%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP624+1 : 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 5.37s 1.64s
% Output : Refutation 6.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 26
% Syntax : Number of formulae : 190 ( 33 unt; 15 def)
% Number of atoms : 933 ( 55 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 1306 ( 563 ~; 628 |; 74 &)
% ( 22 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 32 ( 30 usr; 16 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-6 aty)
% Number of variables : 157 ( 0 sgn 147 !; 10 ?)
% 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] :
( 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(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] :
( 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)],[f1]) ).
fof(f15,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(f18,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(f24,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(f32,axiom,
! [X0] :
( l1_group_1(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(f34,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(f50,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& l1_struct_0(X0) )
=> ~ v1_xboole_0(u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f67,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(f69,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(f70,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(f72,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(f88,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( 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)
& 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,[],[f2]) ).
fof(f89,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( 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)
& 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,[],[f88]) ).
fof(f108,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,[],[f15]) ).
fof(f109,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,[],[f108]) ).
fof(f112,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,[],[f18]) ).
fof(f113,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,[],[f112]) ).
fof(f114,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,[],[f24]) ).
fof(f115,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,[],[f114]) ).
fof(f124,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f125,plain,
! [X0,X1,X2] :
( ( ~ v1_xboole_0(X2)
& v1_fraenkel(X2) )
| ~ m1_fraenkel(X2,X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f136,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f137,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(flattening,[],[f136]) ).
fof(f142,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,[],[f67]) ).
fof(f143,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,[],[f142]) ).
fof(f146,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,[],[f69]) ).
fof(f147,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,[],[f146]) ).
fof(f148,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,[],[f72]) ).
fof(f149,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,[],[f148]) ).
fof(f160,plain,
( k1_binop_1(k2_autgroup(sK0),sK1,sK2) != k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK2,sK1)
& m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
& m2_fraenkel(sK1,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) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f89]) ).
fof(f161,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,[],[f109]) ).
fof(f162,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,[],[f161]) ).
fof(f163,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = k2_autgroup(X0)
| ( k2_binop_1(k1_autgroup(X0),k1_autgroup(X0),k1_autgroup(X0),X1,sK3(X0,X1),sK4(X0,X1)) != k7_funct_2(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),sK4(X0,X1),sK3(X0,X1))
& m2_fraenkel(sK4(X0,X1),u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
& m2_fraenkel(sK3(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,[sK3,sK4]),skolemize(X2,sK3(X0,X1)),skolemize(X3,sK4(X0,X1))],[f162]) ).
fof(f185,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,[],[f147]) ).
fof(f186,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,[],[f70]) ).
fof(f187,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f160]) ).
fof(f188,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f160]) ).
fof(f189,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f160]) ).
fof(f190,plain,
v1_group_1(sK0),
inference(cnf_transformation,[],[f160]) ).
fof(f191,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f160]) ).
fof(f192,plain,
m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)),
inference(cnf_transformation,[],[f160]) ).
fof(f193,plain,
m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)),
inference(cnf_transformation,[],[f160]) ).
fof(f194,plain,
k1_binop_1(k2_autgroup(sK0),sK1,sK2) != k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK2,sK1),
inference(cnf_transformation,[],[f160]) ).
fof(f215,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,[],[f163]) ).
fof(f222,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,[],[f113]) ).
fof(f223,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,[],[f115]) ).
fof(f224,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,[],[f115]) ).
fof(f225,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,[],[f115]) ).
fof(f232,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f234,plain,
! [X2,X0,X1] :
( ~ v1_xboole_0(X2)
| ~ m1_fraenkel(X2,X0,X1) ),
inference(cnf_transformation,[],[f125]) ).
fof(f253,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f292,plain,
! [X2,X3,X0,X1,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(cnf_transformation,[],[f143]) ).
fof(f294,plain,
! [X2,X3,X0,X1] :
( m1_subset_1(X3,X2)
| ~ m2_fraenkel(X3,X0,X1,X2)
| v1_xboole_0(X1)
| ~ m1_fraenkel(X2,X0,X1) ),
inference(cnf_transformation,[],[f185]) ).
fof(f296,plain,
! [X2,X0,X1] :
( m1_relset_1(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f186]) ).
fof(f299,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(cnf_transformation,[],[f149]) ).
fof(f309,plain,
! [X0,X4,X5] :
( 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_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))
| ~ 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(equality_resolution,[],[f215]) ).
fof(f313,definition,
( spl27_1
<=> m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
introduced(definition,[new_symbols(definition,[spl27_1])],[avatar_definition]) ).
fof(f315,plain,
( m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ spl27_1 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f316,plain,
spl27_1,
inference(avatar_split_clause,[],[f192,f313]) ).
fof(f318,definition,
( spl27_2
<=> m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
introduced(definition,[new_symbols(definition,[spl27_2])],[avatar_definition]) ).
fof(f320,plain,
( m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ spl27_2 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f321,plain,
spl27_2,
inference(avatar_split_clause,[],[f193,f318]) ).
