%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP623+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 : n001.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 10:15:03 AM UTC 2026
% Result : Theorem 3.19s 1.33s
% Output : Refutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 24
% Syntax : Number of formulae : 136 ( 29 unt; 13 def)
% Number of atoms : 408 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 463 ( 191 ~; 195 |; 46 &)
% ( 18 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 27 ( 26 usr; 14 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 105 ( 0 sgn 101 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> r1_tarski(k4_autgroup(X0),k1_autgroup(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_autgroup) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> r1_tarski(k4_autgroup(X0),k1_autgroup(X0)) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f13,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(f15,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_autgroup) ).
fof(f19,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_autgroup) ).
fof(f20,axiom,
! [X0] :
( l1_group_1(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(f22,axiom,
! [X0,X1,X2] :
( m1_fraenkel(X2,X0,X1)
=> ( ~ v1_xboole_0(X2)
& v1_fraenkel(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_fraenkel) ).
fof(f37,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& l1_struct_0(X0) )
=> ~ v1_xboole_0(u1_struct_0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f54,axiom,
! [X0,X1,X2] :
( ( ~ v1_xboole_0(X1)
& m1_fraenkel(X2,X0,X1) )
=> ! [X3] :
( m2_fraenkel(X3,X0,X1,X2)
<=> m1_subset_1(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_fraenkel) ).
fof(f57,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
=> m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_autgroup) ).
fof(f58,axiom,
! [X0,X1] :
( r2_hidden(X0,X1)
=> m1_subset_1(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f59,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(f72,plain,
? [X0] :
( ~ r1_tarski(k4_autgroup(X0),k1_autgroup(X0))
& ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f73,plain,
? [X0] :
( ~ r1_tarski(k4_autgroup(X0),k1_autgroup(X0))
& ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) ),
inference(flattening,[],[f72]) ).
fof(f90,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( r2_hidden(X2,X1)
| ~ r2_hidden(X2,X0) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f93,plain,
! [X0] :
( m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f94,plain,
! [X0] :
( m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f93]) ).
fof(f95,plain,
! [X0] :
( m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f96,plain,
! [X0] :
( m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f95]) ).
fof(f97,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ( ~ v1_xboole_0(X2)
& v1_fraenkel(X2) )
| ~ m1_fraenkel(X2,X0,X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f107,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f108,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(flattening,[],[f107]) ).
fof(f113,plain,
! [X0,X1,X2] :
( ! [X3] :
( m2_fraenkel(X3,X0,X1,X2)
<=> m1_subset_1(X3,X2) )
| v1_xboole_0(X1)
| ~ m1_fraenkel(X2,X0,X1) ),
inference(ennf_transformation,[],[f54]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ! [X3] :
( m2_fraenkel(X3,X0,X1,X2)
<=> m1_subset_1(X3,X2) )
| v1_xboole_0(X1)
| ~ m1_fraenkel(X2,X0,X1) ),
inference(flattening,[],[f113]) ).
fof(f115,plain,
! [X0] :
( ! [X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0)) )
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f116,plain,
! [X0] :
( ! [X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0)) )
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f115]) ).
fof(f117,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f58]) ).
fof(f118,plain,
! [X0,X1] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(ennf_transformation,[],[f59]) ).
fof(f119,plain,
! [X0,X1] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(flattening,[],[f118]) ).
fof(f126,plain,
( ~ r1_tarski(k4_autgroup(sK0),k1_autgroup(sK0))
& ~ v3_struct_0(sK0)
& v1_group_1(sK0)
& v3_group_1(sK0)
& v4_group_1(sK0)
& l1_group_1(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f73]) ).
fof(f127,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,[],[f90]) ).
fof(f128,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,[],[f127]) ).
fof(f129,plain,
! [X0,X1] :
( ( r1_tarski(X0,X1)
| ( ~ r2_hidden(sK1(X0,X1),X1)
& r2_hidden(sK1(X0,X1),X0) ) )
& ( ! [X3] :
( r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) )
| ~ r1_tarski(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f128]) ).
