%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU435+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 : Wed Oct 7 10:44:25 AM UTC 2026
% Result : Theorem 0.10s 0.26s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 24
% Syntax : Number of formulae : 215 ( 146 unt; 0 typ; 0 def)
% Number of atoms : 984 ( 260 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 2196 ( 326 ~; 180 |; 18 &;1621 @)
% ( 3 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 32 usr; 9 con; 0-6 aty)
% Number of variables : 515 ( 0 ^; 506 !; 9 ?; 515 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a_6_0_relset_2,type,
a_6_0_relset_2: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_k1_xboole_0,type,
k1_xboole_0: $i ).
thf(tp_k1_zfmisc_1,type,
k1_zfmisc_1: $i > $i ).
thf(tp_k2_zfmisc_1,type,
k2_zfmisc_1: $i > $i > $i ).
thf(tp_k3_pua2mss1,type,
k3_pua2mss1: $i > $i ).
thf(tp_k4_relset_2,type,
k4_relset_2: $i > $i > $i > $i > $i ).
thf(tp_k5_relset_2,type,
k5_relset_2: $i > $i > $i ).
thf(tp_k6_relset_2,type,
k6_relset_2: $i > $i > $i > $i ).
thf(tp_k7_relset_2,type,
k7_relset_2: $i > $i > $i > $i > $i ).
thf(tp_k8_relset_2,type,
k8_relset_2: $i > $i > $i > $i > $i ).
thf(tp_k8_setfam_1,type,
k8_setfam_1: $i > $i > $i ).
thf(tp_k9_relat_1,type,
k9_relat_1: $i > $i > $i ).
thf(tp_m1_eqrel_1,type,
m1_eqrel_1: $i > $i > $o ).
thf(tp_m1_relset_1,type,
m1_relset_1: $i > $i > $i > $o ).
thf(tp_m1_subset_1,type,
m1_subset_1: $i > $i > $o ).
thf(tp_m2_relset_1,type,
m2_relset_1: $i > $i > $i > $o ).
thf(tp_r1_tarski,type,
r1_tarski: $i > $i > $o ).
thf(tp_r2_hidden,type,
r2_hidden: $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY48,type,
sK2_SY48: $i ).
thf(tp_sK3_SY53,type,
sK3_SY53: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SY90,type,
sK5_SY90: $i ).
thf(tp_sK6_SY74,type,
sK6_SY74: $i > $i ).
thf(tp_sK7_SY75,type,
sK7_SY75: $i > $i ).
thf(tp_sK8_SY100,type,
sK8_SY100: $i ).
thf(tp_sK9_SY73,type,
sK9_SY73: $i > $i ).
thf(tp_v1_funct_1,type,
v1_funct_1: $i > $o ).
thf(tp_v1_funct_2,type,
v1_funct_2: $i > $i > $i > $o ).
thf(tp_v1_relat_1,type,
v1_relat_1: $i > $o ).
thf(tp_v1_xboole_0,type,
v1_xboole_0: $i > $o ).
thf(tp_v3_relat_1,type,
v3_relat_1: $i > $o ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
=> ( m1_subset_1 @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
<=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ D ) ) )
=> ( m1_subset_1 @ ( a_6_0_relset_2 @ A @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s8_domain_1__e1_46__relset_2) ).
thf(17,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(20,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(25,axiom,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_sysrel) ).
thf(26,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(29,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(33,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(34,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_eqrel_1) ).
thf(36,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_relat_1) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k8_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_setfam_1) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ( m1_subset_1 @ ( k8_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relset_2) ).
thf(39,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relset_2) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) )
=> ( m1_subset_1 @ ( k4_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relset_2) ).
thf(44,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(45,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(46,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( v1_relat_1 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(51,conjecture,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ! [D: $i,E: $i,F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ D ) )
=> ( m1_subset_1 @ ( a_6_0_relset_2 @ A @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_relset_2) ).
thf(52,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ! [D: $i,E: $i,F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ D ) )
=> ( m1_subset_1 @ ( a_6_0_relset_2 @ A @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ E ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[51]) ).
thf(53,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ! [D: $i,E: $i,F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ D ) )
=> ( m1_subset_1 @ ( a_6_0_relset_2 @ A @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ E ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[52]) ).
thf(54,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
=> ( m1_subset_1 @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(55,plain,
( ( ! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
<=> ( r1_tarski @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(56,plain,
( ( ! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(57,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ D ) ) )
=> ( m1_subset_1 @ ( a_6_0_relset_2 @ A @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ E ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(58,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_xboole_0 @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(59,plain,
( ( ! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(60,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(61,plain,
( ( ! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(62,plain,
( ( ! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(63,plain,
( ( ! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(64,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(65,plain,
$true = $true,
inference(unfold_def,[status(thm)],[33]) ).
thf(66,plain,
$true = $true,
inference(unfold_def,[status(thm)],[34]) ).
thf(67,plain,
( ( ! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(68,plain,
$true = $true,
inference(unfold_def,[status(thm)],[36]) ).
thf(69,plain,
( ( ! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k8_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(70,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ( m1_subset_1 @ ( k8_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(71,plain,
$true = $true,
inference(unfold_def,[status(thm)],[39]) ).
thf(72,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) )
=> ( m1_subset_1 @ ( k4_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(73,plain,
$true = $true,
inference(unfold_def,[status(thm)],[44]) ).
