%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU411+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 08:59:14 AM UTC 2026
% Result : Theorem 274.17s 274.47s
% Output : Proof 275.28s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(t20_latsum_1,conjecture,
! [A] :
( ( l1_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v4_orders_2(A)
& v3_orders_2(A)
& v2_orders_2(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_orders_2(B)
& v1_lattice3(B)
& v1_yellow_0(B)
& v4_orders_2(B)
& v3_orders_2(B)
& v2_orders_2(B)
& ~ v3_struct_0(B) )
=> ( ( m1_subset_1(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B)
& v1_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B)
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B))) )
=> r2_hidden(k3_yellow_0(B),u1_struct_0(A)) ) ) ),
file('theBenchmark.p',t20_latsum_1) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( r2_hidden(A,B)
=> ~ r2_hidden(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d19_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v12_waybel_0(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r1_orders_2(A,D,C)
& r2_hidden(C,B) )
=> r2_hidden(D,B) ) ) ) ) ) ),
file('theBenchmark.p',d19_waybel_0) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = k1_xboole_0
<=> ! [B] : ~ r2_hidden(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
fof(d3_xboole_0,axiom,
! [A,B,C] :
( C = k3_xboole_0(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ( r2_hidden(D,B)
& r2_hidden(D,A) ) ) ),
file('theBenchmark.p',d3_xboole_0) ).
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_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k3_xboole_0) ).
fof(dt_k3_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> m1_subset_1(k3_yellow_0(A),u1_struct_0(A)) ),
file('theBenchmark.p',dt_k3_yellow_0) ).
fof(dt_l1_orders_2,axiom,
! [A] :
( l1_orders_2(A)
=> l1_struct_0(A) ),
file('theBenchmark.p',dt_l1_orders_2) ).
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_orders_2,axiom,
? [A] : l1_orders_2(A),
file('theBenchmark.p',existence_l1_orders_2) ).
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_xboole_0,axiom,
v1_xboole_0(k1_xboole_0),
file('theBenchmark.p',fc1_xboole_0) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : k3_xboole_0(A,A) = A,
file('theBenchmark.p',idempotence_k3_xboole_0) ).
fof(rc1_xboole_0,axiom,
? [A] : v1_xboole_0(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ v1_xboole_0(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(rc3_struct_0,axiom,
? [A] :
( ~ v3_struct_0(A)
& l1_struct_0(A) ),
file('theBenchmark.p',rc3_struct_0) ).
fof(rc5_struct_0,axiom,
! [A] :
( ( l1_struct_0(A)
& ~ v3_struct_0(A) )
=> ? [B] :
( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ),
file('theBenchmark.p',rc5_struct_0) ).
fof(rc9_waybel_0,axiom,
! [A] :
( ( l1_orders_2(A)
& v3_orders_2(A)
& v2_orders_2(A)
& ~ v3_struct_0(A) )
=> ? [B] :
( v12_waybel_0(B,A)
& v1_waybel_0(B,A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ),
file('theBenchmark.p',rc9_waybel_0) ).
fof(redefinition_r3_orders_2,axiom,
! [A,B,C] :
( ( m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(B,u1_struct_0(A))
& l1_orders_2(A)
& v2_orders_2(A)
& ~ v3_struct_0(A) )
=> ( r3_orders_2(A,B,C)
<=> r1_orders_2(A,B,C) ) ),
file('theBenchmark.p',redefinition_r3_orders_2) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : r1_tarski(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(reflexivity_r3_orders_2,axiom,
! [A,B,C] :
( ( m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(B,u1_struct_0(A))
& l1_orders_2(A)
& v2_orders_2(A)
& ~ v3_struct_0(A) )
=> r3_orders_2(A,B,B) ),
file('theBenchmark.p',reflexivity_r3_orders_2) ).
fof(t13_latsum_1,axiom,
! [A] :
( ( l1_orders_2(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_orders_2(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( r2_hidden(C,k3_xboole_0(u1_struct_0(A),u1_struct_0(B)))
=> m1_subset_1(C,u1_struct_0(B)) ) ) ),
file('theBenchmark.p',t13_latsum_1) ).
fof(t1_subset,axiom,
! [A,B] :
( r2_hidden(A,B)
=> m1_subset_1(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t2_boole,axiom,
! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0,
file('theBenchmark.p',t2_boole) ).
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(t44_yellow_0,axiom,
! [A] :
( ( l1_orders_2(A)
& v1_yellow_0(A)
& v4_orders_2(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r1_orders_2(A,k3_yellow_0(A),B) ) ),
file('theBenchmark.p',t44_yellow_0) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_zfmisc_1(C))
& r2_hidden(A,B) )
=> m1_subset_1(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( v1_xboole_0(C)
& m1_subset_1(B,k1_zfmisc_1(C))
& r2_hidden(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t6_boole,axiom,
! [A] :
( v1_xboole_0(A)
=> A = k1_xboole_0 ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(B)
& r2_hidden(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(B)
& A != B
& v1_xboole_0(A) ),
file('theBenchmark.p',t8_boole) ).
fof(f_1_1,negated_conjecture,
~ ! [A] :
( ( l1_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v4_orders_2(A)
& v3_orders_2(A)
& v2_orders_2(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_orders_2(B)
& v1_lattice3(B)
& v1_yellow_0(B)
& v4_orders_2(B)
& v3_orders_2(B)
& v2_orders_2(B)
& ~ v3_struct_0(B) )
=> ( ( m1_subset_1(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B)
& v1_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B)
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B))) )
=> r2_hidden(k3_yellow_0(B),u1_struct_0(A)) ) ) ),
inference(negate,[status(cth)],[t20_latsum_1]) ).
