%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP625+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:15:04 AM UTC 2026
% Result : Theorem 26.56s 5.08s
% Output : Refutation 29.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 34
% Syntax : Number of formulae : 261 ( 27 unt; 7 def)
% Number of atoms : 1376 ( 138 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 1909 ( 794 ~; 937 |; 121 &)
% ( 21 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 6 prp; 0-4 aty)
% Number of functors : 20 ( 20 usr; 2 con; 0-4 aty)
% Number of variables : 528 ( 0 sgn 505 !; 23 ?)
% 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) )
=> m2_fraenkel(k6_partfun1(u1_struct_0(X0)),u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_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) )
=> m2_fraenkel(k6_partfun1(u1_struct_0(X0)),u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0)) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f7,axiom,
! [X0,X1,X2] :
( m1_relset_1(X2,X0,X1)
=> ( ( v1_funct_1(X2)
& v1_partfun1(X2,X0,X1) )
=> ( v1_funct_1(X2)
& v1_funct_2(X2,X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_2) ).
fof(f8,axiom,
! [X0] :
( l1_group_1(X0)
=> ( ( ~ v3_struct_0(X0)
& v3_group_1(X0) )
=> ( ~ v3_struct_0(X0)
& v2_group_1(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_group_1) ).
fof(f20,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> k2_group_3(X0,X1,X2) = k1_group_1(X0,k1_group_1(X0,k3_group_1(X0,X2),X1),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_group_3) ).
fof(f21,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m1_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0))
=> ( X1 = k4_autgroup(X0)
<=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0)))
=> ( r2_hidden(X2,X1)
<=> ? [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
& ! [X4] :
( m1_subset_1(X4,u1_struct_0(X0))
=> k8_funct_2(u1_struct_0(X0),u1_struct_0(X0),X2,X4) = k2_group_3(X0,X4,X3) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_autgroup) ).
fof(f22,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& l1_group_1(X0) )
=> ( v2_group_1(X0)
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ( X1 = k2_group_1(X0)
<=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ( k1_group_1(X0,X2,X1) = X2
& k1_group_1(X0,X1,X2) = X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_group_1) ).
fof(f26,axiom,
! [X0,X1] :
( ~ v1_xboole_0(X1)
=> m1_fraenkel(k1_fraenkel(X0,X1),X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_fraenkel) ).
fof(f29,axiom,
! [X0,X1,X2] :
( ( ~ v3_struct_0(X0)
& l1_group_1(X0)
& m1_subset_1(X1,u1_struct_0(X0))
& m1_subset_1(X2,u1_struct_0(X0)) )
=> m1_subset_1(k1_group_1(X0,X1,X2),u1_struct_0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_group_1) ).
fof(f34,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& l1_group_1(X0) )
=> m1_subset_1(k2_group_1(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_group_1) ).
fof(f39,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v1_group_1(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_autgroup) ).
fof(f41,axiom,
! [X0] :
( v1_partfun1(k6_partfun1(X0),X0,X0)
& m2_relset_1(k6_partfun1(X0),X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_partfun1) ).
fof(f44,axiom,
! [X0] :
( l1_group_1(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(f49,axiom,
! [X0,X1,X2] :
( ( ~ v1_xboole_0(X1)
& m1_fraenkel(X2,X0,X1) )
=> ! [X3] :
( m2_fraenkel(X3,X0,X1,X2)
=> ( v1_funct_1(X3)
& v1_funct_2(X3,X0,X1)
& m2_relset_1(X3,X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_fraenkel) ).
fof(f63,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& l1_struct_0(X0) )
=> ~ v1_xboole_0(u1_struct_0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f64,axiom,
v1_xboole_0(k1_xboole_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f65,axiom,
! [X0] :
( v1_relat_1(k6_relat_1(X0))
& v1_funct_1(k6_relat_1(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f85,axiom,
! [X0,X1] :
( ~ v1_xboole_0(X1)
=> k1_fraenkel(X0,X1) = k1_funct_2(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_fraenkel) ).
fof(f87,axiom,
! [X0] : k6_partfun1(X0) = k6_relat_1(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
fof(f88,axiom,
! [X0,X1,X2,X3] :
( ( ~ v1_xboole_0(X0)
& v1_funct_1(X2)
& v1_funct_2(X2,X0,X1)
& m1_relset_1(X2,X0,X1)
& m1_subset_1(X3,X0) )
=> k8_funct_2(X0,X1,X2,X3) = k1_funct_1(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
fof(f89,axiom,
! [X0,X1,X2] :
( ( ~ v1_xboole_0(X1)
& m1_fraenkel(X2,X0,X1) )
=> ! [X3] :
( m2_fraenkel(X3,X0,X1,X2)
<=> m1_subset_1(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_fraenkel) ).
fof(f90,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
<=> m1_relset_1(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f92,axiom,
! [X0,X1,X2] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,X0,X1)
& m2_relset_1(X2,X0,X1) )
=> ( ( X1 = k1_xboole_0
=> X0 = k1_xboole_0 )
=> r2_hidden(X2,k1_funct_2(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_funct_2) ).
fof(f93,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> k3_group_1(X0,k2_group_1(X0)) = k2_group_1(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_group_1) ).
fof(f94,axiom,
! [X0,X1] :
( r2_hidden(X0,X1)
=> m1_subset_1(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f95,axiom,
! [X0,X1] :
( m1_subset_1(X0,X1)
=> ( v1_xboole_0(X1)
| r2_hidden(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f96,axiom,
! [X0,X1] :
( r2_hidden(X1,X0)
=> k1_funct_1(k6_relat_1(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).
fof(f100,axiom,
! [X0] :
( v1_xboole_0(X0)
=> X0 = k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f107,plain,
? [X0] :
( ~ m2_fraenkel(k6_partfun1(u1_struct_0(X0)),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(f108,plain,
? [X0] :
( ~ m2_fraenkel(k6_partfun1(u1_struct_0(X0)),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,[],[f107]) ).
fof(f111,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(ennf_transformation,[],[f63]) ).
fof(f112,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(flattening,[],[f111]) ).
fof(f114,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,[],[f39]) ).
fof(f115,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,[],[f114]) ).
fof(f120,plain,
! [X0] :
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f121,plain,
! [X0] :
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f120]) ).
fof(f122,plain,
! [X0,X1,X2] :
( m1_subset_1(k1_group_1(X0,X1,X2),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f29]) ).
fof(f123,plain,
! [X0,X1,X2] :
( m1_subset_1(k1_group_1(X0,X1,X2),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0)) ),
inference(flattening,[],[f122]) ).
fof(f124,plain,
! [X0] :
( ! [X1] :
( ( X1 = k2_group_1(X0)
<=> ! [X2] :
( ( k1_group_1(X0,X2,X1) = X2
& k1_group_1(X0,X1,X2) = X2 )
| ~ m1_subset_1(X2,u1_struct_0(X0)) ) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| ~ v2_group_1(X0)
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f125,plain,
! [X0] :
( ! [X1] :
( ( X1 = k2_group_1(X0)
<=> ! [X2] :
( ( k1_group_1(X0,X2,X1) = X2
& k1_group_1(X0,X1,X2) = X2 )
| ~ m1_subset_1(X2,u1_struct_0(X0)) ) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| ~ v2_group_1(X0)
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f124]) ).
fof(f126,plain,
! [X0] :
( ! [X1] :
( ( X1 = k4_autgroup(X0)
<=> ! [X2] :
( ( r2_hidden(X2,X1)
<=> ? [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
& ! [X4] :
( k8_funct_2(u1_struct_0(X0),u1_struct_0(X0),X2,X4) = k2_group_3(X0,X4,X3)
| ~ m1_subset_1(X4,u1_struct_0(X0)) ) ) )
| ~ m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0))) ) )
| ~ m1_fraenkel(X1,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,[],[f21]) ).
fof(f127,plain,
! [X0] :
( ! [X1] :
( ( X1 = k4_autgroup(X0)
<=> ! [X2] :
( ( r2_hidden(X2,X1)
<=> ? [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
& ! [X4] :
( k8_funct_2(u1_struct_0(X0),u1_struct_0(X0),X2,X4) = k2_group_3(X0,X4,X3)
| ~ m1_subset_1(X4,u1_struct_0(X0)) ) ) )
| ~ m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0))) ) )
| ~ m1_fraenkel(X1,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,[],[f126]) ).
fof(f128,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( k2_group_3(X0,X1,X2) = k1_group_1(X0,k1_group_1(X0,k3_group_1(X0,X2),X1),X2)
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f129,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( k2_group_3(X0,X1,X2) = k1_group_1(X0,k1_group_1(X0,k3_group_1(X0,X2),X1),X2)
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f128]) ).
fof(f138,plain,
! [X0] :
( k3_group_1(X0,k2_group_1(X0)) = k2_group_1(X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f93]) ).
fof(f139,plain,
! [X0] :
( k3_group_1(X0,k2_group_1(X0)) = k2_group_1(X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f138]) ).
fof(f140,plain,
! [X0] :
( ( ~ v3_struct_0(X0)
& v2_group_1(X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f141,plain,
! [X0] :
( ( ~ v3_struct_0(X0)
& v2_group_1(X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f140]) ).
fof(f142,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,[],[f89]) ).
fof(f143,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,[],[f142]) ).
fof(f146,plain,
! [X0,X1,X2] :
( ! [X3] :
( ( v1_funct_1(X3)
& v1_funct_2(X3,X0,X1)
& m2_relset_1(X3,X0,X1) )
| ~ m2_fraenkel(X3,X0,X1,X2) )
| v1_xboole_0(X1)
| ~ m1_fraenkel(X2,X0,X1) ),
inference(ennf_transformation,[],[f49]) ).
fof(f147,plain,
! [X0,X1,X2] :
( ! [X3] :
( ( v1_funct_1(X3)
& v1_funct_2(X3,X0,X1)
& m2_relset_1(X3,X0,X1) )
| ~ m2_fraenkel(X3,X0,X1,X2) )
| v1_xboole_0(X1)
| ~ m1_fraenkel(X2,X0,X1) ),
inference(flattening,[],[f146]) ).
fof(f154,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f162,plain,
! [X0,X1,X2] :
( r2_hidden(X2,k1_funct_2(X0,X1))
| ( k1_xboole_0 != X0
& X1 = k1_xboole_0 )
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f92]) ).
fof(f163,plain,
! [X0,X1,X2] :
( r2_hidden(X2,k1_funct_2(X0,X1))
| ( k1_xboole_0 != X0
& X1 = k1_xboole_0 )
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ),
inference(flattening,[],[f162]) ).
fof(f165,plain,
! [X0,X1] :
( m1_fraenkel(k1_fraenkel(X0,X1),X0,X1)
| v1_xboole_0(X1) ),
inference(ennf_transformation,[],[f26]) ).
fof(f168,plain,
! [X0,X1] :
( k1_funct_1(k6_relat_1(X0),X1) = X1
| ~ r2_hidden(X1,X0) ),
inference(ennf_transformation,[],[f96]) ).
fof(f169,plain,
! [X0,X1] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(ennf_transformation,[],[f95]) ).
fof(f170,plain,
! [X0,X1] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(flattening,[],[f169]) ).
fof(f171,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f94]) ).
fof(f173,plain,
! [X0,X1] :
( k1_fraenkel(X0,X1) = k1_funct_2(X0,X1)
| v1_xboole_0(X1) ),
inference(ennf_transformation,[],[f85]) ).
fof(f174,plain,
! [X0,X1,X2,X3] :
( k8_funct_2(X0,X1,X2,X3) = k1_funct_1(X2,X3)
| v1_xboole_0(X0)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X0,X1)
| ~ m1_relset_1(X2,X0,X1)
| ~ m1_subset_1(X3,X0) ),
inference(ennf_transformation,[],[f88]) ).