fof(f151,plain,
! [X0,X1,X2] :
( ! [X3] :
( ( m2_fraenkel(X3,X0,X1,X2)
| ~ m1_subset_1(X3,X2) )
& ( m1_subset_1(X3,X2)
| ~ m2_fraenkel(X3,X0,X1,X2) ) )
| v1_xboole_0(X1)
| ~ m1_fraenkel(X2,X0,X1) ),
inference(nnf_transformation,[],[f114]) ).
fof(f154,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f126]) ).
fof(f155,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f126]) ).
fof(f156,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f126]) ).
fof(f157,plain,
v1_group_1(sK0),
inference(cnf_transformation,[],[f126]) ).
fof(f158,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f126]) ).
fof(f159,plain,
~ r1_tarski(k4_autgroup(sK0),k1_autgroup(sK0)),
inference(cnf_transformation,[],[f126]) ).
fof(f179,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
| r2_hidden(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f180,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
| ~ r2_hidden(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f183,plain,
! [X0] :
( ~ v4_group_1(X0)
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f184,plain,
! [X0] :
( ~ v4_group_1(X0)
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f185,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f187,plain,
! [X2,X0,X1] :
( ~ m1_fraenkel(X2,X0,X1)
| ~ v1_xboole_0(X2) ),
inference(cnf_transformation,[],[f98]) ).
fof(f204,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f243,plain,
! [X2,X3,X0,X1] :
( ~ m2_fraenkel(X3,X0,X1,X2)
| m1_subset_1(X3,X2)
| v1_xboole_0(X1)
| ~ m1_fraenkel(X2,X0,X1) ),
inference(cnf_transformation,[],[f151]) ).
fof(f244,plain,
! [X2,X3,X0,X1] :
( m2_fraenkel(X3,X0,X1,X2)
| ~ m1_subset_1(X3,X2)
| v1_xboole_0(X1)
| ~ m1_fraenkel(X2,X0,X1) ),
inference(cnf_transformation,[],[f151]) ).
fof(f248,plain,
! [X0,X1] :
( ~ v4_group_1(X0)
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f249,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f250,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
fof(f280,plain,
! [X0] :
( v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0))
| ~ l1_group_1(X0) ),
inference(resolution,[],[f204,f185]) ).
fof(f309,plain,
( ~ v1_xboole_0(u1_struct_0(sK0))
| ~ l1_group_1(sK0) ),
inference(resolution,[],[f280,f158]) ).
fof(f328,definition,
( spl24_11
<=> l1_group_1(sK0) ),
introduced(definition,[new_symbols(definition,[spl24_11])],[avatar_definition]) ).
fof(f329,plain,
( ~ l1_group_1(sK0)
| spl24_11 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f331,definition,
( spl24_12
<=> v1_xboole_0(u1_struct_0(sK0)) ),
introduced(definition,[new_symbols(definition,[spl24_12])],[avatar_definition]) ).
fof(f333,plain,
( ~ spl24_11
| ~ spl24_12 ),
inference(avatar_split_clause,[],[f309,f331,f328]) ).
fof(f336,plain,
r2_hidden(sK1(k4_autgroup(sK0),k1_autgroup(sK0)),k4_autgroup(sK0)),
inference(resolution,[],[f179,f159]) ).
fof(f338,plain,
m1_subset_1(sK1(k4_autgroup(sK0),k1_autgroup(sK0)),k4_autgroup(sK0)),
inference(resolution,[],[f336,f249]) ).
fof(f342,plain,
~ r2_hidden(sK1(k4_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0)),
inference(resolution,[],[f180,f159]) ).
fof(f351,plain,
( v1_xboole_0(k1_autgroup(sK0))
| ~ m1_subset_1(sK1(k4_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0)) ),
inference(resolution,[],[f250,f342]) ).
fof(f353,definition,
( spl24_13
<=> m1_subset_1(sK1(k4_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0)) ),
introduced(definition,[new_symbols(definition,[spl24_13])],[avatar_definition]) ).