fof(f323,definition,
( spl27_3
<=> v4_group_1(sK0) ),
introduced(definition,[new_symbols(definition,[spl27_3])],[avatar_definition]) ).
fof(f325,plain,
( v4_group_1(sK0)
| ~ spl27_3 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f326,plain,
spl27_3,
inference(avatar_split_clause,[],[f188,f323]) ).
fof(f328,definition,
( spl27_4
<=> l1_group_1(sK0) ),
introduced(definition,[new_symbols(definition,[spl27_4])],[avatar_definition]) ).
fof(f330,plain,
( l1_group_1(sK0)
| ~ spl27_4 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f331,plain,
spl27_4,
inference(avatar_split_clause,[],[f187,f328]) ).
fof(f333,definition,
( spl27_5
<=> v3_group_1(sK0) ),
introduced(definition,[new_symbols(definition,[spl27_5])],[avatar_definition]) ).
fof(f335,plain,
( v3_group_1(sK0)
| ~ spl27_5 ),
inference(avatar_component_clause,[],[f333]) ).
fof(f336,plain,
spl27_5,
inference(avatar_split_clause,[],[f189,f333]) ).
fof(f337,plain,
( m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl27_1 ),
inference(resolution,[],[f315,f299]) ).
fof(f342,plain,
( m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl27_1 ),
inference(forward_subsumption_resolution,[],[f337,f191]) ).
fof(f343,plain,
( m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl27_1 ),
inference(forward_subsumption_resolution,[],[f342,f190]) ).
fof(f344,plain,
( m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl27_1
| ~ spl27_5 ),
inference(forward_subsumption_resolution,[],[f343,f335]) ).
fof(f345,plain,
( m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ spl27_1
| ~ spl27_3
| ~ spl27_5 ),
inference(forward_subsumption_resolution,[],[f344,f325]) ).
fof(f346,plain,
( m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ spl27_1
| ~ spl27_3
| ~ spl27_4
| ~ spl27_5 ),
inference(forward_subsumption_resolution,[],[f345,f330]) ).
fof(f348,definition,
( spl27_6
<=> v3_struct_0(sK0) ),
introduced(definition,[new_symbols(definition,[spl27_6])],[avatar_definition]) ).
fof(f350,plain,
( ~ v3_struct_0(sK0)
| spl27_6 ),
inference(avatar_component_clause,[],[f348]) ).
fof(f351,plain,
~ spl27_6,
inference(avatar_split_clause,[],[f191,f348]) ).
fof(f352,plain,
( m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl27_2 ),
inference(resolution,[],[f320,f299]) ).
fof(f357,plain,
( m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl27_2
| spl27_6 ),
inference(forward_subsumption_resolution,[],[f352,f350]) ).
fof(f358,plain,
( m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl27_2
| spl27_6 ),
inference(forward_subsumption_resolution,[],[f357,f190]) ).
fof(f359,plain,
( m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl27_2
| ~ spl27_5
| spl27_6 ),
inference(forward_subsumption_resolution,[],[f358,f335]) ).
fof(f360,plain,
( m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ spl27_2
| ~ spl27_3
| ~ spl27_5
| spl27_6 ),
inference(forward_subsumption_resolution,[],[f359,f325]) ).
fof(f361,plain,
( m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ spl27_2
| ~ spl27_3
| ~ spl27_4
| ~ spl27_5
| spl27_6 ),
inference(forward_subsumption_resolution,[],[f360,f330]) ).
fof(f363,definition,
( spl27_7
<=> v1_group_1(sK0) ),
introduced(definition,[new_symbols(definition,[spl27_7])],[avatar_definition]) ).
fof(f365,plain,
( v1_group_1(sK0)
| ~ spl27_7 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f366,plain,
spl27_7,
inference(avatar_split_clause,[],[f190,f363]) ).
fof(f370,plain,
( m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl27_3 ),
inference(resolution,[],[f325,f222]) ).
fof(f371,plain,
( m2_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl27_3 ),
inference(resolution,[],[f325,f223]) ).
fof(f372,plain,
( v1_funct_2(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl27_3 ),
inference(resolution,[],[f325,f224]) ).
fof(f373,plain,
( v1_funct_1(k2_autgroup(sK0))
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl27_3 ),
inference(resolution,[],[f325,f225]) ).
fof(f380,plain,
( v1_funct_1(k2_autgroup(sK0))
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl27_3
| spl27_6 ),
inference(forward_subsumption_resolution,[],[f373,f350]) ).
fof(f381,plain,
( v1_funct_2(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl27_3
| spl27_6 ),
inference(forward_subsumption_resolution,[],[f372,f350]) ).
fof(f382,plain,
( m2_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl27_3
| spl27_6 ),
inference(forward_subsumption_resolution,[],[f371,f350]) ).
fof(f383,plain,
( m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl27_3
| spl27_6 ),
inference(forward_subsumption_resolution,[],[f370,f350]) ).