thf(74,plain,
$true = $true,
inference(unfold_def,[status(thm)],[45]) ).
thf(75,plain,
$true = $true,
inference(unfold_def,[status(thm)],[46]) ).
thf(76,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( v1_relat_1 @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(77,plain,
( ( ! [SY48: $i,SY49: $i] :
( ( m1_subset_1 @ SY49 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ sK1_A @ SY48 ) ) ) )
=> ! [SY50: $i,SY51: $i,SY52: $i] :
( ( m1_subset_1 @ SY52 @ ( k1_zfmisc_1 @ SY50 ) )
=> ( m1_subset_1 @ ( a_6_0_relset_2 @ sK1_A @ SY48 @ SY49 @ SY50 @ SY51 @ SY52 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SY51 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[53]) ).
thf(78,plain,
( ( ! [SY53: $i] :
( ( m1_subset_1 @ SY53 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ sK1_A @ sK2_SY48 ) ) ) )
=> ! [SY54: $i,SY55: $i,SY56: $i] :
( ( m1_subset_1 @ SY56 @ ( k1_zfmisc_1 @ SY54 ) )
=> ( m1_subset_1 @ ( a_6_0_relset_2 @ sK1_A @ sK2_SY48 @ SY53 @ SY54 @ SY55 @ SY56 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SY55 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[77]) ).
thf(79,plain,
( ( ( m1_subset_1 @ sK3_SY53 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ sK1_A @ sK2_SY48 ) ) ) )
=> ! [SY57: $i,SY58: $i,SY59: $i] :
( ( m1_subset_1 @ SY59 @ ( k1_zfmisc_1 @ SY57 ) )
=> ( m1_subset_1 @ ( a_6_0_relset_2 @ sK1_A @ sK2_SY48 @ sK3_SY53 @ SY57 @ SY58 @ SY59 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SY58 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[78]) ).
thf(80,plain,
( ( m1_subset_1 @ sK3_SY53 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ sK1_A @ sK2_SY48 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[79]) ).
thf(81,plain,
( ( ! [SY57: $i,SY58: $i,SY59: $i] :
( ( m1_subset_1 @ SY59 @ ( k1_zfmisc_1 @ SY57 ) )
=> ( m1_subset_1 @ ( a_6_0_relset_2 @ sK1_A @ sK2_SY48 @ sK3_SY53 @ SY57 @ SY58 @ SY59 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SY58 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[79]) ).
thf(82,plain,
( ( ~ ! [SY57: $i,SY58: $i,SY59: $i] :
( ( m1_subset_1 @ SY59 @ ( k1_zfmisc_1 @ SY57 ) )
=> ( m1_subset_1 @ ( a_6_0_relset_2 @ sK1_A @ sK2_SY48 @ sK3_SY53 @ SY57 @ SY58 @ SY59 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SY58 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[81]) ).
thf(83,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( v1_relat_1 @ C ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(84,plain,
$true = $true,
inference(copy,[status(thm)],[75]) ).
thf(85,plain,
$true = $true,
inference(copy,[status(thm)],[74]) ).
thf(86,plain,
$true = $true,
inference(copy,[status(thm)],[73]) ).
thf(87,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) )
=> ( m1_subset_1 @ ( k4_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(88,plain,
$true = $true,
inference(copy,[status(thm)],[71]) ).
thf(89,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ( m1_subset_1 @ ( k8_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(90,plain,
( ( ! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k8_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(91,plain,
$true = $true,
inference(copy,[status(thm)],[68]) ).
thf(92,plain,
( ( ! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(93,plain,
$true = $true,
inference(copy,[status(thm)],[66]) ).
thf(94,plain,
$true = $true,
inference(copy,[status(thm)],[65]) ).
thf(95,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(96,plain,
( ( ! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(97,plain,
( ( ! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(98,plain,
( ( ! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(99,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(100,plain,
( ( ! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(101,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_xboole_0 @ B ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(102,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ D ) ) )
=> ( m1_subset_1 @ ( a_6_0_relset_2 @ A @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ E ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(103,plain,
( ( ! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(104,plain,
( ( ! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
<=> ( r1_tarski @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(105,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
=> ( m1_subset_1 @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(106,plain,
( ( m1_subset_1 @ sK3_SY53 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ sK1_A @ sK2_SY48 ) ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(107,plain,
( ( ~ ! [SY57: $i,SY58: $i,SY59: $i] :