fof(f_1_2,negated_conjecture,
? [A] :
( ? [B] :
( ~ r2_hidden(k3_yellow_0(B),u1_struct_0(A))
& m1_subset_1(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B)
& v1_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B)
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)))
& l1_orders_2(B)
& v1_lattice3(B)
& v1_yellow_0(B)
& v4_orders_2(B)
& v3_orders_2(B)
& v2_orders_2(B)
& ~ v3_struct_0(B) )
& l1_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v4_orders_2(A)
& v3_orders_2(A)
& v2_orders_2(A)
& ~ v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
? [U_1] :
( ? [U_0] :
( ~ r2_hidden(k3_yellow_0(U_0),u1_struct_0(U_1))
& m1_subset_1(k3_xboole_0(u1_struct_0(U_1),u1_struct_0(U_0)),k1_zfmisc_1(u1_struct_0(U_0)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(U_1),u1_struct_0(U_0)),U_0)
& v1_waybel_0(k3_xboole_0(u1_struct_0(U_1),u1_struct_0(U_0)),U_0)
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(U_1),u1_struct_0(U_0)))
& l1_orders_2(U_0)
& v1_lattice3(U_0)
& v1_yellow_0(U_0)
& v4_orders_2(U_0)
& v3_orders_2(U_0)
& v2_orders_2(U_0)
& ~ v3_struct_0(U_0) )
& l1_orders_2(U_1)
& v1_lattice3(U_1)
& v1_yellow_0(U_1)
& v4_orders_2(U_1)
& v3_orders_2(U_1)
& v2_orders_2(U_1)
& ~ v3_struct_0(U_1) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
( ? [U_0] :
( ~ r2_hidden(k3_yellow_0(U_0),u1_struct_0(sK1))
& m1_subset_1(k3_xboole_0(u1_struct_0(sK1),u1_struct_0(U_0)),k1_zfmisc_1(u1_struct_0(U_0)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(sK1),u1_struct_0(U_0)),U_0)
& v1_waybel_0(k3_xboole_0(u1_struct_0(sK1),u1_struct_0(U_0)),U_0)
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(sK1),u1_struct_0(U_0)))
& l1_orders_2(U_0)
& v1_lattice3(U_0)
& v1_yellow_0(U_0)
& v4_orders_2(U_0)
& v3_orders_2(U_0)
& v2_orders_2(U_0)
& ~ v3_struct_0(U_0) )
& l1_orders_2(sK1)
& v1_lattice3(sK1)
& v1_yellow_0(sK1)
& v4_orders_2(sK1)
& v3_orders_2(sK1)
& v2_orders_2(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,
( ~ r2_hidden(k3_yellow_0(sK2),u1_struct_0(sK1))
& m1_subset_1(k3_xboole_0(u1_struct_0(sK1),u1_struct_0(sK2)),k1_zfmisc_1(u1_struct_0(sK2)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(sK1),u1_struct_0(sK2)),sK2)
& v1_waybel_0(k3_xboole_0(u1_struct_0(sK1),u1_struct_0(sK2)),sK2)
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(sK1),u1_struct_0(sK2)))
& l1_orders_2(sK2)
& v1_lattice3(sK2)
& v1_yellow_0(sK2)
& v4_orders_2(sK2)
& v3_orders_2(sK2)
& v2_orders_2(sK2)
& ~ v3_struct_0(sK2)
& l1_orders_2(sK1)
& v1_lattice3(sK1)
& v1_yellow_0(sK1)
& v4_orders_2(sK1)
& v3_orders_2(sK1)
& v2_orders_2(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,
( ~ r2_hidden(k3_yellow_0(sK2),u1_struct_0(sK1))
& m1_subset_1(k3_xboole_0(u1_struct_0(sK1),u1_struct_0(sK2)),k1_zfmisc_1(u1_struct_0(sK2)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(sK1),u1_struct_0(sK2)),sK2)
& v1_waybel_0(k3_xboole_0(u1_struct_0(sK1),u1_struct_0(sK2)),sK2)
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(sK1),u1_struct_0(sK2)))
& l1_orders_2(sK2)
& v1_lattice3(sK2)
& v1_yellow_0(sK2)
& v4_orders_2(sK2)
& v3_orders_2(sK2)
& v2_orders_2(sK2)
& ~ v3_struct_0(sK2)
& l1_orders_2(sK1)
& v1_lattice3(sK1)
& v1_yellow_0(sK1)
& v4_orders_2(sK1)
& v3_orders_2(sK1)
& v2_orders_2(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_orders_2(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_9,negated_conjecture,
v3_orders_2(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_10,negated_conjecture,
v4_orders_2(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_11,negated_conjecture,
v1_yellow_0(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_12,negated_conjecture,
v1_lattice3(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_13,negated_conjecture,
l1_orders_2(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_14,negated_conjecture,
~ v3_struct_0(sK2),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_15,negated_conjecture,
v2_orders_2(sK2),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_16,negated_conjecture,
v3_orders_2(sK2),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_17,negated_conjecture,
v4_orders_2(sK2),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_18,negated_conjecture,
v1_yellow_0(sK2),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_19,negated_conjecture,
v1_lattice3(sK2),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_20,negated_conjecture,
l1_orders_2(sK2),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_21,negated_conjecture,
~ v1_xboole_0(k3_xboole_0(u1_struct_0(sK1),u1_struct_0(sK2))),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_22,negated_conjecture,
v1_waybel_0(k3_xboole_0(u1_struct_0(sK1),u1_struct_0(sK2)),sK2),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_23,negated_conjecture,
v12_waybel_0(k3_xboole_0(u1_struct_0(sK1),u1_struct_0(sK2)),sK2),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_24,negated_conjecture,
m1_subset_1(k3_xboole_0(u1_struct_0(sK1),u1_struct_0(sK2)),k1_zfmisc_1(u1_struct_0(sK2))),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_25,negated_conjecture,
~ r2_hidden(k3_yellow_0(sK2),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_2,U_3] :
( ~ 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] : k3_xboole_0(A,B) = k3_xboole_0(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_3_2,plain,
! [U_5,U_4] : k3_xboole_0(U_5,U_4) = k3_xboole_0(U_4,U_5),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_5,U_4] : k3_xboole_0(U_5,U_4) = k3_xboole_0(U_4,U_5),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
k3_xboole_0(U_5,U_4) = k3_xboole_0(U_4,U_5),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [A] :
( ! [B] :
( ( ( v12_waybel_0(B,A)
| ? [C] :
( ? [D] :
( ~ r2_hidden(D,B)
& r1_orders_2(A,D,C)
& r2_hidden(C,B)
& m1_subset_1(D,u1_struct_0(A)) )
& m1_subset_1(C,u1_struct_0(A)) ) )
& ( ! [C] :
( ! [D] :
( r2_hidden(D,B)
| ~ r1_orders_2(A,D,C)
| ~ r2_hidden(C,B)
| ~ m1_subset_1(D,u1_struct_0(A)) )
| ~ m1_subset_1(C,u1_struct_0(A)) )
| ~ v12_waybel_0(B,A) ) )
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l1_orders_2(A) ),
inference(fof_nnf,[status(thm)],[d19_waybel_0]) ).
fof(f_4_2,plain,
! [U_11] :
( ! [U_10] :
( ( ( v12_waybel_0(U_10,U_11)
| ? [U_9] :
( ? [U_8] :
( ~ r2_hidden(U_8,U_10)
& r1_orders_2(U_11,U_8,U_9)
& r2_hidden(U_9,U_10)
& m1_subset_1(U_8,u1_struct_0(U_11)) )
& m1_subset_1(U_9,u1_struct_0(U_11)) ) )
& ( ! [U_7] :
( ! [U_6] :
( r2_hidden(U_6,U_10)
| ~ r1_orders_2(U_11,U_6,U_7)
| ~ r2_hidden(U_7,U_10)
| ~ m1_subset_1(U_6,u1_struct_0(U_11)) )
| ~ m1_subset_1(U_7,u1_struct_0(U_11)) )
| ~ v12_waybel_0(U_10,U_11) ) )
| ~ m1_subset_1(U_10,k1_zfmisc_1(u1_struct_0(U_11))) )
| ~ l1_orders_2(U_11) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_11] :
( ! [U_10] :
( ( ( v12_waybel_0(U_10,U_11)
| ( ? [U_8] :
( ~ r2_hidden(U_8,U_10)
& r1_orders_2(U_11,U_8,sK3(U_11,U_10))
& r2_hidden(sK3(U_11,U_10),U_10)
& m1_subset_1(U_8,u1_struct_0(U_11)) )
& m1_subset_1(sK3(U_11,U_10),u1_struct_0(U_11)) ) )
& ( ! [U_7] :
( ! [U_6] :
( r2_hidden(U_6,U_10)
| ~ r1_orders_2(U_11,U_6,U_7)
| ~ r2_hidden(U_7,U_10)
| ~ m1_subset_1(U_6,u1_struct_0(U_11)) )
| ~ m1_subset_1(U_7,u1_struct_0(U_11)) )
| ~ v12_waybel_0(U_10,U_11) ) )
| ~ m1_subset_1(U_10,k1_zfmisc_1(u1_struct_0(U_11))) )
| ~ l1_orders_2(U_11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_9,sK3(U_11,U_10))],[f_4_2]) ).
