%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU422+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 : Tue Sep 29 12:48:54 PM UTC 2026
% Result : Theorem 4.40s 1.59s
% Output : Refutation 5.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 94 ( 22 unt; 9 def)
% Number of atoms : 264 ( 12 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 279 ( 109 ~; 119 |; 28 &)
% ( 16 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 10 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 91 ( 0 sgn 82 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( m1_subset_1(X1,k1_zfmisc_1(X0))
=> m1_subset_1(a_2_0_relset_2(X0,X1),k1_zfmisc_1(k1_zfmisc_1(X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_2) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( m1_subset_1(X1,k1_zfmisc_1(X0))
=> m1_subset_1(a_2_0_relset_2(X0,X1),k1_zfmisc_1(k1_zfmisc_1(X0))) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f5,axiom,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( r2_hidden(X2,X0)
=> r2_hidden(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f12,axiom,
! [X0] : ~ v1_xboole_0(k1_zfmisc_1(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f15,axiom,
! [X0,X1,X2] :
( ( ~ v1_xboole_0(X1)
& m1_subset_1(X2,k1_zfmisc_1(X1)) )
=> ( r2_hidden(X0,a_2_0_relset_2(X1,X2))
<=> ? [X3] :
( m1_subset_1(X3,X1)
& X0 = k1_tarski(X3)
& r2_hidden(X3,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_relset_2) ).
fof(f23,axiom,
! [X0,X1] :
( m1_subset_1(X0,X1)
=> ( v1_xboole_0(X1)
| r2_hidden(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f25,axiom,
! [X0,X1] :
( r1_tarski(k1_tarski(X0),X1)
<=> r2_hidden(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
fof(f26,axiom,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
<=> r1_tarski(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f41,plain,
? [X0] :
( ? [X1] :
( ~ m1_subset_1(a_2_0_relset_2(X0,X1),k1_zfmisc_1(k1_zfmisc_1(X0)))
& m1_subset_1(X1,k1_zfmisc_1(X0)) )
& ~ v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f43,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( r2_hidden(X2,X1)
| ~ r2_hidden(X2,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ( r2_hidden(X0,a_2_0_relset_2(X1,X2))
<=> ? [X3] :
( m1_subset_1(X3,X1)
& X0 = k1_tarski(X3)
& r2_hidden(X3,X2) ) )
| v1_xboole_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(X1)) ),
inference(ennf_transformation,[],[f15]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( r2_hidden(X0,a_2_0_relset_2(X1,X2))
<=> ? [X3] :
( m1_subset_1(X3,X1)
& X0 = k1_tarski(X3)
& r2_hidden(X3,X2) ) )
| v1_xboole_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(X1)) ),
inference(flattening,[],[f44]) ).
fof(f48,plain,
! [X0,X1] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f49,plain,
! [X0,X1] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(flattening,[],[f48]) ).
fof(f57,plain,
( ~ m1_subset_1(a_2_0_relset_2(sK0,sK1),k1_zfmisc_1(k1_zfmisc_1(sK0)))
& m1_subset_1(sK1,k1_zfmisc_1(sK0))
& ~ v1_xboole_0(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f41]) ).
fof(f58,plain,
! [X0,X1] :
( ( r1_tarski(X0,X1)
| ? [X2] :
( ~ r2_hidden(X2,X1)
& r2_hidden(X2,X0) ) )
& ( ! [X2] :
( r2_hidden(X2,X1)
| ~ r2_hidden(X2,X0) )
| ~ r1_tarski(X0,X1) ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f59,plain,
! [X0,X1] :
( ( r1_tarski(X0,X1)
| ? [X2] :
( ~ r2_hidden(X2,X1)
& r2_hidden(X2,X0) ) )
& ( ! [X3] :
( r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) )
| ~ r1_tarski(X0,X1) ) ),
inference(rectify,[],[f58]) ).
