%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : TOP025+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 09:12:55 AM UTC 2026
% Result : Theorem 34.66s 34.91s
% Output : Proof 34.66s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(t3_tsp_2,conjecture,
! [A] :
( ( l1_pre_topc(A)
& v2_pre_topc(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_tsp_2(B,A)
& ( v4_pre_topc(B,A)
| v3_pre_topc(B,A) ) ) ) ),
file('theBenchmark.p',t3_tsp_2) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( r2_hidden(A,B)
=> ~ r2_hidden(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(cc10_membered,axiom,
! [A] :
( v1_membered(A)
=> ! [B] :
( m1_subset_1(B,A)
=> v1_xcmplx_0(B) ) ),
file('theBenchmark.p',cc10_membered) ).
fof(cc11_membered,axiom,
! [A] :
( v2_membered(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ( v1_xreal_0(B)
& v1_xcmplx_0(B) ) ) ),
file('theBenchmark.p',cc11_membered) ).
fof(cc12_membered,axiom,
! [A] :
( v3_membered(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ( v1_rat_1(B)
& v1_xreal_0(B)
& v1_xcmplx_0(B) ) ) ),
file('theBenchmark.p',cc12_membered) ).
fof(cc13_membered,axiom,
! [A] :
( v4_membered(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ( v1_rat_1(B)
& v1_int_1(B)
& v1_xreal_0(B)
& v1_xcmplx_0(B) ) ) ),
file('theBenchmark.p',cc13_membered) ).
fof(cc14_membered,axiom,
! [A] :
( v5_membered(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ( v1_rat_1(B)
& v1_int_1(B)
& v1_xreal_0(B)
& v4_ordinal2(B)
& v1_xcmplx_0(B) ) ) ),
file('theBenchmark.p',cc14_membered) ).
fof(cc15_membered,axiom,
! [A] :
( v1_xboole_0(A)
=> ( v5_membered(A)
& v4_membered(A)
& v3_membered(A)
& v2_membered(A)
& v1_membered(A) ) ),
file('theBenchmark.p',cc15_membered) ).
fof(cc16_membered,axiom,
! [A] :
( v1_membered(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> v1_membered(B) ) ),
file('theBenchmark.p',cc16_membered) ).
fof(cc17_membered,axiom,
! [A] :
( v2_membered(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ( v2_membered(B)
& v1_membered(B) ) ) ),
file('theBenchmark.p',cc17_membered) ).
fof(cc18_membered,axiom,
! [A] :
( v3_membered(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ( v3_membered(B)
& v2_membered(B)
& v1_membered(B) ) ) ),
file('theBenchmark.p',cc18_membered) ).
fof(cc19_membered,axiom,
! [A] :
( v4_membered(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ( v4_membered(B)
& v3_membered(B)
& v2_membered(B)
& v1_membered(B) ) ) ),
file('theBenchmark.p',cc19_membered) ).
fof(cc1_membered,axiom,
! [A] :
( v5_membered(A)
=> v4_membered(A) ),
file('theBenchmark.p',cc1_membered) ).
fof(cc1_tops_1,axiom,
! [A] :
( ( l1_pre_topc(A)
& v2_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_xboole_0(B)
=> ( v4_pre_topc(B,A)
& v3_pre_topc(B,A) ) ) ) ),
file('theBenchmark.p',cc1_tops_1) ).
fof(cc20_membered,axiom,
! [A] :
( v5_membered(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ( v5_membered(B)
& v4_membered(B)
& v3_membered(B)
& v2_membered(B)
& v1_membered(B) ) ) ),
file('theBenchmark.p',cc20_membered) ).
fof(cc2_membered,axiom,
! [A] :
( v4_membered(A)
=> v3_membered(A) ),
file('theBenchmark.p',cc2_membered) ).
fof(cc2_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_xboole_0(B)
=> v2_tops_1(B,A) ) ) ),
file('theBenchmark.p',cc2_tops_1) ).
fof(cc3_membered,axiom,
! [A] :
( v3_membered(A)
=> v2_membered(A) ),
file('theBenchmark.p',cc3_membered) ).
fof(cc3_tops_1,axiom,
! [A] :
( ( l1_pre_topc(A)
& v2_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_xboole_0(B)
=> v3_tops_1(B,A) ) ) ),
file('theBenchmark.p',cc3_tops_1) ).
fof(cc4_membered,axiom,
! [A] :
( v2_membered(A)
=> v1_membered(A) ),
file('theBenchmark.p',cc4_membered) ).
fof(cc4_tops_1,axiom,
! [A] :
( ( l1_pre_topc(A)
& v2_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_tops_1(B,A)
=> v2_tops_1(B,A) ) ) ),
file('theBenchmark.p',cc4_tops_1) ).
fof(cc5_tops_1,axiom,
! [A] :
( ( l1_pre_topc(A)
& v2_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v2_tops_1(B,A)
& v4_pre_topc(B,A) )
=> ( v3_tops_1(B,A)
& v2_tops_1(B,A) ) ) ) ),
file('theBenchmark.p',cc5_tops_1) ).
fof(cc6_tops_1,axiom,
! [A] :
( ( l1_pre_topc(A)
& v2_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_tops_1(B,A)
& v3_pre_topc(B,A) )
=> ( v3_tops_1(B,A)
& v2_tops_1(B,A)
& v5_membered(B)
& v4_membered(B)
& v3_membered(B)
& v2_membered(B)
& v1_membered(B)
& v4_pre_topc(B,A)
& v3_pre_topc(B,A)
& v1_xboole_0(B) ) ) ) ),
file('theBenchmark.p',cc6_tops_1) ).
fof(d5_tsp_2,axiom,
! [A] :
( ( l1_pre_topc(A)
& v2_pre_topc(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_tsp_2(B,A)
<=> ( k3_tex_4(A,B) = u1_struct_0(A)
& v1_tsp_1(B,A) ) ) ) ),
file('theBenchmark.p',d5_tsp_2) ).
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_k3_tex_4,axiom,
! [A,B] :
( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& l1_pre_topc(A)
& ~ v3_struct_0(A) )
=> m1_subset_1(k3_tex_4(A,B),k1_zfmisc_1(u1_struct_0(A))) ),
file('theBenchmark.p',dt_k3_tex_4) ).
fof(dt_l1_pre_topc,axiom,
! [A] :
( l1_pre_topc(A)
=> l1_struct_0(A) ),
file('theBenchmark.p',dt_l1_pre_topc) ).
fof(dt_l1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_l1_struct_0) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(dt_u1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_u1_struct_0) ).
fof(existence_l1_pre_topc,axiom,
? [A] : l1_pre_topc(A),
file('theBenchmark.p',existence_l1_pre_topc) ).
fof(existence_l1_struct_0,axiom,
? [A] : l1_struct_0(A),
file('theBenchmark.p',existence_l1_struct_0) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : m1_subset_1(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
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(fc6_membered,axiom,
( v5_membered(k1_xboole_0)
& v4_membered(k1_xboole_0)
& v3_membered(k1_xboole_0)
& v2_membered(k1_xboole_0)
& v1_membered(k1_xboole_0)
& v1_xboole_0(k1_xboole_0) ),
file('theBenchmark.p',fc6_membered) ).
fof(rc1_membered,axiom,
? [A] :
( v5_membered(A)
& v4_membered(A)
& v3_membered(A)
& v2_membered(A)
& v1_membered(A)
& ~ v1_xboole_0(A) ),
file('theBenchmark.p',rc1_membered) ).
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_tops_1,axiom,
! [A] :
( ( l1_pre_topc(A)
& v2_pre_topc(A) )
=> ? [B] :
( v3_pre_topc(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ),
file('theBenchmark.p',rc1_tops_1) ).
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_tops_1,axiom,
! [A] :
( ( l1_pre_topc(A)
& v2_pre_topc(A) )
=> ? [B] :
( v4_pre_topc(B,A)
& v3_pre_topc(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ),
file('theBenchmark.p',rc2_tops_1) ).
fof(rc3_struct_0,axiom,
? [A] :
( ~ v3_struct_0(A)
& l1_struct_0(A) ),
file('theBenchmark.p',rc3_struct_0) ).
fof(rc3_tops_1,axiom,
! [A] :
( ( l1_pre_topc(A)
& v2_pre_topc(A)
& ~ v3_struct_0(A) )
=> ? [B] :
( v4_pre_topc(B,A)
& v3_pre_topc(B,A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ),
file('theBenchmark.p',rc3_tops_1) ).
fof(rc4_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ? [B] :
( v2_tops_1(B,A)
& v5_membered(B)
& v4_membered(B)
& v3_membered(B)
& v2_membered(B)
& v1_membered(B)
& v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ),
file('theBenchmark.p',rc4_tops_1) ).
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(rc5_tops_1,axiom,
! [A] :
( ( l1_pre_topc(A)
& v2_pre_topc(A) )
=> ? [B] :
( v3_tops_1(B,A)
& v2_tops_1(B,A)
& v5_membered(B)
& v4_membered(B)
& v3_membered(B)
& v2_membered(B)
& v1_membered(B)
& v4_pre_topc(B,A)
& v3_pre_topc(B,A)
& v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ),
file('theBenchmark.p',rc5_tops_1) ).
fof(rc6_pre_topc,axiom,
! [A] :
( ( l1_pre_topc(A)
& v2_pre_topc(A) )
=> ? [B] :
( v4_pre_topc(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ),
file('theBenchmark.p',rc6_pre_topc) ).
fof(rc7_pre_topc,axiom,
! [A] :
( ( l1_pre_topc(A)
& v2_pre_topc(A)
& ~ v3_struct_0(A) )
=> ? [B] :
( v4_pre_topc(B,A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ),
file('theBenchmark.p',rc7_pre_topc) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : r1_tarski(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
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(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(t58_tex_4,axiom,
! [A] :
( ( l1_pre_topc(A)
& v2_pre_topc(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(B,A)
=> k3_tex_4(A,B) = B ) ) ),
file('theBenchmark.p',t58_tex_4) ).
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(t5_tex_2,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ( v1_tex_2(B,k1_zfmisc_1(A))
<=> B != A ) ),
file('theBenchmark.p',t5_tex_2) ).
fof(t62_tex_4,axiom,
! [A] :
( ( l1_pre_topc(A)
& v2_pre_topc(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_pre_topc(B,A)
=> k3_tex_4(A,B) = B ) ) ),
file('theBenchmark.p',t62_tex_4) ).