( ( m1_subset_1 @ SY59 @ ( k1_zfmisc_1 @ SY57 ) )
=> ( m1_subset_1 @ ( a_6_0_relset_2 @ sK1_A @ sK2_SY48 @ sK3_SY53 @ SY57 @ SY58 @ SY59 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SY58 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(108,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( m1_subset_1 @ SX2 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SX0 @ SX1 ) ) )
| ( v1_relat_1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(109,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( m1_eqrel_1 @ SX1 @ SX0 )
| ( m1_subset_1 @ SX1 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(110,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( m2_relset_1 @ SX2 @ SX0 @ SX1 )
| ( m1_subset_1 @ SX2 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(111,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( v1_xboole_0 @ SX0 )
| ~ ~ ( v1_xboole_0 @ SX1 ) )
| ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(112,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( m1_subset_1 @ SX2 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SX0 @ ( k1_zfmisc_1 @ SX1 ) ) ) )
| ( m1_subset_1 @ ( k4_relset_2 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(113,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( m1_subset_1 @ SX1 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SX0 ) ) )
| ( m1_subset_1 @ ( k8_setfam_1 @ SX0 @ SX1 ) @ ( k1_zfmisc_1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(114,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( m1_subset_1 @ SX2 @ ( k1_zfmisc_1 @ SX0 ) )
| ( m1_subset_1 @ ( a_6_0_relset_2 @ sK1_A @ sK2_SY48 @ sK3_SY53 @ SX0 @ SX1 @ SX2 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(115,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( r2_hidden @ SX0 @ SX1 )
| ~ ( m1_subset_1 @ SX1 @ ( k1_zfmisc_1 @ SX2 ) ) )
| ( m1_subset_1 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(116,plain,
( ( ! [SX0: $i] :
( ~ ~ ( v1_xboole_0 @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( m1_subset_1 @ SX1 @ ( k1_zfmisc_1 @ SX0 ) )
| ~ ~ ( v1_xboole_0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(117,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( m1_subset_1 @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(118,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( m1_subset_1 @ SX1 @ ( k1_zfmisc_1 @ SX0 ) )
| ~ ( v1_xboole_0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(119,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( m1_subset_1 @ SX2 @ ( k1_zfmisc_1 @ SX0 ) )
| ~ ( m1_subset_1 @ SX3 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SX0 @ SX1 ) ) ) )
| ( m1_subset_1 @ ( k8_relset_2 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( k1_zfmisc_1 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(120,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ~ ( ~ ( m1_subset_1 @ SX2 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SX0 @ SX1 ) ) ) )
| ~ ( m1_subset_1 @ SX5 @ ( k1_zfmisc_1 @ SX3 ) ) )
| ( m1_subset_1 @ ( a_6_0_relset_2 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 @ SX5 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(121,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( r2_hidden @ SX0 @ SX1 )
| ( m1_subset_1 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(122,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( m1_subset_1 @ SX0 @ ( k1_zfmisc_1 @ SX1 ) )
| ( r1_tarski @ SX0 @ SX1 ) )
| ~ ( ~ ( r1_tarski @ SX0 @ SX1 )
| ( m1_subset_1 @ SX0 @ ( k1_zfmisc_1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(123,plain,
! [SV1: $i] :
( ( ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(124,plain,
! [SV2: $i] :
( ( ! [SY60: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ SV2 @ SY60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(125,plain,
! [SV3: $i] :
( ( ! [SY61: $i,SY62: $i] :
( ~ ( m1_subset_1 @ SY62 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV3 @ SY61 ) ) )
| ( v1_relat_1 @ SY62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(126,plain,
! [SV4: $i] :
( ( ! [SY63: $i] :
( ~ ( m1_eqrel_1 @ SY63 @ SV4 )
| ( m1_subset_1 @ SY63 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SV4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(127,plain,
! [SV5: $i] :
( ( ! [SY64: $i,SY65: $i] :
( ~ ( m2_relset_1 @ SY65 @ SV5 @ SY64 )
| ( m1_subset_1 @ SY65 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV5 @ SY64 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(128,plain,
! [SV6: $i] :
( ( ! [SY66: $i] :
( ~ ~ ( ~ ~ ( v1_xboole_0 @ SV6 )
| ~ ~ ( v1_xboole_0 @ SY66 ) )
| ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ SV6 @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(129,plain,
! [SV7: $i] :