fof(f_4_4,plain,
! [U_11] :
( ! [U_10] :
( ( ( v12_waybel_0(U_10,U_11)
| ( ~ r2_hidden(sK4(U_11,U_10),U_10)
& r1_orders_2(U_11,sK4(U_11,U_10),sK3(U_11,U_10))
& r2_hidden(sK3(U_11,U_10),U_10)
& m1_subset_1(sK4(U_11,U_10),u1_struct_0(U_11))
& m1_subset_1(sK3(U_11,U_10),u1_struct_0(U_11)) ) )
& ( ! [U_7] :
( ! [U_6] :
( r2_hidden(U_6,U_10)
| ~ r1_orders_2(U_11,U_6,U_7)
| ~ r2_hidden(U_7,U_10)
| ~ m1_subset_1(U_6,u1_struct_0(U_11)) )
| ~ m1_subset_1(U_7,u1_struct_0(U_11)) )
| ~ v12_waybel_0(U_10,U_11) ) )
| ~ m1_subset_1(U_10,k1_zfmisc_1(u1_struct_0(U_11))) )
| ~ l1_orders_2(U_11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_8,sK4(U_11,U_10))],[f_4_3]) ).
fof(f_4_5,plain,
( ! [U_10,U_11] :
( ~ r2_hidden(sK4(U_11,U_10),U_10)
| ~ sP0(U_10,U_11) )
& ! [U_10,U_11] :
( r1_orders_2(U_11,sK4(U_11,U_10),sK3(U_11,U_10))
| ~ sP0(U_10,U_11) )
& ! [U_10,U_11] :
( r2_hidden(sK3(U_11,U_10),U_10)
| ~ sP0(U_10,U_11) )
& ! [U_10,U_11] :
( m1_subset_1(sK4(U_11,U_10),u1_struct_0(U_11))
| ~ sP0(U_10,U_11) )
& ! [U_10,U_11] :
( m1_subset_1(sK3(U_11,U_10),u1_struct_0(U_11))
| ~ sP0(U_10,U_11) )
& ! [U_10,U_11,U_7,U_6] :
( v12_waybel_0(U_10,U_11)
| sP0(U_10,U_11)
| ~ sP1(U_10,U_11,U_7,U_6) )
& ! [U_10,U_11,U_7,U_6] :
( r2_hidden(U_6,U_10)
| ~ r1_orders_2(U_11,U_6,U_7)
| ~ r2_hidden(U_7,U_10)
| ~ m1_subset_1(U_6,u1_struct_0(U_11))
| ~ m1_subset_1(U_7,u1_struct_0(U_11))
| ~ v12_waybel_0(U_10,U_11)
| ~ sP1(U_10,U_11,U_7,U_6) )
& ! [U_10,U_11,U_7,U_6] :
( sP1(U_10,U_11,U_7,U_6)
| ~ m1_subset_1(U_10,k1_zfmisc_1(u1_struct_0(U_11)))
| ~ l1_orders_2(U_11) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_4_4]) ).
cnf(f_4_6,plain,
( sP1(U_10,U_11,U_7,U_6)
| ~ m1_subset_1(U_10,k1_zfmisc_1(u1_struct_0(U_11)))
| ~ l1_orders_2(U_11) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_7,plain,
( r2_hidden(U_6,U_10)
| ~ r1_orders_2(U_11,U_6,U_7)
| ~ r2_hidden(U_7,U_10)
| ~ m1_subset_1(U_6,u1_struct_0(U_11))
| ~ m1_subset_1(U_7,u1_struct_0(U_11))
| ~ v12_waybel_0(U_10,U_11)
| ~ sP1(U_10,U_11,U_7,U_6) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_8,plain,
( v12_waybel_0(U_10,U_11)
| sP0(U_10,U_11)
| ~ sP1(U_10,U_11,U_7,U_6) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_9,plain,
( m1_subset_1(sK3(U_11,U_10),u1_struct_0(U_11))
| ~ sP0(U_10,U_11) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_10,plain,
( m1_subset_1(sK4(U_11,U_10),u1_struct_0(U_11))
| ~ sP0(U_10,U_11) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_11,plain,
( r2_hidden(sK3(U_11,U_10),U_10)
| ~ sP0(U_10,U_11) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_12,plain,
( r1_orders_2(U_11,sK4(U_11,U_10),sK3(U_11,U_10))
| ~ sP0(U_10,U_11) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_13,plain,
( ~ r2_hidden(sK4(U_11,U_10),U_10)
| ~ sP0(U_10,U_11) ),
inference(clausify,[status(thm)],[f_4_5]) ).
fof(f_5_1,plain,
! [A] :
( ( A = k1_xboole_0
| ? [B] : r2_hidden(B,A) )
& ( ! [B] : ~ r2_hidden(B,A)
| A != k1_xboole_0 ) ),
inference(fof_nnf,[status(thm)],[d1_xboole_0]) ).
fof(f_5_2,plain,
! [U_14] :
( ( U_14 = k1_xboole_0
| ? [U_13] : r2_hidden(U_13,U_14) )
& ( ! [U_12] : ~ r2_hidden(U_12,U_14)
| U_14 != k1_xboole_0 ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_16] :
( U_16 = k1_xboole_0
| ? [U_13] : r2_hidden(U_13,U_16) )
& ! [U_15] :
( ! [U_12] : ~ r2_hidden(U_12,U_15)
| U_15 != k1_xboole_0 ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_16] :
( U_16 = k1_xboole_0
| r2_hidden(sK5(U_16),U_16) )
& ! [U_15] :
( ! [U_12] : ~ r2_hidden(U_12,U_15)
| U_15 != k1_xboole_0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_13,sK5(U_16))],[f_5_3]) ).
fof(f_5_5,plain,
( ! [U_16] :
( U_16 = k1_xboole_0
| r2_hidden(sK5(U_16),U_16) )
& ! [U_15,U_12] :
( ~ r2_hidden(U_12,U_15)
| U_15 != k1_xboole_0 ) ),
inference(definitional_conversion,[status(esa)],[f_5_4]) ).
cnf(f_5_6,plain,
( ~ r2_hidden(U_12,U_15)
| U_15 != k1_xboole_0 ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_7,plain,
( U_16 = k1_xboole_0
| r2_hidden(sK5(U_16),U_16) ),
inference(clausify,[status(thm)],[f_5_5]) ).
fof(f_6_1,plain,
! [A,B,C] :
( ( C = k3_xboole_0(A,B)
| ? [D] :
( ( ~ r2_hidden(D,C)
& r2_hidden(D,B)
& r2_hidden(D,A) )
| ( ( ~ r2_hidden(D,B)
| ~ r2_hidden(D,A) )
& r2_hidden(D,C) ) ) )
& ( ! [D] :
( ( r2_hidden(D,C)
| ~ r2_hidden(D,B)
| ~ r2_hidden(D,A) )
& ( ( r2_hidden(D,B)
& r2_hidden(D,A) )
| ~ r2_hidden(D,C) ) )
| C != k3_xboole_0(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_xboole_0]) ).
