%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP653+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 : Thu Sep 24 08:42:10 AM UTC 2026
% Result : Theorem 34.65s 35.02s
% Output : Proof 34.78s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(t38_latsubgr,conjecture,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_group_1(B)
& v4_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) )
=> ( v2_funct_1(C)
=> m1_lattice4(k3_latsubgr(A,B,C),k11_group_4(A),k11_group_4(B)) ) ) ) ),
file('theBenchmark.p',t38_latsubgr) ).
fof(abstractness_v3_lattices,axiom,
! [A] :
( l3_lattices(A)
=> ( v3_lattices(A)
=> A = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) ) ),
file('theBenchmark.p',abstractness_v3_lattices) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( r2_hidden(A,B)
=> ~ r2_hidden(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(cc1_funct_2,axiom,
! [A,B,C] :
( m1_relset_1(C,A,B)
=> ( ( v1_partfun1(C,A,B)
& v1_funct_1(C) )
=> ( v1_funct_2(C,A,B)
& v1_funct_1(C) ) ) ),
file('theBenchmark.p',cc1_funct_2) ).
fof(cc1_relset_1,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> v1_relat_1(C) ),
file('theBenchmark.p',cc1_relset_1) ).
fof(cc5_funct_2,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_relset_1(C,A,B)
=> ( ( v1_funct_2(C,A,B)
& v1_funct_1(C) )
=> ( v1_funct_2(C,A,B)
& v1_partfun1(C,A,B)
& v1_funct_1(C) ) ) ) ),
file('theBenchmark.p',cc5_funct_2) ).
fof(cc6_funct_2,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& ~ v1_xboole_0(A) )
=> ! [C] :
( m1_relset_1(C,A,B)
=> ( ( v1_funct_2(C,A,B)
& v1_funct_1(C) )
=> ( v1_funct_2(C,A,B)
& v1_partfun1(C,A,B)
& ~ v1_xboole_0(C)
& v1_funct_1(C) ) ) ) ),
file('theBenchmark.p',cc6_funct_2) ).
fof(dt_g3_lattices,axiom,
! [A,B,C] :
( ( m1_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(C)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& v1_funct_1(B) )
=> ( l3_lattices(g3_lattices(A,B,C))
& v3_lattices(g3_lattices(A,B,C)) ) ),
file('theBenchmark.p',dt_g3_lattices) ).
fof(dt_k11_group_4,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ( l3_lattices(k11_group_4(A))
& v10_lattices(k11_group_4(A))
& v3_lattices(k11_group_4(A))
& ~ v3_struct_0(k11_group_4(A)) ) ),
file('theBenchmark.p',dt_k11_group_4) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(dt_k2_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k2_zfmisc_1) ).
fof(dt_k3_latsubgr,axiom,
! [A,B,C] :
( ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C)
& l1_group_1(B)
& v4_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B)
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ( m2_relset_1(k3_latsubgr(A,B,C),u1_struct_0(k11_group_4(A)),u1_struct_0(k11_group_4(B)))
& v1_funct_2(k3_latsubgr(A,B,C),u1_struct_0(k11_group_4(A)),u1_struct_0(k11_group_4(B)))
& v1_funct_1(k3_latsubgr(A,B,C)) ) ),
file('theBenchmark.p',dt_k3_latsubgr) ).
fof(dt_l1_group_1,axiom,
! [A] :
( l1_group_1(A)
=> l1_struct_0(A) ),
file('theBenchmark.p',dt_l1_group_1) ).
fof(dt_l1_lattices,axiom,
! [A] :
( l1_lattices(A)
=> l1_struct_0(A) ),
file('theBenchmark.p',dt_l1_lattices) ).
fof(dt_l1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_l1_struct_0) ).
fof(dt_l2_lattices,axiom,
! [A] :
( l2_lattices(A)
=> l1_struct_0(A) ),
file('theBenchmark.p',dt_l2_lattices) ).
fof(dt_l3_lattices,axiom,
! [A] :
( l3_lattices(A)
=> ( l2_lattices(A)
& l1_lattices(A) ) ),
file('theBenchmark.p',dt_l3_lattices) ).
fof(dt_m1_lattice4,axiom,
! [A,B] :
( ( l3_lattices(B)
& v10_lattices(B)
& ~ v3_struct_0(B)
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [C] :
( m1_lattice4(C,A,B)
=> ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) ) ) ),
file('theBenchmark.p',dt_m1_lattice4) ).
fof(dt_m1_relset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_relset_1) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(dt_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
=> m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
file('theBenchmark.p',dt_m2_relset_1) ).
fof(dt_m3_vectsp_8,axiom,
! [A,B] :
( ( l3_lattices(B)
& v10_lattices(B)
& ~ v3_struct_0(B)
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [C] :
( m3_vectsp_8(C,A,B)
=> ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) ) ) ),
file('theBenchmark.p',dt_m3_vectsp_8) ).
fof(dt_m4_vectsp_8,axiom,
! [A,B] :
( ( l3_lattices(B)
& v10_lattices(B)
& ~ v3_struct_0(B)
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [C] :
( m4_vectsp_8(C,A,B)
=> ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) ) ) ),
file('theBenchmark.p',dt_m4_vectsp_8) ).
fof(dt_u1_lattices,axiom,
! [A] :
( l1_lattices(A)
=> ( m2_relset_1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_1(u1_lattices(A)) ) ),
file('theBenchmark.p',dt_u1_lattices) ).
fof(dt_u1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_u1_struct_0) ).
fof(dt_u2_lattices,axiom,
! [A] :
( l2_lattices(A)
=> ( m2_relset_1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_1(u2_lattices(A)) ) ),
file('theBenchmark.p',dt_u2_lattices) ).
fof(existence_l1_group_1,axiom,
? [A] : l1_group_1(A),
file('theBenchmark.p',existence_l1_group_1) ).
fof(existence_l1_lattices,axiom,
? [A] : l1_lattices(A),
file('theBenchmark.p',existence_l1_lattices) ).
fof(existence_l1_struct_0,axiom,
? [A] : l1_struct_0(A),
file('theBenchmark.p',existence_l1_struct_0) ).
fof(existence_l2_lattices,axiom,
? [A] : l2_lattices(A),
file('theBenchmark.p',existence_l2_lattices) ).
fof(existence_l3_lattices,axiom,
? [A] : l3_lattices(A),
file('theBenchmark.p',existence_l3_lattices) ).
fof(existence_m1_lattice4,axiom,
! [A,B] :
( ( l3_lattices(B)
& v10_lattices(B)
& ~ v3_struct_0(B)
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ? [C] : m1_lattice4(C,A,B) ),
file('theBenchmark.p',existence_m1_lattice4) ).
fof(existence_m1_relset_1,axiom,
! [A,B] :
? [C] : m1_relset_1(C,A,B),
file('theBenchmark.p',existence_m1_relset_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : m1_subset_1(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(existence_m2_relset_1,axiom,
! [A,B] :
? [C] : m2_relset_1(C,A,B),
file('theBenchmark.p',existence_m2_relset_1) ).
fof(existence_m3_vectsp_8,axiom,
! [A,B] :
( ( l3_lattices(B)
& v10_lattices(B)
& ~ v3_struct_0(B)
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ? [C] : m3_vectsp_8(C,A,B) ),
file('theBenchmark.p',existence_m3_vectsp_8) ).
fof(existence_m4_vectsp_8,axiom,
! [A,B] :
( ( l3_lattices(B)
& v10_lattices(B)
& ~ v3_struct_0(B)
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ? [C] : m4_vectsp_8(C,A,B) ),
file('theBenchmark.p',existence_m4_vectsp_8) ).
fof(fc1_group_4,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ( v15_lattices(k11_group_4(A))
& v14_lattices(k11_group_4(A))
& v13_lattices(k11_group_4(A))
& v10_lattices(k11_group_4(A))
& v9_lattices(k11_group_4(A))
& v8_lattices(k11_group_4(A))
& v7_lattices(k11_group_4(A))
& v6_lattices(k11_group_4(A))
& v5_lattices(k11_group_4(A))
& v4_lattices(k11_group_4(A))
& v3_lattices(k11_group_4(A))
& ~ v3_struct_0(k11_group_4(A)) ) ),
file('theBenchmark.p',fc1_group_4) ).
fof(fc1_struct_0,axiom,
! [A] :
( ( l1_struct_0(A)
& ~ v3_struct_0(A) )
=> ~ v1_xboole_0(u1_struct_0(A)) ),
file('theBenchmark.p',fc1_struct_0) ).
fof(fc1_subset_1,axiom,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(fc1_xboole_0,axiom,
v1_xboole_0(k1_xboole_0),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc4_subset_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& ~ v1_xboole_0(A) )
=> ~ v1_xboole_0(k2_zfmisc_1(A,B)) ),
file('theBenchmark.p',fc4_subset_1) ).
fof(free_g3_lattices,axiom,
! [A,B,C] :
( ( m1_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(C)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& v1_funct_1(B) )
=> ! [D,E,F] :
( g3_lattices(A,B,C) = g3_lattices(D,E,F)
=> ( C = F
& B = E
& A = D ) ) ),
file('theBenchmark.p',free_g3_lattices) ).
fof(rc1_funct_2,axiom,
! [A,B] :
? [C] :
( v1_funct_2(C,A,B)
& v1_funct_1(C)
& v1_relat_1(C)
& m1_relset_1(C,A,B) ),
file('theBenchmark.p',rc1_funct_2) ).
fof(rc1_partfun1,axiom,
? [A] :
( v1_xboole_0(A)
& v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A) ),
file('theBenchmark.p',rc1_partfun1) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) ) ),
file('theBenchmark.p',rc1_subset_1) ).
fof(rc1_xboole_0,axiom,
? [A] : v1_xboole_0(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_partfun1,axiom,
! [A,B] :
? [C] :
( v1_funct_1(C)
& v1_relat_1(C)
& m1_relset_1(C,A,B) ),
file('theBenchmark.p',rc2_partfun1) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ v1_xboole_0(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(rc3_struct_0,axiom,
? [A] :
( ~ v3_struct_0(A)
& l1_struct_0(A) ),
file('theBenchmark.p',rc3_struct_0) ).
fof(rc5_struct_0,axiom,
! [A] :
( ( l1_struct_0(A)
& ~ v3_struct_0(A) )
=> ? [B] :
( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ),
file('theBenchmark.p',rc5_struct_0) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
<=> m1_relset_1(C,A,B) ),
file('theBenchmark.p',redefinition_m2_relset_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : r1_tarski(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t11_vectsp_8,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l3_lattices(B)
& v10_lattices(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) )
=> ( m1_lattice4(C,A,B)
<=> ( m3_vectsp_8(C,A,B)
& m4_vectsp_8(C,A,B) ) ) ) ) ),
file('theBenchmark.p',t11_vectsp_8) ).
fof(t1_subset,axiom,
! [A,B] :
( r2_hidden(A,B)
=> m1_subset_1(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t2_subset,axiom,
! [A,B] :
( m1_subset_1(A,B)
=> ( r2_hidden(A,B)
| v1_xboole_0(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t36_latsubgr,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_group_1(B)
& v4_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) )
=> ( v2_funct_1(C)
=> m3_vectsp_8(k3_latsubgr(A,B,C),k11_group_4(A),k11_group_4(B)) ) ) ) ),
file('theBenchmark.p',t36_latsubgr) ).
fof(t37_latsubgr,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_group_1(B)
& v4_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) )
=> m4_vectsp_8(k3_latsubgr(A,B,C),k11_group_4(A),k11_group_4(B)) ) ) ),
file('theBenchmark.p',t37_latsubgr) ).
fof(t3_subset,axiom,
! [A,B] :
( m1_subset_1(A,k1_zfmisc_1(B))
<=> r1_tarski(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_zfmisc_1(C))
& r2_hidden(A,B) )
=> m1_subset_1(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( v1_xboole_0(C)
& m1_subset_1(B,k1_zfmisc_1(C))
& r2_hidden(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t6_boole,axiom,
! [A] :
( v1_xboole_0(A)
=> A = k1_xboole_0 ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(B)
& r2_hidden(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(B)
& A != B
& v1_xboole_0(A) ),
file('theBenchmark.p',t8_boole) ).
fof(f_1_1,negated_conjecture,
~ ! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_group_1(B)
& v4_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) )
=> ( v2_funct_1(C)
=> m1_lattice4(k3_latsubgr(A,B,C),k11_group_4(A),k11_group_4(B)) ) ) ) ),
inference(negate,[status(cth)],[t38_latsubgr]) ).