fof(f390,plain,
( v1_funct_1(k2_autgroup(sK0))
| ~ v3_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl27_3
| spl27_6
| ~ spl27_7 ),
inference(forward_subsumption_resolution,[],[f380,f365]) ).
fof(f391,plain,
( v1_funct_2(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ v3_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl27_3
| spl27_6
| ~ spl27_7 ),
inference(forward_subsumption_resolution,[],[f381,f365]) ).
fof(f392,plain,
( m2_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ v3_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl27_3
| spl27_6
| ~ spl27_7 ),
inference(forward_subsumption_resolution,[],[f382,f365]) ).
fof(f393,plain,
( m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ v3_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl27_3
| spl27_6
| ~ spl27_7 ),
inference(forward_subsumption_resolution,[],[f383,f365]) ).
fof(f400,plain,
( v1_funct_1(k2_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ spl27_3
| ~ spl27_5
| spl27_6
| ~ spl27_7 ),
inference(forward_subsumption_resolution,[],[f390,f335]) ).
fof(f401,plain,
( v1_funct_2(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ spl27_3
| ~ spl27_5
| spl27_6
| ~ spl27_7 ),
inference(forward_subsumption_resolution,[],[f391,f335]) ).
fof(f402,plain,
( m2_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ spl27_3
| ~ spl27_5
| spl27_6
| ~ spl27_7 ),
inference(forward_subsumption_resolution,[],[f392,f335]) ).
fof(f403,plain,
( m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ l1_group_1(sK0)
| ~ spl27_3
| ~ spl27_5
| spl27_6
| ~ spl27_7 ),
inference(forward_subsumption_resolution,[],[f393,f335]) ).
fof(f410,plain,
( v1_funct_1(k2_autgroup(sK0))
| ~ spl27_3
| ~ spl27_4
| ~ spl27_5
| spl27_6
| ~ spl27_7 ),
inference(forward_subsumption_resolution,[],[f400,f330]) ).
fof(f411,plain,
( v1_funct_2(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ spl27_3
| ~ spl27_4
| ~ spl27_5
| spl27_6
| ~ spl27_7 ),
inference(forward_subsumption_resolution,[],[f401,f330]) ).
fof(f412,plain,
( m2_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ spl27_3
| ~ spl27_4
| ~ spl27_5
| spl27_6
| ~ spl27_7 ),
inference(forward_subsumption_resolution,[],[f402,f330]) ).
fof(f413,plain,
( m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ spl27_3
| ~ spl27_4
| ~ spl27_5
| spl27_6
| ~ spl27_7 ),
inference(forward_subsumption_resolution,[],[f403,f330]) ).
fof(f437,plain,
( l1_struct_0(sK0)
| ~ spl27_4 ),
inference(resolution,[],[f330,f232]) ).
fof(f455,definition,
( spl27_8
<=> m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) ),
introduced(definition,[new_symbols(definition,[spl27_8])],[avatar_definition]) ).
fof(f457,plain,
( m2_fraenkel(sK1,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ spl27_8 ),
inference(avatar_component_clause,[],[f455]) ).
fof(f458,plain,
( spl27_8
| ~ spl27_1
| ~ spl27_3
| ~ spl27_4
| ~ spl27_5 ),
inference(avatar_split_clause,[],[f346,f333,f328,f323,f313,f455]) ).
fof(f471,definition,
( spl27_9
<=> m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) ),
introduced(definition,[new_symbols(definition,[spl27_9])],[avatar_definition]) ).
fof(f473,plain,
( m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ spl27_9 ),
inference(avatar_component_clause,[],[f471]) ).
fof(f474,plain,
( spl27_9
| ~ spl27_2
| ~ spl27_3
| ~ spl27_4
| ~ spl27_5
| spl27_6 ),
inference(avatar_split_clause,[],[f361,f348,f333,f328,f323,f318,f471]) ).
fof(f483,plain,
( ~ v1_xboole_0(u1_struct_0(sK0))
| ~ l1_struct_0(sK0)
| spl27_6 ),
inference(resolution,[],[f350,f253]) ).
fof(f490,plain,
( ~ v1_xboole_0(u1_struct_0(sK0))
| ~ spl27_4
| spl27_6 ),
inference(forward_subsumption_resolution,[],[f483,f437]) ).
fof(f530,definition,
( spl27_16
<=> k1_binop_1(k2_autgroup(sK0),sK1,sK2) = k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK2,sK1) ),
introduced(definition,[new_symbols(definition,[spl27_16])],[avatar_definition]) ).
fof(f532,plain,
( k1_binop_1(k2_autgroup(sK0),sK1,sK2) != k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),sK2,sK1)
| spl27_16 ),
inference(avatar_component_clause,[],[f530]) ).
fof(f533,plain,
~ spl27_16,
inference(avatar_split_clause,[],[f194,f530]) ).