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_pre_topc(A)
& v2_pre_topc(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_tsp_2(B,A)
& ( v4_pre_topc(B,A)
| v3_pre_topc(B,A) ) ) ) ),
inference(negate,[status(cth)],[t3_tsp_2]) ).
fof(f_1_2,negated_conjecture,
? [A] :
( ? [B] :
( v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_tsp_2(B,A)
& ( v4_pre_topc(B,A)
| v3_pre_topc(B,A) )
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
& l1_pre_topc(A)
& v2_pre_topc(A)
& ~ v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
? [U_1] :
( ? [U_0] :
( v1_tex_2(U_0,k1_zfmisc_1(u1_struct_0(U_1)))
& v1_tsp_2(U_0,U_1)
& ( v4_pre_topc(U_0,U_1)
| v3_pre_topc(U_0,U_1) )
& m1_subset_1(U_0,k1_zfmisc_1(u1_struct_0(U_1))) )
& l1_pre_topc(U_1)
& v2_pre_topc(U_1)
& ~ v3_struct_0(U_1) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
( ? [U_0] :
( v1_tex_2(U_0,k1_zfmisc_1(u1_struct_0(sK1)))
& v1_tsp_2(U_0,sK1)
& ( v4_pre_topc(U_0,sK1)
| v3_pre_topc(U_0,sK1) )
& m1_subset_1(U_0,k1_zfmisc_1(u1_struct_0(sK1))) )
& l1_pre_topc(sK1)
& v2_pre_topc(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_1,sK1)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
( v1_tex_2(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
& v1_tsp_2(sK2,sK1)
& ( v4_pre_topc(sK2,sK1)
| v3_pre_topc(sK2,sK1) )
& m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
& l1_pre_topc(sK1)
& v2_pre_topc(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_0,sK2)],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( v1_tex_2(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
& v1_tsp_2(sK2,sK1)
& ( v4_pre_topc(sK2,sK1)
| v3_pre_topc(sK2,sK1) )
& m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1)))
& l1_pre_topc(sK1)
& v2_pre_topc(sK1)
& ~ v3_struct_0(sK1) ),
inference(definitional_conversion,[status(esa)],[f_1_5]) ).
cnf(f_1_7,negated_conjecture,
~ v3_struct_0(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_8,negated_conjecture,
v2_pre_topc(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_9,negated_conjecture,
l1_pre_topc(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_10,negated_conjecture,
m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK1))),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_11,negated_conjecture,
( v4_pre_topc(sK2,sK1)
| v3_pre_topc(sK2,sK1) ),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_12,negated_conjecture,
v1_tsp_2(sK2,sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_13,negated_conjecture,
v1_tex_2(sK2,k1_zfmisc_1(u1_struct_0(sK1))),
inference(clausify,[status(thm)],[f_1_6]) ).
fof(f_2_1,plain,
! [A,B] :
( ~ r2_hidden(B,A)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_2_2,plain,
! [U_3,U_2] :
( ~ r2_hidden(U_2,U_3)
| ~ r2_hidden(U_3,U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_3,U_2] :
( ~ r2_hidden(U_2,U_3)
| ~ r2_hidden(U_3,U_2) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( ~ r2_hidden(U_2,U_3)
| ~ r2_hidden(U_3,U_2) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A] :
( ! [B] :
( v1_xcmplx_0(B)
| ~ m1_subset_1(B,A) )
| ~ v1_membered(A) ),
inference(fof_nnf,[status(thm)],[cc10_membered]) ).
fof(f_3_2,plain,
! [U_5] :
( ! [U_4] :
( v1_xcmplx_0(U_4)
| ~ m1_subset_1(U_4,U_5) )
| ~ v1_membered(U_5) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_5,U_4] :
( v1_xcmplx_0(U_4)
| ~ m1_subset_1(U_4,U_5)
| ~ v1_membered(U_5) ),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
( v1_xcmplx_0(U_4)
| ~ m1_subset_1(U_4,U_5)
| ~ v1_membered(U_5) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [A] :
( ! [B] :
( ( v1_xreal_0(B)
& v1_xcmplx_0(B) )
| ~ m1_subset_1(B,A) )
| ~ v2_membered(A) ),
inference(fof_nnf,[status(thm)],[cc11_membered]) ).
fof(f_4_2,plain,
! [U_7] :
( ! [U_6] :
( ( v1_xreal_0(U_6)
& v1_xcmplx_0(U_6) )
| ~ m1_subset_1(U_6,U_7) )
| ~ v2_membered(U_7) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_6] :
( v1_xreal_0(U_6)
| ~ sP0(U_6) )
& ! [U_6] :
( v1_xcmplx_0(U_6)
| ~ sP0(U_6) )
& ! [U_6,U_7] :
( sP0(U_6)
| ~ m1_subset_1(U_6,U_7)
| ~ v2_membered(U_7) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_4_2]) ).
cnf(f_4_4,plain,
( sP0(U_6)
| ~ m1_subset_1(U_6,U_7)
| ~ v2_membered(U_7) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( v1_xcmplx_0(U_6)
| ~ sP0(U_6) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( v1_xreal_0(U_6)
| ~ sP0(U_6) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [A] :
( ! [B] :
( ( v1_rat_1(B)
& v1_xreal_0(B)
& v1_xcmplx_0(B) )
| ~ m1_subset_1(B,A) )
| ~ v3_membered(A) ),
inference(fof_nnf,[status(thm)],[cc12_membered]) ).
fof(f_5_2,plain,
! [U_9] :
( ! [U_8] :
( ( v1_rat_1(U_8)
& v1_xreal_0(U_8)
& v1_xcmplx_0(U_8) )
| ~ m1_subset_1(U_8,U_9) )
| ~ v3_membered(U_9) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_8] :
( v1_rat_1(U_8)
| ~ sP1(U_8) )
& ! [U_8] :
( v1_xreal_0(U_8)
| ~ sP1(U_8) )
& ! [U_8] :
( v1_xcmplx_0(U_8)
| ~ sP1(U_8) )
& ! [U_9,U_8] :
( sP1(U_8)
| ~ m1_subset_1(U_8,U_9)
| ~ v3_membered(U_9) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_5_2]) ).
cnf(f_5_4,plain,
( sP1(U_8)
| ~ m1_subset_1(U_8,U_9)
| ~ v3_membered(U_9) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( v1_xcmplx_0(U_8)
| ~ sP1(U_8) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_6,plain,
( v1_xreal_0(U_8)
| ~ sP1(U_8) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_7,plain,
( v1_rat_1(U_8)
| ~ sP1(U_8) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A] :
( ! [B] :
( ( v1_rat_1(B)
& v1_int_1(B)
& v1_xreal_0(B)
& v1_xcmplx_0(B) )
| ~ m1_subset_1(B,A) )
| ~ v4_membered(A) ),
inference(fof_nnf,[status(thm)],[cc13_membered]) ).
fof(f_6_2,plain,
! [U_11] :
( ! [U_10] :
( ( v1_rat_1(U_10)
& v1_int_1(U_10)
& v1_xreal_0(U_10)
& v1_xcmplx_0(U_10) )
| ~ m1_subset_1(U_10,U_11) )
| ~ v4_membered(U_11) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_10] :
( v1_rat_1(U_10)
| ~ sP2(U_10) )
& ! [U_10] :
( v1_int_1(U_10)
| ~ sP2(U_10) )
& ! [U_10] :
( v1_xreal_0(U_10)
| ~ sP2(U_10) )
& ! [U_10] :
( v1_xcmplx_0(U_10)
| ~ sP2(U_10) )
& ! [U_11,U_10] :
( sP2(U_10)
| ~ m1_subset_1(U_10,U_11)
| ~ v4_membered(U_11) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_6_2]) ).
cnf(f_6_4,plain,
( sP2(U_10)
| ~ m1_subset_1(U_10,U_11)
| ~ v4_membered(U_11) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( v1_xcmplx_0(U_10)
| ~ sP2(U_10) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
( v1_xreal_0(U_10)
| ~ sP2(U_10) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_7,plain,
( v1_int_1(U_10)
| ~ sP2(U_10) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_8,plain,
( v1_rat_1(U_10)
| ~ sP2(U_10) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [A] :
( ! [B] :
( ( v1_rat_1(B)
& v1_int_1(B)
& v1_xreal_0(B)
& v4_ordinal2(B)
& v1_xcmplx_0(B) )
| ~ m1_subset_1(B,A) )
| ~ v5_membered(A) ),
inference(fof_nnf,[status(thm)],[cc14_membered]) ).
fof(f_7_2,plain,
! [U_13] :
( ! [U_12] :
( ( v1_rat_1(U_12)
& v1_int_1(U_12)
& v1_xreal_0(U_12)
& v4_ordinal2(U_12)
& v1_xcmplx_0(U_12) )
| ~ m1_subset_1(U_12,U_13) )
| ~ v5_membered(U_13) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_12] :
( v1_rat_1(U_12)
| ~ sP3(U_12) )
& ! [U_12] :
( v1_int_1(U_12)
| ~ sP3(U_12) )
& ! [U_12] :
( v1_xreal_0(U_12)
| ~ sP3(U_12) )
& ! [U_12] :
( v4_ordinal2(U_12)
| ~ sP3(U_12) )
& ! [U_12] :
( v1_xcmplx_0(U_12)
| ~ sP3(U_12) )
& ! [U_13,U_12] :
( sP3(U_12)
| ~ m1_subset_1(U_12,U_13)
| ~ v5_membered(U_13) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_7_2]) ).
cnf(f_7_4,plain,
( sP3(U_12)
| ~ m1_subset_1(U_12,U_13)
| ~ v5_membered(U_13) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( v1_xcmplx_0(U_12)
| ~ sP3(U_12) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_6,plain,
( v4_ordinal2(U_12)
| ~ sP3(U_12) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_7,plain,
( v1_xreal_0(U_12)
| ~ sP3(U_12) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_8,plain,
( v1_int_1(U_12)
| ~ sP3(U_12) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_9,plain,
( v1_rat_1(U_12)
| ~ sP3(U_12) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [A] :
( ( v5_membered(A)
& v4_membered(A)
& v3_membered(A)
& v2_membered(A)
& v1_membered(A) )
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[cc15_membered]) ).
fof(f_8_2,plain,
! [U_14] :
( ( v5_membered(U_14)
& v4_membered(U_14)
& v3_membered(U_14)
& v2_membered(U_14)
& v1_membered(U_14) )
| ~ v1_xboole_0(U_14) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_14] :
( v5_membered(U_14)
| ~ sP4(U_14) )
& ! [U_14] :
( v4_membered(U_14)
| ~ sP4(U_14) )
& ! [U_14] :
( v3_membered(U_14)
| ~ sP4(U_14) )
& ! [U_14] :
( v2_membered(U_14)
| ~ sP4(U_14) )
& ! [U_14] :
( v1_membered(U_14)
| ~ sP4(U_14) )
& ! [U_14] :
( sP4(U_14)
| ~ v1_xboole_0(U_14) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_8_2]) ).
cnf(f_8_4,plain,
( sP4(U_14)
| ~ v1_xboole_0(U_14) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( v1_membered(U_14)
| ~ sP4(U_14) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_6,plain,
( v2_membered(U_14)
| ~ sP4(U_14) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_7,plain,
( v3_membered(U_14)
| ~ sP4(U_14) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_8,plain,
( v4_membered(U_14)
| ~ sP4(U_14) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_9,plain,
( v5_membered(U_14)
| ~ sP4(U_14) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [A] :
( ! [B] :
( v1_membered(B)
| ~ m1_subset_1(B,k1_zfmisc_1(A)) )
| ~ v1_membered(A) ),
inference(fof_nnf,[status(thm)],[cc16_membered]) ).
fof(f_9_2,plain,
! [U_16] :
( ! [U_15] :
( v1_membered(U_15)
| ~ m1_subset_1(U_15,k1_zfmisc_1(U_16)) )
| ~ v1_membered(U_16) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_15,U_16] :
( v1_membered(U_15)
| ~ m1_subset_1(U_15,k1_zfmisc_1(U_16))
| ~ v1_membered(U_16) ),
inference(definitional_conversion,[status(esa)],[f_9_2]) ).
cnf(f_9_4,plain,
( v1_membered(U_15)
| ~ m1_subset_1(U_15,k1_zfmisc_1(U_16))
| ~ v1_membered(U_16) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [A] :
( ! [B] :
( ( v2_membered(B)
& v1_membered(B) )
| ~ m1_subset_1(B,k1_zfmisc_1(A)) )
| ~ v2_membered(A) ),
inference(fof_nnf,[status(thm)],[cc17_membered]) ).
fof(f_10_2,plain,
! [U_18] :
( ! [U_17] :
( ( v2_membered(U_17)
& v1_membered(U_17) )
| ~ m1_subset_1(U_17,k1_zfmisc_1(U_18)) )
| ~ v2_membered(U_18) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_17] :
( v2_membered(U_17)
| ~ sP5(U_17) )
& ! [U_17] :
( v1_membered(U_17)
| ~ sP5(U_17) )
& ! [U_18,U_17] :
( sP5(U_17)
| ~ m1_subset_1(U_17,k1_zfmisc_1(U_18))
| ~ v2_membered(U_18) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_10_2]) ).
