%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET162+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 : n009.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 02:09:32 PM UTC 2026
% Result : Theorem 0.18s 0.44s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 13 unt; 4 def)
% Number of atoms : 118 ( 22 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 124 ( 51 ~; 53 |; 13 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 49 !; 3 ?)
% 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] : ~ member(B,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C] : union(B,C) = union(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [B] : union(B,empty_set) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [B] : union(B,empty_set) = 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(f13,plain,
! [X0,X1,X2] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f16,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f22,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f36,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)],[f8]) ).
fof(f37,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)],[f36]) ).
fof(f38,plain,
( ! [B,C] :
( ( ( member(sK2_skl(C,B),C)
| member(sK2_skl(C,B),B) )
& ( ~ member(sK2_skl(C,B),C)
| ~ member(sK2_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,[sK2_skl]),skolemize(D,sK2_skl(C,B))],[f37]) ).
fof(f41,plain,
! [X0,X1] :
( ~ member(sK2_skl(X1,X0),X1)
| ~ member(sK2_skl(X1,X0),X0)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f42,plain,
! [X0,X1] :
( member(sK2_skl(X1,X0),X1)
| member(sK2_skl(X1,X0),X0)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f43,plain,
? [B] : union(B,empty_set) != B,
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f44,plain,
union(sK3_skl,empty_set) != sK3_skl,
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(B,sK3_skl)],[f43]) ).
fof(f45,plain,
union(sK3_skl,empty_set) != sK3_skl,
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f52,plain,
union(empty_set,sK3_skl) != sK3_skl,
inference(paramodulation,[status(thm)],[f22,f45]) ).
fof(f85,plain,
( ~ member(sK2_skl(union(sK3_skl,empty_set),sK3_skl),union(sK3_skl,empty_set))
| ~ member(sK2_skl(union(sK3_skl,empty_set),sK3_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f41,f45]) ).
fof(f107,definition,
( sQ10_spl
<=> member(sK2_skl(union(sK3_skl,empty_set),sK3_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f109,plain,
( sQ10_spl
| ~ member(sK2_skl(union(sK3_skl,empty_set),sK3_skl),sK3_skl) ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,definition,
( sQ11_spl
<=> member(sK2_skl(union(sK3_skl,empty_set),sK3_skl),union(sK3_skl,empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f111,plain,
( ~ sQ11_spl
| member(sK2_skl(union(sK3_skl,empty_set),sK3_skl),union(sK3_skl,empty_set)) ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f112,plain,
( sQ11_spl
| ~ member(sK2_skl(union(sK3_skl,empty_set),sK3_skl),union(sK3_skl,empty_set)) ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f113,plain,
( ~ sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f85,f107,f110]) ).
fof(f129,plain,
( sQ10_spl
| member(sK2_skl(union(sK3_skl,empty_set),sK3_skl),union(sK3_skl,empty_set))
| sK3_skl = union(sK3_skl,empty_set) ),
inference(resolution,[status(thm)],[f109,f42]) ).
fof(f130,plain,
! [X0] :
( sQ10_spl
| member(sK2_skl(union(sK3_skl,empty_set),sK3_skl),X0)
| ~ member(sK2_skl(union(sK3_skl,empty_set),sK3_skl),union(sK3_skl,X0)) ),
inference(resolution,[status(thm)],[f109,f13]) ).
fof(f134,definition,
( sQ12_spl
<=> sK3_skl = union(sK3_skl,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f135,plain,
( ~ sQ12_spl
| sK3_skl = union(sK3_skl,empty_set) ),
inference(component_clause,[status(thm)],[f134]) ).
fof(f137,plain,
( sQ10_spl
| sQ11_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f129,f134,f110,f107]) ).
fof(f138,plain,
( ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f135,f45]) ).
fof(f139,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f138]) ).
fof(f144,definition,
( sQ13_spl
<=> sK3_skl = union(empty_set,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f145,plain,
( ~ sQ13_spl
| sK3_skl = union(empty_set,sK3_skl) ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f148,plain,
( ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f145,f52]) ).
fof(f149,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f148]) ).
fof(f198,plain,
( sQ10_spl
| ~ member(sK2_skl(union(sK3_skl,empty_set),sK3_skl),union(sK3_skl,empty_set)) ),
inference(resolution,[status(thm)],[f130,f16]) ).
fof(f202,plain,
( sQ10_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f198,f111]) ).
fof(f203,plain,
( sQ10_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f202]) ).
fof(f206,plain,
( sQ11_spl
| ~ member(sK2_skl(union(sK3_skl,empty_set),sK3_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f112,f14]) ).
fof(f217,plain,
( sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f206,f107,f110]) ).
fof(f218,plain,
$false,
inference(sat_refutation,[status(thm)],[f113,f137,f139,f149,f203,f217]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET162+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.40 % Computer : n009.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Mon Sep 21 04:57:28 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.18/0.42 % Drodi V4.1.1
% 0.18/0.44 % Refutation found
% 0.18/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.47 % Elapsed time: 0.058852 seconds
% 0.18/0.47 % CPU time: 0.202598 seconds
% 0.18/0.47 % Total memory used: 42.476 MB
% 0.18/0.47 % Net memory used: 42.296 MB
%------------------------------------------------------------------------------