fof(f569,plain,
( ! [X0] :
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),X0,sK1) = k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),sK1,X0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ v1_funct_1(k2_autgroup(sK0))
| ~ v1_funct_2(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ m2_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) )
| ~ spl27_8 ),
inference(resolution,[],[f457,f309]) ).
fof(f571,plain,
( m1_subset_1(sK1,k1_autgroup(sK0))
| v1_xboole_0(u1_struct_0(sK0))
| ~ m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ spl27_8 ),
inference(resolution,[],[f457,f294]) ).
fof(f575,plain,
( m1_subset_1(sK1,k1_autgroup(sK0))
| ~ m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ spl27_4
| spl27_6
| ~ spl27_8 ),
inference(forward_subsumption_resolution,[],[f571,f490]) ).
fof(f577,plain,
( ! [X0] :
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),X0,sK1) = k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),sK1,X0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ v1_funct_2(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ m2_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) )
| ~ spl27_8 ),
inference(forward_subsumption_resolution,[],[f569,f225]) ).
fof(f578,plain,
( m1_subset_1(sK1,k1_autgroup(sK0))
| ~ spl27_3
| ~ spl27_4
| ~ spl27_5
| spl27_6
| ~ spl27_7
| ~ spl27_8 ),
inference(forward_subsumption_resolution,[],[f575,f413]) ).
fof(f580,plain,
( ! [X0] :
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),X0,sK1) = k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),sK1,X0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ m2_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) )
| ~ spl27_8 ),
inference(forward_subsumption_resolution,[],[f577,f224]) ).
fof(f582,plain,
( ! [X0] :
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),X0,sK1) = k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),sK1,X0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| v3_struct_0(sK0)
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) )
| ~ spl27_8 ),
inference(forward_subsumption_resolution,[],[f580,f223]) ).
fof(f584,plain,
( ! [X0] :
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),X0,sK1) = k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),sK1,X0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ v1_group_1(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) )
| spl27_6
| ~ spl27_8 ),
inference(forward_subsumption_resolution,[],[f582,f350]) ).
fof(f586,plain,
( ! [X0] :
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),X0,sK1) = k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),sK1,X0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) )
| spl27_6
| ~ spl27_7
| ~ spl27_8 ),
inference(forward_subsumption_resolution,[],[f584,f365]) ).
fof(f588,plain,
( ! [X0] :
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),X0,sK1) = k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),sK1,X0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) )
| ~ spl27_5
| spl27_6
| ~ spl27_7
| ~ spl27_8 ),
inference(forward_subsumption_resolution,[],[f586,f335]) ).
fof(f590,plain,
( ! [X0] :
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),X0,sK1) = k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),sK1,X0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ l1_group_1(sK0) )
| ~ spl27_3
| ~ spl27_5
| spl27_6
| ~ spl27_7
| ~ spl27_8 ),
inference(forward_subsumption_resolution,[],[f588,f325]) ).
fof(f592,plain,
( ! [X0] :
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),X0,sK1) = k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),sK1,X0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) )
| ~ spl27_3
| ~ spl27_4
| ~ spl27_5
| spl27_6
| ~ spl27_7
| ~ spl27_8 ),
inference(forward_subsumption_resolution,[],[f590,f330]) ).
fof(f704,definition,
( spl27_20
<=> m1_subset_1(sK1,k1_autgroup(sK0)) ),
introduced(definition,[new_symbols(definition,[spl27_20])],[avatar_definition]) ).
fof(f706,plain,
( m1_subset_1(sK1,k1_autgroup(sK0))
| ~ spl27_20 ),
inference(avatar_component_clause,[],[f704]) ).
fof(f707,plain,
( spl27_20
| ~ spl27_3
| ~ spl27_4
| ~ spl27_5
| spl27_6
| ~ spl27_7
| ~ spl27_8 ),
inference(avatar_split_clause,[],[f578,f455,f363,f348,f333,f328,f323,f704]) ).
fof(f813,definition,
( spl27_23
<=> ! [X0] :
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),X0,sK1) = k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),sK1,X0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) ) ),
introduced(definition,[new_symbols(definition,[spl27_23])],[avatar_definition]) ).
fof(f814,plain,
( ! [X0] :
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),X0,sK1) = k2_binop_1(k1_autgroup(sK0),k1_autgroup(sK0),k1_autgroup(sK0),k2_autgroup(sK0),sK1,X0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) )
| ~ spl27_23 ),
inference(avatar_component_clause,[],[f813]) ).
fof(f815,plain,
( spl27_23
| ~ spl27_3
| ~ spl27_4
| ~ spl27_5
| spl27_6
| ~ spl27_7
| ~ spl27_8 ),
inference(avatar_split_clause,[],[f592,f455,f363,f348,f333,f328,f323,f813]) ).
