%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LAT294+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 08:48:05 AM UTC 2026
% Result : Theorem 48.36s 48.63s
% Output : Proof 48.72s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(t4_filter_2,conjecture,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(B) )
=> ! [C] :
( ( m2_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(C) )
=> ! [D] :
( ( m2_relset_1(D,k2_zfmisc_1(A,A),A)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& v1_funct_1(D) )
=> ! [E] :
( ( m2_relset_1(E,k2_zfmisc_1(B,B),B)
& v1_funct_2(E,k2_zfmisc_1(B,B),B)
& v1_funct_1(E) )
=> ! [F] :
( ( m2_relset_1(F,k2_zfmisc_1(B,B),B)
& v1_funct_2(F,k2_zfmisc_1(B,B),B)
& v1_funct_1(F) )
=> ( ( r6_binop_1(A,C,D)
& F = k1_realset1(D,B)
& E = k1_realset1(C,B) )
=> r6_binop_1(B,E,F) ) ) ) ) ) ) ),
file('theBenchmark.p',t4_filter_2) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( r2_hidden(A,B)
=> ~ r2_hidden(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(cc1_funct_1,axiom,
! [A] :
( v1_xboole_0(A)
=> v1_funct_1(A) ),
file('theBenchmark.p',cc1_funct_1) ).
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(cc2_funct_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_xboole_0(A)
& v1_relat_1(A) )
=> ( v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A) ) ),
file('theBenchmark.p',cc2_funct_1) ).
fof(d11_binop_1,axiom,
! [A,B] :
( ( m2_relset_1(B,k2_zfmisc_1(A,A),A)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& v1_funct_1(B) )
=> ! [C] :
( ( m2_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(C) )
=> ( r6_binop_1(A,B,C)
<=> ( r5_binop_1(A,B,C)
& r4_binop_1(A,B,C) ) ) ) ),
file('theBenchmark.p',d11_binop_1) ).
fof(d3_realset1,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] : k1_realset1(A,B) = k7_relat_1(A,k2_zfmisc_1(B,B)) ),
file('theBenchmark.p',d3_realset1) ).
fof(dt_k1_realset1,axiom,
$true,
file('theBenchmark.p',dt_k1_realset1) ).
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_k7_relat_1,axiom,
! [A,B] :
( v1_relat_1(A)
=> v1_relat_1(k7_relat_1(A,B)) ),
file('theBenchmark.p',dt_k7_relat_1) ).
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(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(fc1_realset1,axiom,
! [A,B] :
( v1_relat_1(A)
=> v1_relat_1(k1_realset1(A,B)) ),
file('theBenchmark.p',fc1_realset1) ).
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(fc2_realset1,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_relat_1(A) )
=> ( v1_funct_1(k1_realset1(A,B))
& v1_relat_1(k1_realset1(A,B)) ) ),
file('theBenchmark.p',fc2_realset1) ).
fof(fc4_funct_1,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_relat_1(A) )
=> ( v1_funct_1(k7_relat_1(A,B))
& v1_relat_1(k7_relat_1(A,B)) ) ),
file('theBenchmark.p',fc4_funct_1) ).
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(rc1_funct_1,axiom,
? [A] :
( v1_funct_1(A)
& v1_relat_1(A) ),
file('theBenchmark.p',rc1_funct_1) ).
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_funct_1,axiom,
? [A] :
( v1_funct_1(A)
& v1_xboole_0(A)
& v1_relat_1(A) ),
file('theBenchmark.p',rc2_funct_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_xboole_0,axiom,
? [A] : ~ v1_xboole_0(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(rc3_funct_1,axiom,
? [A] :
( v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A) ),
file('theBenchmark.p',rc3_funct_1) ).
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(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_filter_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(B) )
=> ! [C] :
( ( m2_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(C) )
=> ! [D] :
( ( m2_relset_1(D,k2_zfmisc_1(A,A),A)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& v1_funct_1(D) )
=> ! [E] :
( ( m2_relset_1(E,k2_zfmisc_1(B,B),B)
& v1_funct_2(E,k2_zfmisc_1(B,B),B)
& v1_funct_1(E) )
=> ! [F] :
( ( m2_relset_1(F,k2_zfmisc_1(B,B),B)
& v1_funct_2(F,k2_zfmisc_1(B,B),B)
& v1_funct_1(F) )
=> ( ( F = k1_realset1(D,B)
& E = k1_realset1(C,B) )
=> ( ( r5_binop_1(A,C,D)
=> r5_binop_1(B,E,F) )
& ( r4_binop_1(A,C,D)
=> r4_binop_1(B,E,F) ) ) ) ) ) ) ) ) ),
file('theBenchmark.p',t3_filter_2) ).
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] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(B) )
=> ! [C] :
( ( m2_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(C) )
=> ! [D] :
( ( m2_relset_1(D,k2_zfmisc_1(A,A),A)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& v1_funct_1(D) )
=> ! [E] :
( ( m2_relset_1(E,k2_zfmisc_1(B,B),B)
& v1_funct_2(E,k2_zfmisc_1(B,B),B)
& v1_funct_1(E) )
=> ! [F] :
( ( m2_relset_1(F,k2_zfmisc_1(B,B),B)
& v1_funct_2(F,k2_zfmisc_1(B,B),B)
& v1_funct_1(F) )
=> ( ( r6_binop_1(A,C,D)
& F = k1_realset1(D,B)
& E = k1_realset1(C,B) )
=> r6_binop_1(B,E,F) ) ) ) ) ) ) ),
inference(negate,[status(cth)],[t4_filter_2]) ).