fof(f_6_2,plain,
! [U_21,U_20,U_19] :
( ( U_19 = k3_xboole_0(U_21,U_20)
| ? [U_18] :
( ( ~ r2_hidden(U_18,U_19)
& r2_hidden(U_18,U_20)
& r2_hidden(U_18,U_21) )
| ( ( ~ r2_hidden(U_18,U_20)
| ~ r2_hidden(U_18,U_21) )
& r2_hidden(U_18,U_19) ) ) )
& ( ! [U_17] :
( ( r2_hidden(U_17,U_19)
| ~ r2_hidden(U_17,U_20)
| ~ r2_hidden(U_17,U_21) )
& ( ( r2_hidden(U_17,U_20)
& r2_hidden(U_17,U_21) )
| ~ r2_hidden(U_17,U_19) ) )
| U_19 != k3_xboole_0(U_21,U_20) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_31,U_29,U_27] :
( U_27 = k3_xboole_0(U_31,U_29)
| ? [U_25] :
( ~ r2_hidden(U_25,U_27)
& r2_hidden(U_25,U_29)
& r2_hidden(U_25,U_31) )
| ? [U_24] :
( ( ~ r2_hidden(U_24,U_29)
| ~ r2_hidden(U_24,U_31) )
& r2_hidden(U_24,U_27) ) )
& ! [U_30,U_28,U_26] :
( ( ! [U_23] :
( r2_hidden(U_23,U_26)
| ~ r2_hidden(U_23,U_28)
| ~ r2_hidden(U_23,U_30) )
& ! [U_22] :
( ( r2_hidden(U_22,U_28)
& r2_hidden(U_22,U_30) )
| ~ r2_hidden(U_22,U_26) ) )
| U_26 != k3_xboole_0(U_30,U_28) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_31,U_29,U_27] :
( U_27 = k3_xboole_0(U_31,U_29)
| ? [U_25] :
( ~ r2_hidden(U_25,U_27)
& r2_hidden(U_25,U_29)
& r2_hidden(U_25,U_31) )
| ( ( ~ r2_hidden(sK6(U_31,U_29,U_27),U_29)
| ~ r2_hidden(sK6(U_31,U_29,U_27),U_31) )
& r2_hidden(sK6(U_31,U_29,U_27),U_27) ) )
& ! [U_30,U_28,U_26] :
( ( ! [U_23] :
( r2_hidden(U_23,U_26)
| ~ r2_hidden(U_23,U_28)
| ~ r2_hidden(U_23,U_30) )
& ! [U_22] :
( ( r2_hidden(U_22,U_28)
& r2_hidden(U_22,U_30) )
| ~ r2_hidden(U_22,U_26) ) )
| U_26 != k3_xboole_0(U_30,U_28) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_24,sK6(U_31,U_29,U_27))],[f_6_3]) ).
fof(f_6_5,plain,
( ! [U_31,U_29,U_27] :
( U_27 = k3_xboole_0(U_31,U_29)
| ( ~ r2_hidden(sK7(U_31,U_29,U_27),U_27)
& r2_hidden(sK7(U_31,U_29,U_27),U_29)
& r2_hidden(sK7(U_31,U_29,U_27),U_31) )
| ( ( ~ r2_hidden(sK6(U_31,U_29,U_27),U_29)
| ~ r2_hidden(sK6(U_31,U_29,U_27),U_31) )
& r2_hidden(sK6(U_31,U_29,U_27),U_27) ) )
& ! [U_30,U_28,U_26] :
( ( ! [U_23] :
( r2_hidden(U_23,U_26)
| ~ r2_hidden(U_23,U_28)
| ~ r2_hidden(U_23,U_30) )
& ! [U_22] :
( ( r2_hidden(U_22,U_28)
& r2_hidden(U_22,U_30) )
| ~ r2_hidden(U_22,U_26) ) )
| U_26 != k3_xboole_0(U_30,U_28) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_25,sK7(U_31,U_29,U_27))],[f_6_4]) ).
fof(f_6_6,plain,
( ! [U_31,U_27,U_29] :
( ~ r2_hidden(sK7(U_31,U_29,U_27),U_27)
| ~ sP5(U_31,U_27,U_29) )
& ! [U_31,U_27,U_29] :
( r2_hidden(sK7(U_31,U_29,U_27),U_29)
| ~ sP5(U_31,U_27,U_29) )
& ! [U_31,U_27,U_29] :
( r2_hidden(sK7(U_31,U_29,U_27),U_31)
| ~ sP5(U_31,U_27,U_29) )
& ! [U_31,U_27,U_29] :
( ~ r2_hidden(sK6(U_31,U_29,U_27),U_29)
| ~ r2_hidden(sK6(U_31,U_29,U_27),U_31)
| ~ sP4(U_31,U_27,U_29) )
& ! [U_31,U_27,U_29] :
( r2_hidden(sK6(U_31,U_29,U_27),U_27)
| ~ sP4(U_31,U_27,U_29) )
& ! [U_22,U_28,U_30] :
( r2_hidden(U_22,U_28)
| ~ sP2(U_22,U_28,U_30) )
& ! [U_22,U_28,U_30] :
( r2_hidden(U_22,U_30)
| ~ sP2(U_22,U_28,U_30) )
& ! [U_22,U_23,U_26,U_28,U_30] :
( r2_hidden(U_23,U_26)
| ~ r2_hidden(U_23,U_28)
| ~ r2_hidden(U_23,U_30)
| ~ sP3(U_22,U_23,U_26,U_28,U_30) )
& ! [U_22,U_23,U_26,U_28,U_30] :
( sP2(U_22,U_28,U_30)
| ~ r2_hidden(U_22,U_26)
| ~ sP3(U_22,U_23,U_26,U_28,U_30) )
& ! [U_31,U_27,U_29] :
( U_27 = k3_xboole_0(U_31,U_29)
| sP5(U_31,U_27,U_29)
| sP4(U_31,U_27,U_29) )
& ! [U_22,U_23,U_26,U_28,U_30] :
( sP3(U_22,U_23,U_26,U_28,U_30)
| U_26 != k3_xboole_0(U_30,U_28) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2,sP3,sP4,sP5])],[f_6_5]) ).