fof(f175,plain,
! [X0,X1,X2,X3] :
( k8_funct_2(X0,X1,X2,X3) = k1_funct_1(X2,X3)
| v1_xboole_0(X0)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X0,X1)
| ~ m1_relset_1(X2,X0,X1)
| ~ m1_subset_1(X3,X0) ),
inference(flattening,[],[f174]) ).
fof(f184,plain,
! [X0,X1,X2] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,X0,X1) )
| ~ v1_funct_1(X2)
| ~ v1_partfun1(X2,X0,X1)
| ~ m1_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f185,plain,
! [X0,X1,X2] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,X0,X1) )
| ~ v1_funct_1(X2)
| ~ v1_partfun1(X2,X0,X1)
| ~ m1_relset_1(X2,X0,X1) ),
inference(flattening,[],[f184]) ).
fof(f194,plain,
! [X0] :
( X0 = k1_xboole_0
| ~ v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f100]) ).
fof(f199,definition,
! [X0,X1] :
( sP0(X0,X1)
<=> ! [X2] :
( ( r2_hidden(X2,X1)
<=> ? [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
& ! [X4] :
( k8_funct_2(u1_struct_0(X0),u1_struct_0(X0),X2,X4) = k2_group_3(X0,X4,X3)
| ~ m1_subset_1(X4,u1_struct_0(X0)) ) ) )
| ~ m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0))) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f200,definition,
! [X1,X0] :
( ( X1 = k4_autgroup(X0)
<=> sP0(X0,X1) )
| ~ sP1(X1,X0) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f201,plain,
! [X0] :
( ! [X1] :
( sP1(X1,X0)
| ~ m1_fraenkel(X1,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(definition_folding,[],[f127,f200,f199]) ).
fof(f202,plain,
( ~ m2_fraenkel(k6_partfun1(u1_struct_0(sK2)),u1_struct_0(sK2),u1_struct_0(sK2),k4_autgroup(sK2))
& ~ v3_struct_0(sK2)
& v1_group_1(sK2)
& v3_group_1(sK2)
& v4_group_1(sK2)
& l1_group_1(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f108]) ).
fof(f204,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = k2_group_1(X0)
| ? [X2] :
( ( k1_group_1(X0,X2,X1) != X2
| k1_group_1(X0,X1,X2) != X2 )
& m1_subset_1(X2,u1_struct_0(X0)) ) )
& ( ! [X2] :
( ( k1_group_1(X0,X2,X1) = X2
& k1_group_1(X0,X1,X2) = X2 )
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| k2_group_1(X0) != X1 ) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| ~ v2_group_1(X0)
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(nnf_transformation,[],[f125]) ).
fof(f205,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = k2_group_1(X0)
| ? [X2] :
( ( k1_group_1(X0,X2,X1) != X2
| k1_group_1(X0,X1,X2) != X2 )
& m1_subset_1(X2,u1_struct_0(X0)) ) )
& ( ! [X3] :
( ( k1_group_1(X0,X3,X1) = X3
& k1_group_1(X0,X1,X3) = X3 )
| ~ m1_subset_1(X3,u1_struct_0(X0)) )
| k2_group_1(X0) != X1 ) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| ~ v2_group_1(X0)
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(rectify,[],[f204]) ).
fof(f206,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = k2_group_1(X0)
| ( ( sK4(X0,X1) != k1_group_1(X0,sK4(X0,X1),X1)
| sK4(X0,X1) != k1_group_1(X0,X1,sK4(X0,X1)) )
& m1_subset_1(sK4(X0,X1),u1_struct_0(X0)) ) )
& ( ! [X3] :
( ( k1_group_1(X0,X3,X1) = X3
& k1_group_1(X0,X1,X3) = X3 )
| ~ m1_subset_1(X3,u1_struct_0(X0)) )
| k2_group_1(X0) != X1 ) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| ~ v2_group_1(X0)
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f205]) ).
fof(f207,plain,
! [X1,X0] :
( ( ( X1 = k4_autgroup(X0)
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| k4_autgroup(X0) != X1 ) )
| ~ sP1(X1,X0) ),
inference(nnf_transformation,[],[f200]) ).
fof(f208,plain,
! [X0,X1] :
( ( ( k4_autgroup(X1) = X0
| ~ sP0(X1,X0) )
& ( sP0(X1,X0)
| k4_autgroup(X1) != X0 ) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f207]) ).
fof(f209,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X0))
| ? [X4] :
( k8_funct_2(u1_struct_0(X0),u1_struct_0(X0),X2,X4) != k2_group_3(X0,X4,X3)
& m1_subset_1(X4,u1_struct_0(X0)) ) )
| ~ r2_hidden(X2,X1) )
& ( ? [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
& ! [X4] :
( k8_funct_2(u1_struct_0(X0),u1_struct_0(X0),X2,X4) = k2_group_3(X0,X4,X3)
| ~ m1_subset_1(X4,u1_struct_0(X0)) ) )
| r2_hidden(X2,X1) )
& m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0))) ) )
& ( ! [X2] :
( ( ( r2_hidden(X2,X1)
| ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X0))
| ? [X4] :
( k8_funct_2(u1_struct_0(X0),u1_struct_0(X0),X2,X4) != k2_group_3(X0,X4,X3)
& m1_subset_1(X4,u1_struct_0(X0)) ) ) )
& ( ? [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
& ! [X4] :
( k8_funct_2(u1_struct_0(X0),u1_struct_0(X0),X2,X4) = k2_group_3(X0,X4,X3)
| ~ m1_subset_1(X4,u1_struct_0(X0)) ) )
| ~ r2_hidden(X2,X1) ) )
| ~ m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0))) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f199]) ).
fof(f210,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X0))
| ? [X4] :
( k8_funct_2(u1_struct_0(X0),u1_struct_0(X0),X2,X4) != k2_group_3(X0,X4,X3)
& m1_subset_1(X4,u1_struct_0(X0)) ) )
| ~ r2_hidden(X2,X1) )
& ( ? [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
& ! [X4] :
( k8_funct_2(u1_struct_0(X0),u1_struct_0(X0),X2,X4) = k2_group_3(X0,X4,X3)
| ~ m1_subset_1(X4,u1_struct_0(X0)) ) )
| r2_hidden(X2,X1) )
& m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0))) ) )
& ( ! [X2] :
( ( ( r2_hidden(X2,X1)
| ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X0))
| ? [X4] :
( k8_funct_2(u1_struct_0(X0),u1_struct_0(X0),X2,X4) != k2_group_3(X0,X4,X3)
& m1_subset_1(X4,u1_struct_0(X0)) ) ) )
& ( ? [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
& ! [X4] :
( k8_funct_2(u1_struct_0(X0),u1_struct_0(X0),X2,X4) = k2_group_3(X0,X4,X3)
| ~ m1_subset_1(X4,u1_struct_0(X0)) ) )
| ~ r2_hidden(X2,X1) ) )
| ~ m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0))) )
| ~ sP0(X0,X1) ) ),
inference(flattening,[],[f209]) ).
fof(f211,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X0))
| ? [X4] :
( k8_funct_2(u1_struct_0(X0),u1_struct_0(X0),X2,X4) != k2_group_3(X0,X4,X3)
& m1_subset_1(X4,u1_struct_0(X0)) ) )
| ~ r2_hidden(X2,X1) )
& ( ? [X5] :
( m1_subset_1(X5,u1_struct_0(X0))
& ! [X6] :
( k8_funct_2(u1_struct_0(X0),u1_struct_0(X0),X2,X6) = k2_group_3(X0,X6,X5)
| ~ m1_subset_1(X6,u1_struct_0(X0)) ) )
| r2_hidden(X2,X1) )
& m2_fraenkel(X2,u1_struct_0(X0),u1_struct_0(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0))) ) )
& ( ! [X7] :
( ( ( r2_hidden(X7,X1)
| ! [X8] :
( ~ m1_subset_1(X8,u1_struct_0(X0))
| ? [X9] :
( k8_funct_2(u1_struct_0(X0),u1_struct_0(X0),X7,X9) != k2_group_3(X0,X9,X8)
& m1_subset_1(X9,u1_struct_0(X0)) ) ) )
& ( ? [X10] :
( m1_subset_1(X10,u1_struct_0(X0))
& ! [X11] :
( k8_funct_2(u1_struct_0(X0),u1_struct_0(X0),X7,X11) = k2_group_3(X0,X11,X10)
| ~ m1_subset_1(X11,u1_struct_0(X0)) ) )
| ~ r2_hidden(X7,X1) ) )
| ~ m2_fraenkel(X7,u1_struct_0(X0),u1_struct_0(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0))) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f210]) ).
fof(f212,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X0))
| ( k8_funct_2(u1_struct_0(X0),u1_struct_0(X0),sK5(X0,X1),sK6(X0,X1,X3)) != k2_group_3(X0,sK6(X0,X1,X3),X3)
& m1_subset_1(sK6(X0,X1,X3),u1_struct_0(X0)) ) )
| ~ r2_hidden(sK5(X0,X1),X1) )
& ( ( m1_subset_1(sK7(X0,X1),u1_struct_0(X0))
& ! [X6] :
( k8_funct_2(u1_struct_0(X0),u1_struct_0(X0),sK5(X0,X1),X6) = k2_group_3(X0,X6,sK7(X0,X1))
| ~ m1_subset_1(X6,u1_struct_0(X0)) ) )
| r2_hidden(sK5(X0,X1),X1) )
& m2_fraenkel(sK5(X0,X1),u1_struct_0(X0),u1_struct_0(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0))) ) )
& ( ! [X7] :
( ( ( r2_hidden(X7,X1)
| ! [X8] :
( ~ m1_subset_1(X8,u1_struct_0(X0))
| ( k8_funct_2(u1_struct_0(X0),u1_struct_0(X0),X7,sK8(X0,X7,X8)) != k2_group_3(X0,sK8(X0,X7,X8),X8)
& m1_subset_1(sK8(X0,X7,X8),u1_struct_0(X0)) ) ) )
& ( ( m1_subset_1(sK9(X0,X7),u1_struct_0(X0))
& ! [X11] :
( k8_funct_2(u1_struct_0(X0),u1_struct_0(X0),X7,X11) = k2_group_3(X0,X11,sK9(X0,X7))
| ~ m1_subset_1(X11,u1_struct_0(X0)) ) )
| ~ r2_hidden(X7,X1) ) )
| ~ m2_fraenkel(X7,u1_struct_0(X0),u1_struct_0(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0))) )
| ~ sP0(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9]),skolemize(X2,sK5(X0,X1)),skolemize(X4,sK6(X0,X1,X3)),skolemize(X5,sK7(X0,X1)),skolemize(X9,sK8(X0,X7,X8)),skolemize(X10,sK9(X0,X7))],[f211]) ).
fof(f217,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,[],[f143]) ).
fof(f224,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,[],[f90]) ).
fof(f237,plain,
l1_group_1(sK2),
inference(cnf_transformation,[],[f202]) ).
fof(f238,plain,
v4_group_1(sK2),
inference(cnf_transformation,[],[f202]) ).
fof(f239,plain,
v3_group_1(sK2),
inference(cnf_transformation,[],[f202]) ).
fof(f240,plain,
v1_group_1(sK2),
inference(cnf_transformation,[],[f202]) ).
fof(f241,plain,
~ v3_struct_0(sK2),
inference(cnf_transformation,[],[f202]) ).
fof(f242,plain,
~ m2_fraenkel(k6_partfun1(u1_struct_0(sK2)),u1_struct_0(sK2),u1_struct_0(sK2),k4_autgroup(sK2)),
inference(cnf_transformation,[],[f202]) ).
fof(f245,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_struct_0(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f249,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,[],[f115]) ).
fof(f252,plain,
! [X0] :
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f253,plain,
! [X2,X0,X1] :
( m1_subset_1(k1_group_1(X0,X1,X2),u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f123]) ).