fof(f_1_2,negated_conjecture,
? [A] :
( ? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ? [F] :
( ~ r6_binop_1(B,E,F)
& r6_binop_1(A,C,D)
& F = k1_realset1(D,B)
& E = k1_realset1(C,B)
& m2_relset_1(F,k2_zfmisc_1(B,B),B)
& v1_funct_2(F,k2_zfmisc_1(B,B),B)
& v1_funct_1(F) )
& m2_relset_1(E,k2_zfmisc_1(B,B),B)
& v1_funct_2(E,k2_zfmisc_1(B,B),B)
& v1_funct_1(E) )
& m2_relset_1(D,k2_zfmisc_1(A,A),A)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& v1_funct_1(D) )
& m2_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(C) )
& m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(B) )
& ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
? [U_5] :
( ? [U_4] :
( ? [U_3] :
( ? [U_2] :
( ? [U_1] :
( ? [U_0] :
( ~ r6_binop_1(U_4,U_1,U_0)
& r6_binop_1(U_5,U_3,U_2)
& U_0 = k1_realset1(U_2,U_4)
& U_1 = k1_realset1(U_3,U_4)
& m2_relset_1(U_0,k2_zfmisc_1(U_4,U_4),U_4)
& v1_funct_2(U_0,k2_zfmisc_1(U_4,U_4),U_4)
& v1_funct_1(U_0) )
& m2_relset_1(U_1,k2_zfmisc_1(U_4,U_4),U_4)
& v1_funct_2(U_1,k2_zfmisc_1(U_4,U_4),U_4)
& v1_funct_1(U_1) )
& m2_relset_1(U_2,k2_zfmisc_1(U_5,U_5),U_5)
& v1_funct_2(U_2,k2_zfmisc_1(U_5,U_5),U_5)
& v1_funct_1(U_2) )
& m2_relset_1(U_3,k2_zfmisc_1(U_5,U_5),U_5)
& v1_funct_2(U_3,k2_zfmisc_1(U_5,U_5),U_5)
& v1_funct_1(U_3) )
& m1_subset_1(U_4,k1_zfmisc_1(U_5))
& ~ v1_xboole_0(U_4) )
& ~ v1_xboole_0(U_5) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
( ? [U_4] :
( ? [U_3] :
( ? [U_2] :
( ? [U_1] :
( ? [U_0] :
( ~ r6_binop_1(U_4,U_1,U_0)
& r6_binop_1(sK1,U_3,U_2)
& U_0 = k1_realset1(U_2,U_4)
& U_1 = k1_realset1(U_3,U_4)
& m2_relset_1(U_0,k2_zfmisc_1(U_4,U_4),U_4)
& v1_funct_2(U_0,k2_zfmisc_1(U_4,U_4),U_4)
& v1_funct_1(U_0) )
& m2_relset_1(U_1,k2_zfmisc_1(U_4,U_4),U_4)
& v1_funct_2(U_1,k2_zfmisc_1(U_4,U_4),U_4)
& v1_funct_1(U_1) )
& m2_relset_1(U_2,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_2(U_2,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_1(U_2) )
& m2_relset_1(U_3,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_2(U_3,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_1(U_3) )
& m1_subset_1(U_4,k1_zfmisc_1(sK1))
& ~ v1_xboole_0(U_4) )
& ~ v1_xboole_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_5,sK1)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
( ? [U_3] :
( ? [U_2] :
( ? [U_1] :
( ? [U_0] :
( ~ r6_binop_1(sK2,U_1,U_0)
& r6_binop_1(sK1,U_3,U_2)
& U_0 = k1_realset1(U_2,sK2)
& U_1 = k1_realset1(U_3,sK2)
& m2_relset_1(U_0,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_2(U_0,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_1(U_0) )
& m2_relset_1(U_1,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_2(U_1,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_1(U_1) )
& m2_relset_1(U_2,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_2(U_2,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_1(U_2) )
& m2_relset_1(U_3,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_2(U_3,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_1(U_3) )
& m1_subset_1(sK2,k1_zfmisc_1(sK1))
& ~ v1_xboole_0(sK2)
& ~ v1_xboole_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_4,sK2)],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( ? [U_2] :
( ? [U_1] :
( ? [U_0] :
( ~ r6_binop_1(sK2,U_1,U_0)
& r6_binop_1(sK1,sK3,U_2)
& U_0 = k1_realset1(U_2,sK2)
& U_1 = k1_realset1(sK3,sK2)
& m2_relset_1(U_0,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_2(U_0,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_1(U_0) )
& m2_relset_1(U_1,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_2(U_1,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_1(U_1) )
& m2_relset_1(U_2,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_2(U_2,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_1(U_2) )
& m2_relset_1(sK3,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_2(sK3,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_1(sK3)
& m1_subset_1(sK2,k1_zfmisc_1(sK1))
& ~ v1_xboole_0(sK2)
& ~ v1_xboole_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_3,sK3)],[f_1_5]) ).
fof(f_1_7,negated_conjecture,
( ? [U_1] :
( ? [U_0] :
( ~ r6_binop_1(sK2,U_1,U_0)
& r6_binop_1(sK1,sK3,sK4)
& U_0 = k1_realset1(sK4,sK2)
& U_1 = k1_realset1(sK3,sK2)
& m2_relset_1(U_0,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_2(U_0,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_1(U_0) )
& m2_relset_1(U_1,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_2(U_1,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_1(U_1) )
& m2_relset_1(sK4,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_2(sK4,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_1(sK4)
& m2_relset_1(sK3,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_2(sK3,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_1(sK3)
& m1_subset_1(sK2,k1_zfmisc_1(sK1))
& ~ v1_xboole_0(sK2)
& ~ v1_xboole_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_2,sK4)],[f_1_6]) ).
fof(f_1_8,negated_conjecture,
( ? [U_0] :
( ~ r6_binop_1(sK2,sK5,U_0)
& r6_binop_1(sK1,sK3,sK4)
& U_0 = k1_realset1(sK4,sK2)
& sK5 = k1_realset1(sK3,sK2)
& m2_relset_1(U_0,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_2(U_0,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_1(U_0) )
& m2_relset_1(sK5,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_2(sK5,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_1(sK5)
& m2_relset_1(sK4,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_2(sK4,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_1(sK4)
& m2_relset_1(sK3,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_2(sK3,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_1(sK3)
& m1_subset_1(sK2,k1_zfmisc_1(sK1))
& ~ v1_xboole_0(sK2)
& ~ v1_xboole_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_1,sK5)],[f_1_7]) ).
fof(f_1_9,negated_conjecture,
( ~ r6_binop_1(sK2,sK5,sK6)
& r6_binop_1(sK1,sK3,sK4)
& sK6 = k1_realset1(sK4,sK2)
& sK5 = k1_realset1(sK3,sK2)
& m2_relset_1(sK6,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_2(sK6,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_1(sK6)
& m2_relset_1(sK5,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_2(sK5,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_1(sK5)
& m2_relset_1(sK4,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_2(sK4,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_1(sK4)
& m2_relset_1(sK3,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_2(sK3,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_1(sK3)
& m1_subset_1(sK2,k1_zfmisc_1(sK1))
& ~ v1_xboole_0(sK2)
& ~ v1_xboole_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_0,sK6)],[f_1_8]) ).
fof(f_1_10,negated_conjecture,
( ~ r6_binop_1(sK2,sK5,sK6)
& r6_binop_1(sK1,sK3,sK4)
& sK6 = k1_realset1(sK4,sK2)
& sK5 = k1_realset1(sK3,sK2)
& m2_relset_1(sK6,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_2(sK6,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_1(sK6)
& m2_relset_1(sK5,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_2(sK5,k2_zfmisc_1(sK2,sK2),sK2)
& v1_funct_1(sK5)
& m2_relset_1(sK4,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_2(sK4,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_1(sK4)
& m2_relset_1(sK3,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_2(sK3,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_1(sK3)
& m1_subset_1(sK2,k1_zfmisc_1(sK1))
& ~ v1_xboole_0(sK2)
& ~ v1_xboole_0(sK1) ),
inference(definitional_conversion,[status(esa)],[f_1_9]) ).
