plain,
( sQ4_spl
| member(sK1_skl(sK2_skl,union(sK3_skl,sK4_skl)),sK3_skl)
| ~ member(sK1_skl(sK2_skl,union(sK3_skl,sK4_skl)),sK2_skl) ),
inference(resolution,[status(thm)],[f81,f39]) ).
fof(f100,definition,
( sQ7_spl
<=> member(sK1_skl(sK2_skl,union(sK3_skl,sK4_skl)),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f101,plain,
( ~ sQ7_spl
| member(sK1_skl(sK2_skl,union(sK3_skl,sK4_skl)),sK3_skl) ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f103,plain,
( sQ4_spl
| sQ7_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f97,f76,f100,f73]) ).
fof(f104,plain,
( ~ sQ7_spl
| sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f101,f82]) ).
fof(f105,plain,
( ~ sQ7_spl
| sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f104]) ).
fof(f115,plain,
( sQ5_spl
| ~ member(sK1_skl(sK2_skl,union(sK3_skl,sK4_skl)),sK4_skl) ),
inference(resolution,[status(thm)],[f78,f41]) ).
fof(f116,plain,
( sQ5_spl
| ~ member(sK1_skl(sK2_skl,union(sK3_skl,sK4_skl)),sK3_skl) ),
inference(resolution,[status(thm)],[f78,f40]) ).
fof(f123,plain,
! [X0] :
( sQ5_spl
| member(sK1_skl(sK2_skl,union(sK3_skl,sK4_skl)),X0)
| ~ member(sK1_skl(sK2_skl,union(sK3_skl,sK4_skl)),union(sK3_skl,X0)) ),
inference(resolution,[status(thm)],[f116,f11]) ).
fof(f153,definition,
( sQ11_spl
<=> subset(sK2_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f155,plain,
( sQ11_spl
| ~ subset(sK2_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f166,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f155,f43]) ).
fof(f167,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f166]) ).
fof(f277,plain,
( sQ5_spl
| ~ member(sK1_skl(sK2_skl,union(sK3_skl,sK4_skl)),union(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f123,f115]) ).
fof(f281,plain,
( sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f277,f73,f76]) ).
fof(f282,plain,
$false,
inference(sat_refutation,[status(thm)],[f79,f88,f90,f103,f105,f167,f281]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET577+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.46 % Computer : n006.cluster.edu
% 0.17/0.46 % Model : x86_64 x86_64
% 0.17/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.46 % Memory : 8046.5625MB
% 0.17/0.46 % OS : Linux 6.8.0-71-generic
% 0.17/0.46 % CPULimit : 300
% 0.17/0.46 % WCLimit : 300
% 0.17/0.46 % DateTime : Mon Sep 21 05:26:44 UTC 2026
% 0.17/0.46 % CPUTime :
% 0.17/0.49 % Drodi V4.1.1
% 0.17/0.53 % Refutation found
% 0.17/0.53 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.58 % Elapsed time: 0.098724 seconds
% 0.17/0.58 % CPU time: 0.247418 seconds
% 0.17/0.58 % Total memory used: 59.444 MB
% 0.17/0.58 % Net memory used: 59.038 MB
%------------------------------------------------------------------------------