%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP624+2 : 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 : n002.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 10:15:04 AM UTC 2026
% Result : Theorem 12.25s 2.79s
% Output : Refutation 13.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 21
% Syntax : Number of formulae : 182 ( 37 unt; 9 def)
% Number of atoms : 803 ( 73 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 1070 ( 449 ~; 510 |; 78 &)
% ( 13 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 5 prp; 0-4 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-6 aty)
% Number of variables : 206 ( 0 sgn 196 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f973,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
<=> m1_relset_1(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f1483,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( ~ v1_xboole_0(X0)
& ~ v1_xboole_0(X1)
& v1_funct_1(X3)
& v1_funct_2(X3,k2_zfmisc_1(X0,X1),X2)
& m1_relset_1(X3,k2_zfmisc_1(X0,X1),X2)
& m1_subset_1(X4,X0)
& m1_subset_1(X5,X1) )
=> k2_binop_1(X0,X1,X2,X3,X4,X5) = k1_binop_1(X3,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
fof(f1870,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(f1874,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(f2483,axiom,
! [X0] :
( l1_struct_0(X0)
=> ( v3_struct_0(X0)
<=> v1_xboole_0(u1_struct_0(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_struct_0) ).
fof(f2766,axiom,
! [X0] :
( l1_group_1(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(f3801,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(f3802,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ( v1_funct_1(k2_autgroup(X0))
& v1_funct_2(k2_autgroup(X0),k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
& m2_relset_1(k2_autgroup(X0),k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_autgroup) ).
fof(f3804,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(f3819,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( ( v1_funct_1(X1)
& v1_funct_2(X1,k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
& m2_relset_1(X1,k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0)) )
=> ( X1 = k2_autgroup(X0)
<=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
=> ! [X3] :
( m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
=> k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),X1,X2,X3) = k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_autgroup) ).
fof(f3826,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(f3828,conjecture,
! [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))
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
=> k1_binop_1(k2_autgroup(X0),X1,X2) = k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_autgroup) ).
fof(f3829,negated_conjecture,
~ ! [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))
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
=> k1_binop_1(k2_autgroup(X0),X1,X2) = k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X2,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f3828]) ).
fof(f5524,plain,
! [X0,X1,X2,X3,X4,X5] :
( k2_binop_1(X0,X1,X2,X3,X4,X5) = k1_binop_1(X3,X4,X5)
| v1_xboole_0(X0)
| v1_xboole_0(X1)
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,k2_zfmisc_1(X0,X1),X2)
| ~ m1_relset_1(X3,k2_zfmisc_1(X0,X1),X2)
| ~ m1_subset_1(X4,X0)
| ~ m1_subset_1(X5,X1) ),
inference(ennf_transformation,[],[f1483]) ).
fof(f5525,plain,
! [X0,X1,X2,X3,X4,X5] :
( k2_binop_1(X0,X1,X2,X3,X4,X5) = k1_binop_1(X3,X4,X5)
| v1_xboole_0(X0)
| v1_xboole_0(X1)
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,k2_zfmisc_1(X0,X1),X2)
| ~ m1_relset_1(X3,k2_zfmisc_1(X0,X1),X2)
| ~ m1_subset_1(X4,X0)
| ~ m1_subset_1(X5,X1) ),
inference(flattening,[],[f5524]) ).
fof(f5998,plain,
! [X0,X1,X2] :
( ( ~ v1_xboole_0(X2)
& v1_fraenkel(X2) )
| ~ m1_fraenkel(X2,X0,X1) ),
inference(ennf_transformation,[],[f1870]) ).
fof(f6003,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,[],[f1874]) ).
fof(f6004,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,[],[f6003]) ).
fof(f6568,plain,
! [X0] :
( ( v3_struct_0(X0)
<=> v1_xboole_0(u1_struct_0(X0)) )
| ~ l1_struct_0(X0) ),
inference(ennf_transformation,[],[f2483]) ).
fof(f6988,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f2766]) ).
fof(f8576,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,[],[f3801]) ).
fof(f8577,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,[],[f8576]) ).
fof(f8578,plain,
! [X0] :
( ( v1_funct_1(k2_autgroup(X0))
& v1_funct_2(k2_autgroup(X0),k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
& m2_relset_1(k2_autgroup(X0),k2_zfmisc_1(k1_autgroup(X0),k1_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,[],[f3802]) ).
fof(f8579,plain,
! [X0] :
( ( v1_funct_1(k2_autgroup(X0))
& v1_funct_2(k2_autgroup(X0),k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
& m2_relset_1(k2_autgroup(X0),k2_zfmisc_1(k1_autgroup(X0),k1_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,[],[f8578]) ).
fof(f8582,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,[],[f3804]) ).
fof(f8583,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,[],[f8582]) ).
fof(f8610,plain,
! [X0] :
( ! [X1] :
( ( X1 = k2_autgroup(X0)
<=> ! [X2] :
( ! [X3] :
( k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),X1,X2,X3) = k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X3,X2)
| ~ m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) )
| ~ m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ) )
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| ~ m2_relset_1(X1,k2_zfmisc_1(k1_autgroup(X0),k1_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,[],[f3819]) ).
fof(f8611,plain,
! [X0] :
( ! [X1] :
( ( X1 = k2_autgroup(X0)
<=> ! [X2] :
( ! [X3] :
( k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),X1,X2,X3) = k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X3,X2)
| ~ m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) )
| ~ m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ) )
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| ~ m2_relset_1(X1,k2_zfmisc_1(k1_autgroup(X0),k1_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,[],[f8610]) ).
fof(f8624,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,[],[f3826]) ).
fof(f8625,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,[],[f8624]) ).
fof(f8628,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X2,X1) != k1_binop_1(k2_autgroup(X0),X1,X2)
& m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k4_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,[],[f3829]) ).
fof(f8629,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X2,X1) != k1_binop_1(k2_autgroup(X0),X1,X2)
& m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k4_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,[],[f8628]) ).
fof(f9357,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,[],[f973]) ).
fof(f9876,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,[],[f6004]) ).
fof(f10288,plain,
! [X0] :
( ( ( v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) )
& ( v1_xboole_0(u1_struct_0(X0))
| ~ v3_struct_0(X0) ) )
| ~ l1_struct_0(X0) ),
inference(nnf_transformation,[],[f6568]) ).
fof(f10938,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = k2_autgroup(X0)
| ? [X2] :
( ? [X3] :
( k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),X1,X2,X3) != k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X3,X2)
& m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) )
& m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ) )
& ( ! [X2] :
( ! [X3] :
( k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),X1,X2,X3) = k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X3,X2)
| ~ m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) )
| ~ m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) )
| k2_autgroup(X0) != X1 ) )
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| ~ m2_relset_1(X1,k2_zfmisc_1(k1_autgroup(X0),k1_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(nnf_transformation,[],[f8611]) ).
fof(f10939,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = k2_autgroup(X0)
| ? [X2] :
( ? [X3] :
( k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),X1,X2,X3) != k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X3,X2)
& m2_fraenkel(X3,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) )
& m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ) )
& ( ! [X4] :
( ! [X5] :
( k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),X1,X4,X5) = k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X5,X4)
| ~ m2_fraenkel(X5,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) )
| ~ m2_fraenkel(X4,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) )
| k2_autgroup(X0) != X1 ) )
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| ~ m2_relset_1(X1,k2_zfmisc_1(k1_autgroup(X0),k1_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(rectify,[],[f10938]) ).