cnf(f_10_4,plain,
( sP5(U_17)
| ~ m1_subset_1(U_17,k1_zfmisc_1(U_18))
| ~ v2_membered(U_18) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_5,plain,
( v1_membered(U_17)
| ~ sP5(U_17) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_6,plain,
( v2_membered(U_17)
| ~ sP5(U_17) ),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [A] :
( ! [B] :
( ( v3_membered(B)
& v2_membered(B)
& v1_membered(B) )
| ~ m1_subset_1(B,k1_zfmisc_1(A)) )
| ~ v3_membered(A) ),
inference(fof_nnf,[status(thm)],[cc18_membered]) ).
fof(f_11_2,plain,
! [U_20] :
( ! [U_19] :
( ( v3_membered(U_19)
& v2_membered(U_19)
& v1_membered(U_19) )
| ~ m1_subset_1(U_19,k1_zfmisc_1(U_20)) )
| ~ v3_membered(U_20) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
( ! [U_19] :
( v3_membered(U_19)
| ~ sP6(U_19) )
& ! [U_19] :
( v2_membered(U_19)
| ~ sP6(U_19) )
& ! [U_19] :
( v1_membered(U_19)
| ~ sP6(U_19) )
& ! [U_19,U_20] :
( sP6(U_19)
| ~ m1_subset_1(U_19,k1_zfmisc_1(U_20))
| ~ v3_membered(U_20) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_11_2]) ).
cnf(f_11_4,plain,
( sP6(U_19)
| ~ m1_subset_1(U_19,k1_zfmisc_1(U_20))
| ~ v3_membered(U_20) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_5,plain,
( v1_membered(U_19)
| ~ sP6(U_19) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_6,plain,
( v2_membered(U_19)
| ~ sP6(U_19) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_7,plain,
( v3_membered(U_19)
| ~ sP6(U_19) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [A] :
( ! [B] :
( ( v4_membered(B)
& v3_membered(B)
& v2_membered(B)
& v1_membered(B) )
| ~ m1_subset_1(B,k1_zfmisc_1(A)) )
| ~ v4_membered(A) ),
inference(fof_nnf,[status(thm)],[cc19_membered]) ).
fof(f_12_2,plain,
! [U_22] :
( ! [U_21] :
( ( v4_membered(U_21)
& v3_membered(U_21)
& v2_membered(U_21)
& v1_membered(U_21) )
| ~ m1_subset_1(U_21,k1_zfmisc_1(U_22)) )
| ~ v4_membered(U_22) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_21] :
( v4_membered(U_21)
| ~ sP7(U_21) )
& ! [U_21] :
( v3_membered(U_21)
| ~ sP7(U_21) )
& ! [U_21] :
( v2_membered(U_21)
| ~ sP7(U_21) )
& ! [U_21] :
( v1_membered(U_21)
| ~ sP7(U_21) )
& ! [U_22,U_21] :
( sP7(U_21)
| ~ m1_subset_1(U_21,k1_zfmisc_1(U_22))
| ~ v4_membered(U_22) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_12_2]) ).
cnf(f_12_4,plain,
( sP7(U_21)
| ~ m1_subset_1(U_21,k1_zfmisc_1(U_22))
| ~ v4_membered(U_22) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_5,plain,
( v1_membered(U_21)
| ~ sP7(U_21) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_6,plain,
( v2_membered(U_21)
| ~ sP7(U_21) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_7,plain,
( v3_membered(U_21)
| ~ sP7(U_21) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_8,plain,
( v4_membered(U_21)
| ~ sP7(U_21) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [A] :
( v4_membered(A)
| ~ v5_membered(A) ),
inference(fof_nnf,[status(thm)],[cc1_membered]) ).
fof(f_13_2,plain,
! [U_23] :
( v4_membered(U_23)
| ~ v5_membered(U_23) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_23] :
( v4_membered(U_23)
| ~ v5_membered(U_23) ),
inference(definitional_conversion,[status(esa)],[f_13_2]) ).
cnf(f_13_4,plain,
( v4_membered(U_23)
| ~ v5_membered(U_23) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [A] :
( ! [B] :
( ( v4_pre_topc(B,A)
& v3_pre_topc(B,A) )
| ~ v1_xboole_0(B)
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l1_pre_topc(A)
| ~ v2_pre_topc(A) ),
inference(fof_nnf,[status(thm)],[cc1_tops_1]) ).
fof(f_14_2,plain,
! [U_25] :
( ! [U_24] :
( ( v4_pre_topc(U_24,U_25)
& v3_pre_topc(U_24,U_25) )
| ~ v1_xboole_0(U_24)
| ~ m1_subset_1(U_24,k1_zfmisc_1(u1_struct_0(U_25))) )
| ~ l1_pre_topc(U_25)
| ~ v2_pre_topc(U_25) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_25,U_24] :
( v4_pre_topc(U_24,U_25)
| ~ sP8(U_25,U_24) )
& ! [U_25,U_24] :
( v3_pre_topc(U_24,U_25)
| ~ sP8(U_25,U_24) )
& ! [U_25,U_24] :
( sP8(U_25,U_24)
| ~ v1_xboole_0(U_24)
| ~ m1_subset_1(U_24,k1_zfmisc_1(u1_struct_0(U_25)))
| ~ l1_pre_topc(U_25)
| ~ v2_pre_topc(U_25) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_14_2]) ).
cnf(f_14_4,plain,
( sP8(U_25,U_24)
| ~ v1_xboole_0(U_24)
| ~ m1_subset_1(U_24,k1_zfmisc_1(u1_struct_0(U_25)))
| ~ l1_pre_topc(U_25)
| ~ v2_pre_topc(U_25) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_5,plain,
( v3_pre_topc(U_24,U_25)
| ~ sP8(U_25,U_24) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_6,plain,
( v4_pre_topc(U_24,U_25)
| ~ sP8(U_25,U_24) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [A] :
( ! [B] :
( ( v5_membered(B)
& v4_membered(B)
& v3_membered(B)
& v2_membered(B)
& v1_membered(B) )
| ~ m1_subset_1(B,k1_zfmisc_1(A)) )
| ~ v5_membered(A) ),
inference(fof_nnf,[status(thm)],[cc20_membered]) ).
fof(f_15_2,plain,
! [U_27] :
( ! [U_26] :
( ( v5_membered(U_26)
& v4_membered(U_26)
& v3_membered(U_26)
& v2_membered(U_26)
& v1_membered(U_26) )
| ~ m1_subset_1(U_26,k1_zfmisc_1(U_27)) )
| ~ v5_membered(U_27) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ! [U_26] :
( v5_membered(U_26)
| ~ sP9(U_26) )
& ! [U_26] :
( v4_membered(U_26)
| ~ sP9(U_26) )
& ! [U_26] :
( v3_membered(U_26)
| ~ sP9(U_26) )
& ! [U_26] :
( v2_membered(U_26)
| ~ sP9(U_26) )
& ! [U_26] :
( v1_membered(U_26)
| ~ sP9(U_26) )
& ! [U_27,U_26] :
( sP9(U_26)
| ~ m1_subset_1(U_26,k1_zfmisc_1(U_27))
| ~ v5_membered(U_27) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9])],[f_15_2]) ).
cnf(f_15_4,plain,
( sP9(U_26)
| ~ m1_subset_1(U_26,k1_zfmisc_1(U_27))
| ~ v5_membered(U_27) ),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_5,plain,
( v1_membered(U_26)
| ~ sP9(U_26) ),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_6,plain,
( v2_membered(U_26)
| ~ sP9(U_26) ),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_7,plain,
( v3_membered(U_26)
| ~ sP9(U_26) ),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_8,plain,
( v4_membered(U_26)
| ~ sP9(U_26) ),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_9,plain,
( v5_membered(U_26)
| ~ sP9(U_26) ),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
! [A] :
( v3_membered(A)
| ~ v4_membered(A) ),
inference(fof_nnf,[status(thm)],[cc2_membered]) ).
fof(f_16_2,plain,
! [U_28] :
( v3_membered(U_28)
| ~ v4_membered(U_28) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_28] :
( v3_membered(U_28)
| ~ v4_membered(U_28) ),
inference(definitional_conversion,[status(esa)],[f_16_2]) ).
cnf(f_16_4,plain,
( v3_membered(U_28)
| ~ v4_membered(U_28) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
! [A] :
( ! [B] :
( v2_tops_1(B,A)
| ~ v1_xboole_0(B)
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l1_pre_topc(A) ),
inference(fof_nnf,[status(thm)],[cc2_tops_1]) ).
fof(f_17_2,plain,
! [U_30] :
( ! [U_29] :
( v2_tops_1(U_29,U_30)
| ~ v1_xboole_0(U_29)
| ~ m1_subset_1(U_29,k1_zfmisc_1(u1_struct_0(U_30))) )
| ~ l1_pre_topc(U_30) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_30,U_29] :
( v2_tops_1(U_29,U_30)
| ~ v1_xboole_0(U_29)
| ~ m1_subset_1(U_29,k1_zfmisc_1(u1_struct_0(U_30)))
| ~ l1_pre_topc(U_30) ),
inference(definitional_conversion,[status(esa)],[f_17_2]) ).
cnf(f_17_4,plain,
( v2_tops_1(U_29,U_30)
| ~ v1_xboole_0(U_29)
| ~ m1_subset_1(U_29,k1_zfmisc_1(u1_struct_0(U_30)))
| ~ l1_pre_topc(U_30) ),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
! [A] :
( v2_membered(A)
| ~ v3_membered(A) ),
inference(fof_nnf,[status(thm)],[cc3_membered]) ).
fof(f_18_2,plain,
! [U_31] :
( v2_membered(U_31)
| ~ v3_membered(U_31) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_31] :
( v2_membered(U_31)
| ~ v3_membered(U_31) ),
inference(definitional_conversion,[status(esa)],[f_18_2]) ).
cnf(f_18_4,plain,
( v2_membered(U_31)
| ~ v3_membered(U_31) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
! [A] :
( ! [B] :
( v3_tops_1(B,A)
| ~ v1_xboole_0(B)
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l1_pre_topc(A)
| ~ v2_pre_topc(A) ),
inference(fof_nnf,[status(thm)],[cc3_tops_1]) ).
fof(f_19_2,plain,
! [U_33] :
( ! [U_32] :
( v3_tops_1(U_32,U_33)
| ~ v1_xboole_0(U_32)
| ~ m1_subset_1(U_32,k1_zfmisc_1(u1_struct_0(U_33))) )
| ~ l1_pre_topc(U_33)
| ~ v2_pre_topc(U_33) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_32,U_33] :
( v3_tops_1(U_32,U_33)
| ~ v1_xboole_0(U_32)
| ~ m1_subset_1(U_32,k1_zfmisc_1(u1_struct_0(U_33)))
| ~ l1_pre_topc(U_33)
| ~ v2_pre_topc(U_33) ),
inference(definitional_conversion,[status(esa)],[f_19_2]) ).
cnf(f_19_4,plain,
( v3_tops_1(U_32,U_33)
| ~ v1_xboole_0(U_32)
| ~ m1_subset_1(U_32,k1_zfmisc_1(u1_struct_0(U_33)))
| ~ l1_pre_topc(U_33)
| ~ v2_pre_topc(U_33) ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [A] :
( v1_membered(A)
| ~ v2_membered(A) ),
inference(fof_nnf,[status(thm)],[cc4_membered]) ).
fof(f_20_2,plain,
! [U_34] :
( v1_membered(U_34)
| ~ v2_membered(U_34) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_34] :
( v1_membered(U_34)
| ~ v2_membered(U_34) ),
inference(definitional_conversion,[status(esa)],[f_20_2]) ).
cnf(f_20_4,plain,
( v1_membered(U_34)
| ~ v2_membered(U_34) ),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
! [A] :
( ! [B] :
( v2_tops_1(B,A)
| ~ v3_tops_1(B,A)
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l1_pre_topc(A)
| ~ v2_pre_topc(A) ),
inference(fof_nnf,[status(thm)],[cc4_tops_1]) ).