cnf(f_1_11,negated_conjecture,
~ v1_xboole_0(sK1),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_12,negated_conjecture,
~ v1_xboole_0(sK2),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_13,negated_conjecture,
m1_subset_1(sK2,k1_zfmisc_1(sK1)),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_14,negated_conjecture,
v1_funct_1(sK3),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_15,negated_conjecture,
v1_funct_2(sK3,k2_zfmisc_1(sK1,sK1),sK1),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_16,negated_conjecture,
m2_relset_1(sK3,k2_zfmisc_1(sK1,sK1),sK1),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_17,negated_conjecture,
v1_funct_1(sK4),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_18,negated_conjecture,
v1_funct_2(sK4,k2_zfmisc_1(sK1,sK1),sK1),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_19,negated_conjecture,
m2_relset_1(sK4,k2_zfmisc_1(sK1,sK1),sK1),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_20,negated_conjecture,
v1_funct_1(sK5),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_21,negated_conjecture,
v1_funct_2(sK5,k2_zfmisc_1(sK2,sK2),sK2),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_22,negated_conjecture,
m2_relset_1(sK5,k2_zfmisc_1(sK2,sK2),sK2),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_23,negated_conjecture,
v1_funct_1(sK6),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_24,negated_conjecture,
v1_funct_2(sK6,k2_zfmisc_1(sK2,sK2),sK2),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_25,negated_conjecture,
m2_relset_1(sK6,k2_zfmisc_1(sK2,sK2),sK2),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_26,negated_conjecture,
sK5 = k1_realset1(sK3,sK2),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_27,negated_conjecture,
sK6 = k1_realset1(sK4,sK2),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_28,negated_conjecture,
r6_binop_1(sK1,sK3,sK4),
inference(clausify,[status(thm)],[f_1_10]) ).
cnf(f_1_29,negated_conjecture,
~ r6_binop_1(sK2,sK5,sK6),
inference(clausify,[status(thm)],[f_1_10]) ).
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_7,U_6] :
( ~ r2_hidden(U_6,U_7)
| ~ r2_hidden(U_7,U_6) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_6,U_7] :
( ~ r2_hidden(U_6,U_7)
| ~ r2_hidden(U_7,U_6) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( ~ r2_hidden(U_6,U_7)
| ~ r2_hidden(U_7,U_6) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A] :
( v1_funct_1(A)
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_3_2,plain,
! [U_8] :
( v1_funct_1(U_8)
| ~ v1_xboole_0(U_8) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_8] :
( v1_funct_1(U_8)
| ~ v1_xboole_0(U_8) ),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
( v1_funct_1(U_8)
| ~ v1_xboole_0(U_8) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_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_4_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_4_1]) ).
fof(f_4_3,plain,
! [U_9,U_11,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_4_2]) ).
cnf(f_4_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_4_3]) ).
fof(f_5_1,plain,
! [A] :
( ( v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A) )
| ~ v1_funct_1(A)
| ~ v1_xboole_0(A)
| ~ v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[cc2_funct_1]) ).
fof(f_5_2,plain,
! [U_12] :
( ( v2_funct_1(U_12)
& v1_funct_1(U_12)
& v1_relat_1(U_12) )
| ~ v1_funct_1(U_12)
| ~ v1_xboole_0(U_12)
| ~ v1_relat_1(U_12) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_12] :
( v2_funct_1(U_12)
| ~ sP0(U_12) )
& ! [U_12] :
( v1_funct_1(U_12)
| ~ sP0(U_12) )
& ! [U_12] :
( v1_relat_1(U_12)
| ~ sP0(U_12) )
& ! [U_12] :
( sP0(U_12)
| ~ v1_funct_1(U_12)
| ~ v1_xboole_0(U_12)
| ~ v1_relat_1(U_12) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_5_2]) ).
cnf(f_5_4,plain,
( sP0(U_12)
| ~ v1_funct_1(U_12)
| ~ v1_xboole_0(U_12)
| ~ v1_relat_1(U_12) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( v1_relat_1(U_12)
| ~ sP0(U_12) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_6,plain,
( v1_funct_1(U_12)
| ~ sP0(U_12) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_7,plain,
( v2_funct_1(U_12)
| ~ sP0(U_12) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A,B] :
( ! [C] :
( ( ( r6_binop_1(A,B,C)
| ~ r5_binop_1(A,B,C)
| ~ r4_binop_1(A,B,C) )
& ( ( r5_binop_1(A,B,C)
& r4_binop_1(A,B,C) )
| ~ r6_binop_1(A,B,C) ) )
| ~ m2_relset_1(C,k2_zfmisc_1(A,A),A)
| ~ v1_funct_2(C,k2_zfmisc_1(A,A),A)
| ~ v1_funct_1(C) )
| ~ m2_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)],[d11_binop_1]) ).
fof(f_6_2,plain,
! [U_15,U_14] :
( ! [U_13] :
( ( ( r6_binop_1(U_15,U_14,U_13)
| ~ r5_binop_1(U_15,U_14,U_13)
| ~ r4_binop_1(U_15,U_14,U_13) )
& ( ( r5_binop_1(U_15,U_14,U_13)
& r4_binop_1(U_15,U_14,U_13) )
| ~ r6_binop_1(U_15,U_14,U_13) ) )
| ~ m2_relset_1(U_13,k2_zfmisc_1(U_15,U_15),U_15)
| ~ v1_funct_2(U_13,k2_zfmisc_1(U_15,U_15),U_15)
| ~ v1_funct_1(U_13) )
| ~ m2_relset_1(U_14,k2_zfmisc_1(U_15,U_15),U_15)
| ~ v1_funct_2(U_14,k2_zfmisc_1(U_15,U_15),U_15)
| ~ v1_funct_1(U_14) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_14,U_15,U_13] :
( r5_binop_1(U_15,U_14,U_13)
| ~ sP1(U_14,U_15,U_13) )
& ! [U_14,U_15,U_13] :
( r4_binop_1(U_15,U_14,U_13)
| ~ sP1(U_14,U_15,U_13) )
& ! [U_14,U_15,U_13] :
( r6_binop_1(U_15,U_14,U_13)
| ~ r5_binop_1(U_15,U_14,U_13)
| ~ r4_binop_1(U_15,U_14,U_13)
| ~ sP2(U_14,U_15,U_13) )
& ! [U_14,U_15,U_13] :
( sP1(U_14,U_15,U_13)
| ~ r6_binop_1(U_15,U_14,U_13)
| ~ sP2(U_14,U_15,U_13) )
& ! [U_14,U_15,U_13] :
( sP2(U_14,U_15,U_13)
| ~ m2_relset_1(U_13,k2_zfmisc_1(U_15,U_15),U_15)
| ~ v1_funct_2(U_13,k2_zfmisc_1(U_15,U_15),U_15)
| ~ v1_funct_1(U_13)
| ~ m2_relset_1(U_14,k2_zfmisc_1(U_15,U_15),U_15)
| ~ v1_funct_2(U_14,k2_zfmisc_1(U_15,U_15),U_15)
| ~ v1_funct_1(U_14) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1,sP2])],[f_6_2]) ).