fof(f60,plain,
! [X0,X1] :
( ( r1_tarski(X0,X1)
| ( ~ r2_hidden(sK2(X0,X1),X1)
& r2_hidden(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) )
| ~ r1_tarski(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f59]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ( ( r2_hidden(X0,a_2_0_relset_2(X1,X2))
| ! [X3] :
( ~ m1_subset_1(X3,X1)
| k1_tarski(X3) != X0
| ~ r2_hidden(X3,X2) ) )
& ( ? [X3] :
( m1_subset_1(X3,X1)
& X0 = k1_tarski(X3)
& r2_hidden(X3,X2) )
| ~ r2_hidden(X0,a_2_0_relset_2(X1,X2)) ) )
| v1_xboole_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(X1)) ),
inference(nnf_transformation,[],[f45]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ( ( r2_hidden(X0,a_2_0_relset_2(X1,X2))
| ! [X3] :
( ~ m1_subset_1(X3,X1)
| k1_tarski(X3) != X0
| ~ r2_hidden(X3,X2) ) )
& ( ? [X4] :
( m1_subset_1(X4,X1)
& k1_tarski(X4) = X0
& r2_hidden(X4,X2) )
| ~ r2_hidden(X0,a_2_0_relset_2(X1,X2)) ) )
| v1_xboole_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(X1)) ),
inference(rectify,[],[f62]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ( ( r2_hidden(X0,a_2_0_relset_2(X1,X2))
| ! [X3] :
( ~ m1_subset_1(X3,X1)
| k1_tarski(X3) != X0
| ~ r2_hidden(X3,X2) ) )
& ( ( m1_subset_1(sK4(X0,X1,X2),X1)
& k1_tarski(sK4(X0,X1,X2)) = X0
& r2_hidden(sK4(X0,X1,X2),X2) )
| ~ r2_hidden(X0,a_2_0_relset_2(X1,X2)) ) )
| v1_xboole_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X4,sK4(X0,X1,X2))],[f63]) ).
fof(f71,plain,
! [X0,X1] :
( ( r1_tarski(k1_tarski(X0),X1)
| ~ r2_hidden(X0,X1) )
& ( r2_hidden(X0,X1)
| ~ r1_tarski(k1_tarski(X0),X1) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f72,plain,
! [X0,X1] :
( ( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) )
& ( r1_tarski(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f73,plain,
~ v1_xboole_0(sK0),
inference(cnf_transformation,[],[f57]) ).
fof(f74,plain,
m1_subset_1(sK1,k1_zfmisc_1(sK0)),
inference(cnf_transformation,[],[f57]) ).
fof(f75,plain,
~ m1_subset_1(a_2_0_relset_2(sK0,sK1),k1_zfmisc_1(k1_zfmisc_1(sK0))),
inference(cnf_transformation,[],[f57]) ).
fof(f78,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
| r2_hidden(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f79,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
| ~ r2_hidden(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f82,plain,
! [X0] : ~ v1_xboole_0(k1_zfmisc_1(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f86,plain,
! [X2,X0,X1] :
( k1_tarski(sK4(X0,X1,X2)) = X0
| ~ r2_hidden(X0,a_2_0_relset_2(X1,X2))
| v1_xboole_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f64]) ).
fof(f87,plain,
! [X2,X0,X1] :
( m1_subset_1(sK4(X0,X1,X2),X1)
| ~ r2_hidden(X0,a_2_0_relset_2(X1,X2))
| v1_xboole_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f64]) ).
fof(f97,plain,
! [X0,X1] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f101,plain,
! [X0,X1] :
( r1_tarski(k1_tarski(X0),X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f102,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f103,plain,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f110,definition,
( spl10_1
<=> v1_xboole_0(sK0) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
fof(f112,plain,
( ~ v1_xboole_0(sK0)
| spl10_1 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f113,plain,
~ spl10_1,
inference(avatar_split_clause,[],[f73,f110]) ).
fof(f114,plain,
r1_tarski(sK1,sK0),
inference(forward_literal_rewriting,[],[f74,f102]) ).
fof(f115,plain,
~ r1_tarski(a_2_0_relset_2(sK0,sK1),k1_zfmisc_1(sK0)),
inference(forward_literal_rewriting,[],[f75,f103]) ).
fof(f117,definition,
( spl10_2
<=> r1_tarski(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
fof(f120,plain,
spl10_2,
inference(avatar_split_clause,[],[f114,f117]) ).
fof(f122,definition,
( spl10_3
<=> r1_tarski(a_2_0_relset_2(sK0,sK1),k1_zfmisc_1(sK0)) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
fof(f124,plain,
( ~ r1_tarski(a_2_0_relset_2(sK0,sK1),k1_zfmisc_1(sK0))
| spl10_3 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f125,plain,
~ spl10_3,
inference(avatar_split_clause,[],[f115,f122]) ).
fof(f127,plain,
( ! [X0,X1] :
( k1_tarski(sK4(X0,sK0,X1)) = X0
| ~ r2_hidden(X0,a_2_0_relset_2(sK0,X1))
| ~ m1_subset_1(X1,k1_zfmisc_1(sK0)) )
| spl10_1 ),
inference(resolution,[],[f112,f86]) ).
