%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP631+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 : n006.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 10:15:07 AM UTC 2026
% Result : Theorem 6.69s 2.00s
% Output : Refutation 8.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 30
% Syntax : Number of formulae : 223 ( 45 unt; 17 def)
% Number of atoms : 748 ( 90 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 903 ( 378 ~; 438 |; 60 &)
% ( 12 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 12 prp; 0-4 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-6 aty)
% Number of variables : 159 ( 0 sgn 155 !; 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) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ( k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),k6_autgroup(X0,k2_group_1(X0)),k6_autgroup(X0,X1)) = k6_autgroup(X0,X1)
& k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),k6_autgroup(X0,X1),k6_autgroup(X0,k2_group_1(X0))) = k6_autgroup(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_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) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ( k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),k6_autgroup(X0,k2_group_1(X0)),k6_autgroup(X0,X1)) = k6_autgroup(X0,X1)
& k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),k6_autgroup(X0,X1),k6_autgroup(X0,k2_group_1(X0))) = k6_autgroup(X0,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f20,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& l1_group_1(X0) )
=> m1_subset_1(k2_group_1(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_group_1) ).
fof(f22,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(f24,axiom,
! [X0,X1] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0)
& m1_subset_1(X1,u1_struct_0(X0)) )
=> m2_fraenkel(k6_autgroup(X0,X1),u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_autgroup) ).
fof(f29,axiom,
! [X0] :
( l1_group_1(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(f34,axiom,
! [X0,X1,X2] :
( ( ~ v1_xboole_0(X1)
& m1_fraenkel(X2,X0,X1) )
=> ! [X3] :
( m2_fraenkel(X3,X0,X1,X2)
=> ( v1_funct_1(X3)
& v1_funct_2(X3,X0,X1)
& m2_relset_1(X3,X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_fraenkel) ).
fof(f47,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(f68,axiom,
! [X0] : k6_partfun1(X0) = k6_relat_1(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
fof(f69,axiom,
! [X0,X1,X2,X3,X4] :
( ( ~ v1_xboole_0(X1)
& v1_funct_1(X3)
& v1_funct_2(X3,X0,X1)
& m1_relset_1(X3,X0,X1)
& v1_funct_1(X4)
& v1_funct_2(X4,X1,X2)
& m1_relset_1(X4,X1,X2) )
=> k7_funct_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_funct_2) ).
fof(f70,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( m1_relset_1(X4,X0,X1)
& m1_relset_1(X5,X2,X3) )
=> k7_relset_1(X0,X1,X2,X3,X4,X5) = k5_relat_1(X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_relset_1) ).
fof(f72,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
<=> m1_relset_1(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f75,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
=> ( k7_relset_1(X0,X0,X0,X1,k6_partfun1(X0),X2) = X2
& k7_relset_1(X0,X1,X1,X1,X2,k6_partfun1(X1)) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_2) ).
fof(f76,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> k6_autgroup(X0,k2_group_1(X0)) = k6_partfun1(u1_struct_0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_autgroup) ).
fof(f90,plain,
? [X0] :
( ? [X1] :
( ( k6_autgroup(X0,X1) != k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),k6_autgroup(X0,k2_group_1(X0)),k6_autgroup(X0,X1))
| k6_autgroup(X0,X1) != k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),k6_autgroup(X0,X1),k6_autgroup(X0,k2_group_1(X0))) )
& m1_subset_1(X1,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,[],[f2]) ).
fof(f91,plain,
? [X0] :
( ? [X1] :
( ( k6_autgroup(X0,X1) != k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),k6_autgroup(X0,k2_group_1(X0)),k6_autgroup(X0,X1))
| k6_autgroup(X0,X1) != k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),k6_autgroup(X0,X1),k6_autgroup(X0,k2_group_1(X0))) )
& m1_subset_1(X1,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,[],[f90]) ).
fof(f118,plain,
! [X0] :
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f119,plain,
! [X0] :
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f118]) ).
fof(f120,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,[],[f22]) ).
fof(f121,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,[],[f120]) ).
fof(f124,plain,
! [X0,X1] :
( m2_fraenkel(k6_autgroup(X0,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)
| ~ m1_subset_1(X1,u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f24]) ).
fof(f125,plain,
! [X0,X1] :
( m2_fraenkel(k6_autgroup(X0,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)
| ~ m1_subset_1(X1,u1_struct_0(X0)) ),
inference(flattening,[],[f124]) ).
fof(f130,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f132,plain,
! [X0,X1,X2] :
( ! [X3] :
( ( v1_funct_1(X3)
& v1_funct_2(X3,X0,X1)
& m2_relset_1(X3,X0,X1) )
| ~ m2_fraenkel(X3,X0,X1,X2) )
| v1_xboole_0(X1)
| ~ m1_fraenkel(X2,X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f133,plain,
! [X0,X1,X2] :
( ! [X3] :
( ( v1_funct_1(X3)
& v1_funct_2(X3,X0,X1)
& m2_relset_1(X3,X0,X1) )
| ~ m2_fraenkel(X3,X0,X1,X2) )
| v1_xboole_0(X1)
| ~ m1_fraenkel(X2,X0,X1) ),
inference(flattening,[],[f132]) ).
fof(f142,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f143,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(flattening,[],[f142]) ).
fof(f148,plain,
! [X0,X1,X2,X3,X4] :
( k7_funct_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4)
| v1_xboole_0(X1)
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,X0,X1)
| ~ m1_relset_1(X3,X0,X1)
| ~ v1_funct_1(X4)
| ~ v1_funct_2(X4,X1,X2)
| ~ m1_relset_1(X4,X1,X2) ),
inference(ennf_transformation,[],[f69]) ).
fof(f149,plain,
! [X0,X1,X2,X3,X4] :
( k7_funct_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4)
| v1_xboole_0(X1)
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,X0,X1)
| ~ m1_relset_1(X3,X0,X1)
| ~ v1_funct_1(X4)
| ~ v1_funct_2(X4,X1,X2)
| ~ m1_relset_1(X4,X1,X2) ),
inference(flattening,[],[f148]) ).
fof(f150,plain,
! [X0,X1,X2,X3,X4,X5] :
( k7_relset_1(X0,X1,X2,X3,X4,X5) = k5_relat_1(X4,X5)
| ~ m1_relset_1(X4,X0,X1)
| ~ m1_relset_1(X5,X2,X3) ),
inference(ennf_transformation,[],[f70]) ).
fof(f151,plain,
! [X0,X1,X2,X3,X4,X5] :
( k7_relset_1(X0,X1,X2,X3,X4,X5) = k5_relat_1(X4,X5)
| ~ m1_relset_1(X4,X0,X1)
| ~ m1_relset_1(X5,X2,X3) ),
inference(flattening,[],[f150]) ).