fof(f254,plain,
! [X3,X0,X1] :
( k1_group_1(X0,X1,X3) = X3
| ~ m1_subset_1(X3,u1_struct_0(X0))
| k2_group_1(X0) != X1
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ v2_group_1(X0)
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f206]) ).
fof(f255,plain,
! [X3,X0,X1] :
( k1_group_1(X0,X3,X1) = X3
| ~ m1_subset_1(X3,u1_struct_0(X0))
| k2_group_1(X0) != X1
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ v2_group_1(X0)
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f206]) ).
fof(f258,plain,
! [X0,X1] :
( sP0(X1,X0)
| k4_autgroup(X1) != X0
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f208]) ).
fof(f260,plain,
! [X0,X11,X1,X7] :
( k8_funct_2(u1_struct_0(X0),u1_struct_0(X0),X7,X11) = k2_group_3(X0,X11,sK9(X0,X7))
| ~ m1_subset_1(X11,u1_struct_0(X0))
| ~ r2_hidden(X7,X1)
| ~ m2_fraenkel(X7,u1_struct_0(X0),u1_struct_0(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0)))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f212]) ).
fof(f261,plain,
! [X0,X1,X7] :
( ~ m2_fraenkel(X7,u1_struct_0(X0),u1_struct_0(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0)))
| ~ r2_hidden(X7,X1)
| m1_subset_1(sK9(X0,X7),u1_struct_0(X0))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f212]) ).
fof(f262,plain,
! [X0,X1,X8,X7] :
( ~ m2_fraenkel(X7,u1_struct_0(X0),u1_struct_0(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0)))
| ~ m1_subset_1(X8,u1_struct_0(X0))
| m1_subset_1(sK8(X0,X7,X8),u1_struct_0(X0))
| r2_hidden(X7,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f212]) ).
fof(f263,plain,
! [X0,X1,X8,X7] :
( k8_funct_2(u1_struct_0(X0),u1_struct_0(X0),X7,sK8(X0,X7,X8)) != k2_group_3(X0,sK8(X0,X7,X8),X8)
| ~ m1_subset_1(X8,u1_struct_0(X0))
| r2_hidden(X7,X1)
| ~ m2_fraenkel(X7,u1_struct_0(X0),u1_struct_0(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0)))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f212]) ).
fof(f269,plain,
! [X0,X1] :
( ~ m1_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0))
| sP1(X1,X0)
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f201]) ).
fof(f270,plain,
! [X2,X0,X1] :
( k2_group_3(X0,X1,X2) = k1_group_1(X0,k1_group_1(X0,k3_group_1(X0,X2),X1),X2)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f273,plain,
! [X0] : k6_partfun1(X0) = k6_relat_1(X0),
inference(cnf_transformation,[],[f87]) ).
fof(f274,plain,
! [X0] : m2_relset_1(k6_partfun1(X0),X0,X0),
inference(cnf_transformation,[],[f41]) ).
fof(f275,plain,
! [X0] : v1_partfun1(k6_partfun1(X0),X0,X0),
inference(cnf_transformation,[],[f41]) ).
fof(f291,plain,
! [X0] :
( k2_group_1(X0) = k3_group_1(X0,k2_group_1(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f292,plain,
! [X0] :
( v2_group_1(X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f296,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,[],[f217]) ).
fof(f298,plain,
! [X2,X3,X0,X1] :
( ~ m2_fraenkel(X3,X0,X1,X2)
| m2_relset_1(X3,X0,X1)
| v1_xboole_0(X1)
| ~ m1_fraenkel(X2,X0,X1) ),
inference(cnf_transformation,[],[f147]) ).
fof(f299,plain,
! [X2,X3,X0,X1] :
( ~ m2_fraenkel(X3,X0,X1,X2)
| v1_funct_2(X3,X0,X1)
| v1_xboole_0(X1)
| ~ m1_fraenkel(X2,X0,X1) ),
inference(cnf_transformation,[],[f147]) ).
fof(f312,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f154]) ).
fof(f318,plain,
! [X2,X0,X1] :
( r2_hidden(X2,k1_funct_2(X0,X1))
| k1_xboole_0 = X1
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f163]) ).
fof(f320,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f224]) ).
fof(f326,plain,
! [X0,X1] :
( m1_fraenkel(k1_fraenkel(X0,X1),X0,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f165]) ).
fof(f329,plain,
! [X0,X1] :
( k1_funct_1(k6_relat_1(X0),X1) = X1
| ~ r2_hidden(X1,X0) ),
inference(cnf_transformation,[],[f168]) ).
fof(f330,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f170]) ).
fof(f331,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f171]) ).
fof(f333,plain,
! [X0,X1] :
( k1_fraenkel(X0,X1) = k1_funct_2(X0,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f173]) ).
fof(f334,plain,
! [X2,X3,X0,X1] :
( k8_funct_2(X0,X1,X2,X3) = k1_funct_1(X2,X3)
| v1_xboole_0(X0)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X0,X1)
| ~ m1_relset_1(X2,X0,X1)
| ~ m1_subset_1(X3,X0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f341,plain,
! [X0] : v1_funct_1(k6_relat_1(X0)),
inference(cnf_transformation,[],[f65]) ).
fof(f362,plain,
! [X2,X0,X1] :
( v1_funct_2(X2,X0,X1)
| ~ v1_funct_1(X2)
| ~ v1_partfun1(X2,X0,X1)
| ~ m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f185]) ).
fof(f403,plain,
! [X0] :
( k1_xboole_0 = X0
| ~ v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f194]) ).
fof(f404,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f64]) ).
fof(f416,plain,
~ m2_fraenkel(k6_relat_1(u1_struct_0(sK2)),u1_struct_0(sK2),u1_struct_0(sK2),k4_autgroup(sK2)),
inference(definition_unfolding,[],[f242,f273]) ).
fof(f417,plain,
! [X0] : v1_partfun1(k6_relat_1(X0),X0,X0),
inference(definition_unfolding,[],[f275,f273]) ).
fof(f418,plain,
! [X0] : m2_relset_1(k6_relat_1(X0),X0,X0),
inference(definition_unfolding,[],[f274,f273]) ).
fof(f420,plain,
! [X3,X0] :
( k1_group_1(X0,X3,k2_group_1(X0)) = X3
| ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| ~ v2_group_1(X0)
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(equality_resolution,[],[f255]) ).
fof(f421,plain,
! [X3,X0] :
( k1_group_1(X0,k2_group_1(X0),X3) = X3
| ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| ~ v2_group_1(X0)
| v3_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(equality_resolution,[],[f254]) ).
fof(f422,plain,
! [X1] :
( ~ sP1(k4_autgroup(X1),X1)
| sP0(X1,k4_autgroup(X1)) ),
inference(equality_resolution,[],[f258]) ).
fof(f428,plain,
( ~ m1_subset_1(k6_relat_1(u1_struct_0(sK2)),k4_autgroup(sK2))
| v1_xboole_0(u1_struct_0(sK2))
| ~ m1_fraenkel(k4_autgroup(sK2),u1_struct_0(sK2),u1_struct_0(sK2)) ),
inference(resolution,[],[f296,f416]) ).
fof(f430,definition,
( spl32_1
<=> m1_fraenkel(k4_autgroup(sK2),u1_struct_0(sK2),u1_struct_0(sK2)) ),
introduced(definition,[new_symbols(definition,[spl32_1])],[avatar_definition]) ).
fof(f431,plain,
( m1_fraenkel(k4_autgroup(sK2),u1_struct_0(sK2),u1_struct_0(sK2))
| ~ spl32_1 ),
inference(avatar_component_clause,[],[f430]) ).
fof(f432,plain,
( ~ m1_fraenkel(k4_autgroup(sK2),u1_struct_0(sK2),u1_struct_0(sK2))
| spl32_1 ),
inference(avatar_component_clause,[],[f430]) ).
fof(f434,definition,
( spl32_2
<=> v1_xboole_0(u1_struct_0(sK2)) ),
introduced(definition,[new_symbols(definition,[spl32_2])],[avatar_definition]) ).
fof(f435,plain,
( ~ v1_xboole_0(u1_struct_0(sK2))
| spl32_2 ),
inference(avatar_component_clause,[],[f434]) ).
fof(f436,plain,
( v1_xboole_0(u1_struct_0(sK2))
| ~ spl32_2 ),
inference(avatar_component_clause,[],[f434]) ).
fof(f438,definition,
( spl32_3
<=> m1_subset_1(k6_relat_1(u1_struct_0(sK2)),k4_autgroup(sK2)) ),
introduced(definition,[new_symbols(definition,[spl32_3])],[avatar_definition]) ).
fof(f440,plain,
( ~ m1_subset_1(k6_relat_1(u1_struct_0(sK2)),k4_autgroup(sK2))
| spl32_3 ),
inference(avatar_component_clause,[],[f438]) ).
fof(f441,plain,
( ~ spl32_1
| spl32_2
| ~ spl32_3 ),
inference(avatar_split_clause,[],[f428,f438,f434,f430]) ).
fof(f442,plain,
( v3_struct_0(sK2)
| ~ v1_group_1(sK2)
| ~ v3_group_1(sK2)
| ~ v4_group_1(sK2)
| ~ l1_group_1(sK2)
| spl32_1 ),
inference(resolution,[],[f432,f249]) ).
fof(f443,plain,
( ~ v1_group_1(sK2)
| ~ v3_group_1(sK2)
| ~ v4_group_1(sK2)
| ~ l1_group_1(sK2)
| spl32_1 ),
inference(forward_subsumption_resolution,[],[f442,f241]) ).
fof(f444,plain,
( ~ v3_group_1(sK2)
| ~ v4_group_1(sK2)
| ~ l1_group_1(sK2)
| spl32_1 ),
inference(forward_subsumption_resolution,[],[f443,f240]) ).
fof(f445,plain,
( ~ v4_group_1(sK2)
| ~ l1_group_1(sK2)
| spl32_1 ),
inference(forward_subsumption_resolution,[],[f444,f239]) ).
fof(f446,plain,
( ~ l1_group_1(sK2)
| spl32_1 ),
inference(forward_subsumption_resolution,[],[f445,f238]) ).
fof(f447,plain,
( $false
| spl32_1 ),
inference(forward_subsumption_resolution,[],[f446,f237]) ).
fof(f448,plain,
spl32_1,
inference(avatar_contradiction_clause,[],[f447]) ).
fof(f451,plain,
! [X0] :
( sP1(k4_autgroup(X0),X0)
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(resolution,[],[f269,f249]) ).
fof(f452,plain,
( sP1(k4_autgroup(sK2),sK2)
| v3_struct_0(sK2)
| ~ v1_group_1(sK2)
| ~ v3_group_1(sK2)
| ~ v4_group_1(sK2)
| ~ l1_group_1(sK2)
| ~ spl32_1 ),
inference(resolution,[],[f269,f431]) ).
fof(f453,plain,
! [X0] :
( sP1(k4_autgroup(X0),X0)
| v3_struct_0(X0)
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(duplicate_literal_removal,[],[f451]) ).
fof(f454,plain,
( sP1(k4_autgroup(sK2),sK2)
| ~ v1_group_1(sK2)
| ~ v3_group_1(sK2)
| ~ v4_group_1(sK2)
| ~ l1_group_1(sK2)
| ~ spl32_1 ),
inference(forward_subsumption_resolution,[],[f452,f241]) ).
fof(f455,plain,
( sP1(k4_autgroup(sK2),sK2)
| ~ v3_group_1(sK2)
| ~ v4_group_1(sK2)
| ~ l1_group_1(sK2)
| ~ spl32_1 ),
inference(forward_subsumption_resolution,[],[f454,f240]) ).
fof(f456,plain,
( sP1(k4_autgroup(sK2),sK2)
| ~ v4_group_1(sK2)
| ~ l1_group_1(sK2)
| ~ spl32_1 ),
inference(forward_subsumption_resolution,[],[f455,f239]) ).