fof(f820,plain,
( ! [X0] :
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),X0,sK1) = k1_binop_1(k2_autgroup(sK0),sK1,X0)
| v1_xboole_0(k1_autgroup(sK0))
| v1_xboole_0(k1_autgroup(sK0))
| ~ v1_funct_1(k2_autgroup(sK0))
| ~ v1_funct_2(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ m1_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ m1_subset_1(sK1,k1_autgroup(sK0))
| ~ m1_subset_1(X0,k1_autgroup(sK0))
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) )
| ~ spl27_23 ),
inference(superposition,[],[f292,f814]) ).
fof(f823,plain,
( ! [X0] :
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),X0,sK1) = k1_binop_1(k2_autgroup(sK0),sK1,X0)
| v1_xboole_0(k1_autgroup(sK0))
| ~ v1_funct_1(k2_autgroup(sK0))
| ~ v1_funct_2(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ m1_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ m1_subset_1(sK1,k1_autgroup(sK0))
| ~ m1_subset_1(X0,k1_autgroup(sK0))
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) )
| ~ spl27_23 ),
inference(duplicate_literal_removal,[],[f820]) ).
fof(f826,plain,
( ! [X0] :
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),X0,sK1) = k1_binop_1(k2_autgroup(sK0),sK1,X0)
| v1_xboole_0(k1_autgroup(sK0))
| ~ v1_funct_2(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ m1_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ m1_subset_1(sK1,k1_autgroup(sK0))
| ~ m1_subset_1(X0,k1_autgroup(sK0))
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) )
| ~ spl27_3
| ~ spl27_4
| ~ spl27_5
| spl27_6
| ~ spl27_7
| ~ spl27_23 ),
inference(forward_subsumption_resolution,[],[f823,f410]) ).
fof(f832,plain,
( ! [X0] :
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),X0,sK1) = k1_binop_1(k2_autgroup(sK0),sK1,X0)
| v1_xboole_0(k1_autgroup(sK0))
| ~ m1_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ m1_subset_1(sK1,k1_autgroup(sK0))
| ~ m1_subset_1(X0,k1_autgroup(sK0))
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) )
| ~ spl27_3
| ~ spl27_4
| ~ spl27_5
| spl27_6
| ~ spl27_7
| ~ spl27_23 ),
inference(forward_subsumption_resolution,[],[f826,f411]) ).
fof(f838,plain,
( ! [X0] :
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),X0,sK1) = k1_binop_1(k2_autgroup(sK0),sK1,X0)
| v1_xboole_0(k1_autgroup(sK0))
| ~ m1_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ m1_subset_1(X0,k1_autgroup(sK0))
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) )
| ~ spl27_3
| ~ spl27_4
| ~ spl27_5
| spl27_6
| ~ spl27_7
| ~ spl27_20
| ~ spl27_23 ),
inference(forward_subsumption_resolution,[],[f832,f706]) ).
fof(f1026,definition,
( spl27_28
<=> m2_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0)) ),
introduced(definition,[new_symbols(definition,[spl27_28])],[avatar_definition]) ).
fof(f1028,plain,
( m2_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ spl27_28 ),
inference(avatar_component_clause,[],[f1026]) ).
fof(f1029,plain,
( spl27_28
| ~ spl27_3
| ~ spl27_4
| ~ spl27_5
| spl27_6
| ~ spl27_7 ),
inference(avatar_split_clause,[],[f412,f363,f348,f333,f328,f323,f1026]) ).
fof(f1031,definition,
( spl27_29
<=> m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0)) ),
introduced(definition,[new_symbols(definition,[spl27_29])],[avatar_definition]) ).
fof(f1033,plain,
( m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ spl27_29 ),
inference(avatar_component_clause,[],[f1031]) ).
fof(f1034,plain,
( spl27_29
| ~ spl27_3
| ~ spl27_4
| ~ spl27_5
| spl27_6
| ~ spl27_7 ),
inference(avatar_split_clause,[],[f413,f363,f348,f333,f328,f323,f1031]) ).
fof(f1036,plain,
( ~ v1_xboole_0(k1_autgroup(sK0))
| ~ spl27_29 ),
inference(resolution,[],[f1033,f234]) ).
fof(f1041,plain,
( ! [X0] :
( m1_subset_1(X0,k1_autgroup(sK0))
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| v1_xboole_0(u1_struct_0(sK0)) )
| ~ spl27_29 ),
inference(resolution,[],[f1033,f294]) ).
fof(f1044,plain,
( ! [X0] :
( m1_subset_1(X0,k1_autgroup(sK0))
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) )
| ~ spl27_4
| spl27_6
| ~ spl27_29 ),
inference(forward_subsumption_resolution,[],[f1041,f490]) ).
fof(f1052,plain,
( ! [X0] :
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),X0,sK1) = k1_binop_1(k2_autgroup(sK0),sK1,X0)
| ~ m1_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ m1_subset_1(X0,k1_autgroup(sK0))
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) )
| ~ spl27_3
| ~ spl27_4
| ~ spl27_5
| spl27_6
| ~ spl27_7
| ~ spl27_20
| ~ spl27_23
| ~ spl27_29 ),
inference(backward_subsumption_resolution,[],[f838,f1036]) ).
