%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU429+4 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 02:20:34 PM UTC 2026
% Result : Theorem 61.58s 21.43s
% Output : CNFRefutation 65.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 47 ( 10 unt; 5 def)
% Number of atoms : 128 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 135 ( 54 ~; 43 |; 20 &)
% ( 9 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 6 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-4 aty)
% Number of variables : 56 ( 48 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f68,axiom,
! [A,B] :
~ ( v1_xboole_0(B)
& r2_hidden(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f471,axiom,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f480,axiom,
! [A,B] :
( ( v1_xboole_0(A)
=> ( m1_subset_1(B,A)
<=> v1_xboole_0(B) ) )
& ( ~ v1_xboole_0(A)
=> ( m1_subset_1(B,A)
<=> r2_hidden(B,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f71064,axiom,
! [A,B,C,D] :
( ( m2_relset_1(D,A,B)
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
& ~ v1_xboole_0(A) )
=> m1_subset_1(a_4_1_relset_2(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(B))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f71112,conjecture,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B,C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ! [D] :
( m2_relset_1(D,A,B)
=> m1_subset_1(a_4_1_relset_2(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(B))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f71113,negated_conjecture,
~ ! [A] :
( ~ v1_xboole_0(A)
=> ! [B,C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ! [D] :
( m2_relset_1(D,A,B)
=> m1_subset_1(a_4_1_relset_2(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(B))) ) ) ),
inference(negated_conjecture,[status(cth)],[f71112]) ).
fof(f71333,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f68]) ).
fof(f71334,plain,
! [B] :
( ~ v1_xboole_0(B)
| ! [A] : ~ r2_hidden(A,B) ),
inference(miniscoping,[status(thm)],[f71333]) ).
fof(f71335,plain,
! [X0,X1] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f71334]) ).
fof(f72081,plain,
! [X0] : ~ v1_xboole_0(k1_zfmisc_1(X0)),
inference(cnf_transformation,[status(thm)],[f471]) ).
fof(f72097,plain,
! [A,B] :
( ( ( m1_subset_1(B,A)
<=> v1_xboole_0(B) )
| ~ v1_xboole_0(A) )
& ( ( m1_subset_1(B,A)
<=> r2_hidden(B,A) )
| v1_xboole_0(A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f480]) ).
fof(f72098,plain,
! [A,B] :
( ( ( ( ~ v1_xboole_0(B)
| m1_subset_1(B,A) )
& ( v1_xboole_0(B)
| ~ m1_subset_1(B,A) ) )
| ~ v1_xboole_0(A) )
& ( ( ( ~ r2_hidden(B,A)
| m1_subset_1(B,A) )
& ( r2_hidden(B,A)
| ~ m1_subset_1(B,A) ) )
| v1_xboole_0(A) ) ),
inference(NNF_transformation,[status(thm)],[f72097]) ).
fof(f72099,plain,
( ! [A] :
( ( ! [B] :
( ~ v1_xboole_0(B)
| m1_subset_1(B,A) )
& ! [B] :
( v1_xboole_0(B)
| ~ m1_subset_1(B,A) ) )
| ~ v1_xboole_0(A) )
& ! [A] :
( ( ! [B] :
( ~ r2_hidden(B,A)
| m1_subset_1(B,A) )
& ! [B] :
( r2_hidden(B,A)
| ~ m1_subset_1(B,A) ) )
| v1_xboole_0(A) ) ),
inference(miniscoping,[status(thm)],[f72098]) ).
fof(f72100,plain,
! [X0,X1] :
( r2_hidden(X1,X0)
| ~ m1_subset_1(X1,X0)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[status(thm)],[f72099]) ).
fof(f72101,plain,
! [X0,X1] :
( ~ r2_hidden(X1,X0)
| m1_subset_1(X1,X0)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[status(thm)],[f72099]) ).