cnf(f_6_4,plain,
( sP2(U_14,U_15,U_13)
| ~ m2_relset_1(U_13,k2_zfmisc_1(U_15,U_15),U_15)
| ~ v1_funct_2(U_13,k2_zfmisc_1(U_15,U_15),U_15)
| ~ v1_funct_1(U_13)
| ~ m2_relset_1(U_14,k2_zfmisc_1(U_15,U_15),U_15)
| ~ v1_funct_2(U_14,k2_zfmisc_1(U_15,U_15),U_15)
| ~ v1_funct_1(U_14) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( sP1(U_14,U_15,U_13)
| ~ r6_binop_1(U_15,U_14,U_13)
| ~ sP2(U_14,U_15,U_13) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
( r6_binop_1(U_15,U_14,U_13)
| ~ r5_binop_1(U_15,U_14,U_13)
| ~ r4_binop_1(U_15,U_14,U_13)
| ~ sP2(U_14,U_15,U_13) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_7,plain,
( r4_binop_1(U_15,U_14,U_13)
| ~ sP1(U_14,U_15,U_13) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_8,plain,
( r5_binop_1(U_15,U_14,U_13)
| ~ sP1(U_14,U_15,U_13) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [A] :
( ! [B] : k1_realset1(A,B) = k7_relat_1(A,k2_zfmisc_1(B,B))
| ~ v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[d3_realset1]) ).
fof(f_7_2,plain,
! [U_17] :
( ! [U_16] : k1_realset1(U_17,U_16) = k7_relat_1(U_17,k2_zfmisc_1(U_16,U_16))
| ~ v1_relat_1(U_17) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_16,U_17] :
( k1_realset1(U_17,U_16) = k7_relat_1(U_17,k2_zfmisc_1(U_16,U_16))
| ~ v1_relat_1(U_17) ),
inference(definitional_conversion,[status(esa)],[f_7_2]) ).
cnf(f_7_4,plain,
( k1_realset1(U_17,U_16) = k7_relat_1(U_17,k2_zfmisc_1(U_16,U_16))
| ~ v1_relat_1(U_17) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_realset1]) ).
fof(f_8_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_8_1]) ).
cnf(f_8_3,plain,
$true,
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
fof(f_9_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_9_1]) ).
cnf(f_9_3,plain,
$true,
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
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_k2_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,
! [A,B] :
( v1_relat_1(k7_relat_1(A,B))
| ~ v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[dt_k7_relat_1]) ).
fof(f_12_2,plain,
! [U_19,U_18] :
( v1_relat_1(k7_relat_1(U_19,U_18))
| ~ v1_relat_1(U_19) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_19] :
( ! [U_18] : v1_relat_1(k7_relat_1(U_19,U_18))
| ~ v1_relat_1(U_19) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
! [U_19,U_18] :
( v1_relat_1(k7_relat_1(U_19,U_18))
| ~ v1_relat_1(U_19) ),
inference(definitional_conversion,[status(esa)],[f_12_3]) ).
cnf(f_12_5,plain,
( v1_relat_1(k7_relat_1(U_19,U_18))
| ~ v1_relat_1(U_19) ),
inference(clausify,[status(thm)],[f_12_4]) ).
fof(f_13_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_relset_1]) ).
fof(f_13_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_13_1]) ).
cnf(f_13_3,plain,
$true,
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
fof(f_14_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_14_1]) ).
cnf(f_14_3,plain,
$true,
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_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_15_2,plain,
! [U_22,U_21,U_20] :
( m1_subset_1(U_20,k1_zfmisc_1(k2_zfmisc_1(U_22,U_21)))
| ~ m2_relset_1(U_20,U_22,U_21) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_22,U_21,U_20] :
( m1_subset_1(U_20,k1_zfmisc_1(k2_zfmisc_1(U_22,U_21)))
| ~ m2_relset_1(U_20,U_22,U_21) ),
inference(definitional_conversion,[status(esa)],[f_15_2]) ).
cnf(f_15_4,plain,
( m1_subset_1(U_20,k1_zfmisc_1(k2_zfmisc_1(U_22,U_21)))
| ~ m2_relset_1(U_20,U_22,U_21) ),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
! [A,B] :
? [C] : m1_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_relset_1]) ).
fof(f_16_2,plain,
! [U_25,U_24] :
? [U_23] : m1_relset_1(U_23,U_25,U_24),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_25,U_24] : m1_relset_1(sK7(U_25,U_24),U_25,U_24),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_23,sK7(U_25,U_24))],[f_16_2]) ).
fof(f_16_4,plain,
! [U_24,U_25] : m1_relset_1(sK7(U_25,U_24),U_25,U_24),
inference(definitional_conversion,[status(esa)],[f_16_3]) ).
cnf(f_16_5,plain,
m1_relset_1(sK7(U_25,U_24),U_25,U_24),
inference(clausify,[status(thm)],[f_16_4]) ).
fof(f_17_1,plain,
! [A] :
? [B] : m1_subset_1(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_17_2,plain,
! [U_27] :
? [U_26] : m1_subset_1(U_26,U_27),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_27] : m1_subset_1(sK8(U_27),U_27),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_26,sK8(U_27))],[f_17_2]) ).
fof(f_17_4,plain,
! [U_27] : m1_subset_1(sK8(U_27),U_27),
inference(definitional_conversion,[status(esa)],[f_17_3]) ).
cnf(f_17_5,plain,
m1_subset_1(sK8(U_27),U_27),
inference(clausify,[status(thm)],[f_17_4]) ).
fof(f_18_1,plain,
! [A,B] :
? [C] : m2_relset_1(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m2_relset_1]) ).
fof(f_18_2,plain,
! [U_30,U_29] :
? [U_28] : m2_relset_1(U_28,U_30,U_29),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_30,U_29] : m2_relset_1(sK9(U_30,U_29),U_30,U_29),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_28,sK9(U_30,U_29))],[f_18_2]) ).
fof(f_18_4,plain,
! [U_30,U_29] : m2_relset_1(sK9(U_30,U_29),U_30,U_29),
inference(definitional_conversion,[status(esa)],[f_18_3]) ).
cnf(f_18_5,plain,
m2_relset_1(sK9(U_30,U_29),U_30,U_29),
inference(clausify,[status(thm)],[f_18_4]) ).
fof(f_19_1,plain,
! [A,B] :
( v1_relat_1(k1_realset1(A,B))
| ~ v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[fc1_realset1]) ).
fof(f_19_2,plain,
! [U_32,U_31] :
( v1_relat_1(k1_realset1(U_32,U_31))
| ~ v1_relat_1(U_32) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_32] :
( ! [U_31] : v1_relat_1(k1_realset1(U_32,U_31))
| ~ v1_relat_1(U_32) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
fof(f_19_4,plain,
! [U_32,U_31] :
( v1_relat_1(k1_realset1(U_32,U_31))
| ~ v1_relat_1(U_32) ),
inference(definitional_conversion,[status(esa)],[f_19_3]) ).