fof(f132,plain,
( ! [X0] :
( ~ m1_subset_1(X0,sK0)
| r2_hidden(X0,sK0) )
| spl10_1 ),
inference(resolution,[],[f112,f97]) ).
fof(f141,plain,
( ! [X0,X1] :
( k1_tarski(sK4(X0,sK0,X1)) = X0
| ~ r1_tarski(X1,sK0)
| ~ r2_hidden(X0,a_2_0_relset_2(sK0,X1)) )
| spl10_1 ),
inference(forward_literal_rewriting,[],[f127,f103]) ).
fof(f152,plain,
( r2_hidden(sK2(a_2_0_relset_2(sK0,sK1),k1_zfmisc_1(sK0)),a_2_0_relset_2(sK0,sK1))
| spl10_3 ),
inference(resolution,[],[f124,f78]) ).
fof(f153,plain,
( ~ r2_hidden(sK2(a_2_0_relset_2(sK0,sK1),k1_zfmisc_1(sK0)),k1_zfmisc_1(sK0))
| spl10_3 ),
inference(resolution,[],[f124,f79]) ).
fof(f155,definition,
( spl10_6
<=> r2_hidden(sK2(a_2_0_relset_2(sK0,sK1),k1_zfmisc_1(sK0)),k1_zfmisc_1(sK0)) ),
introduced(definition,[new_symbols(definition,[spl10_6])],[avatar_definition]) ).
fof(f157,plain,
( ~ r2_hidden(sK2(a_2_0_relset_2(sK0,sK1),k1_zfmisc_1(sK0)),k1_zfmisc_1(sK0))
| spl10_6 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f158,plain,
( ~ spl10_6
| spl10_3 ),
inference(avatar_split_clause,[],[f153,f122,f155]) ).
fof(f160,definition,
( spl10_7
<=> r2_hidden(sK2(a_2_0_relset_2(sK0,sK1),k1_zfmisc_1(sK0)),a_2_0_relset_2(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl10_7])],[avatar_definition]) ).
fof(f162,plain,
( r2_hidden(sK2(a_2_0_relset_2(sK0,sK1),k1_zfmisc_1(sK0)),a_2_0_relset_2(sK0,sK1))
| ~ spl10_7 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f163,plain,
( spl10_7
| spl10_3 ),
inference(avatar_split_clause,[],[f152,f122,f160]) ).
fof(f223,plain,
( v1_xboole_0(k1_zfmisc_1(sK0))
| ~ m1_subset_1(sK2(a_2_0_relset_2(sK0,sK1),k1_zfmisc_1(sK0)),k1_zfmisc_1(sK0))
| spl10_6 ),
inference(resolution,[],[f157,f97]) ).
fof(f225,plain,
( ~ r1_tarski(sK2(a_2_0_relset_2(sK0,sK1),k1_zfmisc_1(sK0)),sK0)
| v1_xboole_0(k1_zfmisc_1(sK0))
| spl10_6 ),
inference(forward_literal_rewriting,[],[f223,f103]) ).
fof(f228,definition,
( spl10_14
<=> v1_xboole_0(k1_zfmisc_1(sK0)) ),
introduced(definition,[new_symbols(definition,[spl10_14])],[avatar_definition]) ).
fof(f230,plain,
( v1_xboole_0(k1_zfmisc_1(sK0))
| ~ spl10_14 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f232,definition,
( spl10_15
<=> r1_tarski(sK2(a_2_0_relset_2(sK0,sK1),k1_zfmisc_1(sK0)),sK0) ),
introduced(definition,[new_symbols(definition,[spl10_15])],[avatar_definition]) ).
fof(f235,plain,
( spl10_14
| ~ spl10_15
| spl10_6 ),
inference(avatar_split_clause,[],[f225,f155,f232,f228]) ).
fof(f238,plain,
( m1_subset_1(sK4(sK2(a_2_0_relset_2(sK0,sK1),k1_zfmisc_1(sK0)),sK0,sK1),sK0)
| v1_xboole_0(sK0)
| ~ m1_subset_1(sK1,k1_zfmisc_1(sK0))
| ~ spl10_7 ),
inference(resolution,[],[f162,f87]) ).
fof(f267,plain,
( ~ r1_tarski(sK1,sK0)
| m1_subset_1(sK4(sK2(a_2_0_relset_2(sK0,sK1),k1_zfmisc_1(sK0)),sK0,sK1),sK0)
| v1_xboole_0(sK0)
| ~ spl10_7 ),
inference(forward_literal_rewriting,[],[f238,f103]) ).