fof(f10940,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = k2_autgroup(X0)
| ( k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),X1,sK1307(X0,X1),sK1308(X0,X1)) != k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),sK1308(X0,X1),sK1307(X0,X1))
& m2_fraenkel(sK1308(X0,X1),u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
& m2_fraenkel(sK1307(X0,X1),u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ) )
& ( ! [X4] :
( ! [X5] :
( k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),X1,X4,X5) = k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X5,X4)
| ~ m2_fraenkel(X5,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) )
| ~ m2_fraenkel(X4,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) )
| k2_autgroup(X0) != X1 ) )
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| ~ m2_relset_1(X1,k2_zfmisc_1(k1_autgroup(X0),k1_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(skolemize,[status(esa),new_symbols(skolem,[sK1307,sK1308]),skolemize(X2,sK1307(X0,X1)),skolemize(X3,sK1308(X0,X1))],[f10939]) ).
fof(f10947,plain,
( k7_funct_2(u1_struct_0(sK1314),u1_struct_0(sK1314),u1_struct_0(sK1314),sK1316,sK1315) != k1_binop_1(k2_autgroup(sK1314),sK1315,sK1316)
& m2_fraenkel(sK1316,u1_struct_0(sK1314),u1_struct_0(sK1314),k4_autgroup(sK1314))
& m2_fraenkel(sK1315,u1_struct_0(sK1314),u1_struct_0(sK1314),k4_autgroup(sK1314))
& ~ v3_struct_0(sK1314)
& v1_group_1(sK1314)
& v3_group_1(sK1314)
& v4_group_1(sK1314)
& l1_group_1(sK1314) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1314,sK1315,sK1316]),skolemize(X0,sK1314),skolemize(X1,sK1315),skolemize(X2,sK1316)],[f8629]) ).
fof(f12406,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f9357]) ).
fof(f13306,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ v1_funct_2(X3,k2_zfmisc_1(X0,X1),X2)
| v1_xboole_0(X0)
| v1_xboole_0(X1)
| ~ v1_funct_1(X3)
| k2_binop_1(X0,X1,X2,X3,X4,X5) = k1_binop_1(X3,X4,X5)
| ~ m1_relset_1(X3,k2_zfmisc_1(X0,X1),X2)
| ~ m1_subset_1(X4,X0)
| ~ m1_subset_1(X5,X1) ),
inference(cnf_transformation,[],[f5525]) ).
fof(f14273,plain,
! [X2,X0,X1] :
( ~ m1_fraenkel(X2,X0,X1)
| ~ v1_xboole_0(X2) ),
inference(cnf_transformation,[],[f5998]) ).
fof(f14279,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,[],[f9876]) ).
fof(f14280,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,[],[f9876]) ).
fof(f15564,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(cnf_transformation,[],[f10288]) ).
fof(f16045,plain,
! [X0] :
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f6988]) ).
fof(f18051,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,[],[f8577]) ).
fof(f18052,plain,
! [X0] :
( m2_relset_1(k2_autgroup(X0),k2_zfmisc_1(k1_autgroup(X0),k1_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(cnf_transformation,[],[f8579]) ).
fof(f18053,plain,
! [X0] :
( v1_funct_2(k2_autgroup(X0),k2_zfmisc_1(k1_autgroup(X0),k1_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(cnf_transformation,[],[f8579]) ).
fof(f18054,plain,
! [X0] :
( v1_funct_1(k2_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,[],[f8579]) ).
fof(f18060,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,[],[f8583]) ).
fof(f18104,plain,
! [X0,X1,X4,X5] :
( k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),X1,X4,X5) = k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X5,X4)
| ~ m2_fraenkel(X5,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ m2_fraenkel(X4,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| k2_autgroup(X0) != X1
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| ~ m2_relset_1(X1,k2_zfmisc_1(k1_autgroup(X0),k1_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(cnf_transformation,[],[f10940]) ).
fof(f18125,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,[],[f8625]) ).
fof(f18127,plain,
l1_group_1(sK1314),
inference(cnf_transformation,[],[f10947]) ).
fof(f18128,plain,
v4_group_1(sK1314),
inference(cnf_transformation,[],[f10947]) ).
fof(f18129,plain,
v3_group_1(sK1314),
inference(cnf_transformation,[],[f10947]) ).
fof(f18130,plain,
v1_group_1(sK1314),
inference(cnf_transformation,[],[f10947]) ).
fof(f18131,plain,
~ v3_struct_0(sK1314),
inference(cnf_transformation,[],[f10947]) ).
fof(f18132,plain,
m2_fraenkel(sK1315,u1_struct_0(sK1314),u1_struct_0(sK1314),k4_autgroup(sK1314)),
inference(cnf_transformation,[],[f10947]) ).
fof(f18133,plain,
m2_fraenkel(sK1316,u1_struct_0(sK1314),u1_struct_0(sK1314),k4_autgroup(sK1314)),
inference(cnf_transformation,[],[f10947]) ).
fof(f18134,plain,
k7_funct_2(u1_struct_0(sK1314),u1_struct_0(sK1314),u1_struct_0(sK1314),sK1316,sK1315) != k1_binop_1(k2_autgroup(sK1314),sK1315,sK1316),
inference(cnf_transformation,[],[f10947]) ).
fof(f20110,plain,
! [X0,X4,X5] :
( ~ v1_funct_2(k2_autgroup(X0),k2_zfmisc_1(k1_autgroup(X0),k1_autgroup(X0)),k1_autgroup(X0))
| ~ m2_fraenkel(X5,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ m2_fraenkel(X4,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ v1_funct_1(k2_autgroup(X0))
| k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X5,X4) = k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),k2_autgroup(X0),X4,X5)
| ~ m2_relset_1(k2_autgroup(X0),k2_zfmisc_1(k1_autgroup(X0),k1_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(equality_resolution,[],[f18104]) ).
fof(f20115,definition,
sF1317 = u1_struct_0(sK1314),
introduced(definition,[new_symbols(definition,[sF1317])],[function_definition]) ).
fof(f20116,plain,
u1_struct_0(sK1314) = sF1317,
inference(reorient_equations,[],[f20115]) ).
fof(f20117,definition,
sF1318 = k7_funct_2(sF1317,sF1317,sF1317,sK1316,sK1315),
introduced(definition,[new_symbols(definition,[sF1318])],[function_definition]) ).
fof(f20118,plain,
k7_funct_2(sF1317,sF1317,sF1317,sK1316,sK1315) = sF1318,
inference(reorient_equations,[],[f20117]) ).
fof(f20119,definition,
sF1319 = k2_autgroup(sK1314),
introduced(definition,[new_symbols(definition,[sF1319])],[function_definition]) ).
fof(f20120,plain,
k2_autgroup(sK1314) = sF1319,
inference(reorient_equations,[],[f20119]) ).
fof(f20121,definition,
sF1320 = k1_binop_1(sF1319,sK1315,sK1316),
introduced(definition,[new_symbols(definition,[sF1320])],[function_definition]) ).
fof(f20122,plain,
k1_binop_1(sF1319,sK1315,sK1316) = sF1320,
inference(reorient_equations,[],[f20121]) ).
fof(f20123,plain,
sF1318 != sF1320,
inference(definition_folding,[],[f18134,f20122,f20120,f20118,f20116,f20116,f20116]) ).
fof(f20124,definition,
sF1321 = k4_autgroup(sK1314),
introduced(definition,[new_symbols(definition,[sF1321])],[function_definition]) ).
fof(f20125,plain,
k4_autgroup(sK1314) = sF1321,
inference(reorient_equations,[],[f20124]) ).
fof(f20126,plain,
m2_fraenkel(sK1316,sF1317,sF1317,sF1321),
inference(definition_folding,[],[f18133,f20125,f20116,f20116]) ).
fof(f20127,plain,
m2_fraenkel(sK1315,sF1317,sF1317,sF1321),
inference(definition_folding,[],[f18132,f20125,f20116,f20116]) ).
fof(f23031,plain,
( m1_fraenkel(k4_autgroup(sK1314),sF1317,sF1317)
| v3_struct_0(sK1314)
| ~ v1_group_1(sK1314)
| ~ v3_group_1(sK1314)
| ~ v4_group_1(sK1314)
| ~ l1_group_1(sK1314) ),
inference(superposition,[],[f18060,f20116]) ).