cnf(f_19_5,plain,
( v1_relat_1(k1_realset1(U_32,U_31))
| ~ v1_relat_1(U_32) ),
inference(clausify,[status(thm)],[f_19_4]) ).
fof(f_20_1,plain,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_20_2,plain,
! [U_33] : ~ v1_xboole_0(k1_zfmisc_1(U_33)),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_33] : ~ v1_xboole_0(k1_zfmisc_1(U_33)),
inference(definitional_conversion,[status(esa)],[f_20_2]) ).
cnf(f_20_4,plain,
~ v1_xboole_0(k1_zfmisc_1(U_33)),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
v1_xboole_0(k1_xboole_0),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_21_2,plain,
v1_xboole_0(k1_xboole_0),
inference(definitional_conversion,[status(esa)],[f_21_1]) ).
cnf(f_21_3,plain,
v1_xboole_0(k1_xboole_0),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
! [A,B] :
( ( v1_funct_1(k1_realset1(A,B))
& v1_relat_1(k1_realset1(A,B)) )
| ~ v1_funct_1(A)
| ~ v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[fc2_realset1]) ).
fof(f_22_2,plain,
! [U_35,U_34] :
( ( v1_funct_1(k1_realset1(U_35,U_34))
& v1_relat_1(k1_realset1(U_35,U_34)) )
| ~ v1_funct_1(U_35)
| ~ v1_relat_1(U_35) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_35] :
( ( ! [U_37] : v1_funct_1(k1_realset1(U_35,U_37))
& ! [U_36] : v1_relat_1(k1_realset1(U_35,U_36)) )
| ~ v1_funct_1(U_35)
| ~ v1_relat_1(U_35) ),
inference(miniscope,[status(thm)],[f_22_2]) ).
fof(f_22_4,plain,
( ! [U_35,U_37,U_36] :
( v1_funct_1(k1_realset1(U_35,U_37))
| ~ sP3(U_35,U_37,U_36) )
& ! [U_35,U_37,U_36] :
( v1_relat_1(k1_realset1(U_35,U_36))
| ~ sP3(U_35,U_37,U_36) )
& ! [U_35,U_37,U_36] :
( sP3(U_35,U_37,U_36)
| ~ v1_funct_1(U_35)
| ~ v1_relat_1(U_35) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_22_3]) ).
cnf(f_22_5,plain,
( sP3(U_35,U_37,U_36)
| ~ v1_funct_1(U_35)
| ~ v1_relat_1(U_35) ),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_6,plain,
( v1_relat_1(k1_realset1(U_35,U_36))
| ~ sP3(U_35,U_37,U_36) ),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_7,plain,
( v1_funct_1(k1_realset1(U_35,U_37))
| ~ sP3(U_35,U_37,U_36) ),
inference(clausify,[status(thm)],[f_22_4]) ).
fof(f_23_1,plain,
! [A,B] :
( ( v1_funct_1(k7_relat_1(A,B))
& v1_relat_1(k7_relat_1(A,B)) )
| ~ v1_funct_1(A)
| ~ v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[fc4_funct_1]) ).
fof(f_23_2,plain,
! [U_39,U_38] :
( ( v1_funct_1(k7_relat_1(U_39,U_38))
& v1_relat_1(k7_relat_1(U_39,U_38)) )
| ~ v1_funct_1(U_39)
| ~ v1_relat_1(U_39) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_39] :
( ( ! [U_41] : v1_funct_1(k7_relat_1(U_39,U_41))
& ! [U_40] : v1_relat_1(k7_relat_1(U_39,U_40)) )
| ~ v1_funct_1(U_39)
| ~ v1_relat_1(U_39) ),
inference(miniscope,[status(thm)],[f_23_2]) ).
fof(f_23_4,plain,
( ! [U_41,U_40,U_39] :
( v1_funct_1(k7_relat_1(U_39,U_41))
| ~ sP4(U_41,U_40,U_39) )
& ! [U_41,U_40,U_39] :
( v1_relat_1(k7_relat_1(U_39,U_40))
| ~ sP4(U_41,U_40,U_39) )
& ! [U_41,U_40,U_39] :
( sP4(U_41,U_40,U_39)
| ~ v1_funct_1(U_39)
| ~ v1_relat_1(U_39) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_23_3]) ).
cnf(f_23_5,plain,
( sP4(U_41,U_40,U_39)
| ~ v1_funct_1(U_39)
| ~ v1_relat_1(U_39) ),
inference(clausify,[status(thm)],[f_23_4]) ).
cnf(f_23_6,plain,
( v1_relat_1(k7_relat_1(U_39,U_40))
| ~ sP4(U_41,U_40,U_39) ),
inference(clausify,[status(thm)],[f_23_4]) ).
cnf(f_23_7,plain,
( v1_funct_1(k7_relat_1(U_39,U_41))
| ~ sP4(U_41,U_40,U_39) ),
inference(clausify,[status(thm)],[f_23_4]) ).
fof(f_24_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_24_2,plain,
! [U_43,U_42] :
( ~ v1_xboole_0(k2_zfmisc_1(U_43,U_42))
| v1_xboole_0(U_42)
| v1_xboole_0(U_43) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_43,U_42] :
( ~ v1_xboole_0(k2_zfmisc_1(U_43,U_42))
| v1_xboole_0(U_42)
| v1_xboole_0(U_43) ),
inference(definitional_conversion,[status(esa)],[f_24_2]) ).
cnf(f_24_4,plain,
( ~ v1_xboole_0(k2_zfmisc_1(U_43,U_42))
| v1_xboole_0(U_42)
| v1_xboole_0(U_43) ),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
? [A] :
( v1_funct_1(A)
& v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_25_2,plain,
? [U_44] :
( v1_funct_1(U_44)
& v1_relat_1(U_44) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( v1_funct_1(sK10)
& v1_relat_1(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_44,sK10)],[f_25_2]) ).
fof(f_25_4,plain,
( v1_funct_1(sK10)
& v1_relat_1(sK10) ),
inference(definitional_conversion,[status(esa)],[f_25_3]) ).
cnf(f_25_5,plain,
v1_relat_1(sK10),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_6,plain,
v1_funct_1(sK10),
inference(clausify,[status(thm)],[f_25_4]) ).
fof(f_26_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_26_2,plain,
! [U_46] :
( ? [U_45] :
( ~ v1_xboole_0(U_45)
& m1_subset_1(U_45,k1_zfmisc_1(U_46)) )
| v1_xboole_0(U_46) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_46] :
( ( ~ v1_xboole_0(sK11(U_46))
& m1_subset_1(sK11(U_46),k1_zfmisc_1(U_46)) )
| v1_xboole_0(U_46) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_45,sK11(U_46))],[f_26_2]) ).
fof(f_26_4,plain,
( ! [U_46] :
( ~ v1_xboole_0(sK11(U_46))
| ~ sP5(U_46) )
& ! [U_46] :
( m1_subset_1(sK11(U_46),k1_zfmisc_1(U_46))
| ~ sP5(U_46) )
& ! [U_46] :
( sP5(U_46)
| v1_xboole_0(U_46) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_26_3]) ).