cnf(f_6_7,plain,
( sP3(U_22,U_23,U_26,U_28,U_30)
| U_26 != k3_xboole_0(U_30,U_28) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_8,plain,
( U_27 = k3_xboole_0(U_31,U_29)
| sP5(U_31,U_27,U_29)
| sP4(U_31,U_27,U_29) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_9,plain,
( sP2(U_22,U_28,U_30)
| ~ r2_hidden(U_22,U_26)
| ~ sP3(U_22,U_23,U_26,U_28,U_30) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_10,plain,
( r2_hidden(U_23,U_26)
| ~ r2_hidden(U_23,U_28)
| ~ r2_hidden(U_23,U_30)
| ~ sP3(U_22,U_23,U_26,U_28,U_30) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_11,plain,
( r2_hidden(U_22,U_30)
| ~ sP2(U_22,U_28,U_30) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_12,plain,
( r2_hidden(U_22,U_28)
| ~ sP2(U_22,U_28,U_30) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_13,plain,
( r2_hidden(sK6(U_31,U_29,U_27),U_27)
| ~ sP4(U_31,U_27,U_29) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_14,plain,
( ~ r2_hidden(sK6(U_31,U_29,U_27),U_29)
| ~ r2_hidden(sK6(U_31,U_29,U_27),U_31)
| ~ sP4(U_31,U_27,U_29) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_15,plain,
( r2_hidden(sK7(U_31,U_29,U_27),U_31)
| ~ sP5(U_31,U_27,U_29) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_16,plain,
( r2_hidden(sK7(U_31,U_29,U_27),U_29)
| ~ sP5(U_31,U_27,U_29) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_17,plain,
( ~ r2_hidden(sK7(U_31,U_29,U_27),U_27)
| ~ sP5(U_31,U_27,U_29) ),
inference(clausify,[status(thm)],[f_6_6]) ).
fof(f_7_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
fof(f_7_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_7_1]) ).
cnf(f_7_3,plain,
$true,
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
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_k3_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,
! [A] :
( m1_subset_1(k3_yellow_0(A),u1_struct_0(A))
| ~ l1_orders_2(A) ),
inference(fof_nnf,[status(thm)],[dt_k3_yellow_0]) ).
fof(f_10_2,plain,
! [U_32] :
( m1_subset_1(k3_yellow_0(U_32),u1_struct_0(U_32))
| ~ l1_orders_2(U_32) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_32] :
( m1_subset_1(k3_yellow_0(U_32),u1_struct_0(U_32))
| ~ l1_orders_2(U_32) ),
inference(definitional_conversion,[status(esa)],[f_10_2]) ).
cnf(f_10_4,plain,
( m1_subset_1(k3_yellow_0(U_32),u1_struct_0(U_32))
| ~ l1_orders_2(U_32) ),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [A] :
( l1_struct_0(A)
| ~ l1_orders_2(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_orders_2]) ).
fof(f_11_2,plain,
! [U_33] :
( l1_struct_0(U_33)
| ~ l1_orders_2(U_33) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_33] :
( l1_struct_0(U_33)
| ~ l1_orders_2(U_33) ),
inference(definitional_conversion,[status(esa)],[f_11_2]) ).
cnf(f_11_4,plain,
( l1_struct_0(U_33)
| ~ l1_orders_2(U_33) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
fof(f_12_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_12_1]) ).
cnf(f_12_3,plain,
$true,
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_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_u1_struct_0]) ).
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] : l1_orders_2(A),
inference(fof_nnf,[status(thm)],[existence_l1_orders_2]) ).
fof(f_15_2,plain,
? [U_34] : l1_orders_2(U_34),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
l1_orders_2(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_34,sK8)],[f_15_2]) ).
fof(f_15_4,plain,
l1_orders_2(sK8),
inference(definitional_conversion,[status(esa)],[f_15_3]) ).
cnf(f_15_5,plain,
l1_orders_2(sK8),
inference(clausify,[status(thm)],[f_15_4]) ).
fof(f_16_1,plain,
? [A] : l1_struct_0(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_16_2,plain,
? [U_35] : l1_struct_0(U_35),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
l1_struct_0(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_35,sK9)],[f_16_2]) ).
fof(f_16_4,plain,
l1_struct_0(sK9),
inference(definitional_conversion,[status(esa)],[f_16_3]) ).
cnf(f_16_5,plain,
l1_struct_0(sK9),
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_37] :
? [U_36] : m1_subset_1(U_36,U_37),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_37] : m1_subset_1(sK10(U_37),U_37),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_36,sK10(U_37))],[f_17_2]) ).
fof(f_17_4,plain,
! [U_37] : m1_subset_1(sK10(U_37),U_37),
inference(definitional_conversion,[status(esa)],[f_17_3]) ).
cnf(f_17_5,plain,
m1_subset_1(sK10(U_37),U_37),
inference(clausify,[status(thm)],[f_17_4]) ).
fof(f_18_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_18_2,plain,
! [U_38] :
( ~ v1_xboole_0(u1_struct_0(U_38))
| ~ l1_struct_0(U_38)
| v3_struct_0(U_38) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_38] :
( ~ v1_xboole_0(u1_struct_0(U_38))
| ~ l1_struct_0(U_38)
| v3_struct_0(U_38) ),
inference(definitional_conversion,[status(esa)],[f_18_2]) ).
cnf(f_18_4,plain,
( ~ v1_xboole_0(u1_struct_0(U_38))
| ~ l1_struct_0(U_38)
| v3_struct_0(U_38) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
v1_xboole_0(k1_xboole_0),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_19_2,plain,
v1_xboole_0(k1_xboole_0),
inference(definitional_conversion,[status(esa)],[f_19_1]) ).
cnf(f_19_3,plain,
v1_xboole_0(k1_xboole_0),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
! [A,B] : k3_xboole_0(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_20_2,plain,
! [U_40,U_39] : k3_xboole_0(U_40,U_40) = U_40,
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_40] : k3_xboole_0(U_40,U_40) = U_40,
inference(miniscope,[status(thm)],[f_20_2]) ).
fof(f_20_4,plain,
! [U_40] : k3_xboole_0(U_40,U_40) = U_40,
inference(definitional_conversion,[status(esa)],[f_20_3]) ).
cnf(f_20_5,plain,
k3_xboole_0(U_40,U_40) = U_40,
inference(clausify,[status(thm)],[f_20_4]) ).
fof(f_21_1,plain,
? [A] : v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_21_2,plain,
? [U_41] : v1_xboole_0(U_41),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
v1_xboole_0(sK11),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_41,sK11)],[f_21_2]) ).
fof(f_21_4,plain,
v1_xboole_0(sK11),
inference(definitional_conversion,[status(esa)],[f_21_3]) ).
cnf(f_21_5,plain,
v1_xboole_0(sK11),
inference(clausify,[status(thm)],[f_21_4]) ).
fof(f_22_1,plain,
? [A] : ~ v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_22_2,plain,
? [U_42] : ~ v1_xboole_0(U_42),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
~ v1_xboole_0(sK12),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_42,sK12)],[f_22_2]) ).
fof(f_22_4,plain,
~ v1_xboole_0(sK12),
inference(definitional_conversion,[status(esa)],[f_22_3]) ).
cnf(f_22_5,plain,
~ v1_xboole_0(sK12),
inference(clausify,[status(thm)],[f_22_4]) ).
fof(f_23_1,plain,
? [A] :
( ~ v3_struct_0(A)
& l1_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc3_struct_0]) ).
fof(f_23_2,plain,
? [U_43] :
( ~ v3_struct_0(U_43)
& l1_struct_0(U_43) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( ~ v3_struct_0(sK13)
& l1_struct_0(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_43,sK13)],[f_23_2]) ).
fof(f_23_4,plain,
( ~ v3_struct_0(sK13)
& l1_struct_0(sK13) ),
inference(definitional_conversion,[status(esa)],[f_23_3]) ).
cnf(f_23_5,plain,
l1_struct_0(sK13),
inference(clausify,[status(thm)],[f_23_4]) ).