fof(f155,plain,
! [X0,X1,X2] :
( ( k7_relset_1(X0,X0,X0,X1,k6_partfun1(X0),X2) = X2
& k7_relset_1(X0,X1,X1,X1,X2,k6_partfun1(X1)) = X2 )
| ~ m2_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f75]) ).
fof(f156,plain,
! [X0] :
( k6_autgroup(X0,k2_group_1(X0)) = k6_partfun1(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,[],[f76]) ).
fof(f157,plain,
! [X0] :
( k6_autgroup(X0,k2_group_1(X0)) = k6_partfun1(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,[],[f156]) ).
fof(f167,plain,
( ( k6_autgroup(sK0,sK1) != k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_autgroup(sK0,k2_group_1(sK0)),k6_autgroup(sK0,sK1))
| k6_autgroup(sK0,sK1) != k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_autgroup(sK0,sK1),k6_autgroup(sK0,k2_group_1(sK0))) )
& m1_subset_1(sK1,u1_struct_0(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,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f91]) ).
fof(f192,plain,
! [X0,X1,X2] :
( ( m2_relset_1(X2,X0,X1)
| ~ m1_relset_1(X2,X0,X1) )
& ( m1_relset_1(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f72]) ).
fof(f193,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f167]) ).
fof(f194,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f167]) ).
fof(f195,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f167]) ).
fof(f196,plain,
v1_group_1(sK0),
inference(cnf_transformation,[],[f167]) ).
fof(f197,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f167]) ).
fof(f198,plain,
m1_subset_1(sK1,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f167]) ).
fof(f199,plain,
( k6_autgroup(sK0,sK1) != k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_autgroup(sK0,k2_group_1(sK0)),k6_autgroup(sK0,sK1))
| k6_autgroup(sK0,sK1) != k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),k6_autgroup(sK0,sK1),k6_autgroup(sK0,k2_group_1(sK0))) ),
inference(cnf_transformation,[],[f167]) ).
fof(f235,plain,
! [X0] :
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f236,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,[],[f121]) ).
fof(f238,plain,
! [X0,X1] :
( m2_fraenkel(k6_autgroup(X0,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)
| ~ m1_subset_1(X1,u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f125]) ).
fof(f246,plain,
! [X0] :
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f249,plain,
! [X2,X3,X0,X1] :
( ~ m2_fraenkel(X3,X0,X1,X2)
| m2_relset_1(X3,X0,X1)
| v1_xboole_0(X1)
| ~ m1_fraenkel(X2,X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f250,plain,
! [X2,X3,X0,X1] :
( ~ m2_fraenkel(X3,X0,X1,X2)
| v1_funct_2(X3,X0,X1)
| v1_xboole_0(X1)
| ~ m1_fraenkel(X2,X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f251,plain,
! [X2,X3,X0,X1] :
( ~ m2_fraenkel(X3,X0,X1,X2)
| v1_funct_1(X3)
| v1_xboole_0(X1)
| ~ m1_fraenkel(X2,X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f267,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f328,plain,
! [X0] : k6_partfun1(X0) = k6_relat_1(X0),
inference(cnf_transformation,[],[f68]) ).
fof(f329,plain,
! [X2,X3,X0,X1,X4] :
( ~ v1_funct_2(X4,X1,X2)
| v1_xboole_0(X1)
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,X0,X1)
| ~ m1_relset_1(X3,X0,X1)
| ~ v1_funct_1(X4)
| k7_funct_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4)
| ~ m1_relset_1(X4,X1,X2) ),
inference(cnf_transformation,[],[f149]) ).
fof(f330,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ m1_relset_1(X5,X2,X3)
| ~ m1_relset_1(X4,X0,X1)
| k7_relset_1(X0,X1,X2,X3,X4,X5) = k5_relat_1(X4,X5) ),
inference(cnf_transformation,[],[f151]) ).
fof(f333,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f192]) ).
fof(f337,plain,
! [X2,X0,X1] :
( k7_relset_1(X0,X1,X1,X1,X2,k6_partfun1(X1)) = X2
| ~ m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f155]) ).
fof(f338,plain,
! [X2,X0,X1] :
( k7_relset_1(X0,X0,X0,X1,k6_partfun1(X0),X2) = X2
| ~ m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f155]) ).
fof(f339,plain,
! [X0] :
( k6_autgroup(X0,k2_group_1(X0)) = k6_partfun1(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,[],[f157]) ).
fof(f349,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| k7_relset_1(X0,X0,X0,X1,k6_relat_1(X0),X2) = X2 ),
inference(definition_unfolding,[],[f338,f328]) ).
fof(f350,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| k7_relset_1(X0,X1,X1,X1,X2,k6_relat_1(X1)) = X2 ),
inference(definition_unfolding,[],[f337,f328]) ).
fof(f351,plain,
! [X0] :
( ~ l1_group_1(X0)
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| k6_autgroup(X0,k2_group_1(X0)) = k6_relat_1(u1_struct_0(X0)) ),
inference(definition_unfolding,[],[f339,f328]) ).
fof(f352,definition,
sF25 = k6_autgroup(sK0,sK1),
introduced(definition,[new_symbols(definition,[sF25])],[function_definition]) ).
fof(f353,plain,
k6_autgroup(sK0,sK1) = sF25,
inference(reorient_equations,[],[f352]) ).
fof(f354,definition,
sF26 = u1_struct_0(sK0),
introduced(definition,[new_symbols(definition,[sF26])],[function_definition]) ).
fof(f355,plain,
u1_struct_0(sK0) = sF26,
inference(reorient_equations,[],[f354]) ).
fof(f356,definition,
sF27 = k2_group_1(sK0),
introduced(definition,[new_symbols(definition,[sF27])],[function_definition]) ).
fof(f357,plain,
k2_group_1(sK0) = sF27,
inference(reorient_equations,[],[f356]) ).
fof(f358,definition,
sF28 = k6_autgroup(sK0,sF27),
introduced(definition,[new_symbols(definition,[sF28])],[function_definition]) ).
fof(f359,plain,
k6_autgroup(sK0,sF27) = sF28,
inference(reorient_equations,[],[f358]) ).
fof(f360,definition,
sF29 = k7_funct_2(sF26,sF26,sF26,sF28,sF25),
introduced(definition,[new_symbols(definition,[sF29])],[function_definition]) ).
fof(f361,plain,
k7_funct_2(sF26,sF26,sF26,sF28,sF25) = sF29,
inference(reorient_equations,[],[f360]) ).
fof(f362,definition,
sF30 = k7_funct_2(sF26,sF26,sF26,sF25,sF28),
introduced(definition,[new_symbols(definition,[sF30])],[function_definition]) ).
