%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP648+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 : n008.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 10:15:17 AM UTC 2026
% Result : Theorem 4.94s 2.15s
% Output : Refutation 8.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 62
% Number of leaves : 41
% Syntax : Number of formulae : 427 ( 57 unt; 19 def)
% Number of atoms : 2493 ( 191 equ)
% Maximal formula atoms : 23 ( 5 avg)
% Number of connectives : 3626 (1560 ~;1671 |; 286 &)
% ( 41 <=>; 66 =>; 0 <=; 2 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 49 ( 47 usr; 18 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 7 con; 0-6 aty)
% Number of variables : 465 ( 0 sgn 437 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m1_group_2(X1,X0)
=> ! [X2] :
( m1_group_2(X2,X0)
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k11_group_4(X0)))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(k11_group_4(X0)))
=> ( ( X3 = X1
& X4 = X2 )
=> ( r3_lattices(k11_group_4(X0),X3,X4)
<=> m1_group_6(X1,X0,X2) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_latsubgr) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m1_group_2(X1,X0)
=> ! [X2] :
( m1_group_2(X2,X0)
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k11_group_4(X0)))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(k11_group_4(X0)))
=> ( ( X3 = X1
& X4 = X2 )
=> ( r3_lattices(k11_group_4(X0),X3,X4)
<=> m1_group_6(X1,X0,X2) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f4,axiom,
! [X0] :
( l3_lattices(X0)
=> ( v3_lattices(X0)
=> X0 = g3_lattices(u1_struct_0(X0),u2_lattices(X0),u1_lattices(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v3_lattices) ).
fof(f12,axiom,
! [X0] :
( ( ~ v3_struct_0(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_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
& m2_relset_1(X1,k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0)) )
=> ( X1 = k10_group_4(X0)
<=> ! [X2] :
( m1_subset_1(X2,k1_group_3(X0))
=> ! [X3] :
( m1_subset_1(X3,k1_group_3(X0))
=> ! [X4] :
( m1_group_2(X4,X0)
=> ! [X5] :
( m1_group_2(X5,X0)
=> ( ( X2 = X4
& X3 = X5 )
=> k2_binop_1(k1_group_3(X0),k1_group_3(X0),k1_group_3(X0),X1,X2,X3) = k9_group_2(X0,X4,X5) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_group_4) ).
fof(f13,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> k11_group_4(X0) = g3_lattices(k1_group_3(X0),k9_group_4(X0),k10_group_4(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_group_4) ).
fof(f14,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& l1_lattices(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> k2_lattices(X0,X1,X2) = k2_binop_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),u1_lattices(X0),X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_lattices) ).
fof(f17,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ( v1_funct_1(k10_group_4(X0))
& v1_funct_2(k10_group_4(X0),k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
& m2_relset_1(k10_group_4(X0),k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_group_4) ).
fof(f18,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ( ~ v3_struct_0(k11_group_4(X0))
& v3_lattices(k11_group_4(X0))
& v10_lattices(k11_group_4(X0))
& l3_lattices(k11_group_4(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_group_4) ).
fof(f28,axiom,
! [X0,X1,X2] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0)
& m1_group_2(X1,X0)
& m1_group_2(X2,X0) )
=> ( v1_group_1(k9_group_2(X0,X1,X2))
& m1_group_2(k9_group_2(X0,X1,X2),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_group_2) ).
fof(f29,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ( v1_funct_1(k9_group_4(X0))
& v1_funct_2(k9_group_4(X0),k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
& m2_relset_1(k9_group_4(X0),k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_group_4) ).
fof(f34,axiom,
! [X0] :
( l3_lattices(X0)
=> ( l1_lattices(X0)
& l2_lattices(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(f36,axiom,
! [X0,X1] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0)
& m1_group_2(X1,X0) )
=> ! [X2] :
( m1_group_6(X2,X0,X1)
=> m1_group_2(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_group_6) ).
fof(f55,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ( ~ v3_struct_0(k11_group_4(X0))
& v3_lattices(k11_group_4(X0))
& v4_lattices(k11_group_4(X0))
& v5_lattices(k11_group_4(X0))
& v6_lattices(k11_group_4(X0))
& v7_lattices(k11_group_4(X0))
& v8_lattices(k11_group_4(X0))
& v9_lattices(k11_group_4(X0))
& v10_lattices(k11_group_4(X0))
& v13_lattices(k11_group_4(X0))
& v14_lattices(k11_group_4(X0))
& v15_lattices(k11_group_4(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_group_4) ).
fof(f61,axiom,
! [X0,X1,X2] :
( ( v1_funct_1(X1)
& v1_funct_2(X1,k2_zfmisc_1(X0,X0),X0)
& m1_relset_1(X1,k2_zfmisc_1(X0,X0),X0)
& v1_funct_1(X2)
& v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
& m1_relset_1(X2,k2_zfmisc_1(X0,X0),X0) )
=> ! [X3,X4,X5] :
( g3_lattices(X0,X1,X2) = g3_lattices(X3,X4,X5)
=> ( X0 = X3
& X1 = X4
& X2 = X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g3_lattices) ).
fof(f73,axiom,
! [X0,X1] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0)
& m1_group_2(X1,X0) )
=> ! [X2] :
( m1_group_6(X2,X0,X1)
<=> m1_group_2(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m1_group_6) ).
fof(f74,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
<=> m1_relset_1(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f75,axiom,
! [X0,X1,X2] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0)
& v1_group_1(X1)
& m1_group_2(X1,X0)
& v1_group_1(X2)
& m1_group_2(X2,X0) )
=> ( r1_group_2(X0,X1,X2)
<=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_group_2) ).
fof(f76,axiom,
! [X0,X1,X2] :
( ( ~ v3_struct_0(X0)
& v6_lattices(X0)
& v8_lattices(X0)
& v9_lattices(X0)
& l3_lattices(X0)
& m1_subset_1(X1,u1_struct_0(X0))
& m1_subset_1(X2,u1_struct_0(X0)) )
=> ( r3_lattices(X0,X1,X2)
<=> r1_lattices(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
fof(f81,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m1_group_2(X1,X0)
=> ! [X2] :
( ( v1_group_1(X2)
& m1_group_2(X2,X0) )
=> ( m1_group_2(X2,X1)
<=> r1_group_2(X0,k9_group_2(X0,X2,X1),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t107_group_2) ).
fof(f83,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v8_lattices(X0)
& v9_lattices(X0)
& l3_lattices(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ( r1_lattices(X0,X1,X2)
<=> k2_lattices(X0,X1,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_lattices) ).
fof(f84,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(k11_group_4(X0)))
=> ! [X2] :
( m1_group_2(X2,X0)
=> ( X1 = X2
=> ( v1_group_1(X2)
& m1_group_2(X2,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_latsubgr) ).
fof(f86,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m1_group_2(X1,X0)
=> ! [X2] :
( m1_group_2(X2,X0)
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k11_group_4(X0)))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(k11_group_4(X0)))
=> ( ( X3 = X1
& X4 = X2 )
=> ( r3_lattices(k11_group_4(X0),X3,X4)
<=> r1_tarski(u1_struct_0(X1),u1_struct_0(X2)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_latsubgr) ).
fof(f90,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ! [X1] :
( m1_group_2(X1,X0)
=> ! [X2] :
( m1_group_2(X2,X0)
=> ( r1_tarski(u1_struct_0(X1),u1_struct_0(X2))
=> m1_group_2(X1,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_group_2) ).
fof(f95,plain,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ( ~ v3_struct_0(k11_group_4(X0))
& v3_lattices(k11_group_4(X0))
& v4_lattices(k11_group_4(X0))
& v5_lattices(k11_group_4(X0))
& v6_lattices(k11_group_4(X0))
& v7_lattices(k11_group_4(X0))
& v8_lattices(k11_group_4(X0))
& v9_lattices(k11_group_4(X0))
& v10_lattices(k11_group_4(X0))
& v13_lattices(k11_group_4(X0))
& v14_lattices(k11_group_4(X0)) ) ),
inference(pure_predicate_removal,[],[f55]) ).
fof(f96,plain,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ( ~ v3_struct_0(k11_group_4(X0))
& v3_lattices(k11_group_4(X0))
& v4_lattices(k11_group_4(X0))
& v5_lattices(k11_group_4(X0))
& v6_lattices(k11_group_4(X0))
& v7_lattices(k11_group_4(X0))
& v8_lattices(k11_group_4(X0))
& v9_lattices(k11_group_4(X0))
& v10_lattices(k11_group_4(X0))
& v13_lattices(k11_group_4(X0)) ) ),
inference(pure_predicate_removal,[],[f95]) ).
fof(f97,plain,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ( ~ v3_struct_0(k11_group_4(X0))
& v3_lattices(k11_group_4(X0))
& v4_lattices(k11_group_4(X0))
& v5_lattices(k11_group_4(X0))
& v6_lattices(k11_group_4(X0))
& v7_lattices(k11_group_4(X0))
& v8_lattices(k11_group_4(X0))
& v9_lattices(k11_group_4(X0))
& v10_lattices(k11_group_4(X0)) ) ),
inference(pure_predicate_removal,[],[f96]) ).
fof(f98,plain,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ( ~ v3_struct_0(k11_group_4(X0))
& v3_lattices(k11_group_4(X0))
& v4_lattices(k11_group_4(X0))
& v5_lattices(k11_group_4(X0))
& v6_lattices(k11_group_4(X0))
& v8_lattices(k11_group_4(X0))
& v9_lattices(k11_group_4(X0))
& v10_lattices(k11_group_4(X0)) ) ),
inference(pure_predicate_removal,[],[f97]) ).
fof(f99,plain,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ( ~ v3_struct_0(k11_group_4(X0))
& v3_lattices(k11_group_4(X0))
& v4_lattices(k11_group_4(X0))
& v6_lattices(k11_group_4(X0))
& v8_lattices(k11_group_4(X0))
& v9_lattices(k11_group_4(X0))
& v10_lattices(k11_group_4(X0)) ) ),
inference(pure_predicate_removal,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ( ~ v3_struct_0(k11_group_4(X0))
& v3_lattices(k11_group_4(X0))
& v6_lattices(k11_group_4(X0))
& v8_lattices(k11_group_4(X0))
& v9_lattices(k11_group_4(X0))
& v10_lattices(k11_group_4(X0)) ) ),
inference(pure_predicate_removal,[],[f99]) ).
fof(f101,plain,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ( ~ v3_struct_0(k11_group_4(X0))
& v3_lattices(k11_group_4(X0))
& l3_lattices(k11_group_4(X0)) ) ),
inference(pure_predicate_removal,[],[f18]) ).
fof(f102,plain,
! [X0] :
( ( ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) )
=> ( ~ v3_struct_0(k11_group_4(X0))
& v3_lattices(k11_group_4(X0))
& v6_lattices(k11_group_4(X0))
& v8_lattices(k11_group_4(X0))
& v9_lattices(k11_group_4(X0)) ) ),
inference(pure_predicate_removal,[],[f100]) ).
fof(f106,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( r3_lattices(k11_group_4(X0),X3,X4)
<~> m1_group_6(X1,X0,X2) )
& X3 = X1
& X4 = X2
& m1_subset_1(X4,u1_struct_0(k11_group_4(X0))) )
& m1_subset_1(X3,u1_struct_0(k11_group_4(X0))) )
& m1_group_2(X2,X0) )
& m1_group_2(X1,X0) )
& ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f107,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( r3_lattices(k11_group_4(X0),X3,X4)
<~> m1_group_6(X1,X0,X2) )
& X3 = X1
& X4 = X2
& m1_subset_1(X4,u1_struct_0(k11_group_4(X0))) )
& m1_subset_1(X3,u1_struct_0(k11_group_4(X0))) )
& m1_group_2(X2,X0) )
& m1_group_2(X1,X0) )
& ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) ),
inference(flattening,[],[f106]) ).
fof(f110,plain,
! [X0] :
( X0 = g3_lattices(u1_struct_0(X0),u2_lattices(X0),u1_lattices(X0))
| ~ v3_lattices(X0)
| ~ l3_lattices(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f111,plain,
! [X0] :
( X0 = g3_lattices(u1_struct_0(X0),u2_lattices(X0),u1_lattices(X0))
| ~ v3_lattices(X0)
| ~ l3_lattices(X0) ),
inference(flattening,[],[f110]) ).
fof(f123,plain,
! [X0] :
( ! [X1] :
( ( X1 = k10_group_4(X0)
<=> ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( k2_binop_1(k1_group_3(X0),k1_group_3(X0),k1_group_3(X0),X1,X2,X3) = k9_group_2(X0,X4,X5)
| X2 != X4
| X3 != X5
| ~ m1_group_2(X5,X0) )
| ~ m1_group_2(X4,X0) )
| ~ m1_subset_1(X3,k1_group_3(X0)) )
| ~ m1_subset_1(X2,k1_group_3(X0)) ) )
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
| ~ m2_relset_1(X1,k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0)) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f124,plain,
! [X0] :
( ! [X1] :
( ( X1 = k10_group_4(X0)
<=> ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( k2_binop_1(k1_group_3(X0),k1_group_3(X0),k1_group_3(X0),X1,X2,X3) = k9_group_2(X0,X4,X5)
| X2 != X4
| X3 != X5
| ~ m1_group_2(X5,X0) )
| ~ m1_group_2(X4,X0) )
| ~ m1_subset_1(X3,k1_group_3(X0)) )
| ~ m1_subset_1(X2,k1_group_3(X0)) ) )
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
| ~ m2_relset_1(X1,k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0)) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f123]) ).
fof(f125,plain,
! [X0] :
( k11_group_4(X0) = g3_lattices(k1_group_3(X0),k9_group_4(X0),k10_group_4(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f126,plain,
! [X0] :
( k11_group_4(X0) = g3_lattices(k1_group_3(X0),k9_group_4(X0),k10_group_4(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f125]) ).
fof(f127,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( k2_lattices(X0,X1,X2) = k2_binop_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),u1_lattices(X0),X1,X2)
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| v3_struct_0(X0)
| ~ l1_lattices(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f128,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( k2_lattices(X0,X1,X2) = k2_binop_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),u1_lattices(X0),X1,X2)
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| v3_struct_0(X0)
| ~ l1_lattices(X0) ),
inference(flattening,[],[f127]) ).