fof(f271,definition,
( spl10_19
<=> m1_subset_1(sK4(sK2(a_2_0_relset_2(sK0,sK1),k1_zfmisc_1(sK0)),sK0,sK1),sK0) ),
introduced(definition,[new_symbols(definition,[spl10_19])],[avatar_definition]) ).
fof(f273,plain,
( m1_subset_1(sK4(sK2(a_2_0_relset_2(sK0,sK1),k1_zfmisc_1(sK0)),sK0,sK1),sK0)
| ~ spl10_19 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f274,plain,
( spl10_1
| spl10_19
| ~ spl10_2
| ~ spl10_7 ),
inference(avatar_split_clause,[],[f267,f160,f117,f271,f110]) ).
fof(f304,plain,
( ! [X2,X0,X1] :
( ~ r2_hidden(sK4(X0,sK0,X1),X2)
| r1_tarski(X0,X2)
| ~ r1_tarski(X1,sK0)
| ~ r2_hidden(X0,a_2_0_relset_2(sK0,X1)) )
| spl10_1 ),
inference(superposition,[],[f101,f141]) ).
fof(f503,plain,
( r2_hidden(sK4(sK2(a_2_0_relset_2(sK0,sK1),k1_zfmisc_1(sK0)),sK0,sK1),sK0)
| spl10_1
| ~ spl10_19 ),
inference(resolution,[],[f273,f132]) ).
fof(f508,definition,
( spl10_42
<=> r2_hidden(sK4(sK2(a_2_0_relset_2(sK0,sK1),k1_zfmisc_1(sK0)),sK0,sK1),sK0) ),
introduced(definition,[new_symbols(definition,[spl10_42])],[avatar_definition]) ).
fof(f510,plain,
( r2_hidden(sK4(sK2(a_2_0_relset_2(sK0,sK1),k1_zfmisc_1(sK0)),sK0,sK1),sK0)
| ~ spl10_42 ),
inference(avatar_component_clause,[],[f508]) ).
fof(f512,plain,
( spl10_42
| spl10_1
| ~ spl10_19 ),
inference(avatar_split_clause,[],[f503,f271,f110,f508]) ).
fof(f1782,plain,
( r1_tarski(sK2(a_2_0_relset_2(sK0,sK1),k1_zfmisc_1(sK0)),sK0)
| ~ r1_tarski(sK1,sK0)
| ~ r2_hidden(sK2(a_2_0_relset_2(sK0,sK1),k1_zfmisc_1(sK0)),a_2_0_relset_2(sK0,sK1))
| spl10_1
| ~ spl10_42 ),
inference(resolution,[],[f510,f304]) ).
fof(f1783,plain,
( ~ spl10_7
| ~ spl10_2
| spl10_15
| spl10_1
| ~ spl10_42 ),
inference(avatar_split_clause,[],[f1782,f508,f110,f232,f117,f160]) ).
fof(f1793,plain,
( $false
| ~ spl10_14 ),
inference(resolution,[],[f230,f82]) ).
fof(f1800,plain,
~ spl10_14,
inference(avatar_contradiction_clause,[],[f1793]) ).
cnf(s1,plain,
~ spl10_1,
inference(sat_conversion,[],[f113]) ).
cnf(s2,plain,
spl10_2,
inference(sat_conversion,[],[f120]) ).
cnf(s3,plain,
~ spl10_3,
inference(sat_conversion,[],[f125]) ).
cnf(s6,plain,
( spl10_3
| ~ spl10_6 ),
inference(sat_conversion,[],[f158]) ).
cnf(s7,plain,
( spl10_3
| spl10_7 ),
inference(sat_conversion,[],[f163]) ).
cnf(s14,plain,
( spl10_6
| spl10_14
| ~ spl10_15 ),
inference(sat_conversion,[],[f235]) ).
cnf(s19,plain,
( spl10_1
| ~ spl10_2
| ~ spl10_7
| spl10_19 ),
inference(sat_conversion,[],[f274]) ).
cnf(s48,plain,
( spl10_1
| ~ spl10_19
| spl10_42 ),
inference(sat_conversion,[],[f512]) ).
cnf(s205,plain,
( spl10_1
| ~ spl10_2
| ~ spl10_7
| spl10_15
| ~ spl10_42 ),
inference(sat_conversion,[],[f1783]) ).