cnf(f_26_5,plain,
( sP5(U_46)
| v1_xboole_0(U_46) ),
inference(clausify,[status(thm)],[f_26_4]) ).
cnf(f_26_6,plain,
( m1_subset_1(sK11(U_46),k1_zfmisc_1(U_46))
| ~ sP5(U_46) ),
inference(clausify,[status(thm)],[f_26_4]) ).
cnf(f_26_7,plain,
( ~ v1_xboole_0(sK11(U_46))
| ~ sP5(U_46) ),
inference(clausify,[status(thm)],[f_26_4]) ).
fof(f_27_1,plain,
? [A] : v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_27_2,plain,
? [U_47] : v1_xboole_0(U_47),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
v1_xboole_0(sK12),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_47,sK12)],[f_27_2]) ).
fof(f_27_4,plain,
v1_xboole_0(sK12),
inference(definitional_conversion,[status(esa)],[f_27_3]) ).
cnf(f_27_5,plain,
v1_xboole_0(sK12),
inference(clausify,[status(thm)],[f_27_4]) ).
fof(f_28_1,plain,
? [A] :
( v1_funct_1(A)
& v1_xboole_0(A)
& v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_28_2,plain,
? [U_48] :
( v1_funct_1(U_48)
& v1_xboole_0(U_48)
& v1_relat_1(U_48) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( v1_funct_1(sK13)
& v1_xboole_0(sK13)
& v1_relat_1(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_48,sK13)],[f_28_2]) ).
fof(f_28_4,plain,
( v1_funct_1(sK13)
& v1_xboole_0(sK13)
& v1_relat_1(sK13) ),
inference(definitional_conversion,[status(esa)],[f_28_3]) ).
cnf(f_28_5,plain,
v1_relat_1(sK13),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_6,plain,
v1_xboole_0(sK13),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_7,plain,
v1_funct_1(sK13),
inference(clausify,[status(thm)],[f_28_4]) ).
fof(f_29_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_29_2,plain,
! [U_50] :
? [U_49] :
( v1_xboole_0(U_49)
& m1_subset_1(U_49,k1_zfmisc_1(U_50)) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_50] :
( v1_xboole_0(sK14(U_50))
& m1_subset_1(sK14(U_50),k1_zfmisc_1(U_50)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_49,sK14(U_50))],[f_29_2]) ).
fof(f_29_4,plain,
( ! [U_50] : v1_xboole_0(sK14(U_50))
& ! [U_50] : m1_subset_1(sK14(U_50),k1_zfmisc_1(U_50)) ),
inference(definitional_conversion,[status(esa)],[f_29_3]) ).
cnf(f_29_5,plain,
m1_subset_1(sK14(U_50),k1_zfmisc_1(U_50)),
inference(clausify,[status(thm)],[f_29_4]) ).
cnf(f_29_6,plain,
v1_xboole_0(sK14(U_50)),
inference(clausify,[status(thm)],[f_29_4]) ).
fof(f_30_1,plain,
? [A] : ~ v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_30_2,plain,
? [U_51] : ~ v1_xboole_0(U_51),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
~ v1_xboole_0(sK15),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_51,sK15)],[f_30_2]) ).
fof(f_30_4,plain,
~ v1_xboole_0(sK15),
inference(definitional_conversion,[status(esa)],[f_30_3]) ).
cnf(f_30_5,plain,
~ v1_xboole_0(sK15),
inference(clausify,[status(thm)],[f_30_4]) ).
fof(f_31_1,plain,
? [A] :
( v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_31_2,plain,
? [U_52] :
( v2_funct_1(U_52)
& v1_funct_1(U_52)
& v1_relat_1(U_52) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( v2_funct_1(sK16)
& v1_funct_1(sK16)
& v1_relat_1(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_52,sK16)],[f_31_2]) ).
fof(f_31_4,plain,
( v2_funct_1(sK16)
& v1_funct_1(sK16)
& v1_relat_1(sK16) ),
inference(definitional_conversion,[status(esa)],[f_31_3]) ).
cnf(f_31_5,plain,
v1_relat_1(sK16),
inference(clausify,[status(thm)],[f_31_4]) ).
cnf(f_31_6,plain,
v1_funct_1(sK16),
inference(clausify,[status(thm)],[f_31_4]) ).
cnf(f_31_7,plain,
v2_funct_1(sK16),
inference(clausify,[status(thm)],[f_31_4]) ).
fof(f_32_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_32_2,plain,
! [U_55,U_54,U_53] :
( ( m2_relset_1(U_53,U_55,U_54)
| ~ m1_relset_1(U_53,U_55,U_54) )
& ( m1_relset_1(U_53,U_55,U_54)
| ~ m2_relset_1(U_53,U_55,U_54) ) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
( ! [U_61,U_59,U_57] :
( m2_relset_1(U_57,U_61,U_59)
| ~ m1_relset_1(U_57,U_61,U_59) )
& ! [U_60,U_58,U_56] :
( m1_relset_1(U_56,U_60,U_58)
| ~ m2_relset_1(U_56,U_60,U_58) ) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
fof(f_32_4,plain,
( ! [U_59,U_57,U_61] :
( m2_relset_1(U_57,U_61,U_59)
| ~ m1_relset_1(U_57,U_61,U_59) )
& ! [U_60,U_56,U_58] :
( m1_relset_1(U_56,U_60,U_58)
| ~ m2_relset_1(U_56,U_60,U_58) ) ),
inference(definitional_conversion,[status(esa)],[f_32_3]) ).
cnf(f_32_5,plain,
( m1_relset_1(U_56,U_60,U_58)
| ~ m2_relset_1(U_56,U_60,U_58) ),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_6,plain,
( m2_relset_1(U_57,U_61,U_59)
| ~ m1_relset_1(U_57,U_61,U_59) ),
inference(clausify,[status(thm)],[f_32_4]) ).
fof(f_33_1,plain,
! [A,B] : r1_tarski(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_33_2,plain,
! [U_63,U_62] : r1_tarski(U_63,U_63),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_63] : r1_tarski(U_63,U_63),
inference(miniscope,[status(thm)],[f_33_2]) ).
fof(f_33_4,plain,
! [U_63] : r1_tarski(U_63,U_63),
inference(definitional_conversion,[status(esa)],[f_33_3]) ).
cnf(f_33_5,plain,
r1_tarski(U_63,U_63),
inference(clausify,[status(thm)],[f_33_4]) ).
fof(f_34_1,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_34_2,plain,
! [U_65,U_64] :
( m1_subset_1(U_65,U_64)
| ~ r2_hidden(U_65,U_64) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_65,U_64] :
( m1_subset_1(U_65,U_64)
| ~ r2_hidden(U_65,U_64) ),
inference(definitional_conversion,[status(esa)],[f_34_2]) ).
