%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP623+3 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 17.87s 4.65s
% Output : Refutation 21.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of formulae : 110 ( 15 unt; 4 def)
% Number of atoms : 408 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 493 ( 195 ~; 220 |; 51 &)
% ( 13 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 17 usr; 5 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 123 ( 0 sgn 119 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( r2_hidden(X2,X0)
=> r2_hidden(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f480,axiom,
! [X0,X1] :
( ( ~ v1_xboole_0(X0)
=> ( m1_subset_1(X1,X0)
<=> r2_hidden(X1,X0) ) )
& ( v1_xboole_0(X0)
=> ( m1_subset_1(X1,X0)
<=> v1_xboole_0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
fof(f675,axiom,
! [X0,X1] :
( r2_hidden(X0,X1)
=> m1_subset_1(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f2933,axiom,
! [X0,X1,X2] :
( m1_fraenkel(X2,X0,X1)
=> ( ~ v1_xboole_0(X2)
& v1_fraenkel(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_fraenkel) ).
fof(f2937,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/sandbox/benchmark/theBenchmark.p',redefinition_m2_fraenkel) ).
fof(f6422,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& l1_struct_0(X0) )
=> ~ v1_xboole_0(u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f7466,axiom,
! [X0] :
( l1_group_1(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(f12867,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/sandbox/benchmark/theBenchmark.p',dt_k1_autgroup) ).
fof(f12870,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/sandbox/benchmark/theBenchmark.p',dt_k4_autgroup) ).
fof(f12892,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/sandbox/benchmark/theBenchmark.p',t13_autgroup) ).
fof(f12893,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/sandbox/benchmark/theBenchmark.p',t14_autgroup) ).
fof(f12894,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)],[f12893]) ).
fof(f12934,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,[],[f12867]) ).
fof(f12935,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,[],[f12934]) ).
fof(f12940,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,[],[f12870]) ).
fof(f12941,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,[],[f12940]) ).
fof(f12982,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,[],[f12892]) ).
fof(f12983,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,[],[f12982]) ).
fof(f12984,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,[],[f12894]) ).
fof(f12985,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,[],[f12984]) ).
fof(f12987,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,[],[f2937]) ).
fof(f12988,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,[],[f12987]) ).
fof(f12993,plain,
! [X0,X1,X2] :
( ( ~ v1_xboole_0(X2)
& v1_fraenkel(X2) )
| ~ m1_fraenkel(X2,X0,X1) ),
inference(ennf_transformation,[],[f2933]) ).
fof(f13095,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f675]) ).
fof(f13185,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( r2_hidden(X2,X1)
| ~ r2_hidden(X2,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f13443,plain,
! [X0,X1] :
( ( ( m1_subset_1(X1,X0)
<=> r2_hidden(X1,X0) )
| v1_xboole_0(X0) )
& ( ( m1_subset_1(X1,X0)
<=> v1_xboole_0(X1) )
| ~ v1_xboole_0(X0) ) ),
inference(ennf_transformation,[],[f480]) ).
fof(f14362,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f7466]) ).
fof(f14371,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(ennf_transformation,[],[f6422]) ).
fof(f14372,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(flattening,[],[f14371]) ).
fof(f16149,plain,
( ~ r1_tarski(k4_autgroup(sK31),k1_autgroup(sK31))
& ~ v3_struct_0(sK31)
& v1_group_1(sK31)
& v3_group_1(sK31)
& v4_group_1(sK31)
& l1_group_1(sK31) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(X0,sK31)],[f12985]) ).
fof(f16150,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,[],[f12988]) ).
fof(f16211,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,[],[f13185]) ).
fof(f16212,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,[],[f16211]) ).
fof(f16213,plain,
! [X0,X1] :
( ( r1_tarski(X0,X1)
| ( ~ r2_hidden(sK72(X0,X1),X1)
& r2_hidden(sK72(X0,X1),X0) ) )
& ( ! [X3] :
( r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) )
| ~ r1_tarski(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(X2,sK72(X0,X1))],[f16212]) ).
fof(f16278,plain,
! [X0,X1] :
( ( ( ( m1_subset_1(X1,X0)
| ~ r2_hidden(X1,X0) )
& ( r2_hidden(X1,X0)
| ~ m1_subset_1(X1,X0) ) )
| v1_xboole_0(X0) )
& ( ( ( m1_subset_1(X1,X0)
| ~ v1_xboole_0(X1) )
& ( v1_xboole_0(X1)
| ~ m1_subset_1(X1,X0) ) )
| ~ v1_xboole_0(X0) ) ),
inference(nnf_transformation,[],[f13443]) ).
fof(f17114,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(cnf_transformation,[],[f12935]) ).
fof(f17123,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(cnf_transformation,[],[f12941]) ).
fof(f17192,plain,
! [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))
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f12983]) ).
fof(f17193,plain,
l1_group_1(sK31),
inference(cnf_transformation,[],[f16149]) ).
fof(f17194,plain,
v4_group_1(sK31),
inference(cnf_transformation,[],[f16149]) ).
