%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n026.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 10:18:16 AM UTC 2026
% Result : Theorem 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 90 ( 19 unt; 2 def)
% Number of atoms : 280 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 317 ( 127 ~; 136 |; 34 &)
% ( 7 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 15 usr; 3 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 90 !; 2 ?)
% 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,
l1_group_1(sK0),
inference(cnf_transformation,[],[f73]) ).
fof(f127,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f73]) ).
fof(f128,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f73]) ).
fof(f129,plain,
v1_group_1(sK0),
inference(cnf_transformation,[],[f73]) ).
fof(f130,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f73]) ).
fof(f131,plain,
~ r1_tarski(k4_autgroup(sK0),k1_autgroup(sK0)),
inference(cnf_transformation,[],[f73]) ).
fof(f143,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
| r2_hidden(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f144,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
| ~ r2_hidden(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f147,plain,
! [X0] :
( ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f94]) ).
fof(f148,plain,
! [X0] :
( ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f96]) ).
fof(f149,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f151,plain,
! [X2,X0,X1] :
( ~ m1_fraenkel(X2,X0,X1)
| ~ v1_xboole_0(X2) ),
inference(cnf_transformation,[],[f98]) ).
fof(f168,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f207,plain,
! [X2,X3,X0,X1] :
( m2_fraenkel(X3,X0,X1,X2)
| v1_xboole_0(X1)
| ~ m1_subset_1(X3,X2)
| ~ m1_fraenkel(X2,X0,X1) ),
inference(cnf_transformation,[],[f114]) ).
fof(f208,plain,
! [X2,X3,X0,X1] :
( ~ m2_fraenkel(X3,X0,X1,X2)
| v1_xboole_0(X1)
| m1_subset_1(X3,X2)
| ~ m1_fraenkel(X2,X0,X1) ),
inference(cnf_transformation,[],[f114]) ).
fof(f212,plain,
! [X0,X1] :
( ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ~ 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)) ),
inference(cnf_transformation,[],[f116]) ).
fof(f213,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f214,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f119]) ).
fof(f241,plain,
! [X0] :
( v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0))
| ~ l1_group_1(X0) ),
inference(resolution,[],[f168,f149]) ).
fof(f278,plain,
r2_hidden(sK1(k4_autgroup(sK0),k1_autgroup(sK0)),k4_autgroup(sK0)),
inference(resolution,[],[f143,f131]) ).
fof(f280,plain,
m1_subset_1(sK1(k4_autgroup(sK0),k1_autgroup(sK0)),k4_autgroup(sK0)),
inference(resolution,[],[f278,f213]) ).
fof(f284,plain,
~ r2_hidden(sK1(k4_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0)),
inference(resolution,[],[f144,f131]) ).
fof(f292,plain,
( ~ m1_subset_1(sK1(k4_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| v1_xboole_0(k1_autgroup(sK0)) ),
inference(resolution,[],[f214,f284]) ).
fof(f294,definition,
( spl23_4
<=> v1_xboole_0(k1_autgroup(sK0)) ),
introduced(definition,[new_symbols(definition,[spl23_4])],[avatar_definition]) ).
fof(f298,definition,
( spl23_5
<=> m1_subset_1(sK1(k4_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0)) ),
introduced(definition,[new_symbols(definition,[spl23_5])],[avatar_definition]) ).
fof(f300,plain,
( ~ m1_subset_1(sK1(k4_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| spl23_5 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f301,plain,
( spl23_4
| ~ spl23_5 ),
inference(avatar_split_clause,[],[f292,f298,f294]) ).
fof(f364,plain,
( ~ v1_xboole_0(u1_struct_0(sK0))
| ~ l1_group_1(sK0) ),
inference(resolution,[],[f241,f130]) ).
fof(f370,plain,
~ v1_xboole_0(u1_struct_0(sK0)),
inference(forward_subsumption_resolution,[],[f364,f126]) ).
fof(f381,plain,
( ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(sK0)
| v3_struct_0(sK0)
| m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0)) ),
inference(resolution,[],[f147,f127]) ).
fof(f384,plain,
( ~ v3_group_1(sK0)
| ~ v1_group_1(sK0)
| v3_struct_0(sK0)
| m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f381,f126]) ).
fof(f386,plain,
( ~ v1_group_1(sK0)
| v3_struct_0(sK0)
| m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f384,f128]) ).
fof(f388,plain,
( v3_struct_0(sK0)
| m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f386,f129]) ).
fof(f390,plain,
m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0)),
inference(forward_subsumption_resolution,[],[f388,f130]) ).
fof(f391,plain,
~ v1_xboole_0(k1_autgroup(sK0)),
inference(resolution,[],[f390,f151]) ).
fof(f392,plain,
~ spl23_4,
inference(avatar_split_clause,[],[f391,f294]) ).
fof(f393,plain,
( ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(sK0)
| v3_struct_0(sK0)
| m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0)) ),
inference(resolution,[],[f148,f127]) ).
fof(f396,plain,
( ~ v3_group_1(sK0)
| ~ v1_group_1(sK0)
| v3_struct_0(sK0)
| m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f393,f126]) ).