fof(f363,plain,
k7_funct_2(sF26,sF26,sF26,sF25,sF28) = sF30,
inference(reorient_equations,[],[f362]) ).
fof(f364,plain,
( sF25 != sF29
| sF25 != sF30 ),
inference(definition_folding,[],[f199,f363,f359,f357,f353,f355,f355,f355,f353,f361,f353,f359,f357,f355,f355,f355,f353]) ).
fof(f365,plain,
m1_subset_1(sK1,sF26),
inference(definition_folding,[],[f198,f355]) ).
fof(f367,definition,
( spl31_1
<=> sF25 = sF30 ),
introduced(definition,[new_symbols(definition,[spl31_1])],[avatar_definition]) ).
fof(f369,plain,
( sF25 != sF30
| spl31_1 ),
inference(avatar_component_clause,[],[f367]) ).
fof(f371,definition,
( spl31_2
<=> sF25 = sF29 ),
introduced(definition,[new_symbols(definition,[spl31_2])],[avatar_definition]) ).
fof(f374,plain,
( ~ spl31_1
| ~ spl31_2 ),
inference(avatar_split_clause,[],[f364,f371,f367]) ).
fof(f375,plain,
( m2_fraenkel(sF25,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_subset_1(sK1,u1_struct_0(sK0)) ),
inference(superposition,[],[f238,f353]) ).
fof(f376,plain,
( m2_fraenkel(sF28,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_subset_1(sF27,u1_struct_0(sK0)) ),
inference(superposition,[],[f238,f359]) ).
fof(f379,plain,
( m2_fraenkel(sF28,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_subset_1(sF27,u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f376,f197]) ).
fof(f380,plain,
( m2_fraenkel(sF25,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_subset_1(sK1,u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f375,f197]) ).
fof(f382,plain,
( m2_fraenkel(sF28,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_subset_1(sF27,u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f379,f196]) ).
fof(f383,plain,
( m2_fraenkel(sF25,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_subset_1(sK1,u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f380,f196]) ).
fof(f385,plain,
( m2_fraenkel(sF28,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_subset_1(sF27,u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f382,f195]) ).
fof(f386,plain,
( m2_fraenkel(sF25,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_subset_1(sK1,u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f383,f195]) ).
fof(f388,plain,
( m2_fraenkel(sF28,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ m1_subset_1(sF27,u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f385,f194]) ).
fof(f389,plain,
( m2_fraenkel(sF25,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ m1_subset_1(sK1,u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f386,f194]) ).
fof(f391,plain,
( m2_fraenkel(sF28,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ m1_subset_1(sF27,u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f388,f193]) ).
fof(f392,plain,
( m2_fraenkel(sF25,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ m1_subset_1(sK1,u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f389,f193]) ).
fof(f393,plain,
( m2_fraenkel(sF28,sF26,sF26,k4_autgroup(sK0))
| ~ m1_subset_1(sF27,u1_struct_0(sK0)) ),
inference(forward_demodulation,[],[f391,f355]) ).
fof(f394,plain,
( m2_fraenkel(sF25,sF26,sF26,k4_autgroup(sK0))
| ~ m1_subset_1(sK1,u1_struct_0(sK0)) ),
inference(forward_demodulation,[],[f392,f355]) ).
fof(f395,plain,
( ~ m1_subset_1(sF27,sF26)
| m2_fraenkel(sF28,sF26,sF26,k4_autgroup(sK0)) ),
inference(forward_demodulation,[],[f393,f355]) ).
fof(f396,plain,
( ~ m1_subset_1(sK1,sF26)
| m2_fraenkel(sF25,sF26,sF26,k4_autgroup(sK0)) ),
inference(forward_demodulation,[],[f394,f355]) ).
fof(f398,definition,
( spl31_3
<=> m2_fraenkel(sF28,sF26,sF26,k4_autgroup(sK0)) ),
introduced(definition,[new_symbols(definition,[spl31_3])],[avatar_definition]) ).
fof(f400,plain,
( m2_fraenkel(sF28,sF26,sF26,k4_autgroup(sK0))
| ~ spl31_3 ),
inference(avatar_component_clause,[],[f398]) ).
fof(f402,definition,
( spl31_4
<=> m1_subset_1(sF27,sF26) ),
introduced(definition,[new_symbols(definition,[spl31_4])],[avatar_definition]) ).
fof(f404,plain,
( ~ m1_subset_1(sF27,sF26)
| spl31_4 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f405,plain,
( spl31_3
| ~ spl31_4 ),
inference(avatar_split_clause,[],[f395,f402,f398]) ).
fof(f406,plain,
m2_fraenkel(sF25,sF26,sF26,k4_autgroup(sK0)),
inference(forward_subsumption_resolution,[],[f396,f365]) ).
fof(f407,plain,
( v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| k6_autgroup(sK0,k2_group_1(sK0)) = k6_relat_1(u1_struct_0(sK0)) ),
inference(resolution,[],[f351,f193]) ).
fof(f408,plain,
( ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| k6_autgroup(sK0,k2_group_1(sK0)) = k6_relat_1(u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f407,f197]) ).
fof(f409,plain,
( ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| k6_autgroup(sK0,k2_group_1(sK0)) = k6_relat_1(u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f408,f196]) ).
fof(f410,plain,
( ~ v4_group_1(sK0)
| k6_autgroup(sK0,k2_group_1(sK0)) = k6_relat_1(u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f409,f195]) ).
fof(f411,plain,
k6_autgroup(sK0,k2_group_1(sK0)) = k6_relat_1(u1_struct_0(sK0)),
inference(forward_subsumption_resolution,[],[f410,f194]) ).
fof(f412,plain,
k6_autgroup(sK0,k2_group_1(sK0)) = k6_relat_1(sF26),
inference(forward_demodulation,[],[f411,f355]) ).
fof(f413,plain,
k6_autgroup(sK0,sF27) = k6_relat_1(sF26),
inference(forward_demodulation,[],[f412,f357]) ).
fof(f414,plain,
sF28 = k6_relat_1(sF26),
inference(forward_demodulation,[],[f413,f359]) ).
fof(f415,plain,
( m1_subset_1(sF27,u1_struct_0(sK0))
| v3_struct_0(sK0)
| ~ l1_group_1(sK0) ),
inference(superposition,[],[f235,f357]) ).
fof(f418,plain,
( m1_subset_1(sF27,u1_struct_0(sK0))
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f415,f197]) ).
fof(f420,plain,
m1_subset_1(sF27,u1_struct_0(sK0)),
inference(forward_subsumption_resolution,[],[f418,f193]) ).
fof(f422,plain,
m1_subset_1(sF27,sF26),
inference(forward_demodulation,[],[f420,f355]) ).