cnf(f_23_6,plain,
~ v3_struct_0(sK13),
inference(clausify,[status(thm)],[f_23_4]) ).
fof(f_24_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_24_2,plain,
! [U_45] :
( ? [U_44] :
( ~ v1_xboole_0(U_44)
& m1_subset_1(U_44,k1_zfmisc_1(u1_struct_0(U_45))) )
| ~ l1_struct_0(U_45)
| v3_struct_0(U_45) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_45] :
( ( ~ v1_xboole_0(sK14(U_45))
& m1_subset_1(sK14(U_45),k1_zfmisc_1(u1_struct_0(U_45))) )
| ~ l1_struct_0(U_45)
| v3_struct_0(U_45) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_44,sK14(U_45))],[f_24_2]) ).
fof(f_24_4,plain,
( ! [U_45] :
( ~ v1_xboole_0(sK14(U_45))
| ~ sP6(U_45) )
& ! [U_45] :
( m1_subset_1(sK14(U_45),k1_zfmisc_1(u1_struct_0(U_45)))
| ~ sP6(U_45) )
& ! [U_45] :
( sP6(U_45)
| ~ l1_struct_0(U_45)
| v3_struct_0(U_45) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_24_3]) ).
cnf(f_24_5,plain,
( sP6(U_45)
| ~ l1_struct_0(U_45)
| v3_struct_0(U_45) ),
inference(clausify,[status(thm)],[f_24_4]) ).
cnf(f_24_6,plain,
( m1_subset_1(sK14(U_45),k1_zfmisc_1(u1_struct_0(U_45)))
| ~ sP6(U_45) ),
inference(clausify,[status(thm)],[f_24_4]) ).
cnf(f_24_7,plain,
( ~ v1_xboole_0(sK14(U_45))
| ~ sP6(U_45) ),
inference(clausify,[status(thm)],[f_24_4]) ).
fof(f_25_1,plain,
! [A] :
( ? [B] :
( v12_waybel_0(B,A)
& v1_waybel_0(B,A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l1_orders_2(A)
| ~ v3_orders_2(A)
| ~ v2_orders_2(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[rc9_waybel_0]) ).
fof(f_25_2,plain,
! [U_47] :
( ? [U_46] :
( v12_waybel_0(U_46,U_47)
& v1_waybel_0(U_46,U_47)
& ~ v1_xboole_0(U_46)
& m1_subset_1(U_46,k1_zfmisc_1(u1_struct_0(U_47))) )
| ~ l1_orders_2(U_47)
| ~ v3_orders_2(U_47)
| ~ v2_orders_2(U_47)
| v3_struct_0(U_47) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_47] :
( ( v12_waybel_0(sK15(U_47),U_47)
& v1_waybel_0(sK15(U_47),U_47)
& ~ v1_xboole_0(sK15(U_47))
& m1_subset_1(sK15(U_47),k1_zfmisc_1(u1_struct_0(U_47))) )
| ~ l1_orders_2(U_47)
| ~ v3_orders_2(U_47)
| ~ v2_orders_2(U_47)
| v3_struct_0(U_47) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_46,sK15(U_47))],[f_25_2]) ).
fof(f_25_4,plain,
( ! [U_47] :
( v12_waybel_0(sK15(U_47),U_47)
| ~ sP7(U_47) )
& ! [U_47] :
( v1_waybel_0(sK15(U_47),U_47)
| ~ sP7(U_47) )
& ! [U_47] :
( ~ v1_xboole_0(sK15(U_47))
| ~ sP7(U_47) )
& ! [U_47] :
( m1_subset_1(sK15(U_47),k1_zfmisc_1(u1_struct_0(U_47)))
| ~ sP7(U_47) )
& ! [U_47] :
( sP7(U_47)
| ~ l1_orders_2(U_47)
| ~ v3_orders_2(U_47)
| ~ v2_orders_2(U_47)
| v3_struct_0(U_47) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_25_3]) ).
cnf(f_25_5,plain,
( sP7(U_47)
| ~ l1_orders_2(U_47)
| ~ v3_orders_2(U_47)
| ~ v2_orders_2(U_47)
| v3_struct_0(U_47) ),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_6,plain,
( m1_subset_1(sK15(U_47),k1_zfmisc_1(u1_struct_0(U_47)))
| ~ sP7(U_47) ),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_7,plain,
( ~ v1_xboole_0(sK15(U_47))
| ~ sP7(U_47) ),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_8,plain,
( v1_waybel_0(sK15(U_47),U_47)
| ~ sP7(U_47) ),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_9,plain,
( v12_waybel_0(sK15(U_47),U_47)
| ~ sP7(U_47) ),
inference(clausify,[status(thm)],[f_25_4]) ).
fof(f_26_1,plain,
! [A,B,C] :
( ( ( r3_orders_2(A,B,C)
| ~ r1_orders_2(A,B,C) )
& ( r1_orders_2(A,B,C)
| ~ r3_orders_2(A,B,C) ) )
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l1_orders_2(A)
| ~ v2_orders_2(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[redefinition_r3_orders_2]) ).
fof(f_26_2,plain,
! [U_50,U_49,U_48] :
( ( ( r3_orders_2(U_50,U_49,U_48)
| ~ r1_orders_2(U_50,U_49,U_48) )
& ( r1_orders_2(U_50,U_49,U_48)
| ~ r3_orders_2(U_50,U_49,U_48) ) )
| ~ m1_subset_1(U_48,u1_struct_0(U_50))
| ~ m1_subset_1(U_49,u1_struct_0(U_50))
| ~ l1_orders_2(U_50)
| ~ v2_orders_2(U_50)
| v3_struct_0(U_50) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( ! [U_50,U_49,U_48] :
( r3_orders_2(U_50,U_49,U_48)
| ~ r1_orders_2(U_50,U_49,U_48)
| ~ sP8(U_50,U_49,U_48) )
& ! [U_50,U_49,U_48] :
( r1_orders_2(U_50,U_49,U_48)
| ~ r3_orders_2(U_50,U_49,U_48)
| ~ sP8(U_50,U_49,U_48) )
& ! [U_50,U_49,U_48] :
( sP8(U_50,U_49,U_48)
| ~ m1_subset_1(U_48,u1_struct_0(U_50))
| ~ m1_subset_1(U_49,u1_struct_0(U_50))
| ~ l1_orders_2(U_50)
| ~ v2_orders_2(U_50)
| v3_struct_0(U_50) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_26_2]) ).
cnf(f_26_4,plain,
( sP8(U_50,U_49,U_48)
| ~ m1_subset_1(U_48,u1_struct_0(U_50))
| ~ m1_subset_1(U_49,u1_struct_0(U_50))
| ~ l1_orders_2(U_50)
| ~ v2_orders_2(U_50)
| v3_struct_0(U_50) ),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_5,plain,
( r1_orders_2(U_50,U_49,U_48)
| ~ r3_orders_2(U_50,U_49,U_48)
| ~ sP8(U_50,U_49,U_48) ),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_6,plain,
( r3_orders_2(U_50,U_49,U_48)
| ~ r1_orders_2(U_50,U_49,U_48)
| ~ sP8(U_50,U_49,U_48) ),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [A,B] : r1_tarski(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_27_2,plain,
! [U_52,U_51] : r1_tarski(U_52,U_52),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_52] : r1_tarski(U_52,U_52),
inference(miniscope,[status(thm)],[f_27_2]) ).