fof(f398,plain,
( ~ v1_group_1(sK0)
| v3_struct_0(sK0)
| m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f396,f128]) ).
fof(f400,plain,
( v3_struct_0(sK0)
| m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f398,f129]) ).
fof(f402,plain,
m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0)),
inference(forward_subsumption_resolution,[],[f400,f130]) ).
fof(f443,plain,
! [X0] :
( ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v1_group_1(sK0)
| v3_struct_0(sK0)
| ~ 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)) ),
inference(resolution,[],[f212,f127]) ).
fof(f446,plain,
! [X0] :
( ~ v3_group_1(sK0)
| ~ v1_group_1(sK0)
| v3_struct_0(sK0)
| ~ 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)) ),
inference(forward_subsumption_resolution,[],[f443,f126]) ).
fof(f448,plain,
! [X0] :
( ~ v1_group_1(sK0)
| v3_struct_0(sK0)
| ~ 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)) ),
inference(forward_subsumption_resolution,[],[f446,f128]) ).
fof(f450,plain,
! [X0] :
( v3_struct_0(sK0)
| ~ 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)) ),
inference(forward_subsumption_resolution,[],[f448,f129]) ).
fof(f452,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)) ),
inference(forward_subsumption_resolution,[],[f450,f130]) ).
fof(f454,plain,
! [X0] :
( ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| v1_xboole_0(u1_struct_0(sK0))
| m1_subset_1(X0,k1_autgroup(sK0))
| ~ m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0)) ),
inference(resolution,[],[f452,f208]) ).
fof(f457,plain,
! [X0] :
( ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| m1_subset_1(X0,k1_autgroup(sK0))
| ~ m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f454,f370]) ).
fof(f460,plain,
! [X0] :
( ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| m1_subset_1(X0,k1_autgroup(sK0)) ),
inference(forward_subsumption_resolution,[],[f457,f390]) ).
fof(f465,plain,
! [X0] :
( m1_subset_1(X0,k1_autgroup(sK0))
| v1_xboole_0(u1_struct_0(sK0))
| ~ m1_subset_1(X0,k4_autgroup(sK0))
| ~ m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0)) ),
inference(resolution,[],[f460,f207]) ).
fof(f466,plain,
! [X0] :
( m1_subset_1(X0,k1_autgroup(sK0))
| ~ m1_subset_1(X0,k4_autgroup(sK0))
| ~ m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f465,f370]) ).
fof(f468,plain,
! [X0] :
( m1_subset_1(X0,k1_autgroup(sK0))
| ~ m1_subset_1(X0,k4_autgroup(sK0)) ),
inference(forward_subsumption_resolution,[],[f466,f402]) ).
fof(f470,plain,
( ~ m1_subset_1(sK1(k4_autgroup(sK0),k1_autgroup(sK0)),k4_autgroup(sK0))
| spl23_5 ),
inference(resolution,[],[f468,f300]) ).
fof(f471,plain,
( $false
| spl23_5 ),
inference(forward_subsumption_resolution,[],[f470,f280]) ).
fof(f472,plain,
spl23_5,
inference(avatar_contradiction_clause,[],[f471]) ).
cnf(s3,plain,
( spl23_4
| ~ spl23_5 ),
inference(sat_conversion,[],[f301]) ).
cnf(s7,plain,
~ spl23_4,
inference(sat_conversion,[],[f392]) ).
cnf(s8,plain,
spl23_5,
inference(sat_conversion,[],[f472]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s3,s8,s7]) ).
fof(f473,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----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 SAT
% 0.14/0.40 % Computer : n026.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 : Sun Sep 27 10:12:57 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.44 Running first-order model finding
% 0.14/0.44 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.49 % (2608729)Will run a generic schedule for satisfiability detection.
% 0.19/0.49 % (2608747)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2256339573:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.49 % (2608743)% WARNING: option uhcvi not known.
% 0.19/0.49 % (2608745)dis+10_1_sil=32000:sp=arity:random_seed=2511962710:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.49 % (2608743)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=153844033:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.49 % (2608746)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2188557844:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.49 % (2608742)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=286879069_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.49 % (2608744)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3291866122:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.49 % (2608748)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3151687799:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.49 % TRYING [1]
% 0.19/0.49 % TRYING [2]
% 0.19/0.49 % TRYING [3]
% 0.19/0.49 % (2608746) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2608729-2608746"...
% 0.19/0.49 % (2608746)...printing done.
% 0.19/0.49 % (2608746)Refutation found. Thanks to Tanya!
% 0.19/0.49 % SZS status Theorem for theBenchmark
% 0.19/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.50 % (2608746)------------------------------
% 0.19/0.50 % (2608746)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.50 % (2608746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.50 % (2608746)CaDiCaL version: 2.1.3
% 0.19/0.50 % (2608746)Termination reason: Refutation
% 0.19/0.50 % (2608746)Time elapsed: 0.010 s
% 0.19/0.50 % (2608746)Peak memory usage: 12 MB
% 0.19/0.50 % (2608746)Instructions burned: 14 (million)
% 0.19/0.50 % (2608729)Success in time 0.047 s
% 0.19/0.50 % Vampire exiting
%------------------------------------------------------------------------------