fof(f_1_2,negated_conjecture,
? [A] :
( ? [B] :
( ? [C] :
( ~ m1_lattice4(k3_latsubgr(A,B,C),k11_group_4(A),k11_group_4(B))
& v2_funct_1(C)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) )
& l1_group_1(B)
& v4_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
? [U_2] :
( ? [U_1] :
( ? [U_0] :
( ~ m1_lattice4(k3_latsubgr(U_2,U_1,U_0),k11_group_4(U_2),k11_group_4(U_1))
& v2_funct_1(U_0)
& m2_relset_1(U_0,u1_struct_0(U_2),u1_struct_0(U_1))
& v1_group_6(U_0,U_2,U_1)
& v1_funct_2(U_0,u1_struct_0(U_2),u1_struct_0(U_1))
& v1_funct_1(U_0) )
& l1_group_1(U_1)
& v4_group_1(U_1)
& v3_group_1(U_1)
& ~ v3_struct_0(U_1) )
& l1_group_1(U_2)
& v4_group_1(U_2)
& v3_group_1(U_2)
& ~ v3_struct_0(U_2) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
( ? [U_1] :
( ? [U_0] :
( ~ m1_lattice4(k3_latsubgr(sK1,U_1,U_0),k11_group_4(sK1),k11_group_4(U_1))
& v2_funct_1(U_0)
& m2_relset_1(U_0,u1_struct_0(sK1),u1_struct_0(U_1))
& v1_group_6(U_0,sK1,U_1)
& v1_funct_2(U_0,u1_struct_0(sK1),u1_struct_0(U_1))
& v1_funct_1(U_0) )
& l1_group_1(U_1)
& v4_group_1(U_1)
& v3_group_1(U_1)
& ~ v3_struct_0(U_1) )
& l1_group_1(sK1)
& v4_group_1(sK1)
& v3_group_1(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_2,sK1)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
( ? [U_0] :
( ~ m1_lattice4(k3_latsubgr(sK1,sK2,U_0),k11_group_4(sK1),k11_group_4(sK2))
& v2_funct_1(U_0)
& m2_relset_1(U_0,u1_struct_0(sK1),u1_struct_0(sK2))
& v1_group_6(U_0,sK1,sK2)
& v1_funct_2(U_0,u1_struct_0(sK1),u1_struct_0(sK2))
& v1_funct_1(U_0) )
& l1_group_1(sK2)
& v4_group_1(sK2)
& v3_group_1(sK2)
& ~ v3_struct_0(sK2)
& l1_group_1(sK1)
& v4_group_1(sK1)
& v3_group_1(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_1,sK2)],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( ~ m1_lattice4(k3_latsubgr(sK1,sK2,sK3),k11_group_4(sK1),k11_group_4(sK2))
& v2_funct_1(sK3)
& m2_relset_1(sK3,u1_struct_0(sK1),u1_struct_0(sK2))
& v1_group_6(sK3,sK1,sK2)
& v1_funct_2(sK3,u1_struct_0(sK1),u1_struct_0(sK2))
& v1_funct_1(sK3)
& l1_group_1(sK2)
& v4_group_1(sK2)
& v3_group_1(sK2)
& ~ v3_struct_0(sK2)
& l1_group_1(sK1)
& v4_group_1(sK1)
& v3_group_1(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_0,sK3)],[f_1_5]) ).
fof(f_1_7,negated_conjecture,
( ~ m1_lattice4(k3_latsubgr(sK1,sK2,sK3),k11_group_4(sK1),k11_group_4(sK2))
& v2_funct_1(sK3)
& m2_relset_1(sK3,u1_struct_0(sK1),u1_struct_0(sK2))
& v1_group_6(sK3,sK1,sK2)
& v1_funct_2(sK3,u1_struct_0(sK1),u1_struct_0(sK2))
& v1_funct_1(sK3)
& l1_group_1(sK2)
& v4_group_1(sK2)
& v3_group_1(sK2)
& ~ v3_struct_0(sK2)
& l1_group_1(sK1)
& v4_group_1(sK1)
& v3_group_1(sK1)
& ~ v3_struct_0(sK1) ),
inference(definitional_conversion,[status(esa)],[f_1_6]) ).
cnf(f_1_8,negated_conjecture,
~ v3_struct_0(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_9,negated_conjecture,
v3_group_1(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_10,negated_conjecture,
v4_group_1(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_11,negated_conjecture,
l1_group_1(sK1),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_12,negated_conjecture,
~ v3_struct_0(sK2),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_13,negated_conjecture,
v3_group_1(sK2),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_14,negated_conjecture,
v4_group_1(sK2),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_15,negated_conjecture,
l1_group_1(sK2),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_16,negated_conjecture,
v1_funct_1(sK3),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_17,negated_conjecture,
v1_funct_2(sK3,u1_struct_0(sK1),u1_struct_0(sK2)),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_18,negated_conjecture,
v1_group_6(sK3,sK1,sK2),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_19,negated_conjecture,
m2_relset_1(sK3,u1_struct_0(sK1),u1_struct_0(sK2)),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_20,negated_conjecture,
v2_funct_1(sK3),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_21,negated_conjecture,
~ m1_lattice4(k3_latsubgr(sK1,sK2,sK3),k11_group_4(sK1),k11_group_4(sK2)),
inference(clausify,[status(thm)],[f_1_7]) ).
fof(f_2_1,plain,
! [A] :
( A = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A))
| ~ v3_lattices(A)
| ~ l3_lattices(A) ),
inference(fof_nnf,[status(thm)],[abstractness_v3_lattices]) ).
fof(f_2_2,plain,
! [U_3] :
( U_3 = g3_lattices(u1_struct_0(U_3),u2_lattices(U_3),u1_lattices(U_3))
| ~ v3_lattices(U_3)
| ~ l3_lattices(U_3) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_3] :
( U_3 = g3_lattices(u1_struct_0(U_3),u2_lattices(U_3),u1_lattices(U_3))
| ~ v3_lattices(U_3)
| ~ l3_lattices(U_3) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( U_3 = g3_lattices(u1_struct_0(U_3),u2_lattices(U_3),u1_lattices(U_3))
| ~ v3_lattices(U_3)
| ~ l3_lattices(U_3) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A,B] :
( ~ r2_hidden(B,A)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_3_2,plain,
! [U_5,U_4] :
( ~ r2_hidden(U_4,U_5)
| ~ r2_hidden(U_5,U_4) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_5,U_4] :
( ~ r2_hidden(U_4,U_5)
| ~ r2_hidden(U_5,U_4) ),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
( ~ r2_hidden(U_4,U_5)
| ~ r2_hidden(U_5,U_4) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [A,B,C] :
( ( v1_funct_2(C,A,B)
& v1_funct_1(C) )
| ~ v1_partfun1(C,A,B)
| ~ v1_funct_1(C)
| ~ m1_relset_1(C,A,B) ),
inference(fof_nnf,[status(thm)],[cc1_funct_2]) ).
fof(f_4_2,plain,
! [U_8,U_7,U_6] :
( ( v1_funct_2(U_6,U_8,U_7)
& v1_funct_1(U_6) )
| ~ v1_partfun1(U_6,U_8,U_7)
| ~ v1_funct_1(U_6)
| ~ m1_relset_1(U_6,U_8,U_7) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_8,U_6,U_7] :
( v1_funct_2(U_6,U_8,U_7)
| ~ sP0(U_8,U_6,U_7) )
& ! [U_8,U_6,U_7] :
( v1_funct_1(U_6)
| ~ sP0(U_8,U_6,U_7) )
& ! [U_8,U_6,U_7] :
( sP0(U_8,U_6,U_7)
| ~ v1_partfun1(U_6,U_8,U_7)
| ~ v1_funct_1(U_6)
| ~ m1_relset_1(U_6,U_8,U_7) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_4_2]) ).
cnf(f_4_4,plain,
( sP0(U_8,U_6,U_7)
| ~ v1_partfun1(U_6,U_8,U_7)
| ~ v1_funct_1(U_6)
| ~ m1_relset_1(U_6,U_8,U_7) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( v1_funct_1(U_6)
| ~ sP0(U_8,U_6,U_7) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( v1_funct_2(U_6,U_8,U_7)
| ~ sP0(U_8,U_6,U_7) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [A,B,C] :
( v1_relat_1(C)
| ~ m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
inference(fof_nnf,[status(thm)],[cc1_relset_1]) ).
fof(f_5_2,plain,
! [U_11,U_10,U_9] :
( v1_relat_1(U_9)
| ~ m1_subset_1(U_9,k1_zfmisc_1(k2_zfmisc_1(U_11,U_10))) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_11,U_9,U_10] :
( v1_relat_1(U_9)
| ~ m1_subset_1(U_9,k1_zfmisc_1(k2_zfmisc_1(U_11,U_10))) ),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
( v1_relat_1(U_9)
| ~ m1_subset_1(U_9,k1_zfmisc_1(k2_zfmisc_1(U_11,U_10))) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A,B] :
( ! [C] :
( ( v1_funct_2(C,A,B)
& v1_partfun1(C,A,B)
& v1_funct_1(C) )
| ~ v1_funct_2(C,A,B)
| ~ v1_funct_1(C)
| ~ m1_relset_1(C,A,B) )
| v1_xboole_0(B) ),
inference(fof_nnf,[status(thm)],[cc5_funct_2]) ).
fof(f_6_2,plain,
! [U_14,U_13] :
( ! [U_12] :
( ( v1_funct_2(U_12,U_14,U_13)
& v1_partfun1(U_12,U_14,U_13)
& v1_funct_1(U_12) )
| ~ v1_funct_2(U_12,U_14,U_13)
| ~ v1_funct_1(U_12)
| ~ m1_relset_1(U_12,U_14,U_13) )
| v1_xboole_0(U_13) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_14,U_13,U_12] :
( v1_funct_2(U_12,U_14,U_13)
| ~ sP1(U_14,U_13,U_12) )
& ! [U_14,U_13,U_12] :
( v1_partfun1(U_12,U_14,U_13)
| ~ sP1(U_14,U_13,U_12) )
& ! [U_14,U_13,U_12] :
( v1_funct_1(U_12)
| ~ sP1(U_14,U_13,U_12) )
& ! [U_14,U_13,U_12] :
( sP1(U_14,U_13,U_12)
| ~ v1_funct_2(U_12,U_14,U_13)
| ~ v1_funct_1(U_12)
| ~ m1_relset_1(U_12,U_14,U_13)
| v1_xboole_0(U_13) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_6_2]) ).
cnf(f_6_4,plain,
( sP1(U_14,U_13,U_12)
| ~ v1_funct_2(U_12,U_14,U_13)
| ~ v1_funct_1(U_12)
| ~ m1_relset_1(U_12,U_14,U_13)
| v1_xboole_0(U_13) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( v1_funct_1(U_12)
| ~ sP1(U_14,U_13,U_12) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
( v1_partfun1(U_12,U_14,U_13)
| ~ sP1(U_14,U_13,U_12) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_7,plain,
( v1_funct_2(U_12,U_14,U_13)
| ~ sP1(U_14,U_13,U_12) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [A,B] :
( ! [C] :
( ( v1_funct_2(C,A,B)
& v1_partfun1(C,A,B)
& ~ v1_xboole_0(C)
& v1_funct_1(C) )
| ~ v1_funct_2(C,A,B)
| ~ v1_funct_1(C)
| ~ m1_relset_1(C,A,B) )
| v1_xboole_0(B)
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[cc6_funct_2]) ).
fof(f_7_2,plain,
! [U_17,U_16] :
( ! [U_15] :
( ( v1_funct_2(U_15,U_17,U_16)
& v1_partfun1(U_15,U_17,U_16)
& ~ v1_xboole_0(U_15)
& v1_funct_1(U_15) )
| ~ v1_funct_2(U_15,U_17,U_16)
| ~ v1_funct_1(U_15)
| ~ m1_relset_1(U_15,U_17,U_16) )
| v1_xboole_0(U_16)
| v1_xboole_0(U_17) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_15,U_17,U_16] :
( v1_funct_2(U_15,U_17,U_16)
| ~ sP2(U_15,U_17,U_16) )
& ! [U_15,U_17,U_16] :
( v1_partfun1(U_15,U_17,U_16)
| ~ sP2(U_15,U_17,U_16) )
& ! [U_15,U_17,U_16] :
( ~ v1_xboole_0(U_15)
| ~ sP2(U_15,U_17,U_16) )
& ! [U_15,U_17,U_16] :
( v1_funct_1(U_15)
| ~ sP2(U_15,U_17,U_16) )
& ! [U_15,U_17,U_16] :
( sP2(U_15,U_17,U_16)
| ~ v1_funct_2(U_15,U_17,U_16)
| ~ v1_funct_1(U_15)
| ~ m1_relset_1(U_15,U_17,U_16)
| v1_xboole_0(U_16)
| v1_xboole_0(U_17) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_7_2]) ).
cnf(f_7_4,plain,
( sP2(U_15,U_17,U_16)
| ~ v1_funct_2(U_15,U_17,U_16)
| ~ v1_funct_1(U_15)
| ~ m1_relset_1(U_15,U_17,U_16)
| v1_xboole_0(U_16)
| v1_xboole_0(U_17) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( v1_funct_1(U_15)
| ~ sP2(U_15,U_17,U_16) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_6,plain,
( ~ v1_xboole_0(U_15)
| ~ sP2(U_15,U_17,U_16) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_7,plain,
( v1_partfun1(U_15,U_17,U_16)
| ~ sP2(U_15,U_17,U_16) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_8,plain,
( v1_funct_2(U_15,U_17,U_16)
| ~ sP2(U_15,U_17,U_16) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [A,B,C] :
( ( l3_lattices(g3_lattices(A,B,C))
& v3_lattices(g3_lattices(A,B,C)) )
| ~ m1_relset_1(C,k2_zfmisc_1(A,A),A)
| ~ v1_funct_2(C,k2_zfmisc_1(A,A),A)
| ~ v1_funct_1(C)
| ~ m1_relset_1(B,k2_zfmisc_1(A,A),A)
| ~ v1_funct_2(B,k2_zfmisc_1(A,A),A)
| ~ v1_funct_1(B) ),
inference(fof_nnf,[status(thm)],[dt_g3_lattices]) ).