( ( ! [SY67: $i,SY68: $i,SY69: $i] :
( ~ ( m1_subset_1 @ SY68 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV7 @ ( k1_zfmisc_1 @ SY67 ) ) ) )
| ( m1_subset_1 @ ( k4_relset_2 @ SV7 @ SY67 @ SY68 @ SY69 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SY67 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(130,plain,
! [SV8: $i] :
( ( ! [SY70: $i] :
( ~ ( m1_subset_1 @ SY70 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SV8 ) ) )
| ( m1_subset_1 @ ( k8_setfam_1 @ SV8 @ SY70 ) @ ( k1_zfmisc_1 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(131,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( m1_subset_1 @ SX2 @ ( k1_zfmisc_1 @ SX0 ) )
| ( m1_subset_1 @ ( a_6_0_relset_2 @ sK1_A @ sK2_SY48 @ sK3_SY53 @ SX0 @ SX1 @ SX2 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(132,plain,
! [SV9: $i] :
( ( ! [SY71: $i,SY72: $i] :
( ~ ~ ( ~ ( r2_hidden @ SV9 @ SY71 )
| ~ ( m1_subset_1 @ SY71 @ ( k1_zfmisc_1 @ SY72 ) ) )
| ( m1_subset_1 @ SV9 @ SY72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(133,plain,
! [SV10: $i] :
( ( ~ ~ ( v1_xboole_0 @ SV10 )
| ~ ! [SY73: $i] :
~ ~ ( ~ ( m1_subset_1 @ SY73 @ ( k1_zfmisc_1 @ SV10 ) )
| ~ ~ ( v1_xboole_0 @ SY73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(134,plain,
! [SV11: $i] :
( ( ~ ! [SY74: $i] :
~ ( m1_subset_1 @ SY74 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(135,plain,
! [SV12: $i] :
( ( ~ ! [SY75: $i] :
~ ~ ( ~ ( m1_subset_1 @ SY75 @ ( k1_zfmisc_1 @ SV12 ) )
| ~ ( v1_xboole_0 @ SY75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(136,plain,
! [SV13: $i] :
( ( ! [SY76: $i,SY77: $i,SY78: $i] :
( ~ ~ ( ~ ( m1_subset_1 @ SY77 @ ( k1_zfmisc_1 @ SV13 ) )
| ~ ( m1_subset_1 @ SY78 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV13 @ SY76 ) ) ) )
| ( m1_subset_1 @ ( k8_relset_2 @ SV13 @ SY76 @ SY77 @ SY78 ) @ ( k1_zfmisc_1 @ SY76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(137,plain,
! [SV14: $i] :
( ( ! [SY79: $i,SY80: $i,SY81: $i,SY82: $i,SY83: $i] :
( ~ ~ ( ~ ( m1_subset_1 @ SY80 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV14 @ SY79 ) ) ) )
| ~ ( m1_subset_1 @ SY83 @ ( k1_zfmisc_1 @ SY81 ) ) )
| ( m1_subset_1 @ ( a_6_0_relset_2 @ SV14 @ SY79 @ SY80 @ SY81 @ SY82 @ SY83 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SY82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(138,plain,
! [SV15: $i] :
( ( ! [SY84: $i] :
( ~ ( r2_hidden @ SV15 @ SY84 )
| ( m1_subset_1 @ SV15 @ SY84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(139,plain,
! [SV16: $i] :
( ( ! [SY85: $i] :
~ ( ~ ( ~ ( m1_subset_1 @ SV16 @ ( k1_zfmisc_1 @ SY85 ) )
| ( r1_tarski @ SV16 @ SY85 ) )
| ~ ( ~ ( r1_tarski @ SV16 @ SY85 )
| ( m1_subset_1 @ SV16 @ ( k1_zfmisc_1 @ SY85 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(140,plain,
! [SV1: $i] :
( ( v1_xboole_0 @ ( k1_zfmisc_1 @ SV1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(141,plain,
! [SV17: $i,SV2: $i] :
( ( v1_relat_1 @ ( k2_zfmisc_1 @ SV2 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(142,plain,
! [SV18: $i,SV3: $i] :
( ( ! [SY86: $i] :
( ~ ( m1_subset_1 @ SY86 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV3 @ SV18 ) ) )
| ( v1_relat_1 @ SY86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(143,plain,
! [SV4: $i,SV19: $i] :
( ( ~ ( m1_eqrel_1 @ SV19 @ SV4 )
| ( m1_subset_1 @ SV19 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(144,plain,
! [SV20: $i,SV5: $i] :
( ( ! [SY87: $i] :
( ~ ( m2_relset_1 @ SY87 @ SV5 @ SV20 )
| ( m1_subset_1 @ SY87 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV5 @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(145,plain,
! [SV21: $i,SV6: $i] :
( ( ~ ~ ( ~ ~ ( v1_xboole_0 @ SV6 )
| ~ ~ ( v1_xboole_0 @ SV21 ) )
| ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ SV6 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(146,plain,
! [SV22: $i,SV7: $i] :
( ( ! [SY88: $i,SY89: $i] :
( ~ ( m1_subset_1 @ SY88 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV7 @ ( k1_zfmisc_1 @ SV22 ) ) ) )
| ( m1_subset_1 @ ( k4_relset_2 @ SV7 @ SV22 @ SY88 @ SY89 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SV22 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(147,plain,
! [SV8: $i,SV23: $i] :
( ( ~ ( m1_subset_1 @ SV23 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SV8 ) ) )
| ( m1_subset_1 @ ( k8_setfam_1 @ SV8 @ SV23 ) @ ( k1_zfmisc_1 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(148,plain,
( ( ! [SY90: $i,SY91: $i] :
( ~ ( m1_subset_1 @ SY91 @ ( k1_zfmisc_1 @ sK4_SX0 ) )
| ( m1_subset_1 @ ( a_6_0_relset_2 @ sK1_A @ sK2_SY48 @ sK3_SY53 @ sK4_SX0 @ SY90 @ SY91 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SY90 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[131]) ).