fof(f_21_2,plain,
! [U_36] :
( ! [U_35] :
( v2_tops_1(U_35,U_36)
| ~ v3_tops_1(U_35,U_36)
| ~ m1_subset_1(U_35,k1_zfmisc_1(u1_struct_0(U_36))) )
| ~ l1_pre_topc(U_36)
| ~ v2_pre_topc(U_36) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_35,U_36] :
( v2_tops_1(U_35,U_36)
| ~ v3_tops_1(U_35,U_36)
| ~ m1_subset_1(U_35,k1_zfmisc_1(u1_struct_0(U_36)))
| ~ l1_pre_topc(U_36)
| ~ v2_pre_topc(U_36) ),
inference(definitional_conversion,[status(esa)],[f_21_2]) ).
cnf(f_21_4,plain,
( v2_tops_1(U_35,U_36)
| ~ v3_tops_1(U_35,U_36)
| ~ m1_subset_1(U_35,k1_zfmisc_1(u1_struct_0(U_36)))
| ~ l1_pre_topc(U_36)
| ~ v2_pre_topc(U_36) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
! [A] :
( ! [B] :
( ( v3_tops_1(B,A)
& v2_tops_1(B,A) )
| ~ v2_tops_1(B,A)
| ~ v4_pre_topc(B,A)
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l1_pre_topc(A)
| ~ v2_pre_topc(A) ),
inference(fof_nnf,[status(thm)],[cc5_tops_1]) ).
fof(f_22_2,plain,
! [U_38] :
( ! [U_37] :
( ( v3_tops_1(U_37,U_38)
& v2_tops_1(U_37,U_38) )
| ~ v2_tops_1(U_37,U_38)
| ~ v4_pre_topc(U_37,U_38)
| ~ m1_subset_1(U_37,k1_zfmisc_1(u1_struct_0(U_38))) )
| ~ l1_pre_topc(U_38)
| ~ v2_pre_topc(U_38) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( ! [U_37,U_38] :
( v3_tops_1(U_37,U_38)
| ~ sP10(U_37,U_38) )
& ! [U_37,U_38] :
( v2_tops_1(U_37,U_38)
| ~ sP10(U_37,U_38) )
& ! [U_37,U_38] :
( sP10(U_37,U_38)
| ~ v2_tops_1(U_37,U_38)
| ~ v4_pre_topc(U_37,U_38)
| ~ m1_subset_1(U_37,k1_zfmisc_1(u1_struct_0(U_38)))
| ~ l1_pre_topc(U_38)
| ~ v2_pre_topc(U_38) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10])],[f_22_2]) ).
cnf(f_22_4,plain,
( sP10(U_37,U_38)
| ~ v2_tops_1(U_37,U_38)
| ~ v4_pre_topc(U_37,U_38)
| ~ m1_subset_1(U_37,k1_zfmisc_1(u1_struct_0(U_38)))
| ~ l1_pre_topc(U_38)
| ~ v2_pre_topc(U_38) ),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_5,plain,
( v2_tops_1(U_37,U_38)
| ~ sP10(U_37,U_38) ),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_6,plain,
( v3_tops_1(U_37,U_38)
| ~ sP10(U_37,U_38) ),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
! [A] :
( ! [B] :
( ( v3_tops_1(B,A)
& v2_tops_1(B,A)
& v5_membered(B)
& v4_membered(B)
& v3_membered(B)
& v2_membered(B)
& v1_membered(B)
& v4_pre_topc(B,A)
& v3_pre_topc(B,A)
& v1_xboole_0(B) )
| ~ v3_tops_1(B,A)
| ~ v3_pre_topc(B,A)
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l1_pre_topc(A)
| ~ v2_pre_topc(A) ),
inference(fof_nnf,[status(thm)],[cc6_tops_1]) ).
fof(f_23_2,plain,
! [U_40] :
( ! [U_39] :
( ( v3_tops_1(U_39,U_40)
& v2_tops_1(U_39,U_40)
& v5_membered(U_39)
& v4_membered(U_39)
& v3_membered(U_39)
& v2_membered(U_39)
& v1_membered(U_39)
& v4_pre_topc(U_39,U_40)
& v3_pre_topc(U_39,U_40)
& v1_xboole_0(U_39) )
| ~ v3_tops_1(U_39,U_40)
| ~ v3_pre_topc(U_39,U_40)
| ~ m1_subset_1(U_39,k1_zfmisc_1(u1_struct_0(U_40))) )
| ~ l1_pre_topc(U_40)
| ~ v2_pre_topc(U_40) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( ! [U_40,U_39] :
( v3_tops_1(U_39,U_40)
| ~ sP11(U_40,U_39) )
& ! [U_40,U_39] :
( v2_tops_1(U_39,U_40)
| ~ sP11(U_40,U_39) )
& ! [U_40,U_39] :
( v5_membered(U_39)
| ~ sP11(U_40,U_39) )
& ! [U_40,U_39] :
( v4_membered(U_39)
| ~ sP11(U_40,U_39) )
& ! [U_40,U_39] :
( v3_membered(U_39)
| ~ sP11(U_40,U_39) )
& ! [U_40,U_39] :
( v2_membered(U_39)
| ~ sP11(U_40,U_39) )
& ! [U_40,U_39] :
( v1_membered(U_39)
| ~ sP11(U_40,U_39) )
& ! [U_40,U_39] :
( v4_pre_topc(U_39,U_40)
| ~ sP11(U_40,U_39) )
& ! [U_40,U_39] :
( v3_pre_topc(U_39,U_40)
| ~ sP11(U_40,U_39) )
& ! [U_40,U_39] :
( v1_xboole_0(U_39)
| ~ sP11(U_40,U_39) )
& ! [U_40,U_39] :
( sP11(U_40,U_39)
| ~ v3_tops_1(U_39,U_40)
| ~ v3_pre_topc(U_39,U_40)
| ~ m1_subset_1(U_39,k1_zfmisc_1(u1_struct_0(U_40)))
| ~ l1_pre_topc(U_40)
| ~ v2_pre_topc(U_40) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11])],[f_23_2]) ).
cnf(f_23_4,plain,
( sP11(U_40,U_39)
| ~ v3_tops_1(U_39,U_40)
| ~ v3_pre_topc(U_39,U_40)
| ~ m1_subset_1(U_39,k1_zfmisc_1(u1_struct_0(U_40)))
| ~ l1_pre_topc(U_40)
| ~ v2_pre_topc(U_40) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_5,plain,
( v1_xboole_0(U_39)
| ~ sP11(U_40,U_39) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_6,plain,
( v3_pre_topc(U_39,U_40)
| ~ sP11(U_40,U_39) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_7,plain,
( v4_pre_topc(U_39,U_40)
| ~ sP11(U_40,U_39) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_8,plain,
( v1_membered(U_39)
| ~ sP11(U_40,U_39) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_9,plain,
( v2_membered(U_39)
| ~ sP11(U_40,U_39) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_10,plain,
( v3_membered(U_39)
| ~ sP11(U_40,U_39) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_11,plain,
( v4_membered(U_39)
| ~ sP11(U_40,U_39) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_12,plain,
( v5_membered(U_39)
| ~ sP11(U_40,U_39) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_13,plain,
( v2_tops_1(U_39,U_40)
| ~ sP11(U_40,U_39) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_14,plain,
( v3_tops_1(U_39,U_40)
| ~ sP11(U_40,U_39) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
! [A] :
( ! [B] :
( ( ( v1_tsp_2(B,A)
| k3_tex_4(A,B) != u1_struct_0(A)
| ~ v1_tsp_1(B,A) )
& ( ( k3_tex_4(A,B) = u1_struct_0(A)
& v1_tsp_1(B,A) )
| ~ v1_tsp_2(B,A) ) )
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l1_pre_topc(A)
| ~ v2_pre_topc(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[d5_tsp_2]) ).
fof(f_24_2,plain,
! [U_42] :
( ! [U_41] :
( ( ( v1_tsp_2(U_41,U_42)
| k3_tex_4(U_42,U_41) != u1_struct_0(U_42)
| ~ v1_tsp_1(U_41,U_42) )
& ( ( k3_tex_4(U_42,U_41) = u1_struct_0(U_42)
& v1_tsp_1(U_41,U_42) )
| ~ v1_tsp_2(U_41,U_42) ) )
| ~ m1_subset_1(U_41,k1_zfmisc_1(u1_struct_0(U_42))) )
| ~ l1_pre_topc(U_42)
| ~ v2_pre_topc(U_42)
| v3_struct_0(U_42) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( ! [U_42,U_41] :
( k3_tex_4(U_42,U_41) = u1_struct_0(U_42)
| ~ sP12(U_42,U_41) )
& ! [U_42,U_41] :
( v1_tsp_1(U_41,U_42)
| ~ sP12(U_42,U_41) )
& ! [U_42,U_41] :
( v1_tsp_2(U_41,U_42)
| k3_tex_4(U_42,U_41) != u1_struct_0(U_42)
| ~ v1_tsp_1(U_41,U_42)
| ~ sP13(U_42,U_41) )
& ! [U_42,U_41] :
( sP12(U_42,U_41)
| ~ v1_tsp_2(U_41,U_42)
| ~ sP13(U_42,U_41) )
& ! [U_42,U_41] :
( sP13(U_42,U_41)
| ~ m1_subset_1(U_41,k1_zfmisc_1(u1_struct_0(U_42)))
| ~ l1_pre_topc(U_42)
| ~ v2_pre_topc(U_42)
| v3_struct_0(U_42) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12,sP13])],[f_24_2]) ).
cnf(f_24_4,plain,
( sP13(U_42,U_41)
| ~ m1_subset_1(U_41,k1_zfmisc_1(u1_struct_0(U_42)))
| ~ l1_pre_topc(U_42)
| ~ v2_pre_topc(U_42)
| v3_struct_0(U_42) ),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
( sP12(U_42,U_41)
| ~ v1_tsp_2(U_41,U_42)
| ~ sP13(U_42,U_41) ),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_6,plain,
( v1_tsp_2(U_41,U_42)
| k3_tex_4(U_42,U_41) != u1_struct_0(U_42)
| ~ v1_tsp_1(U_41,U_42)
| ~ sP13(U_42,U_41) ),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_7,plain,
( v1_tsp_1(U_41,U_42)
| ~ sP12(U_42,U_41) ),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_8,plain,
( k3_tex_4(U_42,U_41) = u1_struct_0(U_42)
| ~ sP12(U_42,U_41) ),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
fof(f_25_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_25_1]) ).
cnf(f_25_3,plain,
$true,
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
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,B] :
( m1_subset_1(k3_tex_4(A,B),k1_zfmisc_1(u1_struct_0(A)))
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| ~ l1_pre_topc(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[dt_k3_tex_4]) ).
fof(f_27_2,plain,
! [U_44,U_43] :
( m1_subset_1(k3_tex_4(U_44,U_43),k1_zfmisc_1(u1_struct_0(U_44)))
| ~ m1_subset_1(U_43,k1_zfmisc_1(u1_struct_0(U_44)))
| ~ l1_pre_topc(U_44)
| v3_struct_0(U_44) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_44,U_43] :
( m1_subset_1(k3_tex_4(U_44,U_43),k1_zfmisc_1(u1_struct_0(U_44)))
| ~ m1_subset_1(U_43,k1_zfmisc_1(u1_struct_0(U_44)))
| ~ l1_pre_topc(U_44)
| v3_struct_0(U_44) ),
inference(definitional_conversion,[status(esa)],[f_27_2]) ).
cnf(f_27_4,plain,
( m1_subset_1(k3_tex_4(U_44,U_43),k1_zfmisc_1(u1_struct_0(U_44)))
| ~ m1_subset_1(U_43,k1_zfmisc_1(u1_struct_0(U_44)))
| ~ l1_pre_topc(U_44)
| v3_struct_0(U_44) ),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
! [A] :
( l1_struct_0(A)
| ~ l1_pre_topc(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_pre_topc]) ).
fof(f_28_2,plain,
! [U_45] :
( l1_struct_0(U_45)
| ~ l1_pre_topc(U_45) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_45] :
( l1_struct_0(U_45)
| ~ l1_pre_topc(U_45) ),
inference(definitional_conversion,[status(esa)],[f_28_2]) ).