fof(f133,plain,
! [X0] :
( ( v1_funct_1(k10_group_4(X0))
& v1_funct_2(k10_group_4(X0),k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
& m2_relset_1(k10_group_4(X0),k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0)) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f134,plain,
! [X0] :
( ( v1_funct_1(k10_group_4(X0))
& v1_funct_2(k10_group_4(X0),k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
& m2_relset_1(k10_group_4(X0),k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0)) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f133]) ).
fof(f135,plain,
! [X0] :
( ( ~ v3_struct_0(k11_group_4(X0))
& v3_lattices(k11_group_4(X0))
& l3_lattices(k11_group_4(X0)) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f101]) ).
fof(f136,plain,
! [X0] :
( ( ~ v3_struct_0(k11_group_4(X0))
& v3_lattices(k11_group_4(X0))
& l3_lattices(k11_group_4(X0)) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f135]) ).
fof(f145,plain,
! [X0,X1,X2] :
( ( v1_group_1(k9_group_2(X0,X1,X2))
& m1_group_2(k9_group_2(X0,X1,X2),X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_group_2(X1,X0)
| ~ m1_group_2(X2,X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f146,plain,
! [X0,X1,X2] :
( ( v1_group_1(k9_group_2(X0,X1,X2))
& m1_group_2(k9_group_2(X0,X1,X2),X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_group_2(X1,X0)
| ~ m1_group_2(X2,X0) ),
inference(flattening,[],[f145]) ).
fof(f147,plain,
! [X0] :
( ( v1_funct_1(k9_group_4(X0))
& v1_funct_2(k9_group_4(X0),k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
& m2_relset_1(k9_group_4(X0),k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0)) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f148,plain,
! [X0] :
( ( v1_funct_1(k9_group_4(X0))
& v1_funct_2(k9_group_4(X0),k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
& m2_relset_1(k9_group_4(X0),k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0)) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f147]) ).
fof(f152,plain,
! [X0] :
( ( l1_lattices(X0)
& l2_lattices(X0) )
| ~ l3_lattices(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f155,plain,
! [X0,X1] :
( ! [X2] :
( m1_group_2(X2,X0)
| ~ m1_group_6(X2,X0,X1) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_group_2(X1,X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f156,plain,
! [X0,X1] :
( ! [X2] :
( m1_group_2(X2,X0)
| ~ m1_group_6(X2,X0,X1) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_group_2(X1,X0) ),
inference(flattening,[],[f155]) ).
fof(f167,plain,
! [X0] :
( ( ~ v3_struct_0(k11_group_4(X0))
& v3_lattices(k11_group_4(X0))
& v6_lattices(k11_group_4(X0))
& v8_lattices(k11_group_4(X0))
& v9_lattices(k11_group_4(X0)) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f102]) ).
fof(f168,plain,
! [X0] :
( ( ~ v3_struct_0(k11_group_4(X0))
& v3_lattices(k11_group_4(X0))
& v6_lattices(k11_group_4(X0))
& v8_lattices(k11_group_4(X0))
& v9_lattices(k11_group_4(X0)) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f167]) ).
fof(f175,plain,
! [X0,X1,X2] :
( ! [X3,X4,X5] :
( ( X0 = X3
& X1 = X4
& X2 = X5 )
| g3_lattices(X0,X1,X2) != g3_lattices(X3,X4,X5) )
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k2_zfmisc_1(X0,X0),X0)
| ~ m1_relset_1(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ m1_relset_1(X2,k2_zfmisc_1(X0,X0),X0) ),
inference(ennf_transformation,[],[f61]) ).
fof(f176,plain,
! [X0,X1,X2] :
( ! [X3,X4,X5] :
( ( X0 = X3
& X1 = X4
& X2 = X5 )
| g3_lattices(X0,X1,X2) != g3_lattices(X3,X4,X5) )
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k2_zfmisc_1(X0,X0),X0)
| ~ m1_relset_1(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ m1_relset_1(X2,k2_zfmisc_1(X0,X0),X0) ),
inference(flattening,[],[f175]) ).
fof(f186,plain,
! [X0,X1] :
( ! [X2] :
( m1_group_6(X2,X0,X1)
<=> m1_group_2(X2,X1) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_group_2(X1,X0) ),
inference(ennf_transformation,[],[f73]) ).
fof(f187,plain,
! [X0,X1] :
( ! [X2] :
( m1_group_6(X2,X0,X1)
<=> m1_group_2(X2,X1) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_group_2(X1,X0) ),
inference(flattening,[],[f186]) ).
fof(f188,plain,
! [X0,X1,X2] :
( ( r1_group_2(X0,X1,X2)
<=> X1 = X2 )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,X0)
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0) ),
inference(ennf_transformation,[],[f75]) ).
fof(f189,plain,
! [X0,X1,X2] :
( ( r1_group_2(X0,X1,X2)
<=> X1 = X2 )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,X0)
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0) ),
inference(flattening,[],[f188]) ).
fof(f190,plain,
! [X0,X1,X2] :
( ( r3_lattices(X0,X1,X2)
<=> r1_lattices(X0,X1,X2) )
| v3_struct_0(X0)
| ~ v6_lattices(X0)
| ~ v8_lattices(X0)
| ~ v9_lattices(X0)
| ~ l3_lattices(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f76]) ).
fof(f191,plain,
! [X0,X1,X2] :
( ( r3_lattices(X0,X1,X2)
<=> r1_lattices(X0,X1,X2) )
| v3_struct_0(X0)
| ~ v6_lattices(X0)
| ~ v8_lattices(X0)
| ~ v9_lattices(X0)
| ~ l3_lattices(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0)) ),
inference(flattening,[],[f190]) ).
fof(f198,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( m1_group_2(X2,X1)
<=> r1_group_2(X0,k9_group_2(X0,X2,X1),X2) )
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0) )
| ~ m1_group_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f199,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( m1_group_2(X2,X1)
<=> r1_group_2(X0,k9_group_2(X0,X2,X1),X2) )
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0) )
| ~ m1_group_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f198]) ).
fof(f201,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( r1_lattices(X0,X1,X2)
<=> k2_lattices(X0,X1,X2) = X1 )
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| v3_struct_0(X0)
| ~ v8_lattices(X0)
| ~ v9_lattices(X0)
| ~ l3_lattices(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f202,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( r1_lattices(X0,X1,X2)
<=> k2_lattices(X0,X1,X2) = X1 )
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| v3_struct_0(X0)
| ~ v8_lattices(X0)
| ~ v9_lattices(X0)
| ~ l3_lattices(X0) ),
inference(flattening,[],[f201]) ).
fof(f203,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( v1_group_1(X2)
& m1_group_2(X2,X0) )
| X1 != X2
| ~ m1_group_2(X2,X0) )
| ~ m1_subset_1(X1,u1_struct_0(k11_group_4(X0))) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f204,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( v1_group_1(X2)
& m1_group_2(X2,X0) )
| X1 != X2
| ~ m1_group_2(X2,X0) )
| ~ m1_subset_1(X1,u1_struct_0(k11_group_4(X0))) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f203]) ).
fof(f207,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( r3_lattices(k11_group_4(X0),X3,X4)
<=> r1_tarski(u1_struct_0(X1),u1_struct_0(X2)) )
| X1 != X3
| X2 != X4
| ~ m1_subset_1(X4,u1_struct_0(k11_group_4(X0))) )
| ~ m1_subset_1(X3,u1_struct_0(k11_group_4(X0))) )
| ~ m1_group_2(X2,X0) )
| ~ m1_group_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f86]) ).
fof(f208,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( r3_lattices(k11_group_4(X0),X3,X4)
<=> r1_tarski(u1_struct_0(X1),u1_struct_0(X2)) )
| X1 != X3
| X2 != X4
| ~ m1_subset_1(X4,u1_struct_0(k11_group_4(X0))) )
| ~ m1_subset_1(X3,u1_struct_0(k11_group_4(X0))) )
| ~ m1_group_2(X2,X0) )
| ~ m1_group_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f207]) ).
fof(f212,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( m1_group_2(X1,X2)
| ~ r1_tarski(u1_struct_0(X1),u1_struct_0(X2))
| ~ m1_group_2(X2,X0) )
| ~ m1_group_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f90]) ).
fof(f213,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( m1_group_2(X1,X2)
| ~ r1_tarski(u1_struct_0(X1),u1_struct_0(X2))
| ~ m1_group_2(X2,X0) )
| ~ m1_group_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(flattening,[],[f212]) ).
fof(f217,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ~ m1_group_6(X1,X0,X2)
| ~ r3_lattices(k11_group_4(X0),X3,X4) )
& ( m1_group_6(X1,X0,X2)
| r3_lattices(k11_group_4(X0),X3,X4) )
& X3 = X1
& X4 = X2
& m1_subset_1(X4,u1_struct_0(k11_group_4(X0))) )
& m1_subset_1(X3,u1_struct_0(k11_group_4(X0))) )
& m1_group_2(X2,X0) )
& m1_group_2(X1,X0) )
& ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) ),
inference(nnf_transformation,[],[f107]) ).
fof(f218,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ~ m1_group_6(X1,X0,X2)
| ~ r3_lattices(k11_group_4(X0),X3,X4) )
& ( m1_group_6(X1,X0,X2)
| r3_lattices(k11_group_4(X0),X3,X4) )
& X3 = X1
& X4 = X2
& m1_subset_1(X4,u1_struct_0(k11_group_4(X0))) )
& m1_subset_1(X3,u1_struct_0(k11_group_4(X0))) )
& m1_group_2(X2,X0) )
& m1_group_2(X1,X0) )
& ~ v3_struct_0(X0)
& v3_group_1(X0)
& v4_group_1(X0)
& l1_group_1(X0) ),
inference(flattening,[],[f217]) ).
fof(f219,plain,
( ( ~ m1_group_6(sK1,sK0,sK2)
| ~ r3_lattices(k11_group_4(sK0),sK3,sK4) )
& ( m1_group_6(sK1,sK0,sK2)
| r3_lattices(k11_group_4(sK0),sK3,sK4) )
& sK1 = sK3
& sK2 = sK4
& m1_subset_1(sK4,u1_struct_0(k11_group_4(sK0)))
& m1_subset_1(sK3,u1_struct_0(k11_group_4(sK0)))
& m1_group_2(sK2,sK0)
& m1_group_2(sK1,sK0)
& ~ v3_struct_0(sK0)
& v3_group_1(sK0)
& v4_group_1(sK0)
& l1_group_1(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f218]) ).
fof(f220,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = k10_group_4(X0)
| ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( k2_binop_1(k1_group_3(X0),k1_group_3(X0),k1_group_3(X0),X1,X2,X3) != k9_group_2(X0,X4,X5)
& X2 = X4
& X3 = X5
& m1_group_2(X5,X0) )
& m1_group_2(X4,X0) )
& m1_subset_1(X3,k1_group_3(X0)) )
& m1_subset_1(X2,k1_group_3(X0)) ) )
& ( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( k2_binop_1(k1_group_3(X0),k1_group_3(X0),k1_group_3(X0),X1,X2,X3) = k9_group_2(X0,X4,X5)
| X2 != X4
| X3 != X5
| ~ m1_group_2(X5,X0) )
| ~ m1_group_2(X4,X0) )
| ~ m1_subset_1(X3,k1_group_3(X0)) )
| ~ m1_subset_1(X2,k1_group_3(X0)) )
| k10_group_4(X0) != X1 ) )
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
| ~ m2_relset_1(X1,k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0)) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(nnf_transformation,[],[f124]) ).
fof(f221,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = k10_group_4(X0)
| ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( k2_binop_1(k1_group_3(X0),k1_group_3(X0),k1_group_3(X0),X1,X2,X3) != k9_group_2(X0,X4,X5)
& X2 = X4
& X3 = X5
& m1_group_2(X5,X0) )
& m1_group_2(X4,X0) )
& m1_subset_1(X3,k1_group_3(X0)) )
& m1_subset_1(X2,k1_group_3(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( k2_binop_1(k1_group_3(X0),k1_group_3(X0),k1_group_3(X0),X1,X6,X7) = k9_group_2(X0,X8,X9)
| X6 != X8
| X7 != X9
| ~ m1_group_2(X9,X0) )
| ~ m1_group_2(X8,X0) )
| ~ m1_subset_1(X7,k1_group_3(X0)) )
| ~ m1_subset_1(X6,k1_group_3(X0)) )
| k10_group_4(X0) != X1 ) )
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
| ~ m2_relset_1(X1,k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0)) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(rectify,[],[f220]) ).
fof(f222,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = k10_group_4(X0)
| ( k2_binop_1(k1_group_3(X0),k1_group_3(X0),k1_group_3(X0),X1,sK5(X0,X1),sK6(X0,X1)) != k9_group_2(X0,sK7(X0,X1),sK8(X0,X1))
& sK5(X0,X1) = sK7(X0,X1)
& sK6(X0,X1) = sK8(X0,X1)
& m1_group_2(sK8(X0,X1),X0)
& m1_group_2(sK7(X0,X1),X0)
& m1_subset_1(sK6(X0,X1),k1_group_3(X0))
& m1_subset_1(sK5(X0,X1),k1_group_3(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( k2_binop_1(k1_group_3(X0),k1_group_3(X0),k1_group_3(X0),X1,X6,X7) = k9_group_2(X0,X8,X9)
| X6 != X8
| X7 != X9
| ~ m1_group_2(X9,X0) )
| ~ m1_group_2(X8,X0) )
| ~ m1_subset_1(X7,k1_group_3(X0)) )
| ~ m1_subset_1(X6,k1_group_3(X0)) )
| k10_group_4(X0) != X1 ) )
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
| ~ m2_relset_1(X1,k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0)) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8]),skolemize(X2,sK5(X0,X1)),skolemize(X3,sK6(X0,X1)),skolemize(X4,sK7(X0,X1)),skolemize(X5,sK8(X0,X1))],[f221]) ).
fof(f241,plain,
! [X0,X1] :
( ! [X2] :
( ( m1_group_6(X2,X0,X1)
| ~ m1_group_2(X2,X1) )
& ( m1_group_2(X2,X1)
| ~ m1_group_6(X2,X0,X1) ) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_group_2(X1,X0) ),
inference(nnf_transformation,[],[f187]) ).
fof(f242,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,[],[f74]) ).
fof(f243,plain,
! [X0,X1,X2] :
( ( ( r1_group_2(X0,X1,X2)
| X1 != X2 )
& ( X1 = X2
| ~ r1_group_2(X0,X1,X2) ) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,X0)
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0) ),
inference(nnf_transformation,[],[f189]) ).