thf(149,plain,
! [SV24: $i,SV9: $i] :
( ( ! [SY92: $i] :
( ~ ~ ( ~ ( r2_hidden @ SV9 @ SV24 )
| ~ ( m1_subset_1 @ SV24 @ ( k1_zfmisc_1 @ SY92 ) ) )
| ( m1_subset_1 @ SV9 @ SY92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(150,plain,
! [SV10: $i] :
( ( ( ~ ~ ( v1_xboole_0 @ SV10 ) )
= $true )
| ( ( ~ ! [SY73: $i] :
~ ~ ( ~ ( m1_subset_1 @ SY73 @ ( k1_zfmisc_1 @ SV10 ) )
| ~ ~ ( v1_xboole_0 @ SY73 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(151,plain,
! [SV11: $i] :
( ( ! [SY74: $i] :
~ ( m1_subset_1 @ SY74 @ SV11 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(152,plain,
! [SV12: $i] :
( ( ! [SY75: $i] :
~ ~ ( ~ ( m1_subset_1 @ SY75 @ ( k1_zfmisc_1 @ SV12 ) )
| ~ ( v1_xboole_0 @ SY75 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(153,plain,
! [SV25: $i,SV13: $i] :
( ( ! [SY93: $i,SY94: $i] :
( ~ ~ ( ~ ( m1_subset_1 @ SY93 @ ( k1_zfmisc_1 @ SV13 ) )
| ~ ( m1_subset_1 @ SY94 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV13 @ SV25 ) ) ) )
| ( m1_subset_1 @ ( k8_relset_2 @ SV13 @ SV25 @ SY93 @ SY94 ) @ ( k1_zfmisc_1 @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(154,plain,
! [SV26: $i,SV14: $i] :
( ( ! [SY95: $i,SY96: $i,SY97: $i,SY98: $i] :
( ~ ~ ( ~ ( m1_subset_1 @ SY95 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV14 @ SV26 ) ) ) )
| ~ ( m1_subset_1 @ SY98 @ ( k1_zfmisc_1 @ SY96 ) ) )
| ( m1_subset_1 @ ( a_6_0_relset_2 @ SV14 @ SV26 @ SY95 @ SY96 @ SY97 @ SY98 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SY97 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(155,plain,
! [SV27: $i,SV15: $i] :
( ( ~ ( r2_hidden @ SV15 @ SV27 )
| ( m1_subset_1 @ SV15 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(156,plain,
! [SV28: $i,SV16: $i] :
( ( ~ ( ~ ( ~ ( m1_subset_1 @ SV16 @ ( k1_zfmisc_1 @ SV28 ) )
| ( r1_tarski @ SV16 @ SV28 ) )
| ~ ( ~ ( r1_tarski @ SV16 @ SV28 )
| ( m1_subset_1 @ SV16 @ ( k1_zfmisc_1 @ SV28 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(157,plain,
! [SV18: $i,SV3: $i,SV29: $i] :
( ( ~ ( m1_subset_1 @ SV29 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV3 @ SV18 ) ) )
| ( v1_relat_1 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(158,plain,
! [SV4: $i,SV19: $i] :
( ( ( ~ ( m1_eqrel_1 @ SV19 @ SV4 ) )
= $true )
| ( ( m1_subset_1 @ SV19 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(159,plain,
! [SV20: $i,SV5: $i,SV30: $i] :
( ( ~ ( m2_relset_1 @ SV30 @ SV5 @ SV20 )
| ( m1_subset_1 @ SV30 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV5 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(160,plain,
! [SV21: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ~ ( v1_xboole_0 @ SV6 )
| ~ ~ ( v1_xboole_0 @ SV21 ) ) )
= $true )
| ( ( ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ SV6 @ SV21 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(161,plain,
! [SV22: $i,SV7: $i,SV31: $i] :
( ( ! [SY99: $i] :
( ~ ( m1_subset_1 @ SV31 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV7 @ ( k1_zfmisc_1 @ SV22 ) ) ) )
| ( m1_subset_1 @ ( k4_relset_2 @ SV7 @ SV22 @ SV31 @ SY99 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SV22 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(162,plain,
! [SV8: $i,SV23: $i] :
( ( ( ~ ( m1_subset_1 @ SV23 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SV8 ) ) ) )
= $true )
| ( ( m1_subset_1 @ ( k8_setfam_1 @ SV8 @ SV23 ) @ ( k1_zfmisc_1 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(163,plain,
( ( ! [SY100: $i] :
( ~ ( m1_subset_1 @ SY100 @ ( k1_zfmisc_1 @ sK4_SX0 ) )
| ( m1_subset_1 @ ( a_6_0_relset_2 @ sK1_A @ sK2_SY48 @ sK3_SY53 @ sK4_SX0 @ sK5_SY90 @ SY100 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ sK5_SY90 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[148]) ).
thf(164,plain,
! [SV32: $i,SV24: $i,SV9: $i] :
( ( ~ ~ ( ~ ( r2_hidden @ SV9 @ SV24 )
| ~ ( m1_subset_1 @ SV24 @ ( k1_zfmisc_1 @ SV32 ) ) )
| ( m1_subset_1 @ SV9 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(165,plain,
! [SV10: $i] :
( ( ( ~ ( v1_xboole_0 @ SV10 ) )
= $false )
| ( ( ~ ! [SY73: $i] :
~ ~ ( ~ ( m1_subset_1 @ SY73 @ ( k1_zfmisc_1 @ SV10 ) )
| ~ ~ ( v1_xboole_0 @ SY73 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(166,plain,
! [SV11: $i] :
( ( ~ ( m1_subset_1 @ ( sK6_SY74 @ SV11 ) @ SV11 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[151]) ).
thf(167,plain,
! [SV12: $i] :
( ( ~ ~ ( ~ ( m1_subset_1 @ ( sK7_SY75 @ SV12 ) @ ( k1_zfmisc_1 @ SV12 ) )
| ~ ( v1_xboole_0 @ ( sK7_SY75 @ SV12 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[152]) ).