fof(f17195,plain,
v3_group_1(sK31),
inference(cnf_transformation,[],[f16149]) ).
fof(f17196,plain,
v1_group_1(sK31),
inference(cnf_transformation,[],[f16149]) ).
fof(f17197,plain,
~ v3_struct_0(sK31),
inference(cnf_transformation,[],[f16149]) ).
fof(f17198,plain,
~ r1_tarski(k4_autgroup(sK31),k1_autgroup(sK31)),
inference(cnf_transformation,[],[f16149]) ).
fof(f17200,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,[],[f16150]) ).
fof(f17201,plain,
! [X2,X3,X0,X1] :
( ~ m1_subset_1(X3,X2)
| m2_fraenkel(X3,X0,X1,X2)
| v1_xboole_0(X1)
| ~ m1_fraenkel(X2,X0,X1) ),
inference(cnf_transformation,[],[f16150]) ).
fof(f17208,plain,
! [X2,X0,X1] :
( ~ v1_xboole_0(X2)
| ~ m1_fraenkel(X2,X0,X1) ),
inference(cnf_transformation,[],[f12993]) ).
fof(f17312,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f13095]) ).
fof(f17448,plain,
! [X0,X1] :
( r2_hidden(sK72(X0,X1),X0)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f16213]) ).
fof(f17449,plain,
! [X0,X1] :
( ~ r2_hidden(sK72(X0,X1),X1)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f16213]) ).
fof(f17806,plain,
! [X0,X1] :
( r2_hidden(X1,X0)
| ~ m1_subset_1(X1,X0)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f16278]) ).
fof(f18989,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f14362]) ).
fof(f19000,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(cnf_transformation,[],[f14372]) ).
fof(f23287,plain,
! [X0,X1] :
( ~ m1_subset_1(sK72(X0,X1),X1)
| v1_xboole_0(X1)
| r1_tarski(X0,X1) ),
inference(resolution,[],[f17806,f17449]) ).
fof(f23360,plain,
! [X0,X1] :
( m1_subset_1(sK72(X0,X1),X0)
| r1_tarski(X0,X1) ),
inference(resolution,[],[f17312,f17448]) ).
fof(f23365,plain,
! [X2,X3,X0,X1] :
( ~ m1_fraenkel(X0,X2,X3)
| m2_fraenkel(sK72(X0,X1),X2,X3,X0)
| v1_xboole_0(X3)
| r1_tarski(X0,X1) ),
inference(resolution,[],[f23360,f17201]) ).
fof(f23367,plain,
! [X0,X1] :
( ~ v1_group_1(X0)
| v1_xboole_0(u1_struct_0(X0))
| r1_tarski(k4_autgroup(X0),X1)
| v3_struct_0(X0)
| m2_fraenkel(sK72(k4_autgroup(X0),X1),u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(resolution,[],[f23365,f17123]) ).
fof(f23369,plain,
! [X0] :
( v1_xboole_0(u1_struct_0(sK31))
| r1_tarski(k4_autgroup(sK31),X0)
| v3_struct_0(sK31)
| m2_fraenkel(sK72(k4_autgroup(sK31),X0),u1_struct_0(sK31),u1_struct_0(sK31),k4_autgroup(sK31))
| ~ v3_group_1(sK31)
| ~ v4_group_1(sK31)
| ~ l1_group_1(sK31) ),
inference(resolution,[],[f23367,f17196]) ).
fof(f23370,plain,
! [X0] :
( v1_xboole_0(u1_struct_0(sK31))
| r1_tarski(k4_autgroup(sK31),X0)
| m2_fraenkel(sK72(k4_autgroup(sK31),X0),u1_struct_0(sK31),u1_struct_0(sK31),k4_autgroup(sK31))
| ~ v3_group_1(sK31)
| ~ v4_group_1(sK31)
| ~ l1_group_1(sK31) ),
inference(forward_subsumption_resolution,[],[f23369,f17197]) ).
fof(f23371,plain,
! [X0] :
( v1_xboole_0(u1_struct_0(sK31))
| r1_tarski(k4_autgroup(sK31),X0)
| m2_fraenkel(sK72(k4_autgroup(sK31),X0),u1_struct_0(sK31),u1_struct_0(sK31),k4_autgroup(sK31))
| ~ v4_group_1(sK31)
| ~ l1_group_1(sK31) ),
inference(forward_subsumption_resolution,[],[f23370,f17195]) ).
fof(f23372,plain,
! [X0] :
( v1_xboole_0(u1_struct_0(sK31))
| r1_tarski(k4_autgroup(sK31),X0)
| m2_fraenkel(sK72(k4_autgroup(sK31),X0),u1_struct_0(sK31),u1_struct_0(sK31),k4_autgroup(sK31))
| ~ l1_group_1(sK31) ),
inference(forward_subsumption_resolution,[],[f23371,f17194]) ).