fof(f457,plain,
( sP1(k4_autgroup(sK2),sK2)
| ~ l1_group_1(sK2)
| ~ spl32_1 ),
inference(forward_subsumption_resolution,[],[f456,f238]) ).
fof(f458,plain,
( sP1(k4_autgroup(sK2),sK2)
| ~ spl32_1 ),
inference(forward_subsumption_resolution,[],[f457,f237]) ).
fof(f459,plain,
( sP0(sK2,k4_autgroup(sK2))
| ~ spl32_1 ),
inference(resolution,[],[f458,f422]) ).
fof(f496,plain,
! [X0,X1] :
( k2_group_3(X0,X1,k2_group_1(X0)) = k1_group_1(X0,k1_group_1(X0,k2_group_1(X0),X1),k2_group_1(X0))
| ~ m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(superposition,[],[f270,f291]) ).
fof(f499,plain,
! [X0,X1] :
( k2_group_3(X0,X1,k2_group_1(X0)) = k1_group_1(X0,k1_group_1(X0,k2_group_1(X0),X1),k2_group_1(X0))
| ~ m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(duplicate_literal_removal,[],[f496]) ).
fof(f501,plain,
! [X0,X1] :
( k2_group_3(X0,X1,k2_group_1(X0)) = k1_group_1(X0,k1_group_1(X0,k2_group_1(X0),X1),k2_group_1(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(forward_subsumption_resolution,[],[f499,f252]) ).
fof(f503,plain,
! [X0,X1] :
( k1_group_1(X1,X0,k2_group_1(X1)) = k2_group_3(X1,X0,k2_group_1(X1))
| ~ m1_subset_1(X0,u1_struct_0(X1))
| v3_struct_0(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_subset_1(X0,u1_struct_0(X1))
| ~ m1_subset_1(k2_group_1(X1),u1_struct_0(X1))
| ~ v2_group_1(X1)
| v3_struct_0(X1)
| ~ l1_group_1(X1) ),
inference(superposition,[],[f501,f421]) ).
fof(f506,plain,
! [X0,X1] :
( k2_group_3(X0,X1,k2_group_1(X0)) = k1_group_1(X0,k2_group_1(X0),X1)
| ~ m1_subset_1(k1_group_1(X0,k2_group_1(X0),X1),u1_struct_0(X0))
| ~ m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| ~ v2_group_1(X0)
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(superposition,[],[f420,f501]) ).
fof(f509,plain,
! [X0,X1] :
( k2_group_3(X0,X1,k2_group_1(X0)) = k1_group_1(X0,k2_group_1(X0),X1)
| ~ m1_subset_1(k1_group_1(X0,k2_group_1(X0),X1),u1_struct_0(X0))
| ~ m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| ~ v2_group_1(X0)
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ v3_group_1(X0)
| ~ v4_group_1(X0) ),
inference(duplicate_literal_removal,[],[f506]) ).
fof(f512,plain,
! [X0,X1] :
( k1_group_1(X1,X0,k2_group_1(X1)) = k2_group_3(X1,X0,k2_group_1(X1))
| ~ m1_subset_1(X0,u1_struct_0(X1))
| v3_struct_0(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_subset_1(k2_group_1(X1),u1_struct_0(X1))
| ~ v2_group_1(X1) ),
inference(duplicate_literal_removal,[],[f503]) ).
fof(f514,plain,
! [X0,X1] :
( k2_group_3(X0,X1,k2_group_1(X0)) = k1_group_1(X0,k2_group_1(X0),X1)
| ~ m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| ~ v2_group_1(X0)
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ v3_group_1(X0)
| ~ v4_group_1(X0) ),
inference(forward_subsumption_resolution,[],[f509,f253]) ).
fof(f516,plain,
! [X0,X1] :
( k1_group_1(X1,X0,k2_group_1(X1)) = k2_group_3(X1,X0,k2_group_1(X1))
| ~ m1_subset_1(X0,u1_struct_0(X1))
| v3_struct_0(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ v2_group_1(X1) ),
inference(forward_subsumption_resolution,[],[f512,f252]) ).
fof(f517,plain,
! [X0,X1] :
( k2_group_3(X0,X1,k2_group_1(X0)) = k1_group_1(X0,k2_group_1(X0),X1)
| ~ v2_group_1(X0)
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ v3_group_1(X0)
| ~ v4_group_1(X0) ),
inference(forward_subsumption_resolution,[],[f514,f252]) ).
fof(f519,plain,
! [X0,X1] :
( k1_group_1(X1,X0,k2_group_1(X1)) = k2_group_3(X1,X0,k2_group_1(X1))
| ~ m1_subset_1(X0,u1_struct_0(X1))
| v3_struct_0(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(forward_subsumption_resolution,[],[f516,f292]) ).
fof(f520,plain,
! [X0,X1] :
( k2_group_3(X0,X1,k2_group_1(X0)) = k1_group_1(X0,k2_group_1(X0),X1)
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ v3_group_1(X0)
| ~ v4_group_1(X0) ),
inference(forward_subsumption_resolution,[],[f517,f292]) ).
fof(f534,plain,
( ~ r2_hidden(k6_relat_1(u1_struct_0(sK2)),k4_autgroup(sK2))
| spl32_3 ),
inference(resolution,[],[f331,f440]) ).
fof(f535,plain,
! [X0] :
( sP0(X0,k4_autgroup(X0))
| ~ v1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| v3_struct_0(X0) ),
inference(resolution,[],[f453,f422]) ).
fof(f538,plain,
! [X0,X1] :
( k1_group_1(X0,X1,k2_group_1(X0)) = k1_group_1(X0,k2_group_1(X0),X1)
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(superposition,[],[f520,f519]) ).
fof(f543,plain,
! [X0,X1] :
( k1_group_1(X0,X1,k2_group_1(X0)) = k1_group_1(X0,k2_group_1(X0),X1)
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ v3_group_1(X0)
| ~ v4_group_1(X0) ),
inference(duplicate_literal_removal,[],[f538]) ).
fof(f615,plain,
! [X2,X3,X0,X1,X4] :
( k2_group_3(X0,sK8(X0,X1,X2),X2) != k2_group_3(X0,sK8(X0,X1,X2),sK9(X0,X1))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| r2_hidden(X1,X3)
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0)))
| ~ sP0(X0,X3)
| ~ m1_subset_1(sK8(X0,X1,X2),u1_struct_0(X0))
| ~ r2_hidden(X1,X4)
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0)))
| ~ sP0(X0,X4) ),
inference(superposition,[],[f263,f260]) ).
fof(f616,plain,
! [X2,X3,X0,X1] :
( k1_funct_1(X0,sK8(X1,X0,X2)) != k2_group_3(X1,sK8(X1,X0,X2),X2)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| r2_hidden(X0,X3)
| ~ m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k1_fraenkel(u1_struct_0(X1),u1_struct_0(X1)))
| ~ sP0(X1,X3)
| v1_xboole_0(u1_struct_0(X1))
| ~ v1_funct_1(X0)
| ~ v1_funct_2(X0,u1_struct_0(X1),u1_struct_0(X1))
| ~ m1_relset_1(X0,u1_struct_0(X1),u1_struct_0(X1))
| ~ m1_subset_1(sK8(X1,X0,X2),u1_struct_0(X1)) ),
inference(superposition,[],[f263,f334]) ).
fof(f617,plain,
! [X2,X3,X0,X1,X4] :
( k2_group_3(X0,sK8(X0,X1,X2),X2) != k2_group_3(X0,sK8(X0,X1,X2),sK9(X0,X1))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| r2_hidden(X1,X3)
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0)))
| ~ sP0(X0,X3)
| ~ m1_subset_1(sK8(X0,X1,X2),u1_struct_0(X0))
| ~ r2_hidden(X1,X4)
| ~ sP0(X0,X4) ),
inference(duplicate_literal_removal,[],[f615]) ).
fof(f618,plain,
! [X2,X3,X0,X1] :
( k1_funct_1(X0,sK8(X1,X0,X2)) != k2_group_3(X1,sK8(X1,X0,X2),X2)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| r2_hidden(X0,X3)
| ~ m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k1_fraenkel(u1_struct_0(X1),u1_struct_0(X1)))
| ~ sP0(X1,X3)
| v1_xboole_0(u1_struct_0(X1))
| ~ v1_funct_1(X0)
| ~ v1_funct_2(X0,u1_struct_0(X1),u1_struct_0(X1))
| ~ m1_relset_1(X0,u1_struct_0(X1),u1_struct_0(X1)) ),
inference(forward_subsumption_resolution,[],[f616,f262]) ).
fof(f619,plain,
! [X2,X3,X0,X1,X4] :
( k2_group_3(X0,sK8(X0,X1,X2),X2) != k2_group_3(X0,sK8(X0,X1,X2),sK9(X0,X1))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| r2_hidden(X1,X3)
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0)))
| ~ sP0(X0,X3)
| ~ r2_hidden(X1,X4)
| ~ sP0(X0,X4) ),
inference(forward_subsumption_resolution,[],[f617,f262]) ).
fof(f620,plain,
! [X2,X3,X0,X1] :
( ~ m1_subset_1(sK9(X0,X1),u1_struct_0(X0))
| r2_hidden(X1,X2)
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0)))
| ~ sP0(X0,X2)
| ~ r2_hidden(X1,X3)
| ~ sP0(X0,X3) ),
inference(equality_resolution,[],[f619]) ).
fof(f621,plain,
! [X2,X3,X0,X1] :
( ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0)))
| r2_hidden(X1,X2)
| ~ sP0(X0,X2)
| ~ r2_hidden(X1,X3)
| ~ sP0(X0,X3) ),
inference(forward_subsumption_resolution,[],[f620,f261]) ).
fof(f622,plain,
! [X2,X3,X0,X1] :
( r2_hidden(X0,X1)
| ~ sP0(X2,X1)
| ~ r2_hidden(X0,X3)
| ~ sP0(X2,X3)
| ~ m1_subset_1(X0,k1_fraenkel(u1_struct_0(X2),u1_struct_0(X2)))
| v1_xboole_0(u1_struct_0(X2))
| ~ m1_fraenkel(k1_fraenkel(u1_struct_0(X2),u1_struct_0(X2)),u1_struct_0(X2),u1_struct_0(X2)) ),
inference(resolution,[],[f621,f296]) ).
fof(f624,plain,
! [X2,X3,X0,X1] :
( ~ m1_subset_1(X0,k1_fraenkel(u1_struct_0(X2),u1_struct_0(X2)))
| ~ sP0(X2,X1)
| ~ r2_hidden(X0,X3)
| ~ sP0(X2,X3)
| r2_hidden(X0,X1)
| v1_xboole_0(u1_struct_0(X2)) ),
inference(forward_subsumption_resolution,[],[f622,f326]) ).
fof(f629,plain,
! [X2,X3,X0,X1] :
( v1_funct_2(X0,X1,X2)
| v1_xboole_0(X2)
| ~ m1_fraenkel(X3,X1,X2)
| ~ m1_subset_1(X0,X3)
| v1_xboole_0(X2)
| ~ m1_fraenkel(X3,X1,X2) ),
inference(resolution,[],[f299,f296]) ).
fof(f631,plain,
! [X2,X3,X0,X1] :
( ~ m1_fraenkel(X3,X1,X2)
| v1_xboole_0(X2)
| v1_funct_2(X0,X1,X2)
| ~ m1_subset_1(X0,X3) ),
inference(duplicate_literal_removal,[],[f629]) ).