thf(168,plain,
! [SV25: $i,SV13: $i,SV33: $i] :
( ( ! [SY101: $i] :
( ~ ~ ( ~ ( m1_subset_1 @ SV33 @ ( k1_zfmisc_1 @ SV13 ) )
| ~ ( m1_subset_1 @ SY101 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV13 @ SV25 ) ) ) )
| ( m1_subset_1 @ ( k8_relset_2 @ SV13 @ SV25 @ SV33 @ SY101 ) @ ( k1_zfmisc_1 @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(169,plain,
! [SV26: $i,SV14: $i,SV34: $i] :
( ( ! [SY102: $i,SY103: $i,SY104: $i] :
( ~ ~ ( ~ ( m1_subset_1 @ SV34 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV14 @ SV26 ) ) ) )
| ~ ( m1_subset_1 @ SY104 @ ( k1_zfmisc_1 @ SY102 ) ) )
| ( m1_subset_1 @ ( a_6_0_relset_2 @ SV14 @ SV26 @ SV34 @ SY102 @ SY103 @ SY104 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SY103 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(170,plain,
! [SV27: $i,SV15: $i] :
( ( ( ~ ( r2_hidden @ SV15 @ SV27 ) )
= $true )
| ( ( m1_subset_1 @ SV15 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(171,plain,
! [SV28: $i,SV16: $i] :
( ( ~ ( ~ ( m1_subset_1 @ SV16 @ ( k1_zfmisc_1 @ SV28 ) )
| ( r1_tarski @ SV16 @ SV28 ) )
| ~ ( ~ ( r1_tarski @ SV16 @ SV28 )
| ( m1_subset_1 @ SV16 @ ( k1_zfmisc_1 @ SV28 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(172,plain,
! [SV18: $i,SV3: $i,SV29: $i] :
( ( ( ~ ( m1_subset_1 @ SV29 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV3 @ SV18 ) ) ) )
= $true )
| ( ( v1_relat_1 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(173,plain,
! [SV4: $i,SV19: $i] :
( ( ( m1_eqrel_1 @ SV19 @ SV4 )
= $false )
| ( ( m1_subset_1 @ SV19 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(174,plain,
! [SV20: $i,SV5: $i,SV30: $i] :
( ( ( ~ ( m2_relset_1 @ SV30 @ SV5 @ SV20 ) )
= $true )
| ( ( m1_subset_1 @ SV30 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV5 @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(175,plain,
! [SV21: $i,SV6: $i] :
( ( ( ~ ( ~ ~ ( v1_xboole_0 @ SV6 )
| ~ ~ ( v1_xboole_0 @ SV21 ) ) )
= $false )
| ( ( ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ SV6 @ SV21 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(176,plain,
! [SV35: $i,SV22: $i,SV7: $i,SV31: $i] :
( ( ~ ( m1_subset_1 @ SV31 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV7 @ ( k1_zfmisc_1 @ SV22 ) ) ) )
| ( m1_subset_1 @ ( k4_relset_2 @ SV7 @ SV22 @ SV31 @ SV35 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(177,plain,
! [SV8: $i,SV23: $i] :
( ( ( m1_subset_1 @ SV23 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SV8 ) ) )
= $false )
| ( ( m1_subset_1 @ ( k8_setfam_1 @ SV8 @ SV23 ) @ ( k1_zfmisc_1 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(178,plain,
( ( ~ ( m1_subset_1 @ sK8_SY100 @ ( k1_zfmisc_1 @ sK4_SX0 ) )
| ( m1_subset_1 @ ( a_6_0_relset_2 @ sK1_A @ sK2_SY48 @ sK3_SY53 @ sK4_SX0 @ sK5_SY90 @ sK8_SY100 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ sK5_SY90 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[163]) ).
thf(179,plain,
! [SV32: $i,SV24: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( r2_hidden @ SV9 @ SV24 )
| ~ ( m1_subset_1 @ SV24 @ ( k1_zfmisc_1 @ SV32 ) ) ) )
= $true )
| ( ( m1_subset_1 @ SV9 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(180,plain,
! [SV10: $i] :
( ( ( v1_xboole_0 @ SV10 )
= $true )
| ( ( ~ ! [SY73: $i] :
~ ~ ( ~ ( m1_subset_1 @ SY73 @ ( k1_zfmisc_1 @ SV10 ) )
| ~ ~ ( v1_xboole_0 @ SY73 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(181,plain,
! [SV11: $i] :
( ( m1_subset_1 @ ( sK6_SY74 @ SV11 ) @ SV11 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(182,plain,
! [SV12: $i] :
( ( ~ ( ~ ( m1_subset_1 @ ( sK7_SY75 @ SV12 ) @ ( k1_zfmisc_1 @ SV12 ) )
| ~ ( v1_xboole_0 @ ( sK7_SY75 @ SV12 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(183,plain,
! [SV25: $i,SV36: $i,SV13: $i,SV33: $i] :
( ( ~ ~ ( ~ ( m1_subset_1 @ SV33 @ ( k1_zfmisc_1 @ SV13 ) )
| ~ ( m1_subset_1 @ SV36 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV13 @ SV25 ) ) ) )
| ( m1_subset_1 @ ( k8_relset_2 @ SV13 @ SV25 @ SV33 @ SV36 ) @ ( k1_zfmisc_1 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(184,plain,
! [SV37: $i,SV26: $i,SV14: $i,SV34: $i] :
( ( ! [SY105: $i,SY106: $i] :
( ~ ~ ( ~ ( m1_subset_1 @ SV34 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV14 @ SV26 ) ) ) )
| ~ ( m1_subset_1 @ SY106 @ ( k1_zfmisc_1 @ SV37 ) ) )