fof(f23032,plain,
! [X0,X1] :
( m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| v3_struct_0(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_subset_1(X0,k4_autgroup(X1))
| v1_xboole_0(u1_struct_0(X1))
| ~ m1_fraenkel(k4_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
inference(resolution,[],[f18125,f14280]) ).
fof(f23033,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF1317,sF1317,k4_autgroup(sK1314))
| m2_fraenkel(X0,sF1317,sF1317,k1_autgroup(sK1314))
| v3_struct_0(sK1314)
| ~ v1_group_1(sK1314)
| ~ v3_group_1(sK1314)
| ~ v4_group_1(sK1314)
| ~ l1_group_1(sK1314) ),
inference(superposition,[],[f18125,f20116]) ).
fof(f23042,plain,
( v1_funct_2(sF1319,k2_zfmisc_1(k1_autgroup(sK1314),k1_autgroup(sK1314)),k1_autgroup(sK1314))
| v3_struct_0(sK1314)
| ~ v1_group_1(sK1314)
| ~ v3_group_1(sK1314)
| ~ v4_group_1(sK1314)
| ~ l1_group_1(sK1314) ),
inference(superposition,[],[f18053,f20120]) ).
fof(f23043,plain,
( m2_relset_1(sF1319,k2_zfmisc_1(k1_autgroup(sK1314),k1_autgroup(sK1314)),k1_autgroup(sK1314))
| v3_struct_0(sK1314)
| ~ v1_group_1(sK1314)
| ~ v3_group_1(sK1314)
| ~ v4_group_1(sK1314)
| ~ l1_group_1(sK1314) ),
inference(superposition,[],[f18052,f20120]) ).
fof(f23044,plain,
( m1_subset_1(sK1315,sF1321)
| v1_xboole_0(sF1317)
| ~ m1_fraenkel(sF1321,sF1317,sF1317) ),
inference(resolution,[],[f14279,f20127]) ).
fof(f23048,plain,
! [X2,X0,X1] :
( ~ m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ v1_funct_1(k2_autgroup(X1))
| k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X0,X2) = k2_binop_1(k1_autgroup(X1),k1_autgroup(X1),k1_autgroup(X1),k2_autgroup(X1),X2,X0)
| ~ m2_relset_1(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
| v3_struct_0(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| v3_struct_0(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(resolution,[],[f20110,f18053]) ).
fof(f23050,plain,
! [X2,X0,X1] :
( ~ m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ v1_funct_1(k2_autgroup(X1))
| k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X0,X2) = k2_binop_1(k1_autgroup(X1),k1_autgroup(X1),k1_autgroup(X1),k2_autgroup(X1),X2,X0)
| ~ m2_relset_1(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
| v3_struct_0(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(duplicate_literal_removal,[],[f23048]) ).
fof(f23056,plain,
( v1_funct_1(sF1319)
| v3_struct_0(sK1314)
| ~ v1_group_1(sK1314)
| ~ v3_group_1(sK1314)
| ~ v4_group_1(sK1314)
| ~ l1_group_1(sK1314) ),
inference(superposition,[],[f18054,f20120]) ).
fof(f23063,plain,
( ~ v1_xboole_0(sF1317)
| v3_struct_0(sK1314)
| ~ l1_struct_0(sK1314) ),
inference(superposition,[],[f15564,f20116]) ).
fof(f23067,plain,
( m1_fraenkel(k1_autgroup(sK1314),sF1317,sF1317)
| v3_struct_0(sK1314)
| ~ v1_group_1(sK1314)
| ~ v3_group_1(sK1314)
| ~ v4_group_1(sK1314)
| ~ l1_group_1(sK1314) ),
inference(superposition,[],[f18051,f20116]) ).
fof(f23115,plain,
( m1_fraenkel(k4_autgroup(sK1314),sF1317,sF1317)
| ~ v1_group_1(sK1314)
| ~ v3_group_1(sK1314)
| ~ v4_group_1(sK1314)
| ~ l1_group_1(sK1314) ),
inference(forward_subsumption_resolution,[],[f23031,f18131]) ).
fof(f23118,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF1317,sF1317,k4_autgroup(sK1314))
| m2_fraenkel(X0,sF1317,sF1317,k1_autgroup(sK1314))
| ~ v1_group_1(sK1314)
| ~ v3_group_1(sK1314)
| ~ v4_group_1(sK1314)
| ~ l1_group_1(sK1314) ),
inference(forward_subsumption_resolution,[],[f23033,f18131]) ).
fof(f23121,plain,
( v1_funct_2(sF1319,k2_zfmisc_1(k1_autgroup(sK1314),k1_autgroup(sK1314)),k1_autgroup(sK1314))
| ~ v1_group_1(sK1314)
| ~ v3_group_1(sK1314)
| ~ v4_group_1(sK1314)
| ~ l1_group_1(sK1314) ),
inference(forward_subsumption_resolution,[],[f23042,f18131]) ).
fof(f23122,plain,
( m2_relset_1(sF1319,k2_zfmisc_1(k1_autgroup(sK1314),k1_autgroup(sK1314)),k1_autgroup(sK1314))
| ~ v1_group_1(sK1314)
| ~ v3_group_1(sK1314)
| ~ v4_group_1(sK1314)
| ~ l1_group_1(sK1314) ),
inference(forward_subsumption_resolution,[],[f23043,f18131]) ).
fof(f23124,plain,
! [X2,X0,X1] :
( ~ m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X0,X2) = k2_binop_1(k1_autgroup(X1),k1_autgroup(X1),k1_autgroup(X1),k2_autgroup(X1),X2,X0)
| ~ m2_relset_1(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
| v3_struct_0(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(forward_subsumption_resolution,[],[f23050,f18054]) ).
fof(f23126,plain,
( v1_funct_1(sF1319)
| ~ v1_group_1(sK1314)
| ~ v3_group_1(sK1314)
| ~ v4_group_1(sK1314)
| ~ l1_group_1(sK1314) ),
inference(forward_subsumption_resolution,[],[f23056,f18131]) ).
fof(f23127,plain,
( m1_fraenkel(k1_autgroup(sK1314),sF1317,sF1317)
| ~ v1_group_1(sK1314)
| ~ v3_group_1(sK1314)
| ~ v4_group_1(sK1314)
| ~ l1_group_1(sK1314) ),
inference(forward_subsumption_resolution,[],[f23067,f18131]) ).
fof(f23129,plain,
( m1_fraenkel(k4_autgroup(sK1314),sF1317,sF1317)
| ~ v3_group_1(sK1314)
| ~ v4_group_1(sK1314)
| ~ l1_group_1(sK1314) ),
inference(forward_subsumption_resolution,[],[f23115,f18130]) ).
fof(f23132,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF1317,sF1317,k4_autgroup(sK1314))
| m2_fraenkel(X0,sF1317,sF1317,k1_autgroup(sK1314))
| ~ v3_group_1(sK1314)
| ~ v4_group_1(sK1314)
| ~ l1_group_1(sK1314) ),
inference(forward_subsumption_resolution,[],[f23118,f18130]) ).
fof(f23135,plain,
( v1_funct_2(sF1319,k2_zfmisc_1(k1_autgroup(sK1314),k1_autgroup(sK1314)),k1_autgroup(sK1314))
| ~ v3_group_1(sK1314)
| ~ v4_group_1(sK1314)
| ~ l1_group_1(sK1314) ),
inference(forward_subsumption_resolution,[],[f23121,f18130]) ).
fof(f23136,plain,
( m2_relset_1(sF1319,k2_zfmisc_1(k1_autgroup(sK1314),k1_autgroup(sK1314)),k1_autgroup(sK1314))
| ~ v3_group_1(sK1314)
| ~ v4_group_1(sK1314)
| ~ l1_group_1(sK1314) ),
inference(forward_subsumption_resolution,[],[f23122,f18130]) ).