fof(f658,plain,
! [X2,X3,X0,X1] :
( sK8(X0,k6_relat_1(X1),X2) != k2_group_3(X0,sK8(X0,k6_relat_1(X1),X2),X2)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| r2_hidden(k6_relat_1(X1),X3)
| ~ m2_fraenkel(k6_relat_1(X1),u1_struct_0(X0),u1_struct_0(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0)))
| ~ sP0(X0,X3)
| v1_xboole_0(u1_struct_0(X0))
| ~ v1_funct_1(k6_relat_1(X1))
| ~ v1_funct_2(k6_relat_1(X1),u1_struct_0(X0),u1_struct_0(X0))
| ~ m1_relset_1(k6_relat_1(X1),u1_struct_0(X0),u1_struct_0(X0))
| ~ r2_hidden(sK8(X0,k6_relat_1(X1),X2),X1) ),
inference(superposition,[],[f618,f329]) ).
fof(f663,plain,
! [X2,X3,X0,X1] :
( sK8(X0,k6_relat_1(X1),X2) != k2_group_3(X0,sK8(X0,k6_relat_1(X1),X2),X2)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| r2_hidden(k6_relat_1(X1),X3)
| ~ m2_fraenkel(k6_relat_1(X1),u1_struct_0(X0),u1_struct_0(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0)))
| ~ sP0(X0,X3)
| v1_xboole_0(u1_struct_0(X0))
| ~ v1_funct_2(k6_relat_1(X1),u1_struct_0(X0),u1_struct_0(X0))
| ~ m1_relset_1(k6_relat_1(X1),u1_struct_0(X0),u1_struct_0(X0))
| ~ r2_hidden(sK8(X0,k6_relat_1(X1),X2),X1) ),
inference(forward_subsumption_resolution,[],[f658,f341]) ).
fof(f682,plain,
! [X2,X3,X0,X1] :
( ~ r2_hidden(X2,k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0)))
| ~ r2_hidden(X2,X3)
| ~ sP0(X0,X3)
| r2_hidden(X2,X1)
| v1_xboole_0(u1_struct_0(X0))
| ~ sP0(X0,X1) ),
inference(resolution,[],[f624,f331]) ).
fof(f684,plain,
! [X2,X3,X0,X1] :
( ~ m1_subset_1(X0,u1_struct_0(X1))
| m1_subset_1(sK8(X1,X2,X0),u1_struct_0(X1))
| r2_hidden(X2,X3)
| ~ sP0(X1,X3)
| ~ m1_subset_1(X2,k1_fraenkel(u1_struct_0(X1),u1_struct_0(X1)))
| v1_xboole_0(u1_struct_0(X1))
| ~ m1_fraenkel(k1_fraenkel(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1),u1_struct_0(X1)) ),
inference(resolution,[],[f262,f296]) ).
fof(f686,plain,
! [X2,X3,X0,X1] :
( m1_subset_1(sK8(X1,X2,X0),u1_struct_0(X1))
| ~ m1_subset_1(X0,u1_struct_0(X1))
| r2_hidden(X2,X3)
| ~ sP0(X1,X3)
| ~ m1_subset_1(X2,k1_fraenkel(u1_struct_0(X1),u1_struct_0(X1)))
| v1_xboole_0(u1_struct_0(X1)) ),
inference(forward_subsumption_resolution,[],[f684,f326]) ).
fof(f688,plain,
! [X2,X3,X0,X1] :
( ~ m1_subset_1(X0,u1_struct_0(X1))
| r2_hidden(X2,X3)
| ~ sP0(X1,X3)
| ~ m1_subset_1(X2,k1_fraenkel(u1_struct_0(X1),u1_struct_0(X1)))
| v1_xboole_0(u1_struct_0(X1))
| r2_hidden(sK8(X1,X2,X0),u1_struct_0(X1))
| v1_xboole_0(u1_struct_0(X1)) ),
inference(resolution,[],[f686,f330]) ).
fof(f689,plain,
! [X2,X3,X0,X1] :
( ~ m1_subset_1(X2,k1_fraenkel(u1_struct_0(X1),u1_struct_0(X1)))
| r2_hidden(X2,X3)
| ~ sP0(X1,X3)
| ~ m1_subset_1(X0,u1_struct_0(X1))
| v1_xboole_0(u1_struct_0(X1))
| r2_hidden(sK8(X1,X2,X0),u1_struct_0(X1)) ),
inference(duplicate_literal_removal,[],[f688]) ).
fof(f772,plain,
! [X0] : m1_relset_1(k6_relat_1(X0),X0,X0),
inference(resolution,[],[f320,f418]) ).
fof(f792,plain,
! [X2,X3,X0,X1] :
( m2_relset_1(X0,X1,X2)
| v1_xboole_0(X2)
| ~ m1_fraenkel(X3,X1,X2)
| ~ m1_subset_1(X0,X3)
| v1_xboole_0(X2)
| ~ m1_fraenkel(X3,X1,X2) ),
inference(resolution,[],[f298,f296]) ).
fof(f794,plain,
! [X2,X3,X0,X1] :
( m2_relset_1(X0,X1,X2)
| v1_xboole_0(X2)
| ~ m1_fraenkel(X3,X1,X2)
| ~ m1_subset_1(X0,X3) ),
inference(duplicate_literal_removal,[],[f792]) ).
fof(f985,plain,
! [X2,X0,X1] :
( v1_xboole_0(X0)
| v1_xboole_0(X0)
| v1_funct_2(X1,X2,X0)
| ~ m1_subset_1(X1,k1_fraenkel(X2,X0)) ),
inference(resolution,[],[f326,f631]) ).
fof(f986,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X1,k1_fraenkel(X2,X0))
| v1_funct_2(X1,X2,X0)
| v1_xboole_0(X0) ),
inference(duplicate_literal_removal,[],[f985]) ).
fof(f988,plain,
! [X0,X1] :
( k1_group_1(X1,k2_group_1(X1),X0) = X0
| v3_struct_0(X1)
| ~ l1_group_1(X1)
| ~ m1_subset_1(X0,u1_struct_0(X1))
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ m1_subset_1(X0,u1_struct_0(X1))
| ~ m1_subset_1(k2_group_1(X1),u1_struct_0(X1))
| ~ v2_group_1(X1)
| v3_struct_0(X1)
| ~ l1_group_1(X1) ),
inference(superposition,[],[f543,f420]) ).
fof(f1035,plain,
! [X0,X1] :
( k1_group_1(X1,k2_group_1(X1),X0) = X0
| v3_struct_0(X1)
| ~ l1_group_1(X1)
| ~ m1_subset_1(X0,u1_struct_0(X1))
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ m1_subset_1(k2_group_1(X1),u1_struct_0(X1))
| ~ v2_group_1(X1) ),
inference(duplicate_literal_removal,[],[f988]) ).
fof(f1052,plain,
! [X0,X1] :
( k1_group_1(X1,k2_group_1(X1),X0) = X0
| v3_struct_0(X1)
| ~ l1_group_1(X1)
| ~ m1_subset_1(X0,u1_struct_0(X1))
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ v2_group_1(X1) ),
inference(forward_subsumption_resolution,[],[f1035,f252]) ).
fof(f1060,plain,
! [X0,X1] :
( k1_group_1(X1,k2_group_1(X1),X0) = X0
| v3_struct_0(X1)
| ~ l1_group_1(X1)
| ~ m1_subset_1(X0,u1_struct_0(X1))
| ~ v3_group_1(X1)
| ~ v4_group_1(X1) ),
inference(forward_subsumption_resolution,[],[f1052,f292]) ).
fof(f1225,plain,
! [X2,X0,X1] :
( r2_hidden(X2,k1_fraenkel(X0,X1))
| k1_xboole_0 = X1
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1)
| v1_xboole_0(X1) ),
inference(superposition,[],[f318,f333]) ).
fof(f1226,plain,
! [X2,X0,X1] :
( r2_hidden(X2,k1_fraenkel(X0,X1))
| k1_xboole_0 = X1
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ),
inference(forward_subsumption_resolution,[],[f1225,f403]) ).
fof(f1236,plain,
! [X2,X3,X0,X1] :
( r2_hidden(sK8(X2,X0,X3),u1_struct_0(X2))
| ~ sP0(X2,X1)
| ~ m1_subset_1(X3,u1_struct_0(X2))
| v1_xboole_0(u1_struct_0(X2))
| r2_hidden(X0,X1)
| ~ r2_hidden(X0,k1_fraenkel(u1_struct_0(X2),u1_struct_0(X2))) ),
inference(resolution,[],[f689,f331]) ).
fof(f1247,plain,
! [X2,X3,X0,X1] :
( ~ m1_fraenkel(X1,X2,X0)
| v1_xboole_0(X0)
| ~ m1_subset_1(X3,X1)
| m1_relset_1(X3,X2,X0) ),
inference(resolution,[],[f794,f320]) ).
fof(f1251,plain,
! [X2,X0,X1] :
( v1_xboole_0(X0)
| ~ m1_subset_1(X1,k1_fraenkel(X2,X0))
| m1_relset_1(X1,X2,X0)
| v1_xboole_0(X0) ),
inference(resolution,[],[f1247,f326]) ).
fof(f1252,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X1,k1_fraenkel(X2,X0))
| v1_xboole_0(X0)
| m1_relset_1(X1,X2,X0) ),
inference(duplicate_literal_removal,[],[f1251]) ).
fof(f1350,plain,
( v3_struct_0(sK2)
| ~ l1_struct_0(sK2)
| ~ spl32_2 ),
inference(resolution,[],[f245,f436]) ).
fof(f1351,plain,
( ~ l1_struct_0(sK2)
| ~ spl32_2 ),
inference(forward_subsumption_resolution,[],[f1350,f241]) ).
fof(f1352,plain,
( ~ l1_group_1(sK2)
| ~ spl32_2 ),
inference(resolution,[],[f1351,f312]) ).
fof(f1353,plain,
( $false
| ~ spl32_2 ),
inference(forward_subsumption_resolution,[],[f1352,f237]) ).
fof(f1354,plain,
~ spl32_2,
inference(avatar_contradiction_clause,[],[f1353]) ).
fof(f1768,plain,
! [X2,X0,X1] :
( sK8(X0,k6_relat_1(X1),k2_group_1(X0)) != k1_group_1(X0,k2_group_1(X0),sK8(X0,k6_relat_1(X1),k2_group_1(X0)))
| ~ m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| r2_hidden(k6_relat_1(X1),X2)
| ~ m2_fraenkel(k6_relat_1(X1),u1_struct_0(X0),u1_struct_0(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0)))
| ~ sP0(X0,X2)
| v1_xboole_0(u1_struct_0(X0))
| ~ v1_funct_2(k6_relat_1(X1),u1_struct_0(X0),u1_struct_0(X0))
| ~ m1_relset_1(k6_relat_1(X1),u1_struct_0(X0),u1_struct_0(X0))
| ~ r2_hidden(sK8(X0,k6_relat_1(X1),k2_group_1(X0)),X1)
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(sK8(X0,k6_relat_1(X1),k2_group_1(X0)),u1_struct_0(X0))
| ~ v3_group_1(X0)
| ~ v4_group_1(X0) ),
inference(superposition,[],[f663,f520]) ).
fof(f1783,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| r2_hidden(k6_relat_1(X1),X2)
| ~ m2_fraenkel(k6_relat_1(X1),u1_struct_0(X0),u1_struct_0(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0)))
| ~ sP0(X0,X2)
| v1_xboole_0(u1_struct_0(X0))
| ~ v1_funct_2(k6_relat_1(X1),u1_struct_0(X0),u1_struct_0(X0))
| ~ m1_relset_1(k6_relat_1(X1),u1_struct_0(X0),u1_struct_0(X0))
| ~ r2_hidden(sK8(X0,k6_relat_1(X1),k2_group_1(X0)),X1)
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(sK8(X0,k6_relat_1(X1),k2_group_1(X0)),u1_struct_0(X0))
| ~ v3_group_1(X0)
| ~ v4_group_1(X0) ),
inference(forward_subsumption_resolution,[],[f1768,f1060]) ).