fof(f23373,plain,
! [X0] :
( v1_xboole_0(u1_struct_0(sK31))
| r1_tarski(k4_autgroup(sK31),X0)
| m2_fraenkel(sK72(k4_autgroup(sK31),X0),u1_struct_0(sK31),u1_struct_0(sK31),k4_autgroup(sK31)) ),
inference(forward_subsumption_resolution,[],[f23372,f17193]) ).
fof(f23375,definition,
( spl619_33
<=> ! [X0] :
( r1_tarski(k4_autgroup(sK31),X0)
| m2_fraenkel(sK72(k4_autgroup(sK31),X0),u1_struct_0(sK31),u1_struct_0(sK31),k4_autgroup(sK31)) ) ),
introduced(definition,[new_symbols(definition,[spl619_33])],[avatar_definition]) ).
fof(f23376,plain,
( ! [X0] :
( m2_fraenkel(sK72(k4_autgroup(sK31),X0),u1_struct_0(sK31),u1_struct_0(sK31),k4_autgroup(sK31))
| r1_tarski(k4_autgroup(sK31),X0) )
| ~ spl619_33 ),
inference(avatar_component_clause,[],[f23375]) ).
fof(f23378,definition,
( spl619_34
<=> v1_xboole_0(u1_struct_0(sK31)) ),
introduced(definition,[new_symbols(definition,[spl619_34])],[avatar_definition]) ).
fof(f23379,plain,
( v1_xboole_0(u1_struct_0(sK31))
| ~ spl619_34 ),
inference(avatar_component_clause,[],[f23378]) ).
fof(f23380,plain,
( spl619_33
| spl619_34 ),
inference(avatar_split_clause,[],[f23373,f23378,f23375]) ).
fof(f23381,plain,
( ! [X0] :
( r1_tarski(k4_autgroup(sK31),X0)
| m2_fraenkel(sK72(k4_autgroup(sK31),X0),u1_struct_0(sK31),u1_struct_0(sK31),k1_autgroup(sK31))
| v3_struct_0(sK31)
| ~ v1_group_1(sK31)
| ~ v3_group_1(sK31)
| ~ v4_group_1(sK31)
| ~ l1_group_1(sK31) )
| ~ spl619_33 ),
inference(resolution,[],[f23376,f17192]) ).
fof(f23401,plain,
( ! [X0] :
( r1_tarski(k4_autgroup(sK31),X0)
| m2_fraenkel(sK72(k4_autgroup(sK31),X0),u1_struct_0(sK31),u1_struct_0(sK31),k1_autgroup(sK31))
| ~ v1_group_1(sK31)
| ~ v3_group_1(sK31)
| ~ v4_group_1(sK31)
| ~ l1_group_1(sK31) )
| ~ spl619_33 ),
inference(forward_subsumption_resolution,[],[f23381,f17197]) ).
fof(f23402,plain,
( ! [X0] :
( r1_tarski(k4_autgroup(sK31),X0)
| m2_fraenkel(sK72(k4_autgroup(sK31),X0),u1_struct_0(sK31),u1_struct_0(sK31),k1_autgroup(sK31))
| ~ v3_group_1(sK31)
| ~ v4_group_1(sK31)
| ~ l1_group_1(sK31) )
| ~ spl619_33 ),
inference(forward_subsumption_resolution,[],[f23401,f17196]) ).
fof(f23403,plain,
( ! [X0] :
( r1_tarski(k4_autgroup(sK31),X0)
| m2_fraenkel(sK72(k4_autgroup(sK31),X0),u1_struct_0(sK31),u1_struct_0(sK31),k1_autgroup(sK31))
| ~ v4_group_1(sK31)
| ~ l1_group_1(sK31) )
| ~ spl619_33 ),
inference(forward_subsumption_resolution,[],[f23402,f17195]) ).
fof(f23404,plain,
( ! [X0] :
( r1_tarski(k4_autgroup(sK31),X0)
| m2_fraenkel(sK72(k4_autgroup(sK31),X0),u1_struct_0(sK31),u1_struct_0(sK31),k1_autgroup(sK31))
| ~ l1_group_1(sK31) )
| ~ spl619_33 ),
inference(forward_subsumption_resolution,[],[f23403,f17194]) ).
fof(f23405,plain,
( ! [X0] :
( m2_fraenkel(sK72(k4_autgroup(sK31),X0),u1_struct_0(sK31),u1_struct_0(sK31),k1_autgroup(sK31))
| r1_tarski(k4_autgroup(sK31),X0) )
| ~ spl619_33 ),
inference(forward_subsumption_resolution,[],[f23404,f17193]) ).
fof(f23409,plain,
( ! [X0] :
( r1_tarski(k4_autgroup(sK31),X0)
| m1_subset_1(sK72(k4_autgroup(sK31),X0),k1_autgroup(sK31))
| v1_xboole_0(u1_struct_0(sK31))
| ~ m1_fraenkel(k1_autgroup(sK31),u1_struct_0(sK31),u1_struct_0(sK31)) )
| ~ spl619_33 ),
inference(resolution,[],[f23405,f17200]) ).