fof(f244,plain,
! [X0,X1,X2] :
( ( ( r3_lattices(X0,X1,X2)
| ~ r1_lattices(X0,X1,X2) )
& ( r1_lattices(X0,X1,X2)
| ~ r3_lattices(X0,X1,X2) ) )
| v3_struct_0(X0)
| ~ v6_lattices(X0)
| ~ v8_lattices(X0)
| ~ v9_lattices(X0)
| ~ l3_lattices(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0)) ),
inference(nnf_transformation,[],[f191]) ).
fof(f245,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( m1_group_2(X2,X1)
| ~ r1_group_2(X0,k9_group_2(X0,X2,X1),X2) )
& ( r1_group_2(X0,k9_group_2(X0,X2,X1),X2)
| ~ m1_group_2(X2,X1) ) )
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0) )
| ~ m1_group_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(nnf_transformation,[],[f199]) ).
fof(f246,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( r1_lattices(X0,X1,X2)
| k2_lattices(X0,X1,X2) != X1 )
& ( k2_lattices(X0,X1,X2) = X1
| ~ r1_lattices(X0,X1,X2) ) )
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| v3_struct_0(X0)
| ~ v8_lattices(X0)
| ~ v9_lattices(X0)
| ~ l3_lattices(X0) ),
inference(nnf_transformation,[],[f202]) ).
fof(f247,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( ( r3_lattices(k11_group_4(X0),X3,X4)
| ~ r1_tarski(u1_struct_0(X1),u1_struct_0(X2)) )
& ( r1_tarski(u1_struct_0(X1),u1_struct_0(X2))
| ~ r3_lattices(k11_group_4(X0),X3,X4) ) )
| X1 != X3
| X2 != X4
| ~ m1_subset_1(X4,u1_struct_0(k11_group_4(X0))) )
| ~ m1_subset_1(X3,u1_struct_0(k11_group_4(X0))) )
| ~ m1_group_2(X2,X0) )
| ~ m1_group_2(X1,X0) )
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(nnf_transformation,[],[f208]) ).
fof(f249,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f219]) ).
fof(f250,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f219]) ).
fof(f251,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f219]) ).
fof(f252,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f219]) ).
fof(f253,plain,
m1_group_2(sK1,sK0),
inference(cnf_transformation,[],[f219]) ).
fof(f254,plain,
m1_group_2(sK2,sK0),
inference(cnf_transformation,[],[f219]) ).
fof(f255,plain,
m1_subset_1(sK3,u1_struct_0(k11_group_4(sK0))),
inference(cnf_transformation,[],[f219]) ).
fof(f256,plain,
m1_subset_1(sK4,u1_struct_0(k11_group_4(sK0))),
inference(cnf_transformation,[],[f219]) ).
fof(f257,plain,
sK2 = sK4,
inference(cnf_transformation,[],[f219]) ).
fof(f258,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f219]) ).
fof(f259,plain,
( m1_group_6(sK1,sK0,sK2)
| r3_lattices(k11_group_4(sK0),sK3,sK4) ),
inference(cnf_transformation,[],[f219]) ).
fof(f260,plain,
( ~ m1_group_6(sK1,sK0,sK2)
| ~ r3_lattices(k11_group_4(sK0),sK3,sK4) ),
inference(cnf_transformation,[],[f219]) ).
fof(f262,plain,
! [X0] :
( ~ v3_lattices(X0)
| g3_lattices(u1_struct_0(X0),u2_lattices(X0),u1_lattices(X0)) = X0
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f275,plain,
! [X0,X1,X8,X6,X9,X7] :
( k2_binop_1(k1_group_3(X0),k1_group_3(X0),k1_group_3(X0),X1,X6,X7) = k9_group_2(X0,X8,X9)
| X6 != X8
| X7 != X9
| ~ m1_group_2(X9,X0)
| ~ m1_group_2(X8,X0)
| ~ m1_subset_1(X7,k1_group_3(X0))
| ~ m1_subset_1(X6,k1_group_3(X0))
| k10_group_4(X0) != X1
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
| ~ m2_relset_1(X1,k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f222]) ).
fof(f283,plain,
! [X0] :
( ~ l1_group_1(X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| k11_group_4(X0) = g3_lattices(k1_group_3(X0),k9_group_4(X0),k10_group_4(X0)) ),
inference(cnf_transformation,[],[f126]) ).
fof(f284,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| k2_lattices(X0,X1,X2) = k2_binop_1(u1_struct_0(X0),u1_struct_0(X0),u1_struct_0(X0),u1_lattices(X0),X1,X2)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| v3_struct_0(X0)
| ~ l1_lattices(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f289,plain,
! [X0] :
( m2_relset_1(k10_group_4(X0),k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f290,plain,
! [X0] :
( v1_funct_2(k10_group_4(X0),k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f291,plain,
! [X0] :
( v1_funct_1(k10_group_4(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f292,plain,
! [X0] :
( l3_lattices(k11_group_4(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f300,plain,
! [X2,X0,X1] :
( m1_group_2(k9_group_2(X0,X1,X2),X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_group_2(X1,X0)
| ~ m1_group_2(X2,X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f301,plain,
! [X2,X0,X1] :
( v1_group_1(k9_group_2(X0,X1,X2))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_group_2(X1,X0)
| ~ m1_group_2(X2,X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f302,plain,
! [X0] :
( m2_relset_1(k9_group_4(X0),k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f303,plain,
! [X0] :
( v1_funct_2(k9_group_4(X0),k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f304,plain,
! [X0] :
( v1_funct_1(k9_group_4(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f309,plain,
! [X0] :
( ~ l3_lattices(X0)
| l1_lattices(X0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f313,plain,
! [X2,X0,X1] :
( ~ m1_group_6(X2,X0,X1)
| m1_group_2(X2,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_group_2(X1,X0) ),
inference(cnf_transformation,[],[f156]) ).
fof(f335,plain,
! [X0] :
( v9_lattices(k11_group_4(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f168]) ).
fof(f336,plain,
! [X0] :
( v8_lattices(k11_group_4(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f168]) ).
fof(f337,plain,
! [X0] :
( v6_lattices(k11_group_4(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f168]) ).
fof(f338,plain,
! [X0] :
( v3_lattices(k11_group_4(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f168]) ).
fof(f339,plain,
! [X0] :
( ~ v3_struct_0(k11_group_4(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f168]) ).
fof(f346,plain,
! [X2,X3,X0,X1,X4,X5] :
( g3_lattices(X0,X1,X2) != g3_lattices(X3,X4,X5)
| X2 = X5
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k2_zfmisc_1(X0,X0),X0)
| ~ m1_relset_1(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ m1_relset_1(X2,k2_zfmisc_1(X0,X0),X0) ),
inference(cnf_transformation,[],[f176]) ).
fof(f348,plain,
! [X2,X3,X0,X1,X4,X5] :
( g3_lattices(X0,X1,X2) != g3_lattices(X3,X4,X5)
| X0 = X3
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k2_zfmisc_1(X0,X0),X0)
| ~ m1_relset_1(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X2)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ m1_relset_1(X2,k2_zfmisc_1(X0,X0),X0) ),
inference(cnf_transformation,[],[f176]) ).
fof(f367,plain,
! [X2,X0,X1] :
( ~ m1_group_6(X2,X0,X1)
| m1_group_2(X2,X1)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_group_2(X1,X0) ),
inference(cnf_transformation,[],[f241]) ).
fof(f368,plain,
! [X2,X0,X1] :
( m1_group_6(X2,X0,X1)
| ~ m1_group_2(X2,X1)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_group_2(X1,X0) ),
inference(cnf_transformation,[],[f241]) ).
fof(f369,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f242]) ).
fof(f371,plain,
! [X2,X0,X1] :
( ~ r1_group_2(X0,X1,X2)
| X1 = X2
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,X0)
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0) ),
inference(cnf_transformation,[],[f243]) ).
fof(f374,plain,
! [X2,X0,X1] :
( ~ r1_lattices(X0,X1,X2)
| r3_lattices(X0,X1,X2)
| v3_struct_0(X0)
| ~ v6_lattices(X0)
| ~ v8_lattices(X0)
| ~ v9_lattices(X0)
| ~ l3_lattices(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f244]) ).
fof(f379,plain,
! [X2,X0,X1] :
( r1_group_2(X0,k9_group_2(X0,X2,X1),X2)
| ~ m1_group_2(X2,X1)
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0)
| ~ m1_group_2(X1,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f245]) ).
fof(f383,plain,
! [X2,X0,X1] :
( k2_lattices(X0,X1,X2) != X1
| r1_lattices(X0,X1,X2)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v8_lattices(X0)
| ~ v9_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f246]) ).
fof(f385,plain,
! [X2,X0,X1] :
( v1_group_1(X2)
| X1 != X2
| ~ m1_group_2(X2,X0)
| ~ m1_subset_1(X1,u1_struct_0(k11_group_4(X0)))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f204]) ).
fof(f387,plain,
! [X2,X3,X0,X1,X4] :
( r1_tarski(u1_struct_0(X1),u1_struct_0(X2))
| ~ r3_lattices(k11_group_4(X0),X3,X4)
| X1 != X3
| X2 != X4
| ~ m1_subset_1(X4,u1_struct_0(k11_group_4(X0)))
| ~ m1_subset_1(X3,u1_struct_0(k11_group_4(X0)))
| ~ m1_group_2(X2,X0)
| ~ m1_group_2(X1,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f247]) ).
fof(f393,plain,
! [X2,X0,X1] :
( ~ r1_tarski(u1_struct_0(X1),u1_struct_0(X2))
| m1_group_2(X1,X2)
| ~ m1_group_2(X2,X0)
| ~ m1_group_2(X1,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f213]) ).
fof(f397,plain,
( ~ m1_group_6(sK3,sK0,sK4)
| ~ r3_lattices(k11_group_4(sK0),sK3,sK4) ),
inference(definition_unfolding,[],[f260,f258,f257]) ).
fof(f398,plain,
( m1_group_6(sK3,sK0,sK4)
| r3_lattices(k11_group_4(sK0),sK3,sK4) ),
inference(definition_unfolding,[],[f259,f258,f257]) ).
fof(f399,plain,
m1_group_2(sK4,sK0),
inference(definition_unfolding,[],[f254,f257]) ).
fof(f400,plain,
m1_group_2(sK3,sK0),
inference(definition_unfolding,[],[f253,f258]) ).
fof(f401,plain,
! [X0,X1,X8,X9,X7] :
( k9_group_2(X0,X8,X9) = k2_binop_1(k1_group_3(X0),k1_group_3(X0),k1_group_3(X0),X1,X8,X7)
| X7 != X9
| ~ m1_group_2(X9,X0)
| ~ m1_group_2(X8,X0)
| ~ m1_subset_1(X7,k1_group_3(X0))
| ~ m1_subset_1(X8,k1_group_3(X0))
| k10_group_4(X0) != X1
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
| ~ m2_relset_1(X1,k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(equality_resolution,[],[f275]) ).
fof(f402,plain,
! [X0,X1,X8,X9] :
( k9_group_2(X0,X8,X9) = k2_binop_1(k1_group_3(X0),k1_group_3(X0),k1_group_3(X0),X1,X8,X9)
| ~ m1_group_2(X9,X0)
| ~ m1_group_2(X8,X0)
| ~ m1_subset_1(X9,k1_group_3(X0))
| ~ m1_subset_1(X8,k1_group_3(X0))
| k10_group_4(X0) != X1
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
| ~ m2_relset_1(X1,k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(equality_resolution,[],[f401]) ).
fof(f403,plain,
! [X0,X8,X9] :
( k9_group_2(X0,X8,X9) = k2_binop_1(k1_group_3(X0),k1_group_3(X0),k1_group_3(X0),k10_group_4(X0),X8,X9)
| ~ m1_group_2(X9,X0)
| ~ m1_group_2(X8,X0)
| ~ m1_subset_1(X9,k1_group_3(X0))
| ~ m1_subset_1(X8,k1_group_3(X0))
| ~ v1_funct_1(k10_group_4(X0))
| ~ v1_funct_2(k10_group_4(X0),k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
| ~ m2_relset_1(k10_group_4(X0),k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(equality_resolution,[],[f402]) ).
fof(f405,plain,
! [X2,X0] :
( ~ m1_subset_1(X2,u1_struct_0(k11_group_4(X0)))
| ~ m1_group_2(X2,X0)
| v1_group_1(X2)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(equality_resolution,[],[f385]) ).
fof(f409,plain,
! [X2,X3,X0,X4] :
( r1_tarski(u1_struct_0(X3),u1_struct_0(X2))
| ~ r3_lattices(k11_group_4(X0),X3,X4)
| X2 != X4
| ~ m1_subset_1(X4,u1_struct_0(k11_group_4(X0)))
| ~ m1_subset_1(X3,u1_struct_0(k11_group_4(X0)))
| ~ m1_group_2(X2,X0)
| ~ m1_group_2(X3,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(equality_resolution,[],[f387]) ).
fof(f410,plain,
! [X3,X0,X4] :
( ~ r3_lattices(k11_group_4(X0),X3,X4)
| r1_tarski(u1_struct_0(X3),u1_struct_0(X4))
| ~ m1_subset_1(X4,u1_struct_0(k11_group_4(X0)))
| ~ m1_subset_1(X3,u1_struct_0(k11_group_4(X0)))
| ~ m1_group_2(X4,X0)
| ~ m1_group_2(X3,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(equality_resolution,[],[f409]) ).
fof(f411,definition,
sF27 = k11_group_4(sK0),
introduced(definition,[new_symbols(definition,[sF27])],[function_definition]) ).
fof(f412,plain,
k11_group_4(sK0) = sF27,
inference(reorient_equations,[],[f411]) ).
fof(f413,plain,
( ~ m1_group_6(sK3,sK0,sK4)
| ~ r3_lattices(sF27,sK3,sK4) ),
inference(definition_folding,[],[f397,f412]) ).
fof(f414,plain,
( m1_group_6(sK3,sK0,sK4)
| r3_lattices(sF27,sK3,sK4) ),
inference(definition_folding,[],[f398,f412]) ).
fof(f415,definition,
sF28 = u1_struct_0(sF27),
introduced(definition,[new_symbols(definition,[sF28])],[function_definition]) ).
fof(f416,plain,
u1_struct_0(sF27) = sF28,
inference(reorient_equations,[],[f415]) ).
fof(f417,plain,
m1_subset_1(sK4,sF28),
inference(definition_folding,[],[f256,f416,f412]) ).