cnf(f_28_4,plain,
( l1_struct_0(U_45)
| ~ l1_pre_topc(U_45) ),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
fof(f_29_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_29_1]) ).
cnf(f_29_3,plain,
$true,
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
fof(f_30_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_30_1]) ).
cnf(f_30_3,plain,
$true,
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
fof(f_31_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_31_1]) ).
cnf(f_31_3,plain,
$true,
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
? [A] : l1_pre_topc(A),
inference(fof_nnf,[status(thm)],[existence_l1_pre_topc]) ).
fof(f_32_2,plain,
? [U_46] : l1_pre_topc(U_46),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
l1_pre_topc(sK3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_46,sK3)],[f_32_2]) ).
fof(f_32_4,plain,
l1_pre_topc(sK3),
inference(definitional_conversion,[status(esa)],[f_32_3]) ).
cnf(f_32_5,plain,
l1_pre_topc(sK3),
inference(clausify,[status(thm)],[f_32_4]) ).
fof(f_33_1,plain,
? [A] : l1_struct_0(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_33_2,plain,
? [U_47] : l1_struct_0(U_47),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
l1_struct_0(sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_47,sK4)],[f_33_2]) ).
fof(f_33_4,plain,
l1_struct_0(sK4),
inference(definitional_conversion,[status(esa)],[f_33_3]) ).
cnf(f_33_5,plain,
l1_struct_0(sK4),
inference(clausify,[status(thm)],[f_33_4]) ).
fof(f_34_1,plain,
! [A] :
? [B] : m1_subset_1(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_34_2,plain,
! [U_49] :
? [U_48] : m1_subset_1(U_48,U_49),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_49] : m1_subset_1(sK5(U_49),U_49),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_48,sK5(U_49))],[f_34_2]) ).
fof(f_34_4,plain,
! [U_49] : m1_subset_1(sK5(U_49),U_49),
inference(definitional_conversion,[status(esa)],[f_34_3]) ).
cnf(f_34_5,plain,
m1_subset_1(sK5(U_49),U_49),
inference(clausify,[status(thm)],[f_34_4]) ).
fof(f_35_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_35_2,plain,
! [U_50] :
( ~ v1_xboole_0(u1_struct_0(U_50))
| ~ l1_struct_0(U_50)
| v3_struct_0(U_50) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_50] :
( ~ v1_xboole_0(u1_struct_0(U_50))
| ~ l1_struct_0(U_50)
| v3_struct_0(U_50) ),
inference(definitional_conversion,[status(esa)],[f_35_2]) ).
cnf(f_35_4,plain,
( ~ v1_xboole_0(u1_struct_0(U_50))
| ~ l1_struct_0(U_50)
| v3_struct_0(U_50) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_36_2,plain,
! [U_51] : ~ v1_xboole_0(k1_zfmisc_1(U_51)),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_51] : ~ v1_xboole_0(k1_zfmisc_1(U_51)),
inference(definitional_conversion,[status(esa)],[f_36_2]) ).
cnf(f_36_4,plain,
~ v1_xboole_0(k1_zfmisc_1(U_51)),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
( v5_membered(k1_xboole_0)
& v4_membered(k1_xboole_0)
& v3_membered(k1_xboole_0)
& v2_membered(k1_xboole_0)
& v1_membered(k1_xboole_0)
& v1_xboole_0(k1_xboole_0) ),
inference(fof_nnf,[status(thm)],[fc6_membered]) ).
fof(f_37_2,plain,
( v5_membered(k1_xboole_0)
& v4_membered(k1_xboole_0)
& v3_membered(k1_xboole_0)
& v2_membered(k1_xboole_0)
& v1_membered(k1_xboole_0)
& v1_xboole_0(k1_xboole_0) ),
inference(definitional_conversion,[status(esa)],[f_37_1]) ).
cnf(f_37_3,plain,
v1_xboole_0(k1_xboole_0),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_4,plain,
v1_membered(k1_xboole_0),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_5,plain,
v2_membered(k1_xboole_0),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_6,plain,
v3_membered(k1_xboole_0),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_7,plain,
v4_membered(k1_xboole_0),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_8,plain,
v5_membered(k1_xboole_0),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,plain,
? [A] :
( v5_membered(A)
& v4_membered(A)
& v3_membered(A)
& v2_membered(A)
& v1_membered(A)
& ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[rc1_membered]) ).
fof(f_38_2,plain,
? [U_52] :
( v5_membered(U_52)
& v4_membered(U_52)
& v3_membered(U_52)
& v2_membered(U_52)
& v1_membered(U_52)
& ~ v1_xboole_0(U_52) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
( v5_membered(sK6)
& v4_membered(sK6)
& v3_membered(sK6)
& v2_membered(sK6)
& v1_membered(sK6)
& ~ v1_xboole_0(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_52,sK6)],[f_38_2]) ).
fof(f_38_4,plain,
( v5_membered(sK6)
& v4_membered(sK6)
& v3_membered(sK6)
& v2_membered(sK6)
& v1_membered(sK6)
& ~ v1_xboole_0(sK6) ),
inference(definitional_conversion,[status(esa)],[f_38_3]) ).
cnf(f_38_5,plain,
~ v1_xboole_0(sK6),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_38_6,plain,
v1_membered(sK6),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_38_7,plain,
v2_membered(sK6),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_38_8,plain,
v3_membered(sK6),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_38_9,plain,
v4_membered(sK6),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_38_10,plain,
v5_membered(sK6),
inference(clausify,[status(thm)],[f_38_4]) ).
fof(f_39_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_39_2,plain,
! [U_54] :
( ? [U_53] :
( ~ v1_xboole_0(U_53)
& m1_subset_1(U_53,k1_zfmisc_1(U_54)) )
| v1_xboole_0(U_54) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_54] :
( ( ~ v1_xboole_0(sK7(U_54))
& m1_subset_1(sK7(U_54),k1_zfmisc_1(U_54)) )
| v1_xboole_0(U_54) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_53,sK7(U_54))],[f_39_2]) ).
fof(f_39_4,plain,
( ! [U_54] :
( ~ v1_xboole_0(sK7(U_54))
| ~ sP14(U_54) )
& ! [U_54] :
( m1_subset_1(sK7(U_54),k1_zfmisc_1(U_54))
| ~ sP14(U_54) )
& ! [U_54] :
( sP14(U_54)
| v1_xboole_0(U_54) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14])],[f_39_3]) ).
cnf(f_39_5,plain,
( sP14(U_54)
| v1_xboole_0(U_54) ),
inference(clausify,[status(thm)],[f_39_4]) ).
cnf(f_39_6,plain,
( m1_subset_1(sK7(U_54),k1_zfmisc_1(U_54))
| ~ sP14(U_54) ),
inference(clausify,[status(thm)],[f_39_4]) ).
cnf(f_39_7,plain,
( ~ v1_xboole_0(sK7(U_54))
| ~ sP14(U_54) ),
inference(clausify,[status(thm)],[f_39_4]) ).
fof(f_40_1,plain,
! [A] :
( ? [B] :
( v3_pre_topc(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l1_pre_topc(A)
| ~ v2_pre_topc(A) ),
inference(fof_nnf,[status(thm)],[rc1_tops_1]) ).
fof(f_40_2,plain,
! [U_56] :
( ? [U_55] :
( v3_pre_topc(U_55,U_56)
& m1_subset_1(U_55,k1_zfmisc_1(u1_struct_0(U_56))) )
| ~ l1_pre_topc(U_56)
| ~ v2_pre_topc(U_56) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_56] :
( ( v3_pre_topc(sK8(U_56),U_56)
& m1_subset_1(sK8(U_56),k1_zfmisc_1(u1_struct_0(U_56))) )
| ~ l1_pre_topc(U_56)
| ~ v2_pre_topc(U_56) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_55,sK8(U_56))],[f_40_2]) ).
fof(f_40_4,plain,
( ! [U_56] :
( v3_pre_topc(sK8(U_56),U_56)
| ~ sP15(U_56) )
& ! [U_56] :
( m1_subset_1(sK8(U_56),k1_zfmisc_1(u1_struct_0(U_56)))
| ~ sP15(U_56) )
& ! [U_56] :
( sP15(U_56)
| ~ l1_pre_topc(U_56)
| ~ v2_pre_topc(U_56) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP15])],[f_40_3]) ).
cnf(f_40_5,plain,
( sP15(U_56)
| ~ l1_pre_topc(U_56)
| ~ v2_pre_topc(U_56) ),
inference(clausify,[status(thm)],[f_40_4]) ).
cnf(f_40_6,plain,
( m1_subset_1(sK8(U_56),k1_zfmisc_1(u1_struct_0(U_56)))
| ~ sP15(U_56) ),
inference(clausify,[status(thm)],[f_40_4]) ).
cnf(f_40_7,plain,
( v3_pre_topc(sK8(U_56),U_56)
| ~ sP15(U_56) ),
inference(clausify,[status(thm)],[f_40_4]) ).
fof(f_41_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_41_2,plain,
! [U_58] :
? [U_57] :
( v1_xboole_0(U_57)
& m1_subset_1(U_57,k1_zfmisc_1(U_58)) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_58] :
( v1_xboole_0(sK9(U_58))
& m1_subset_1(sK9(U_58),k1_zfmisc_1(U_58)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_57,sK9(U_58))],[f_41_2]) ).
fof(f_41_4,plain,
( ! [U_58] : v1_xboole_0(sK9(U_58))
& ! [U_58] : m1_subset_1(sK9(U_58),k1_zfmisc_1(U_58)) ),
inference(definitional_conversion,[status(esa)],[f_41_3]) ).
cnf(f_41_5,plain,
m1_subset_1(sK9(U_58),k1_zfmisc_1(U_58)),
inference(clausify,[status(thm)],[f_41_4]) ).
cnf(f_41_6,plain,
v1_xboole_0(sK9(U_58)),
inference(clausify,[status(thm)],[f_41_4]) ).
fof(f_42_1,plain,
! [A] :
( ? [B] :
( v4_pre_topc(B,A)
& v3_pre_topc(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l1_pre_topc(A)
| ~ v2_pre_topc(A) ),
inference(fof_nnf,[status(thm)],[rc2_tops_1]) ).
fof(f_42_2,plain,
! [U_60] :
( ? [U_59] :
( v4_pre_topc(U_59,U_60)
& v3_pre_topc(U_59,U_60)
& m1_subset_1(U_59,k1_zfmisc_1(u1_struct_0(U_60))) )
| ~ l1_pre_topc(U_60)
| ~ v2_pre_topc(U_60) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_60] :
( ( v4_pre_topc(sK10(U_60),U_60)
& v3_pre_topc(sK10(U_60),U_60)
& m1_subset_1(sK10(U_60),k1_zfmisc_1(u1_struct_0(U_60))) )
| ~ l1_pre_topc(U_60)
| ~ v2_pre_topc(U_60) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_59,sK10(U_60))],[f_42_2]) ).
fof(f_42_4,plain,
( ! [U_60] :
( v4_pre_topc(sK10(U_60),U_60)
| ~ sP16(U_60) )
& ! [U_60] :
( v3_pre_topc(sK10(U_60),U_60)
| ~ sP16(U_60) )
& ! [U_60] :
( m1_subset_1(sK10(U_60),k1_zfmisc_1(u1_struct_0(U_60)))
| ~ sP16(U_60) )
& ! [U_60] :
( sP16(U_60)
| ~ l1_pre_topc(U_60)
| ~ v2_pre_topc(U_60) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16])],[f_42_3]) ).
cnf(f_42_5,plain,
( sP16(U_60)
| ~ l1_pre_topc(U_60)
| ~ v2_pre_topc(U_60) ),
inference(clausify,[status(thm)],[f_42_4]) ).