fof(f425,plain,
( $false
| spl31_4 ),
inference(forward_subsumption_resolution,[],[f422,f404]) ).
fof(f426,plain,
spl31_4,
inference(avatar_contradiction_clause,[],[f425]) ).
fof(f429,plain,
l1_struct_0(sK0),
inference(resolution,[],[f246,f193]) ).
fof(f431,plain,
( m1_fraenkel(k4_autgroup(sK0),sF26,sF26)
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(superposition,[],[f236,f355]) ).
fof(f432,plain,
( m1_fraenkel(k4_autgroup(sK0),sF26,sF26)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f431,f197]) ).
fof(f433,plain,
( m1_fraenkel(k4_autgroup(sK0),sF26,sF26)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f432,f196]) ).
fof(f434,plain,
( m1_fraenkel(k4_autgroup(sK0),sF26,sF26)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f433,f195]) ).
fof(f435,plain,
( m1_fraenkel(k4_autgroup(sK0),sF26,sF26)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f434,f194]) ).
fof(f436,plain,
m1_fraenkel(k4_autgroup(sK0),sF26,sF26),
inference(forward_subsumption_resolution,[],[f435,f193]) ).
fof(f440,plain,
( v1_funct_2(sF25,sF26,sF26)
| v1_xboole_0(sF26)
| ~ m1_fraenkel(k4_autgroup(sK0),sF26,sF26) ),
inference(resolution,[],[f250,f406]) ).
fof(f441,plain,
( v1_funct_2(sF28,sF26,sF26)
| v1_xboole_0(sF26)
| ~ m1_fraenkel(k4_autgroup(sK0),sF26,sF26)
| ~ spl31_3 ),
inference(resolution,[],[f250,f400]) ).
fof(f444,plain,
( v1_funct_2(sF28,sF26,sF26)
| v1_xboole_0(sF26)
| ~ spl31_3 ),
inference(forward_subsumption_resolution,[],[f441,f436]) ).
fof(f445,plain,
( v1_funct_2(sF25,sF26,sF26)
| v1_xboole_0(sF26) ),
inference(forward_subsumption_resolution,[],[f440,f436]) ).
fof(f449,definition,
( spl31_5
<=> v1_xboole_0(sF26) ),
introduced(definition,[new_symbols(definition,[spl31_5])],[avatar_definition]) ).
fof(f450,plain,
( ~ v1_xboole_0(sF26)
| spl31_5 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f451,plain,
( v1_xboole_0(sF26)
| ~ spl31_5 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f453,definition,
( spl31_6
<=> v1_funct_2(sF28,sF26,sF26) ),
introduced(definition,[new_symbols(definition,[spl31_6])],[avatar_definition]) ).
fof(f455,plain,
( v1_funct_2(sF28,sF26,sF26)
| ~ spl31_6 ),
inference(avatar_component_clause,[],[f453]) ).
fof(f456,plain,
( spl31_5
| spl31_6
| ~ spl31_3 ),
inference(avatar_split_clause,[],[f444,f398,f453,f449]) ).
fof(f458,definition,
( spl31_7
<=> v1_funct_2(sF25,sF26,sF26) ),
introduced(definition,[new_symbols(definition,[spl31_7])],[avatar_definition]) ).
fof(f460,plain,
( v1_funct_2(sF25,sF26,sF26)
| ~ spl31_7 ),
inference(avatar_component_clause,[],[f458]) ).
fof(f461,plain,
( spl31_5
| spl31_7 ),
inference(avatar_split_clause,[],[f445,f458,f449]) ).
fof(f477,plain,
( v1_funct_1(sF25)
| v1_xboole_0(sF26)
| ~ m1_fraenkel(k4_autgroup(sK0),sF26,sF26) ),
inference(resolution,[],[f251,f406]) ).
fof(f478,plain,
( v1_funct_1(sF28)
| v1_xboole_0(sF26)
| ~ m1_fraenkel(k4_autgroup(sK0),sF26,sF26)
| ~ spl31_3 ),
inference(resolution,[],[f251,f400]) ).
fof(f491,plain,
( ~ v1_xboole_0(sF26)
| v3_struct_0(sK0)
| ~ l1_struct_0(sK0) ),
inference(superposition,[],[f267,f355]) ).
fof(f492,plain,
( v3_struct_0(sK0)
| ~ l1_struct_0(sK0)
| ~ spl31_5 ),
inference(forward_subsumption_resolution,[],[f491,f451]) ).
fof(f493,plain,
( ~ l1_struct_0(sK0)
| ~ spl31_5 ),
inference(forward_subsumption_resolution,[],[f492,f197]) ).
fof(f494,plain,
( $false
| ~ spl31_5 ),
inference(forward_subsumption_resolution,[],[f493,f429]) ).
fof(f495,plain,
~ spl31_5,
inference(avatar_contradiction_clause,[],[f494]) ).
fof(f500,plain,
( v1_funct_1(sF28)
| ~ m1_fraenkel(k4_autgroup(sK0),sF26,sF26)
| ~ spl31_3
| spl31_5 ),
inference(forward_subsumption_resolution,[],[f478,f450]) ).
fof(f501,plain,
( v1_funct_1(sF25)
| ~ m1_fraenkel(k4_autgroup(sK0),sF26,sF26)
| spl31_5 ),
inference(forward_subsumption_resolution,[],[f477,f450]) ).
fof(f509,plain,
( v1_funct_1(sF28)
| ~ spl31_3
| spl31_5 ),
inference(forward_subsumption_resolution,[],[f500,f436]) ).
fof(f510,plain,
( v1_funct_1(sF25)
| spl31_5 ),
inference(forward_subsumption_resolution,[],[f501,f436]) ).
fof(f514,plain,
( ! [X0,X1] :
( v1_xboole_0(sF26)
| ~ v1_funct_1(X0)
| ~ v1_funct_2(X0,X1,sF26)
| ~ m1_relset_1(X0,X1,sF26)
| ~ v1_funct_1(sF25)
| k7_funct_2(X1,sF26,sF26,X0,sF25) = k5_relat_1(X0,sF25)
| ~ m1_relset_1(sF25,sF26,sF26) )
| ~ spl31_7 ),
inference(resolution,[],[f460,f329]) ).
fof(f515,plain,
( ! [X0,X1] :
( ~ v1_funct_1(X0)
| ~ v1_funct_2(X0,X1,sF26)
| ~ m1_relset_1(X0,X1,sF26)
| ~ v1_funct_1(sF25)
| k7_funct_2(X1,sF26,sF26,X0,sF25) = k5_relat_1(X0,sF25)
| ~ m1_relset_1(sF25,sF26,sF26) )
| spl31_5
| ~ spl31_7 ),
inference(forward_subsumption_resolution,[],[f514,f450]) ).