| ( m1_subset_1 @ ( a_6_0_relset_2 @ SV14 @ SV26 @ SV34 @ SV37 @ SY105 @ SY106 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SY105 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(185,plain,
! [SV27: $i,SV15: $i] :
( ( ( r2_hidden @ SV15 @ SV27 )
= $false )
| ( ( m1_subset_1 @ SV15 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(186,plain,
! [SV28: $i,SV16: $i] :
( ( ~ ( ~ ( m1_subset_1 @ SV16 @ ( k1_zfmisc_1 @ SV28 ) )
| ( r1_tarski @ SV16 @ SV28 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(187,plain,
! [SV28: $i,SV16: $i] :
( ( ~ ( ~ ( r1_tarski @ SV16 @ SV28 )
| ( m1_subset_1 @ SV16 @ ( k1_zfmisc_1 @ SV28 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(188,plain,
! [SV18: $i,SV3: $i,SV29: $i] :
( ( ( m1_subset_1 @ SV29 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV3 @ SV18 ) ) )
= $false )
| ( ( v1_relat_1 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(189,plain,
! [SV20: $i,SV5: $i,SV30: $i] :
( ( ( m2_relset_1 @ SV30 @ SV5 @ SV20 )
= $false )
| ( ( m1_subset_1 @ SV30 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV5 @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(190,plain,
! [SV21: $i,SV6: $i] :
( ( ( ~ ~ ( v1_xboole_0 @ SV6 )
| ~ ~ ( v1_xboole_0 @ SV21 ) )
= $true )
| ( ( ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ SV6 @ SV21 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(191,plain,
! [SV35: $i,SV22: $i,SV7: $i,SV31: $i] :
( ( ( ~ ( m1_subset_1 @ SV31 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV7 @ ( k1_zfmisc_1 @ SV22 ) ) ) ) )
= $true )
| ( ( m1_subset_1 @ ( k4_relset_2 @ SV7 @ SV22 @ SV31 @ SV35 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(192,plain,
( ( ~ ( m1_subset_1 @ sK8_SY100 @ ( k1_zfmisc_1 @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(193,plain,
( ( m1_subset_1 @ ( a_6_0_relset_2 @ sK1_A @ sK2_SY48 @ sK3_SY53 @ sK4_SX0 @ sK5_SY90 @ sK8_SY100 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ sK5_SY90 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(194,plain,
! [SV32: $i,SV24: $i,SV9: $i] :
( ( ( ~ ( ~ ( r2_hidden @ SV9 @ SV24 )
| ~ ( m1_subset_1 @ SV24 @ ( k1_zfmisc_1 @ SV32 ) ) ) )
= $false )
| ( ( m1_subset_1 @ SV9 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(195,plain,
! [SV10: $i] :
( ( ( ! [SY73: $i] :
~ ~ ( ~ ( m1_subset_1 @ SY73 @ ( k1_zfmisc_1 @ SV10 ) )
| ~ ~ ( v1_xboole_0 @ SY73 ) ) )
= $false )
| ( ( v1_xboole_0 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(196,plain,
! [SV12: $i] :
( ( ~ ( m1_subset_1 @ ( sK7_SY75 @ SV12 ) @ ( k1_zfmisc_1 @ SV12 ) )
| ~ ( v1_xboole_0 @ ( sK7_SY75 @ SV12 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(197,plain,
! [SV25: $i,SV36: $i,SV13: $i,SV33: $i] :
( ( ( ~ ~ ( ~ ( m1_subset_1 @ SV33 @ ( k1_zfmisc_1 @ SV13 ) )
| ~ ( m1_subset_1 @ SV36 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV13 @ SV25 ) ) ) ) )
= $true )
| ( ( m1_subset_1 @ ( k8_relset_2 @ SV13 @ SV25 @ SV33 @ SV36 ) @ ( k1_zfmisc_1 @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(198,plain,
! [SV38: $i,SV37: $i,SV26: $i,SV14: $i,SV34: $i] :
( ( ! [SY107: $i] :
( ~ ~ ( ~ ( m1_subset_1 @ SV34 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV14 @ SV26 ) ) ) )
| ~ ( m1_subset_1 @ SY107 @ ( k1_zfmisc_1 @ SV37 ) ) )
| ( m1_subset_1 @ ( a_6_0_relset_2 @ SV14 @ SV26 @ SV34 @ SV37 @ SV38 @ SY107 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SV38 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(199,plain,
! [SV28: $i,SV16: $i] :
( ( ~ ( m1_subset_1 @ SV16 @ ( k1_zfmisc_1 @ SV28 ) )
| ( r1_tarski @ SV16 @ SV28 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(200,plain,
! [SV28: $i,SV16: $i] :
( ( ~ ( r1_tarski @ SV16 @ SV28 )
| ( m1_subset_1 @ SV16 @ ( k1_zfmisc_1 @ SV28 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(201,plain,
! [SV21: $i,SV6: $i] :
( ( ( ~ ~ ( v1_xboole_0 @ SV6 ) )
= $true )
| ( ( ~ ~ ( v1_xboole_0 @ SV21 ) )
= $true )
| ( ( ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ SV6 @ SV21 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(202,plain,
! [SV35: $i,SV22: $i,SV7: $i,SV31: $i] :
( ( ( m1_subset_1 @ SV31 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV7 @ ( k1_zfmisc_1 @ SV22 ) ) ) )
= $false )
| ( ( m1_subset_1 @ ( k4_relset_2 @ SV7 @ SV22 @ SV31 @ SV35 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(203,plain,
( ( m1_subset_1 @ sK8_SY100 @ ( k1_zfmisc_1 @ sK4_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[192]) ).