fof(f418,plain,
m1_subset_1(sK3,sF28),
inference(definition_folding,[],[f255,f416,f412]) ).
fof(f420,plain,
! [X0,X8,X9] :
( k9_group_2(X0,X8,X9) = k2_binop_1(k1_group_3(X0),k1_group_3(X0),k1_group_3(X0),k10_group_4(X0),X8,X9)
| ~ m1_group_2(X9,X0)
| ~ m1_group_2(X8,X0)
| ~ m1_subset_1(X9,k1_group_3(X0))
| ~ m1_subset_1(X8,k1_group_3(X0))
| ~ v1_funct_2(k10_group_4(X0),k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
| ~ m2_relset_1(k10_group_4(X0),k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(forward_subsumption_resolution,[],[f403,f291]) ).
fof(f422,definition,
( spl29_1
<=> r3_lattices(sF27,sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl29_1])],[avatar_definition]) ).
fof(f423,plain,
( ~ r3_lattices(sF27,sK3,sK4)
| spl29_1 ),
inference(avatar_component_clause,[],[f422]) ).
fof(f424,plain,
( r3_lattices(sF27,sK3,sK4)
| ~ spl29_1 ),
inference(avatar_component_clause,[],[f422]) ).
fof(f426,definition,
( spl29_2
<=> m1_group_6(sK3,sK0,sK4) ),
introduced(definition,[new_symbols(definition,[spl29_2])],[avatar_definition]) ).
fof(f427,plain,
( ~ m1_group_6(sK3,sK0,sK4)
| spl29_2 ),
inference(avatar_component_clause,[],[f426]) ).
fof(f428,plain,
( m1_group_6(sK3,sK0,sK4)
| ~ spl29_2 ),
inference(avatar_component_clause,[],[f426]) ).
fof(f429,plain,
( spl29_1
| spl29_2 ),
inference(avatar_split_clause,[],[f414,f426,f422]) ).
fof(f430,plain,
( ~ spl29_1
| ~ spl29_2 ),
inference(avatar_split_clause,[],[f413,f426,f422]) ).
fof(f431,plain,
! [X0,X8,X9] :
( k9_group_2(X0,X8,X9) = k2_binop_1(k1_group_3(X0),k1_group_3(X0),k1_group_3(X0),k10_group_4(X0),X8,X9)
| ~ m1_group_2(X9,X0)
| ~ m1_group_2(X8,X0)
| ~ m1_subset_1(X9,k1_group_3(X0))
| ~ m1_subset_1(X8,k1_group_3(X0))
| ~ m2_relset_1(k10_group_4(X0),k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(forward_subsumption_resolution,[],[f420,f290]) ).
fof(f432,plain,
! [X0,X8,X9] :
( ~ m1_subset_1(X9,k1_group_3(X0))
| ~ m1_group_2(X9,X0)
| ~ m1_group_2(X8,X0)
| k9_group_2(X0,X8,X9) = k2_binop_1(k1_group_3(X0),k1_group_3(X0),k1_group_3(X0),k10_group_4(X0),X8,X9)
| ~ m1_subset_1(X8,k1_group_3(X0))
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0) ),
inference(forward_subsumption_resolution,[],[f431,f289]) ).
fof(f435,plain,
! [X0,X1] :
( ~ r3_lattices(sF27,X0,X1)
| r1_tarski(u1_struct_0(X0),u1_struct_0(X1))
| ~ m1_subset_1(X1,u1_struct_0(sF27))
| ~ m1_subset_1(X0,u1_struct_0(sF27))
| ~ m1_group_2(X1,sK0)
| ~ m1_group_2(X0,sK0)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(superposition,[],[f410,f412]) ).
fof(f436,plain,
! [X0,X1] :
( ~ r3_lattices(sF27,X0,X1)
| r1_tarski(u1_struct_0(X0),u1_struct_0(X1))
| ~ m1_subset_1(X1,u1_struct_0(sF27))
| ~ m1_subset_1(X0,u1_struct_0(sF27))
| ~ m1_group_2(X1,sK0)
| ~ m1_group_2(X0,sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f435,f252]) ).
fof(f437,plain,
! [X0,X1] :
( ~ r3_lattices(sF27,X0,X1)
| r1_tarski(u1_struct_0(X0),u1_struct_0(X1))
| ~ m1_subset_1(X1,u1_struct_0(sF27))
| ~ m1_subset_1(X0,u1_struct_0(sF27))
| ~ m1_group_2(X1,sK0)
| ~ m1_group_2(X0,sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f436,f251]) ).
fof(f438,plain,
! [X0,X1] :
( ~ r3_lattices(sF27,X0,X1)
| r1_tarski(u1_struct_0(X0),u1_struct_0(X1))
| ~ m1_subset_1(X1,u1_struct_0(sF27))
| ~ m1_subset_1(X0,u1_struct_0(sF27))
| ~ m1_group_2(X1,sK0)
| ~ m1_group_2(X0,sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f437,f250]) ).
fof(f439,plain,
! [X0,X1] :
( ~ r3_lattices(sF27,X0,X1)
| r1_tarski(u1_struct_0(X0),u1_struct_0(X1))
| ~ m1_subset_1(X1,u1_struct_0(sF27))
| ~ m1_subset_1(X0,u1_struct_0(sF27))
| ~ m1_group_2(X1,sK0)
| ~ m1_group_2(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f438,f249]) ).
fof(f440,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,sF28)
| ~ r3_lattices(sF27,X0,X1)
| r1_tarski(u1_struct_0(X0),u1_struct_0(X1))
| ~ m1_subset_1(X0,u1_struct_0(sF27))
| ~ m1_group_2(X1,sK0)
| ~ m1_group_2(X0,sK0) ),
inference(forward_demodulation,[],[f439,f416]) ).
fof(f441,plain,
! [X0,X1] :
( r1_tarski(u1_struct_0(X0),u1_struct_0(X1))
| ~ m1_subset_1(X1,sF28)
| ~ r3_lattices(sF27,X0,X1)
| ~ m1_subset_1(X0,sF28)
| ~ m1_group_2(X1,sK0)
| ~ m1_group_2(X0,sK0) ),
inference(forward_demodulation,[],[f440,f416]) ).
fof(f461,plain,
! [X0] :
( ~ m1_subset_1(X0,u1_struct_0(sF27))
| ~ m1_group_2(X0,sK0)
| v1_group_1(X0)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(superposition,[],[f405,f412]) ).
fof(f462,plain,
! [X0] :
( ~ m1_subset_1(X0,u1_struct_0(sF27))
| ~ m1_group_2(X0,sK0)
| v1_group_1(X0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f461,f252]) ).
fof(f463,plain,
! [X0] :
( ~ m1_subset_1(X0,u1_struct_0(sF27))
| ~ m1_group_2(X0,sK0)
| v1_group_1(X0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f462,f251]) ).
fof(f464,plain,
! [X0] :
( ~ m1_subset_1(X0,u1_struct_0(sF27))
| ~ m1_group_2(X0,sK0)
| v1_group_1(X0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f463,f250]) ).
fof(f465,plain,
! [X0] :
( ~ m1_subset_1(X0,u1_struct_0(sF27))
| ~ m1_group_2(X0,sK0)
| v1_group_1(X0) ),
inference(forward_subsumption_resolution,[],[f464,f249]) ).
fof(f466,plain,
! [X0] :
( ~ m1_subset_1(X0,sF28)
| ~ m1_group_2(X0,sK0)
| v1_group_1(X0) ),
inference(forward_demodulation,[],[f465,f416]) ).
fof(f468,plain,
( ~ m1_group_2(sK3,sK0)
| v1_group_1(sK3) ),
inference(resolution,[],[f466,f418]) ).
fof(f469,plain,
v1_group_1(sK3),
inference(forward_subsumption_resolution,[],[f468,f400]) ).
fof(f471,plain,
( m1_group_2(sK3,sK4)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_group_2(sK4,sK0)
| ~ spl29_2 ),
inference(resolution,[],[f367,f428]) ).
fof(f474,plain,
( m1_group_2(sK3,sK4)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_group_2(sK4,sK0)
| ~ spl29_2 ),
inference(forward_subsumption_resolution,[],[f471,f252]) ).
fof(f475,plain,
( m1_group_2(sK3,sK4)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_group_2(sK4,sK0)
| ~ spl29_2 ),
inference(forward_subsumption_resolution,[],[f474,f251]) ).
fof(f476,plain,
( m1_group_2(sK3,sK4)
| ~ l1_group_1(sK0)
| ~ m1_group_2(sK4,sK0)
| ~ spl29_2 ),
inference(forward_subsumption_resolution,[],[f475,f250]) ).
fof(f477,plain,
( m1_group_2(sK3,sK4)
| ~ m1_group_2(sK4,sK0)
| ~ spl29_2 ),
inference(forward_subsumption_resolution,[],[f476,f249]) ).
fof(f478,plain,
( m1_group_2(sK3,sK4)
| ~ spl29_2 ),
inference(forward_subsumption_resolution,[],[f477,f399]) ).
fof(f482,plain,
! [X2,X0,X1] :
( m1_group_2(X0,X1)
| v3_struct_0(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_group_2(X2,X1)
| ~ m1_group_2(X0,X2)
| v3_struct_0(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_group_2(X2,X1) ),
inference(resolution,[],[f313,f368]) ).
fof(f483,plain,
! [X2,X0,X1] :
( ~ m1_group_2(X2,X1)
| v3_struct_0(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| m1_group_2(X0,X1)
| ~ m1_group_2(X0,X2) ),
inference(duplicate_literal_removal,[],[f482]) ).
fof(f534,definition,
( spl29_12
<=> l3_lattices(sF27) ),
introduced(definition,[new_symbols(definition,[spl29_12])],[avatar_definition]) ).
fof(f535,plain,
( l3_lattices(sF27)
| ~ spl29_12 ),
inference(avatar_component_clause,[],[f534]) ).
fof(f536,plain,
( ~ l3_lattices(sF27)
| spl29_12 ),
inference(avatar_component_clause,[],[f534]) ).
fof(f538,definition,
( spl29_13
<=> v9_lattices(sF27) ),
introduced(definition,[new_symbols(definition,[spl29_13])],[avatar_definition]) ).
fof(f539,plain,
( v9_lattices(sF27)
| ~ spl29_13 ),
inference(avatar_component_clause,[],[f538]) ).
fof(f542,definition,
( spl29_14
<=> v8_lattices(sF27) ),
introduced(definition,[new_symbols(definition,[spl29_14])],[avatar_definition]) ).
fof(f543,plain,
( v8_lattices(sF27)
| ~ spl29_14 ),
inference(avatar_component_clause,[],[f542]) ).
fof(f546,definition,
( spl29_15
<=> v6_lattices(sF27) ),
introduced(definition,[new_symbols(definition,[spl29_15])],[avatar_definition]) ).
fof(f547,plain,
( v6_lattices(sF27)
| ~ spl29_15 ),
inference(avatar_component_clause,[],[f546]) ).
fof(f550,definition,
( spl29_16
<=> v3_struct_0(sF27) ),
introduced(definition,[new_symbols(definition,[spl29_16])],[avatar_definition]) ).
fof(f551,plain,
( ~ v3_struct_0(sF27)
| spl29_16 ),
inference(avatar_component_clause,[],[f550]) ).
fof(f573,plain,
( ~ v3_struct_0(sF27)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(superposition,[],[f339,f412]) ).
fof(f574,plain,
( ~ v3_struct_0(sF27)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f573,f252]) ).
fof(f575,plain,
( ~ v3_struct_0(sF27)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f574,f251]) ).
fof(f576,plain,
( ~ v3_struct_0(sF27)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f575,f250]) ).
fof(f577,plain,
~ v3_struct_0(sF27),
inference(forward_subsumption_resolution,[],[f576,f249]) ).
fof(f578,plain,
~ spl29_16,
inference(avatar_split_clause,[],[f577,f550]) ).
fof(f579,plain,
( v9_lattices(sF27)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(superposition,[],[f335,f412]) ).
fof(f580,plain,
( v9_lattices(sF27)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f579,f252]) ).
fof(f581,plain,
( v9_lattices(sF27)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f580,f251]) ).
fof(f582,plain,
( v9_lattices(sF27)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f581,f250]) ).
fof(f583,plain,
v9_lattices(sF27),
inference(forward_subsumption_resolution,[],[f582,f249]) ).
fof(f584,plain,
spl29_13,
inference(avatar_split_clause,[],[f583,f538]) ).
fof(f585,plain,
( v6_lattices(sF27)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(superposition,[],[f337,f412]) ).
fof(f586,plain,
( v6_lattices(sF27)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f585,f252]) ).
fof(f587,plain,
( v6_lattices(sF27)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f586,f251]) ).
fof(f588,plain,
( v6_lattices(sF27)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f587,f250]) ).
fof(f589,plain,
v6_lattices(sF27),
inference(forward_subsumption_resolution,[],[f588,f249]) ).
fof(f590,plain,
spl29_15,
inference(avatar_split_clause,[],[f589,f546]) ).
fof(f592,plain,
( v8_lattices(sF27)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(superposition,[],[f336,f412]) ).
fof(f593,plain,
( v8_lattices(sF27)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f592,f252]) ).
fof(f594,plain,
( v8_lattices(sF27)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f593,f251]) ).
fof(f595,plain,
( v8_lattices(sF27)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f594,f250]) ).
fof(f596,plain,
v8_lattices(sF27),
inference(forward_subsumption_resolution,[],[f595,f249]) ).
fof(f597,plain,
spl29_14,
inference(avatar_split_clause,[],[f596,f542]) ).
fof(f598,plain,
( l3_lattices(sF27)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(superposition,[],[f292,f412]) ).
fof(f599,plain,
( v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl29_12 ),
inference(forward_subsumption_resolution,[],[f598,f536]) ).
fof(f600,plain,
( ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl29_12 ),
inference(forward_subsumption_resolution,[],[f599,f252]) ).
fof(f601,plain,
( ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl29_12 ),
inference(forward_subsumption_resolution,[],[f600,f251]) ).
fof(f602,plain,
( ~ l1_group_1(sK0)
| spl29_12 ),
inference(forward_subsumption_resolution,[],[f601,f250]) ).
fof(f603,plain,
( $false
| spl29_12 ),
inference(forward_subsumption_resolution,[],[f602,f249]) ).
fof(f604,plain,
spl29_12,
inference(avatar_contradiction_clause,[],[f603]) ).