fof(f516,plain,
( ! [X0,X1] :
( ~ v1_funct_1(X0)
| ~ v1_funct_2(X0,X1,sF26)
| ~ m1_relset_1(X0,X1,sF26)
| k7_funct_2(X1,sF26,sF26,X0,sF25) = k5_relat_1(X0,sF25)
| ~ m1_relset_1(sF25,sF26,sF26) )
| spl31_5
| ~ spl31_7 ),
inference(forward_subsumption_resolution,[],[f515,f510]) ).
fof(f518,definition,
( spl31_9
<=> m1_relset_1(sF25,sF26,sF26) ),
introduced(definition,[new_symbols(definition,[spl31_9])],[avatar_definition]) ).
fof(f519,plain,
( m1_relset_1(sF25,sF26,sF26)
| ~ spl31_9 ),
inference(avatar_component_clause,[],[f518]) ).
fof(f520,plain,
( ~ m1_relset_1(sF25,sF26,sF26)
| spl31_9 ),
inference(avatar_component_clause,[],[f518]) ).
fof(f522,definition,
( spl31_10
<=> ! [X0,X1] :
( ~ v1_funct_1(X0)
| k7_funct_2(X1,sF26,sF26,X0,sF25) = k5_relat_1(X0,sF25)
| ~ m1_relset_1(X0,X1,sF26)
| ~ v1_funct_2(X0,X1,sF26) ) ),
introduced(definition,[new_symbols(definition,[spl31_10])],[avatar_definition]) ).
fof(f523,plain,
( ! [X0,X1] :
( ~ v1_funct_2(X0,X1,sF26)
| k7_funct_2(X1,sF26,sF26,X0,sF25) = k5_relat_1(X0,sF25)
| ~ m1_relset_1(X0,X1,sF26)
| ~ v1_funct_1(X0) )
| ~ spl31_10 ),
inference(avatar_component_clause,[],[f522]) ).
fof(f524,plain,
( ~ spl31_9
| spl31_10
| spl31_5
| ~ spl31_7 ),
inference(avatar_split_clause,[],[f516,f458,f449,f522,f518]) ).
fof(f527,plain,
( ! [X0,X1] :
( v1_xboole_0(sF26)
| ~ v1_funct_1(X0)
| ~ v1_funct_2(X0,X1,sF26)
| ~ m1_relset_1(X0,X1,sF26)
| ~ v1_funct_1(sF28)
| k7_funct_2(X1,sF26,sF26,X0,sF28) = k5_relat_1(X0,sF28)
| ~ m1_relset_1(sF28,sF26,sF26) )
| ~ spl31_6 ),
inference(resolution,[],[f455,f329]) ).
fof(f528,plain,
( ! [X0,X1] :
( ~ v1_funct_1(X0)
| ~ v1_funct_2(X0,X1,sF26)
| ~ m1_relset_1(X0,X1,sF26)
| ~ v1_funct_1(sF28)
| k7_funct_2(X1,sF26,sF26,X0,sF28) = k5_relat_1(X0,sF28)
| ~ m1_relset_1(sF28,sF26,sF26) )
| spl31_5
| ~ spl31_6 ),
inference(forward_subsumption_resolution,[],[f527,f450]) ).
fof(f529,plain,
( ! [X0,X1] :
( ~ v1_funct_1(X0)
| ~ v1_funct_2(X0,X1,sF26)
| ~ m1_relset_1(X0,X1,sF26)
| k7_funct_2(X1,sF26,sF26,X0,sF28) = k5_relat_1(X0,sF28)
| ~ m1_relset_1(sF28,sF26,sF26) )
| ~ spl31_3
| spl31_5
| ~ spl31_6 ),
inference(forward_subsumption_resolution,[],[f528,f509]) ).
fof(f531,definition,
( spl31_11
<=> m1_relset_1(sF28,sF26,sF26) ),
introduced(definition,[new_symbols(definition,[spl31_11])],[avatar_definition]) ).
fof(f532,plain,
( m1_relset_1(sF28,sF26,sF26)
| ~ spl31_11 ),
inference(avatar_component_clause,[],[f531]) ).
fof(f533,plain,
( ~ m1_relset_1(sF28,sF26,sF26)
| spl31_11 ),
inference(avatar_component_clause,[],[f531]) ).
fof(f535,definition,
( spl31_12
<=> ! [X0,X1] :
( ~ v1_funct_1(X0)
| k7_funct_2(X1,sF26,sF26,X0,sF28) = k5_relat_1(X0,sF28)
| ~ m1_relset_1(X0,X1,sF26)
| ~ v1_funct_2(X0,X1,sF26) ) ),
introduced(definition,[new_symbols(definition,[spl31_12])],[avatar_definition]) ).
fof(f536,plain,
( ! [X0,X1] :
( ~ v1_funct_2(X0,X1,sF26)
| k7_funct_2(X1,sF26,sF26,X0,sF28) = k5_relat_1(X0,sF28)
| ~ m1_relset_1(X0,X1,sF26)
| ~ v1_funct_1(X0) )
| ~ spl31_12 ),
inference(avatar_component_clause,[],[f535]) ).
fof(f537,plain,
( ~ spl31_11
| spl31_12
| ~ spl31_3
| spl31_5
| ~ spl31_6 ),
inference(avatar_split_clause,[],[f529,f453,f449,f398,f535,f531]) ).
fof(f570,plain,
( m2_relset_1(sF25,sF26,sF26)
| v1_xboole_0(sF26)
| ~ m1_fraenkel(k4_autgroup(sK0),sF26,sF26) ),
inference(resolution,[],[f249,f406]) ).
fof(f571,plain,
( m2_relset_1(sF28,sF26,sF26)
| v1_xboole_0(sF26)
| ~ m1_fraenkel(k4_autgroup(sK0),sF26,sF26)
| ~ spl31_3 ),
inference(resolution,[],[f249,f400]) ).
fof(f574,plain,
( m2_relset_1(sF28,sF26,sF26)
| ~ m1_fraenkel(k4_autgroup(sK0),sF26,sF26)
| ~ spl31_3
| spl31_5 ),
inference(forward_subsumption_resolution,[],[f571,f450]) ).
fof(f575,plain,
( m2_relset_1(sF25,sF26,sF26)
| ~ m1_fraenkel(k4_autgroup(sK0),sF26,sF26)
| spl31_5 ),
inference(forward_subsumption_resolution,[],[f570,f450]) ).
fof(f578,plain,
( m2_relset_1(sF28,sF26,sF26)
| ~ spl31_3
| spl31_5 ),
inference(forward_subsumption_resolution,[],[f574,f436]) ).
fof(f579,plain,
( m2_relset_1(sF25,sF26,sF26)
| spl31_5 ),
inference(forward_subsumption_resolution,[],[f575,f436]) ).