fof(f23412,definition,
( spl619_39
<=> m1_fraenkel(k1_autgroup(sK31),u1_struct_0(sK31),u1_struct_0(sK31)) ),
introduced(definition,[new_symbols(definition,[spl619_39])],[avatar_definition]) ).
fof(f23413,plain,
( ~ m1_fraenkel(k1_autgroup(sK31),u1_struct_0(sK31),u1_struct_0(sK31))
| spl619_39 ),
inference(avatar_component_clause,[],[f23412]) ).
fof(f23416,definition,
( spl619_40
<=> ! [X0] :
( r1_tarski(k4_autgroup(sK31),X0)
| m1_subset_1(sK72(k4_autgroup(sK31),X0),k1_autgroup(sK31)) ) ),
introduced(definition,[new_symbols(definition,[spl619_40])],[avatar_definition]) ).
fof(f23417,plain,
( ! [X0] :
( m1_subset_1(sK72(k4_autgroup(sK31),X0),k1_autgroup(sK31))
| r1_tarski(k4_autgroup(sK31),X0) )
| ~ spl619_40 ),
inference(avatar_component_clause,[],[f23416]) ).
fof(f23418,plain,
( ~ spl619_39
| spl619_34
| spl619_40
| ~ spl619_33 ),
inference(avatar_split_clause,[],[f23409,f23375,f23416,f23378,f23412]) ).
fof(f23439,plain,
( v3_struct_0(sK31)
| ~ l1_struct_0(sK31)
| ~ spl619_34 ),
inference(resolution,[],[f23379,f19000]) ).
fof(f23441,plain,
( ~ l1_struct_0(sK31)
| ~ spl619_34 ),
inference(forward_subsumption_resolution,[],[f23439,f17197]) ).
fof(f23443,plain,
( ~ l1_group_1(sK31)
| ~ spl619_34 ),
inference(resolution,[],[f23441,f18989]) ).
fof(f23445,plain,
( $false
| ~ spl619_34 ),
inference(forward_subsumption_resolution,[],[f23443,f17193]) ).
fof(f23446,plain,
~ spl619_34,
inference(avatar_contradiction_clause,[],[f23445]) ).
fof(f23497,plain,
( v3_struct_0(sK31)
| ~ v1_group_1(sK31)
| ~ v3_group_1(sK31)
| ~ v4_group_1(sK31)
| ~ l1_group_1(sK31)
| spl619_39 ),
inference(resolution,[],[f23413,f17114]) ).
fof(f23499,plain,
( ~ v1_group_1(sK31)
| ~ v3_group_1(sK31)
| ~ v4_group_1(sK31)
| ~ l1_group_1(sK31)
| spl619_39 ),
inference(forward_subsumption_resolution,[],[f23497,f17197]) ).
fof(f23500,plain,
( ~ v3_group_1(sK31)
| ~ v4_group_1(sK31)
| ~ l1_group_1(sK31)
| spl619_39 ),
inference(forward_subsumption_resolution,[],[f23499,f17196]) ).
fof(f23501,plain,
( ~ v4_group_1(sK31)
| ~ l1_group_1(sK31)
| spl619_39 ),
inference(forward_subsumption_resolution,[],[f23500,f17195]) ).
fof(f23502,plain,
( ~ l1_group_1(sK31)
| spl619_39 ),
inference(forward_subsumption_resolution,[],[f23501,f17194]) ).
fof(f23503,plain,
( $false
| spl619_39 ),
inference(forward_subsumption_resolution,[],[f23502,f17193]) ).
fof(f23504,plain,
spl619_39,
inference(avatar_contradiction_clause,[],[f23503]) ).
fof(f23535,plain,
( r1_tarski(k4_autgroup(sK31),k1_autgroup(sK31))
| v1_xboole_0(k1_autgroup(sK31))
| r1_tarski(k4_autgroup(sK31),k1_autgroup(sK31))
| ~ spl619_40 ),
inference(resolution,[],[f23417,f23287]) ).
fof(f23537,plain,
( r1_tarski(k4_autgroup(sK31),k1_autgroup(sK31))
| v1_xboole_0(k1_autgroup(sK31))
| ~ spl619_40 ),
inference(duplicate_literal_removal,[],[f23535]) ).
fof(f23538,plain,
( v1_xboole_0(k1_autgroup(sK31))
| ~ spl619_40 ),
inference(forward_subsumption_resolution,[],[f23537,f17198]) ).
fof(f23539,plain,
( ! [X0,X1] : ~ m1_fraenkel(k1_autgroup(sK31),X0,X1)
| ~ spl619_40 ),
inference(resolution,[],[f23538,f17208]) ).
fof(f23544,plain,
( v3_struct_0(sK31)
| ~ v1_group_1(sK31)
| ~ v3_group_1(sK31)
| ~ v4_group_1(sK31)
| ~ l1_group_1(sK31)
| ~ spl619_40 ),
inference(resolution,[],[f23539,f17114]) ).