fof(f_8_2,plain,
! [U_20,U_19,U_18] :
( ( l3_lattices(g3_lattices(U_20,U_19,U_18))
& v3_lattices(g3_lattices(U_20,U_19,U_18)) )
| ~ m1_relset_1(U_18,k2_zfmisc_1(U_20,U_20),U_20)
| ~ v1_funct_2(U_18,k2_zfmisc_1(U_20,U_20),U_20)
| ~ v1_funct_1(U_18)
| ~ m1_relset_1(U_19,k2_zfmisc_1(U_20,U_20),U_20)
| ~ v1_funct_2(U_19,k2_zfmisc_1(U_20,U_20),U_20)
| ~ v1_funct_1(U_19) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_20,U_19,U_18] :
( l3_lattices(g3_lattices(U_20,U_19,U_18))
| ~ sP3(U_20,U_19,U_18) )
& ! [U_20,U_19,U_18] :
( v3_lattices(g3_lattices(U_20,U_19,U_18))
| ~ sP3(U_20,U_19,U_18) )
& ! [U_20,U_19,U_18] :
( sP3(U_20,U_19,U_18)
| ~ m1_relset_1(U_18,k2_zfmisc_1(U_20,U_20),U_20)
| ~ v1_funct_2(U_18,k2_zfmisc_1(U_20,U_20),U_20)
| ~ v1_funct_1(U_18)
| ~ m1_relset_1(U_19,k2_zfmisc_1(U_20,U_20),U_20)
| ~ v1_funct_2(U_19,k2_zfmisc_1(U_20,U_20),U_20)
| ~ v1_funct_1(U_19) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_8_2]) ).
cnf(f_8_4,plain,
( sP3(U_20,U_19,U_18)
| ~ m1_relset_1(U_18,k2_zfmisc_1(U_20,U_20),U_20)
| ~ v1_funct_2(U_18,k2_zfmisc_1(U_20,U_20),U_20)
| ~ v1_funct_1(U_18)
| ~ m1_relset_1(U_19,k2_zfmisc_1(U_20,U_20),U_20)
| ~ v1_funct_2(U_19,k2_zfmisc_1(U_20,U_20),U_20)
| ~ v1_funct_1(U_19) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( v3_lattices(g3_lattices(U_20,U_19,U_18))
| ~ sP3(U_20,U_19,U_18) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_6,plain,
( l3_lattices(g3_lattices(U_20,U_19,U_18))
| ~ sP3(U_20,U_19,U_18) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [A] :
( ( l3_lattices(k11_group_4(A))
& v10_lattices(k11_group_4(A))
& v3_lattices(k11_group_4(A))
& ~ v3_struct_0(k11_group_4(A)) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_k11_group_4]) ).
fof(f_9_2,plain,
! [U_21] :
( ( l3_lattices(k11_group_4(U_21))
& v10_lattices(k11_group_4(U_21))
& v3_lattices(k11_group_4(U_21))
& ~ v3_struct_0(k11_group_4(U_21)) )
| ~ l1_group_1(U_21)
| ~ v4_group_1(U_21)
| ~ v3_group_1(U_21)
| v3_struct_0(U_21) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_21] :
( l3_lattices(k11_group_4(U_21))
| ~ sP4(U_21) )
& ! [U_21] :
( v10_lattices(k11_group_4(U_21))
| ~ sP4(U_21) )
& ! [U_21] :
( v3_lattices(k11_group_4(U_21))
| ~ sP4(U_21) )
& ! [U_21] :
( ~ v3_struct_0(k11_group_4(U_21))
| ~ sP4(U_21) )
& ! [U_21] :
( sP4(U_21)
| ~ l1_group_1(U_21)
| ~ v4_group_1(U_21)
| ~ v3_group_1(U_21)
| v3_struct_0(U_21) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_9_2]) ).
cnf(f_9_4,plain,
( sP4(U_21)
| ~ l1_group_1(U_21)
| ~ v4_group_1(U_21)
| ~ v3_group_1(U_21)
| v3_struct_0(U_21) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( ~ v3_struct_0(k11_group_4(U_21))
| ~ sP4(U_21) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_6,plain,
( v3_lattices(k11_group_4(U_21))
| ~ sP4(U_21) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_7,plain,
( v10_lattices(k11_group_4(U_21))
| ~ sP4(U_21) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_8,plain,
( l3_lattices(k11_group_4(U_21))
| ~ sP4(U_21) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
fof(f_10_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_10_1]) ).
cnf(f_10_3,plain,
$true,
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
fof(f_11_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_11_1]) ).
cnf(f_11_3,plain,
$true,
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
fof(f_12_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_12_1]) ).
cnf(f_12_3,plain,
$true,
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [A,B,C] :
( ( m2_relset_1(k3_latsubgr(A,B,C),u1_struct_0(k11_group_4(A)),u1_struct_0(k11_group_4(B)))
& v1_funct_2(k3_latsubgr(A,B,C),u1_struct_0(k11_group_4(A)),u1_struct_0(k11_group_4(B)))
& v1_funct_1(k3_latsubgr(A,B,C)) )
| ~ m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_funct_1(C)
| ~ l1_group_1(B)
| ~ v4_group_1(B)
| ~ v3_group_1(B)
| v3_struct_0(B)
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_k3_latsubgr]) ).
fof(f_13_2,plain,
! [U_24,U_23,U_22] :
( ( m2_relset_1(k3_latsubgr(U_24,U_23,U_22),u1_struct_0(k11_group_4(U_24)),u1_struct_0(k11_group_4(U_23)))
& v1_funct_2(k3_latsubgr(U_24,U_23,U_22),u1_struct_0(k11_group_4(U_24)),u1_struct_0(k11_group_4(U_23)))
& v1_funct_1(k3_latsubgr(U_24,U_23,U_22)) )
| ~ m1_relset_1(U_22,u1_struct_0(U_24),u1_struct_0(U_23))
| ~ v1_funct_2(U_22,u1_struct_0(U_24),u1_struct_0(U_23))
| ~ v1_funct_1(U_22)
| ~ l1_group_1(U_23)
| ~ v4_group_1(U_23)
| ~ v3_group_1(U_23)
| v3_struct_0(U_23)
| ~ l1_group_1(U_24)
| ~ v4_group_1(U_24)
| ~ v3_group_1(U_24)
| v3_struct_0(U_24) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_22,U_23,U_24] :
( m2_relset_1(k3_latsubgr(U_24,U_23,U_22),u1_struct_0(k11_group_4(U_24)),u1_struct_0(k11_group_4(U_23)))
| ~ sP5(U_22,U_23,U_24) )
& ! [U_22,U_23,U_24] :
( v1_funct_2(k3_latsubgr(U_24,U_23,U_22),u1_struct_0(k11_group_4(U_24)),u1_struct_0(k11_group_4(U_23)))
| ~ sP5(U_22,U_23,U_24) )
& ! [U_22,U_23,U_24] :
( v1_funct_1(k3_latsubgr(U_24,U_23,U_22))
| ~ sP5(U_22,U_23,U_24) )
& ! [U_22,U_23,U_24] :
( sP5(U_22,U_23,U_24)
| ~ m1_relset_1(U_22,u1_struct_0(U_24),u1_struct_0(U_23))
| ~ v1_funct_2(U_22,u1_struct_0(U_24),u1_struct_0(U_23))
| ~ v1_funct_1(U_22)
| ~ l1_group_1(U_23)
| ~ v4_group_1(U_23)
| ~ v3_group_1(U_23)
| v3_struct_0(U_23)
| ~ l1_group_1(U_24)
| ~ v4_group_1(U_24)
| ~ v3_group_1(U_24)
| v3_struct_0(U_24) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_13_2]) ).
cnf(f_13_4,plain,
( sP5(U_22,U_23,U_24)
| ~ m1_relset_1(U_22,u1_struct_0(U_24),u1_struct_0(U_23))
| ~ v1_funct_2(U_22,u1_struct_0(U_24),u1_struct_0(U_23))
| ~ v1_funct_1(U_22)
| ~ l1_group_1(U_23)
| ~ v4_group_1(U_23)
| ~ v3_group_1(U_23)
| v3_struct_0(U_23)
| ~ l1_group_1(U_24)
| ~ v4_group_1(U_24)
| ~ v3_group_1(U_24)
| v3_struct_0(U_24) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_5,plain,
( v1_funct_1(k3_latsubgr(U_24,U_23,U_22))
| ~ sP5(U_22,U_23,U_24) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_6,plain,
( v1_funct_2(k3_latsubgr(U_24,U_23,U_22),u1_struct_0(k11_group_4(U_24)),u1_struct_0(k11_group_4(U_23)))
| ~ sP5(U_22,U_23,U_24) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_7,plain,
( m2_relset_1(k3_latsubgr(U_24,U_23,U_22),u1_struct_0(k11_group_4(U_24)),u1_struct_0(k11_group_4(U_23)))
| ~ sP5(U_22,U_23,U_24) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [A] :
( l1_struct_0(A)
| ~ l1_group_1(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_group_1]) ).
fof(f_14_2,plain,
! [U_25] :
( l1_struct_0(U_25)
| ~ l1_group_1(U_25) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_25] :
( l1_struct_0(U_25)
| ~ l1_group_1(U_25) ),
inference(definitional_conversion,[status(esa)],[f_14_2]) ).
cnf(f_14_4,plain,
( l1_struct_0(U_25)
| ~ l1_group_1(U_25) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [A] :
( l1_struct_0(A)
| ~ l1_lattices(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_lattices]) ).
fof(f_15_2,plain,
! [U_26] :
( l1_struct_0(U_26)
| ~ l1_lattices(U_26) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_26] :
( l1_struct_0(U_26)
| ~ l1_lattices(U_26) ),
inference(definitional_conversion,[status(esa)],[f_15_2]) ).
cnf(f_15_4,plain,
( l1_struct_0(U_26)
| ~ l1_lattices(U_26) ),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
fof(f_16_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_16_1]) ).
cnf(f_16_3,plain,
$true,
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [A] :
( l1_struct_0(A)
| ~ l2_lattices(A) ),
inference(fof_nnf,[status(thm)],[dt_l2_lattices]) ).
fof(f_17_2,plain,
! [U_27] :
( l1_struct_0(U_27)
| ~ l2_lattices(U_27) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_27] :
( l1_struct_0(U_27)
| ~ l2_lattices(U_27) ),
inference(definitional_conversion,[status(esa)],[f_17_2]) ).
cnf(f_17_4,plain,
( l1_struct_0(U_27)
| ~ l2_lattices(U_27) ),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
! [A] :
( ( l2_lattices(A)
& l1_lattices(A) )
| ~ l3_lattices(A) ),
inference(fof_nnf,[status(thm)],[dt_l3_lattices]) ).
fof(f_18_2,plain,
! [U_28] :
( ( l2_lattices(U_28)
& l1_lattices(U_28) )
| ~ l3_lattices(U_28) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( ! [U_28] :
( l2_lattices(U_28)
| ~ sP6(U_28) )
& ! [U_28] :
( l1_lattices(U_28)
| ~ sP6(U_28) )
& ! [U_28] :
( sP6(U_28)
| ~ l3_lattices(U_28) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_18_2]) ).
cnf(f_18_4,plain,
( sP6(U_28)
| ~ l3_lattices(U_28) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_5,plain,
( l1_lattices(U_28)
| ~ sP6(U_28) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_6,plain,
( l2_lattices(U_28)
| ~ sP6(U_28) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
! [A,B] :
( ! [C] :
( ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) )
| ~ m1_lattice4(C,A,B) )
| ~ l3_lattices(B)
| ~ v10_lattices(B)
| v3_struct_0(B)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_m1_lattice4]) ).
fof(f_19_2,plain,
! [U_31,U_30] :
( ! [U_29] :
( ( m2_relset_1(U_29,u1_struct_0(U_31),u1_struct_0(U_30))
& v1_funct_2(U_29,u1_struct_0(U_31),u1_struct_0(U_30))
& v1_funct_1(U_29) )
| ~ m1_lattice4(U_29,U_31,U_30) )
| ~ l3_lattices(U_30)
| ~ v10_lattices(U_30)
| v3_struct_0(U_30)
| ~ l3_lattices(U_31)
| ~ v10_lattices(U_31)
| v3_struct_0(U_31) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( ! [U_30,U_31,U_29] :
( m2_relset_1(U_29,u1_struct_0(U_31),u1_struct_0(U_30))
| ~ sP7(U_30,U_31,U_29) )
& ! [U_30,U_31,U_29] :
( v1_funct_2(U_29,u1_struct_0(U_31),u1_struct_0(U_30))
| ~ sP7(U_30,U_31,U_29) )
& ! [U_30,U_31,U_29] :
( v1_funct_1(U_29)
| ~ sP7(U_30,U_31,U_29) )
& ! [U_30,U_31,U_29] :
( sP7(U_30,U_31,U_29)
| ~ m1_lattice4(U_29,U_31,U_30)
| ~ l3_lattices(U_30)
| ~ v10_lattices(U_30)
| v3_struct_0(U_30)
| ~ l3_lattices(U_31)
| ~ v10_lattices(U_31)
| v3_struct_0(U_31) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_19_2]) ).
cnf(f_19_4,plain,
( sP7(U_30,U_31,U_29)
| ~ m1_lattice4(U_29,U_31,U_30)
| ~ l3_lattices(U_30)
| ~ v10_lattices(U_30)
| v3_struct_0(U_30)
| ~ l3_lattices(U_31)
| ~ v10_lattices(U_31)
| v3_struct_0(U_31) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_5,plain,
( v1_funct_1(U_29)
| ~ sP7(U_30,U_31,U_29) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_6,plain,
( v1_funct_2(U_29,u1_struct_0(U_31),u1_struct_0(U_30))
| ~ sP7(U_30,U_31,U_29) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_7,plain,
( m2_relset_1(U_29,u1_struct_0(U_31),u1_struct_0(U_30))
| ~ sP7(U_30,U_31,U_29) ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_relset_1]) ).