fof(f641,plain,
( v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| k11_group_4(sK0) = g3_lattices(k1_group_3(sK0),k9_group_4(sK0),k10_group_4(sK0)) ),
inference(resolution,[],[f283,f249]) ).
fof(f642,plain,
( ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| k11_group_4(sK0) = g3_lattices(k1_group_3(sK0),k9_group_4(sK0),k10_group_4(sK0)) ),
inference(forward_subsumption_resolution,[],[f641,f252]) ).
fof(f643,plain,
( ~ v4_group_1(sK0)
| k11_group_4(sK0) = g3_lattices(k1_group_3(sK0),k9_group_4(sK0),k10_group_4(sK0)) ),
inference(forward_subsumption_resolution,[],[f642,f251]) ).
fof(f644,plain,
k11_group_4(sK0) = g3_lattices(k1_group_3(sK0),k9_group_4(sK0),k10_group_4(sK0)),
inference(forward_subsumption_resolution,[],[f643,f250]) ).
fof(f645,plain,
sF27 = g3_lattices(k1_group_3(sK0),k9_group_4(sK0),k10_group_4(sK0)),
inference(forward_demodulation,[],[f644,f412]) ).
fof(f646,plain,
! [X2,X0,X1] :
( ~ r3_lattices(sF27,X0,X1)
| ~ m1_group_2(X1,X2)
| ~ m1_group_2(X0,X2)
| v3_struct_0(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2)
| ~ m1_subset_1(X1,sF28)
| m1_group_2(X0,X1)
| ~ m1_subset_1(X0,sF28)
| ~ m1_group_2(X1,sK0)
| ~ m1_group_2(X0,sK0) ),
inference(resolution,[],[f393,f441]) ).
fof(f665,plain,
( v3_lattices(sF27)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(superposition,[],[f338,f412]) ).
fof(f666,plain,
( v3_lattices(sF27)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f665,f252]) ).
fof(f667,plain,
( v3_lattices(sF27)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f666,f251]) ).
fof(f668,plain,
( v3_lattices(sF27)
| ~ l1_group_1(sK0) ),
inference(forward_subsumption_resolution,[],[f667,f250]) ).
fof(f669,plain,
v3_lattices(sF27),
inference(forward_subsumption_resolution,[],[f668,f249]) ).
fof(f690,definition,
( spl29_22
<=> l1_lattices(sF27) ),
introduced(definition,[new_symbols(definition,[spl29_22])],[avatar_definition]) ).
fof(f691,plain,
( l1_lattices(sF27)
| ~ spl29_22 ),
inference(avatar_component_clause,[],[f690]) ).
fof(f692,plain,
( ~ l1_lattices(sF27)
| spl29_22 ),
inference(avatar_component_clause,[],[f690]) ).
fof(f720,plain,
( l1_lattices(sF27)
| ~ spl29_12 ),
inference(resolution,[],[f309,f535]) ).
fof(f721,plain,
( $false
| ~ spl29_12
| spl29_22 ),
inference(forward_subsumption_resolution,[],[f720,f692]) ).
fof(f722,plain,
( ~ spl29_12
| spl29_22 ),
inference(avatar_contradiction_clause,[],[f721]) ).
fof(f749,plain,
! [X2,X0,X1] :
( ~ m1_group_2(X0,X1)
| ~ v1_group_1(X0)
| ~ m1_group_2(X0,X2)
| ~ m1_group_2(X1,X2)
| v3_struct_0(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2)
| k9_group_2(X2,X0,X1) = X0
| v3_struct_0(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2)
| ~ v1_group_1(k9_group_2(X2,X0,X1))
| ~ m1_group_2(k9_group_2(X2,X0,X1),X2)
| ~ v1_group_1(X0)
| ~ m1_group_2(X0,X2) ),
inference(resolution,[],[f379,f371]) ).
fof(f751,plain,
! [X2,X0,X1] :
( ~ m1_group_2(X0,X1)
| ~ v1_group_1(X0)
| ~ m1_group_2(X0,X2)
| ~ m1_group_2(X1,X2)
| v3_struct_0(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2)
| k9_group_2(X2,X0,X1) = X0
| ~ v1_group_1(k9_group_2(X2,X0,X1))
| ~ m1_group_2(k9_group_2(X2,X0,X1),X2) ),
inference(duplicate_literal_removal,[],[f749]) ).
fof(f753,plain,
! [X2,X0,X1] :
( ~ m1_group_2(X0,X1)
| ~ v1_group_1(X0)
| ~ m1_group_2(X0,X2)
| ~ m1_group_2(X1,X2)
| v3_struct_0(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2)
| k9_group_2(X2,X0,X1) = X0
| ~ m1_group_2(k9_group_2(X2,X0,X1),X2) ),
inference(forward_subsumption_resolution,[],[f751,f301]) ).
fof(f755,plain,
! [X2,X0,X1] :
( ~ m1_group_2(X0,X1)
| ~ v1_group_1(X0)
| ~ m1_group_2(X0,X2)
| ~ m1_group_2(X1,X2)
| v3_struct_0(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2)
| k9_group_2(X2,X0,X1) = X0 ),
inference(forward_subsumption_resolution,[],[f753,f300]) ).
fof(f757,plain,
! [X2,X0,X1] :
( ~ m1_group_2(X1,X2)
| ~ v1_group_1(X0)
| ~ m1_group_2(X0,X1)
| v3_struct_0(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2)
| k9_group_2(X2,X0,X1) = X0 ),
inference(forward_subsumption_resolution,[],[f755,f483]) ).
fof(f772,plain,
! [X0] :
( ~ v1_group_1(X0)
| ~ m1_group_2(X0,sK4)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| k9_group_2(sK0,X0,sK4) = X0 ),
inference(resolution,[],[f757,f399]) ).
fof(f774,plain,
! [X0] :
( ~ v1_group_1(X0)
| ~ m1_group_2(X0,sK4)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| k9_group_2(sK0,X0,sK4) = X0 ),
inference(forward_subsumption_resolution,[],[f772,f252]) ).
fof(f776,plain,
! [X0] :
( ~ v1_group_1(X0)
| ~ m1_group_2(X0,sK4)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| k9_group_2(sK0,X0,sK4) = X0 ),
inference(forward_subsumption_resolution,[],[f774,f251]) ).
fof(f778,plain,
! [X0] :
( ~ v1_group_1(X0)
| ~ m1_group_2(X0,sK4)
| ~ l1_group_1(sK0)
| k9_group_2(sK0,X0,sK4) = X0 ),
inference(forward_subsumption_resolution,[],[f776,f250]) ).
fof(f780,plain,
! [X0] :
( ~ m1_group_2(X0,sK4)
| ~ v1_group_1(X0)
| k9_group_2(sK0,X0,sK4) = X0 ),
inference(forward_subsumption_resolution,[],[f778,f249]) ).
fof(f782,plain,
( ~ v1_group_1(sK3)
| sK3 = k9_group_2(sK0,sK3,sK4)
| ~ spl29_2 ),
inference(resolution,[],[f780,f478]) ).
fof(f783,plain,
( sK3 = k9_group_2(sK0,sK3,sK4)
| ~ spl29_2 ),
inference(forward_subsumption_resolution,[],[f782,f469]) ).
fof(f820,plain,
( sF27 = g3_lattices(u1_struct_0(sF27),u2_lattices(sF27),u1_lattices(sF27))
| ~ l3_lattices(sF27) ),
inference(resolution,[],[f262,f669]) ).
fof(f821,plain,
( sF27 = g3_lattices(u1_struct_0(sF27),u2_lattices(sF27),u1_lattices(sF27))
| ~ spl29_12 ),
inference(forward_subsumption_resolution,[],[f820,f535]) ).
fof(f823,plain,
( sF27 = g3_lattices(sF28,u2_lattices(sF27),u1_lattices(sF27))
| ~ spl29_12 ),
inference(forward_demodulation,[],[f821,f416]) ).
fof(f879,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,sF28)
| k2_lattices(sF27,X1,X0) = k2_binop_1(sF28,sF28,sF28,u1_lattices(sF27),X1,X0)
| ~ m1_subset_1(X1,sF28)
| v3_struct_0(sF27)
| ~ l1_lattices(sF27) ),
inference(superposition,[],[f284,f416]) ).
fof(f880,plain,
( ! [X0,X1] :
( ~ m1_subset_1(X0,sF28)
| k2_lattices(sF27,X1,X0) = k2_binop_1(sF28,sF28,sF28,u1_lattices(sF27),X1,X0)
| ~ m1_subset_1(X1,sF28)
| ~ l1_lattices(sF27) )
| spl29_16 ),
inference(forward_subsumption_resolution,[],[f879,f551]) ).
fof(f881,plain,
( ! [X0,X1] :
( ~ m1_subset_1(X1,sF28)
| k2_lattices(sF27,X1,X0) = k2_binop_1(sF28,sF28,sF28,u1_lattices(sF27),X1,X0)
| ~ m1_subset_1(X0,sF28) )
| spl29_16
| ~ spl29_22 ),
inference(forward_subsumption_resolution,[],[f880,f691]) ).
fof(f901,plain,
( ! [X0] :
( ~ m1_subset_1(X0,sF28)
| k2_lattices(sF27,sK3,X0) = k2_binop_1(sF28,sF28,sF28,u1_lattices(sF27),sK3,X0) )
| spl29_16
| ~ spl29_22 ),
inference(resolution,[],[f881,f418]) ).
fof(f906,plain,
( k2_lattices(sF27,sK3,sK4) = k2_binop_1(sF28,sF28,sF28,u1_lattices(sF27),sK3,sK4)
| spl29_16
| ~ spl29_22 ),
inference(resolution,[],[f901,f417]) ).
fof(f1015,plain,
! [X0] :
( m1_relset_1(k9_group_4(X0),k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| v3_struct_0(X0) ),
inference(resolution,[],[f302,f369]) ).
fof(f1035,plain,
! [X2,X0,X1] :
( g3_lattices(X0,X1,X2) != sF27
| k1_group_3(sK0) = X0
| ~ v1_funct_1(k9_group_4(sK0))
| ~ v1_funct_2(k9_group_4(sK0),k2_zfmisc_1(k1_group_3(sK0),k1_group_3(sK0)),k1_group_3(sK0))
| ~ m1_relset_1(k9_group_4(sK0),k2_zfmisc_1(k1_group_3(sK0),k1_group_3(sK0)),k1_group_3(sK0))
| ~ v1_funct_1(k10_group_4(sK0))
| ~ v1_funct_2(k10_group_4(sK0),k2_zfmisc_1(k1_group_3(sK0),k1_group_3(sK0)),k1_group_3(sK0))
| ~ m1_relset_1(k10_group_4(sK0),k2_zfmisc_1(k1_group_3(sK0),k1_group_3(sK0)),k1_group_3(sK0)) ),
inference(superposition,[],[f348,f645]) ).
fof(f1069,definition,
( spl29_37
<=> m1_relset_1(k10_group_4(sK0),k2_zfmisc_1(k1_group_3(sK0),k1_group_3(sK0)),k1_group_3(sK0)) ),
introduced(definition,[new_symbols(definition,[spl29_37])],[avatar_definition]) ).
fof(f1070,plain,
( m1_relset_1(k10_group_4(sK0),k2_zfmisc_1(k1_group_3(sK0),k1_group_3(sK0)),k1_group_3(sK0))
| ~ spl29_37 ),
inference(avatar_component_clause,[],[f1069]) ).
fof(f1071,plain,
( ~ m1_relset_1(k10_group_4(sK0),k2_zfmisc_1(k1_group_3(sK0),k1_group_3(sK0)),k1_group_3(sK0))
| spl29_37 ),
inference(avatar_component_clause,[],[f1069]) ).
fof(f1073,definition,
( spl29_38
<=> v1_funct_2(k10_group_4(sK0),k2_zfmisc_1(k1_group_3(sK0),k1_group_3(sK0)),k1_group_3(sK0)) ),
introduced(definition,[new_symbols(definition,[spl29_38])],[avatar_definition]) ).
fof(f1074,plain,
( v1_funct_2(k10_group_4(sK0),k2_zfmisc_1(k1_group_3(sK0),k1_group_3(sK0)),k1_group_3(sK0))
| ~ spl29_38 ),
inference(avatar_component_clause,[],[f1073]) ).
fof(f1075,plain,
( ~ v1_funct_2(k10_group_4(sK0),k2_zfmisc_1(k1_group_3(sK0),k1_group_3(sK0)),k1_group_3(sK0))
| spl29_38 ),
inference(avatar_component_clause,[],[f1073]) ).
fof(f1077,definition,
( spl29_39
<=> v1_funct_1(k10_group_4(sK0)) ),
introduced(definition,[new_symbols(definition,[spl29_39])],[avatar_definition]) ).
fof(f1078,plain,
( v1_funct_1(k10_group_4(sK0))
| ~ spl29_39 ),
inference(avatar_component_clause,[],[f1077]) ).
fof(f1079,plain,
( ~ v1_funct_1(k10_group_4(sK0))
| spl29_39 ),
inference(avatar_component_clause,[],[f1077]) ).
fof(f1081,definition,
( spl29_40
<=> m1_relset_1(k9_group_4(sK0),k2_zfmisc_1(k1_group_3(sK0),k1_group_3(sK0)),k1_group_3(sK0)) ),
introduced(definition,[new_symbols(definition,[spl29_40])],[avatar_definition]) ).
fof(f1082,plain,
( m1_relset_1(k9_group_4(sK0),k2_zfmisc_1(k1_group_3(sK0),k1_group_3(sK0)),k1_group_3(sK0))
| ~ spl29_40 ),
inference(avatar_component_clause,[],[f1081]) ).
fof(f1083,plain,
( ~ m1_relset_1(k9_group_4(sK0),k2_zfmisc_1(k1_group_3(sK0),k1_group_3(sK0)),k1_group_3(sK0))
| spl29_40 ),
inference(avatar_component_clause,[],[f1081]) ).
fof(f1085,definition,
( spl29_41
<=> v1_funct_2(k9_group_4(sK0),k2_zfmisc_1(k1_group_3(sK0),k1_group_3(sK0)),k1_group_3(sK0)) ),
introduced(definition,[new_symbols(definition,[spl29_41])],[avatar_definition]) ).
fof(f1087,plain,
( ~ v1_funct_2(k9_group_4(sK0),k2_zfmisc_1(k1_group_3(sK0),k1_group_3(sK0)),k1_group_3(sK0))
| spl29_41 ),
inference(avatar_component_clause,[],[f1085]) ).