fof(f23546,plain,
( ~ v1_group_1(sK31)
| ~ v3_group_1(sK31)
| ~ v4_group_1(sK31)
| ~ l1_group_1(sK31)
| ~ spl619_40 ),
inference(forward_subsumption_resolution,[],[f23544,f17197]) ).
fof(f23547,plain,
( ~ v3_group_1(sK31)
| ~ v4_group_1(sK31)
| ~ l1_group_1(sK31)
| ~ spl619_40 ),
inference(forward_subsumption_resolution,[],[f23546,f17196]) ).
fof(f23548,plain,
( ~ v4_group_1(sK31)
| ~ l1_group_1(sK31)
| ~ spl619_40 ),
inference(forward_subsumption_resolution,[],[f23547,f17195]) ).
fof(f23549,plain,
( ~ l1_group_1(sK31)
| ~ spl619_40 ),
inference(forward_subsumption_resolution,[],[f23548,f17194]) ).
fof(f23550,plain,
( $false
| ~ spl619_40 ),
inference(forward_subsumption_resolution,[],[f23549,f17193]) ).
fof(f23551,plain,
~ spl619_40,
inference(avatar_contradiction_clause,[],[f23550]) ).
cnf(s34,plain,
( spl619_33
| spl619_34 ),
inference(sat_conversion,[],[f23380]) ).
cnf(s39,plain,
( ~ spl619_33
| spl619_34
| ~ spl619_39
| spl619_40 ),
inference(sat_conversion,[],[f23418]) ).
cnf(s44,plain,
~ spl619_34,
inference(sat_conversion,[],[f23446]) ).
cnf(s48,plain,
spl619_39,
inference(sat_conversion,[],[f23504]) ).
cnf(s53,plain,
~ spl619_40,
inference(sat_conversion,[],[f23551]) ).
cnf(s60,plain,
~ spl619_33,
inference(rat,[],[s39,s53,s48,s44]) ).
cnf(s61,plain,
$false,
inference(rat,[],[s34,s44,s60]) ).
fof(f23552,plain,
$false,
inference(avatar_sat_refutation,[],[s61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP623+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 % Computer : n010.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sun Sep 27 10:10:18 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.22/3.94 % (732724)Detected formulas, will run a generic FOF schedule.
% 15.22/3.94 % (732736)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2614059573:i=109:sd=1:ins=1:gsp=on:ss=axioms_2992 on theBenchmark for (2992ds/109Mi)
% 15.22/3.94 % (732739)dis-21_1_sil=8000:lcm=predicate:random_seed=1862509442:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2992 on theBenchmark for (2992ds/129Mi)
% 15.22/3.94 % (732738)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=350540367:s2a=on:i=139:gtg=position_2992 on theBenchmark for (2992ds/139Mi)
% 15.22/3.94 % (732733)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=2947064817:i=141193_2992 on theBenchmark for (2992ds/141193Mi)
% 15.22/3.94 % (732737)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1961297506:i=119:av=off:ss=axioms_2992 on theBenchmark for (2992ds/119Mi)
% 15.22/3.94 % (732734)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=1660476974:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2992 on theBenchmark for (2992ds/134677Mi)
% 15.22/3.94 % (732735)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=323317711:i=141695:sd=1:nm=32:gsp=on:ss=included_2992 on theBenchmark for (2992ds/141695Mi)
% 15.22/3.94 % (732736)Refutation not found, incomplete strategy
% 15.22/3.94 % (732736)------------------------------
% 15.22/3.94 % (732736)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.22/3.94 % (732736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.22/3.94 % (732736)CaDiCaL version: 2.1.3
% 15.22/3.94 % (732736)Termination reason: Refutation not found, incomplete strategy
% 15.22/3.94 % (732736)Time elapsed: 0.056 s
% 15.22/3.94 % (732736)Peak memory usage: 106 MB
% 15.22/3.94 % (732736)Instructions burned: 80 (million)
% 15.22/3.94 % (732738)Instruction limit reached!
% 15.22/3.94 % (732738)------------------------------
% 15.22/3.94 % (732738)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.22/3.94 % (732738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.22/3.94 % (732738)CaDiCaL version: 2.1.3
% 15.22/3.94 % (732738)Termination reason: Instruction limit
% 15.22/3.94 % (732738)Termination phase: Property scanning
% 15.22/3.94 % (732738)Time elapsed: 0.114 s
% 15.22/3.94 % (732738)Peak memory usage: 101 MB
% 15.22/3.94 % (732738)Instructions burned: 139 (million)
% 15.22/3.94 % (732739)Instruction limit reached!
% 15.22/3.94 % (732739)------------------------------
% 15.22/3.94 % (732739)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.22/3.94 % (732739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.22/3.94 % (732739)CaDiCaL version: 2.1.3
% 15.22/3.94 % (732739)Termination reason: Instruction limit
% 15.22/3.94 % (732739)Termination phase: Preprocessing 1
% 15.22/3.94 % (732739)Time elapsed: 0.146 s
% 15.22/3.94 % (732739)Peak memory usage: 103 MB
% 15.22/3.94 % (732739)Instructions burned: 129 (million)
% 15.22/3.94 % (732737)Instruction limit reached!