fof(f581,plain,
( m1_relset_1(sF25,sF26,sF26)
| spl31_5 ),
inference(resolution,[],[f579,f333]) ).
fof(f582,plain,
( sF25 = k7_relset_1(sF26,sF26,sF26,sF26,sF25,k6_relat_1(sF26))
| spl31_5 ),
inference(resolution,[],[f579,f350]) ).
fof(f583,plain,
( sF25 = k7_relset_1(sF26,sF26,sF26,sF26,k6_relat_1(sF26),sF25)
| spl31_5 ),
inference(resolution,[],[f579,f349]) ).
fof(f584,plain,
( sF25 = k7_relset_1(sF26,sF26,sF26,sF26,sF28,sF25)
| spl31_5 ),
inference(forward_demodulation,[],[f583,f414]) ).
fof(f585,plain,
( sF25 = k7_relset_1(sF26,sF26,sF26,sF26,sF25,sF28)
| spl31_5 ),
inference(forward_demodulation,[],[f582,f414]) ).
fof(f586,plain,
( $false
| spl31_5
| spl31_9 ),
inference(forward_subsumption_resolution,[],[f581,f520]) ).
fof(f587,plain,
( spl31_5
| spl31_9 ),
inference(avatar_contradiction_clause,[],[f586]) ).
fof(f588,plain,
( ! [X2,X0,X1] :
( ~ m1_relset_1(X0,X1,X2)
| k5_relat_1(X0,sF25) = k7_relset_1(X1,X2,sF26,sF26,X0,sF25) )
| ~ spl31_9 ),
inference(resolution,[],[f519,f330]) ).
fof(f590,plain,
( k7_funct_2(sF26,sF26,sF26,sF28,sF25) = k5_relat_1(sF28,sF25)
| ~ m1_relset_1(sF28,sF26,sF26)
| ~ v1_funct_1(sF28)
| ~ spl31_6
| ~ spl31_10 ),
inference(resolution,[],[f523,f455]) ).
fof(f596,plain,
( m1_relset_1(sF28,sF26,sF26)
| ~ spl31_3
| spl31_5 ),
inference(resolution,[],[f578,f333]) ).
fof(f601,plain,
( $false
| ~ spl31_3
| spl31_5
| spl31_11 ),
inference(forward_subsumption_resolution,[],[f596,f533]) ).
fof(f602,plain,
( ~ spl31_3
| spl31_5
| spl31_11 ),
inference(avatar_contradiction_clause,[],[f601]) ).
fof(f603,plain,
( k7_funct_2(sF26,sF26,sF26,sF28,sF25) = k5_relat_1(sF28,sF25)
| ~ v1_funct_1(sF28)
| ~ spl31_6
| ~ spl31_10
| ~ spl31_11 ),
inference(forward_subsumption_resolution,[],[f590,f532]) ).
fof(f604,plain,
( k7_funct_2(sF26,sF26,sF26,sF28,sF25) = k5_relat_1(sF28,sF25)
| ~ spl31_3
| spl31_5
| ~ spl31_6
| ~ spl31_10
| ~ spl31_11 ),
inference(forward_subsumption_resolution,[],[f603,f509]) ).
fof(f605,plain,
( sF29 = k5_relat_1(sF28,sF25)
| ~ spl31_3
| spl31_5
| ~ spl31_6
| ~ spl31_10
| ~ spl31_11 ),
inference(forward_demodulation,[],[f604,f361]) ).
fof(f606,plain,
( ! [X2,X0,X1] :
( ~ m1_relset_1(X0,X1,X2)
| k5_relat_1(X0,sF28) = k7_relset_1(X1,X2,sF26,sF26,X0,sF28) )
| ~ spl31_11 ),
inference(resolution,[],[f532,f330]) ).
fof(f607,plain,
( k7_funct_2(sF26,sF26,sF26,sF25,sF28) = k5_relat_1(sF25,sF28)
| ~ m1_relset_1(sF25,sF26,sF26)
| ~ v1_funct_1(sF25)
| ~ spl31_7
| ~ spl31_12 ),
inference(resolution,[],[f536,f460]) ).
fof(f613,plain,
( k7_funct_2(sF26,sF26,sF26,sF25,sF28) = k5_relat_1(sF25,sF28)
| ~ v1_funct_1(sF25)
| ~ spl31_7
| ~ spl31_9
| ~ spl31_12 ),
inference(forward_subsumption_resolution,[],[f607,f519]) ).
fof(f615,plain,
( k7_funct_2(sF26,sF26,sF26,sF25,sF28) = k5_relat_1(sF25,sF28)
| spl31_5
| ~ spl31_7
| ~ spl31_9
| ~ spl31_12 ),
inference(forward_subsumption_resolution,[],[f613,f510]) ).
fof(f616,plain,
( sF30 = k5_relat_1(sF25,sF28)
| spl31_5
| ~ spl31_7
| ~ spl31_9
| ~ spl31_12 ),
inference(forward_demodulation,[],[f615,f363]) ).
fof(f621,plain,
( k7_relset_1(sF26,sF26,sF26,sF26,sF28,sF25) = k5_relat_1(sF28,sF25)
| ~ spl31_9
| ~ spl31_11 ),
inference(resolution,[],[f588,f532]) ).
fof(f622,plain,
( sF29 = k7_relset_1(sF26,sF26,sF26,sF26,sF28,sF25)
| ~ spl31_3
| spl31_5
| ~ spl31_6
| ~ spl31_9
| ~ spl31_10
| ~ spl31_11 ),
inference(forward_demodulation,[],[f621,f605]) ).
fof(f623,plain,
( sF25 = sF29
| ~ spl31_3
| spl31_5
| ~ spl31_6
| ~ spl31_9
| ~ spl31_10
| ~ spl31_11 ),
inference(forward_demodulation,[],[f622,f584]) ).
fof(f624,plain,
( spl31_2
| ~ spl31_3
| spl31_5
| ~ spl31_6
| ~ spl31_9
| ~ spl31_10
| ~ spl31_11 ),
inference(avatar_split_clause,[],[f623,f531,f522,f518,f453,f449,f398,f371]) ).
fof(f755,plain,
( k7_relset_1(sF26,sF26,sF26,sF26,sF25,sF28) = k5_relat_1(sF25,sF28)
| ~ spl31_9
| ~ spl31_11 ),
inference(resolution,[],[f606,f519]) ).
fof(f758,plain,
( sF30 = k7_relset_1(sF26,sF26,sF26,sF26,sF25,sF28)
| spl31_5
| ~ spl31_7
| ~ spl31_9
| ~ spl31_11
| ~ spl31_12 ),
inference(forward_demodulation,[],[f755,f616]) ).
