%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU424+3 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 02:20:32 PM UTC 2026
% Result : Theorem 14.56s 6.96s
% Output : CNFRefutation 15.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 42 ( 10 unt; 5 def)
% Number of atoms : 120 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 124 ( 46 ~; 41 |; 19 &)
% ( 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 : 46 ( 38 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
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(f19053,axiom,
! [A,B,C,D] :
( ( m2_relset_1(D,A,B)
& m1_subset_1(C,k1_zfmisc_1(A))
& ~ v1_xboole_0(A) )
=> m1_subset_1(a_4_0_relset_2(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(B))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19089,conjecture,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B,C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ! [D] :
( m2_relset_1(D,A,B)
=> m1_subset_1(a_4_0_relset_2(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(B))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19090,negated_conjecture,
~ ! [A] :
( ~ v1_xboole_0(A)
=> ! [B,C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ! [D] :
( m2_relset_1(D,A,B)
=> m1_subset_1(a_4_0_relset_2(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(B))) ) ) ),
inference(negated_conjecture,[status(cth)],[f19089]) ).
fof(f20058,plain,
! [X0] : ~ v1_xboole_0(k1_zfmisc_1(X0)),
inference(cnf_transformation,[status(thm)],[f471]) ).
fof(f20074,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(f20075,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)],[f20074]) ).
fof(f20076,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)],[f20075]) ).
fof(f20077,plain,
! [X0,X1] :
( r2_hidden(X1,X0)
| ~ m1_subset_1(X1,X0)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[status(thm)],[f20076]) ).
fof(f20078,plain,
! [X0,X1] :
( ~ r2_hidden(X1,X0)
| m1_subset_1(X1,X0)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[status(thm)],[f20076]) ).
fof(f89181,plain,
! [A,B,C,D] :
( m1_subset_1(a_4_0_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(A))
| v1_xboole_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f19053]) ).
fof(f89182,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(a_4_0_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(X0))
| v1_xboole_0(X0) ),
inference(cnf_transformation,[status(thm)],[f89181]) ).
fof(f89271,plain,
? [A] :
( ? [B,C] :
( ? [D] :
( ~ m1_subset_1(a_4_0_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(A)) )
& ~ v1_xboole_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f19090]) ).
fof(f89272,plain,
? [A] :
( ? [C] :
( ? [B,D] :
( ~ m1_subset_1(a_4_0_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(A)) )
& ~ v1_xboole_0(A) ),
inference(miniscoping,[status(thm)],[f89271]) ).
fof(f89273,plain,
( ~ m1_subset_1(a_4_0_relset_2(sK6522_skl,sK6524_skl,sK6523_skl,sK6525_skl),k1_zfmisc_1(k1_zfmisc_1(sK6524_skl)))
& m2_relset_1(sK6525_skl,sK6522_skl,sK6524_skl)
& m1_subset_1(sK6523_skl,k1_zfmisc_1(sK6522_skl))
& ~ v1_xboole_0(sK6522_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6522_skl,sK6523_skl,sK6524_skl,sK6525_skl]),skolemize(A,sK6522_skl),skolemize(C,sK6523_skl),skolemize(B,sK6524_skl),skolemize(D,sK6525_skl)],[f89272]) ).
fof(f89274,plain,
~ v1_xboole_0(sK6522_skl),
inference(cnf_transformation,[status(thm)],[f89273]) ).
fof(f89275,plain,
m1_subset_1(sK6523_skl,k1_zfmisc_1(sK6522_skl)),
inference(cnf_transformation,[status(thm)],[f89273]) ).
fof(f89276,plain,
m2_relset_1(sK6525_skl,sK6522_skl,sK6524_skl),
inference(cnf_transformation,[status(thm)],[f89273]) ).
fof(f89277,plain,
~ m1_subset_1(a_4_0_relset_2(sK6522_skl,sK6524_skl,sK6523_skl,sK6525_skl),k1_zfmisc_1(k1_zfmisc_1(sK6524_skl))),
inference(cnf_transformation,[status(thm)],[f89273]) ).
fof(f110672,definition,
( sQ2477_spl
<=> v1_xboole_0(k1_zfmisc_1(sK6522_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2477_spl])],[split_symbol_definition]) ).
fof(f110673,plain,
( ~ sQ2477_spl
| v1_xboole_0(k1_zfmisc_1(sK6522_skl)) ),
inference(component_clause,[status(thm)],[f110672]) ).