fof(f23138,plain,
! [X2,X0,X1] :
( ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X0,X2) = k2_binop_1(k1_autgroup(X1),k1_autgroup(X1),k1_autgroup(X1),k2_autgroup(X1),X2,X0)
| v3_struct_0(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(forward_subsumption_resolution,[],[f23124,f18052]) ).
fof(f23140,plain,
( v1_funct_1(sF1319)
| ~ v3_group_1(sK1314)
| ~ v4_group_1(sK1314)
| ~ l1_group_1(sK1314) ),
inference(forward_subsumption_resolution,[],[f23126,f18130]) ).
fof(f23141,plain,
( m1_fraenkel(k1_autgroup(sK1314),sF1317,sF1317)
| ~ v3_group_1(sK1314)
| ~ v4_group_1(sK1314)
| ~ l1_group_1(sK1314) ),
inference(forward_subsumption_resolution,[],[f23127,f18130]) ).
fof(f23143,plain,
( m1_fraenkel(k4_autgroup(sK1314),sF1317,sF1317)
| ~ v4_group_1(sK1314)
| ~ l1_group_1(sK1314) ),
inference(forward_subsumption_resolution,[],[f23129,f18129]) ).
fof(f23146,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF1317,sF1317,k4_autgroup(sK1314))
| m2_fraenkel(X0,sF1317,sF1317,k1_autgroup(sK1314))
| ~ v4_group_1(sK1314)
| ~ l1_group_1(sK1314) ),
inference(forward_subsumption_resolution,[],[f23132,f18129]) ).
fof(f23149,plain,
( v1_funct_2(sF1319,k2_zfmisc_1(k1_autgroup(sK1314),k1_autgroup(sK1314)),k1_autgroup(sK1314))
| ~ v4_group_1(sK1314)
| ~ l1_group_1(sK1314) ),
inference(forward_subsumption_resolution,[],[f23135,f18129]) ).
fof(f23150,plain,
( m2_relset_1(sF1319,k2_zfmisc_1(k1_autgroup(sK1314),k1_autgroup(sK1314)),k1_autgroup(sK1314))
| ~ v4_group_1(sK1314)
| ~ l1_group_1(sK1314) ),
inference(forward_subsumption_resolution,[],[f23136,f18129]) ).
fof(f23153,plain,
( v1_funct_1(sF1319)
| ~ v4_group_1(sK1314)
| ~ l1_group_1(sK1314) ),
inference(forward_subsumption_resolution,[],[f23140,f18129]) ).
fof(f23154,plain,
( m1_fraenkel(k1_autgroup(sK1314),sF1317,sF1317)
| ~ v4_group_1(sK1314)
| ~ l1_group_1(sK1314) ),
inference(forward_subsumption_resolution,[],[f23141,f18129]) ).
fof(f23156,plain,
( m1_fraenkel(k4_autgroup(sK1314),sF1317,sF1317)
| ~ l1_group_1(sK1314) ),
inference(forward_subsumption_resolution,[],[f23143,f18128]) ).
fof(f23159,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF1317,sF1317,k4_autgroup(sK1314))
| m2_fraenkel(X0,sF1317,sF1317,k1_autgroup(sK1314))
| ~ l1_group_1(sK1314) ),
inference(forward_subsumption_resolution,[],[f23146,f18128]) ).
fof(f23162,plain,
( v1_funct_2(sF1319,k2_zfmisc_1(k1_autgroup(sK1314),k1_autgroup(sK1314)),k1_autgroup(sK1314))
| ~ l1_group_1(sK1314) ),
inference(forward_subsumption_resolution,[],[f23149,f18128]) ).
fof(f23163,plain,
( m2_relset_1(sF1319,k2_zfmisc_1(k1_autgroup(sK1314),k1_autgroup(sK1314)),k1_autgroup(sK1314))
| ~ l1_group_1(sK1314) ),
inference(forward_subsumption_resolution,[],[f23150,f18128]) ).
fof(f23166,plain,
( v1_funct_1(sF1319)
| ~ l1_group_1(sK1314) ),
inference(forward_subsumption_resolution,[],[f23153,f18128]) ).
fof(f23167,plain,
( m1_fraenkel(k1_autgroup(sK1314),sF1317,sF1317)
| ~ l1_group_1(sK1314) ),
inference(forward_subsumption_resolution,[],[f23154,f18128]) ).
fof(f23169,plain,
m1_fraenkel(k4_autgroup(sK1314),sF1317,sF1317),
inference(forward_subsumption_resolution,[],[f23156,f18127]) ).
fof(f23172,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF1317,sF1317,k4_autgroup(sK1314))
| m2_fraenkel(X0,sF1317,sF1317,k1_autgroup(sK1314)) ),
inference(forward_subsumption_resolution,[],[f23159,f18127]) ).
fof(f23175,plain,
v1_funct_2(sF1319,k2_zfmisc_1(k1_autgroup(sK1314),k1_autgroup(sK1314)),k1_autgroup(sK1314)),
inference(forward_subsumption_resolution,[],[f23162,f18127]) ).
fof(f23176,plain,
m2_relset_1(sF1319,k2_zfmisc_1(k1_autgroup(sK1314),k1_autgroup(sK1314)),k1_autgroup(sK1314)),
inference(forward_subsumption_resolution,[],[f23163,f18127]) ).
fof(f23179,plain,
v1_funct_1(sF1319),
inference(forward_subsumption_resolution,[],[f23166,f18127]) ).
fof(f23180,plain,
m1_fraenkel(k1_autgroup(sK1314),sF1317,sF1317),
inference(forward_subsumption_resolution,[],[f23167,f18127]) ).
fof(f23182,plain,
m1_fraenkel(sF1321,sF1317,sF1317),
inference(forward_demodulation,[],[f23169,f20125]) ).
fof(f23185,plain,
! [X0] :
( m2_fraenkel(X0,sF1317,sF1317,k1_autgroup(sK1314))
| ~ m2_fraenkel(X0,sF1317,sF1317,sF1321) ),
inference(forward_demodulation,[],[f23172,f20125]) ).
fof(f23205,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF1317,sF1317,sF1321)
| m1_subset_1(X0,k1_autgroup(sK1314))
| v1_xboole_0(sF1317)
| ~ m1_fraenkel(k1_autgroup(sK1314),sF1317,sF1317) ),
inference(resolution,[],[f23185,f14279]) ).
fof(f23220,plain,
m1_relset_1(sF1319,k2_zfmisc_1(k1_autgroup(sK1314),k1_autgroup(sK1314)),k1_autgroup(sK1314)),
inference(resolution,[],[f23176,f12406]) ).
fof(f23282,plain,
~ v1_xboole_0(k1_autgroup(sK1314)),
inference(resolution,[],[f14273,f23180]) ).
fof(f23293,plain,
( m1_subset_1(sK1315,sF1321)
| v1_xboole_0(sF1317) ),
inference(forward_subsumption_resolution,[],[f23044,f23182]) ).
fof(f23295,plain,
( ~ v1_xboole_0(sF1317)
| ~ l1_struct_0(sK1314) ),
inference(forward_subsumption_resolution,[],[f23063,f18131]) ).
fof(f23321,definition,
( spl1322_568
<=> v1_xboole_0(sF1317) ),
introduced(definition,[new_symbols(definition,[spl1322_568])],[avatar_definition]) ).
fof(f23322,plain,
( ~ v1_xboole_0(sF1317)
| spl1322_568 ),
inference(avatar_component_clause,[],[f23321]) ).
fof(f23329,plain,
! [X0,X1] :
( m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| v3_struct_0(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_subset_1(X0,k4_autgroup(X1))
| v1_xboole_0(u1_struct_0(X1)) ),
inference(forward_subsumption_resolution,[],[f23032,f18060]) ).