fof(f_27_4,plain,
! [U_52] : r1_tarski(U_52,U_52),
inference(definitional_conversion,[status(esa)],[f_27_3]) ).
cnf(f_27_5,plain,
r1_tarski(U_52,U_52),
inference(clausify,[status(thm)],[f_27_4]) ).
fof(f_28_1,plain,
! [A,B,C] :
( r3_orders_2(A,B,B)
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l1_orders_2(A)
| ~ v2_orders_2(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[reflexivity_r3_orders_2]) ).
fof(f_28_2,plain,
! [U_55,U_54,U_53] :
( r3_orders_2(U_55,U_54,U_54)
| ~ m1_subset_1(U_53,u1_struct_0(U_55))
| ~ m1_subset_1(U_54,u1_struct_0(U_55))
| ~ l1_orders_2(U_55)
| ~ v2_orders_2(U_55)
| v3_struct_0(U_55) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_55,U_54] :
( ! [U_53] : ~ m1_subset_1(U_53,u1_struct_0(U_55))
| ~ m1_subset_1(U_54,u1_struct_0(U_55))
| ~ l1_orders_2(U_55)
| ~ v2_orders_2(U_55)
| v3_struct_0(U_55)
| r3_orders_2(U_55,U_54,U_54) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
fof(f_28_4,plain,
! [U_53,U_54,U_55] :
( ~ m1_subset_1(U_53,u1_struct_0(U_55))
| ~ m1_subset_1(U_54,u1_struct_0(U_55))
| ~ l1_orders_2(U_55)
| ~ v2_orders_2(U_55)
| v3_struct_0(U_55)
| r3_orders_2(U_55,U_54,U_54) ),
inference(definitional_conversion,[status(esa)],[f_28_3]) ).
cnf(f_28_5,plain,
( ~ m1_subset_1(U_53,u1_struct_0(U_55))
| ~ m1_subset_1(U_54,u1_struct_0(U_55))
| ~ l1_orders_2(U_55)
| ~ v2_orders_2(U_55)
| v3_struct_0(U_55)
| r3_orders_2(U_55,U_54,U_54) ),
inference(clausify,[status(thm)],[f_28_4]) ).
fof(f_29_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( m1_subset_1(C,u1_struct_0(B))
| ~ r2_hidden(C,k3_xboole_0(u1_struct_0(A),u1_struct_0(B))) )
| ~ l1_orders_2(B)
| v3_struct_0(B) )
| ~ l1_orders_2(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t13_latsum_1]) ).
fof(f_29_2,plain,
! [U_58] :
( ! [U_57] :
( ! [U_56] :
( m1_subset_1(U_56,u1_struct_0(U_57))
| ~ r2_hidden(U_56,k3_xboole_0(u1_struct_0(U_58),u1_struct_0(U_57))) )
| ~ l1_orders_2(U_57)
| v3_struct_0(U_57) )
| ~ l1_orders_2(U_58)
| v3_struct_0(U_58) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_57,U_58,U_56] :
( m1_subset_1(U_56,u1_struct_0(U_57))
| ~ r2_hidden(U_56,k3_xboole_0(u1_struct_0(U_58),u1_struct_0(U_57)))
| ~ l1_orders_2(U_57)
| v3_struct_0(U_57)
| ~ l1_orders_2(U_58)
| v3_struct_0(U_58) ),
inference(definitional_conversion,[status(esa)],[f_29_2]) ).
cnf(f_29_4,plain,
( m1_subset_1(U_56,u1_struct_0(U_57))
| ~ r2_hidden(U_56,k3_xboole_0(u1_struct_0(U_58),u1_struct_0(U_57)))
| ~ l1_orders_2(U_57)
| v3_struct_0(U_57)
| ~ l1_orders_2(U_58)
| v3_struct_0(U_58) ),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_30_2,plain,
! [U_60,U_59] :
( m1_subset_1(U_60,U_59)
| ~ r2_hidden(U_60,U_59) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_59,U_60] :
( m1_subset_1(U_60,U_59)
| ~ r2_hidden(U_60,U_59) ),
inference(definitional_conversion,[status(esa)],[f_30_2]) ).
cnf(f_30_4,plain,
( m1_subset_1(U_60,U_59)
| ~ r2_hidden(U_60,U_59) ),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_31_2,plain,
! [U_61] : k3_xboole_0(U_61,k1_xboole_0) = k1_xboole_0,
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_61] : k3_xboole_0(U_61,k1_xboole_0) = k1_xboole_0,
inference(definitional_conversion,[status(esa)],[f_31_2]) ).
cnf(f_31_4,plain,
k3_xboole_0(U_61,k1_xboole_0) = k1_xboole_0,
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_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_32_2,plain,
! [U_63,U_62] :
( r2_hidden(U_63,U_62)
| v1_xboole_0(U_62)
| ~ m1_subset_1(U_63,U_62) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_63,U_62] :
( r2_hidden(U_63,U_62)
| v1_xboole_0(U_62)
| ~ m1_subset_1(U_63,U_62) ),
inference(definitional_conversion,[status(esa)],[f_32_2]) ).
cnf(f_32_4,plain,
( r2_hidden(U_63,U_62)
| v1_xboole_0(U_62)
| ~ m1_subset_1(U_63,U_62) ),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_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_33_2,plain,
! [U_65,U_64] :
( ( m1_subset_1(U_65,k1_zfmisc_1(U_64))
| ~ r1_tarski(U_65,U_64) )
& ( r1_tarski(U_65,U_64)
| ~ m1_subset_1(U_65,k1_zfmisc_1(U_64)) ) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( ! [U_69,U_67] :
( m1_subset_1(U_69,k1_zfmisc_1(U_67))
| ~ r1_tarski(U_69,U_67) )
& ! [U_68,U_66] :
( r1_tarski(U_68,U_66)
| ~ m1_subset_1(U_68,k1_zfmisc_1(U_66)) ) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
fof(f_33_4,plain,
( ! [U_69,U_67] :
( m1_subset_1(U_69,k1_zfmisc_1(U_67))
| ~ r1_tarski(U_69,U_67) )
& ! [U_68,U_66] :
( r1_tarski(U_68,U_66)
| ~ m1_subset_1(U_68,k1_zfmisc_1(U_66)) ) ),
inference(definitional_conversion,[status(esa)],[f_33_3]) ).
cnf(f_33_5,plain,
( r1_tarski(U_68,U_66)
| ~ m1_subset_1(U_68,k1_zfmisc_1(U_66)) ),
inference(clausify,[status(thm)],[f_33_4]) ).
cnf(f_33_6,plain,
( m1_subset_1(U_69,k1_zfmisc_1(U_67))
| ~ r1_tarski(U_69,U_67) ),
inference(clausify,[status(thm)],[f_33_4]) ).
fof(f_34_1,plain,
! [A] :
( ! [B] :
( r1_orders_2(A,k3_yellow_0(A),B)
| ~ m1_subset_1(B,u1_struct_0(A)) )
| ~ l1_orders_2(A)
| ~ v1_yellow_0(A)
| ~ v4_orders_2(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t44_yellow_0]) ).