fof(f_20_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_20_1]) ).
cnf(f_20_3,plain,
$true,
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
fof(f_21_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_21_1]) ).
cnf(f_21_3,plain,
$true,
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
| ~ m2_relset_1(C,A,B) ),
inference(fof_nnf,[status(thm)],[dt_m2_relset_1]) ).
fof(f_22_2,plain,
! [U_34,U_33,U_32] :
( m1_subset_1(U_32,k1_zfmisc_1(k2_zfmisc_1(U_34,U_33)))
| ~ m2_relset_1(U_32,U_34,U_33) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_34,U_33,U_32] :
( m1_subset_1(U_32,k1_zfmisc_1(k2_zfmisc_1(U_34,U_33)))
| ~ m2_relset_1(U_32,U_34,U_33) ),
inference(definitional_conversion,[status(esa)],[f_22_2]) ).
cnf(f_22_4,plain,
( m1_subset_1(U_32,k1_zfmisc_1(k2_zfmisc_1(U_34,U_33)))
| ~ m2_relset_1(U_32,U_34,U_33) ),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
! [A,B] :
( ! [C] :
( ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) )
| ~ m3_vectsp_8(C,A,B) )
| ~ l3_lattices(B)
| ~ v10_lattices(B)
| v3_struct_0(B)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_m3_vectsp_8]) ).
fof(f_23_2,plain,
! [U_37,U_36] :
( ! [U_35] :
( ( m2_relset_1(U_35,u1_struct_0(U_37),u1_struct_0(U_36))
& v1_funct_2(U_35,u1_struct_0(U_37),u1_struct_0(U_36))
& v1_funct_1(U_35) )
| ~ m3_vectsp_8(U_35,U_37,U_36) )
| ~ l3_lattices(U_36)
| ~ v10_lattices(U_36)
| v3_struct_0(U_36)
| ~ l3_lattices(U_37)
| ~ v10_lattices(U_37)
| v3_struct_0(U_37) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( ! [U_36,U_35,U_37] :
( m2_relset_1(U_35,u1_struct_0(U_37),u1_struct_0(U_36))
| ~ sP8(U_36,U_35,U_37) )
& ! [U_36,U_35,U_37] :
( v1_funct_2(U_35,u1_struct_0(U_37),u1_struct_0(U_36))
| ~ sP8(U_36,U_35,U_37) )
& ! [U_36,U_35,U_37] :
( v1_funct_1(U_35)
| ~ sP8(U_36,U_35,U_37) )
& ! [U_36,U_35,U_37] :
( sP8(U_36,U_35,U_37)
| ~ m3_vectsp_8(U_35,U_37,U_36)
| ~ l3_lattices(U_36)
| ~ v10_lattices(U_36)
| v3_struct_0(U_36)
| ~ l3_lattices(U_37)
| ~ v10_lattices(U_37)
| v3_struct_0(U_37) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_23_2]) ).
cnf(f_23_4,plain,
( sP8(U_36,U_35,U_37)
| ~ m3_vectsp_8(U_35,U_37,U_36)
| ~ l3_lattices(U_36)
| ~ v10_lattices(U_36)
| v3_struct_0(U_36)
| ~ l3_lattices(U_37)
| ~ v10_lattices(U_37)
| v3_struct_0(U_37) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_5,plain,
( v1_funct_1(U_35)
| ~ sP8(U_36,U_35,U_37) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_6,plain,
( v1_funct_2(U_35,u1_struct_0(U_37),u1_struct_0(U_36))
| ~ sP8(U_36,U_35,U_37) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_7,plain,
( m2_relset_1(U_35,u1_struct_0(U_37),u1_struct_0(U_36))
| ~ sP8(U_36,U_35,U_37) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
! [A,B] :
( ! [C] :
( ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) )
| ~ m4_vectsp_8(C,A,B) )
| ~ l3_lattices(B)
| ~ v10_lattices(B)
| v3_struct_0(B)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_m4_vectsp_8]) ).
fof(f_24_2,plain,
! [U_40,U_39] :
( ! [U_38] :
( ( m2_relset_1(U_38,u1_struct_0(U_40),u1_struct_0(U_39))
& v1_funct_2(U_38,u1_struct_0(U_40),u1_struct_0(U_39))
& v1_funct_1(U_38) )
| ~ m4_vectsp_8(U_38,U_40,U_39) )
| ~ l3_lattices(U_39)
| ~ v10_lattices(U_39)
| v3_struct_0(U_39)
| ~ l3_lattices(U_40)
| ~ v10_lattices(U_40)
| v3_struct_0(U_40) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( ! [U_39,U_38,U_40] :
( m2_relset_1(U_38,u1_struct_0(U_40),u1_struct_0(U_39))
| ~ sP9(U_39,U_38,U_40) )
& ! [U_39,U_38,U_40] :
( v1_funct_2(U_38,u1_struct_0(U_40),u1_struct_0(U_39))
| ~ sP9(U_39,U_38,U_40) )
& ! [U_39,U_38,U_40] :
( v1_funct_1(U_38)
| ~ sP9(U_39,U_38,U_40) )
& ! [U_39,U_38,U_40] :
( sP9(U_39,U_38,U_40)
| ~ m4_vectsp_8(U_38,U_40,U_39)
| ~ l3_lattices(U_39)
| ~ v10_lattices(U_39)
| v3_struct_0(U_39)
| ~ l3_lattices(U_40)
| ~ v10_lattices(U_40)
| v3_struct_0(U_40) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9])],[f_24_2]) ).
cnf(f_24_4,plain,
( sP9(U_39,U_38,U_40)
| ~ m4_vectsp_8(U_38,U_40,U_39)
| ~ l3_lattices(U_39)
| ~ v10_lattices(U_39)
| v3_struct_0(U_39)
| ~ l3_lattices(U_40)
| ~ v10_lattices(U_40)
| v3_struct_0(U_40) ),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
( v1_funct_1(U_38)
| ~ sP9(U_39,U_38,U_40) ),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_6,plain,
( v1_funct_2(U_38,u1_struct_0(U_40),u1_struct_0(U_39))
| ~ sP9(U_39,U_38,U_40) ),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_7,plain,
( m2_relset_1(U_38,u1_struct_0(U_40),u1_struct_0(U_39))
| ~ sP9(U_39,U_38,U_40) ),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
! [A] :
( ( m2_relset_1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_1(u1_lattices(A)) )
| ~ l1_lattices(A) ),
inference(fof_nnf,[status(thm)],[dt_u1_lattices]) ).
fof(f_25_2,plain,
! [U_41] :
( ( m2_relset_1(u1_lattices(U_41),k2_zfmisc_1(u1_struct_0(U_41),u1_struct_0(U_41)),u1_struct_0(U_41))
& v1_funct_2(u1_lattices(U_41),k2_zfmisc_1(u1_struct_0(U_41),u1_struct_0(U_41)),u1_struct_0(U_41))
& v1_funct_1(u1_lattices(U_41)) )
| ~ l1_lattices(U_41) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( ! [U_41] :
( m2_relset_1(u1_lattices(U_41),k2_zfmisc_1(u1_struct_0(U_41),u1_struct_0(U_41)),u1_struct_0(U_41))
| ~ sP10(U_41) )
& ! [U_41] :
( v1_funct_2(u1_lattices(U_41),k2_zfmisc_1(u1_struct_0(U_41),u1_struct_0(U_41)),u1_struct_0(U_41))
| ~ sP10(U_41) )
& ! [U_41] :
( v1_funct_1(u1_lattices(U_41))
| ~ sP10(U_41) )
& ! [U_41] :
( sP10(U_41)
| ~ l1_lattices(U_41) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10])],[f_25_2]) ).
cnf(f_25_4,plain,
( sP10(U_41)
| ~ l1_lattices(U_41) ),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
( v1_funct_1(u1_lattices(U_41))
| ~ sP10(U_41) ),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_6,plain,
( v1_funct_2(u1_lattices(U_41),k2_zfmisc_1(u1_struct_0(U_41),u1_struct_0(U_41)),u1_struct_0(U_41))
| ~ sP10(U_41) ),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_7,plain,
( m2_relset_1(u1_lattices(U_41),k2_zfmisc_1(u1_struct_0(U_41),u1_struct_0(U_41)),u1_struct_0(U_41))
| ~ sP10(U_41) ),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
fof(f_26_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_26_1]) ).
cnf(f_26_3,plain,
$true,
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
! [A] :
( ( m2_relset_1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& v1_funct_1(u2_lattices(A)) )
| ~ l2_lattices(A) ),
inference(fof_nnf,[status(thm)],[dt_u2_lattices]) ).
fof(f_27_2,plain,
! [U_42] :
( ( m2_relset_1(u2_lattices(U_42),k2_zfmisc_1(u1_struct_0(U_42),u1_struct_0(U_42)),u1_struct_0(U_42))
& v1_funct_2(u2_lattices(U_42),k2_zfmisc_1(u1_struct_0(U_42),u1_struct_0(U_42)),u1_struct_0(U_42))
& v1_funct_1(u2_lattices(U_42)) )
| ~ l2_lattices(U_42) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( ! [U_42] :
( m2_relset_1(u2_lattices(U_42),k2_zfmisc_1(u1_struct_0(U_42),u1_struct_0(U_42)),u1_struct_0(U_42))
| ~ sP11(U_42) )
& ! [U_42] :
( v1_funct_2(u2_lattices(U_42),k2_zfmisc_1(u1_struct_0(U_42),u1_struct_0(U_42)),u1_struct_0(U_42))
| ~ sP11(U_42) )
& ! [U_42] :
( v1_funct_1(u2_lattices(U_42))
| ~ sP11(U_42) )
& ! [U_42] :
( sP11(U_42)
| ~ l2_lattices(U_42) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11])],[f_27_2]) ).
cnf(f_27_4,plain,
( sP11(U_42)
| ~ l2_lattices(U_42) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_5,plain,
( v1_funct_1(u2_lattices(U_42))
| ~ sP11(U_42) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_6,plain,
( v1_funct_2(u2_lattices(U_42),k2_zfmisc_1(u1_struct_0(U_42),u1_struct_0(U_42)),u1_struct_0(U_42))
| ~ sP11(U_42) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_7,plain,
( m2_relset_1(u2_lattices(U_42),k2_zfmisc_1(u1_struct_0(U_42),u1_struct_0(U_42)),u1_struct_0(U_42))
| ~ sP11(U_42) ),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
? [A] : l1_group_1(A),
inference(fof_nnf,[status(thm)],[existence_l1_group_1]) ).
fof(f_28_2,plain,
? [U_43] : l1_group_1(U_43),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
l1_group_1(sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_43,sK4)],[f_28_2]) ).
fof(f_28_4,plain,
l1_group_1(sK4),
inference(definitional_conversion,[status(esa)],[f_28_3]) ).
cnf(f_28_5,plain,
l1_group_1(sK4),
inference(clausify,[status(thm)],[f_28_4]) ).
fof(f_29_1,plain,
? [A] : l1_lattices(A),
inference(fof_nnf,[status(thm)],[existence_l1_lattices]) ).
fof(f_29_2,plain,
? [U_44] : l1_lattices(U_44),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
l1_lattices(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_44,sK5)],[f_29_2]) ).
fof(f_29_4,plain,
l1_lattices(sK5),
inference(definitional_conversion,[status(esa)],[f_29_3]) ).
cnf(f_29_5,plain,
l1_lattices(sK5),
inference(clausify,[status(thm)],[f_29_4]) ).
fof(f_30_1,plain,
? [A] : l1_struct_0(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_30_2,plain,
? [U_45] : l1_struct_0(U_45),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
l1_struct_0(sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_45,sK6)],[f_30_2]) ).
fof(f_30_4,plain,
l1_struct_0(sK6),
inference(definitional_conversion,[status(esa)],[f_30_3]) ).
cnf(f_30_5,plain,
l1_struct_0(sK6),
inference(clausify,[status(thm)],[f_30_4]) ).
fof(f_31_1,plain,
? [A] : l2_lattices(A),
inference(fof_nnf,[status(thm)],[existence_l2_lattices]) ).
fof(f_31_2,plain,
? [U_46] : l2_lattices(U_46),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
l2_lattices(sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_46,sK7)],[f_31_2]) ).
fof(f_31_4,plain,
l2_lattices(sK7),
inference(definitional_conversion,[status(esa)],[f_31_3]) ).
cnf(f_31_5,plain,
l2_lattices(sK7),
inference(clausify,[status(thm)],[f_31_4]) ).
fof(f_32_1,plain,
? [A] : l3_lattices(A),
inference(fof_nnf,[status(thm)],[existence_l3_lattices]) ).
fof(f_32_2,plain,
? [U_47] : l3_lattices(U_47),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
l3_lattices(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_47,sK8)],[f_32_2]) ).
fof(f_32_4,plain,
l3_lattices(sK8),
inference(definitional_conversion,[status(esa)],[f_32_3]) ).
cnf(f_32_5,plain,
l3_lattices(sK8),
inference(clausify,[status(thm)],[f_32_4]) ).
fof(f_33_1,plain,
! [A,B] :
( ? [C] : m1_lattice4(C,A,B)
| ~ l3_lattices(B)
| ~ v10_lattices(B)
| v3_struct_0(B)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[existence_m1_lattice4]) ).