fof(f110701,plain,
( r2_hidden(sK6523_skl,k1_zfmisc_1(sK6522_skl))
| v1_xboole_0(k1_zfmisc_1(sK6522_skl)) ),
inference(resolution,[status(thm)],[f20077,f89275]) ).
fof(f110702,definition,
( sQ2483_spl
<=> r2_hidden(sK6523_skl,k1_zfmisc_1(sK6522_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2483_spl])],[split_symbol_definition]) ).
fof(f110703,plain,
( ~ sQ2483_spl
| r2_hidden(sK6523_skl,k1_zfmisc_1(sK6522_skl)) ),
inference(component_clause,[status(thm)],[f110702]) ).
fof(f110705,plain,
( sQ2483_spl
| sQ2477_spl ),
inference(split_clause,[status(thm)],[f110701,f110672,f110702]) ).
fof(f110711,plain,
( ~ sQ2483_spl
| m1_subset_1(sK6523_skl,k1_zfmisc_1(sK6522_skl))
| v1_xboole_0(k1_zfmisc_1(sK6522_skl)) ),
inference(resolution,[status(thm)],[f110703,f20078]) ).
fof(f110712,definition,
( sQ2484_spl
<=> m1_subset_1(sK6523_skl,k1_zfmisc_1(sK6522_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2484_spl])],[split_symbol_definition]) ).
fof(f110715,plain,
( ~ sQ2483_spl
| sQ2484_spl
| sQ2477_spl ),
inference(split_clause,[status(thm)],[f110711,f110672,f110712,f110702]) ).
fof(f110717,plain,
( ~ sQ2477_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f110673,f20058]) ).
fof(f110718,plain,
~ sQ2477_spl,
inference(contradiction_clause,[status(thm)],[f110717]) ).
fof(f110744,definition,
( sQ2486_spl
<=> v1_xboole_0(sK6522_skl) ),
introduced(definition,[new_symbols(definition,[sQ2486_spl])],[split_symbol_definition]) ).
fof(f110745,plain,
( ~ sQ2486_spl
| v1_xboole_0(sK6522_skl) ),
inference(component_clause,[status(thm)],[f110744]) ).
fof(f110804,definition,
( sQ2492_spl
<=> m2_relset_1(sK6525_skl,sK6522_skl,sK6524_skl) ),
introduced(definition,[new_symbols(definition,[sQ2492_spl])],[split_symbol_definition]) ).
fof(f110806,plain,
( sQ2492_spl
| ~ m2_relset_1(sK6525_skl,sK6522_skl,sK6524_skl) ),
inference(component_clause,[status(thm)],[f110804]) ).
fof(f110808,plain,
( sQ2492_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f110806,f89276]) ).
fof(f110809,plain,
sQ2492_spl,
inference(contradiction_clause,[status(thm)],[f110808]) ).
fof(f110849,plain,
( ~ m2_relset_1(sK6525_skl,sK6522_skl,sK6524_skl)
| ~ m1_subset_1(sK6523_skl,k1_zfmisc_1(sK6522_skl))
| v1_xboole_0(sK6522_skl) ),
inference(resolution,[status(thm)],[f89182,f89277]) ).
fof(f110853,plain,
( ~ sQ2492_spl
| ~ sQ2484_spl
| sQ2486_spl ),
inference(split_clause,[status(thm)],[f110849,f110744,f110712,f110804]) ).
fof(f110855,plain,
( ~ sQ2486_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f110745,f89274]) ).
fof(f110856,plain,
~ sQ2486_spl,
inference(contradiction_clause,[status(thm)],[f110855]) ).
fof(f110857,plain,
$false,
inference(sat_refutation,[status(thm)],[f110705,f110715,f110718,f110809,f110853,f110856]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU424+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n003.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 06:28:19 UTC 2026
% 0.16/0.43 % CPUTime :
% 5.31/5.62 % Drodi V4.1.1
% 14.56/6.96 % Refutation found
% 14.56/6.96 % SZS status Theorem for theBenchmark: Theorem is valid
% 14.56/6.96 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.67/7.94 % Elapsed time: 7.423379 seconds
% 5.67/7.94 % CPU time: 16.614930 seconds
% 5.67/7.94 % Total memory used: 5.295 GB
% 5.67/7.94 % Net memory used: 5.265 GB
%------------------------------------------------------------------------------