fof(f23336,plain,
! [X0] :
( ~ m2_fraenkel(X0,sF1317,sF1317,sF1321)
| m1_subset_1(X0,k1_autgroup(sK1314))
| v1_xboole_0(sF1317) ),
inference(forward_subsumption_resolution,[],[f23205,f23180]) ).
fof(f23353,definition,
( spl1322_571
<=> m1_subset_1(sK1315,sF1321) ),
introduced(definition,[new_symbols(definition,[spl1322_571])],[avatar_definition]) ).
fof(f23355,plain,
( m1_subset_1(sK1315,sF1321)
| ~ spl1322_571 ),
inference(avatar_component_clause,[],[f23353]) ).
fof(f23356,plain,
( spl1322_568
| spl1322_571 ),
inference(avatar_split_clause,[],[f23293,f23353,f23321]) ).
fof(f23359,definition,
( spl1322_572
<=> l1_struct_0(sK1314) ),
introduced(definition,[new_symbols(definition,[spl1322_572])],[avatar_definition]) ).
fof(f23361,plain,
( ~ l1_struct_0(sK1314)
| spl1322_572 ),
inference(avatar_component_clause,[],[f23359]) ).
fof(f23362,plain,
( ~ spl1322_572
| ~ spl1322_568 ),
inference(avatar_split_clause,[],[f23295,f23321,f23359]) ).
fof(f23372,definition,
( spl1322_575
<=> ! [X0] :
( ~ m2_fraenkel(X0,sF1317,sF1317,sF1321)
| m1_subset_1(X0,k1_autgroup(sK1314)) ) ),
introduced(definition,[new_symbols(definition,[spl1322_575])],[avatar_definition]) ).
fof(f23373,plain,
( ! [X0] :
( ~ m2_fraenkel(X0,sF1317,sF1317,sF1321)
| m1_subset_1(X0,k1_autgroup(sK1314)) )
| ~ spl1322_575 ),
inference(avatar_component_clause,[],[f23372]) ).
fof(f23374,plain,
( spl1322_568
| spl1322_575 ),
inference(avatar_split_clause,[],[f23336,f23372,f23321]) ).
fof(f23414,plain,
! [X2,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,k4_autgroup(X0))
| v1_xboole_0(u1_struct_0(X0))
| ~ m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X2,X1) = k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),k2_autgroup(X0),X1,X2)
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(resolution,[],[f23329,f23138]) ).
fof(f23422,plain,
! [X2,X0,X1] :
( ~ m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(X1,k4_autgroup(X0))
| v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X2,X1) = k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),k2_autgroup(X0),X1,X2) ),
inference(duplicate_literal_removal,[],[f23414]) ).
fof(f23431,plain,
! [X2,X0,X1] :
( ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(X1,k4_autgroup(X0))
| v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X2,X1) = k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),k2_autgroup(X0),X1,X2)
| ~ m1_subset_1(X2,k1_autgroup(X0))
| v1_xboole_0(u1_struct_0(X0))
| ~ m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(resolution,[],[f23422,f14280]) ).
fof(f23433,plain,
! [X2,X0,X1] :
( ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(X1,k4_autgroup(X0))
| v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X2,X1) = k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),k2_autgroup(X0),X1,X2)
| ~ m1_subset_1(X2,k1_autgroup(X0))
| ~ m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(duplicate_literal_removal,[],[f23431]) ).
fof(f23436,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,k1_autgroup(X0))
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(X1,k4_autgroup(X0))
| v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),X2,X1) = k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),k2_autgroup(X0),X1,X2)
| ~ v1_group_1(X0) ),
inference(forward_subsumption_resolution,[],[f23433,f18051]) ).
fof(f23478,plain,
l1_struct_0(sK1314),
inference(resolution,[],[f16045,f18127]) ).
fof(f23479,plain,
( $false
| spl1322_572 ),
inference(forward_subsumption_resolution,[],[f23478,f23361]) ).
fof(f23480,plain,
spl1322_572,
inference(avatar_contradiction_clause,[],[f23479]) ).
fof(f23519,plain,
( m1_subset_1(sK1315,k1_autgroup(sK1314))
| ~ spl1322_575 ),
inference(resolution,[],[f23373,f20127]) ).
fof(f23520,plain,
( m1_subset_1(sK1316,k1_autgroup(sK1314))
| ~ spl1322_575 ),
inference(resolution,[],[f23373,f20126]) ).
fof(f23605,plain,
! [X0,X1] :
( v1_xboole_0(k1_autgroup(sK1314))
| v1_xboole_0(k1_autgroup(sK1314))
| ~ v1_funct_1(sF1319)
| k2_binop_1(k1_autgroup(sK1314),k1_autgroup(sK1314),k1_autgroup(sK1314),sF1319,X0,X1) = k1_binop_1(sF1319,X0,X1)
| ~ m1_relset_1(sF1319,k2_zfmisc_1(k1_autgroup(sK1314),k1_autgroup(sK1314)),k1_autgroup(sK1314))
| ~ m1_subset_1(X0,k1_autgroup(sK1314))
| ~ m1_subset_1(X1,k1_autgroup(sK1314)) ),
inference(resolution,[],[f13306,f23175]) ).
fof(f23606,plain,
! [X0,X1] :
( v1_xboole_0(k1_autgroup(sK1314))
| ~ v1_funct_1(sF1319)
| k2_binop_1(k1_autgroup(sK1314),k1_autgroup(sK1314),k1_autgroup(sK1314),sF1319,X0,X1) = k1_binop_1(sF1319,X0,X1)
| ~ m1_relset_1(sF1319,k2_zfmisc_1(k1_autgroup(sK1314),k1_autgroup(sK1314)),k1_autgroup(sK1314))
| ~ m1_subset_1(X0,k1_autgroup(sK1314))
| ~ m1_subset_1(X1,k1_autgroup(sK1314)) ),
inference(duplicate_literal_removal,[],[f23605]) ).
fof(f23608,plain,
! [X0,X1] :
( ~ v1_funct_1(sF1319)
| k2_binop_1(k1_autgroup(sK1314),k1_autgroup(sK1314),k1_autgroup(sK1314),sF1319,X0,X1) = k1_binop_1(sF1319,X0,X1)
| ~ m1_relset_1(sF1319,k2_zfmisc_1(k1_autgroup(sK1314),k1_autgroup(sK1314)),k1_autgroup(sK1314))
| ~ m1_subset_1(X0,k1_autgroup(sK1314))
| ~ m1_subset_1(X1,k1_autgroup(sK1314)) ),
inference(forward_subsumption_resolution,[],[f23606,f23282]) ).
fof(f23610,plain,
! [X0,X1] :
( k2_binop_1(k1_autgroup(sK1314),k1_autgroup(sK1314),k1_autgroup(sK1314),sF1319,X0,X1) = k1_binop_1(sF1319,X0,X1)
| ~ m1_relset_1(sF1319,k2_zfmisc_1(k1_autgroup(sK1314),k1_autgroup(sK1314)),k1_autgroup(sK1314))
| ~ m1_subset_1(X0,k1_autgroup(sK1314))
| ~ m1_subset_1(X1,k1_autgroup(sK1314)) ),
inference(forward_subsumption_resolution,[],[f23608,f23179]) ).
fof(f23612,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,k1_autgroup(sK1314))
| ~ m1_subset_1(X0,k1_autgroup(sK1314))
| k2_binop_1(k1_autgroup(sK1314),k1_autgroup(sK1314),k1_autgroup(sK1314),sF1319,X0,X1) = k1_binop_1(sF1319,X0,X1) ),
inference(forward_subsumption_resolution,[],[f23610,f23220]) ).
fof(f23616,plain,
( ! [X0] :
( ~ m1_subset_1(X0,k1_autgroup(sK1314))
| k2_binop_1(k1_autgroup(sK1314),k1_autgroup(sK1314),k1_autgroup(sK1314),sF1319,X0,sK1316) = k1_binop_1(sF1319,X0,sK1316) )
| ~ spl1322_575 ),
inference(resolution,[],[f23612,f23520]) ).