fof(f_33_2,plain,
! [U_50,U_49] :
( ? [U_48] : m1_lattice4(U_48,U_50,U_49)
| ~ l3_lattices(U_49)
| ~ v10_lattices(U_49)
| v3_struct_0(U_49)
| ~ l3_lattices(U_50)
| ~ v10_lattices(U_50)
| v3_struct_0(U_50) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_50,U_49] :
( m1_lattice4(sK9(U_50,U_49),U_50,U_49)
| ~ l3_lattices(U_49)
| ~ v10_lattices(U_49)
| v3_struct_0(U_49)
| ~ l3_lattices(U_50)
| ~ v10_lattices(U_50)
| v3_struct_0(U_50) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_48,sK9(U_50,U_49))],[f_33_2]) ).
fof(f_33_4,plain,
! [U_49,U_50] :
( m1_lattice4(sK9(U_50,U_49),U_50,U_49)
| ~ l3_lattices(U_49)
| ~ v10_lattices(U_49)
| v3_struct_0(U_49)
| ~ l3_lattices(U_50)
| ~ v10_lattices(U_50)
| v3_struct_0(U_50) ),
inference(definitional_conversion,[status(esa)],[f_33_3]) ).
cnf(f_33_5,plain,
( m1_lattice4(sK9(U_50,U_49),U_50,U_49)
| ~ l3_lattices(U_49)
| ~ v10_lattices(U_49)
| v3_struct_0(U_49)
| ~ l3_lattices(U_50)
| ~ v10_lattices(U_50)
| v3_struct_0(U_50) ),
inference(clausify,[status(thm)],[f_33_4]) ).
fof(f_34_1,plain,
! [A,B] :
? [C] : m1_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_relset_1]) ).
fof(f_34_2,plain,
! [U_53,U_52] :
? [U_51] : m1_relset_1(U_51,U_53,U_52),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_53,U_52] : m1_relset_1(sK10(U_53,U_52),U_53,U_52),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_51,sK10(U_53,U_52))],[f_34_2]) ).
fof(f_34_4,plain,
! [U_52,U_53] : m1_relset_1(sK10(U_53,U_52),U_53,U_52),
inference(definitional_conversion,[status(esa)],[f_34_3]) ).
cnf(f_34_5,plain,
m1_relset_1(sK10(U_53,U_52),U_53,U_52),
inference(clausify,[status(thm)],[f_34_4]) ).
fof(f_35_1,plain,
! [A] :
? [B] : m1_subset_1(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_35_2,plain,
! [U_55] :
? [U_54] : m1_subset_1(U_54,U_55),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_55] : m1_subset_1(sK11(U_55),U_55),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_54,sK11(U_55))],[f_35_2]) ).
fof(f_35_4,plain,
! [U_55] : m1_subset_1(sK11(U_55),U_55),
inference(definitional_conversion,[status(esa)],[f_35_3]) ).
cnf(f_35_5,plain,
m1_subset_1(sK11(U_55),U_55),
inference(clausify,[status(thm)],[f_35_4]) ).
fof(f_36_1,plain,
! [A,B] :
? [C] : m2_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m2_relset_1]) ).
fof(f_36_2,plain,
! [U_58,U_57] :
? [U_56] : m2_relset_1(U_56,U_58,U_57),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_58,U_57] : m2_relset_1(sK12(U_58,U_57),U_58,U_57),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_56,sK12(U_58,U_57))],[f_36_2]) ).
fof(f_36_4,plain,
! [U_57,U_58] : m2_relset_1(sK12(U_58,U_57),U_58,U_57),
inference(definitional_conversion,[status(esa)],[f_36_3]) ).
cnf(f_36_5,plain,
m2_relset_1(sK12(U_58,U_57),U_58,U_57),
inference(clausify,[status(thm)],[f_36_4]) ).
fof(f_37_1,plain,
! [A,B] :
( ? [C] : m3_vectsp_8(C,A,B)
| ~ l3_lattices(B)
| ~ v10_lattices(B)
| v3_struct_0(B)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[existence_m3_vectsp_8]) ).
fof(f_37_2,plain,
! [U_61,U_60] :
( ? [U_59] : m3_vectsp_8(U_59,U_61,U_60)
| ~ l3_lattices(U_60)
| ~ v10_lattices(U_60)
| v3_struct_0(U_60)
| ~ l3_lattices(U_61)
| ~ v10_lattices(U_61)
| v3_struct_0(U_61) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_61,U_60] :
( m3_vectsp_8(sK13(U_61,U_60),U_61,U_60)
| ~ l3_lattices(U_60)
| ~ v10_lattices(U_60)
| v3_struct_0(U_60)
| ~ l3_lattices(U_61)
| ~ v10_lattices(U_61)
| v3_struct_0(U_61) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_59,sK13(U_61,U_60))],[f_37_2]) ).
fof(f_37_4,plain,
! [U_61,U_60] :
( m3_vectsp_8(sK13(U_61,U_60),U_61,U_60)
| ~ l3_lattices(U_60)
| ~ v10_lattices(U_60)
| v3_struct_0(U_60)
| ~ l3_lattices(U_61)
| ~ v10_lattices(U_61)
| v3_struct_0(U_61) ),
inference(definitional_conversion,[status(esa)],[f_37_3]) ).
cnf(f_37_5,plain,
( m3_vectsp_8(sK13(U_61,U_60),U_61,U_60)
| ~ l3_lattices(U_60)
| ~ v10_lattices(U_60)
| v3_struct_0(U_60)
| ~ l3_lattices(U_61)
| ~ v10_lattices(U_61)
| v3_struct_0(U_61) ),
inference(clausify,[status(thm)],[f_37_4]) ).
fof(f_38_1,plain,
! [A,B] :
( ? [C] : m4_vectsp_8(C,A,B)
| ~ l3_lattices(B)
| ~ v10_lattices(B)
| v3_struct_0(B)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[existence_m4_vectsp_8]) ).
fof(f_38_2,plain,
! [U_64,U_63] :
( ? [U_62] : m4_vectsp_8(U_62,U_64,U_63)
| ~ l3_lattices(U_63)
| ~ v10_lattices(U_63)
| v3_struct_0(U_63)
| ~ l3_lattices(U_64)
| ~ v10_lattices(U_64)
| v3_struct_0(U_64) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_64,U_63] :
( m4_vectsp_8(sK14(U_64,U_63),U_64,U_63)
| ~ l3_lattices(U_63)
| ~ v10_lattices(U_63)
| v3_struct_0(U_63)
| ~ l3_lattices(U_64)
| ~ v10_lattices(U_64)
| v3_struct_0(U_64) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_62,sK14(U_64,U_63))],[f_38_2]) ).
fof(f_38_4,plain,
! [U_63,U_64] :
( m4_vectsp_8(sK14(U_64,U_63),U_64,U_63)
| ~ l3_lattices(U_63)
| ~ v10_lattices(U_63)
| v3_struct_0(U_63)
| ~ l3_lattices(U_64)
| ~ v10_lattices(U_64)
| v3_struct_0(U_64) ),
inference(definitional_conversion,[status(esa)],[f_38_3]) ).
cnf(f_38_5,plain,
( m4_vectsp_8(sK14(U_64,U_63),U_64,U_63)
| ~ l3_lattices(U_63)
| ~ v10_lattices(U_63)
| v3_struct_0(U_63)
| ~ l3_lattices(U_64)
| ~ v10_lattices(U_64)
| v3_struct_0(U_64) ),
inference(clausify,[status(thm)],[f_38_4]) ).
fof(f_39_1,plain,
! [A] :
( ( v15_lattices(k11_group_4(A))
& v14_lattices(k11_group_4(A))
& v13_lattices(k11_group_4(A))
& v10_lattices(k11_group_4(A))
& v9_lattices(k11_group_4(A))
& v8_lattices(k11_group_4(A))
& v7_lattices(k11_group_4(A))
& v6_lattices(k11_group_4(A))
& v5_lattices(k11_group_4(A))
& v4_lattices(k11_group_4(A))
& v3_lattices(k11_group_4(A))
& ~ v3_struct_0(k11_group_4(A)) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[fc1_group_4]) ).
fof(f_39_2,plain,
! [U_65] :
( ( v15_lattices(k11_group_4(U_65))
& v14_lattices(k11_group_4(U_65))
& v13_lattices(k11_group_4(U_65))
& v10_lattices(k11_group_4(U_65))
& v9_lattices(k11_group_4(U_65))
& v8_lattices(k11_group_4(U_65))
& v7_lattices(k11_group_4(U_65))
& v6_lattices(k11_group_4(U_65))
& v5_lattices(k11_group_4(U_65))
& v4_lattices(k11_group_4(U_65))
& v3_lattices(k11_group_4(U_65))
& ~ v3_struct_0(k11_group_4(U_65)) )
| ~ l1_group_1(U_65)
| ~ v4_group_1(U_65)
| ~ v3_group_1(U_65)
| v3_struct_0(U_65) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
( ! [U_65] :
( v15_lattices(k11_group_4(U_65))
| ~ sP12(U_65) )
& ! [U_65] :
( v14_lattices(k11_group_4(U_65))
| ~ sP12(U_65) )
& ! [U_65] :
( v13_lattices(k11_group_4(U_65))
| ~ sP12(U_65) )
& ! [U_65] :
( v10_lattices(k11_group_4(U_65))
| ~ sP12(U_65) )
& ! [U_65] :
( v9_lattices(k11_group_4(U_65))
| ~ sP12(U_65) )
& ! [U_65] :
( v8_lattices(k11_group_4(U_65))
| ~ sP12(U_65) )
& ! [U_65] :
( v7_lattices(k11_group_4(U_65))
| ~ sP12(U_65) )
& ! [U_65] :
( v6_lattices(k11_group_4(U_65))
| ~ sP12(U_65) )
& ! [U_65] :
( v5_lattices(k11_group_4(U_65))
| ~ sP12(U_65) )
& ! [U_65] :
( v4_lattices(k11_group_4(U_65))
| ~ sP12(U_65) )
& ! [U_65] :
( v3_lattices(k11_group_4(U_65))
| ~ sP12(U_65) )
& ! [U_65] :
( ~ v3_struct_0(k11_group_4(U_65))
| ~ sP12(U_65) )
& ! [U_65] :
( sP12(U_65)
| ~ l1_group_1(U_65)
| ~ v4_group_1(U_65)
| ~ v3_group_1(U_65)
| v3_struct_0(U_65) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12])],[f_39_2]) ).
cnf(f_39_4,plain,
( sP12(U_65)
| ~ l1_group_1(U_65)
| ~ v4_group_1(U_65)
| ~ v3_group_1(U_65)
| v3_struct_0(U_65) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_5,plain,
( ~ v3_struct_0(k11_group_4(U_65))
| ~ sP12(U_65) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_6,plain,
( v3_lattices(k11_group_4(U_65))
| ~ sP12(U_65) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_7,plain,
( v4_lattices(k11_group_4(U_65))
| ~ sP12(U_65) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_8,plain,
( v5_lattices(k11_group_4(U_65))
| ~ sP12(U_65) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_9,plain,
( v6_lattices(k11_group_4(U_65))
| ~ sP12(U_65) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_10,plain,
( v7_lattices(k11_group_4(U_65))
| ~ sP12(U_65) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_11,plain,
( v8_lattices(k11_group_4(U_65))
| ~ sP12(U_65) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_12,plain,
( v9_lattices(k11_group_4(U_65))
| ~ sP12(U_65) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_13,plain,
( v10_lattices(k11_group_4(U_65))
| ~ sP12(U_65) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_14,plain,
( v13_lattices(k11_group_4(U_65))
| ~ sP12(U_65) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_15,plain,
( v14_lattices(k11_group_4(U_65))
| ~ sP12(U_65) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_16,plain,
( v15_lattices(k11_group_4(U_65))
| ~ sP12(U_65) ),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
! [A] :
( ~ v1_xboole_0(u1_struct_0(A))
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[fc1_struct_0]) ).
fof(f_40_2,plain,
! [U_66] :
( ~ v1_xboole_0(u1_struct_0(U_66))
| ~ l1_struct_0(U_66)
| v3_struct_0(U_66) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_66] :
( ~ v1_xboole_0(u1_struct_0(U_66))
| ~ l1_struct_0(U_66)
| v3_struct_0(U_66) ),
inference(definitional_conversion,[status(esa)],[f_40_2]) ).
cnf(f_40_4,plain,
( ~ v1_xboole_0(u1_struct_0(U_66))
| ~ l1_struct_0(U_66)
| v3_struct_0(U_66) ),
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_1,plain,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_41_2,plain,
! [U_67] : ~ v1_xboole_0(k1_zfmisc_1(U_67)),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_67] : ~ v1_xboole_0(k1_zfmisc_1(U_67)),
inference(definitional_conversion,[status(esa)],[f_41_2]) ).
cnf(f_41_4,plain,
~ v1_xboole_0(k1_zfmisc_1(U_67)),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_1,plain,
v1_xboole_0(k1_xboole_0),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_42_2,plain,
v1_xboole_0(k1_xboole_0),
inference(definitional_conversion,[status(esa)],[f_42_1]) ).
cnf(f_42_3,plain,
v1_xboole_0(k1_xboole_0),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_1,plain,
! [A,B] :
( ~ v1_xboole_0(k2_zfmisc_1(A,B))
| v1_xboole_0(B)
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[fc4_subset_1]) ).
fof(f_43_2,plain,
! [U_69,U_68] :
( ~ v1_xboole_0(k2_zfmisc_1(U_69,U_68))
| v1_xboole_0(U_68)
| v1_xboole_0(U_69) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_68,U_69] :
( ~ v1_xboole_0(k2_zfmisc_1(U_69,U_68))
| v1_xboole_0(U_68)
| v1_xboole_0(U_69) ),
inference(definitional_conversion,[status(esa)],[f_43_2]) ).