fof(f759,plain,
( sF25 = sF30
| spl31_5
| ~ spl31_7
| ~ spl31_9
| ~ spl31_11
| ~ spl31_12 ),
inference(forward_demodulation,[],[f758,f585]) ).
fof(f760,plain,
( $false
| spl31_1
| spl31_5
| ~ spl31_7
| ~ spl31_9
| ~ spl31_11
| ~ spl31_12 ),
inference(forward_subsumption_resolution,[],[f759,f369]) ).
fof(f761,plain,
( spl31_1
| spl31_5
| ~ spl31_7
| ~ spl31_9
| ~ spl31_11
| ~ spl31_12 ),
inference(avatar_contradiction_clause,[],[f760]) ).
cnf(s1,plain,
( ~ spl31_1
| ~ spl31_2 ),
inference(sat_conversion,[],[f374]) ).
cnf(s2,plain,
( spl31_3
| ~ spl31_4 ),
inference(sat_conversion,[],[f405]) ).
cnf(s4,plain,
spl31_4,
inference(sat_conversion,[],[f426]) ).
cnf(s5,plain,
( ~ spl31_3
| spl31_5
| spl31_6 ),
inference(sat_conversion,[],[f456]) ).
cnf(s6,plain,
( spl31_5
| spl31_7 ),
inference(sat_conversion,[],[f461]) ).
cnf(s8,plain,
~ spl31_5,
inference(sat_conversion,[],[f495]) ).
cnf(s9,plain,
( spl31_5
| ~ spl31_7
| ~ spl31_9
| spl31_10 ),
inference(sat_conversion,[],[f524]) ).
cnf(s10,plain,
( ~ spl31_3
| spl31_5
| ~ spl31_6
| ~ spl31_11
| spl31_12 ),
inference(sat_conversion,[],[f537]) ).
cnf(s12,plain,
( spl31_5
| spl31_9 ),
inference(sat_conversion,[],[f587]) ).
cnf(s13,plain,
( ~ spl31_3
| spl31_5
| spl31_11 ),
inference(sat_conversion,[],[f602]) ).
cnf(s14,plain,
( spl31_2
| ~ spl31_3
| spl31_5
| ~ spl31_6
| ~ spl31_9
| ~ spl31_10
| ~ spl31_11 ),
inference(sat_conversion,[],[f624]) ).
cnf(s21,plain,
( spl31_1
| spl31_5
| ~ spl31_7
| ~ spl31_9
| ~ spl31_11
| ~ spl31_12 ),
inference(sat_conversion,[],[f761]) ).
cnf(s22,plain,
spl31_9,
inference(rat,[],[s12,s8]) ).
cnf(s24,plain,
spl31_7,
inference(rat,[],[s6,s8]) ).
cnf(s25,plain,
spl31_10,
inference(rat,[],[s9,s8,s22,s24]) ).
cnf(s26,plain,
( ~ spl31_3
| spl31_6 ),
inference(rat,[],[s5,s8]) ).
cnf(s27,plain,
spl31_3,
inference(rat,[],[s2,s4]) ).
cnf(s28,plain,
spl31_11,
inference(rat,[],[s13,s8,s27]) ).
cnf(s29,plain,
spl31_6,
inference(rat,[],[s26,s27]) ).
cnf(s30,plain,
spl31_12,
inference(rat,[],[s10,s27,s28,s8,s29]) ).
cnf(s31,plain,
spl31_2,
inference(rat,[],[s14,s28,s25,s22,s27,s8,s29]) ).
cnf(s32,plain,
spl31_1,
inference(rat,[],[s21,s28,s24,s22,s8,s30]) ).
cnf(s33,plain,
$false,
inference(rat,[],[s1,s31,s32]) ).
fof(f762,plain,
$false,
inference(avatar_sat_refutation,[],[s33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP631+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n006.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 10:15:11 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 6.69/2.00 % (2767886)Detected formulas, will run a generic FOF schedule.
% 6.69/2.00 % (2767895)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=17126320:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.69/2.00 % (2767895)Refutation not found, incomplete strategy
% 6.69/2.00 % (2767895)------------------------------
% 6.69/2.00 % (2767895)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/2.00 % (2767895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/2.00 % (2767895)CaDiCaL version: 2.1.3
% 6.69/2.00 % (2767895)Termination reason: Refutation not found, incomplete strategy
% 6.69/2.00 % (2767895)Time elapsed: 0.005 s
% 6.69/2.00 % (2767895)Peak memory usage: 88 MB
% 6.69/2.00 % (2767895)Instructions burned: 14 (million)
% 6.69/2.00 % (2767897)dis-21_1_sil=8000:lcm=predicate:random_seed=2988011848: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)
% 6.69/2.00 % (2767893)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=2169153864:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.69/2.00 % (2767894)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3666635253:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.69/2.00 % (2767892)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=1991081789:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.69/2.00 % (2767891)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=2934257441:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.69/2.00 % (2767896)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=222808571:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.69/2.00 % (2767894)Refutation not found, incomplete strategy
% 6.69/2.00 % (2767894)------------------------------
% 6.69/2.00 % (2767894)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/2.00 % (2767894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/2.00 % (2767894)CaDiCaL version: 2.1.3
% 6.69/2.00 % (2767894)Termination reason: Refutation not found, incomplete strategy
% 6.69/2.00 % (2767894)Time elapsed: 0.002 s
% 6.69/2.00 % (2767894)Peak memory usage: 88 MB
% 6.69/2.00 % (2767894)Instructions burned: 1 (million)
% 6.69/2.00 % (2767897)Instruction limit reached!
% 6.69/2.00 % (2767897)------------------------------
% 6.69/2.00 % (2767897)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/2.00 % (2767897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/2.00 % (2767897)CaDiCaL version: 2.1.3
% 6.69/2.00 % (2767897)Termination reason: Instruction limit
% 6.69/2.00 % (2767897)Termination phase: Saturation
% 6.69/2.00 % (2767897)Time elapsed: 0.067 s
% 6.69/2.00 % (2767897)Peak memory usage: 90 MB
% 6.69/2.00 % (2767897)Instructions burned: 129 (million)
% 6.69/2.00 % (2767896)Instruction limit reached!