cnf(f_42_6,plain,
( m1_subset_1(sK10(U_60),k1_zfmisc_1(u1_struct_0(U_60)))
| ~ sP16(U_60) ),
inference(clausify,[status(thm)],[f_42_4]) ).
cnf(f_42_7,plain,
( v3_pre_topc(sK10(U_60),U_60)
| ~ sP16(U_60) ),
inference(clausify,[status(thm)],[f_42_4]) ).
cnf(f_42_8,plain,
( v4_pre_topc(sK10(U_60),U_60)
| ~ sP16(U_60) ),
inference(clausify,[status(thm)],[f_42_4]) ).
fof(f_43_1,plain,
? [A] :
( ~ v3_struct_0(A)
& l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc3_struct_0]) ).
fof(f_43_2,plain,
? [U_61] :
( ~ v3_struct_0(U_61)
& l1_struct_0(U_61) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
( ~ v3_struct_0(sK11)
& l1_struct_0(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_61,sK11)],[f_43_2]) ).
fof(f_43_4,plain,
( ~ v3_struct_0(sK11)
& l1_struct_0(sK11) ),
inference(definitional_conversion,[status(esa)],[f_43_3]) ).
cnf(f_43_5,plain,
l1_struct_0(sK11),
inference(clausify,[status(thm)],[f_43_4]) ).
cnf(f_43_6,plain,
~ v3_struct_0(sK11),
inference(clausify,[status(thm)],[f_43_4]) ).
fof(f_44_1,plain,
! [A] :
( ? [B] :
( v4_pre_topc(B,A)
& v3_pre_topc(B,A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l1_pre_topc(A)
| ~ v2_pre_topc(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc3_tops_1]) ).
fof(f_44_2,plain,
! [U_63] :
( ? [U_62] :
( v4_pre_topc(U_62,U_63)
& v3_pre_topc(U_62,U_63)
& ~ v1_xboole_0(U_62)
& m1_subset_1(U_62,k1_zfmisc_1(u1_struct_0(U_63))) )
| ~ l1_pre_topc(U_63)
| ~ v2_pre_topc(U_63)
| v3_struct_0(U_63) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_63] :
( ( v4_pre_topc(sK12(U_63),U_63)
& v3_pre_topc(sK12(U_63),U_63)
& ~ v1_xboole_0(sK12(U_63))
& m1_subset_1(sK12(U_63),k1_zfmisc_1(u1_struct_0(U_63))) )
| ~ l1_pre_topc(U_63)
| ~ v2_pre_topc(U_63)
| v3_struct_0(U_63) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_62,sK12(U_63))],[f_44_2]) ).
fof(f_44_4,plain,
( ! [U_63] :
( v4_pre_topc(sK12(U_63),U_63)
| ~ sP17(U_63) )
& ! [U_63] :
( v3_pre_topc(sK12(U_63),U_63)
| ~ sP17(U_63) )
& ! [U_63] :
( ~ v1_xboole_0(sK12(U_63))
| ~ sP17(U_63) )
& ! [U_63] :
( m1_subset_1(sK12(U_63),k1_zfmisc_1(u1_struct_0(U_63)))
| ~ sP17(U_63) )
& ! [U_63] :
( sP17(U_63)
| ~ l1_pre_topc(U_63)
| ~ v2_pre_topc(U_63)
| v3_struct_0(U_63) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP17])],[f_44_3]) ).
cnf(f_44_5,plain,
( sP17(U_63)
| ~ l1_pre_topc(U_63)
| ~ v2_pre_topc(U_63)
| v3_struct_0(U_63) ),
inference(clausify,[status(thm)],[f_44_4]) ).
cnf(f_44_6,plain,
( m1_subset_1(sK12(U_63),k1_zfmisc_1(u1_struct_0(U_63)))
| ~ sP17(U_63) ),
inference(clausify,[status(thm)],[f_44_4]) ).
cnf(f_44_7,plain,
( ~ v1_xboole_0(sK12(U_63))
| ~ sP17(U_63) ),
inference(clausify,[status(thm)],[f_44_4]) ).
cnf(f_44_8,plain,
( v3_pre_topc(sK12(U_63),U_63)
| ~ sP17(U_63) ),
inference(clausify,[status(thm)],[f_44_4]) ).
cnf(f_44_9,plain,
( v4_pre_topc(sK12(U_63),U_63)
| ~ sP17(U_63) ),
inference(clausify,[status(thm)],[f_44_4]) ).
fof(f_45_1,plain,
! [A] :
( ? [B] :
( v2_tops_1(B,A)
& v5_membered(B)
& v4_membered(B)
& v3_membered(B)
& v2_membered(B)
& v1_membered(B)
& v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l1_pre_topc(A) ),
inference(fof_nnf,[status(thm)],[rc4_tops_1]) ).
fof(f_45_2,plain,
! [U_65] :
( ? [U_64] :
( v2_tops_1(U_64,U_65)
& v5_membered(U_64)
& v4_membered(U_64)
& v3_membered(U_64)
& v2_membered(U_64)
& v1_membered(U_64)
& v1_xboole_0(U_64)
& m1_subset_1(U_64,k1_zfmisc_1(u1_struct_0(U_65))) )
| ~ l1_pre_topc(U_65) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_65] :
( ( v2_tops_1(sK13(U_65),U_65)
& v5_membered(sK13(U_65))
& v4_membered(sK13(U_65))
& v3_membered(sK13(U_65))
& v2_membered(sK13(U_65))
& v1_membered(sK13(U_65))
& v1_xboole_0(sK13(U_65))
& m1_subset_1(sK13(U_65),k1_zfmisc_1(u1_struct_0(U_65))) )
| ~ l1_pre_topc(U_65) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_64,sK13(U_65))],[f_45_2]) ).
fof(f_45_4,plain,
( ! [U_65] :
( v2_tops_1(sK13(U_65),U_65)
| ~ sP18(U_65) )
& ! [U_65] :
( v5_membered(sK13(U_65))
| ~ sP18(U_65) )
& ! [U_65] :
( v4_membered(sK13(U_65))
| ~ sP18(U_65) )
& ! [U_65] :
( v3_membered(sK13(U_65))
| ~ sP18(U_65) )
& ! [U_65] :
( v2_membered(sK13(U_65))
| ~ sP18(U_65) )
& ! [U_65] :
( v1_membered(sK13(U_65))
| ~ sP18(U_65) )
& ! [U_65] :
( v1_xboole_0(sK13(U_65))
| ~ sP18(U_65) )
& ! [U_65] :
( m1_subset_1(sK13(U_65),k1_zfmisc_1(u1_struct_0(U_65)))
| ~ sP18(U_65) )
& ! [U_65] :
( sP18(U_65)
| ~ l1_pre_topc(U_65) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP18])],[f_45_3]) ).
cnf(f_45_5,plain,
( sP18(U_65)
| ~ l1_pre_topc(U_65) ),
inference(clausify,[status(thm)],[f_45_4]) ).
cnf(f_45_6,plain,
( m1_subset_1(sK13(U_65),k1_zfmisc_1(u1_struct_0(U_65)))
| ~ sP18(U_65) ),
inference(clausify,[status(thm)],[f_45_4]) ).
cnf(f_45_7,plain,
( v1_xboole_0(sK13(U_65))
| ~ sP18(U_65) ),
inference(clausify,[status(thm)],[f_45_4]) ).
cnf(f_45_8,plain,
( v1_membered(sK13(U_65))
| ~ sP18(U_65) ),
inference(clausify,[status(thm)],[f_45_4]) ).
cnf(f_45_9,plain,
( v2_membered(sK13(U_65))
| ~ sP18(U_65) ),
inference(clausify,[status(thm)],[f_45_4]) ).
cnf(f_45_10,plain,
( v3_membered(sK13(U_65))
| ~ sP18(U_65) ),
inference(clausify,[status(thm)],[f_45_4]) ).
cnf(f_45_11,plain,
( v4_membered(sK13(U_65))
| ~ sP18(U_65) ),
inference(clausify,[status(thm)],[f_45_4]) ).
cnf(f_45_12,plain,
( v5_membered(sK13(U_65))
| ~ sP18(U_65) ),
inference(clausify,[status(thm)],[f_45_4]) ).
cnf(f_45_13,plain,
( v2_tops_1(sK13(U_65),U_65)
| ~ sP18(U_65) ),
inference(clausify,[status(thm)],[f_45_4]) ).
fof(f_46_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_46_2,plain,
! [U_67] :
( ? [U_66] :
( ~ v1_xboole_0(U_66)
& m1_subset_1(U_66,k1_zfmisc_1(u1_struct_0(U_67))) )
| ~ l1_struct_0(U_67)
| v3_struct_0(U_67) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_67] :
( ( ~ v1_xboole_0(sK14(U_67))
& m1_subset_1(sK14(U_67),k1_zfmisc_1(u1_struct_0(U_67))) )
| ~ l1_struct_0(U_67)
| v3_struct_0(U_67) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_66,sK14(U_67))],[f_46_2]) ).
fof(f_46_4,plain,
( ! [U_67] :
( ~ v1_xboole_0(sK14(U_67))
| ~ sP19(U_67) )
& ! [U_67] :
( m1_subset_1(sK14(U_67),k1_zfmisc_1(u1_struct_0(U_67)))
| ~ sP19(U_67) )
& ! [U_67] :
( sP19(U_67)
| ~ l1_struct_0(U_67)
| v3_struct_0(U_67) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP19])],[f_46_3]) ).
cnf(f_46_5,plain,
( sP19(U_67)
| ~ l1_struct_0(U_67)
| v3_struct_0(U_67) ),
inference(clausify,[status(thm)],[f_46_4]) ).
cnf(f_46_6,plain,
( m1_subset_1(sK14(U_67),k1_zfmisc_1(u1_struct_0(U_67)))
| ~ sP19(U_67) ),
inference(clausify,[status(thm)],[f_46_4]) ).
cnf(f_46_7,plain,
( ~ v1_xboole_0(sK14(U_67))
| ~ sP19(U_67) ),
inference(clausify,[status(thm)],[f_46_4]) ).
fof(f_47_1,plain,
! [A] :
( ? [B] :
( v3_tops_1(B,A)
& v2_tops_1(B,A)
& v5_membered(B)
& v4_membered(B)
& v3_membered(B)
& v2_membered(B)
& v1_membered(B)
& v4_pre_topc(B,A)
& v3_pre_topc(B,A)
& v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l1_pre_topc(A)
| ~ v2_pre_topc(A) ),
inference(fof_nnf,[status(thm)],[rc5_tops_1]) ).
fof(f_47_2,plain,
! [U_69] :
( ? [U_68] :
( v3_tops_1(U_68,U_69)
& v2_tops_1(U_68,U_69)
& v5_membered(U_68)
& v4_membered(U_68)
& v3_membered(U_68)
& v2_membered(U_68)
& v1_membered(U_68)
& v4_pre_topc(U_68,U_69)
& v3_pre_topc(U_68,U_69)
& v1_xboole_0(U_68)
& m1_subset_1(U_68,k1_zfmisc_1(u1_struct_0(U_69))) )
| ~ l1_pre_topc(U_69)
| ~ v2_pre_topc(U_69) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_69] :
( ( v3_tops_1(sK15(U_69),U_69)
& v2_tops_1(sK15(U_69),U_69)
& v5_membered(sK15(U_69))
& v4_membered(sK15(U_69))
& v3_membered(sK15(U_69))
& v2_membered(sK15(U_69))
& v1_membered(sK15(U_69))
& v4_pre_topc(sK15(U_69),U_69)
& v3_pre_topc(sK15(U_69),U_69)
& v1_xboole_0(sK15(U_69))
& m1_subset_1(sK15(U_69),k1_zfmisc_1(u1_struct_0(U_69))) )
| ~ l1_pre_topc(U_69)
| ~ v2_pre_topc(U_69) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_68,sK15(U_69))],[f_47_2]) ).