cnf(f_43_4,plain,
( ~ v1_xboole_0(k2_zfmisc_1(U_69,U_68))
| v1_xboole_0(U_68)
| v1_xboole_0(U_69) ),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
! [A,B,C] :
( ! [D,E,F] :
( ( C = F
& B = E
& A = D )
| g3_lattices(A,B,C) != g3_lattices(D,E,F) )
| ~ m1_relset_1(C,k2_zfmisc_1(A,A),A)
| ~ v1_funct_2(C,k2_zfmisc_1(A,A),A)
| ~ v1_funct_1(C)
| ~ m1_relset_1(B,k2_zfmisc_1(A,A),A)
| ~ v1_funct_2(B,k2_zfmisc_1(A,A),A)
| ~ v1_funct_1(B) ),
inference(fof_nnf,[status(thm)],[free_g3_lattices]) ).
fof(f_44_2,plain,
! [U_75,U_74,U_73] :
( ! [U_72,U_71,U_70] :
( ( U_73 = U_70
& U_74 = U_71
& U_75 = U_72 )
| g3_lattices(U_75,U_74,U_73) != g3_lattices(U_72,U_71,U_70) )
| ~ m1_relset_1(U_73,k2_zfmisc_1(U_75,U_75),U_75)
| ~ v1_funct_2(U_73,k2_zfmisc_1(U_75,U_75),U_75)
| ~ v1_funct_1(U_73)
| ~ m1_relset_1(U_74,k2_zfmisc_1(U_75,U_75),U_75)
| ~ v1_funct_2(U_74,k2_zfmisc_1(U_75,U_75),U_75)
| ~ v1_funct_1(U_74) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
( ! [U_73,U_74,U_70,U_71,U_72,U_75] :
( U_73 = U_70
| ~ sP13(U_73,U_74,U_70,U_71,U_72,U_75) )
& ! [U_73,U_74,U_70,U_71,U_72,U_75] :
( U_74 = U_71
| ~ sP13(U_73,U_74,U_70,U_71,U_72,U_75) )
& ! [U_73,U_74,U_70,U_71,U_72,U_75] :
( U_75 = U_72
| ~ sP13(U_73,U_74,U_70,U_71,U_72,U_75) )
& ! [U_73,U_74,U_70,U_71,U_72,U_75] :
( sP13(U_73,U_74,U_70,U_71,U_72,U_75)
| g3_lattices(U_75,U_74,U_73) != g3_lattices(U_72,U_71,U_70)
| ~ m1_relset_1(U_73,k2_zfmisc_1(U_75,U_75),U_75)
| ~ v1_funct_2(U_73,k2_zfmisc_1(U_75,U_75),U_75)
| ~ v1_funct_1(U_73)
| ~ m1_relset_1(U_74,k2_zfmisc_1(U_75,U_75),U_75)
| ~ v1_funct_2(U_74,k2_zfmisc_1(U_75,U_75),U_75)
| ~ v1_funct_1(U_74) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP13])],[f_44_2]) ).
cnf(f_44_4,plain,
( sP13(U_73,U_74,U_70,U_71,U_72,U_75)
| g3_lattices(U_75,U_74,U_73) != g3_lattices(U_72,U_71,U_70)
| ~ m1_relset_1(U_73,k2_zfmisc_1(U_75,U_75),U_75)
| ~ v1_funct_2(U_73,k2_zfmisc_1(U_75,U_75),U_75)
| ~ v1_funct_1(U_73)
| ~ m1_relset_1(U_74,k2_zfmisc_1(U_75,U_75),U_75)
| ~ v1_funct_2(U_74,k2_zfmisc_1(U_75,U_75),U_75)
| ~ v1_funct_1(U_74) ),
inference(clausify,[status(thm)],[f_44_3]) ).
cnf(f_44_5,plain,
( U_75 = U_72
| ~ sP13(U_73,U_74,U_70,U_71,U_72,U_75) ),
inference(clausify,[status(thm)],[f_44_3]) ).
cnf(f_44_6,plain,
( U_74 = U_71
| ~ sP13(U_73,U_74,U_70,U_71,U_72,U_75) ),
inference(clausify,[status(thm)],[f_44_3]) ).
cnf(f_44_7,plain,
( U_73 = U_70
| ~ sP13(U_73,U_74,U_70,U_71,U_72,U_75) ),
inference(clausify,[status(thm)],[f_44_3]) ).
fof(f_45_1,plain,
! [A,B] :
? [C] :
( v1_funct_2(C,A,B)
& v1_funct_1(C)
& v1_relat_1(C)
& m1_relset_1(C,A,B) ),
inference(fof_nnf,[status(thm)],[rc1_funct_2]) ).
fof(f_45_2,plain,
! [U_78,U_77] :
? [U_76] :
( v1_funct_2(U_76,U_78,U_77)
& v1_funct_1(U_76)
& v1_relat_1(U_76)
& m1_relset_1(U_76,U_78,U_77) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_78,U_77] :
( v1_funct_2(sK15(U_78,U_77),U_78,U_77)
& v1_funct_1(sK15(U_78,U_77))
& v1_relat_1(sK15(U_78,U_77))
& m1_relset_1(sK15(U_78,U_77),U_78,U_77) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_76,sK15(U_78,U_77))],[f_45_2]) ).
fof(f_45_4,plain,
( ! [U_78,U_77] : v1_funct_2(sK15(U_78,U_77),U_78,U_77)
& ! [U_78,U_77] : v1_funct_1(sK15(U_78,U_77))
& ! [U_78,U_77] : v1_relat_1(sK15(U_78,U_77))
& ! [U_78,U_77] : m1_relset_1(sK15(U_78,U_77),U_78,U_77) ),
inference(definitional_conversion,[status(esa)],[f_45_3]) ).
cnf(f_45_5,plain,
m1_relset_1(sK15(U_78,U_77),U_78,U_77),
inference(clausify,[status(thm)],[f_45_4]) ).
cnf(f_45_6,plain,
v1_relat_1(sK15(U_78,U_77)),
inference(clausify,[status(thm)],[f_45_4]) ).
cnf(f_45_7,plain,
v1_funct_1(sK15(U_78,U_77)),
inference(clausify,[status(thm)],[f_45_4]) ).
cnf(f_45_8,plain,
v1_funct_2(sK15(U_78,U_77),U_78,U_77),
inference(clausify,[status(thm)],[f_45_4]) ).
fof(f_46_1,plain,
? [A] :
( v1_xboole_0(A)
& v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[rc1_partfun1]) ).
fof(f_46_2,plain,
? [U_79] :
( v1_xboole_0(U_79)
& v2_funct_1(U_79)
& v1_funct_1(U_79)
& v1_relat_1(U_79) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
( v1_xboole_0(sK16)
& v2_funct_1(sK16)
& v1_funct_1(sK16)
& v1_relat_1(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_79,sK16)],[f_46_2]) ).
fof(f_46_4,plain,
( v1_xboole_0(sK16)
& v2_funct_1(sK16)
& v1_funct_1(sK16)
& v1_relat_1(sK16) ),
inference(definitional_conversion,[status(esa)],[f_46_3]) ).
cnf(f_46_5,plain,
v1_relat_1(sK16),
inference(clausify,[status(thm)],[f_46_4]) ).
cnf(f_46_6,plain,
v1_funct_1(sK16),
inference(clausify,[status(thm)],[f_46_4]) ).
cnf(f_46_7,plain,
v2_funct_1(sK16),
inference(clausify,[status(thm)],[f_46_4]) ).
cnf(f_46_8,plain,
v1_xboole_0(sK16),
inference(clausify,[status(thm)],[f_46_4]) ).
fof(f_47_1,plain,
! [A] :
( ? [B] :
( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_47_2,plain,
! [U_81] :
( ? [U_80] :
( ~ v1_xboole_0(U_80)
& m1_subset_1(U_80,k1_zfmisc_1(U_81)) )
| v1_xboole_0(U_81) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_81] :
( ( ~ v1_xboole_0(sK17(U_81))
& m1_subset_1(sK17(U_81),k1_zfmisc_1(U_81)) )
| v1_xboole_0(U_81) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_80,sK17(U_81))],[f_47_2]) ).
fof(f_47_4,plain,
( ! [U_81] :
( ~ v1_xboole_0(sK17(U_81))
| ~ sP14(U_81) )
& ! [U_81] :
( m1_subset_1(sK17(U_81),k1_zfmisc_1(U_81))
| ~ sP14(U_81) )
& ! [U_81] :
( sP14(U_81)
| v1_xboole_0(U_81) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14])],[f_47_3]) ).
cnf(f_47_5,plain,
( sP14(U_81)
| v1_xboole_0(U_81) ),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_6,plain,
( m1_subset_1(sK17(U_81),k1_zfmisc_1(U_81))
| ~ sP14(U_81) ),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_7,plain,
( ~ v1_xboole_0(sK17(U_81))
| ~ sP14(U_81) ),
inference(clausify,[status(thm)],[f_47_4]) ).
fof(f_48_1,plain,
? [A] : v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_48_2,plain,
? [U_82] : v1_xboole_0(U_82),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
v1_xboole_0(sK18),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_82,sK18)],[f_48_2]) ).
fof(f_48_4,plain,
v1_xboole_0(sK18),
inference(definitional_conversion,[status(esa)],[f_48_3]) ).
cnf(f_48_5,plain,
v1_xboole_0(sK18),
inference(clausify,[status(thm)],[f_48_4]) ).
fof(f_49_1,plain,
! [A,B] :
? [C] :
( v1_funct_1(C)
& v1_relat_1(C)
& m1_relset_1(C,A,B) ),
inference(fof_nnf,[status(thm)],[rc2_partfun1]) ).
fof(f_49_2,plain,
! [U_85,U_84] :
? [U_83] :
( v1_funct_1(U_83)
& v1_relat_1(U_83)
& m1_relset_1(U_83,U_85,U_84) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
! [U_85,U_84] :
( v1_funct_1(sK19(U_85,U_84))
& v1_relat_1(sK19(U_85,U_84))
& m1_relset_1(sK19(U_85,U_84),U_85,U_84) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_83,sK19(U_85,U_84))],[f_49_2]) ).
fof(f_49_4,plain,
( ! [U_84,U_85] : v1_funct_1(sK19(U_85,U_84))
& ! [U_84,U_85] : v1_relat_1(sK19(U_85,U_84))
& ! [U_84,U_85] : m1_relset_1(sK19(U_85,U_84),U_85,U_84) ),
inference(definitional_conversion,[status(esa)],[f_49_3]) ).
cnf(f_49_5,plain,
m1_relset_1(sK19(U_85,U_84),U_85,U_84),
inference(clausify,[status(thm)],[f_49_4]) ).
cnf(f_49_6,plain,
v1_relat_1(sK19(U_85,U_84)),
inference(clausify,[status(thm)],[f_49_4]) ).
cnf(f_49_7,plain,
v1_funct_1(sK19(U_85,U_84)),
inference(clausify,[status(thm)],[f_49_4]) ).
fof(f_50_1,plain,
! [A] :
? [B] :
( v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_50_2,plain,
! [U_87] :
? [U_86] :
( v1_xboole_0(U_86)
& m1_subset_1(U_86,k1_zfmisc_1(U_87)) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_87] :
( v1_xboole_0(sK20(U_87))
& m1_subset_1(sK20(U_87),k1_zfmisc_1(U_87)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_86,sK20(U_87))],[f_50_2]) ).
fof(f_50_4,plain,
( ! [U_87] : v1_xboole_0(sK20(U_87))
& ! [U_87] : m1_subset_1(sK20(U_87),k1_zfmisc_1(U_87)) ),
inference(definitional_conversion,[status(esa)],[f_50_3]) ).
cnf(f_50_5,plain,
m1_subset_1(sK20(U_87),k1_zfmisc_1(U_87)),
inference(clausify,[status(thm)],[f_50_4]) ).
cnf(f_50_6,plain,
v1_xboole_0(sK20(U_87)),
inference(clausify,[status(thm)],[f_50_4]) ).
fof(f_51_1,plain,
? [A] : ~ v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_51_2,plain,
? [U_88] : ~ v1_xboole_0(U_88),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
~ v1_xboole_0(sK21),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_88,sK21)],[f_51_2]) ).
fof(f_51_4,plain,
~ v1_xboole_0(sK21),
inference(definitional_conversion,[status(esa)],[f_51_3]) ).
cnf(f_51_5,plain,
~ v1_xboole_0(sK21),
inference(clausify,[status(thm)],[f_51_4]) ).
fof(f_52_1,plain,
? [A] :
( ~ v3_struct_0(A)
& l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc3_struct_0]) ).
fof(f_52_2,plain,
? [U_89] :
( ~ v3_struct_0(U_89)
& l1_struct_0(U_89) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
( ~ v3_struct_0(sK22)
& l1_struct_0(sK22) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_89,sK22)],[f_52_2]) ).
fof(f_52_4,plain,
( ~ v3_struct_0(sK22)
& l1_struct_0(sK22) ),
inference(definitional_conversion,[status(esa)],[f_52_3]) ).
cnf(f_52_5,plain,
l1_struct_0(sK22),
inference(clausify,[status(thm)],[f_52_4]) ).
cnf(f_52_6,plain,
~ v3_struct_0(sK22),
inference(clausify,[status(thm)],[f_52_4]) ).
fof(f_53_1,plain,
! [A] :
( ? [B] :
( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc5_struct_0]) ).