cnf(s208,plain,
~ spl10_14,
inference(sat_conversion,[],[f1800]) ).
cnf(s211,plain,
( spl10_6
| ~ spl10_15 ),
inference(rat,[],[s14,s208]) ).
cnf(s212,plain,
spl10_7,
inference(rat,[],[s7,s3]) ).
cnf(s213,plain,
~ spl10_6,
inference(rat,[],[s6,s3]) ).
cnf(s219,plain,
~ spl10_15,
inference(rat,[],[s211,s213]) ).
cnf(s229,plain,
~ spl10_42,
inference(rat,[],[s205,s2,s219,s212,s1]) ).
cnf(s242,plain,
~ spl10_19,
inference(rat,[],[s48,s229,s1]) ).
cnf(s248,plain,
$false,
inference(rat,[],[s19,s2,s212,s242,s1]) ).
fof(f1807,plain,
$false,
inference(avatar_sat_refutation,[],[s248]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU422+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 05:21:10 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.40/1.59 % (3025594)Detected formulas, will run a generic FOF schedule.
% 4.40/1.59 % (3025603)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2021604444:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.40/1.59 % (3025605)dis-21_1_sil=8000:lcm=predicate:random_seed=3222315963:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 4.40/1.59 % (3025603)Instruction limit reached!
% 4.40/1.59 % (3025603)------------------------------
% 4.40/1.59 % (3025603)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.40/1.59 % (3025603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.40/1.59 % (3025603)CaDiCaL version: 2.1.3
% 4.40/1.59 % (3025603)Termination reason: Instruction limit
% 4.40/1.59 % (3025603)Termination phase: Saturation
% 4.40/1.59 % (3025603)Time elapsed: 0.042 s
% 4.40/1.59 % (3025603)Peak memory usage: 88 MB
% 4.40/1.59 % (3025603)Instructions burned: 120 (million)
% 4.40/1.59 % (3025600)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=712343490:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.40/1.59 % (3025602)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=324366972:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.40/1.59 % (3025599)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3446151875:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.40/1.59 % (3025601)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1296189108:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.40/1.59 % (3025604)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=147235906:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.40/1.59 % (3025602)Refutation not found, incomplete strategy
% 4.40/1.59 % (3025602)------------------------------
% 4.40/1.59 % (3025602)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.40/1.59 % (3025602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.40/1.59 % (3025602)CaDiCaL version: 2.1.3
% 4.40/1.59 % (3025602)Termination reason: Refutation not found, incomplete strategy
% 4.40/1.59 % (3025602)Time elapsed: 0.002 s
% 4.40/1.59 % (3025602)Peak memory usage: 88 MB
% 4.40/1.59 % (3025602)Instructions burned: 1 (million)
% 4.40/1.59 % (3025605)Instruction limit reached!
% 4.40/1.59 % (3025605)------------------------------
% 4.40/1.59 % (3025605)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.40/1.59 % (3025605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.40/1.59 % (3025605)CaDiCaL version: 2.1.3
% 4.40/1.59 % (3025605)Termination reason: Instruction limit
% 4.40/1.59 % (3025605)Termination phase: Saturation
% 4.40/1.59 % (3025605)Time elapsed: 0.074 s
% 4.40/1.59 % (3025605)Peak memory usage: 89 MB
% 4.40/1.59 % (3025605)Instructions burned: 130 (million)
% 4.40/1.59 % (3025613)lrs+10_1_sil=8000:sp=occurrence:random_seed=4117105356:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.40/1.59 % (3025604)Instruction limit reached!
% 4.40/1.59 % (3025604)------------------------------
% 4.40/1.59 % (3025604)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.40/1.59 % (3025604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.40/1.59 % (3025604)CaDiCaL version: 2.1.3
% 4.40/1.59 % (3025604)Termination reason: Instruction limit
% 4.40/1.59 % (3025604)Termination phase: Saturation
% 4.40/1.59 % (3025604)Time elapsed: 0.098 s
% 4.40/1.59 % (3025604)Peak memory usage: 89 MB
% 4.40/1.59 % (3025604)Instructions burned: 140 (million)
% 4.40/1.59 % (3025613)Instruction limit reached!