fof(f354,plain,
( ~ m1_subset_1(sK1(k4_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| spl24_13 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f356,definition,
( spl24_14
<=> v1_xboole_0(k1_autgroup(sK0)) ),
introduced(definition,[new_symbols(definition,[spl24_14])],[avatar_definition]) ).
fof(f357,plain,
( v1_xboole_0(k1_autgroup(sK0))
| ~ spl24_14 ),
inference(avatar_component_clause,[],[f356]) ).
fof(f358,plain,
( ~ spl24_13
| spl24_14 ),
inference(avatar_split_clause,[],[f351,f356,f353]) ).
fof(f484,plain,
( v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ l1_group_1(sK0) ),
inference(resolution,[],[f183,f155]) ).
fof(f500,definition,
( spl24_34
<=> m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0)) ),
introduced(definition,[new_symbols(definition,[spl24_34])],[avatar_definition]) ).
fof(f501,plain,
( m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ spl24_34 ),
inference(avatar_component_clause,[],[f500]) ).
fof(f503,definition,
( spl24_35
<=> v3_group_1(sK0) ),
introduced(definition,[new_symbols(definition,[spl24_35])],[avatar_definition]) ).
fof(f504,plain,
( ~ v3_group_1(sK0)
| spl24_35 ),
inference(avatar_component_clause,[],[f503]) ).
fof(f506,definition,
( spl24_36
<=> v1_group_1(sK0) ),
introduced(definition,[new_symbols(definition,[spl24_36])],[avatar_definition]) ).
fof(f507,plain,
( ~ v1_group_1(sK0)
| spl24_36 ),
inference(avatar_component_clause,[],[f506]) ).
fof(f509,definition,
( spl24_37
<=> v3_struct_0(sK0) ),
introduced(definition,[new_symbols(definition,[spl24_37])],[avatar_definition]) ).
fof(f510,plain,
( v3_struct_0(sK0)
| ~ spl24_37 ),
inference(avatar_component_clause,[],[f509]) ).
fof(f511,plain,
( ~ spl24_11
| spl24_34
| ~ spl24_35
| ~ spl24_36
| spl24_37 ),
inference(avatar_split_clause,[],[f484,f509,f506,f503,f500,f328]) ).
fof(f514,plain,
( $false
| spl24_11 ),
inference(resolution,[],[f329,f154]) ).
fof(f515,plain,
spl24_11,
inference(avatar_contradiction_clause,[],[f514]) ).
fof(f516,plain,
( $false
| spl24_35 ),
inference(resolution,[],[f504,f156]) ).
fof(f517,plain,
spl24_35,
inference(avatar_contradiction_clause,[],[f516]) ).
fof(f518,plain,
( $false
| spl24_36 ),
inference(resolution,[],[f507,f157]) ).
fof(f519,plain,
spl24_36,
inference(avatar_contradiction_clause,[],[f518]) ).
fof(f522,plain,
( ~ v1_xboole_0(k1_autgroup(sK0))
| ~ spl24_34 ),
inference(resolution,[],[f501,f187]) ).
fof(f535,plain,
( v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ l1_group_1(sK0) ),
inference(resolution,[],[f184,f155]) ).
fof(f542,definition,
( spl24_39
<=> m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0)) ),
introduced(definition,[new_symbols(definition,[spl24_39])],[avatar_definition]) ).
fof(f544,plain,
( ~ spl24_11
| spl24_39
| ~ spl24_35
| ~ spl24_36
| spl24_37 ),
inference(avatar_split_clause,[],[f535,f509,f506,f503,f542,f328]) ).
fof(f545,plain,
( $false
| ~ spl24_37 ),
inference(resolution,[],[f510,f158]) ).
fof(f546,plain,
~ spl24_37,
inference(avatar_contradiction_clause,[],[f545]) ).
fof(f619,plain,
! [X0] :
( ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ l1_group_1(sK0) ),
inference(resolution,[],[f248,f155]) ).
fof(f626,definition,
( spl24_44
<=> ! [X0] :
( ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) ) ),
introduced(definition,[new_symbols(definition,[spl24_44])],[avatar_definition]) ).