fof(f_53_2,plain,
! [U_91] :
( ? [U_90] :
( ~ v1_xboole_0(U_90)
& m1_subset_1(U_90,k1_zfmisc_1(u1_struct_0(U_91))) )
| ~ l1_struct_0(U_91)
| v3_struct_0(U_91) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
! [U_91] :
( ( ~ v1_xboole_0(sK23(U_91))
& m1_subset_1(sK23(U_91),k1_zfmisc_1(u1_struct_0(U_91))) )
| ~ l1_struct_0(U_91)
| v3_struct_0(U_91) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_90,sK23(U_91))],[f_53_2]) ).
fof(f_53_4,plain,
( ! [U_91] :
( ~ v1_xboole_0(sK23(U_91))
| ~ sP15(U_91) )
& ! [U_91] :
( m1_subset_1(sK23(U_91),k1_zfmisc_1(u1_struct_0(U_91)))
| ~ sP15(U_91) )
& ! [U_91] :
( sP15(U_91)
| ~ l1_struct_0(U_91)
| v3_struct_0(U_91) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP15])],[f_53_3]) ).
cnf(f_53_5,plain,
( sP15(U_91)
| ~ l1_struct_0(U_91)
| v3_struct_0(U_91) ),
inference(clausify,[status(thm)],[f_53_4]) ).
cnf(f_53_6,plain,
( m1_subset_1(sK23(U_91),k1_zfmisc_1(u1_struct_0(U_91)))
| ~ sP15(U_91) ),
inference(clausify,[status(thm)],[f_53_4]) ).
cnf(f_53_7,plain,
( ~ v1_xboole_0(sK23(U_91))
| ~ sP15(U_91) ),
inference(clausify,[status(thm)],[f_53_4]) ).
fof(f_54_1,plain,
! [A,B,C] :
( ( m2_relset_1(C,A,B)
| ~ m1_relset_1(C,A,B) )
& ( m1_relset_1(C,A,B)
| ~ m2_relset_1(C,A,B) ) ),
inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1]) ).
fof(f_54_2,plain,
! [U_94,U_93,U_92] :
( ( m2_relset_1(U_92,U_94,U_93)
| ~ m1_relset_1(U_92,U_94,U_93) )
& ( m1_relset_1(U_92,U_94,U_93)
| ~ m2_relset_1(U_92,U_94,U_93) ) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
( ! [U_100,U_98,U_96] :
( m2_relset_1(U_96,U_100,U_98)
| ~ m1_relset_1(U_96,U_100,U_98) )
& ! [U_99,U_97,U_95] :
( m1_relset_1(U_95,U_99,U_97)
| ~ m2_relset_1(U_95,U_99,U_97) ) ),
inference(miniscope,[status(thm)],[f_54_2]) ).
fof(f_54_4,plain,
( ! [U_98,U_96,U_100] :
( m2_relset_1(U_96,U_100,U_98)
| ~ m1_relset_1(U_96,U_100,U_98) )
& ! [U_99,U_95,U_97] :
( m1_relset_1(U_95,U_99,U_97)
| ~ m2_relset_1(U_95,U_99,U_97) ) ),
inference(definitional_conversion,[status(esa)],[f_54_3]) ).
cnf(f_54_5,plain,
( m1_relset_1(U_95,U_99,U_97)
| ~ m2_relset_1(U_95,U_99,U_97) ),
inference(clausify,[status(thm)],[f_54_4]) ).
cnf(f_54_6,plain,
( m2_relset_1(U_96,U_100,U_98)
| ~ m1_relset_1(U_96,U_100,U_98) ),
inference(clausify,[status(thm)],[f_54_4]) ).
fof(f_55_1,plain,
! [A,B] : r1_tarski(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_55_2,plain,
! [U_102,U_101] : r1_tarski(U_102,U_102),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
! [U_102] : r1_tarski(U_102,U_102),
inference(miniscope,[status(thm)],[f_55_2]) ).
fof(f_55_4,plain,
! [U_102] : r1_tarski(U_102,U_102),
inference(definitional_conversion,[status(esa)],[f_55_3]) ).
cnf(f_55_5,plain,
r1_tarski(U_102,U_102),
inference(clausify,[status(thm)],[f_55_4]) ).
fof(f_56_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( m1_lattice4(C,A,B)
| ~ m3_vectsp_8(C,A,B)
| ~ m4_vectsp_8(C,A,B) )
& ( ( m3_vectsp_8(C,A,B)
& m4_vectsp_8(C,A,B) )
| ~ m1_lattice4(C,A,B) ) )
| ~ m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_funct_1(C) )
| ~ l3_lattices(B)
| ~ v10_lattices(B)
| v3_struct_0(B) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t11_vectsp_8]) ).
fof(f_56_2,plain,
! [U_105] :
( ! [U_104] :
( ! [U_103] :
( ( ( m1_lattice4(U_103,U_105,U_104)
| ~ m3_vectsp_8(U_103,U_105,U_104)
| ~ m4_vectsp_8(U_103,U_105,U_104) )
& ( ( m3_vectsp_8(U_103,U_105,U_104)
& m4_vectsp_8(U_103,U_105,U_104) )
| ~ m1_lattice4(U_103,U_105,U_104) ) )
| ~ m2_relset_1(U_103,u1_struct_0(U_105),u1_struct_0(U_104))
| ~ v1_funct_2(U_103,u1_struct_0(U_105),u1_struct_0(U_104))
| ~ v1_funct_1(U_103) )
| ~ l3_lattices(U_104)
| ~ v10_lattices(U_104)
| v3_struct_0(U_104) )
| ~ l3_lattices(U_105)
| ~ v10_lattices(U_105)
| v3_struct_0(U_105) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
( ! [U_103,U_104,U_105] :
( m3_vectsp_8(U_103,U_105,U_104)
| ~ sP16(U_103,U_104,U_105) )
& ! [U_103,U_104,U_105] :
( m4_vectsp_8(U_103,U_105,U_104)
| ~ sP16(U_103,U_104,U_105) )
& ! [U_103,U_104,U_105] :
( m1_lattice4(U_103,U_105,U_104)
| ~ m3_vectsp_8(U_103,U_105,U_104)
| ~ m4_vectsp_8(U_103,U_105,U_104)
| ~ sP17(U_103,U_104,U_105) )
& ! [U_103,U_104,U_105] :
( sP16(U_103,U_104,U_105)
| ~ m1_lattice4(U_103,U_105,U_104)
| ~ sP17(U_103,U_104,U_105) )
& ! [U_103,U_104,U_105] :
( sP17(U_103,U_104,U_105)
| ~ m2_relset_1(U_103,u1_struct_0(U_105),u1_struct_0(U_104))
| ~ v1_funct_2(U_103,u1_struct_0(U_105),u1_struct_0(U_104))
| ~ v1_funct_1(U_103)
| ~ l3_lattices(U_104)
| ~ v10_lattices(U_104)
| v3_struct_0(U_104)
| ~ l3_lattices(U_105)
| ~ v10_lattices(U_105)
| v3_struct_0(U_105) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16,sP17])],[f_56_2]) ).
cnf(f_56_4,plain,
( sP17(U_103,U_104,U_105)
| ~ m2_relset_1(U_103,u1_struct_0(U_105),u1_struct_0(U_104))
| ~ v1_funct_2(U_103,u1_struct_0(U_105),u1_struct_0(U_104))
| ~ v1_funct_1(U_103)
| ~ l3_lattices(U_104)
| ~ v10_lattices(U_104)
| v3_struct_0(U_104)
| ~ l3_lattices(U_105)
| ~ v10_lattices(U_105)
| v3_struct_0(U_105) ),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_5,plain,
( sP16(U_103,U_104,U_105)
| ~ m1_lattice4(U_103,U_105,U_104)
| ~ sP17(U_103,U_104,U_105) ),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_6,plain,
( m1_lattice4(U_103,U_105,U_104)
| ~ m3_vectsp_8(U_103,U_105,U_104)
| ~ m4_vectsp_8(U_103,U_105,U_104)
| ~ sP17(U_103,U_104,U_105) ),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_7,plain,
( m4_vectsp_8(U_103,U_105,U_104)
| ~ sP16(U_103,U_104,U_105) ),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_8,plain,
( m3_vectsp_8(U_103,U_105,U_104)
| ~ sP16(U_103,U_104,U_105) ),
inference(clausify,[status(thm)],[f_56_3]) ).
fof(f_57_1,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_57_2,plain,
! [U_107,U_106] :
( m1_subset_1(U_107,U_106)
| ~ r2_hidden(U_107,U_106) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
! [U_107,U_106] :
( m1_subset_1(U_107,U_106)
| ~ r2_hidden(U_107,U_106) ),
inference(definitional_conversion,[status(esa)],[f_57_2]) ).
cnf(f_57_4,plain,
( m1_subset_1(U_107,U_106)
| ~ r2_hidden(U_107,U_106) ),
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_1,plain,
! [A,B] :
( r2_hidden(A,B)
| v1_xboole_0(B)
| ~ m1_subset_1(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_58_2,plain,
! [U_109,U_108] :
( r2_hidden(U_109,U_108)
| v1_xboole_0(U_108)
| ~ m1_subset_1(U_109,U_108) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
! [U_109,U_108] :
( r2_hidden(U_109,U_108)
| v1_xboole_0(U_108)
| ~ m1_subset_1(U_109,U_108) ),
inference(definitional_conversion,[status(esa)],[f_58_2]) ).
cnf(f_58_4,plain,
( r2_hidden(U_109,U_108)
| v1_xboole_0(U_108)
| ~ m1_subset_1(U_109,U_108) ),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_59_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( m3_vectsp_8(k3_latsubgr(A,B,C),k11_group_4(A),k11_group_4(B))
| ~ v2_funct_1(C)
| ~ m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_group_6(C,A,B)
| ~ v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_funct_1(C) )
| ~ l1_group_1(B)
| ~ v4_group_1(B)
| ~ v3_group_1(B)
| v3_struct_0(B) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t36_latsubgr]) ).
fof(f_59_2,plain,
! [U_112] :
( ! [U_111] :
( ! [U_110] :
( m3_vectsp_8(k3_latsubgr(U_112,U_111,U_110),k11_group_4(U_112),k11_group_4(U_111))
| ~ v2_funct_1(U_110)
| ~ m2_relset_1(U_110,u1_struct_0(U_112),u1_struct_0(U_111))
| ~ v1_group_6(U_110,U_112,U_111)
| ~ v1_funct_2(U_110,u1_struct_0(U_112),u1_struct_0(U_111))
| ~ v1_funct_1(U_110) )
| ~ l1_group_1(U_111)
| ~ v4_group_1(U_111)
| ~ v3_group_1(U_111)
| v3_struct_0(U_111) )
| ~ l1_group_1(U_112)
| ~ v4_group_1(U_112)
| ~ v3_group_1(U_112)
| v3_struct_0(U_112) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
! [U_112,U_110,U_111] :
( m3_vectsp_8(k3_latsubgr(U_112,U_111,U_110),k11_group_4(U_112),k11_group_4(U_111))
| ~ v2_funct_1(U_110)
| ~ m2_relset_1(U_110,u1_struct_0(U_112),u1_struct_0(U_111))
| ~ v1_group_6(U_110,U_112,U_111)
| ~ v1_funct_2(U_110,u1_struct_0(U_112),u1_struct_0(U_111))
| ~ v1_funct_1(U_110)
| ~ l1_group_1(U_111)
| ~ v4_group_1(U_111)
| ~ v3_group_1(U_111)
| v3_struct_0(U_111)
| ~ l1_group_1(U_112)
| ~ v4_group_1(U_112)
| ~ v3_group_1(U_112)
| v3_struct_0(U_112) ),
inference(definitional_conversion,[status(esa)],[f_59_2]) ).
cnf(f_59_4,plain,
( m3_vectsp_8(k3_latsubgr(U_112,U_111,U_110),k11_group_4(U_112),k11_group_4(U_111))
| ~ v2_funct_1(U_110)
| ~ m2_relset_1(U_110,u1_struct_0(U_112),u1_struct_0(U_111))
| ~ v1_group_6(U_110,U_112,U_111)
| ~ v1_funct_2(U_110,u1_struct_0(U_112),u1_struct_0(U_111))
| ~ v1_funct_1(U_110)
| ~ l1_group_1(U_111)
| ~ v4_group_1(U_111)
| ~ v3_group_1(U_111)
| v3_struct_0(U_111)
| ~ l1_group_1(U_112)
| ~ v4_group_1(U_112)
| ~ v3_group_1(U_112)
| v3_struct_0(U_112) ),
inference(clausify,[status(thm)],[f_59_3]) ).
fof(f_60_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( m4_vectsp_8(k3_latsubgr(A,B,C),k11_group_4(A),k11_group_4(B))
| ~ m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_group_6(C,A,B)
| ~ v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
| ~ v1_funct_1(C) )
| ~ l1_group_1(B)
| ~ v4_group_1(B)
| ~ v3_group_1(B)
| v3_struct_0(B) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t37_latsubgr]) ).