% 15.22/3.94 % (732737)------------------------------
% 15.22/3.94 % (732737)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.22/3.94 % (732737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.22/3.94 % (732737)CaDiCaL version: 2.1.3
% 15.22/3.94 % (732737)Termination reason: Instruction limit
% 15.22/3.94 % (732737)Termination phase: Preprocessing 3
% 15.22/3.94 % (732737)Time elapsed: 0.152 s
% 15.22/3.94 % (732737)Peak memory usage: 104 MB
% 15.22/3.94 % (732737)Instructions burned: 120 (million)
% 15.22/3.94 % (732747)lrs+10_1_sil=8000:sp=occurrence:random_seed=297508694:i=285:sd=3:ss=axioms:sgt=8_2989 on theBenchmark for (2989ds/285Mi)
% 15.22/3.94 % (732736)------------------------------
% 15.22/3.94 % (732736)------------------------------
% 15.22/3.94 % (732748)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3823483659:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2989 on theBenchmark for (2989ds/157Mi)
% 15.22/3.94 % (732749)lrs+1011_1_sil=32000:sp=occurrence:random_seed=152878234:i=325:sd=1:ss=axioms:sgt=32_2988 on theBenchmark for (2988ds/325Mi)
% 15.22/3.94 % (732747)Instruction limit reached!
% 15.22/3.94 % (732747)------------------------------
% 15.22/3.94 % (732747)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.22/3.94 % (732747)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.87/4.65 % (732747)CaDiCaL version: 2.1.3
% 17.87/4.65 % (732747)Termination reason: Instruction limit
% 17.87/4.65 % (732747)Termination phase: Saturation
% 17.87/4.65 % (732747)Time elapsed: 0.176 s
% 17.87/4.65 % (732747)Peak memory usage: 109 MB
% 17.87/4.65 % (732747)Instructions burned: 286 (million)
% 17.87/4.65 % (732748)Instruction limit reached!
% 17.87/4.65 % (732748)------------------------------
% 17.87/4.65 % (732748)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.87/4.65 % (732748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.87/4.65 % (732748)CaDiCaL version: 2.1.3
% 17.87/4.65 % (732748)Termination reason: Instruction limit
% 17.87/4.65 % (732748)Termination phase: Property scanning
% 17.87/4.65 % (732748)Time elapsed: 0.129 s
% 17.87/4.65 % (732748)Peak memory usage: 101 MB
% 17.87/4.65 % (732748)Instructions burned: 158 (million)
% 17.87/4.65 % (732751)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=3013757480:s2a=on:i=248:s2at=1.23:gtg=position_2986 on theBenchmark for (2986ds/248Mi)
% 17.87/4.65 % (732755)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=607272794:i=2350_2984 on theBenchmark for (2984ds/2350Mi)
% 17.87/4.65 % (732754)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1049369122:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2985 on theBenchmark for (2985ds/294Mi)
% 17.87/4.65 % (732749)Instruction limit reached!
% 17.87/4.65 % (732749)------------------------------
% 17.87/4.65 % (732749)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.87/4.65 % (732749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.87/4.65 % (732749)CaDiCaL version: 2.1.3
% 17.87/4.65 % (732749)Termination reason: Instruction limit
% 17.87/4.65 % (732749)Termination phase: Saturation
% 17.87/4.65 % (732749)Time elapsed: 0.365 s
% 17.87/4.65 % (732749)Peak memory usage: 108 MB
% 17.87/4.65 % (732749)Instructions burned: 325 (million)
% 17.87/4.65 % (732751)Instruction limit reached!
% 17.87/4.65 % (732751)------------------------------
% 17.87/4.65 % (732751)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.87/4.65 % (732751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.87/4.65 % (732751)CaDiCaL version: 2.1.3
% 17.87/4.65 % (732751)Termination reason: Instruction limit
% 17.87/4.65 % (732751)Termination phase: SInE selection
% 17.87/4.65 % (732751)Time elapsed: 0.215 s
% 17.87/4.65 % (732751)Peak memory usage: 102 MB
% 17.87/4.65 % (732751)Instructions burned: 248 (million)
% 17.87/4.65 % (732759)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2951955369:cts=off:i=113:fsr=off:ss=included:sgt=4_2982 on theBenchmark for (2982ds/113Mi)
% 17.87/4.65 % (732754)Instruction limit reached!
% 17.87/4.65 % (732754)------------------------------
% 17.87/4.65 % (732754)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.87/4.65 % (732754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.87/4.65 % (732754)CaDiCaL version: 2.1.3
% 17.87/4.65 % (732754)Termination reason: Instruction limit
% 17.87/4.65 % (732754)Termination phase: Saturation
% 17.87/4.65 % (732754)Time elapsed: 0.221 s
% 17.87/4.65 % (732754)Peak memory usage: 109 MB
% 17.87/4.65 % (732754)Instructions burned: 294 (million)
% 17.87/4.65 % (732761)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1595634049:i=127:av=off:fsr=off:sup=off_2981 on theBenchmark for (2981ds/127Mi)
% 17.87/4.65 % (732759)Instruction limit reached!