fof(f335896,plain,
! [A,B,C,D] :
( m1_subset_1(a_4_1_relset_2(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(B)))
| ~ m2_relset_1(D,A,B)
| ~ m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
| v1_xboole_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f71064]) ).
fof(f335897,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(a_4_1_relset_2(X0,X3,X1,X2),k1_zfmisc_1(k1_zfmisc_1(X3)))
| ~ m2_relset_1(X2,X0,X3)
| ~ m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0)))
| v1_xboole_0(X0) ),
inference(cnf_transformation,[status(thm)],[f335896]) ).
fof(f336033,plain,
? [A] :
( ? [B,C] :
( ? [D] :
( ~ m1_subset_1(a_4_1_relset_2(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(B)))
& m2_relset_1(D,A,B) )
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
& ~ v1_xboole_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f71113]) ).
fof(f336034,plain,
? [A] :
( ? [C] :
( ? [B,D] :
( ~ m1_subset_1(a_4_1_relset_2(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(B)))
& m2_relset_1(D,A,B) )
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
& ~ v1_xboole_0(A) ),
inference(miniscoping,[status(thm)],[f336033]) ).
fof(f336035,plain,
( ~ m1_subset_1(a_4_1_relset_2(sK23837_skl,sK23839_skl,sK23838_skl,sK23840_skl),k1_zfmisc_1(k1_zfmisc_1(sK23839_skl)))
& m2_relset_1(sK23840_skl,sK23837_skl,sK23839_skl)
& m1_subset_1(sK23838_skl,k1_zfmisc_1(k1_zfmisc_1(sK23837_skl)))
& ~ v1_xboole_0(sK23837_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23837_skl,sK23838_skl,sK23839_skl,sK23840_skl]),skolemize(A,sK23837_skl),skolemize(C,sK23838_skl),skolemize(B,sK23839_skl),skolemize(D,sK23840_skl)],[f336034]) ).
fof(f336036,plain,
~ v1_xboole_0(sK23837_skl),
inference(cnf_transformation,[status(thm)],[f336035]) ).
fof(f336037,plain,
m1_subset_1(sK23838_skl,k1_zfmisc_1(k1_zfmisc_1(sK23837_skl))),
inference(cnf_transformation,[status(thm)],[f336035]) ).
fof(f336038,plain,
m2_relset_1(sK23840_skl,sK23837_skl,sK23839_skl),
inference(cnf_transformation,[status(thm)],[f336035]) ).
fof(f336039,plain,
~ m1_subset_1(a_4_1_relset_2(sK23837_skl,sK23839_skl,sK23838_skl,sK23840_skl),k1_zfmisc_1(k1_zfmisc_1(sK23839_skl))),
inference(cnf_transformation,[status(thm)],[f336035]) ).
fof(f412811,plain,
( r2_hidden(sK23838_skl,k1_zfmisc_1(k1_zfmisc_1(sK23837_skl)))
| v1_xboole_0(k1_zfmisc_1(k1_zfmisc_1(sK23837_skl))) ),
inference(resolution,[status(thm)],[f72100,f336037]) ).
fof(f412812,definition,
( sQ6589_spl
<=> v1_xboole_0(k1_zfmisc_1(k1_zfmisc_1(sK23837_skl))) ),
introduced(definition,[new_symbols(definition,[sQ6589_spl])],[split_symbol_definition]) ).
fof(f412813,plain,
( ~ sQ6589_spl
| v1_xboole_0(k1_zfmisc_1(k1_zfmisc_1(sK23837_skl))) ),
inference(component_clause,[status(thm)],[f412812]) ).
fof(f412815,definition,
( sQ6590_spl
<=> r2_hidden(sK23838_skl,k1_zfmisc_1(k1_zfmisc_1(sK23837_skl))) ),
introduced(definition,[new_symbols(definition,[sQ6590_spl])],[split_symbol_definition]) ).