fof(f1789,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| r2_hidden(k6_relat_1(X1),X2)
| ~ m2_fraenkel(k6_relat_1(X1),u1_struct_0(X0),u1_struct_0(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0)))
| ~ sP0(X0,X2)
| v1_xboole_0(u1_struct_0(X0))
| ~ v1_funct_2(k6_relat_1(X1),u1_struct_0(X0),u1_struct_0(X0))
| ~ m1_relset_1(k6_relat_1(X1),u1_struct_0(X0),u1_struct_0(X0))
| ~ r2_hidden(sK8(X0,k6_relat_1(X1),k2_group_1(X0)),X1)
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0) ),
inference(forward_subsumption_resolution,[],[f1783,f262]) ).
fof(f1792,plain,
! [X2,X0,X1] :
( ~ m2_fraenkel(k6_relat_1(X1),u1_struct_0(X0),u1_struct_0(X0),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0)))
| r2_hidden(k6_relat_1(X1),X2)
| ~ sP0(X0,X2)
| v1_xboole_0(u1_struct_0(X0))
| ~ v1_funct_2(k6_relat_1(X1),u1_struct_0(X0),u1_struct_0(X0))
| ~ m1_relset_1(k6_relat_1(X1),u1_struct_0(X0),u1_struct_0(X0))
| ~ r2_hidden(sK8(X0,k6_relat_1(X1),k2_group_1(X0)),X1)
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0) ),
inference(forward_subsumption_resolution,[],[f1789,f252]) ).
fof(f1952,plain,
! [X2,X0,X1] :
( r2_hidden(k6_relat_1(X0),X1)
| ~ sP0(X2,X1)
| v1_xboole_0(u1_struct_0(X2))
| ~ v1_funct_2(k6_relat_1(X0),u1_struct_0(X2),u1_struct_0(X2))
| ~ m1_relset_1(k6_relat_1(X0),u1_struct_0(X2),u1_struct_0(X2))
| ~ r2_hidden(sK8(X2,k6_relat_1(X0),k2_group_1(X2)),X0)
| v3_struct_0(X2)
| ~ l1_group_1(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ m1_subset_1(k6_relat_1(X0),k1_fraenkel(u1_struct_0(X2),u1_struct_0(X2)))
| v1_xboole_0(u1_struct_0(X2))
| ~ m1_fraenkel(k1_fraenkel(u1_struct_0(X2),u1_struct_0(X2)),u1_struct_0(X2),u1_struct_0(X2)) ),
inference(resolution,[],[f1792,f296]) ).
fof(f1953,plain,
! [X2,X0,X1] :
( r2_hidden(k6_relat_1(X0),X1)
| ~ sP0(X2,X1)
| v1_xboole_0(u1_struct_0(X2))
| ~ v1_funct_2(k6_relat_1(X0),u1_struct_0(X2),u1_struct_0(X2))
| ~ m1_relset_1(k6_relat_1(X0),u1_struct_0(X2),u1_struct_0(X2))
| ~ r2_hidden(sK8(X2,k6_relat_1(X0),k2_group_1(X2)),X0)
| v3_struct_0(X2)
| ~ l1_group_1(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ m1_subset_1(k6_relat_1(X0),k1_fraenkel(u1_struct_0(X2),u1_struct_0(X2)))
| ~ m1_fraenkel(k1_fraenkel(u1_struct_0(X2),u1_struct_0(X2)),u1_struct_0(X2),u1_struct_0(X2)) ),
inference(duplicate_literal_removal,[],[f1952]) ).
fof(f1954,plain,
! [X2,X0,X1] :
( r2_hidden(k6_relat_1(X0),X1)
| ~ sP0(X2,X1)
| v1_xboole_0(u1_struct_0(X2))
| ~ v1_funct_2(k6_relat_1(X0),u1_struct_0(X2),u1_struct_0(X2))
| ~ m1_relset_1(k6_relat_1(X0),u1_struct_0(X2),u1_struct_0(X2))
| ~ r2_hidden(sK8(X2,k6_relat_1(X0),k2_group_1(X2)),X0)
| v3_struct_0(X2)
| ~ l1_group_1(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ m1_subset_1(k6_relat_1(X0),k1_fraenkel(u1_struct_0(X2),u1_struct_0(X2))) ),
inference(forward_subsumption_resolution,[],[f1953,f326]) ).
fof(f1955,plain,
! [X2,X0,X1] :
( r2_hidden(k6_relat_1(X0),X1)
| ~ sP0(X2,X1)
| v1_xboole_0(u1_struct_0(X2))
| ~ m1_relset_1(k6_relat_1(X0),u1_struct_0(X2),u1_struct_0(X2))
| ~ r2_hidden(sK8(X2,k6_relat_1(X0),k2_group_1(X2)),X0)
| v3_struct_0(X2)
| ~ l1_group_1(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ m1_subset_1(k6_relat_1(X0),k1_fraenkel(u1_struct_0(X2),u1_struct_0(X2))) ),
inference(forward_subsumption_resolution,[],[f1954,f986]) ).
fof(f1956,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(k6_relat_1(X0),k1_fraenkel(u1_struct_0(X2),u1_struct_0(X2)))
| ~ sP0(X2,X1)
| v1_xboole_0(u1_struct_0(X2))
| ~ r2_hidden(sK8(X2,k6_relat_1(X0),k2_group_1(X2)),X0)
| v3_struct_0(X2)
| ~ l1_group_1(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| r2_hidden(k6_relat_1(X0),X1) ),
inference(forward_subsumption_resolution,[],[f1955,f1252]) ).
fof(f1957,plain,
! [X2,X0,X1] :
( ~ r2_hidden(sK8(X0,k6_relat_1(X2),k2_group_1(X0)),X2)
| v1_xboole_0(u1_struct_0(X0))
| ~ sP0(X0,X1)
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| r2_hidden(k6_relat_1(X2),X1)
| ~ r2_hidden(k6_relat_1(X2),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0))) ),
inference(resolution,[],[f1956,f331]) ).
fof(f4007,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1)
| ~ m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| v1_xboole_0(u1_struct_0(X0))
| r2_hidden(k6_relat_1(u1_struct_0(X0)),X1)
| ~ r2_hidden(k6_relat_1(u1_struct_0(X0)),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0)))
| v1_xboole_0(u1_struct_0(X0))
| ~ sP0(X0,X2)
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| r2_hidden(k6_relat_1(u1_struct_0(X0)),X2)
| ~ r2_hidden(k6_relat_1(u1_struct_0(X0)),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0))) ),
inference(resolution,[],[f1236,f1957]) ).
fof(f4010,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1)
| ~ m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| v1_xboole_0(u1_struct_0(X0))
| r2_hidden(k6_relat_1(u1_struct_0(X0)),X1)
| ~ r2_hidden(k6_relat_1(u1_struct_0(X0)),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0)))
| ~ sP0(X0,X2)
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| r2_hidden(k6_relat_1(u1_struct_0(X0)),X2) ),
inference(duplicate_literal_removal,[],[f4007]) ).
fof(f4011,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1)
| ~ m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| v1_xboole_0(u1_struct_0(X0))
| ~ r2_hidden(k6_relat_1(u1_struct_0(X0)),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0)))
| ~ sP0(X0,X2)
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| r2_hidden(k6_relat_1(u1_struct_0(X0)),X2) ),
inference(forward_subsumption_resolution,[],[f4010,f682]) ).
fof(f4012,plain,
! [X2,X0,X1] :
( ~ r2_hidden(k6_relat_1(u1_struct_0(X0)),k1_fraenkel(u1_struct_0(X0),u1_struct_0(X0)))
| v1_xboole_0(u1_struct_0(X0))
| ~ sP0(X0,X1)
| ~ sP0(X0,X2)
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| r2_hidden(k6_relat_1(u1_struct_0(X0)),X2) ),
inference(forward_subsumption_resolution,[],[f4011,f252]) ).
fof(f4013,plain,
! [X2,X0,X1] :
( v1_xboole_0(u1_struct_0(X0))
| ~ sP0(X0,X1)
| ~ sP0(X0,X2)
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| r2_hidden(k6_relat_1(u1_struct_0(X0)),X2)
| u1_struct_0(X0) = k1_xboole_0
| ~ v1_funct_1(k6_relat_1(u1_struct_0(X0)))
| ~ v1_funct_2(k6_relat_1(u1_struct_0(X0)),u1_struct_0(X0),u1_struct_0(X0))
| ~ m2_relset_1(k6_relat_1(u1_struct_0(X0)),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(resolution,[],[f4012,f1226]) ).
fof(f4014,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1)
| ~ sP0(X0,X2)
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| r2_hidden(k6_relat_1(u1_struct_0(X0)),X2)
| u1_struct_0(X0) = k1_xboole_0
| ~ v1_funct_1(k6_relat_1(u1_struct_0(X0)))
| ~ v1_funct_2(k6_relat_1(u1_struct_0(X0)),u1_struct_0(X0),u1_struct_0(X0))
| ~ m2_relset_1(k6_relat_1(u1_struct_0(X0)),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(forward_subsumption_resolution,[],[f4013,f403]) ).
fof(f4015,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1)
| ~ sP0(X0,X2)
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| r2_hidden(k6_relat_1(u1_struct_0(X0)),X2)
| u1_struct_0(X0) = k1_xboole_0
| ~ v1_funct_2(k6_relat_1(u1_struct_0(X0)),u1_struct_0(X0),u1_struct_0(X0))
| ~ m2_relset_1(k6_relat_1(u1_struct_0(X0)),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(forward_subsumption_resolution,[],[f4014,f341]) ).
fof(f4016,plain,
! [X2,X0,X1] :
( ~ v1_funct_2(k6_relat_1(u1_struct_0(X0)),u1_struct_0(X0),u1_struct_0(X0))
| ~ sP0(X0,X2)
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| r2_hidden(k6_relat_1(u1_struct_0(X0)),X2)
| u1_struct_0(X0) = k1_xboole_0
| ~ sP0(X0,X1) ),
inference(forward_subsumption_resolution,[],[f4015,f418]) ).
fof(f4021,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1)
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| r2_hidden(k6_relat_1(u1_struct_0(X0)),X1)
| u1_struct_0(X0) = k1_xboole_0
| ~ sP0(X0,X2)
| ~ v1_funct_1(k6_relat_1(u1_struct_0(X0)))
| ~ v1_partfun1(k6_relat_1(u1_struct_0(X0)),u1_struct_0(X0),u1_struct_0(X0))
| ~ m1_relset_1(k6_relat_1(u1_struct_0(X0)),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(resolution,[],[f4016,f362]) ).
fof(f4024,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1)
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| r2_hidden(k6_relat_1(u1_struct_0(X0)),X1)
| u1_struct_0(X0) = k1_xboole_0
| ~ sP0(X0,X2)
| ~ v1_partfun1(k6_relat_1(u1_struct_0(X0)),u1_struct_0(X0),u1_struct_0(X0))
| ~ m1_relset_1(k6_relat_1(u1_struct_0(X0)),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(forward_subsumption_resolution,[],[f4021,f341]) ).
fof(f4027,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1)
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| r2_hidden(k6_relat_1(u1_struct_0(X0)),X1)
| u1_struct_0(X0) = k1_xboole_0
| ~ sP0(X0,X2)
| ~ m1_relset_1(k6_relat_1(u1_struct_0(X0)),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(forward_subsumption_resolution,[],[f4024,f417]) ).
fof(f4028,plain,
! [X2,X0,X1] :
( r2_hidden(k6_relat_1(u1_struct_0(X0)),X1)
| v3_struct_0(X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ sP0(X0,X1)
| u1_struct_0(X0) = k1_xboole_0
| ~ sP0(X0,X2) ),
inference(forward_subsumption_resolution,[],[f4027,f772]) ).
fof(f4031,plain,
( ! [X0] :
( v3_struct_0(sK2)
| ~ l1_group_1(sK2)
| ~ v3_group_1(sK2)
| ~ v4_group_1(sK2)
| ~ sP0(sK2,k4_autgroup(sK2))
| k1_xboole_0 = u1_struct_0(sK2)
| ~ sP0(sK2,X0) )
| spl32_3 ),
inference(resolution,[],[f4028,f534]) ).