cnf(f_34_4,plain,
( m1_subset_1(U_65,U_64)
| ~ r2_hidden(U_65,U_64) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_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_35_2,plain,
! [U_67,U_66] :
( r2_hidden(U_67,U_66)
| v1_xboole_0(U_66)
| ~ m1_subset_1(U_67,U_66) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_66,U_67] :
( r2_hidden(U_67,U_66)
| v1_xboole_0(U_66)
| ~ m1_subset_1(U_67,U_66) ),
inference(definitional_conversion,[status(esa)],[f_35_2]) ).
cnf(f_35_4,plain,
( r2_hidden(U_67,U_66)
| v1_xboole_0(U_66)
| ~ m1_subset_1(U_67,U_66) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( ! [F] :
( ( ( r5_binop_1(B,E,F)
| ~ r5_binop_1(A,C,D) )
& ( r4_binop_1(B,E,F)
| ~ r4_binop_1(A,C,D) ) )
| F != k1_realset1(D,B)
| E != k1_realset1(C,B)
| ~ m2_relset_1(F,k2_zfmisc_1(B,B),B)
| ~ v1_funct_2(F,k2_zfmisc_1(B,B),B)
| ~ v1_funct_1(F) )
| ~ m2_relset_1(E,k2_zfmisc_1(B,B),B)
| ~ v1_funct_2(E,k2_zfmisc_1(B,B),B)
| ~ v1_funct_1(E) )
| ~ m2_relset_1(D,k2_zfmisc_1(A,A),A)
| ~ v1_funct_2(D,k2_zfmisc_1(A,A),A)
| ~ v1_funct_1(D) )
| ~ m2_relset_1(C,k2_zfmisc_1(A,A),A)
| ~ v1_funct_2(C,k2_zfmisc_1(A,A),A)
| ~ v1_funct_1(C) )
| ~ m1_subset_1(B,k1_zfmisc_1(A))
| v1_xboole_0(B) )
| v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t3_filter_2]) ).
fof(f_36_2,plain,
! [U_73] :
( ! [U_72] :
( ! [U_71] :
( ! [U_70] :
( ! [U_69] :
( ! [U_68] :
( ( ( r5_binop_1(U_72,U_69,U_68)
| ~ r5_binop_1(U_73,U_71,U_70) )
& ( r4_binop_1(U_72,U_69,U_68)
| ~ r4_binop_1(U_73,U_71,U_70) ) )
| U_68 != k1_realset1(U_70,U_72)
| U_69 != k1_realset1(U_71,U_72)
| ~ m2_relset_1(U_68,k2_zfmisc_1(U_72,U_72),U_72)
| ~ v1_funct_2(U_68,k2_zfmisc_1(U_72,U_72),U_72)
| ~ v1_funct_1(U_68) )
| ~ m2_relset_1(U_69,k2_zfmisc_1(U_72,U_72),U_72)
| ~ v1_funct_2(U_69,k2_zfmisc_1(U_72,U_72),U_72)
| ~ v1_funct_1(U_69) )
| ~ m2_relset_1(U_70,k2_zfmisc_1(U_73,U_73),U_73)
| ~ v1_funct_2(U_70,k2_zfmisc_1(U_73,U_73),U_73)
| ~ v1_funct_1(U_70) )
| ~ m2_relset_1(U_71,k2_zfmisc_1(U_73,U_73),U_73)
| ~ v1_funct_2(U_71,k2_zfmisc_1(U_73,U_73),U_73)
| ~ v1_funct_1(U_71) )
| ~ m1_subset_1(U_72,k1_zfmisc_1(U_73))
| v1_xboole_0(U_72) )
| v1_xboole_0(U_73) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
( ! [U_69,U_70,U_68,U_71,U_72,U_73] :
( r5_binop_1(U_72,U_69,U_68)
| ~ r5_binop_1(U_73,U_71,U_70)
| ~ sP6(U_69,U_70,U_68,U_71,U_72,U_73) )
& ! [U_69,U_70,U_68,U_71,U_72,U_73] :
( r4_binop_1(U_72,U_69,U_68)
| ~ r4_binop_1(U_73,U_71,U_70)
| ~ sP6(U_69,U_70,U_68,U_71,U_72,U_73) )
& ! [U_69,U_70,U_68,U_71,U_72,U_73] :
( sP6(U_69,U_70,U_68,U_71,U_72,U_73)
| U_68 != k1_realset1(U_70,U_72)
| U_69 != k1_realset1(U_71,U_72)
| ~ m2_relset_1(U_68,k2_zfmisc_1(U_72,U_72),U_72)
| ~ v1_funct_2(U_68,k2_zfmisc_1(U_72,U_72),U_72)
| ~ v1_funct_1(U_68)
| ~ m2_relset_1(U_69,k2_zfmisc_1(U_72,U_72),U_72)
| ~ v1_funct_2(U_69,k2_zfmisc_1(U_72,U_72),U_72)
| ~ v1_funct_1(U_69)
| ~ m2_relset_1(U_70,k2_zfmisc_1(U_73,U_73),U_73)
| ~ v1_funct_2(U_70,k2_zfmisc_1(U_73,U_73),U_73)
| ~ v1_funct_1(U_70)
| ~ m2_relset_1(U_71,k2_zfmisc_1(U_73,U_73),U_73)
| ~ v1_funct_2(U_71,k2_zfmisc_1(U_73,U_73),U_73)
| ~ v1_funct_1(U_71)
| ~ m1_subset_1(U_72,k1_zfmisc_1(U_73))
| v1_xboole_0(U_72)
| v1_xboole_0(U_73) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_36_2]) ).
cnf(f_36_4,plain,
( sP6(U_69,U_70,U_68,U_71,U_72,U_73)
| U_68 != k1_realset1(U_70,U_72)
| U_69 != k1_realset1(U_71,U_72)
| ~ m2_relset_1(U_68,k2_zfmisc_1(U_72,U_72),U_72)
| ~ v1_funct_2(U_68,k2_zfmisc_1(U_72,U_72),U_72)
| ~ v1_funct_1(U_68)
| ~ m2_relset_1(U_69,k2_zfmisc_1(U_72,U_72),U_72)
| ~ v1_funct_2(U_69,k2_zfmisc_1(U_72,U_72),U_72)
| ~ v1_funct_1(U_69)
| ~ m2_relset_1(U_70,k2_zfmisc_1(U_73,U_73),U_73)
| ~ v1_funct_2(U_70,k2_zfmisc_1(U_73,U_73),U_73)
| ~ v1_funct_1(U_70)
| ~ m2_relset_1(U_71,k2_zfmisc_1(U_73,U_73),U_73)
| ~ v1_funct_2(U_71,k2_zfmisc_1(U_73,U_73),U_73)
| ~ v1_funct_1(U_71)
| ~ m1_subset_1(U_72,k1_zfmisc_1(U_73))
| v1_xboole_0(U_72)
| v1_xboole_0(U_73) ),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_5,plain,
( r4_binop_1(U_72,U_69,U_68)
| ~ r4_binop_1(U_73,U_71,U_70)
| ~ sP6(U_69,U_70,U_68,U_71,U_72,U_73) ),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_6,plain,
( r5_binop_1(U_72,U_69,U_68)
| ~ r5_binop_1(U_73,U_71,U_70)
| ~ sP6(U_69,U_70,U_68,U_71,U_72,U_73) ),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_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_37_2,plain,
! [U_75,U_74] :
( ( m1_subset_1(U_75,k1_zfmisc_1(U_74))
| ~ r1_tarski(U_75,U_74) )
& ( r1_tarski(U_75,U_74)
| ~ m1_subset_1(U_75,k1_zfmisc_1(U_74)) ) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
( ! [U_79,U_77] :
( m1_subset_1(U_79,k1_zfmisc_1(U_77))
| ~ r1_tarski(U_79,U_77) )
& ! [U_78,U_76] :
( r1_tarski(U_78,U_76)
| ~ m1_subset_1(U_78,k1_zfmisc_1(U_76)) ) ),
inference(miniscope,[status(thm)],[f_37_2]) ).