% 17.87/4.65 % (732759)------------------------------
% 17.87/4.65 % (732759)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.87/4.65 % (732759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.87/4.65 % (732759)CaDiCaL version: 2.1.3
% 17.87/4.65 % (732759)Termination reason: Instruction limit
% 17.87/4.65 % (732759)Termination phase: Preprocessing 3
% 17.87/4.65 % (732759)Time elapsed: 0.096 s
% 17.87/4.65 % (732759)Peak memory usage: 105 MB
% 17.87/4.65 % (732759)Instructions burned: 113 (million)
% 17.87/4.65 % (732763)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3837168023:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2980 on theBenchmark for (2980ds/114Mi)
% 17.87/4.65 % (732761)Instruction limit reached!
% 17.87/4.65 % (732761)------------------------------
% 17.87/4.65 % (732761)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.87/4.65 % (732761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.87/4.65 % (732761)CaDiCaL version: 2.1.3
% 17.87/4.65 % (732761)Termination reason: Instruction limit
% 17.87/4.65 % (732761)Termination phase: Preprocessing 2
% 17.87/4.65 % (732761)Time elapsed: 0.139 s
% 17.87/4.65 % (732761)Peak memory usage: 106 MB
% 17.87/4.65 % (732761)Instructions burned: 128 (million)
% 17.87/4.65 % (732763)Instruction limit reached!
% 17.87/4.65 % (732763)------------------------------
% 17.87/4.65 % (732763)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.87/4.65 % (732763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.87/4.65 % (732763)CaDiCaL version: 2.1.3
% 17.87/4.65 % (732763)Termination reason: Instruction limit
% 17.87/4.65 % (732763)Termination phase: Property scanning
% 17.87/4.65 % (732763)Time elapsed: 0.048 s
% 17.87/4.65 % (732763)Peak memory usage: 101 MB
% 17.87/4.65 % (732763)Instructions burned: 115 (million)
% 17.87/4.65 % (732765)lrs+10_1_sil=8000:sp=occurrence:random_seed=1391480339:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2979 on theBenchmark for (2979ds/907Mi)
% 17.87/4.65 % (732767)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3137703008:i=437:sd=1:aac=none:ss=included_2978 on theBenchmark for (2978ds/437Mi)
% 17.87/4.65 % (732768)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=4220668896:i=5202:ss=axioms:sgt=16_2978 on theBenchmark for (2978ds/5202Mi)
% 17.87/4.65 % (732755)Instruction limit reached!
% 17.87/4.65 % (732755)------------------------------
% 17.87/4.65 % (732755)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.87/4.65 % (732755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.87/4.65 % (732755)CaDiCaL version: 2.1.3
% 17.87/4.65 % (732755)Termination reason: Instruction limit
% 17.87/4.65 % (732755)Termination phase: Saturation
% 17.87/4.65 % (732755)Time elapsed: 0.831 s
% 17.87/4.65 % (732755)Peak memory usage: 227 MB
% 17.87/4.65 % (732755)Instructions burned: 2353 (million)
% 17.87/4.65 % (732767)Instruction limit reached!
% 17.87/4.65 % (732767)------------------------------
% 17.87/4.65 % (732767)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.87/4.65 % (732767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.87/4.65 % (732767)CaDiCaL version: 2.1.3
% 17.87/4.65 % (732767)Termination reason: Instruction limit
% 17.87/4.65 % (732767)Termination phase: Saturation
% 17.87/4.65 % (732767)Time elapsed: 0.289 s
% 17.87/4.65 % (732767)Peak memory usage: 110 MB
% 17.87/4.65 % (732767)Instructions burned: 437 (million)
% 17.87/4.65 % (732772)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2331870398:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2974 on theBenchmark for (2974ds/134Mi)
% 17.87/4.65 % (732765)Instruction limit reached!
% 17.87/4.65 % (732765)------------------------------
% 17.87/4.65 % (732765)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.87/4.65 % (732765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.87/4.65 % (732765)CaDiCaL version: 2.1.3
% 17.87/4.65 % (732765)Termination reason: Instruction limit
% 17.87/4.65 % (732765)Termination phase: Saturation
% 17.87/4.65 % (732765)Time elapsed: 0.534 s
% 17.87/4.65 % (732765)Peak memory usage: 120 MB
% 17.87/4.65 % (732765)Instructions burned: 907 (million)
% 17.87/4.65 % (732772)Instruction limit reached!