fof(f23642,plain,
( k1_binop_1(sF1319,sK1315,sK1316) = k2_binop_1(k1_autgroup(sK1314),k1_autgroup(sK1314),k1_autgroup(sK1314),sF1319,sK1315,sK1316)
| ~ spl1322_575 ),
inference(resolution,[],[f23616,f23519]) ).
fof(f23644,plain,
( sF1320 = k2_binop_1(k1_autgroup(sK1314),k1_autgroup(sK1314),k1_autgroup(sK1314),sF1319,sK1315,sK1316)
| ~ spl1322_575 ),
inference(forward_demodulation,[],[f23642,f20122]) ).
fof(f24472,plain,
( ! [X0] :
( ~ v3_group_1(sK1314)
| ~ v4_group_1(sK1314)
| ~ l1_group_1(sK1314)
| ~ m1_subset_1(X0,k4_autgroup(sK1314))
| v1_xboole_0(u1_struct_0(sK1314))
| v3_struct_0(sK1314)
| k2_binop_1(k1_autgroup(sK1314),k1_autgroup(sK1314),k1_autgroup(sK1314),k2_autgroup(sK1314),X0,sK1316) = k7_funct_2(u1_struct_0(sK1314),u1_struct_0(sK1314),u1_struct_0(sK1314),sK1316,X0)
| ~ v1_group_1(sK1314) )
| ~ spl1322_575 ),
inference(resolution,[],[f23436,f23520]) ).
fof(f24473,plain,
( ! [X0] :
( ~ v4_group_1(sK1314)
| ~ l1_group_1(sK1314)
| ~ m1_subset_1(X0,k4_autgroup(sK1314))
| v1_xboole_0(u1_struct_0(sK1314))
| v3_struct_0(sK1314)
| k2_binop_1(k1_autgroup(sK1314),k1_autgroup(sK1314),k1_autgroup(sK1314),k2_autgroup(sK1314),X0,sK1316) = k7_funct_2(u1_struct_0(sK1314),u1_struct_0(sK1314),u1_struct_0(sK1314),sK1316,X0)
| ~ v1_group_1(sK1314) )
| ~ spl1322_575 ),
inference(forward_subsumption_resolution,[],[f24472,f18129]) ).
fof(f24477,plain,
( ! [X0] :
( ~ l1_group_1(sK1314)
| ~ m1_subset_1(X0,k4_autgroup(sK1314))
| v1_xboole_0(u1_struct_0(sK1314))
| v3_struct_0(sK1314)
| k2_binop_1(k1_autgroup(sK1314),k1_autgroup(sK1314),k1_autgroup(sK1314),k2_autgroup(sK1314),X0,sK1316) = k7_funct_2(u1_struct_0(sK1314),u1_struct_0(sK1314),u1_struct_0(sK1314),sK1316,X0)
| ~ v1_group_1(sK1314) )
| ~ spl1322_575 ),
inference(forward_subsumption_resolution,[],[f24473,f18128]) ).
fof(f24481,plain,
( ! [X0] :
( ~ m1_subset_1(X0,k4_autgroup(sK1314))
| v1_xboole_0(u1_struct_0(sK1314))
| v3_struct_0(sK1314)
| k2_binop_1(k1_autgroup(sK1314),k1_autgroup(sK1314),k1_autgroup(sK1314),k2_autgroup(sK1314),X0,sK1316) = k7_funct_2(u1_struct_0(sK1314),u1_struct_0(sK1314),u1_struct_0(sK1314),sK1316,X0)
| ~ v1_group_1(sK1314) )
| ~ spl1322_575 ),
inference(forward_subsumption_resolution,[],[f24477,f18127]) ).
fof(f24485,plain,
( ! [X0] :
( ~ m1_subset_1(X0,k4_autgroup(sK1314))
| v1_xboole_0(u1_struct_0(sK1314))
| k2_binop_1(k1_autgroup(sK1314),k1_autgroup(sK1314),k1_autgroup(sK1314),k2_autgroup(sK1314),X0,sK1316) = k7_funct_2(u1_struct_0(sK1314),u1_struct_0(sK1314),u1_struct_0(sK1314),sK1316,X0)
| ~ v1_group_1(sK1314) )
| ~ spl1322_575 ),
inference(forward_subsumption_resolution,[],[f24481,f18131]) ).
fof(f24489,plain,
( ! [X0] :
( ~ m1_subset_1(X0,k4_autgroup(sK1314))
| v1_xboole_0(u1_struct_0(sK1314))
| k2_binop_1(k1_autgroup(sK1314),k1_autgroup(sK1314),k1_autgroup(sK1314),k2_autgroup(sK1314),X0,sK1316) = k7_funct_2(u1_struct_0(sK1314),u1_struct_0(sK1314),u1_struct_0(sK1314),sK1316,X0) )
| ~ spl1322_575 ),
inference(forward_subsumption_resolution,[],[f24485,f18130]) ).
fof(f24493,plain,
( ! [X0] :
( ~ m1_subset_1(X0,sF1321)
| v1_xboole_0(u1_struct_0(sK1314))
| k2_binop_1(k1_autgroup(sK1314),k1_autgroup(sK1314),k1_autgroup(sK1314),k2_autgroup(sK1314),X0,sK1316) = k7_funct_2(u1_struct_0(sK1314),u1_struct_0(sK1314),u1_struct_0(sK1314),sK1316,X0) )
| ~ spl1322_575 ),
inference(forward_demodulation,[],[f24489,f20125]) ).
fof(f24497,plain,
( ! [X0] :
( v1_xboole_0(sF1317)
| ~ m1_subset_1(X0,sF1321)
| k2_binop_1(k1_autgroup(sK1314),k1_autgroup(sK1314),k1_autgroup(sK1314),k2_autgroup(sK1314),X0,sK1316) = k7_funct_2(u1_struct_0(sK1314),u1_struct_0(sK1314),u1_struct_0(sK1314),sK1316,X0) )
| ~ spl1322_575 ),
inference(forward_demodulation,[],[f24493,f20116]) ).
fof(f24501,plain,
( ! [X0] :
( ~ m1_subset_1(X0,sF1321)
| k2_binop_1(k1_autgroup(sK1314),k1_autgroup(sK1314),k1_autgroup(sK1314),k2_autgroup(sK1314),X0,sK1316) = k7_funct_2(u1_struct_0(sK1314),u1_struct_0(sK1314),u1_struct_0(sK1314),sK1316,X0) )
| spl1322_568
| ~ spl1322_575 ),
inference(forward_subsumption_resolution,[],[f24497,f23322]) ).
fof(f24505,plain,
( ! [X0] :
( k2_binop_1(k1_autgroup(sK1314),k1_autgroup(sK1314),k1_autgroup(sK1314),k2_autgroup(sK1314),X0,sK1316) = k7_funct_2(sF1317,sF1317,sF1317,sK1316,X0)
| ~ m1_subset_1(X0,sF1321) )
| spl1322_568
| ~ spl1322_575 ),
inference(forward_demodulation,[],[f24501,f20116]) ).
fof(f24509,plain,
( ! [X0] :
( ~ m1_subset_1(X0,sF1321)
| k2_binop_1(k1_autgroup(sK1314),k1_autgroup(sK1314),k1_autgroup(sK1314),sF1319,X0,sK1316) = k7_funct_2(sF1317,sF1317,sF1317,sK1316,X0) )
| spl1322_568
| ~ spl1322_575 ),
inference(forward_demodulation,[],[f24505,f20120]) ).
fof(f24523,plain,
( k7_funct_2(sF1317,sF1317,sF1317,sK1316,sK1315) = k2_binop_1(k1_autgroup(sK1314),k1_autgroup(sK1314),k1_autgroup(sK1314),sF1319,sK1315,sK1316)
| spl1322_568
| ~ spl1322_571
| ~ spl1322_575 ),
inference(resolution,[],[f24509,f23355]) ).