fof(f627,plain,
( ! [X0] :
( m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) )
| ~ spl24_44 ),
inference(avatar_component_clause,[],[f626]) ).
fof(f628,plain,
( ~ spl24_11
| ~ spl24_35
| ~ spl24_36
| spl24_37
| spl24_44 ),
inference(avatar_split_clause,[],[f619,f626,f509,f506,f503,f328]) ).
fof(f630,plain,
( ! [X0] :
( ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| m1_subset_1(X0,k1_autgroup(sK0))
| v1_xboole_0(u1_struct_0(sK0))
| ~ m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0)) )
| ~ spl24_44 ),
inference(resolution,[],[f627,f243]) ).
fof(f638,definition,
( spl24_46
<=> ! [X0] :
( ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| m1_subset_1(X0,k1_autgroup(sK0)) ) ),
introduced(definition,[new_symbols(definition,[spl24_46])],[avatar_definition]) ).
fof(f639,plain,
( ! [X0] :
( ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| m1_subset_1(X0,k1_autgroup(sK0)) )
| ~ spl24_46 ),
inference(avatar_component_clause,[],[f638]) ).
fof(f640,plain,
( ~ spl24_34
| spl24_12
| spl24_46
| ~ spl24_44 ),
inference(avatar_split_clause,[],[f630,f626,f638,f331,f500]) ).
fof(f670,plain,
( ! [X0] :
( m1_subset_1(X0,k1_autgroup(sK0))
| ~ m1_subset_1(X0,k4_autgroup(sK0))
| v1_xboole_0(u1_struct_0(sK0))
| ~ m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0)) )
| ~ spl24_46 ),
inference(resolution,[],[f639,f244]) ).
fof(f672,definition,
( spl24_52
<=> ! [X0] :
( m1_subset_1(X0,k1_autgroup(sK0))
| ~ m1_subset_1(X0,k4_autgroup(sK0)) ) ),
introduced(definition,[new_symbols(definition,[spl24_52])],[avatar_definition]) ).
fof(f673,plain,
( ! [X0] :
( m1_subset_1(X0,k1_autgroup(sK0))
| ~ m1_subset_1(X0,k4_autgroup(sK0)) )
| ~ spl24_52 ),
inference(avatar_component_clause,[],[f672]) ).
fof(f674,plain,
( ~ spl24_39
| spl24_12
| spl24_52
| ~ spl24_46 ),
inference(avatar_split_clause,[],[f670,f638,f672,f331,f542]) ).
fof(f835,plain,
( ~ m1_subset_1(sK1(k4_autgroup(sK0),k1_autgroup(sK0)),k4_autgroup(sK0))
| spl24_13
| ~ spl24_52 ),
inference(resolution,[],[f673,f354]) ).
fof(f841,definition,
( spl24_88
<=> m1_subset_1(sK1(k4_autgroup(sK0),k1_autgroup(sK0)),k4_autgroup(sK0)) ),
introduced(definition,[new_symbols(definition,[spl24_88])],[avatar_definition]) ).
fof(f842,plain,
( ~ m1_subset_1(sK1(k4_autgroup(sK0),k1_autgroup(sK0)),k4_autgroup(sK0))
| spl24_88 ),
inference(avatar_component_clause,[],[f841]) ).
fof(f844,plain,
( ~ spl24_88
| spl24_13
| ~ spl24_52 ),
inference(avatar_split_clause,[],[f835,f672,f353,f841]) ).
fof(f919,plain,
( $false
| spl24_88 ),
inference(resolution,[],[f842,f338]) ).
fof(f922,plain,
spl24_88,
inference(avatar_contradiction_clause,[],[f919]) ).
fof(f924,plain,
( $false
| ~ spl24_14
| ~ spl24_34 ),
inference(resolution,[],[f357,f522]) ).
fof(f925,plain,
( ~ spl24_14
| ~ spl24_34 ),
inference(avatar_contradiction_clause,[],[f924]) ).
cnf(s7,plain,
( ~ spl24_11
| ~ spl24_12 ),
inference(sat_conversion,[],[f333]) ).