fof(f_47_4,plain,
( ! [U_69] :
( v3_tops_1(sK15(U_69),U_69)
| ~ sP20(U_69) )
& ! [U_69] :
( v2_tops_1(sK15(U_69),U_69)
| ~ sP20(U_69) )
& ! [U_69] :
( v5_membered(sK15(U_69))
| ~ sP20(U_69) )
& ! [U_69] :
( v4_membered(sK15(U_69))
| ~ sP20(U_69) )
& ! [U_69] :
( v3_membered(sK15(U_69))
| ~ sP20(U_69) )
& ! [U_69] :
( v2_membered(sK15(U_69))
| ~ sP20(U_69) )
& ! [U_69] :
( v1_membered(sK15(U_69))
| ~ sP20(U_69) )
& ! [U_69] :
( v4_pre_topc(sK15(U_69),U_69)
| ~ sP20(U_69) )
& ! [U_69] :
( v3_pre_topc(sK15(U_69),U_69)
| ~ sP20(U_69) )
& ! [U_69] :
( v1_xboole_0(sK15(U_69))
| ~ sP20(U_69) )
& ! [U_69] :
( m1_subset_1(sK15(U_69),k1_zfmisc_1(u1_struct_0(U_69)))
| ~ sP20(U_69) )
& ! [U_69] :
( sP20(U_69)
| ~ l1_pre_topc(U_69)
| ~ v2_pre_topc(U_69) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP20])],[f_47_3]) ).
cnf(f_47_5,plain,
( sP20(U_69)
| ~ l1_pre_topc(U_69)
| ~ v2_pre_topc(U_69) ),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_6,plain,
( m1_subset_1(sK15(U_69),k1_zfmisc_1(u1_struct_0(U_69)))
| ~ sP20(U_69) ),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_7,plain,
( v1_xboole_0(sK15(U_69))
| ~ sP20(U_69) ),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_8,plain,
( v3_pre_topc(sK15(U_69),U_69)
| ~ sP20(U_69) ),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_9,plain,
( v4_pre_topc(sK15(U_69),U_69)
| ~ sP20(U_69) ),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_10,plain,
( v1_membered(sK15(U_69))
| ~ sP20(U_69) ),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_11,plain,
( v2_membered(sK15(U_69))
| ~ sP20(U_69) ),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_12,plain,
( v3_membered(sK15(U_69))
| ~ sP20(U_69) ),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_13,plain,
( v4_membered(sK15(U_69))
| ~ sP20(U_69) ),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_14,plain,
( v5_membered(sK15(U_69))
| ~ sP20(U_69) ),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_15,plain,
( v2_tops_1(sK15(U_69),U_69)
| ~ sP20(U_69) ),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_16,plain,
( v3_tops_1(sK15(U_69),U_69)
| ~ sP20(U_69) ),
inference(clausify,[status(thm)],[f_47_4]) ).
fof(f_48_1,plain,
! [A] :
( ? [B] :
( v4_pre_topc(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l1_pre_topc(A)
| ~ v2_pre_topc(A) ),
inference(fof_nnf,[status(thm)],[rc6_pre_topc]) ).
fof(f_48_2,plain,
! [U_71] :
( ? [U_70] :
( v4_pre_topc(U_70,U_71)
& m1_subset_1(U_70,k1_zfmisc_1(u1_struct_0(U_71))) )
| ~ l1_pre_topc(U_71)
| ~ v2_pre_topc(U_71) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
! [U_71] :
( ( v4_pre_topc(sK16(U_71),U_71)
& m1_subset_1(sK16(U_71),k1_zfmisc_1(u1_struct_0(U_71))) )
| ~ l1_pre_topc(U_71)
| ~ v2_pre_topc(U_71) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_70,sK16(U_71))],[f_48_2]) ).
fof(f_48_4,plain,
( ! [U_71] :
( v4_pre_topc(sK16(U_71),U_71)
| ~ sP21(U_71) )
& ! [U_71] :
( m1_subset_1(sK16(U_71),k1_zfmisc_1(u1_struct_0(U_71)))
| ~ sP21(U_71) )
& ! [U_71] :
( sP21(U_71)
| ~ l1_pre_topc(U_71)
| ~ v2_pre_topc(U_71) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP21])],[f_48_3]) ).
cnf(f_48_5,plain,
( sP21(U_71)
| ~ l1_pre_topc(U_71)
| ~ v2_pre_topc(U_71) ),
inference(clausify,[status(thm)],[f_48_4]) ).
cnf(f_48_6,plain,
( m1_subset_1(sK16(U_71),k1_zfmisc_1(u1_struct_0(U_71)))
| ~ sP21(U_71) ),
inference(clausify,[status(thm)],[f_48_4]) ).
cnf(f_48_7,plain,
( v4_pre_topc(sK16(U_71),U_71)
| ~ sP21(U_71) ),
inference(clausify,[status(thm)],[f_48_4]) ).
fof(f_49_1,plain,
! [A] :
( ? [B] :
( v4_pre_topc(B,A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l1_pre_topc(A)
| ~ v2_pre_topc(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc7_pre_topc]) ).
fof(f_49_2,plain,
! [U_73] :
( ? [U_72] :
( v4_pre_topc(U_72,U_73)
& ~ v1_xboole_0(U_72)
& m1_subset_1(U_72,k1_zfmisc_1(u1_struct_0(U_73))) )
| ~ l1_pre_topc(U_73)
| ~ v2_pre_topc(U_73)
| v3_struct_0(U_73) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
! [U_73] :
( ( v4_pre_topc(sK17(U_73),U_73)
& ~ v1_xboole_0(sK17(U_73))
& m1_subset_1(sK17(U_73),k1_zfmisc_1(u1_struct_0(U_73))) )
| ~ l1_pre_topc(U_73)
| ~ v2_pre_topc(U_73)
| v3_struct_0(U_73) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_72,sK17(U_73))],[f_49_2]) ).
fof(f_49_4,plain,
( ! [U_73] :
( v4_pre_topc(sK17(U_73),U_73)
| ~ sP22(U_73) )
& ! [U_73] :
( ~ v1_xboole_0(sK17(U_73))
| ~ sP22(U_73) )
& ! [U_73] :
( m1_subset_1(sK17(U_73),k1_zfmisc_1(u1_struct_0(U_73)))
| ~ sP22(U_73) )
& ! [U_73] :
( sP22(U_73)
| ~ l1_pre_topc(U_73)
| ~ v2_pre_topc(U_73)
| v3_struct_0(U_73) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP22])],[f_49_3]) ).
cnf(f_49_5,plain,
( sP22(U_73)
| ~ l1_pre_topc(U_73)
| ~ v2_pre_topc(U_73)
| v3_struct_0(U_73) ),
inference(clausify,[status(thm)],[f_49_4]) ).
cnf(f_49_6,plain,
( m1_subset_1(sK17(U_73),k1_zfmisc_1(u1_struct_0(U_73)))
| ~ sP22(U_73) ),
inference(clausify,[status(thm)],[f_49_4]) ).
cnf(f_49_7,plain,
( ~ v1_xboole_0(sK17(U_73))
| ~ sP22(U_73) ),
inference(clausify,[status(thm)],[f_49_4]) ).
cnf(f_49_8,plain,
( v4_pre_topc(sK17(U_73),U_73)
| ~ sP22(U_73) ),
inference(clausify,[status(thm)],[f_49_4]) ).
fof(f_50_1,plain,
! [A,B] : r1_tarski(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_50_2,plain,
! [U_75,U_74] : r1_tarski(U_75,U_75),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_75] : r1_tarski(U_75,U_75),
inference(miniscope,[status(thm)],[f_50_2]) ).
fof(f_50_4,plain,
! [U_75] : r1_tarski(U_75,U_75),
inference(definitional_conversion,[status(esa)],[f_50_3]) ).
cnf(f_50_5,plain,
r1_tarski(U_75,U_75),
inference(clausify,[status(thm)],[f_50_4]) ).
fof(f_51_1,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_51_2,plain,
! [U_77,U_76] :
( m1_subset_1(U_77,U_76)
| ~ r2_hidden(U_77,U_76) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
! [U_77,U_76] :
( m1_subset_1(U_77,U_76)
| ~ r2_hidden(U_77,U_76) ),
inference(definitional_conversion,[status(esa)],[f_51_2]) ).
cnf(f_51_4,plain,
( m1_subset_1(U_77,U_76)
| ~ r2_hidden(U_77,U_76) ),
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_52_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_52_2,plain,
! [U_79,U_78] :
( r2_hidden(U_79,U_78)
| v1_xboole_0(U_78)
| ~ m1_subset_1(U_79,U_78) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
! [U_79,U_78] :
( r2_hidden(U_79,U_78)
| v1_xboole_0(U_78)
| ~ m1_subset_1(U_79,U_78) ),
inference(definitional_conversion,[status(esa)],[f_52_2]) ).
cnf(f_52_4,plain,
( r2_hidden(U_79,U_78)
| v1_xboole_0(U_78)
| ~ m1_subset_1(U_79,U_78) ),
inference(clausify,[status(thm)],[f_52_3]) ).
fof(f_53_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_53_2,plain,
! [U_81,U_80] :
( ( m1_subset_1(U_81,k1_zfmisc_1(U_80))
| ~ r1_tarski(U_81,U_80) )
& ( r1_tarski(U_81,U_80)
| ~ m1_subset_1(U_81,k1_zfmisc_1(U_80)) ) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
( ! [U_85,U_83] :
( m1_subset_1(U_85,k1_zfmisc_1(U_83))
| ~ r1_tarski(U_85,U_83) )
& ! [U_84,U_82] :
( r1_tarski(U_84,U_82)
| ~ m1_subset_1(U_84,k1_zfmisc_1(U_82)) ) ),
inference(miniscope,[status(thm)],[f_53_2]) ).
fof(f_53_4,plain,
( ! [U_85,U_83] :
( m1_subset_1(U_85,k1_zfmisc_1(U_83))
| ~ r1_tarski(U_85,U_83) )
& ! [U_84,U_82] :
( r1_tarski(U_84,U_82)
| ~ m1_subset_1(U_84,k1_zfmisc_1(U_82)) ) ),
inference(definitional_conversion,[status(esa)],[f_53_3]) ).
cnf(f_53_5,plain,
( r1_tarski(U_84,U_82)
| ~ m1_subset_1(U_84,k1_zfmisc_1(U_82)) ),
inference(clausify,[status(thm)],[f_53_4]) ).
cnf(f_53_6,plain,
( m1_subset_1(U_85,k1_zfmisc_1(U_83))
| ~ r1_tarski(U_85,U_83) ),
inference(clausify,[status(thm)],[f_53_4]) ).
fof(f_54_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_54_2,plain,
! [U_88,U_87,U_86] :
( m1_subset_1(U_88,U_86)
| ~ m1_subset_1(U_87,k1_zfmisc_1(U_86))
| ~ r2_hidden(U_88,U_87) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_86,U_87,U_88] :
( m1_subset_1(U_88,U_86)
| ~ m1_subset_1(U_87,k1_zfmisc_1(U_86))
| ~ r2_hidden(U_88,U_87) ),
inference(definitional_conversion,[status(esa)],[f_54_2]) ).
cnf(f_54_4,plain,
( m1_subset_1(U_88,U_86)
| ~ m1_subset_1(U_87,k1_zfmisc_1(U_86))
| ~ r2_hidden(U_88,U_87) ),
inference(clausify,[status(thm)],[f_54_3]) ).
fof(f_55_1,plain,
! [A] :
( ! [B] :
( k3_tex_4(A,B) = B
| ~ v3_pre_topc(B,A)
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l1_pre_topc(A)
| ~ v2_pre_topc(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t58_tex_4]) ).