fof(f24526,plain,
( k7_funct_2(sF1317,sF1317,sF1317,sK1316,sK1315) = sF1320
| spl1322_568
| ~ spl1322_571
| ~ spl1322_575 ),
inference(forward_demodulation,[],[f24523,f23644]) ).
fof(f24528,plain,
( sF1318 = sF1320
| spl1322_568
| ~ spl1322_571
| ~ spl1322_575 ),
inference(forward_demodulation,[],[f24526,f20118]) ).
fof(f24529,plain,
( $false
| spl1322_568
| ~ spl1322_571
| ~ spl1322_575 ),
inference(forward_subsumption_resolution,[],[f24528,f20123]) ).
fof(f24530,plain,
( spl1322_568
| ~ spl1322_571
| ~ spl1322_575 ),
inference(avatar_contradiction_clause,[],[f24529]) ).
cnf(s490,plain,
( spl1322_568
| spl1322_571 ),
inference(sat_conversion,[],[f23356]) ).
cnf(s491,plain,
( ~ spl1322_568
| ~ spl1322_572 ),
inference(sat_conversion,[],[f23362]) ).
cnf(s494,plain,
( spl1322_568
| spl1322_575 ),
inference(sat_conversion,[],[f23374]) ).
cnf(s501,plain,
spl1322_572,
inference(sat_conversion,[],[f23480]) ).
cnf(s529,plain,
( spl1322_568
| ~ spl1322_571
| ~ spl1322_575 ),
inference(sat_conversion,[],[f24530]) ).
cnf(s531,plain,
~ spl1322_568,
inference(rat,[],[s491,s501]) ).
cnf(s541,plain,
spl1322_575,
inference(rat,[],[s494,s531]) ).
cnf(s544,plain,
~ spl1322_571,
inference(rat,[],[s529,s531,s541]) ).
cnf(s545,plain,
$false,
inference(rat,[],[s490,s544,s531]) ).
fof(f24531,plain,
$false,
inference(avatar_sat_refutation,[],[s545]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP624+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n002.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 10:13:22 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 12.25/2.79 % (3322218)Detected formulas, will run a generic FOF schedule.
% 12.25/2.79 % (3322223)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=2465861468:i=141193_2998 on theBenchmark for (2998ds/141193Mi)
% 12.25/2.79 % (3322228)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2857760602:s2a=on:i=139:gtg=position_2998 on theBenchmark for (2998ds/139Mi)
% 12.25/2.79 % (3322225)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=3330016292:i=141695:sd=1:nm=32:gsp=on:ss=included_2998 on theBenchmark for (2998ds/141695Mi)
% 12.25/2.79 % (3322227)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1582267491:i=119:av=off:ss=axioms_2998 on theBenchmark for (2998ds/119Mi)
% 12.25/2.79 % (3322226)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4071180263:i=109:sd=1:ins=1:gsp=on:ss=axioms_2998 on theBenchmark for (2998ds/109Mi)
% 12.25/2.79 % (3322224)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=2567587496:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2998 on theBenchmark for (2998ds/134677Mi)
% 12.25/2.79 % (3322229)dis-21_1_sil=8000:lcm=predicate:random_seed=1424325520:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2998 on theBenchmark for (2998ds/129Mi)
% 12.25/2.79 % (3322226)Refutation not found, incomplete strategy
% 12.25/2.79 % (3322226)------------------------------
% 12.25/2.79 % (3322226)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.25/2.79 % (3322226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/2.79 % (3322226)CaDiCaL version: 2.1.3
% 12.25/2.79 % (3322226)Termination reason: Refutation not found, incomplete strategy
% 12.25/2.79 % (3322226)Time elapsed: 0.020 s
% 12.25/2.79 % (3322226)Peak memory usage: 93 MB
% 12.25/2.79 % (3322226)Instructions burned: 26 (million)
% 12.25/2.79 % (3322227)Instruction limit reached!
% 12.25/2.79 % (3322227)------------------------------
% 12.25/2.79 % (3322227)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.25/2.79 % (3322227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/2.79 % (3322227)CaDiCaL version: 2.1.3
% 12.25/2.79 % (3322227)Termination reason: Instruction limit
% 12.25/2.79 % (3322227)Termination phase: Saturation
% 12.25/2.79 % (3322227)Time elapsed: 0.069 s
% 12.25/2.79 % (3322227)Peak memory usage: 94 MB
% 12.25/2.79 % (3322227)Instructions burned: 119 (million)
% 12.25/2.79 % (3322228)Instruction limit reached!
% 12.25/2.79 % (3322228)------------------------------
% 12.25/2.79 % (3322228)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.25/2.79 % (3322228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/2.79 % (3322228)CaDiCaL version: 2.1.3
% 12.25/2.79 % (3322228)Termination reason: Instruction limit
% 12.25/2.79 % (3322228)Termination phase: Preprocessing 3
% 12.25/2.79 % (3322228)Time elapsed: 0.086 s
% 12.25/2.79 % (3322228)Peak memory usage: 94 MB
% 12.25/2.79 % (3322228)Instructions burned: 139 (million)
% 12.25/2.79 % (3322229)Instruction limit reached!
% 12.25/2.79 % (3322229)------------------------------
% 12.25/2.79 % (3322229)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.25/2.79 % (3322229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/2.79 % (3322229)CaDiCaL version: 2.1.3
% 12.25/2.79 % (3322229)Termination reason: Instruction limit
% 12.25/2.79 % (3322229)Termination phase: Preprocessing 3
% 12.25/2.79 % (3322229)Time elapsed: 0.090 s
% 12.25/2.79 % (3322229)Peak memory usage: 94 MB
% 12.25/2.79 % (3322229)Instructions burned: 130 (million)
% 12.25/2.79 % (3322237)lrs+10_1_sil=8000:sp=occurrence:random_seed=1436623982:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 12.25/2.79 % (3322238)lrs+10_1_sil=32000:urr=on:br=off:random_seed=849661517:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 12.25/2.79 % (3322239)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3973412201:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 12.25/2.79 % (3322239)Refutation not found, incomplete strategy
% 12.25/2.79 % (3322239)------------------------------
% 12.25/2.79 % (3322239)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.25/2.79 % (3322239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/2.79 % (3322239)CaDiCaL version: 2.1.3
% 12.25/2.79 % (3322239)Termination reason: Refutation not found, incomplete strategy
% 12.25/2.79 % (3322239)Time elapsed: 0.025 s
% 12.25/2.79 % (3322239)Peak memory usage: 93 MB
% 12.25/2.79 % (3322239)Instructions burned: 35 (million)
% 12.25/2.79 % (3322226)------------------------------
% 12.25/2.79 % (3322226)------------------------------
% 12.25/2.79 % (3322238)Instruction limit reached!
% 12.25/2.79 % (3322238)------------------------------
% 12.25/2.79 % (3322238)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.25/2.79 % (3322238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/2.79 % (3322238)CaDiCaL version: 2.1.3
% 12.25/2.79 % (3322238)Termination reason: Instruction limit
% 12.25/2.79 % (3322238)Termination phase: Saturation
% 12.25/2.79 % (3322238)Time elapsed: 0.076 s
% 12.25/2.79 % (3322238)Peak memory usage: 94 MB
% 12.25/2.79 % (3322238)Instructions burned: 157 (million)
% 12.25/2.79 % (3322237)Instruction limit reached!