% 4.40/1.59 % (3025613)------------------------------
% 4.40/1.59 % (3025613)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.40/1.59 % (3025613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.40/1.59 % (3025613)CaDiCaL version: 2.1.3
% 4.40/1.59 % (3025613)Termination reason: Instruction limit
% 4.40/1.59 % (3025613)Termination phase: Saturation
% 4.40/1.59 % (3025613)Time elapsed: 0.091 s
% 4.40/1.59 % (3025613)Peak memory usage: 91 MB
% 4.40/1.59 % (3025613)Instructions burned: 285 (million)
% 4.40/1.59 % (3025614)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4026837841:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.40/1.59 % (3025616)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2107286314:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.40/1.59 % (3025602)------------------------------
% 4.40/1.59 % (3025602)------------------------------
% 4.40/1.59 % (3025617)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=2122417483:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 4.40/1.59 % (3025614)Instruction limit reached!
% 4.40/1.59 % (3025614)------------------------------
% 4.40/1.59 % (3025614)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.40/1.59 % (3025614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.40/1.59 % (3025614)CaDiCaL version: 2.1.3
% 4.40/1.59 % (3025614)Termination reason: Instruction limit
% 4.40/1.59 % (3025614)Termination phase: Saturation
% 4.40/1.59 % (3025614)Time elapsed: 0.092 s
% 4.40/1.59 % (3025614)Peak memory usage: 90 MB
% 4.40/1.59 % (3025614)Instructions burned: 158 (million)
% 4.40/1.59 % (3025617)Instruction limit reached!
% 4.40/1.59 % (3025617)------------------------------
% 4.40/1.59 % (3025617)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.40/1.59 % (3025617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.40/1.59 % (3025617)CaDiCaL version: 2.1.3
% 4.40/1.59 % (3025617)Termination reason: Instruction limit
% 4.40/1.59 % (3025617)Termination phase: Saturation
% 4.40/1.59 % (3025617)Time elapsed: 0.083 s
% 4.40/1.59 % (3025617)Peak memory usage: 91 MB
% 4.40/1.59 % (3025617)Instructions burned: 250 (million)
% 4.40/1.59 % (3025620)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3999392089:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 4.40/1.59 % (3025622)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=628746668:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 4.40/1.59 % (3025623)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3598963322:cts=off:i=113:fsr=off:ss=included:sgt=4_2995 on theBenchmark for (2995ds/113Mi)
% 4.40/1.59 % (3025623)First to succeed.
% 4.40/1.59 % (3025623)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3025594"
% 4.40/1.59 % (3025616)Instruction limit reached!
% 4.40/1.59 % (3025616)------------------------------
% 4.40/1.59 % (3025616)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.40/1.59 % (3025616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.40/1.59 % (3025616)CaDiCaL version: 2.1.3
% 4.40/1.59 % (3025616)Termination reason: Instruction limit
% 4.40/1.59 % (3025616)Termination phase: Saturation
% 4.40/1.59 % (3025616)Time elapsed: 0.215 s
% 4.40/1.59 % (3025616)Peak memory usage: 91 MB
% 4.40/1.59 % (3025616)Instructions burned: 326 (million)
% 4.40/1.59 % (3025620)Instruction limit reached!
% 4.40/1.59 % (3025620)------------------------------
% 4.40/1.59 % (3025620)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.40/1.59 % (3025620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.40/1.59 % (3025620)CaDiCaL version: 2.1.3
% 4.40/1.59 % (3025620)Termination reason: Instruction limit
% 4.40/1.59 % (3025620)Termination phase: Saturation
% 4.40/1.59 % (3025620)Time elapsed: 0.177 s
% 4.40/1.59 % (3025620)Peak memory usage: 89 MB
% 4.40/1.59 % (3025620)Instructions burned: 294 (million)
% 4.40/1.59 % (3025627)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=358720313:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 4.40/1.59 % (3025623)Refutation found. Thanks to Tanya!
% 4.40/1.59 % SZS status Theorem for theBenchmark
% 4.40/1.59 % SZS output start Proof for theBenchmark
% See solution above
% 5.91/1.78 % (3025623)------------------------------
% 5.91/1.78 % (3025623)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.91/1.78 % (3025623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.91/1.78 % (3025623)CaDiCaL version: 2.1.3
% 5.91/1.78 % (3025623)Termination reason: Refutation
% 5.91/1.78 % (3025623)Time elapsed: 0.019 s
% 5.91/1.78 % (3025623)Peak memory usage: 90 MB
% 5.91/1.78 % (3025623)Instructions burned: 44 (million)
% 5.91/1.78 % (3025623)------------------------------
% 5.91/1.78 % (3025623)------------------------------
% 5.91/1.78 % (3025594)Success in time 0.758 s
% 5.91/1.78 % Vampire exiting
%------------------------------------------------------------------------------