fof(f1089,definition,
( spl29_42
<=> v1_funct_1(k9_group_4(sK0)) ),
introduced(definition,[new_symbols(definition,[spl29_42])],[avatar_definition]) ).
fof(f1090,plain,
( v1_funct_1(k9_group_4(sK0))
| ~ spl29_42 ),
inference(avatar_component_clause,[],[f1089]) ).
fof(f1091,plain,
( ~ v1_funct_1(k9_group_4(sK0))
| spl29_42 ),
inference(avatar_component_clause,[],[f1089]) ).
fof(f1093,definition,
( spl29_43
<=> ! [X2,X0,X1] :
( g3_lattices(X0,X1,X2) != sF27
| k1_group_3(sK0) = X0 ) ),
introduced(definition,[new_symbols(definition,[spl29_43])],[avatar_definition]) ).
fof(f1094,plain,
( ! [X2,X0,X1] :
( g3_lattices(X0,X1,X2) != sF27
| k1_group_3(sK0) = X0 )
| ~ spl29_43 ),
inference(avatar_component_clause,[],[f1093]) ).
fof(f1095,plain,
( ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_41
| ~ spl29_42
| spl29_43 ),
inference(avatar_split_clause,[],[f1035,f1093,f1089,f1085,f1081,f1077,f1073,f1069]) ).
fof(f1096,plain,
( v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl29_42 ),
inference(resolution,[],[f1091,f304]) ).
fof(f1097,plain,
( ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl29_42 ),
inference(forward_subsumption_resolution,[],[f1096,f252]) ).
fof(f1098,plain,
( ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl29_42 ),
inference(forward_subsumption_resolution,[],[f1097,f251]) ).
fof(f1099,plain,
( ~ l1_group_1(sK0)
| spl29_42 ),
inference(forward_subsumption_resolution,[],[f1098,f250]) ).
fof(f1100,plain,
( $false
| spl29_42 ),
inference(forward_subsumption_resolution,[],[f1099,f249]) ).
fof(f1101,plain,
spl29_42,
inference(avatar_contradiction_clause,[],[f1100]) ).
fof(f1115,plain,
! [X0] :
( m1_relset_1(k10_group_4(X0),k2_zfmisc_1(k1_group_3(X0),k1_group_3(X0)),k1_group_3(X0))
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| v3_struct_0(X0) ),
inference(resolution,[],[f289,f369]) ).
fof(f1122,plain,
( ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| v3_struct_0(sK0)
| spl29_37 ),
inference(resolution,[],[f1115,f1071]) ).
fof(f1124,plain,
( ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| v3_struct_0(sK0)
| spl29_37 ),
inference(forward_subsumption_resolution,[],[f1122,f251]) ).
fof(f1125,plain,
( ~ l1_group_1(sK0)
| v3_struct_0(sK0)
| spl29_37 ),
inference(forward_subsumption_resolution,[],[f1124,f250]) ).
fof(f1126,plain,
( v3_struct_0(sK0)
| spl29_37 ),
inference(forward_subsumption_resolution,[],[f1125,f249]) ).
fof(f1127,plain,
( $false
| spl29_37 ),
inference(forward_subsumption_resolution,[],[f1126,f252]) ).
fof(f1128,plain,
spl29_37,
inference(avatar_contradiction_clause,[],[f1127]) ).
fof(f1129,plain,
( v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl29_38 ),
inference(resolution,[],[f1075,f290]) ).
fof(f1130,plain,
( ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl29_38 ),
inference(forward_subsumption_resolution,[],[f1129,f252]) ).
fof(f1131,plain,
( ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl29_38 ),
inference(forward_subsumption_resolution,[],[f1130,f251]) ).
fof(f1132,plain,
( ~ l1_group_1(sK0)
| spl29_38 ),
inference(forward_subsumption_resolution,[],[f1131,f250]) ).
fof(f1133,plain,
( $false
| spl29_38 ),
inference(forward_subsumption_resolution,[],[f1132,f249]) ).
fof(f1134,plain,
spl29_38,
inference(avatar_contradiction_clause,[],[f1133]) ).
fof(f1135,plain,
( v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl29_39 ),
inference(resolution,[],[f1079,f291]) ).
fof(f1136,plain,
( ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl29_39 ),
inference(forward_subsumption_resolution,[],[f1135,f252]) ).
fof(f1137,plain,
( ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl29_39 ),
inference(forward_subsumption_resolution,[],[f1136,f251]) ).
fof(f1138,plain,
( ~ l1_group_1(sK0)
| spl29_39 ),
inference(forward_subsumption_resolution,[],[f1137,f250]) ).
fof(f1139,plain,
( $false
| spl29_39 ),
inference(forward_subsumption_resolution,[],[f1138,f249]) ).
fof(f1140,plain,
spl29_39,
inference(avatar_contradiction_clause,[],[f1139]) ).
fof(f1141,plain,
( ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| v3_struct_0(sK0)
| spl29_40 ),
inference(resolution,[],[f1083,f1015]) ).
fof(f1142,plain,
( ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| v3_struct_0(sK0)
| spl29_40 ),
inference(forward_subsumption_resolution,[],[f1141,f251]) ).
fof(f1143,plain,
( ~ l1_group_1(sK0)
| v3_struct_0(sK0)
| spl29_40 ),
inference(forward_subsumption_resolution,[],[f1142,f250]) ).
fof(f1144,plain,
( v3_struct_0(sK0)
| spl29_40 ),
inference(forward_subsumption_resolution,[],[f1143,f249]) ).
fof(f1145,plain,
( $false
| spl29_40 ),
inference(forward_subsumption_resolution,[],[f1144,f252]) ).
fof(f1146,plain,
spl29_40,
inference(avatar_contradiction_clause,[],[f1145]) ).
fof(f1147,plain,
( v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl29_41 ),
inference(resolution,[],[f1087,f303]) ).
fof(f1148,plain,
( ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl29_41 ),
inference(forward_subsumption_resolution,[],[f1147,f252]) ).
fof(f1149,plain,
( ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| spl29_41 ),
inference(forward_subsumption_resolution,[],[f1148,f251]) ).
fof(f1150,plain,
( ~ l1_group_1(sK0)
| spl29_41 ),
inference(forward_subsumption_resolution,[],[f1149,f250]) ).
fof(f1151,plain,
( $false
| spl29_41 ),
inference(forward_subsumption_resolution,[],[f1150,f249]) ).
fof(f1152,plain,
spl29_41,
inference(avatar_contradiction_clause,[],[f1151]) ).
fof(f1173,plain,
( sF27 != sF27
| sF28 = k1_group_3(sK0)
| ~ spl29_12
| ~ spl29_43 ),
inference(superposition,[],[f1094,f823]) ).
fof(f1174,plain,
( sF28 = k1_group_3(sK0)
| ~ spl29_12
| ~ spl29_43 ),
inference(trivial_inequality_removal,[],[f1173]) ).
fof(f1176,plain,
( v1_funct_2(k10_group_4(sK0),k2_zfmisc_1(sF28,sF28),sF28)
| ~ spl29_12
| ~ spl29_38
| ~ spl29_43 ),
inference(superposition,[],[f1074,f1174]) ).
fof(f1177,plain,
( m1_relset_1(k9_group_4(sK0),k2_zfmisc_1(sF28,sF28),sF28)
| ~ spl29_12
| ~ spl29_40
| ~ spl29_43 ),
inference(superposition,[],[f1082,f1174]) ).
fof(f1178,plain,
( m1_relset_1(k10_group_4(sK0),k2_zfmisc_1(sF28,sF28),sF28)
| ~ spl29_12
| ~ spl29_37
| ~ spl29_43 ),
inference(superposition,[],[f1070,f1174]) ).
fof(f1179,plain,
( sF27 = g3_lattices(sF28,k9_group_4(sK0),k10_group_4(sK0))
| ~ spl29_12
| ~ spl29_43 ),
inference(superposition,[],[f645,f1174]) ).
fof(f1190,plain,
( v1_funct_2(k9_group_4(sK0),k2_zfmisc_1(sF28,sF28),sF28)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl29_12
| ~ spl29_43 ),
inference(superposition,[],[f303,f1174]) ).
fof(f1192,plain,
( ! [X0,X1] :
( ~ m1_subset_1(X0,sF28)
| ~ m1_group_2(X0,sK0)
| ~ m1_group_2(X1,sK0)
| k9_group_2(sK0,X1,X0) = k2_binop_1(sF28,sF28,sF28,k10_group_4(sK0),X1,X0)
| ~ m1_subset_1(X1,sF28)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) )
| ~ spl29_12
| ~ spl29_43 ),
inference(superposition,[],[f432,f1174]) ).
fof(f1197,plain,
( ! [X0,X1] :
( ~ m1_subset_1(X0,sF28)
| ~ m1_group_2(X0,sK0)
| ~ m1_group_2(X1,sK0)
| k9_group_2(sK0,X1,X0) = k2_binop_1(sF28,sF28,sF28,k10_group_4(sK0),X1,X0)
| ~ m1_subset_1(X1,sF28)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) )
| ~ spl29_12
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1192,f252]) ).
fof(f1198,plain,
( v1_funct_2(k9_group_4(sK0),k2_zfmisc_1(sF28,sF28),sF28)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl29_12
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1190,f252]) ).
fof(f1209,plain,
( ! [X0,X1] :
( ~ m1_subset_1(X0,sF28)
| ~ m1_group_2(X0,sK0)
| ~ m1_group_2(X1,sK0)
| k9_group_2(sK0,X1,X0) = k2_binop_1(sF28,sF28,sF28,k10_group_4(sK0),X1,X0)
| ~ m1_subset_1(X1,sF28)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0) )
| ~ spl29_12
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1197,f251]) ).
fof(f1210,plain,
( v1_funct_2(k9_group_4(sK0),k2_zfmisc_1(sF28,sF28),sF28)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ spl29_12
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1198,f251]) ).
fof(f1220,plain,
( ! [X0,X1] :
( ~ m1_subset_1(X0,sF28)
| ~ m1_group_2(X0,sK0)
| ~ m1_group_2(X1,sK0)
| k9_group_2(sK0,X1,X0) = k2_binop_1(sF28,sF28,sF28,k10_group_4(sK0),X1,X0)
| ~ m1_subset_1(X1,sF28)
| ~ l1_group_1(sK0) )
| ~ spl29_12
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1209,f250]) ).
fof(f1221,plain,
( v1_funct_2(k9_group_4(sK0),k2_zfmisc_1(sF28,sF28),sF28)
| ~ l1_group_1(sK0)
| ~ spl29_12
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1210,f250]) ).
fof(f1231,plain,
( ! [X0,X1] :
( ~ m1_subset_1(X1,sF28)
| ~ m1_group_2(X0,sK0)
| ~ m1_group_2(X1,sK0)
| k9_group_2(sK0,X1,X0) = k2_binop_1(sF28,sF28,sF28,k10_group_4(sK0),X1,X0)
| ~ m1_subset_1(X0,sF28) )
| ~ spl29_12
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1220,f249]) ).
fof(f1232,plain,
( v1_funct_2(k9_group_4(sK0),k2_zfmisc_1(sF28,sF28),sF28)
| ~ spl29_12
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1221,f249]) ).
fof(f1270,plain,
( ! [X0] :
( ~ m1_group_2(X0,sK0)
| ~ m1_group_2(sK3,sK0)
| k9_group_2(sK0,sK3,X0) = k2_binop_1(sF28,sF28,sF28,k10_group_4(sK0),sK3,X0)
| ~ m1_subset_1(X0,sF28) )
| ~ spl29_12
| ~ spl29_43 ),
inference(resolution,[],[f1231,f418]) ).
fof(f1271,plain,
( ! [X0] :
( ~ m1_subset_1(X0,sF28)
| k9_group_2(sK0,sK3,X0) = k2_binop_1(sF28,sF28,sF28,k10_group_4(sK0),sK3,X0)
| ~ m1_group_2(X0,sK0) )
| ~ spl29_12
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1270,f400]) ).
fof(f1273,plain,
( k9_group_2(sK0,sK3,sK4) = k2_binop_1(sF28,sF28,sF28,k10_group_4(sK0),sK3,sK4)
| ~ m1_group_2(sK4,sK0)
| ~ spl29_12
| ~ spl29_43 ),
inference(resolution,[],[f1271,f417]) ).
fof(f1276,plain,
( k9_group_2(sK0,sK3,sK4) = k2_binop_1(sF28,sF28,sF28,k10_group_4(sK0),sK3,sK4)
| ~ spl29_12
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1273,f399]) ).
fof(f1278,plain,
( sK3 = k2_binop_1(sF28,sF28,sF28,k10_group_4(sK0),sK3,sK4)
| ~ spl29_2
| ~ spl29_12
| ~ spl29_43 ),
inference(forward_demodulation,[],[f1276,f783]) ).
fof(f1384,plain,
( ! [X2,X0,X1] :
( g3_lattices(X0,X1,X2) != sF27
| k10_group_4(sK0) = X2
| ~ v1_funct_1(k9_group_4(sK0))
| ~ v1_funct_2(k9_group_4(sK0),k2_zfmisc_1(sF28,sF28),sF28)
| ~ m1_relset_1(k9_group_4(sK0),k2_zfmisc_1(sF28,sF28),sF28)
| ~ v1_funct_1(k10_group_4(sK0))
| ~ v1_funct_2(k10_group_4(sK0),k2_zfmisc_1(sF28,sF28),sF28)
| ~ m1_relset_1(k10_group_4(sK0),k2_zfmisc_1(sF28,sF28),sF28) )
| ~ spl29_12
| ~ spl29_43 ),
inference(superposition,[],[f346,f1179]) ).
fof(f1393,plain,
( ! [X2,X0,X1] :
( g3_lattices(X0,X1,X2) != sF27
| k10_group_4(sK0) = X2
| ~ v1_funct_2(k9_group_4(sK0),k2_zfmisc_1(sF28,sF28),sF28)
| ~ m1_relset_1(k9_group_4(sK0),k2_zfmisc_1(sF28,sF28),sF28)
| ~ v1_funct_1(k10_group_4(sK0))
| ~ v1_funct_2(k10_group_4(sK0),k2_zfmisc_1(sF28,sF28),sF28)
| ~ m1_relset_1(k10_group_4(sK0),k2_zfmisc_1(sF28,sF28),sF28) )
| ~ spl29_12
| ~ spl29_42
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1384,f1090]) ).