fof(f_60_2,plain,
! [U_115] :
( ! [U_114] :
( ! [U_113] :
( m4_vectsp_8(k3_latsubgr(U_115,U_114,U_113),k11_group_4(U_115),k11_group_4(U_114))
| ~ m2_relset_1(U_113,u1_struct_0(U_115),u1_struct_0(U_114))
| ~ v1_group_6(U_113,U_115,U_114)
| ~ v1_funct_2(U_113,u1_struct_0(U_115),u1_struct_0(U_114))
| ~ v1_funct_1(U_113) )
| ~ l1_group_1(U_114)
| ~ v4_group_1(U_114)
| ~ v3_group_1(U_114)
| v3_struct_0(U_114) )
| ~ l1_group_1(U_115)
| ~ v4_group_1(U_115)
| ~ v3_group_1(U_115)
| v3_struct_0(U_115) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
! [U_114,U_113,U_115] :
( m4_vectsp_8(k3_latsubgr(U_115,U_114,U_113),k11_group_4(U_115),k11_group_4(U_114))
| ~ m2_relset_1(U_113,u1_struct_0(U_115),u1_struct_0(U_114))
| ~ v1_group_6(U_113,U_115,U_114)
| ~ v1_funct_2(U_113,u1_struct_0(U_115),u1_struct_0(U_114))
| ~ v1_funct_1(U_113)
| ~ l1_group_1(U_114)
| ~ v4_group_1(U_114)
| ~ v3_group_1(U_114)
| v3_struct_0(U_114)
| ~ l1_group_1(U_115)
| ~ v4_group_1(U_115)
| ~ v3_group_1(U_115)
| v3_struct_0(U_115) ),
inference(definitional_conversion,[status(esa)],[f_60_2]) ).
cnf(f_60_4,plain,
( m4_vectsp_8(k3_latsubgr(U_115,U_114,U_113),k11_group_4(U_115),k11_group_4(U_114))
| ~ m2_relset_1(U_113,u1_struct_0(U_115),u1_struct_0(U_114))
| ~ v1_group_6(U_113,U_115,U_114)
| ~ v1_funct_2(U_113,u1_struct_0(U_115),u1_struct_0(U_114))
| ~ v1_funct_1(U_113)
| ~ l1_group_1(U_114)
| ~ v4_group_1(U_114)
| ~ v3_group_1(U_114)
| v3_struct_0(U_114)
| ~ l1_group_1(U_115)
| ~ v4_group_1(U_115)
| ~ v3_group_1(U_115)
| v3_struct_0(U_115) ),
inference(clausify,[status(thm)],[f_60_3]) ).
fof(f_61_1,plain,
! [A,B] :
( ( m1_subset_1(A,k1_zfmisc_1(B))
| ~ r1_tarski(A,B) )
& ( r1_tarski(A,B)
| ~ m1_subset_1(A,k1_zfmisc_1(B)) ) ),
inference(fof_nnf,[status(thm)],[t3_subset]) ).
fof(f_61_2,plain,
! [U_117,U_116] :
( ( m1_subset_1(U_117,k1_zfmisc_1(U_116))
| ~ r1_tarski(U_117,U_116) )
& ( r1_tarski(U_117,U_116)
| ~ m1_subset_1(U_117,k1_zfmisc_1(U_116)) ) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
( ! [U_121,U_119] :
( m1_subset_1(U_121,k1_zfmisc_1(U_119))
| ~ r1_tarski(U_121,U_119) )
& ! [U_120,U_118] :
( r1_tarski(U_120,U_118)
| ~ m1_subset_1(U_120,k1_zfmisc_1(U_118)) ) ),
inference(miniscope,[status(thm)],[f_61_2]) ).
fof(f_61_4,plain,
( ! [U_119,U_121] :
( m1_subset_1(U_121,k1_zfmisc_1(U_119))
| ~ r1_tarski(U_121,U_119) )
& ! [U_120,U_118] :
( r1_tarski(U_120,U_118)
| ~ m1_subset_1(U_120,k1_zfmisc_1(U_118)) ) ),
inference(definitional_conversion,[status(esa)],[f_61_3]) ).
cnf(f_61_5,plain,
( r1_tarski(U_120,U_118)
| ~ m1_subset_1(U_120,k1_zfmisc_1(U_118)) ),
inference(clausify,[status(thm)],[f_61_4]) ).
cnf(f_61_6,plain,
( m1_subset_1(U_121,k1_zfmisc_1(U_119))
| ~ r1_tarski(U_121,U_119) ),
inference(clausify,[status(thm)],[f_61_4]) ).
fof(f_62_1,plain,
! [A,B,C] :
( m1_subset_1(A,C)
| ~ m1_subset_1(B,k1_zfmisc_1(C))
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_62_2,plain,
! [U_124,U_123,U_122] :
( m1_subset_1(U_124,U_122)
| ~ m1_subset_1(U_123,k1_zfmisc_1(U_122))
| ~ r2_hidden(U_124,U_123) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
! [U_124,U_123,U_122] :
( m1_subset_1(U_124,U_122)
| ~ m1_subset_1(U_123,k1_zfmisc_1(U_122))
| ~ r2_hidden(U_124,U_123) ),
inference(definitional_conversion,[status(esa)],[f_62_2]) ).
cnf(f_62_4,plain,
( m1_subset_1(U_124,U_122)
| ~ m1_subset_1(U_123,k1_zfmisc_1(U_122))
| ~ r2_hidden(U_124,U_123) ),
inference(clausify,[status(thm)],[f_62_3]) ).
fof(f_63_1,plain,
! [A,B,C] :
( ~ v1_xboole_0(C)
| ~ m1_subset_1(B,k1_zfmisc_1(C))
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_63_2,plain,
! [U_127,U_126,U_125] :
( ~ v1_xboole_0(U_125)
| ~ m1_subset_1(U_126,k1_zfmisc_1(U_125))
| ~ r2_hidden(U_127,U_126) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
! [U_127,U_126] :
( ! [U_125] :
( ~ v1_xboole_0(U_125)
| ~ m1_subset_1(U_126,k1_zfmisc_1(U_125)) )
| ~ r2_hidden(U_127,U_126) ),
inference(miniscope,[status(thm)],[f_63_2]) ).
fof(f_63_4,plain,
! [U_126,U_125,U_127] :
( ~ v1_xboole_0(U_125)
| ~ m1_subset_1(U_126,k1_zfmisc_1(U_125))
| ~ r2_hidden(U_127,U_126) ),
inference(definitional_conversion,[status(esa)],[f_63_3]) ).
cnf(f_63_5,plain,
( ~ v1_xboole_0(U_125)
| ~ m1_subset_1(U_126,k1_zfmisc_1(U_125))
| ~ r2_hidden(U_127,U_126) ),
inference(clausify,[status(thm)],[f_63_4]) ).
fof(f_64_1,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_64_2,plain,
! [U_128] :
( U_128 = k1_xboole_0
| ~ v1_xboole_0(U_128) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
! [U_128] :
( U_128 = k1_xboole_0
| ~ v1_xboole_0(U_128) ),
inference(definitional_conversion,[status(esa)],[f_64_2]) ).
cnf(f_64_4,plain,
( U_128 = k1_xboole_0
| ~ v1_xboole_0(U_128) ),
inference(clausify,[status(thm)],[f_64_3]) ).
fof(f_65_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_65_2,plain,
! [U_130,U_129] :
( ~ v1_xboole_0(U_129)
| ~ r2_hidden(U_130,U_129) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
! [U_130,U_129] :
( ~ v1_xboole_0(U_129)
| ~ r2_hidden(U_130,U_129) ),
inference(definitional_conversion,[status(esa)],[f_65_2]) ).
cnf(f_65_4,plain,
( ~ v1_xboole_0(U_129)
| ~ r2_hidden(U_130,U_129) ),
inference(clausify,[status(thm)],[f_65_3]) ).
fof(f_66_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| A = B
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_66_2,plain,
! [U_132,U_131] :
( ~ v1_xboole_0(U_131)
| U_132 = U_131
| ~ v1_xboole_0(U_132) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
! [U_132] :
( ! [U_131] :
( ~ v1_xboole_0(U_131)
| U_132 = U_131 )
| ~ v1_xboole_0(U_132) ),
inference(miniscope,[status(thm)],[f_66_2]) ).
fof(f_66_4,plain,
! [U_132,U_131] :
( ~ v1_xboole_0(U_131)
| U_132 = U_131
| ~ v1_xboole_0(U_132) ),
inference(definitional_conversion,[status(esa)],[f_66_3]) ).
cnf(f_66_5,plain,
( ~ v1_xboole_0(U_131)
| U_132 = U_131
| ~ v1_xboole_0(U_132) ),
inference(clausify,[status(thm)],[f_66_4]) ).
cnf(f_10_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_3]) ).
cnf(f_11_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_11_3]) ).
cnf(f_12_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_12_3]) ).
cnf(f_16_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_16_3]) ).
cnf(f_20_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_20_3]) ).
cnf(f_21_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_21_3]) ).
cnf(f_26_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_26_3]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( u1_struct_0(Eq_x_0) = u1_struct_0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( k3_latsubgr(Eq_x_0,Eq_x_1,Eq_x_2) = k3_latsubgr(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( k11_group_4(Eq_x_0) = k11_group_4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( u2_lattices(Eq_x_0) = u2_lattices(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( u1_lattices(Eq_x_0) = u1_lattices(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( g3_lattices(Eq_x_0,Eq_x_1,Eq_x_2) = g3_lattices(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( k2_zfmisc_1(Eq_x_0,Eq_x_1) = k2_zfmisc_1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( k1_zfmisc_1(Eq_x_0) = k1_zfmisc_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK9(Eq_x_0,Eq_x_1) = sK9(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK10(Eq_x_0,Eq_x_1) = sK10(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK11(Eq_x_0) = sK11(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK12(Eq_x_0,Eq_x_1) = sK12(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK13(Eq_x_0,Eq_x_1) = sK13(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( sK14(Eq_x_0,Eq_x_1) = sK14(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK15(Eq_x_0,Eq_x_1) = sK15(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( sK17(Eq_x_0) = sK17(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( sK19(Eq_x_0,Eq_x_1) = sK19(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( sK20(Eq_x_0) = sK20(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( sK23(Eq_x_0) = sK23(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( v3_struct_0(Eq_y_0)
| ~ v3_struct_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( v3_group_1(Eq_y_0)
| ~ v3_group_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( v4_group_1(Eq_y_0)
| ~ v4_group_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( l1_group_1(Eq_y_0)
| ~ l1_group_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( v1_funct_1(Eq_y_0)
| ~ v1_funct_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( v1_funct_2(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ v1_funct_2(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,axiom,
( v1_group_6(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ v1_group_6(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,axiom,
( m2_relset_1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ m2_relset_1(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_31,axiom,
( v2_funct_1(Eq_y_0)
| ~ v2_funct_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( m1_lattice4(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ m1_lattice4(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,axiom,
( l3_lattices(Eq_y_0)
| ~ l3_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,axiom,
( v3_lattices(Eq_y_0)
| ~ v3_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( r2_hidden(Eq_y_0,Eq_y_1)
| ~ r2_hidden(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,axiom,
( m1_relset_1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ m1_relset_1(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_37,axiom,
( v1_partfun1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ v1_partfun1(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_38,axiom,
( m1_subset_1(Eq_y_0,Eq_y_1)
| ~ m1_subset_1(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_39,axiom,
( v1_relat_1(Eq_y_0)
| ~ v1_relat_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_40,axiom,
( v1_xboole_0(Eq_y_0)
| ~ v1_xboole_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_41,axiom,
( v10_lattices(Eq_y_0)
| ~ v10_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_42,axiom,
( l1_struct_0(Eq_y_0)
| ~ l1_struct_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_43,axiom,
( l1_lattices(Eq_y_0)
| ~ l1_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_44,axiom,
( l2_lattices(Eq_y_0)
| ~ l2_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_45,axiom,
( m3_vectsp_8(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ m3_vectsp_8(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_46,axiom,
( m4_vectsp_8(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ m4_vectsp_8(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_47,axiom,
( v4_lattices(Eq_y_0)
| ~ v4_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_48,axiom,
( v5_lattices(Eq_y_0)
| ~ v5_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_49,axiom,
( v6_lattices(Eq_y_0)
| ~ v6_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_50,axiom,
( v7_lattices(Eq_y_0)
| ~ v7_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_51,axiom,
( v8_lattices(Eq_y_0)
| ~ v8_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_52,axiom,
( v9_lattices(Eq_y_0)
| ~ v9_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_53,axiom,
( v13_lattices(Eq_y_0)
| ~ v13_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_54,axiom,
( v14_lattices(Eq_y_0)
| ~ v14_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_55,axiom,
( v15_lattices(Eq_y_0)
| ~ v15_lattices(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_56,axiom,
( r1_tarski(Eq_y_0,Eq_y_1)
| ~ r1_tarski(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_57,axiom,
( sP0(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP0(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_58,axiom,
( sP1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP1(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_59,axiom,
( sP2(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP2(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_60,axiom,
( sP3(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP3(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_61,axiom,
( sP4(Eq_y_0)
| ~ sP4(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_62,axiom,
( sP5(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP5(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_63,axiom,
( sP6(Eq_y_0)
| ~ sP6(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_64,axiom,
( sP7(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP7(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_65,axiom,
( sP8(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP8(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_66,axiom,
( sP9(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP9(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_67,axiom,
( sP10(Eq_y_0)
| ~ sP10(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_68,axiom,
( sP11(Eq_y_0)
| ~ sP11(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_69,axiom,
( sP12(Eq_y_0)
| ~ sP12(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_70,axiom,
( sP13(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP13(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_71,axiom,
( sP14(Eq_y_0)
| ~ sP14(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_72,axiom,
( sP15(Eq_y_0)
| ~ sP15(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_73,axiom,
( sP16(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP16(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_74,axiom,
( sP17(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP17(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP653+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 10:05:34 UTC 2026
% 0.10/0.36 % CPUTime :
% 34.65/35.02 % SZS status Theorem for theBenchmark
% 34.65/35.02 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------