fof(f_37_4,plain,
( ! [U_77,U_79] :
( m1_subset_1(U_79,k1_zfmisc_1(U_77))
| ~ r1_tarski(U_79,U_77) )
& ! [U_76,U_78] :
( r1_tarski(U_78,U_76)
| ~ m1_subset_1(U_78,k1_zfmisc_1(U_76)) ) ),
inference(definitional_conversion,[status(esa)],[f_37_3]) ).
cnf(f_37_5,plain,
( r1_tarski(U_78,U_76)
| ~ m1_subset_1(U_78,k1_zfmisc_1(U_76)) ),
inference(clausify,[status(thm)],[f_37_4]) ).
cnf(f_37_6,plain,
( m1_subset_1(U_79,k1_zfmisc_1(U_77))
| ~ r1_tarski(U_79,U_77) ),
inference(clausify,[status(thm)],[f_37_4]) ).
fof(f_38_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_38_2,plain,
! [U_82,U_81,U_80] :
( m1_subset_1(U_82,U_80)
| ~ m1_subset_1(U_81,k1_zfmisc_1(U_80))
| ~ r2_hidden(U_82,U_81) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_82,U_80,U_81] :
( m1_subset_1(U_82,U_80)
| ~ m1_subset_1(U_81,k1_zfmisc_1(U_80))
| ~ r2_hidden(U_82,U_81) ),
inference(definitional_conversion,[status(esa)],[f_38_2]) ).
cnf(f_38_4,plain,
( m1_subset_1(U_82,U_80)
| ~ m1_subset_1(U_81,k1_zfmisc_1(U_80))
| ~ r2_hidden(U_82,U_81) ),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_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_39_2,plain,
! [U_85,U_84,U_83] :
( ~ v1_xboole_0(U_83)
| ~ m1_subset_1(U_84,k1_zfmisc_1(U_83))
| ~ r2_hidden(U_85,U_84) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_85,U_84] :
( ! [U_83] :
( ~ v1_xboole_0(U_83)
| ~ m1_subset_1(U_84,k1_zfmisc_1(U_83)) )
| ~ r2_hidden(U_85,U_84) ),
inference(miniscope,[status(thm)],[f_39_2]) ).
fof(f_39_4,plain,
! [U_84,U_83,U_85] :
( ~ v1_xboole_0(U_83)
| ~ m1_subset_1(U_84,k1_zfmisc_1(U_83))
| ~ r2_hidden(U_85,U_84) ),
inference(definitional_conversion,[status(esa)],[f_39_3]) ).
cnf(f_39_5,plain,
( ~ v1_xboole_0(U_83)
| ~ m1_subset_1(U_84,k1_zfmisc_1(U_83))
| ~ r2_hidden(U_85,U_84) ),
inference(clausify,[status(thm)],[f_39_4]) ).
fof(f_40_1,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_40_2,plain,
! [U_86] :
( U_86 = k1_xboole_0
| ~ v1_xboole_0(U_86) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_86] :
( U_86 = k1_xboole_0
| ~ v1_xboole_0(U_86) ),
inference(definitional_conversion,[status(esa)],[f_40_2]) ).
cnf(f_40_4,plain,
( U_86 = k1_xboole_0
| ~ v1_xboole_0(U_86) ),
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_41_2,plain,
! [U_88,U_87] :
( ~ v1_xboole_0(U_87)
| ~ r2_hidden(U_88,U_87) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_88,U_87] :
( ~ v1_xboole_0(U_87)
| ~ r2_hidden(U_88,U_87) ),
inference(definitional_conversion,[status(esa)],[f_41_2]) ).
cnf(f_41_4,plain,
( ~ v1_xboole_0(U_87)
| ~ r2_hidden(U_88,U_87) ),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| A = B
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_42_2,plain,
! [U_90,U_89] :
( ~ v1_xboole_0(U_89)
| U_90 = U_89
| ~ v1_xboole_0(U_90) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_90] :
( ! [U_89] :
( ~ v1_xboole_0(U_89)
| U_90 = U_89 )
| ~ v1_xboole_0(U_90) ),
inference(miniscope,[status(thm)],[f_42_2]) ).
fof(f_42_4,plain,
! [U_90,U_89] :
( ~ v1_xboole_0(U_89)
| U_90 = U_89
| ~ v1_xboole_0(U_90) ),
inference(definitional_conversion,[status(esa)],[f_42_3]) ).
cnf(f_42_5,plain,
( ~ v1_xboole_0(U_89)
| U_90 = U_89
| ~ v1_xboole_0(U_90) ),
inference(clausify,[status(thm)],[f_42_4]) ).
cnf(f_8_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_3]) ).
cnf(f_9_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_3]) ).
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_13_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_13_3]) ).
cnf(f_14_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_14_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,
( k1_zfmisc_1(Eq_x_0) = k1_zfmisc_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,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_6,axiom,
( k1_realset1(Eq_x_0,Eq_x_1) = k1_realset1(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,
( k7_relat_1(Eq_x_0,Eq_x_1) = k7_relat_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_8,axiom,
( sK7(Eq_x_0,Eq_x_1) = sK7(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| 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,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_11,axiom,
( sK11(Eq_x_0) = sK11(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK14(Eq_x_0) = sK14(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,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_14,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_15,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_16,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_17,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_18,axiom,
( r6_binop_1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ r6_binop_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_19,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_20,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_21,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_22,axiom,
( r4_binop_1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ r4_binop_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_23,axiom,
( r5_binop_1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ r5_binop_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_24,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_25,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_26,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,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_28,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_29,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_30,axiom,
( sP4(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP4(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,
( sP5(Eq_y_0)
| ~ sP5(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( sP6(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP6(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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT294+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 19 13:13:39 UTC 2026
% 0.11/0.37 % CPUTime :
% 48.36/48.63 % SZS status Theorem for theBenchmark
% 48.36/48.63 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------