% 12.25/2.79 % (3322237)------------------------------
% 12.25/2.79 % (3322237)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.25/2.79 % (3322237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/2.79 % (3322237)CaDiCaL version: 2.1.3
% 12.25/2.79 % (3322237)Termination reason: Instruction limit
% 12.25/2.79 % (3322237)Termination phase: Saturation
% 12.25/2.79 % (3322237)Time elapsed: 0.186 s
% 12.25/2.79 % (3322237)Peak memory usage: 97 MB
% 12.25/2.79 % (3322237)Instructions burned: 285 (million)
% 12.25/2.79 % (3322243)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=3725605110:s2a=on:i=248:s2at=1.23:gtg=position_2994 on theBenchmark for (2994ds/248Mi)
% 12.25/2.79 % (3322244)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1480232350:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 12.25/2.79 % (3322239)------------------------------
% 12.25/2.79 % (3322239)------------------------------
% 12.25/2.79 % (3322245)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=801064480:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 12.25/2.79 % (3322243)Instruction limit reached!
% 12.25/2.79 % (3322243)------------------------------
% 12.25/2.79 % (3322243)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.25/2.79 % (3322243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/2.79 % (3322243)CaDiCaL version: 2.1.3
% 12.25/2.79 % (3322243)Termination reason: Instruction limit
% 12.25/2.79 % (3322243)Termination phase: Property scanning
% 12.25/2.79 % (3322243)Time elapsed: 0.145 s
% 12.25/2.79 % (3322243)Peak memory usage: 97 MB
% 12.25/2.79 % (3322243)Instructions burned: 250 (million)
% 12.25/2.79 % (3322244)Instruction limit reached!
% 12.25/2.79 % (3322244)------------------------------
% 12.25/2.79 % (3322244)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.25/2.79 % (3322244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/2.79 % (3322244)CaDiCaL version: 2.1.3
% 12.25/2.79 % (3322244)Termination reason: Instruction limit
% 12.25/2.79 % (3322244)Termination phase: Saturation
% 12.25/2.79 % (3322244)Time elapsed: 0.172 s
% 12.25/2.79 % (3322244)Peak memory usage: 97 MB
% 12.25/2.79 % (3322244)Instructions burned: 295 (million)
% 12.25/2.79 % (3322248)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2474052708:cts=off:i=113:fsr=off:ss=included:sgt=4_2991 on theBenchmark for (2991ds/113Mi)
% 12.25/2.79 % (3322250)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3007710771:i=127:av=off:fsr=off:sup=off_2991 on theBenchmark for (2991ds/127Mi)
% 12.25/2.79 % (3322248)Instruction limit reached!
% 12.25/2.79 % (3322248)------------------------------
% 12.25/2.79 % (3322248)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.25/2.79 % (3322248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/2.79 % (3322248)CaDiCaL version: 2.1.3
% 12.25/2.79 % (3322248)Termination reason: Instruction limit
% 12.25/2.79 % (3322248)Termination phase: Property scanning
% 12.25/2.79 % (3322248)Time elapsed: 0.071 s
% 12.25/2.79 % (3322248)Peak memory usage: 93 MB
% 12.25/2.79 % (3322248)Instructions burned: 114 (million)
% 12.25/2.79 % (3322251)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2201942624:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 12.25/2.79 % (3322250)Instruction limit reached!
% 12.25/2.79 % (3322250)------------------------------
% 12.25/2.79 % (3322250)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.25/2.79 % (3322250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/2.79 % (3322250)CaDiCaL version: 2.1.3
% 12.25/2.79 % (3322250)Termination reason: Instruction limit
% 12.25/2.79 % (3322250)Termination phase: Preprocessing 3
% 12.25/2.79 % (3322250)Time elapsed: 0.084 s
% 12.25/2.79 % (3322250)Peak memory usage: 96 MB
% 12.25/2.79 % (3322250)Instructions burned: 128 (million)
% 12.25/2.79 % (3322251)Instruction limit reached!
% 12.25/2.79 % (3322251)------------------------------
% 12.25/2.79 % (3322251)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.25/2.79 % (3322251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/2.79 % (3322251)CaDiCaL version: 2.1.3
% 12.25/2.79 % (3322251)Termination reason: Instruction limit
% 12.25/2.79 % (3322251)Termination phase: Unused predicate definition removal
% 12.25/2.79 % (3322251)Time elapsed: 0.058 s
% 12.25/2.79 % (3322251)Peak memory usage: 90 MB
% 12.25/2.79 % (3322251)Instructions burned: 115 (million)
% 12.25/2.79 % (3322255)lrs+10_1_sil=8000:sp=occurrence:random_seed=2220153466:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2989 on theBenchmark for (2989ds/907Mi)
% 12.25/2.79 % (3322256)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=417169479:i=437:sd=1:aac=none:ss=included_2989 on theBenchmark for (2989ds/437Mi)
% 12.25/2.79 % (3322257)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=55820460:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 12.25/2.79 % (3322256)Instruction limit reached!
% 12.25/2.79 % (3322256)------------------------------
% 12.25/2.79 % (3322256)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.25/2.79 % (3322256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/2.79 % (3322256)CaDiCaL version: 2.1.3
% 12.25/2.79 % (3322256)Termination reason: Instruction limit
% 12.25/2.79 % (3322256)Termination phase: Saturation
% 12.25/2.79 % (3322256)Time elapsed: 0.217 s
% 12.25/2.79 % (3322256)Peak memory usage: 95 MB
% 12.25/2.79 % (3322256)Instructions burned: 438 (million)
% 12.25/2.79 % (3322261)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=1644737563:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2985 on theBenchmark for (2985ds/134Mi)
% 12.25/2.79 % (3322261)Instruction limit reached!
% 12.25/2.79 % (3322261)------------------------------
% 12.25/2.79 % (3322261)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.25/2.79 % (3322261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/2.79 % (3322261)CaDiCaL version: 2.1.3
% 12.25/2.79 % (3322261)Termination reason: Instruction limit
% 12.25/2.79 % (3322261)Termination phase: Saturation
% 12.25/2.79 % (3322261)Time elapsed: 0.083 s
% 12.25/2.79 % (3322261)Peak memory usage: 96 MB
% 12.25/2.79 % (3322261)Instructions burned: 135 (million)
% 12.25/2.79 % (3322255)Instruction limit reached!
% 12.25/2.79 % (3322255)------------------------------
% 12.25/2.79 % (3322255)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.25/2.79 % (3322255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.25/2.79 % (3322255)CaDiCaL version: 2.1.3
% 12.25/2.79 % (3322255)Termination reason: Instruction limit
% 12.25/2.79 % (3322255)Termination phase: Saturation
% 12.25/2.79 % (3322255)Time elapsed: 0.573 s
% 12.25/2.79 % (3322255)Peak memory usage: 107 MB
% 12.25/2.79 % (3322255)Instructions burned: 907 (million)
% 12.25/2.79 % (3322223)First to succeed.
% 12.25/2.79 % (3322223)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3322218"
% 12.25/2.79 % (3322263)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=826783942:st=8:i=592:sd=3:ep=RST:ss=axioms_2983 on theBenchmark for (2983ds/592Mi)
% 12.25/2.79 % (3322264)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=2120900799:st=3:i=13193:sd=3:ss=axioms_2982 on theBenchmark for (2982ds/13193Mi)
% 12.25/2.79 % (3322223)Refutation found. Thanks to Tanya!
% 12.25/2.79 % SZS status Theorem for theBenchmark
% 12.25/2.79 % SZS output start Proof for theBenchmark
% See solution above
% 13.32/2.98 % (3322223)------------------------------
% 13.32/2.98 % (3322223)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.32/2.98 % (3322223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.32/2.98 % (3322223)CaDiCaL version: 2.1.3
% 13.32/2.98 % (3322223)Termination reason: Refutation
% 13.32/2.98 % (3322223)Time elapsed: 1.481 s
% 13.32/2.98 % (3322223)Peak memory usage: 229 MB
% 13.32/2.98 % (3322223)Instructions burned: 4288 (million)
% 13.32/2.98 % (3322223)------------------------------
% 13.32/2.98 % (3322223)------------------------------
% 13.32/2.98 % (3322218)Success in time 1.938 s
% 13.32/2.98 % Vampire exiting
%------------------------------------------------------------------------------