fof(f1396,plain,
( ! [X2,X0,X1] :
( g3_lattices(X0,X1,X2) != sF27
| k10_group_4(sK0) = X2
| ~ m1_relset_1(k9_group_4(sK0),k2_zfmisc_1(sF28,sF28),sF28)
| ~ v1_funct_1(k10_group_4(sK0))
| ~ v1_funct_2(k10_group_4(sK0),k2_zfmisc_1(sF28,sF28),sF28)
| ~ m1_relset_1(k10_group_4(sK0),k2_zfmisc_1(sF28,sF28),sF28) )
| ~ spl29_12
| ~ spl29_42
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1393,f1232]) ).
fof(f1399,plain,
( ! [X2,X0,X1] :
( g3_lattices(X0,X1,X2) != sF27
| k10_group_4(sK0) = X2
| ~ v1_funct_1(k10_group_4(sK0))
| ~ v1_funct_2(k10_group_4(sK0),k2_zfmisc_1(sF28,sF28),sF28)
| ~ m1_relset_1(k10_group_4(sK0),k2_zfmisc_1(sF28,sF28),sF28) )
| ~ spl29_12
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1396,f1177]) ).
fof(f1536,plain,
( ! [X0] :
( ~ m1_group_2(sK4,X0)
| ~ m1_group_2(sK3,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_subset_1(sK4,sF28)
| m1_group_2(sK3,sK4)
| ~ m1_subset_1(sK3,sF28)
| ~ m1_group_2(sK4,sK0)
| ~ m1_group_2(sK3,sK0) )
| ~ spl29_1 ),
inference(resolution,[],[f424,f646]) ).
fof(f1539,plain,
( ! [X0] :
( ~ m1_group_2(sK4,X0)
| ~ m1_group_2(sK3,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| m1_group_2(sK3,sK4)
| ~ m1_subset_1(sK3,sF28)
| ~ m1_group_2(sK4,sK0)
| ~ m1_group_2(sK3,sK0) )
| ~ spl29_1 ),
inference(forward_subsumption_resolution,[],[f1536,f417]) ).
fof(f1541,plain,
( ! [X0] :
( ~ m1_group_2(sK4,X0)
| ~ m1_group_2(sK3,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| m1_group_2(sK3,sK4)
| ~ m1_group_2(sK4,sK0)
| ~ m1_group_2(sK3,sK0) )
| ~ spl29_1 ),
inference(forward_subsumption_resolution,[],[f1539,f418]) ).
fof(f1543,plain,
( ! [X0] :
( ~ m1_group_2(sK4,X0)
| ~ m1_group_2(sK3,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| m1_group_2(sK3,sK4)
| ~ m1_group_2(sK3,sK0) )
| ~ spl29_1 ),
inference(forward_subsumption_resolution,[],[f1541,f399]) ).
fof(f1545,plain,
( ! [X0] :
( ~ m1_group_2(sK4,X0)
| ~ m1_group_2(sK3,X0)
| v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| m1_group_2(sK3,sK4) )
| ~ spl29_1 ),
inference(forward_subsumption_resolution,[],[f1543,f400]) ).
fof(f1548,definition,
( spl29_51
<=> m1_group_2(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl29_51])],[avatar_definition]) ).
fof(f1550,plain,
( m1_group_2(sK3,sK4)
| ~ spl29_51 ),
inference(avatar_component_clause,[],[f1548]) ).
fof(f1552,definition,
( spl29_52
<=> ! [X0] :
( ~ m1_group_2(sK4,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m1_group_2(sK3,X0) ) ),
introduced(definition,[new_symbols(definition,[spl29_52])],[avatar_definition]) ).
fof(f1553,plain,
( ! [X0] :
( ~ m1_group_2(sK4,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m1_group_2(sK3,X0) )
| ~ spl29_52 ),
inference(avatar_component_clause,[],[f1552]) ).
fof(f1554,plain,
( spl29_51
| spl29_52
| ~ spl29_1 ),
inference(avatar_split_clause,[],[f1545,f422,f1552,f1548]) ).
fof(f1571,plain,
( ~ m1_group_2(sK3,sK4)
| v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_group_2(sK4,sK0)
| spl29_2 ),
inference(resolution,[],[f427,f368]) ).
fof(f1572,plain,
( v3_struct_0(sK0)
| ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_group_2(sK4,sK0)
| spl29_2
| ~ spl29_51 ),
inference(forward_subsumption_resolution,[],[f1571,f1550]) ).
fof(f1573,plain,
( ~ v3_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_group_2(sK4,sK0)
| spl29_2
| ~ spl29_51 ),
inference(forward_subsumption_resolution,[],[f1572,f252]) ).
fof(f1574,plain,
( ~ v4_group_1(sK0)
| ~ l1_group_1(sK0)
| ~ m1_group_2(sK4,sK0)
| spl29_2
| ~ spl29_51 ),
inference(forward_subsumption_resolution,[],[f1573,f251]) ).
fof(f1575,plain,
( ~ l1_group_1(sK0)
| ~ m1_group_2(sK4,sK0)
| spl29_2
| ~ spl29_51 ),
inference(forward_subsumption_resolution,[],[f1574,f250]) ).
fof(f1576,plain,
( ~ m1_group_2(sK4,sK0)
| spl29_2
| ~ spl29_51 ),
inference(forward_subsumption_resolution,[],[f1575,f249]) ).
fof(f1577,plain,
( $false
| spl29_2
| ~ spl29_51 ),
inference(forward_subsumption_resolution,[],[f1576,f399]) ).
fof(f1578,plain,
( spl29_2
| ~ spl29_51 ),
inference(avatar_contradiction_clause,[],[f1577]) ).
fof(f1579,plain,
( ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0)
| ~ m1_group_2(sK3,sK0)
| ~ spl29_52 ),
inference(resolution,[],[f1553,f399]) ).
fof(f1581,plain,
( ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0)
| ~ m1_group_2(sK3,sK0)
| ~ spl29_52 ),
inference(forward_subsumption_resolution,[],[f1579,f249]) ).
fof(f1582,plain,
( ~ v3_group_1(sK0)
| v3_struct_0(sK0)
| ~ m1_group_2(sK3,sK0)
| ~ spl29_52 ),
inference(forward_subsumption_resolution,[],[f1581,f250]) ).
fof(f1583,plain,
( v3_struct_0(sK0)
| ~ m1_group_2(sK3,sK0)
| ~ spl29_52 ),
inference(forward_subsumption_resolution,[],[f1582,f251]) ).
fof(f1584,plain,
( ~ m1_group_2(sK3,sK0)
| ~ spl29_52 ),
inference(forward_subsumption_resolution,[],[f1583,f252]) ).
fof(f1585,plain,
( $false
| ~ spl29_52 ),
inference(forward_subsumption_resolution,[],[f1584,f400]) ).
fof(f1586,plain,
~ spl29_52,
inference(avatar_contradiction_clause,[],[f1585]) ).
fof(f1587,plain,
( sK3 = k9_group_2(sK0,sK3,sK4)
| ~ spl29_2
| ~ spl29_12
| ~ spl29_43 ),
inference(forward_demodulation,[],[f1278,f1276]) ).
fof(f1592,plain,
( ! [X2,X0,X1] :
( g3_lattices(X0,X1,X2) != sF27
| k10_group_4(sK0) = X2
| ~ v1_funct_2(k10_group_4(sK0),k2_zfmisc_1(sF28,sF28),sF28)
| ~ m1_relset_1(k10_group_4(sK0),k2_zfmisc_1(sF28,sF28),sF28) )
| ~ spl29_12
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1399,f1078]) ).
fof(f1597,plain,
( ! [X2,X0,X1] :
( g3_lattices(X0,X1,X2) != sF27
| k10_group_4(sK0) = X2
| ~ m1_relset_1(k10_group_4(sK0),k2_zfmisc_1(sF28,sF28),sF28) )
| ~ spl29_12
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1592,f1176]) ).
fof(f1600,plain,
( ! [X2,X0,X1] :
( g3_lattices(X0,X1,X2) != sF27
| k10_group_4(sK0) = X2 )
| ~ spl29_12
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1597,f1178]) ).
fof(f1621,plain,
( sF27 != sF27
| k10_group_4(sK0) = u1_lattices(sF27)
| ~ spl29_12
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(superposition,[],[f1600,f823]) ).
fof(f1622,plain,
( k10_group_4(sK0) = u1_lattices(sF27)
| ~ spl29_12
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(trivial_inequality_removal,[],[f1621]) ).
fof(f1625,plain,
( k2_lattices(sF27,sK3,sK4) = k2_binop_1(sF28,sF28,sF28,k10_group_4(sK0),sK3,sK4)
| ~ spl29_12
| spl29_16
| ~ spl29_22
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(superposition,[],[f906,f1622]) ).
fof(f1627,plain,
( k9_group_2(sK0,sK3,sK4) = k2_lattices(sF27,sK3,sK4)
| ~ spl29_12
| spl29_16
| ~ spl29_22
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(forward_demodulation,[],[f1625,f1276]) ).
fof(f1628,plain,
( sK3 = k2_lattices(sF27,sK3,sK4)
| ~ spl29_2
| ~ spl29_12
| spl29_16
| ~ spl29_22
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(forward_demodulation,[],[f1627,f1587]) ).
fof(f1630,plain,
( sK3 != sK3
| r1_lattices(sF27,sK3,sK4)
| ~ m1_subset_1(sK4,u1_struct_0(sF27))
| ~ m1_subset_1(sK3,u1_struct_0(sF27))
| v3_struct_0(sF27)
| ~ v8_lattices(sF27)
| ~ v9_lattices(sF27)
| ~ l3_lattices(sF27)
| ~ spl29_2
| ~ spl29_12
| spl29_16
| ~ spl29_22
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(superposition,[],[f383,f1628]) ).
fof(f1631,plain,
( r1_lattices(sF27,sK3,sK4)
| ~ m1_subset_1(sK4,u1_struct_0(sF27))
| ~ m1_subset_1(sK3,u1_struct_0(sF27))
| v3_struct_0(sF27)
| ~ v8_lattices(sF27)
| ~ v9_lattices(sF27)
| ~ l3_lattices(sF27)
| ~ spl29_2
| ~ spl29_12
| spl29_16
| ~ spl29_22
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(trivial_inequality_removal,[],[f1630]) ).
fof(f1632,plain,
( r1_lattices(sF27,sK3,sK4)
| ~ m1_subset_1(sK4,u1_struct_0(sF27))
| ~ m1_subset_1(sK3,u1_struct_0(sF27))
| ~ v8_lattices(sF27)
| ~ v9_lattices(sF27)
| ~ l3_lattices(sF27)
| ~ spl29_2
| ~ spl29_12
| spl29_16
| ~ spl29_22
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1631,f551]) ).
fof(f1633,plain,
( r1_lattices(sF27,sK3,sK4)
| ~ m1_subset_1(sK4,u1_struct_0(sF27))
| ~ m1_subset_1(sK3,u1_struct_0(sF27))
| ~ v9_lattices(sF27)
| ~ l3_lattices(sF27)
| ~ spl29_2
| ~ spl29_12
| ~ spl29_14
| spl29_16
| ~ spl29_22
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1632,f543]) ).
fof(f1634,plain,
( r1_lattices(sF27,sK3,sK4)
| ~ m1_subset_1(sK4,u1_struct_0(sF27))
| ~ m1_subset_1(sK3,u1_struct_0(sF27))
| ~ l3_lattices(sF27)
| ~ spl29_2
| ~ spl29_12
| ~ spl29_13
| ~ spl29_14
| spl29_16
| ~ spl29_22
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1633,f539]) ).
fof(f1635,plain,
( r1_lattices(sF27,sK3,sK4)
| ~ m1_subset_1(sK4,u1_struct_0(sF27))
| ~ m1_subset_1(sK3,u1_struct_0(sF27))
| ~ spl29_2
| ~ spl29_12
| ~ spl29_13
| ~ spl29_14
| spl29_16
| ~ spl29_22
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1634,f535]) ).
fof(f1636,plain,
( ~ m1_subset_1(sK4,sF28)
| r1_lattices(sF27,sK3,sK4)
| ~ m1_subset_1(sK3,u1_struct_0(sF27))
| ~ spl29_2
| ~ spl29_12
| ~ spl29_13
| ~ spl29_14
| spl29_16
| ~ spl29_22
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(forward_demodulation,[],[f1635,f416]) ).
fof(f1637,plain,
( r1_lattices(sF27,sK3,sK4)
| ~ m1_subset_1(sK3,u1_struct_0(sF27))
| ~ spl29_2
| ~ spl29_12
| ~ spl29_13
| ~ spl29_14
| spl29_16
| ~ spl29_22
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1636,f417]) ).
fof(f1638,plain,
( ~ m1_subset_1(sK3,sF28)
| r1_lattices(sF27,sK3,sK4)
| ~ spl29_2
| ~ spl29_12
| ~ spl29_13
| ~ spl29_14
| spl29_16
| ~ spl29_22
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(forward_demodulation,[],[f1637,f416]) ).
fof(f1639,plain,
( r1_lattices(sF27,sK3,sK4)
| ~ spl29_2
| ~ spl29_12
| ~ spl29_13
| ~ spl29_14
| spl29_16
| ~ spl29_22
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1638,f418]) ).
fof(f1641,plain,
( r3_lattices(sF27,sK3,sK4)
| v3_struct_0(sF27)
| ~ v6_lattices(sF27)
| ~ v8_lattices(sF27)
| ~ v9_lattices(sF27)
| ~ l3_lattices(sF27)
| ~ m1_subset_1(sK3,u1_struct_0(sF27))
| ~ m1_subset_1(sK4,u1_struct_0(sF27))
| ~ spl29_2
| ~ spl29_12
| ~ spl29_13
| ~ spl29_14
| spl29_16
| ~ spl29_22
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(resolution,[],[f1639,f374]) ).
fof(f1642,plain,
( v3_struct_0(sF27)
| ~ v6_lattices(sF27)
| ~ v8_lattices(sF27)
| ~ v9_lattices(sF27)
| ~ l3_lattices(sF27)
| ~ m1_subset_1(sK3,u1_struct_0(sF27))
| ~ m1_subset_1(sK4,u1_struct_0(sF27))
| spl29_1
| ~ spl29_2
| ~ spl29_12
| ~ spl29_13
| ~ spl29_14
| spl29_16
| ~ spl29_22
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1641,f423]) ).