fof(f1084,plain,
( ! [X0] :
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),X0,sK1) = k1_binop_1(k2_autgroup(sK0),sK1,X0)
| ~ m1_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) )
| ~ spl27_3
| ~ spl27_4
| ~ spl27_5
| spl27_6
| ~ spl27_7
| ~ spl27_20
| ~ spl27_23
| ~ spl27_29 ),
inference(forward_subsumption_resolution,[],[f1052,f1044]) ).
fof(f1097,plain,
( m1_relset_1(k2_autgroup(sK0),k2_zfmisc_1(k1_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| ~ spl27_28 ),
inference(resolution,[],[f1028,f296]) ).
fof(f1123,plain,
( ! [X0] :
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),X0,sK1) = k1_binop_1(k2_autgroup(sK0),sK1,X0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) )
| ~ spl27_3
| ~ spl27_4
| ~ spl27_5
| spl27_6
| ~ spl27_7
| ~ spl27_20
| ~ spl27_23
| ~ spl27_28
| ~ spl27_29 ),
inference(backward_subsumption_resolution,[],[f1084,f1097]) ).
fof(f1495,definition,
( spl27_46
<=> ! [X0] :
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),X0,sK1) = k1_binop_1(k2_autgroup(sK0),sK1,X0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) ) ),
introduced(definition,[new_symbols(definition,[spl27_46])],[avatar_definition]) ).
fof(f1496,plain,
( ! [X0] :
( k7_funct_2(u1_struct_0(sK0),u1_struct_0(sK0),u1_struct_0(sK0),X0,sK1) = k1_binop_1(k2_autgroup(sK0),sK1,X0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) )
| ~ spl27_46 ),
inference(avatar_component_clause,[],[f1495]) ).
fof(f1497,plain,
( spl27_46
| ~ spl27_3
| ~ spl27_4
| ~ spl27_5
| spl27_6
| ~ spl27_7
| ~ spl27_20
| ~ spl27_23
| ~ spl27_28
| ~ spl27_29 ),
inference(avatar_split_clause,[],[f1123,f1031,f1026,f813,f704,f363,f348,f333,f328,f323,f1495]) ).
fof(f1502,plain,
( k1_binop_1(k2_autgroup(sK0),sK1,sK2) != k1_binop_1(k2_autgroup(sK0),sK1,sK2)
| ~ m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| spl27_16
| ~ spl27_46 ),
inference(superposition,[],[f532,f1496]) ).
fof(f1511,plain,
( ~ m2_fraenkel(sK2,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| spl27_16
| ~ spl27_46 ),
inference(trivial_inequality_removal,[],[f1502]) ).
fof(f1520,plain,
( $false
| ~ spl27_9
| spl27_16
| ~ spl27_46 ),
inference(forward_subsumption_resolution,[],[f1511,f473]) ).
fof(f1521,plain,
( ~ spl27_9
| spl27_16
| ~ spl27_46 ),
inference(avatar_contradiction_clause,[],[f1520]) ).
cnf(s1,plain,
spl27_1,
inference(sat_conversion,[],[f316]) ).
cnf(s2,plain,
spl27_2,
inference(sat_conversion,[],[f321]) ).
cnf(s3,plain,
spl27_3,
inference(sat_conversion,[],[f326]) ).
cnf(s4,plain,
spl27_4,
inference(sat_conversion,[],[f331]) ).
cnf(s5,plain,
spl27_5,
inference(sat_conversion,[],[f336]) ).
cnf(s6,plain,
~ spl27_6,
inference(sat_conversion,[],[f351]) ).
cnf(s7,plain,
spl27_7,
inference(sat_conversion,[],[f366]) ).
cnf(s8,plain,
( ~ spl27_1
| ~ spl27_3
| ~ spl27_4
| ~ spl27_5
| spl27_8 ),
inference(sat_conversion,[],[f458]) ).
cnf(s9,plain,
( ~ spl27_2
| ~ spl27_3
| ~ spl27_4
| ~ spl27_5
| spl27_6
| spl27_9 ),
inference(sat_conversion,[],[f474]) ).
cnf(s16,plain,
~ spl27_16,
inference(sat_conversion,[],[f533]) ).
cnf(s20,plain,
( ~ spl27_3
| ~ spl27_4
| ~ spl27_5
| spl27_6
| ~ spl27_7
| ~ spl27_8
| spl27_20 ),
inference(sat_conversion,[],[f707]) ).
cnf(s23,plain,
( ~ spl27_3
| ~ spl27_4
| ~ spl27_5
| spl27_6
| ~ spl27_7
| ~ spl27_8
| spl27_23 ),
inference(sat_conversion,[],[f815]) ).