fof(f_55_2,plain,
! [U_90] :
( ! [U_89] :
( k3_tex_4(U_90,U_89) = U_89
| ~ v3_pre_topc(U_89,U_90)
| ~ m1_subset_1(U_89,k1_zfmisc_1(u1_struct_0(U_90))) )
| ~ l1_pre_topc(U_90)
| ~ v2_pre_topc(U_90)
| v3_struct_0(U_90) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
! [U_90,U_89] :
( k3_tex_4(U_90,U_89) = U_89
| ~ v3_pre_topc(U_89,U_90)
| ~ m1_subset_1(U_89,k1_zfmisc_1(u1_struct_0(U_90)))
| ~ l1_pre_topc(U_90)
| ~ v2_pre_topc(U_90)
| v3_struct_0(U_90) ),
inference(definitional_conversion,[status(esa)],[f_55_2]) ).
cnf(f_55_4,plain,
( k3_tex_4(U_90,U_89) = U_89
| ~ v3_pre_topc(U_89,U_90)
| ~ m1_subset_1(U_89,k1_zfmisc_1(u1_struct_0(U_90)))
| ~ l1_pre_topc(U_90)
| ~ v2_pre_topc(U_90)
| v3_struct_0(U_90) ),
inference(clausify,[status(thm)],[f_55_3]) ).
fof(f_56_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_56_2,plain,
! [U_93,U_92,U_91] :
( ~ v1_xboole_0(U_91)
| ~ m1_subset_1(U_92,k1_zfmisc_1(U_91))
| ~ r2_hidden(U_93,U_92) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
! [U_93,U_92] :
( ! [U_91] :
( ~ v1_xboole_0(U_91)
| ~ m1_subset_1(U_92,k1_zfmisc_1(U_91)) )
| ~ r2_hidden(U_93,U_92) ),
inference(miniscope,[status(thm)],[f_56_2]) ).
fof(f_56_4,plain,
! [U_91,U_92,U_93] :
( ~ v1_xboole_0(U_91)
| ~ m1_subset_1(U_92,k1_zfmisc_1(U_91))
| ~ r2_hidden(U_93,U_92) ),
inference(definitional_conversion,[status(esa)],[f_56_3]) ).
cnf(f_56_5,plain,
( ~ v1_xboole_0(U_91)
| ~ m1_subset_1(U_92,k1_zfmisc_1(U_91))
| ~ r2_hidden(U_93,U_92) ),
inference(clausify,[status(thm)],[f_56_4]) ).
fof(f_57_1,plain,
! [A,B] :
( ( ( v1_tex_2(B,k1_zfmisc_1(A))
| B = A )
& ( B != A
| ~ v1_tex_2(B,k1_zfmisc_1(A)) ) )
| ~ m1_subset_1(B,k1_zfmisc_1(A)) ),
inference(fof_nnf,[status(thm)],[t5_tex_2]) ).
fof(f_57_2,plain,
! [U_95,U_94] :
( ( ( v1_tex_2(U_94,k1_zfmisc_1(U_95))
| U_94 = U_95 )
& ( U_94 != U_95
| ~ v1_tex_2(U_94,k1_zfmisc_1(U_95)) ) )
| ~ m1_subset_1(U_94,k1_zfmisc_1(U_95)) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
( ! [U_94,U_95] :
( v1_tex_2(U_94,k1_zfmisc_1(U_95))
| U_94 = U_95
| ~ sP23(U_94,U_95) )
& ! [U_94,U_95] :
( U_94 != U_95
| ~ v1_tex_2(U_94,k1_zfmisc_1(U_95))
| ~ sP23(U_94,U_95) )
& ! [U_94,U_95] :
( sP23(U_94,U_95)
| ~ m1_subset_1(U_94,k1_zfmisc_1(U_95)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP23])],[f_57_2]) ).
cnf(f_57_4,plain,
( sP23(U_94,U_95)
| ~ m1_subset_1(U_94,k1_zfmisc_1(U_95)) ),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_5,plain,
( U_94 != U_95
| ~ v1_tex_2(U_94,k1_zfmisc_1(U_95))
| ~ sP23(U_94,U_95) ),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_6,plain,
( v1_tex_2(U_94,k1_zfmisc_1(U_95))
| U_94 = U_95
| ~ sP23(U_94,U_95) ),
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_1,plain,
! [A] :
( ! [B] :
( k3_tex_4(A,B) = B
| ~ v4_pre_topc(B,A)
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l1_pre_topc(A)
| ~ v2_pre_topc(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t62_tex_4]) ).
fof(f_58_2,plain,
! [U_97] :
( ! [U_96] :
( k3_tex_4(U_97,U_96) = U_96
| ~ v4_pre_topc(U_96,U_97)
| ~ m1_subset_1(U_96,k1_zfmisc_1(u1_struct_0(U_97))) )
| ~ l1_pre_topc(U_97)
| ~ v2_pre_topc(U_97)
| v3_struct_0(U_97) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
! [U_96,U_97] :
( k3_tex_4(U_97,U_96) = U_96
| ~ v4_pre_topc(U_96,U_97)
| ~ m1_subset_1(U_96,k1_zfmisc_1(u1_struct_0(U_97)))
| ~ l1_pre_topc(U_97)
| ~ v2_pre_topc(U_97)
| v3_struct_0(U_97) ),
inference(definitional_conversion,[status(esa)],[f_58_2]) ).
cnf(f_58_4,plain,
( k3_tex_4(U_97,U_96) = U_96
| ~ v4_pre_topc(U_96,U_97)
| ~ m1_subset_1(U_96,k1_zfmisc_1(u1_struct_0(U_97)))
| ~ l1_pre_topc(U_97)
| ~ v2_pre_topc(U_97)
| v3_struct_0(U_97) ),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_59_1,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_59_2,plain,
! [U_98] :
( U_98 = k1_xboole_0
| ~ v1_xboole_0(U_98) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
! [U_98] :
( U_98 = k1_xboole_0
| ~ v1_xboole_0(U_98) ),
inference(definitional_conversion,[status(esa)],[f_59_2]) ).
cnf(f_59_4,plain,
( U_98 = k1_xboole_0
| ~ v1_xboole_0(U_98) ),
inference(clausify,[status(thm)],[f_59_3]) ).
fof(f_60_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_60_2,plain,
! [U_100,U_99] :
( ~ v1_xboole_0(U_99)
| ~ r2_hidden(U_100,U_99) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
! [U_100,U_99] :
( ~ v1_xboole_0(U_99)
| ~ r2_hidden(U_100,U_99) ),
inference(definitional_conversion,[status(esa)],[f_60_2]) ).
cnf(f_60_4,plain,
( ~ v1_xboole_0(U_99)
| ~ r2_hidden(U_100,U_99) ),
inference(clausify,[status(thm)],[f_60_3]) ).
fof(f_61_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| A = B
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_61_2,plain,
! [U_102,U_101] :
( ~ v1_xboole_0(U_101)
| U_102 = U_101
| ~ v1_xboole_0(U_102) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
! [U_102] :
( ! [U_101] :
( ~ v1_xboole_0(U_101)
| U_102 = U_101 )
| ~ v1_xboole_0(U_102) ),
inference(miniscope,[status(thm)],[f_61_2]) ).
fof(f_61_4,plain,
! [U_102,U_101] :
( ~ v1_xboole_0(U_101)
| U_102 = U_101
| ~ v1_xboole_0(U_102) ),
inference(definitional_conversion,[status(esa)],[f_61_3]) ).
cnf(f_61_5,plain,
( ~ v1_xboole_0(U_101)
| U_102 = U_101
| ~ v1_xboole_0(U_102) ),
inference(clausify,[status(thm)],[f_61_4]) ).
cnf(f_25_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_25_3]) ).
cnf(f_26_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_26_3]) ).
cnf(f_29_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_29_3]) ).
cnf(f_30_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_30_3]) ).
cnf(f_31_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_31_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,
( k1_zfmisc_1(Eq_x_0) = k1_zfmisc_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( k3_tex_4(Eq_x_0,Eq_x_1) = k3_tex_4(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sK5(Eq_x_0) = sK5(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK9(Eq_x_0) = sK9(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK10(Eq_x_0) = sK10(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK12(Eq_x_0) = sK12(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK13(Eq_x_0) = sK13(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK14(Eq_x_0) = sK14(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK15(Eq_x_0) = sK15(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK16(Eq_x_0) = sK16(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( sK17(Eq_x_0) = sK17(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,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_19,axiom,
( v2_pre_topc(Eq_y_0)
| ~ v2_pre_topc(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,axiom,
( l1_pre_topc(Eq_y_0)
| ~ l1_pre_topc(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,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_22,axiom,
( v3_pre_topc(Eq_y_0,Eq_y_1)
| ~ v3_pre_topc(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( v4_pre_topc(Eq_y_0,Eq_y_1)
| ~ v4_pre_topc(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( v1_tsp_2(Eq_y_0,Eq_y_1)
| ~ v1_tsp_2(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( v1_tex_2(Eq_y_0,Eq_y_1)
| ~ v1_tex_2(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,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_27,axiom,
( v1_membered(Eq_y_0)
| ~ v1_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( v1_xcmplx_0(Eq_y_0)
| ~ v1_xcmplx_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,axiom,
( v2_membered(Eq_y_0)
| ~ v2_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,axiom,
( v1_xreal_0(Eq_y_0)
| ~ v1_xreal_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_31,axiom,
( v3_membered(Eq_y_0)
| ~ v3_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( v1_rat_1(Eq_y_0)
| ~ v1_rat_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,axiom,
( v4_membered(Eq_y_0)
| ~ v4_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,axiom,
( v1_int_1(Eq_y_0)
| ~ v1_int_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( v5_membered(Eq_y_0)
| ~ v5_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,axiom,
( v4_ordinal2(Eq_y_0)
| ~ v4_ordinal2(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_37,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_38,axiom,
( v2_tops_1(Eq_y_0,Eq_y_1)
| ~ v2_tops_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,
( v3_tops_1(Eq_y_0,Eq_y_1)
| ~ v3_tops_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_40,axiom,
( v1_tsp_1(Eq_y_0,Eq_y_1)
| ~ v1_tsp_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_41,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_42,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_43,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_44,axiom,
( sP1(Eq_y_0)
| ~ sP1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_45,axiom,
( sP2(Eq_y_0)
| ~ sP2(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_46,axiom,
( sP3(Eq_y_0)
| ~ sP3(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_47,axiom,
( sP4(Eq_y_0)
| ~ sP4(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_48,axiom,
( sP5(Eq_y_0)
| ~ sP5(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_49,axiom,
( sP6(Eq_y_0)
| ~ sP6(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_50,axiom,
( sP7(Eq_y_0)
| ~ sP7(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_51,axiom,
( sP8(Eq_y_0,Eq_y_1)
| ~ sP8(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_52,axiom,
( sP9(Eq_y_0)
| ~ sP9(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_53,axiom,
( sP10(Eq_y_0,Eq_y_1)
| ~ sP10(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_54,axiom,
( sP11(Eq_y_0,Eq_y_1)
| ~ sP11(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_55,axiom,
( sP12(Eq_y_0,Eq_y_1)
| ~ sP12(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_56,axiom,
( sP13(Eq_y_0,Eq_y_1)
| ~ sP13(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,
( sP14(Eq_y_0)
| ~ sP14(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_58,axiom,
( sP15(Eq_y_0)
| ~ sP15(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_59,axiom,
( sP16(Eq_y_0)
| ~ sP16(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_60,axiom,
( sP17(Eq_y_0)
| ~ sP17(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_61,axiom,
( sP18(Eq_y_0)
| ~ sP18(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_62,axiom,
( sP19(Eq_y_0)
| ~ sP19(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_63,axiom,
( sP20(Eq_y_0)
| ~ sP20(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_64,axiom,
( sP21(Eq_y_0)
| ~ sP21(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_65,axiom,
( sP22(Eq_y_0)
| ~ sP22(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_66,axiom,
( sP23(Eq_y_0,Eq_y_1)
| ~ sP23(Eq_x_0,Eq_x_1)
| 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
% 0.00/0.02 % Problem : TOP025+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 08:23:41 UTC 2026
% 0.09/0.35 % CPUTime :
% 34.66/34.91 % SZS status Theorem for theBenchmark
% 34.66/34.91 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------