fof(f412816,plain,
( ~ sQ6590_spl
| r2_hidden(sK23838_skl,k1_zfmisc_1(k1_zfmisc_1(sK23837_skl))) ),
inference(component_clause,[status(thm)],[f412815]) ).
fof(f412818,plain,
( sQ6590_spl
| sQ6589_spl ),
inference(split_clause,[status(thm)],[f412811,f412812,f412815]) ).
fof(f412819,plain,
( ~ sQ6589_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f412813,f72081]) ).
fof(f412820,plain,
~ sQ6589_spl,
inference(contradiction_clause,[status(thm)],[f412819]) ).
fof(f412826,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f72101,f71335]) ).
fof(f412987,definition,
( sQ6603_spl
<=> m1_subset_1(sK23838_skl,k1_zfmisc_1(k1_zfmisc_1(sK23837_skl))) ),
introduced(definition,[new_symbols(definition,[sQ6603_spl])],[split_symbol_definition]) ).
fof(f412990,definition,
( sQ6604_spl
<=> m2_relset_1(sK23840_skl,sK23837_skl,sK23839_skl) ),
introduced(definition,[new_symbols(definition,[sQ6604_spl])],[split_symbol_definition]) ).
fof(f412992,plain,
( sQ6604_spl
| ~ m2_relset_1(sK23840_skl,sK23837_skl,sK23839_skl) ),
inference(component_clause,[status(thm)],[f412990]) ).
fof(f412994,plain,
( sQ6604_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f412992,f336038]) ).
fof(f412995,plain,
sQ6604_spl,
inference(contradiction_clause,[status(thm)],[f412994]) ).
fof(f413000,plain,
( ~ m2_relset_1(sK23840_skl,sK23837_skl,sK23839_skl)
| ~ m1_subset_1(sK23838_skl,k1_zfmisc_1(k1_zfmisc_1(sK23837_skl)))
| v1_xboole_0(sK23837_skl) ),
inference(resolution,[status(thm)],[f335897,f336039]) ).
fof(f413002,definition,
( sQ6605_spl
<=> v1_xboole_0(sK23837_skl) ),
introduced(definition,[new_symbols(definition,[sQ6605_spl])],[split_symbol_definition]) ).
fof(f413003,plain,
( ~ sQ6605_spl
| v1_xboole_0(sK23837_skl) ),
inference(component_clause,[status(thm)],[f413002]) ).
fof(f413005,plain,
( ~ sQ6604_spl
| ~ sQ6603_spl
| sQ6605_spl ),
inference(split_clause,[status(thm)],[f413000,f413002,f412987,f412990]) ).
fof(f413009,plain,
( ~ sQ6605_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f413003,f336036]) ).
fof(f413010,plain,
~ sQ6605_spl,
inference(contradiction_clause,[status(thm)],[f413009]) ).
fof(f413052,plain,
( ~ sQ6590_spl
| m1_subset_1(sK23838_skl,k1_zfmisc_1(k1_zfmisc_1(sK23837_skl))) ),
inference(resolution,[status(thm)],[f412816,f412826]) ).
fof(f413054,plain,
( ~ sQ6590_spl
| sQ6603_spl ),
inference(split_clause,[status(thm)],[f413052,f412987,f412815]) ).
fof(f413055,plain,
$false,
inference(sat_refutation,[status(thm)],[f412818,f412820,f412995,f413005,f413010,f413054]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU429+4 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n019.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 06:29:00 UTC 2026
% 0.11/0.37 % CPUTime :
% 15.15/15.49 % Drodi V4.1.1
% 61.58/21.43 % Refutation found
% 61.58/21.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 61.58/21.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 53.00/23.23 % Elapsed time: 22.295585 seconds
% 53.00/23.23 % CPU time: 63.860516 seconds
% 53.00/23.23 % Total memory used: 21.739 GB
% 53.00/23.23 % Net memory used: 21.599 GB
%------------------------------------------------------------------------------