cnf(s28,plain,
( ~ spl27_3
| ~ spl27_4
| ~ spl27_5
| spl27_6
| ~ spl27_7
| spl27_28 ),
inference(sat_conversion,[],[f1029]) ).
cnf(s29,plain,
( ~ spl27_3
| ~ spl27_4
| ~ spl27_5
| spl27_6
| ~ spl27_7
| spl27_29 ),
inference(sat_conversion,[],[f1034]) ).
cnf(s46,plain,
( ~ spl27_3
| ~ spl27_4
| ~ spl27_5
| spl27_6
| ~ spl27_7
| ~ spl27_20
| ~ spl27_23
| ~ spl27_28
| ~ spl27_29
| spl27_46 ),
inference(sat_conversion,[],[f1497]) ).
cnf(s47,plain,
( ~ spl27_9
| spl27_16
| ~ spl27_46 ),
inference(sat_conversion,[],[f1521]) ).
cnf(s53,plain,
spl27_29,
inference(rat,[],[s29,s4,s7,s6,s5,s3]) ).
cnf(s54,plain,
spl27_28,
inference(rat,[],[s28,s4,s7,s6,s5,s3]) ).
cnf(s64,plain,
spl27_9,
inference(rat,[],[s9,s3,s6,s5,s4,s2]) ).
cnf(s66,plain,
~ spl27_46,
inference(rat,[],[s47,s16,s64]) ).
cnf(s78,plain,
spl27_8,
inference(rat,[],[s8,s3,s5,s4,s1]) ).
cnf(s80,plain,
spl27_23,
inference(rat,[],[s23,s3,s4,s7,s6,s5,s78]) ).
cnf(s82,plain,
spl27_20,
inference(rat,[],[s20,s3,s4,s7,s6,s5,s78]) ).
cnf(s88,plain,
$false,
inference(rat,[],[s46,s66,s53,s54,s3,s4,s7,s6,s5,s80,s82]) ).
fof(f1558,plain,
$false,
inference(avatar_sat_refutation,[],[s88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP624+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n002.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Sun Sep 27 10:13:36 UTC 2026
% 0.15/0.38 % CPUTime :
% 0.15/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.40 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
% 5.37/1.64 % (3322647)Detected formulas, will run a generic FOF schedule.
% 5.37/1.64 % (3322654)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=1639941605:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.37/1.64 % (3322652)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=3996208232:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.37/1.64 % (3322656)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2779049849:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.37/1.64 % (3322658)dis-21_1_sil=8000:lcm=predicate:random_seed=1440047871: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)
% 5.37/1.64 % (3322655)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1250967150:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.37/1.64 % (3322653)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=1297781856:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.37/1.64 % (3322657)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1753276573:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.37/1.64 % (3322655)Refutation not found, incomplete strategy
% 5.37/1.64 % (3322655)------------------------------
% 5.37/1.64 % (3322655)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/1.64 % (3322655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/1.64 % (3322655)CaDiCaL version: 2.1.3
% 5.37/1.64 % (3322655)Termination reason: Refutation not found, incomplete strategy
% 5.37/1.64 % (3322655)Time elapsed: 0.004 s
% 5.37/1.64 % (3322655)Peak memory usage: 88 MB
% 5.37/1.64 % (3322655)Instructions burned: 5 (million)
% 5.37/1.64 % (3322656)Instruction limit reached!
% 5.37/1.64 % (3322656)------------------------------
% 5.37/1.64 % (3322656)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/1.64 % (3322656)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/1.64 % (3322656)CaDiCaL version: 2.1.3
% 5.37/1.64 % (3322656)Termination reason: Instruction limit
% 5.37/1.64 % (3322656)Termination phase: Saturation
% 5.37/1.64 % (3322656)Time elapsed: 0.068 s
% 5.37/1.64 % (3322656)Peak memory usage: 88 MB
% 5.37/1.64 % (3322656)Instructions burned: 121 (million)
% 5.37/1.64 % (3322658)Instruction limit reached!
% 5.37/1.64 % (3322658)------------------------------
% 5.37/1.64 % (3322658)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/1.64 % (3322658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/1.64 % (3322658)CaDiCaL version: 2.1.3
% 5.37/1.64 % (3322658)Termination reason: Instruction limit
% 5.37/1.64 % (3322658)Termination phase: Saturation
% 5.37/1.64 % (3322658)Time elapsed: 0.074 s
% 5.37/1.64 % (3322658)Peak memory usage: 90 MB
% 5.37/1.64 % (3322658)Instructions burned: 130 (million)
% 5.37/1.64 % (3322657)Instruction limit reached!