fof(f4048,plain,
( ! [X0] :
( ~ l1_group_1(sK2)
| ~ v3_group_1(sK2)
| ~ v4_group_1(sK2)
| ~ sP0(sK2,k4_autgroup(sK2))
| k1_xboole_0 = u1_struct_0(sK2)
| ~ sP0(sK2,X0) )
| spl32_3 ),
inference(forward_subsumption_resolution,[],[f4031,f241]) ).
fof(f4050,plain,
( ! [X0] :
( ~ v3_group_1(sK2)
| ~ v4_group_1(sK2)
| ~ sP0(sK2,k4_autgroup(sK2))
| k1_xboole_0 = u1_struct_0(sK2)
| ~ sP0(sK2,X0) )
| spl32_3 ),
inference(forward_subsumption_resolution,[],[f4048,f237]) ).
fof(f4052,plain,
( ! [X0] :
( ~ v4_group_1(sK2)
| ~ sP0(sK2,k4_autgroup(sK2))
| k1_xboole_0 = u1_struct_0(sK2)
| ~ sP0(sK2,X0) )
| spl32_3 ),
inference(forward_subsumption_resolution,[],[f4050,f239]) ).
fof(f4054,plain,
( ! [X0] :
( ~ sP0(sK2,k4_autgroup(sK2))
| k1_xboole_0 = u1_struct_0(sK2)
| ~ sP0(sK2,X0) )
| spl32_3 ),
inference(forward_subsumption_resolution,[],[f4052,f238]) ).
fof(f4056,definition,
( spl32_11
<=> ! [X1] : ~ sP0(sK2,X1) ),
introduced(definition,[new_symbols(definition,[spl32_11])],[avatar_definition]) ).
fof(f4057,plain,
( ! [X1] : ~ sP0(sK2,X1)
| ~ spl32_11 ),
inference(avatar_component_clause,[],[f4056]) ).
fof(f4059,definition,
( spl32_12
<=> k1_xboole_0 = u1_struct_0(sK2) ),
introduced(definition,[new_symbols(definition,[spl32_12])],[avatar_definition]) ).
fof(f4061,plain,
( k1_xboole_0 = u1_struct_0(sK2)
| ~ spl32_12 ),
inference(avatar_component_clause,[],[f4059]) ).
fof(f4066,plain,
( ! [X0] :
( k1_xboole_0 = u1_struct_0(sK2)
| ~ sP0(sK2,X0) )
| ~ spl32_1
| spl32_3 ),
inference(forward_subsumption_resolution,[],[f4054,f459]) ).
fof(f4067,plain,
( spl32_11
| spl32_12
| ~ spl32_1
| spl32_3 ),
inference(avatar_split_clause,[],[f4066,f438,f430,f4059,f4056]) ).
fof(f4069,plain,
( ~ v1_group_1(sK2)
| ~ v3_group_1(sK2)
| ~ v4_group_1(sK2)
| ~ l1_group_1(sK2)
| v3_struct_0(sK2)
| ~ spl32_11 ),
inference(resolution,[],[f4057,f535]) ).
fof(f4071,plain,
( ~ v3_group_1(sK2)
| ~ v4_group_1(sK2)
| ~ l1_group_1(sK2)
| v3_struct_0(sK2)
| ~ spl32_11 ),
inference(forward_subsumption_resolution,[],[f4069,f240]) ).
fof(f4072,plain,
( ~ v4_group_1(sK2)
| ~ l1_group_1(sK2)
| v3_struct_0(sK2)
| ~ spl32_11 ),
inference(forward_subsumption_resolution,[],[f4071,f239]) ).
fof(f4073,plain,
( ~ l1_group_1(sK2)
| v3_struct_0(sK2)
| ~ spl32_11 ),
inference(forward_subsumption_resolution,[],[f4072,f238]) ).
fof(f4074,plain,
( v3_struct_0(sK2)
| ~ spl32_11 ),
inference(forward_subsumption_resolution,[],[f4073,f237]) ).
fof(f4075,plain,
( $false
| ~ spl32_11 ),
inference(forward_subsumption_resolution,[],[f4074,f241]) ).
fof(f4076,plain,
~ spl32_11,
inference(avatar_contradiction_clause,[],[f4075]) ).
fof(f4079,plain,
( ~ v1_xboole_0(k1_xboole_0)
| spl32_2
| ~ spl32_12 ),
inference(superposition,[],[f435,f4061]) ).
fof(f4317,plain,
( $false
| spl32_2
| ~ spl32_12 ),
inference(forward_subsumption_resolution,[],[f4079,f404]) ).
fof(f4318,plain,
( spl32_2
| ~ spl32_12 ),
inference(avatar_contradiction_clause,[],[f4317]) ).
cnf(s1,plain,
( ~ spl32_1
| spl32_2
| ~ spl32_3 ),
inference(sat_conversion,[],[f441]) ).
cnf(s2,plain,
spl32_1,
inference(sat_conversion,[],[f448]) ).
cnf(s5,plain,
~ spl32_2,
inference(sat_conversion,[],[f1354]) ).
cnf(s10,plain,
( ~ spl32_1
| spl32_3
| spl32_11
| spl32_12 ),
inference(sat_conversion,[],[f4067]) ).
cnf(s12,plain,
~ spl32_11,
inference(sat_conversion,[],[f4076]) ).
cnf(s13,plain,
( spl32_2
| ~ spl32_12 ),
inference(sat_conversion,[],[f4318]) ).
cnf(s21,plain,
( ~ spl32_1
| spl32_3
| spl32_12 ),
inference(rat,[],[s10,s12]) ).
cnf(s23,plain,
~ spl32_12,
inference(rat,[],[s13,s5]) ).
cnf(s26,plain,
spl32_3,
inference(rat,[],[s21,s23,s2]) ).
cnf(s29,plain,
$false,
inference(rat,[],[s1,s26,s5,s2]) ).
fof(f4467,plain,
$false,
inference(avatar_sat_refutation,[],[s29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP625+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 % Computer : n026.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sun Sep 27 10:13:11 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.46 Running first-order theorem proving
% 0.14/0.46 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.12/3.71 % (2609427)Detected formulas, will run a generic FOF schedule.
% 19.12/3.71 % (2609434)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=2010653544:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 19.12/3.71 % (2609436)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=3100655865:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 19.12/3.71 % (2609435)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=2603078590:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 19.12/3.71 % (2609437)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1614074981:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 19.12/3.71 % (2609439)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=726586025:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 19.12/3.71 % (2609438)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2473614730:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 19.12/3.71 % (2609437)Refutation not found, incomplete strategy
% 19.12/3.71 % (2609437)------------------------------
% 19.12/3.71 % (2609437)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.12/3.71 % (2609437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.12/3.71 % (2609437)CaDiCaL version: 2.1.3
% 19.12/3.71 % (2609437)Termination reason: Refutation not found, incomplete strategy
% 19.12/3.71 % (2609437)Time elapsed: 0.005 s
% 19.12/3.71 % (2609437)Peak memory usage: 88 MB
% 19.12/3.71 % (2609437)Instructions burned: 3 (million)
% 19.12/3.71 % (2609440)dis-21_1_sil=8000:lcm=predicate:random_seed=1633104326: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)
% 19.12/3.71 % (2609438)Instruction limit reached!
% 19.12/3.71 % (2609438)------------------------------
% 19.12/3.71 % (2609438)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.12/3.71 % (2609438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.12/3.71 % (2609438)CaDiCaL version: 2.1.3
% 19.12/3.71 % (2609438)Termination reason: Instruction limit
% 19.12/3.71 % (2609438)Termination phase: Saturation
% 19.12/3.71 % (2609438)Time elapsed: 0.121 s
% 19.12/3.71 % (2609438)Peak memory usage: 88 MB
% 19.12/3.71 % (2609438)Instructions burned: 119 (million)
% 19.12/3.71 % (2609440)Instruction limit reached!
% 19.12/3.71 % (2609440)------------------------------
% 19.12/3.71 % (2609440)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.12/3.71 % (2609440)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.12/3.71 % (2609440)CaDiCaL version: 2.1.3
% 19.12/3.71 % (2609440)Termination reason: Instruction limit
% 19.12/3.71 % (2609440)Termination phase: Saturation
% 19.12/3.71 % (2609440)Time elapsed: 0.124 s
% 19.12/3.71 % (2609440)Peak memory usage: 91 MB
% 19.12/3.71 % (2609440)Instructions burned: 129 (million)
% 19.12/3.71 % (2609439)Instruction limit reached!
% 19.12/3.71 % (2609439)------------------------------
% 19.12/3.71 % (2609439)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.12/3.71 % (2609439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.12/3.71 % (2609439)CaDiCaL version: 2.1.3
% 19.12/3.71 % (2609439)Termination reason: Instruction limit
% 19.12/3.71 % (2609439)Termination phase: Saturation
% 19.12/3.71 % (2609439)Time elapsed: 0.157 s
% 19.12/3.71 % (2609439)Peak memory usage: 90 MB
% 19.12/3.71 % (2609439)Instructions burned: 139 (million)
% 19.12/3.71 % (2609448)lrs+10_1_sil=8000:sp=occurrence:random_seed=612753200:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 19.12/3.71 % (2609449)lrs+10_1_sil=32000:urr=on:br=off:random_seed=968907925:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 19.12/3.71 % (2609449)Refutation not found, incomplete strategy
% 19.12/3.71 % (2609449)------------------------------
% 19.12/3.71 % (2609449)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.12/3.71 % (2609449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.12/3.71 % (2609449)CaDiCaL version: 2.1.3
% 19.12/3.71 % (2609449)Termination reason: Refutation not found, incomplete strategy
% 26.56/5.08 % (2609449)Time elapsed: 0.006 s
% 26.56/5.08 % (2609449)Peak memory usage: 88 MB
% 26.56/5.08 % (2609449)Instructions burned: 4 (million)
% 26.56/5.08 % (2609450)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1471112645:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 26.56/5.08 % (2609437)------------------------------
% 26.56/5.08 % (2609437)------------------------------
% 26.56/5.08 % (2609454)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=293886690:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 26.56/5.08 % (2609448)Instruction limit reached!
% 26.56/5.08 % (2609448)------------------------------
% 26.56/5.08 % (2609448)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.56/5.08 % (2609448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.56/5.08 % (2609448)CaDiCaL version: 2.1.3
% 26.56/5.08 % (2609448)Termination reason: Instruction limit
% 26.56/5.08 % (2609448)Termination phase: Saturation
% 26.56/5.08 % (2609448)Time elapsed: 0.292 s
% 26.56/5.08 % (2609448)Peak memory usage: 92 MB
% 26.56/5.08 % (2609448)Instructions burned: 286 (million)
% 26.56/5.08 % (2609450)Instruction limit reached!
% 26.56/5.08 % (2609450)------------------------------
% 26.56/5.08 % (2609450)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.56/5.08 % (2609450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.56/5.08 % (2609450)CaDiCaL version: 2.1.3
% 26.56/5.08 % (2609450)Termination reason: Instruction limit
% 26.56/5.08 % (2609450)Termination phase: Saturation
% 26.56/5.08 % (2609450)Time elapsed: 0.312 s
% 26.56/5.08 % (2609450)Peak memory usage: 91 MB
% 26.56/5.08 % (2609450)Instructions burned: 326 (million)
% 26.56/5.08 % (2609449)------------------------------
% 26.56/5.08 % (2609449)------------------------------
% 26.56/5.08 % (2609454)Instruction limit reached!