cnf(s9,plain,
( ~ spl24_13
| spl24_14 ),
inference(sat_conversion,[],[f358]) ).
cnf(s23,plain,
( ~ spl24_11
| spl24_34
| ~ spl24_35
| ~ spl24_36
| spl24_37 ),
inference(sat_conversion,[],[f511]) ).
cnf(s25,plain,
spl24_11,
inference(sat_conversion,[],[f515]) ).
cnf(s26,plain,
spl24_35,
inference(sat_conversion,[],[f517]) ).
cnf(s27,plain,
spl24_36,
inference(sat_conversion,[],[f519]) ).
cnf(s30,plain,
( ~ spl24_11
| ~ spl24_35
| ~ spl24_36
| spl24_37
| spl24_39 ),
inference(sat_conversion,[],[f544]) ).
cnf(s31,plain,
~ spl24_37,
inference(sat_conversion,[],[f546]) ).
cnf(s36,plain,
( ~ spl24_11
| ~ spl24_35
| ~ spl24_36
| spl24_37
| spl24_44 ),
inference(sat_conversion,[],[f628]) ).
cnf(s38,plain,
( spl24_12
| ~ spl24_34
| ~ spl24_44
| spl24_46 ),
inference(sat_conversion,[],[f640]) ).
cnf(s44,plain,
( spl24_12
| ~ spl24_39
| ~ spl24_46
| spl24_52 ),
inference(sat_conversion,[],[f674]) ).
cnf(s67,plain,
( spl24_13
| ~ spl24_52
| ~ spl24_88 ),
inference(sat_conversion,[],[f844]) ).
cnf(s76,plain,
spl24_88,
inference(sat_conversion,[],[f922]) ).
cnf(s78,plain,
( ~ spl24_14
| ~ spl24_34 ),
inference(sat_conversion,[],[f925]) ).
cnf(s79,plain,
( spl24_13
| ~ spl24_52 ),
inference(rat,[],[s67,s76]) ).
cnf(s81,plain,
( ~ spl24_11
| ~ spl24_35
| ~ spl24_36
| spl24_39 ),
inference(rat,[],[s30,s31]) ).
cnf(s83,plain,
spl24_44,
inference(rat,[],[s36,s26,s31,s27,s25]) ).
cnf(s84,plain,
spl24_39,
inference(rat,[],[s81,s26,s27,s25]) ).
cnf(s85,plain,
spl24_34,
inference(rat,[],[s23,s31,s27,s26,s25]) ).
cnf(s86,plain,
~ spl24_14,
inference(rat,[],[s78,s85]) ).
cnf(s91,plain,
~ spl24_13,
inference(rat,[],[s9,s86]) ).
cnf(s92,plain,
~ spl24_52,
inference(rat,[],[s79,s91]) ).
cnf(s97,plain,
~ spl24_12,
inference(rat,[],[s7,s25]) ).
cnf(s98,plain,
~ spl24_46,
inference(rat,[],[s44,s92,s84,s97]) ).
cnf(s100,plain,
$false,
inference(rat,[],[s38,s85,s83,s98,s97]) ).
fof(f926,plain,
$false,
inference(avatar_sat_refutation,[],[s100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP623+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 10:16:01 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.19/1.33 % (3340467)Detected formulas, will run a generic FOF schedule.
% 3.19/1.33 % (3340684)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2333733313:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.19/1.33 % (3340678)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=1023063765:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.19/1.33 % (3340680)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=4113087988:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.19/1.33 % (3340685)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3034372184:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.19/1.33 % (3340682)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2213896184:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.19/1.33 % (3340677)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=3776593685:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.19/1.33 % (3340682)Refutation not found, incomplete strategy
% 3.19/1.33 % (3340682)------------------------------
% 3.19/1.33 % (3340682)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.19/1.33 % (3340682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.19/1.33 % (3340682)CaDiCaL version: 2.1.3
% 3.19/1.33 % (3340682)Termination reason: Refutation not found, incomplete strategy
% 3.19/1.33 % (3340682)Time elapsed: 0.001 s
% 3.19/1.33 % (3340682)Peak memory usage: 88 MB
% 3.19/1.33 % (3340684)Instruction limit reached!