fof(f1643,plain,
( ~ v6_lattices(sF27)
| ~ v8_lattices(sF27)
| ~ v9_lattices(sF27)
| ~ l3_lattices(sF27)
| ~ m1_subset_1(sK3,u1_struct_0(sF27))
| ~ m1_subset_1(sK4,u1_struct_0(sF27))
| spl29_1
| ~ spl29_2
| ~ spl29_12
| ~ spl29_13
| ~ spl29_14
| spl29_16
| ~ spl29_22
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1642,f551]) ).
fof(f1644,plain,
( ~ v8_lattices(sF27)
| ~ v9_lattices(sF27)
| ~ l3_lattices(sF27)
| ~ m1_subset_1(sK3,u1_struct_0(sF27))
| ~ m1_subset_1(sK4,u1_struct_0(sF27))
| spl29_1
| ~ spl29_2
| ~ spl29_12
| ~ spl29_13
| ~ spl29_14
| ~ spl29_15
| spl29_16
| ~ spl29_22
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1643,f547]) ).
fof(f1645,plain,
( ~ v9_lattices(sF27)
| ~ l3_lattices(sF27)
| ~ m1_subset_1(sK3,u1_struct_0(sF27))
| ~ m1_subset_1(sK4,u1_struct_0(sF27))
| spl29_1
| ~ spl29_2
| ~ spl29_12
| ~ spl29_13
| ~ spl29_14
| ~ spl29_15
| spl29_16
| ~ spl29_22
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1644,f543]) ).
fof(f1646,plain,
( ~ l3_lattices(sF27)
| ~ m1_subset_1(sK3,u1_struct_0(sF27))
| ~ m1_subset_1(sK4,u1_struct_0(sF27))
| spl29_1
| ~ spl29_2
| ~ spl29_12
| ~ spl29_13
| ~ spl29_14
| ~ spl29_15
| spl29_16
| ~ spl29_22
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1645,f539]) ).
fof(f1647,plain,
( ~ m1_subset_1(sK3,u1_struct_0(sF27))
| ~ m1_subset_1(sK4,u1_struct_0(sF27))
| spl29_1
| ~ spl29_2
| ~ spl29_12
| ~ spl29_13
| ~ spl29_14
| ~ spl29_15
| spl29_16
| ~ spl29_22
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1646,f535]) ).
fof(f1648,plain,
( ~ m1_subset_1(sK3,sF28)
| ~ m1_subset_1(sK4,u1_struct_0(sF27))
| spl29_1
| ~ spl29_2
| ~ spl29_12
| ~ spl29_13
| ~ spl29_14
| ~ spl29_15
| spl29_16
| ~ spl29_22
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(forward_demodulation,[],[f1647,f416]) ).
fof(f1649,plain,
( ~ m1_subset_1(sK4,u1_struct_0(sF27))
| spl29_1
| ~ spl29_2
| ~ spl29_12
| ~ spl29_13
| ~ spl29_14
| ~ spl29_15
| spl29_16
| ~ spl29_22
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1648,f418]) ).
fof(f1650,plain,
( ~ m1_subset_1(sK4,sF28)
| spl29_1
| ~ spl29_2
| ~ spl29_12
| ~ spl29_13
| ~ spl29_14
| ~ spl29_15
| spl29_16
| ~ spl29_22
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(forward_demodulation,[],[f1649,f416]) ).
fof(f1651,plain,
( $false
| spl29_1
| ~ spl29_2
| ~ spl29_12
| ~ spl29_13
| ~ spl29_14
| ~ spl29_15
| spl29_16
| ~ spl29_22
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(forward_subsumption_resolution,[],[f1650,f417]) ).
fof(f1652,plain,
( spl29_1
| ~ spl29_2
| ~ spl29_12
| ~ spl29_13
| ~ spl29_14
| ~ spl29_15
| spl29_16
| ~ spl29_22
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(avatar_contradiction_clause,[],[f1651]) ).
cnf(s1,plain,
( spl29_1
| spl29_2 ),
inference(sat_conversion,[],[f429]) ).
cnf(s2,plain,
( ~ spl29_1
| ~ spl29_2 ),
inference(sat_conversion,[],[f430]) ).
cnf(s7,plain,
~ spl29_16,
inference(sat_conversion,[],[f578]) ).
cnf(s8,plain,
spl29_13,
inference(sat_conversion,[],[f584]) ).
cnf(s9,plain,
spl29_15,
inference(sat_conversion,[],[f590]) ).
cnf(s10,plain,
spl29_14,
inference(sat_conversion,[],[f597]) ).
cnf(s11,plain,
spl29_12,
inference(sat_conversion,[],[f604]) ).
cnf(s17,plain,
( ~ spl29_12
| spl29_22 ),
inference(sat_conversion,[],[f722]) ).
cnf(s24,plain,
( ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_41
| ~ spl29_42
| spl29_43 ),
inference(sat_conversion,[],[f1095]) ).
cnf(s25,plain,
spl29_42,
inference(sat_conversion,[],[f1101]) ).
cnf(s26,plain,
spl29_37,
inference(sat_conversion,[],[f1128]) ).
cnf(s27,plain,
spl29_38,
inference(sat_conversion,[],[f1134]) ).
cnf(s28,plain,
spl29_39,
inference(sat_conversion,[],[f1140]) ).
cnf(s29,plain,
spl29_40,
inference(sat_conversion,[],[f1146]) ).
cnf(s30,plain,
spl29_41,
inference(sat_conversion,[],[f1152]) ).
cnf(s41,plain,
( ~ spl29_1
| spl29_51
| spl29_52 ),
inference(sat_conversion,[],[f1554]) ).
cnf(s42,plain,
( spl29_2
| ~ spl29_51 ),
inference(sat_conversion,[],[f1578]) ).
cnf(s43,plain,
~ spl29_52,
inference(sat_conversion,[],[f1586]) ).
cnf(s45,plain,
( spl29_1
| ~ spl29_2
| ~ spl29_12
| ~ spl29_13
| ~ spl29_14
| ~ spl29_15
| spl29_16
| ~ spl29_22
| ~ spl29_37
| ~ spl29_38
| ~ spl29_39
| ~ spl29_40
| ~ spl29_42
| ~ spl29_43 ),
inference(sat_conversion,[],[f1652]) ).
cnf(s46,plain,
( ~ spl29_1
| spl29_51 ),
inference(rat,[],[s41,s43]) ).
cnf(s49,plain,
spl29_43,
inference(rat,[],[s24,s25,s30,s29,s28,s27,s26]) ).
cnf(s51,plain,
spl29_22,
inference(rat,[],[s17,s11]) ).
cnf(s57,plain,
spl29_1,
inference(rat,[],[s1,s45,s11,s8,s10,s9,s7,s51,s26,s27,s28,s29,s25,s49]) ).
cnf(s58,plain,
spl29_51,
inference(rat,[],[s46,s57]) ).
cnf(s59,plain,
~ spl29_2,
inference(rat,[],[s2,s57]) ).
cnf(s60,plain,
$false,
inference(rat,[],[s42,s58,s59]) ).
fof(f1653,plain,
$false,
inference(avatar_sat_refutation,[],[s60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP648+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.43 % Computer : n008.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sun Sep 27 10:27:39 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.49 Running first-order theorem proving
% 0.23/0.49 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
% 4.94/2.15 % (1017472)Detected formulas, will run a generic FOF schedule.
% 4.94/2.15 % (1017479)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=1835729356:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.94/2.15 % (1017485)dis-21_1_sil=8000:lcm=predicate:random_seed=2448312551: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)
% 4.94/2.15 % (1017485)Instruction limit reached!
% 4.94/2.15 % (1017485)------------------------------
% 4.94/2.15 % (1017485)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.94/2.15 % (1017485)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.94/2.15 % (1017485)CaDiCaL version: 2.1.3
% 4.94/2.15 % (1017485)Termination reason: Instruction limit
% 4.94/2.15 % (1017485)Termination phase: Saturation
% 4.94/2.15 % (1017485)Time elapsed: 0.081 s
% 4.94/2.15 % (1017485)Peak memory usage: 90 MB
% 4.94/2.15 % (1017485)Instructions burned: 130 (million)
% 4.94/2.15 % (1017483)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1391310301:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.94/2.15 % (1017481)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=1947980520:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.94/2.15 % (1017480)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=3691091129:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.94/2.15 % (1017482)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3497306943:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.94/2.15 % (1017484)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1463949720:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.94/2.15 % (1017482)Refutation not found, incomplete strategy
% 4.94/2.15 % (1017482)------------------------------
% 4.94/2.15 % (1017482)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.94/2.15 % (1017482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.94/2.15 % (1017482)CaDiCaL version: 2.1.3
% 4.94/2.15 % (1017482)Termination reason: Refutation not found, incomplete strategy
% 4.94/2.15 % (1017482)Time elapsed: 0.005 s
% 4.94/2.15 % (1017482)Peak memory usage: 88 MB
% 4.94/2.15 % (1017482)Instructions burned: 3 (million)
% 4.94/2.15 % (1017483)Instruction limit reached!
% 4.94/2.15 % (1017483)------------------------------
% 4.94/2.15 % (1017483)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.94/2.15 % (1017483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.94/2.15 % (1017483)CaDiCaL version: 2.1.3
% 4.94/2.15 % (1017483)Termination reason: Instruction limit
% 4.94/2.15 % (1017483)Termination phase: Saturation
% 4.94/2.15 % (1017483)Time elapsed: 0.097 s
% 4.94/2.15 % (1017483)Peak memory usage: 88 MB
% 4.94/2.15 % (1017483)Instructions burned: 119 (million)
% 4.94/2.15 % (1017484)Instruction limit reached!
% 4.94/2.15 % (1017484)------------------------------
% 4.94/2.15 % (1017484)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.94/2.15 % (1017484)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.94/2.15 % (1017484)CaDiCaL version: 2.1.3
% 4.94/2.15 % (1017484)Termination reason: Instruction limit
% 4.94/2.15 % (1017484)Termination phase: Saturation
% 4.94/2.15 % (1017484)Time elapsed: 0.154 s
% 4.94/2.15 % (1017484)Peak memory usage: 90 MB
% 4.94/2.15 % (1017484)Instructions burned: 139 (million)
% 4.94/2.15 % (1017488)lrs+10_1_sil=8000:sp=occurrence:random_seed=2589941963:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.94/2.15 % (1017494)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1690826944:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 4.94/2.15 % (1017495)lrs+1011_1_sil=32000:sp=occurrence:random_seed=520604521:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 4.94/2.15 % (1017482)------------------------------
% 4.94/2.15 % (1017482)------------------------------
% 4.94/2.15 % (1017494)Instruction limit reached!
% 4.94/2.15 % (1017494)------------------------------
% 4.94/2.15 % (1017494)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.94/2.15 % (1017494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.94/2.15 % (1017494)CaDiCaL version: 2.1.3
% 4.94/2.15 % (1017494)Termination reason: Instruction limit
% 4.94/2.15 % (1017494)Termination phase: Saturation
% 4.94/2.15 % (1017494)Time elapsed: 0.120 s
% 4.94/2.15 % (1017494)Peak memory usage: 89 MB
% 4.94/2.15 % (1017494)Instructions burned: 157 (million)
% 4.94/2.15 % (1017488)Instruction limit reached!
% 4.94/2.15 % (1017488)------------------------------
% 4.94/2.15 % (1017488)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.94/2.15 % (1017488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.94/2.15 % (1017488)CaDiCaL version: 2.1.3
% 4.94/2.15 % (1017488)Termination reason: Instruction limit
% 4.94/2.15 % (1017488)Termination phase: Saturation
% 4.94/2.15 % (1017488)Time elapsed: 0.283 s
% 4.94/2.15 % (1017488)Peak memory usage: 92 MB
% 4.94/2.15 % (1017488)Instructions burned: 285 (million)
% 4.94/2.15 % (1017479)First to succeed.
% 4.94/2.15 % (1017479)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1017472"
% 4.94/2.15 % (1017495)Instruction limit reached!
% 4.94/2.15 % (1017495)------------------------------
% 4.94/2.15 % (1017495)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.94/2.15 % (1017495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.94/2.15 % (1017495)CaDiCaL version: 2.1.3
% 4.94/2.15 % (1017495)Termination reason: Instruction limit
% 4.94/2.15 % (1017495)Termination phase: Saturation
% 4.94/2.15 % (1017495)Time elapsed: 0.274 s
% 4.94/2.15 % (1017495)Peak memory usage: 91 MB
% 4.94/2.15 % (1017495)Instructions burned: 325 (million)
% 4.94/2.15 % (1017503)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=80001958:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2992 on theBenchmark for (2992ds/294Mi)
% 4.94/2.15 % (1017503)Refutation not found, incomplete strategy
% 4.94/2.15 % (1017503)------------------------------
% 4.94/2.15 % (1017503)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.94/2.15 % (1017503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.94/2.15 % (1017503)CaDiCaL version: 2.1.3
% 4.94/2.15 % (1017503)Termination reason: Refutation not found, incomplete strategy
% 4.94/2.15 % (1017503)Time elapsed: 0.009 s
% 4.94/2.15 % (1017503)Peak memory usage: 88 MB
% 4.94/2.15 % (1017503)Instructions burned: 7 (million)
% 4.94/2.15 % (1017502)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=1054922477:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 4.94/2.15 % (1017504)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2657101970:i=2350_2992 on theBenchmark for (2992ds/2350Mi)
% 4.94/2.15 % (1017479)Refutation found. Thanks to Tanya!
% 4.94/2.15 % SZS status Theorem for theBenchmark
% 4.94/2.15 % SZS output start Proof for theBenchmark
% See solution above
% 8.40/2.34 % (1017479)------------------------------
% 8.40/2.34 % (1017479)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.40/2.34 % (1017479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.40/2.34 % (1017479)CaDiCaL version: 2.1.3
% 8.40/2.34 % (1017479)Termination reason: Refutation
% 8.40/2.34 % (1017479)Time elapsed: 0.644 s
% 8.40/2.34 % (1017479)Peak memory usage: 132 MB
% 8.40/2.34 % (1017479)Instructions burned: 1162 (million)
% 8.40/2.34 % (1017479)------------------------------
% 8.40/2.34 % (1017479)------------------------------
% 8.40/2.34 % (1017472)Success in time 1.074 s
% 8.40/2.34 % Vampire exiting
%------------------------------------------------------------------------------