% 17.87/4.65 % (732772)------------------------------
% 17.87/4.65 % (732772)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.87/4.65 % (732772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.87/4.65 % (732772)CaDiCaL version: 2.1.3
% 17.87/4.65 % (732772)Termination reason: Instruction limit
% 17.87/4.65 % (732772)Termination phase: Property scanning
% 17.87/4.65 % (732772)Time elapsed: 0.060 s
% 17.87/4.65 % (732772)Peak memory usage: 105 MB
% 17.87/4.65 % (732772)Instructions burned: 139 (million)
% 17.87/4.65 % (732773)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=950316511:st=8:i=592:sd=3:ep=RST:ss=axioms_2974 on theBenchmark for (2974ds/592Mi)
% 17.87/4.65 % (732790)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=2780545934:st=3:i=13193:sd=3:ss=axioms_2972 on theBenchmark for (2972ds/13193Mi)
% 17.87/4.65 % (732803)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=1991236588:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2972 on theBenchmark for (2972ds/125Mi)
% 17.87/4.65 % (732803)Instruction limit reached!
% 17.87/4.65 % (732803)------------------------------
% 17.87/4.65 % (732803)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.87/4.65 % (732803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.87/4.65 % (732803)CaDiCaL version: 2.1.3
% 17.87/4.65 % (732803)Termination reason: Instruction limit
% 17.87/4.65 % (732803)Termination phase: Property scanning
% 17.87/4.65 % (732803)Time elapsed: 0.030 s
% 17.87/4.65 % (732803)Peak memory usage: 101 MB
% 17.87/4.65 % (732803)Instructions burned: 127 (million)
% 17.87/4.65 % (732855)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=1400284328:i=134:gtgl=5:slsql=off:gtg=exists_sym_2970 on theBenchmark for (2970ds/134Mi)
% 17.87/4.65 % (732855)Instruction limit reached!
% 17.87/4.65 % (732855)------------------------------
% 17.87/4.65 % (732855)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.87/4.65 % (732855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.87/4.65 % (732855)CaDiCaL version: 2.1.3
% 17.87/4.65 % (732855)Termination reason: Instruction limit
% 17.87/4.65 % (732855)Termination phase: Property scanning
% 17.87/4.65 % (732855)Time elapsed: 0.032 s
% 17.87/4.65 % (732855)Peak memory usage: 101 MB
% 17.87/4.65 % (732855)Instructions burned: 137 (million)
% 17.87/4.65 % (732773)Instruction limit reached!
% 17.87/4.65 % (732773)------------------------------
% 17.87/4.65 % (732773)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.87/4.65 % (732773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.87/4.65 % (732773)CaDiCaL version: 2.1.3
% 17.87/4.65 % (732773)Termination reason: Instruction limit
% 17.87/4.65 % (732773)Termination phase: Property scanning
% 17.87/4.65 % (732773)Time elapsed: 0.392 s
% 17.87/4.65 % (732773)Peak memory usage: 122 MB
% 17.87/4.65 % (732773)Instructions burned: 592 (million)
% 17.87/4.65 % (732888)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=3726648763:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2969 on theBenchmark for (2969ds/141Mi)
% 17.87/4.65 % (732888)Instruction limit reached!
% 17.87/4.65 % (732888)------------------------------
% 17.87/4.65 % (732888)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.87/4.65 % (732888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.87/4.65 % (732888)CaDiCaL version: 2.1.3
% 17.87/4.65 % (732888)Termination reason: Instruction limit
% 17.87/4.65 % (732888)Termination phase: Saturation
% 17.87/4.65 % (732888)Time elapsed: 0.057 s
% 17.87/4.65 % (732888)Peak memory usage: 106 MB
% 17.87/4.65 % (732888)Instructions burned: 144 (million)
% 17.87/4.65 % (732734)First to succeed.
% 17.87/4.65 % (732734)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-732724"
% 17.87/4.65 % (732889)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=1962123978:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2968 on theBenchmark for (2968ds/431Mi)
% 17.87/4.65 % (732930)lrs+1010_1_ncem=casc2026/models/loop6.pt:sil=64000:tgt=full:npcc=on:prc=on:urr=ec_only:bsr=on:fd=preordered:gs=on:sac=on:newcnf=on:random_seed=1806628661:i=6060:aac=none:ins=25_2967 on theBenchmark for (2967ds/6060Mi)
% 17.87/4.65 % (732734)Refutation found. Thanks to Tanya!
% 17.87/4.65 % SZS status Theorem for theBenchmark
% 17.87/4.65 % SZS output start Proof for theBenchmark
% See solution above
% 21.77/4.85 % (732734)------------------------------
% 21.77/4.85 % (732734)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.77/4.85 % (732734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.77/4.85 % (732734)CaDiCaL version: 2.1.3
% 21.77/4.85 % (732734)Termination reason: Refutation
% 21.77/4.85 % (732734)Time elapsed: 2.332 s
% 21.77/4.85 % (732734)Peak memory usage: 212 MB
% 21.77/4.85 % (732734)Instructions burned: 3111 (million)
% 21.77/4.85 % (732734)------------------------------
% 21.77/4.85 % (732734)------------------------------
% 21.77/4.85 % (732724)Success in time 3.63 s
% 21.77/4.85 % Vampire exiting
%------------------------------------------------------------------------------