% 3.19/1.33 % (3340684)------------------------------
% 3.19/1.33 % (3340684)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.19/1.33 % (3340684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.19/1.33 % (3340684)CaDiCaL version: 2.1.3
% 3.19/1.33 % (3340684)Termination reason: Instruction limit
% 3.19/1.33 % (3340684)Termination phase: Saturation
% 3.19/1.33 % (3340684)Time elapsed: 0.039 s
% 3.19/1.33 % (3340684)Peak memory usage: 88 MB
% 3.19/1.33 % (3340684)Instructions burned: 122 (million)
% 3.19/1.33 % (3340687)dis-21_1_sil=8000:lcm=predicate:random_seed=1171174937: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)
% 3.19/1.33 % (3340687)First to succeed.
% 3.19/1.33 % (3340687)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3340467"
% 3.19/1.33 % (3340685)Instruction limit reached!
% 3.19/1.33 % (3340685)------------------------------
% 3.19/1.33 % (3340685)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.19/1.33 % (3340685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.19/1.33 % (3340685)CaDiCaL version: 2.1.3
% 3.19/1.33 % (3340685)Termination reason: Instruction limit
% 3.19/1.33 % (3340685)Termination phase: Saturation
% 3.19/1.33 % (3340685)Time elapsed: 0.056 s
% 3.19/1.33 % (3340685)Peak memory usage: 88 MB
% 3.19/1.33 % (3340685)Instructions burned: 140 (million)
% 3.19/1.33 % (3340757)lrs+10_1_sil=8000:sp=occurrence:random_seed=3882902987:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.19/1.33 % (3340780)lrs+10_1_sil=32000:urr=on:br=off:random_seed=82267233:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.19/1.33 % (3340780)Refutation not found, incomplete strategy
% 3.19/1.33 % (3340780)------------------------------
% 3.19/1.33 % (3340780)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.19/1.33 % (3340780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.19/1.33 % (3340780)CaDiCaL version: 2.1.3
% 3.19/1.33 % (3340780)Termination reason: Refutation not found, incomplete strategy
% 3.19/1.33 % (3340780)Time elapsed: 0.002 s
% 3.19/1.33 % (3340780)Peak memory usage: 88 MB
% 3.19/1.33 % (3340780)Instructions burned: 1 (million)
% 3.19/1.33 % (3340757)Instruction limit reached!
% 3.19/1.33 % (3340757)------------------------------
% 3.19/1.33 % (3340757)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.19/1.33 % (3340757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.19/1.33 % (3340757)CaDiCaL version: 2.1.3
% 3.19/1.33 % (3340757)Termination reason: Instruction limit
% 3.19/1.33 % (3340757)Termination phase: Saturation
% 3.19/1.33 % (3340757)Time elapsed: 0.102 s
% 3.19/1.33 % (3340757)Peak memory usage: 91 MB
% 3.19/1.33 % (3340757)Instructions burned: 288 (million)
% 3.19/1.33 % (3340682)------------------------------
% 3.19/1.33 % (3340682)------------------------------
% 3.19/1.33 % (3340687)Refutation found. Thanks to Tanya!
% 3.19/1.33 % SZS status Theorem for theBenchmark
% 3.19/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.75/1.42 % (3340687)------------------------------
% 3.75/1.42 % (3340687)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.42 % (3340687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.42 % (3340687)CaDiCaL version: 2.1.3
% 3.75/1.42 % (3340687)Termination reason: Refutation
% 3.75/1.42 % (3340687)Time elapsed: 0.013 s
% 3.75/1.42 % (3340687)Peak memory usage: 89 MB
% 3.75/1.42 % (3340687)Instructions burned: 16 (million)
% 3.75/1.42 % (3340687)------------------------------
% 3.75/1.42 % (3340687)------------------------------
% 3.75/1.42 % (3340467)Success in time 0.468 s
% 3.75/1.42 % Vampire exiting
%------------------------------------------------------------------------------