fof(f_34_2,plain,
! [U_71] :
( ! [U_70] :
( r1_orders_2(U_71,k3_yellow_0(U_71),U_70)
| ~ m1_subset_1(U_70,u1_struct_0(U_71)) )
| ~ l1_orders_2(U_71)
| ~ v1_yellow_0(U_71)
| ~ v4_orders_2(U_71)
| v3_struct_0(U_71) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_70,U_71] :
( r1_orders_2(U_71,k3_yellow_0(U_71),U_70)
| ~ m1_subset_1(U_70,u1_struct_0(U_71))
| ~ l1_orders_2(U_71)
| ~ v1_yellow_0(U_71)
| ~ v4_orders_2(U_71)
| v3_struct_0(U_71) ),
inference(definitional_conversion,[status(esa)],[f_34_2]) ).
cnf(f_34_4,plain,
( r1_orders_2(U_71,k3_yellow_0(U_71),U_70)
| ~ m1_subset_1(U_70,u1_struct_0(U_71))
| ~ l1_orders_2(U_71)
| ~ v1_yellow_0(U_71)
| ~ v4_orders_2(U_71)
| v3_struct_0(U_71) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_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_35_2,plain,
! [U_74,U_73,U_72] :
( m1_subset_1(U_74,U_72)
| ~ m1_subset_1(U_73,k1_zfmisc_1(U_72))
| ~ r2_hidden(U_74,U_73) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_74,U_72,U_73] :
( m1_subset_1(U_74,U_72)
| ~ m1_subset_1(U_73,k1_zfmisc_1(U_72))
| ~ r2_hidden(U_74,U_73) ),
inference(definitional_conversion,[status(esa)],[f_35_2]) ).
cnf(f_35_4,plain,
( m1_subset_1(U_74,U_72)
| ~ m1_subset_1(U_73,k1_zfmisc_1(U_72))
| ~ r2_hidden(U_74,U_73) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_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_36_2,plain,
! [U_77,U_76,U_75] :
( ~ v1_xboole_0(U_75)
| ~ m1_subset_1(U_76,k1_zfmisc_1(U_75))
| ~ r2_hidden(U_77,U_76) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_77,U_76] :
( ! [U_75] :
( ~ v1_xboole_0(U_75)
| ~ m1_subset_1(U_76,k1_zfmisc_1(U_75)) )
| ~ r2_hidden(U_77,U_76) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
fof(f_36_4,plain,
! [U_76,U_75,U_77] :
( ~ v1_xboole_0(U_75)
| ~ m1_subset_1(U_76,k1_zfmisc_1(U_75))
| ~ r2_hidden(U_77,U_76) ),
inference(definitional_conversion,[status(esa)],[f_36_3]) ).
cnf(f_36_5,plain,
( ~ v1_xboole_0(U_75)
| ~ m1_subset_1(U_76,k1_zfmisc_1(U_75))
| ~ r2_hidden(U_77,U_76) ),
inference(clausify,[status(thm)],[f_36_4]) ).
fof(f_37_1,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_37_2,plain,
! [U_78] :
( U_78 = k1_xboole_0
| ~ v1_xboole_0(U_78) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_78] :
( U_78 = k1_xboole_0
| ~ v1_xboole_0(U_78) ),
inference(definitional_conversion,[status(esa)],[f_37_2]) ).
cnf(f_37_4,plain,
( U_78 = k1_xboole_0
| ~ v1_xboole_0(U_78) ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_38_2,plain,
! [U_80,U_79] :
( ~ v1_xboole_0(U_79)
| ~ r2_hidden(U_80,U_79) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_80,U_79] :
( ~ v1_xboole_0(U_79)
| ~ r2_hidden(U_80,U_79) ),
inference(definitional_conversion,[status(esa)],[f_38_2]) ).
cnf(f_38_4,plain,
( ~ v1_xboole_0(U_79)
| ~ r2_hidden(U_80,U_79) ),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| A = B
| ~ v1_xboole_0(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_39_2,plain,
! [U_82,U_81] :
( ~ v1_xboole_0(U_81)
| U_82 = U_81
| ~ v1_xboole_0(U_82) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_82] :
( ! [U_81] :
( ~ v1_xboole_0(U_81)
| U_82 = U_81 )
| ~ v1_xboole_0(U_82) ),
inference(miniscope,[status(thm)],[f_39_2]) ).
fof(f_39_4,plain,
! [U_81,U_82] :
( ~ v1_xboole_0(U_81)
| U_82 = U_81
| ~ v1_xboole_0(U_82) ),
inference(definitional_conversion,[status(esa)],[f_39_3]) ).
cnf(f_39_5,plain,
( ~ v1_xboole_0(U_81)
| U_82 = U_81
| ~ v1_xboole_0(U_82) ),
inference(clausify,[status(thm)],[f_39_4]) ).
cnf(f_7_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_3]) ).
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_12_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_12_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,
( u1_struct_0(Eq_x_0) = u1_struct_0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( k3_xboole_0(Eq_x_0,Eq_x_1) = k3_xboole_0(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_zfmisc_1(Eq_x_0) = k1_zfmisc_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( k3_yellow_0(Eq_x_0) = k3_yellow_0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sK3(Eq_x_0,Eq_x_1) = sK3(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,
( sK4(Eq_x_0,Eq_x_1) = sK4(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK5(Eq_x_0) = sK5(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK6(Eq_x_0,Eq_x_1,Eq_x_2) = sK6(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK7(Eq_x_0,Eq_x_1,Eq_x_2) = sK7(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK10(Eq_x_0) = sK10(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,
( v3_struct_0(Eq_y_0)
| ~ v3_struct_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( v2_orders_2(Eq_y_0)
| ~ v2_orders_2(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( v3_orders_2(Eq_y_0)
| ~ v3_orders_2(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( v4_orders_2(Eq_y_0)
| ~ v4_orders_2(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,axiom,
( v1_yellow_0(Eq_y_0)
| ~ v1_yellow_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( v1_lattice3(Eq_y_0)
| ~ v1_lattice3(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,axiom,
( l1_orders_2(Eq_y_0)
| ~ l1_orders_2(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,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_24,axiom,
( v1_waybel_0(Eq_y_0,Eq_y_1)
| ~ v1_waybel_0(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,
( v12_waybel_0(Eq_y_0,Eq_y_1)
| ~ v12_waybel_0(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,
( 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_27,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_28,axiom,
( r1_orders_2(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ r1_orders_2(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,axiom,
( l1_struct_0(Eq_y_0)
| ~ l1_struct_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,axiom,
( r3_orders_2(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ r3_orders_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_31,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_32,axiom,
( sP0(Eq_y_0,Eq_y_1)
| ~ sP0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,axiom,
( sP1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,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_35,axiom,
( sP3(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP3(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,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_37,axiom,
( sP5(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP5(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_38,axiom,
( sP6(Eq_y_0)
| ~ sP6(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_39,axiom,
( sP7(Eq_y_0)
| ~ sP7(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_40,axiom,
( sP8(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP8(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU411+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n017.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 00:11:10 UTC 2026
% 0.13/0.36 % CPUTime :
% 274.17/274.47 % SZS status Theorem for theBenchmark
% 274.17/274.47 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------