% 5.37/1.64 % (3322657)------------------------------
% 5.37/1.64 % (3322657)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/1.64 % (3322657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/1.64 % (3322657)CaDiCaL version: 2.1.3
% 5.37/1.64 % (3322657)Termination reason: Instruction limit
% 5.37/1.64 % (3322657)Termination phase: Saturation
% 5.37/1.64 % (3322657)Time elapsed: 0.090 s
% 5.37/1.64 % (3322657)Peak memory usage: 90 MB
% 5.37/1.64 % (3322657)Instructions burned: 139 (million)
% 5.37/1.64 % (3322666)lrs+10_1_sil=8000:sp=occurrence:random_seed=80555452:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.37/1.64 % (3322667)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2510634103:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.37/1.64 % (3322667)Refutation not found, incomplete strategy
% 5.37/1.64 % (3322667)------------------------------
% 5.37/1.64 % (3322667)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/1.64 % (3322667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/1.64 % (3322667)CaDiCaL version: 2.1.3
% 5.37/1.64 % (3322667)Termination reason: Refutation not found, incomplete strategy
% 5.37/1.64 % (3322667)Time elapsed: 0.005 s
% 5.37/1.64 % (3322667)Peak memory usage: 88 MB
% 5.37/1.64 % (3322667)Instructions burned: 6 (million)
% 5.37/1.64 % (3322655)------------------------------
% 5.37/1.64 % (3322655)------------------------------
% 5.37/1.64 % (3322668)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3340436019:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.37/1.64 % (3322668)Refutation not found, incomplete strategy
% 5.37/1.64 % (3322668)------------------------------
% 5.37/1.64 % (3322668)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/1.64 % (3322668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/1.64 % (3322668)CaDiCaL version: 2.1.3
% 5.37/1.64 % (3322668)Termination reason: Refutation not found, incomplete strategy
% 5.37/1.64 % (3322668)Time elapsed: 0.006 s
% 5.37/1.64 % (3322668)Peak memory usage: 89 MB
% 5.37/1.64 % (3322668)Instructions burned: 7 (million)
% 5.37/1.64 % (3322666)Instruction limit reached!
% 5.37/1.64 % (3322666)------------------------------
% 5.37/1.64 % (3322666)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/1.64 % (3322666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/1.64 % (3322666)CaDiCaL version: 2.1.3
% 5.37/1.64 % (3322666)Termination reason: Instruction limit
% 5.37/1.64 % (3322666)Termination phase: Saturation
% 5.37/1.64 % (3322666)Time elapsed: 0.169 s
% 5.37/1.64 % (3322666)Peak memory usage: 92 MB
% 5.37/1.64 % (3322666)Instructions burned: 285 (million)
% 5.37/1.64 % (3322672)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=2204378083:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 5.37/1.64 % (3322654)First to succeed.
% 5.37/1.64 % (3322654)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3322647"
% 5.37/1.64 % (3322667)------------------------------
% 5.37/1.64 % (3322667)------------------------------
% 5.37/1.64 % (3322668)------------------------------
% 5.37/1.64 % (3322668)------------------------------
% 5.37/1.64 % (3322672)Instruction limit reached!
% 5.37/1.64 % (3322672)------------------------------
% 5.37/1.64 % (3322672)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/1.64 % (3322672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/1.64 % (3322672)CaDiCaL version: 2.1.3
% 5.37/1.64 % (3322672)Termination reason: Instruction limit
% 5.37/1.64 % (3322672)Termination phase: Saturation
% 5.37/1.64 % (3322672)Time elapsed: 0.135 s
% 5.37/1.64 % (3322672)Peak memory usage: 92 MB
% 5.37/1.64 % (3322672)Instructions burned: 248 (million)
% 5.37/1.64 % (3322673)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2328664374:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 5.37/1.64 % (3322673)Refutation not found, incomplete strategy
% 5.37/1.64 % (3322673)------------------------------
% 5.37/1.64 % (3322673)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/1.64 % (3322673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/1.64 % (3322673)CaDiCaL version: 2.1.3
% 5.37/1.64 % (3322673)Termination reason: Refutation not found, incomplete strategy
% 5.37/1.64 % (3322673)Time elapsed: 0.008 s
% 5.37/1.64 % (3322673)Peak memory usage: 89 MB
% 5.37/1.64 % (3322673)Instructions burned: 10 (million)
% 5.37/1.64 % (3322654)Refutation found. Thanks to Tanya!
% 5.37/1.64 % SZS status Theorem for theBenchmark
% 5.37/1.64 % SZS output start Proof for theBenchmark
% See solution above
% 6.20/1.84 % (3322654)------------------------------
% 6.20/1.84 % (3322654)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.20/1.84 % (3322654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.84 % (3322654)CaDiCaL version: 2.1.3
% 6.20/1.84 % (3322654)Termination reason: Refutation
% 6.20/1.84 % (3322654)Time elapsed: 0.499 s
% 6.20/1.84 % (3322654)Peak memory usage: 132 MB
% 6.20/1.84 % (3322654)Instructions burned: 1148 (million)
% 6.20/1.84 % (3322654)------------------------------
% 6.20/1.84 % (3322654)------------------------------
% 6.20/1.84 % (3322647)Success in time 0.796 s
% 6.20/1.84 % Vampire exiting
%------------------------------------------------------------------------------