% 26.56/5.08 % (2609454)------------------------------
% 26.56/5.08 % (2609454)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.56/5.08 % (2609454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.56/5.08 % (2609454)CaDiCaL version: 2.1.3
% 26.56/5.08 % (2609454)Termination reason: Instruction limit
% 26.56/5.08 % (2609454)Termination phase: Saturation
% 26.56/5.08 % (2609454)Time elapsed: 0.226 s
% 26.56/5.08 % (2609454)Peak memory usage: 94 MB
% 26.56/5.08 % (2609454)Instructions burned: 248 (million)
% 26.56/5.08 % (2609458)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3386327103:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2991 on theBenchmark for (2991ds/294Mi)
% 26.56/5.08 % (2609458)Refutation not found, incomplete strategy
% 26.56/5.08 % (2609458)------------------------------
% 26.56/5.08 % (2609458)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.56/5.08 % (2609458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.56/5.08 % (2609458)CaDiCaL version: 2.1.3
% 26.56/5.08 % (2609458)Termination reason: Refutation not found, incomplete strategy
% 26.56/5.08 % (2609458)Time elapsed: 0.010 s
% 26.56/5.08 % (2609458)Peak memory usage: 89 MB
% 26.56/5.08 % (2609458)Instructions burned: 8 (million)
% 26.56/5.08 % (2609459)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1191918293:i=2350_2990 on theBenchmark for (2990ds/2350Mi)
% 26.56/5.08 % (2609460)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3697472051:cts=off:i=113:fsr=off:ss=included:sgt=4_2990 on theBenchmark for (2990ds/113Mi)
% 26.56/5.08 % (2609461)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=533015768:i=127:av=off:fsr=off:sup=off_2989 on theBenchmark for (2989ds/127Mi)
% 26.56/5.08 % (2609460)Instruction limit reached!
% 26.56/5.08 % (2609460)------------------------------
% 26.56/5.08 % (2609460)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.56/5.08 % (2609460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.56/5.08 % (2609460)CaDiCaL version: 2.1.3
% 26.56/5.08 % (2609460)Termination reason: Instruction limit
% 26.56/5.08 % (2609460)Termination phase: Saturation
% 26.56/5.08 % (2609460)Time elapsed: 0.124 s
% 26.56/5.08 % (2609460)Peak memory usage: 90 MB
% 26.56/5.08 % (2609460)Instructions burned: 113 (million)
% 26.56/5.08 % (2609461)Instruction limit reached!
% 26.56/5.08 % (2609461)------------------------------
% 26.56/5.08 % (2609461)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.56/5.08 % (2609461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.56/5.08 % (2609461)CaDiCaL version: 2.1.3
% 26.56/5.08 % (2609461)Termination reason: Instruction limit
% 26.56/5.08 % (2609461)Termination phase: Saturation
% 26.56/5.08 % (2609461)Time elapsed: 0.112 s
% 26.56/5.08 % (2609461)Peak memory usage: 89 MB
% 26.56/5.08 % (2609461)Instructions burned: 127 (million)
% 26.56/5.08 % (2609458)------------------------------
% 26.56/5.08 % (2609458)------------------------------
% 26.56/5.08 % (2609466)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=136508878:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2987 on theBenchmark for (2987ds/114Mi)
% 26.56/5.08 % (2609466)Instruction limit reached!
% 26.56/5.08 % (2609466)------------------------------
% 26.56/5.08 % (2609466)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.56/5.08 % (2609466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.56/5.08 % (2609466)CaDiCaL version: 2.1.3
% 26.56/5.08 % (2609466)Termination reason: Instruction limit
% 26.56/5.08 % (2609466)Termination phase: Saturation
% 26.56/5.08 % (2609466)Time elapsed: 0.100 s
% 26.56/5.08 % (2609466)Peak memory usage: 89 MB
% 26.56/5.08 % (2609466)Instructions burned: 115 (million)
% 26.56/5.08 % (2609467)lrs+10_1_sil=8000:sp=occurrence:random_seed=1239790621:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2986 on theBenchmark for (2986ds/907Mi)
% 26.56/5.08 % (2609468)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3832675918:i=437:sd=1:aac=none:ss=included_2985 on theBenchmark for (2985ds/437Mi)
% 26.56/5.08 % (2609468)Refutation not found, incomplete strategy
% 26.56/5.08 % (2609468)------------------------------
% 26.56/5.08 % (2609468)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.56/5.08 % (2609468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.56/5.08 % (2609468)CaDiCaL version: 2.1.3
% 26.56/5.08 % (2609468)Termination reason: Refutation not found, incomplete strategy
% 26.56/5.08 % (2609468)Time elapsed: 0.011 s
% 26.56/5.08 % (2609468)Peak memory usage: 89 MB
% 26.56/5.08 % (2609468)Instructions burned: 10 (million)
% 26.56/5.08 % (2609470)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=4050480456:i=5202:ss=axioms:sgt=16_2984 on theBenchmark for (2984ds/5202Mi)
% 26.56/5.08 % (2609468)------------------------------
% 26.56/5.08 % (2609468)------------------------------
% 26.56/5.08 % (2609474)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=1060470568:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2979 on theBenchmark for (2979ds/134Mi)
% 26.56/5.08 % (2609467)Instruction limit reached!
% 26.56/5.08 % (2609467)------------------------------
% 26.56/5.08 % (2609467)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.56/5.08 % (2609467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.56/5.08 % (2609467)CaDiCaL version: 2.1.3
% 26.56/5.08 % (2609467)Termination reason: Instruction limit
% 26.56/5.08 % (2609467)Termination phase: Saturation
% 26.56/5.08 % (2609467)Time elapsed: 0.862 s
% 26.56/5.08 % (2609467)Peak memory usage: 100 MB
% 26.56/5.08 % (2609467)Instructions burned: 908 (million)
% 26.56/5.08 % (2609474)Instruction limit reached!
% 26.56/5.08 % (2609474)------------------------------
% 26.56/5.08 % (2609474)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.56/5.08 % (2609474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.56/5.08 % (2609474)CaDiCaL version: 2.1.3
% 26.56/5.08 % (2609474)Termination reason: Instruction limit
% 26.56/5.08 % (2609474)Termination phase: Saturation
% 26.56/5.08 % (2609474)Time elapsed: 0.125 s
% 26.56/5.08 % (2609474)Peak memory usage: 91 MB
% 26.56/5.08 % (2609474)Instructions burned: 134 (million)
% 26.56/5.08 % (2609476)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=1619536494:st=8:i=592:sd=3:ep=RST:ss=axioms_2975 on theBenchmark for (2975ds/592Mi)
% 26.56/5.08 % (2609476)Refutation not found, incomplete strategy
% 26.56/5.08 % (2609476)------------------------------
% 26.56/5.08 % (2609476)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.56/5.08 % (2609476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.56/5.08 % (2609476)CaDiCaL version: 2.1.3
% 26.56/5.08 % (2609476)Termination reason: Refutation not found, incomplete strategy
% 26.56/5.08 % (2609476)Time elapsed: 0.010 s
% 26.56/5.08 % (2609476)Peak memory usage: 88 MB
% 26.56/5.08 % (2609476)Instructions burned: 9 (million)
% 26.56/5.08 % (2609477)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=2871134031:st=3:i=13193:sd=3:ss=axioms_2975 on theBenchmark for (2975ds/13193Mi)
% 26.56/5.08 % (2609476)------------------------------
% 26.56/5.08 % (2609476)------------------------------
% 26.56/5.08 % (2609480)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=217220650:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2969 on theBenchmark for (2969ds/125Mi)
% 26.56/5.08 % (2609480)Instruction limit reached!
% 26.56/5.08 % (2609480)------------------------------
% 26.56/5.08 % (2609480)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.56/5.08 % (2609480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.56/5.08 % (2609480)CaDiCaL version: 2.1.3
% 26.56/5.08 % (2609480)Termination reason: Instruction limit
% 26.56/5.08 % (2609480)Termination phase: Saturation
% 26.56/5.08 % (2609480)Time elapsed: 0.126 s
% 26.56/5.08 % (2609480)Peak memory usage: 91 MB
% 26.56/5.08 % (2609480)Instructions burned: 126 (million)
% 26.56/5.08 % (2609459)Instruction limit reached!
% 26.56/5.08 % (2609459)------------------------------
% 26.56/5.08 % (2609459)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.56/5.08 % (2609459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.56/5.08 % (2609459)CaDiCaL version: 2.1.3
% 26.56/5.08 % (2609459)Termination reason: Instruction limit
% 26.56/5.08 % (2609459)Termination phase: Saturation
% 26.56/5.08 % (2609459)Time elapsed: 2.406 s
% 26.56/5.08 % (2609459)Peak memory usage: 141 MB
% 26.56/5.08 % (2609459)Instructions burned: 2351 (million)
% 26.56/5.08 % (2609470)First to succeed.
% 26.56/5.08 % (2609482)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=800772343:i=134:gtgl=5:slsql=off:gtg=exists_sym_2965 on theBenchmark for (2965ds/134Mi)
% 26.56/5.08 % (2609470)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2609427"
% 26.56/5.08 % (2609482)Instruction limit reached!
% 26.56/5.08 % (2609482)------------------------------
% 26.56/5.08 % (2609482)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.56/5.08 % (2609482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.56/5.08 % (2609482)CaDiCaL version: 2.1.3
% 26.56/5.08 % (2609482)Termination reason: Instruction limit
% 26.56/5.08 % (2609482)Termination phase: Saturation
% 26.56/5.08 % (2609482)Time elapsed: 0.111 s
% 26.56/5.08 % (2609482)Peak memory usage: 90 MB
% 26.56/5.08 % (2609482)Instructions burned: 135 (million)
% 26.56/5.08 % (2609483)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=965527538:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2965 on theBenchmark for (2965ds/141Mi)
% 26.56/5.08 % (2609483)Refutation not found, incomplete strategy
% 26.56/5.08 % (2609483)------------------------------
% 26.56/5.08 % (2609483)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.56/5.08 % (2609483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.56/5.08 % (2609483)CaDiCaL version: 2.1.3
% 26.56/5.08 % (2609483)Termination reason: Refutation not found, incomplete strategy
% 26.56/5.08 % (2609483)Time elapsed: 0.004 s
% 26.56/5.08 % (2609483)Peak memory usage: 88 MB
% 26.56/5.08 % (2609483)Instructions burned: 3 (million)
% 26.56/5.08 % (2609485)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=262754665:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2963 on theBenchmark for (2963ds/431Mi)
% 26.56/5.08 % (2609485)Refutation not found, incomplete strategy
% 26.56/5.08 % (2609485)------------------------------
% 26.56/5.08 % (2609485)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.56/5.08 % (2609485)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.56/5.08 % (2609485)CaDiCaL version: 2.1.3
% 26.56/5.08 % (2609485)Termination reason: Refutation not found, incomplete strategy
% 26.56/5.08 % (2609485)Time elapsed: 0.007 s
% 26.56/5.08 % (2609485)Peak memory usage: 89 MB
% 26.56/5.08 % (2609485)Instructions burned: 4 (million)
% 26.56/5.08 % (2609470)Refutation found. Thanks to Tanya!
% 26.56/5.08 % SZS status Theorem for theBenchmark
% 26.56/5.08 % SZS output start Proof for theBenchmark
% See solution above
% 29.46/5.37 % (2609470)------------------------------
% 29.46/5.37 % (2609470)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.46/5.37 % (2609470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.46/5.37 % (2609470)CaDiCaL version: 2.1.3
% 29.46/5.37 % (2609470)Termination reason: Refutation
% 29.46/5.37 % (2609470)Time elapsed: 1.849 s
% 29.46/5.37 % (2609470)Peak memory usage: 136 MB
% 29.46/5.37 % (2609470)Instructions burned: 1731 (million)
% 29.46/5.37 % (2609470)------------------------------
% 29.46/5.37 % (2609470)------------------------------
% 29.46/5.37 % (2609427)Success in time 4.06 s
% 29.46/5.37 % Vampire exiting
%------------------------------------------------------------------------------