% 6.69/2.00 % (2767896)------------------------------
% 6.69/2.00 % (2767896)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/2.00 % (2767896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/2.00 % (2767896)CaDiCaL version: 2.1.3
% 6.69/2.00 % (2767896)Termination reason: Instruction limit
% 6.69/2.00 % (2767896)Termination phase: Saturation
% 6.69/2.00 % (2767896)Time elapsed: 0.103 s
% 6.69/2.00 % (2767896)Peak memory usage: 90 MB
% 6.69/2.00 % (2767896)Instructions burned: 139 (million)
% 6.69/2.00 % (2767895)------------------------------
% 6.69/2.00 % (2767895)------------------------------
% 6.69/2.00 % (2767905)lrs+10_1_sil=8000:sp=occurrence:random_seed=73831659:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.69/2.00 % (2767907)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4259782841:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.69/2.00 % (2767907)Refutation not found, incomplete strategy
% 6.69/2.00 % (2767907)------------------------------
% 6.69/2.00 % (2767907)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/2.00 % (2767907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/2.00 % (2767907)CaDiCaL version: 2.1.3
% 6.69/2.00 % (2767907)Termination reason: Refutation not found, incomplete strategy
% 6.69/2.00 % (2767907)Time elapsed: 0.002 s
% 6.69/2.00 % (2767907)Peak memory usage: 88 MB
% 6.69/2.00 % (2767907)Instructions burned: 4 (million)
% 6.69/2.00 % (2767894)------------------------------
% 6.69/2.00 % (2767894)------------------------------
% 6.69/2.00 % (2767906)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1058821317:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.69/2.00 % (2767906)Refutation not found, incomplete strategy
% 6.69/2.00 % (2767906)------------------------------
% 6.69/2.00 % (2767906)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/2.00 % (2767906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/2.00 % (2767906)CaDiCaL version: 2.1.3
% 6.69/2.00 % (2767906)Termination reason: Refutation not found, incomplete strategy
% 6.69/2.00 % (2767906)Time elapsed: 0.003 s
% 6.69/2.00 % (2767906)Peak memory usage: 89 MB
% 6.69/2.00 % (2767906)Instructions burned: 2 (million)
% 6.69/2.00 % (2767907)------------------------------
% 6.69/2.00 % (2767907)------------------------------
% 6.69/2.00 % (2767905)Instruction limit reached!
% 6.69/2.00 % (2767905)------------------------------
% 6.69/2.00 % (2767905)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/2.00 % (2767905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/2.00 % (2767905)CaDiCaL version: 2.1.3
% 6.69/2.00 % (2767905)Termination reason: Instruction limit
% 6.69/2.00 % (2767905)Termination phase: Saturation
% 6.69/2.00 % (2767905)Time elapsed: 0.166 s
% 6.69/2.00 % (2767905)Peak memory usage: 92 MB
% 6.69/2.00 % (2767905)Instructions burned: 287 (million)
% 6.69/2.00 % (2767910)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=3452565286:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 6.69/2.00 % (2767912)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1465637505:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 6.69/2.00 % (2767912)Refutation not found, incomplete strategy
% 6.69/2.00 % (2767912)------------------------------
% 6.69/2.00 % (2767912)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/2.00 % (2767912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/2.00 % (2767912)CaDiCaL version: 2.1.3
% 6.69/2.00 % (2767912)Termination reason: Refutation not found, incomplete strategy
% 6.69/2.00 % (2767912)Time elapsed: 0.002 s
% 6.69/2.00 % (2767912)Peak memory usage: 88 MB
% 6.69/2.00 % (2767912)Instructions burned: 5 (million)
% 6.69/2.00 % (2767906)------------------------------
% 6.69/2.00 % (2767906)------------------------------
% 6.69/2.00 % (2767913)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4165485608:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.69/2.00 % (2767910)Instruction limit reached!
% 6.69/2.00 % (2767910)------------------------------
% 6.69/2.00 % (2767910)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/2.00 % (2767910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/2.00 % (2767910)CaDiCaL version: 2.1.3
% 6.69/2.00 % (2767910)Termination reason: Instruction limit
% 6.69/2.00 % (2767910)Termination phase: Saturation
% 6.69/2.00 % (2767910)Time elapsed: 0.144 s
% 6.69/2.00 % (2767910)Peak memory usage: 92 MB
% 6.69/2.00 % (2767910)Instructions burned: 248 (million)
% 6.69/2.00 % (2767912)------------------------------
% 6.69/2.00 % (2767912)------------------------------
% 6.69/2.00 % (2767891)First to succeed.
% 6.69/2.00 % (2767891)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2767886"
% 6.69/2.00 % (2767916)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=614442498:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 6.69/2.00 % (2767893)Also succeeded, but the first one will report.
% 6.69/2.00 % (2767918)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1952409627:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 6.69/2.00 % (2767916)Also succeeded, but the first one will report.
% 6.69/2.00 % (2767919)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3785243341:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 6.69/2.00 % (2767919)Refutation not found, incomplete strategy
% 6.69/2.00 % (2767919)------------------------------
% 6.69/2.00 % (2767919)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/2.00 % (2767919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/2.00 % (2767919)CaDiCaL version: 2.1.3
% 6.69/2.00 % (2767919)Termination reason: Refutation not found, incomplete strategy
% 6.69/2.00 % (2767919)Time elapsed: 0.001 s
% 6.69/2.00 % (2767919)Peak memory usage: 88 MB
% 6.69/2.00 % (2767919)Instructions burned: 2 (million)
% 6.69/2.00 % (2767918)Instruction limit reached!
% 6.69/2.00 % (2767918)------------------------------
% 6.69/2.00 % (2767918)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/2.00 % (2767918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/2.00 % (2767918)CaDiCaL version: 2.1.3
% 6.69/2.00 % (2767918)Termination reason: Instruction limit
% 6.69/2.00 % (2767918)Termination phase: Saturation
% 6.69/2.00 % (2767918)Time elapsed: 0.067 s
% 6.69/2.00 % (2767918)Peak memory usage: 89 MB
% 6.69/2.00 % (2767918)Instructions burned: 129 (million)
% 6.69/2.00 % (2767919)------------------------------
% 6.69/2.00 % (2767919)------------------------------
% 6.69/2.00 % (2767891)Refutation found. Thanks to Tanya!
% 6.69/2.00 % SZS status Theorem for theBenchmark
% 6.69/2.00 % SZS output start Proof for theBenchmark
% See solution above
% 8.46/2.09 % (2767891)------------------------------
% 8.46/2.09 % (2767891)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.46/2.09 % (2767891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.46/2.09 % (2767891)CaDiCaL version: 2.1.3
% 8.46/2.09 % (2767891)Termination reason: Refutation
% 8.46/2.09 % (2767891)Time elapsed: 0.685 s
% 8.46/2.09 % (2767891)Peak memory usage: 130 MB
% 8.46/2.09 % (2767891)Instructions burned: 1014 (million)
% 8.46/2.09 % (2767891)------------------------------
% 8.46/2.09 % (2767891)------------------------------
% 8.46/2.09 % (2767886)Success in time 1.13 s
% 8.46/2.09 % Vampire exiting
%------------------------------------------------------------------------------