thf(204,plain,
! [SV32: $i,SV24: $i,SV9: $i] :
( ( ( ~ ( r2_hidden @ SV9 @ SV24 )
| ~ ( m1_subset_1 @ SV24 @ ( k1_zfmisc_1 @ SV32 ) ) )
= $true )
| ( ( m1_subset_1 @ SV9 @ SV32 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(205,plain,
! [SV10: $i] :
( ( ( ~ ~ ( ~ ( m1_subset_1 @ ( sK9_SY73 @ SV10 ) @ ( k1_zfmisc_1 @ SV10 ) )
| ~ ~ ( v1_xboole_0 @ ( sK9_SY73 @ SV10 ) ) ) )
= $false )
| ( ( v1_xboole_0 @ SV10 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[195]) ).
thf(206,plain,
! [SV12: $i] :
( ( ~ ( m1_subset_1 @ ( sK7_SY75 @ SV12 ) @ ( k1_zfmisc_1 @ SV12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(207,plain,
! [SV12: $i] :
( ( ~ ( v1_xboole_0 @ ( sK7_SY75 @ SV12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(208,plain,
! [SV25: $i,SV36: $i,SV13: $i,SV33: $i] :
( ( ( ~ ( ~ ( m1_subset_1 @ SV33 @ ( k1_zfmisc_1 @ SV13 ) )
| ~ ( m1_subset_1 @ SV36 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV13 @ SV25 ) ) ) ) )
= $false )
| ( ( m1_subset_1 @ ( k8_relset_2 @ SV13 @ SV25 @ SV33 @ SV36 ) @ ( k1_zfmisc_1 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(209,plain,
! [SV38: $i,SV37: $i,SV39: $i,SV26: $i,SV14: $i,SV34: $i] :
( ( ~ ~ ( ~ ( m1_subset_1 @ SV34 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV14 @ SV26 ) ) ) )
| ~ ( m1_subset_1 @ SV39 @ ( k1_zfmisc_1 @ SV37 ) ) )
| ( m1_subset_1 @ ( a_6_0_relset_2 @ SV14 @ SV26 @ SV34 @ SV37 @ SV38 @ SV39 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(210,plain,
! [SV28: $i,SV16: $i] :
( ( ( ~ ( m1_subset_1 @ SV16 @ ( k1_zfmisc_1 @ SV28 ) ) )
= $true )
| ( ( r1_tarski @ SV16 @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(211,plain,
! [SV28: $i,SV16: $i] :
( ( ( ~ ( r1_tarski @ SV16 @ SV28 ) )
= $true )
| ( ( m1_subset_1 @ SV16 @ ( k1_zfmisc_1 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(212,plain,
! [SV21: $i,SV6: $i] :
( ( ( ~ ( v1_xboole_0 @ SV6 ) )
= $false )
| ( ( ~ ~ ( v1_xboole_0 @ SV21 ) )
= $true )
| ( ( ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ SV6 @ SV21 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(213,plain,
! [SV32: $i,SV24: $i,SV9: $i] :
( ( ( ~ ( r2_hidden @ SV9 @ SV24 ) )
= $true )
| ( ( ~ ( m1_subset_1 @ SV24 @ ( k1_zfmisc_1 @ SV32 ) ) )
= $true )
| ( ( m1_subset_1 @ SV9 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(214,plain,
! [SV10: $i] :
( ( ( ~ ( ~ ( m1_subset_1 @ ( sK9_SY73 @ SV10 ) @ ( k1_zfmisc_1 @ SV10 ) )
| ~ ~ ( v1_xboole_0 @ ( sK9_SY73 @ SV10 ) ) ) )
= $true )
| ( ( v1_xboole_0 @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(215,plain,
! [SV12: $i] :
( ( m1_subset_1 @ ( sK7_SY75 @ SV12 ) @ ( k1_zfmisc_1 @ SV12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(216,plain,
! [SV12: $i] :
( ( v1_xboole_0 @ ( sK7_SY75 @ SV12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(217,plain,
! [SV25: $i,SV36: $i,SV13: $i,SV33: $i] :
( ( ( ~ ( m1_subset_1 @ SV33 @ ( k1_zfmisc_1 @ SV13 ) )
| ~ ( m1_subset_1 @ SV36 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV13 @ SV25 ) ) ) )
= $true )
| ( ( m1_subset_1 @ ( k8_relset_2 @ SV13 @ SV25 @ SV33 @ SV36 ) @ ( k1_zfmisc_1 @ SV25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(218,plain,
! [SV38: $i,SV37: $i,SV39: $i,SV26: $i,SV14: $i,SV34: $i] :
( ( ( ~ ~ ( ~ ( m1_subset_1 @ SV34 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV14 @ SV26 ) ) ) )
| ~ ( m1_subset_1 @ SV39 @ ( k1_zfmisc_1 @ SV37 ) ) ) )
= $true )
| ( ( m1_subset_1 @ ( a_6_0_relset_2 @ SV14 @ SV26 @ SV34 @ SV37 @ SV38 @ SV39 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SV38 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(219,plain,
! [SV28: $i,SV16: $i] :
( ( ( m1_subset_1 @ SV16 @ ( k1_zfmisc_1 @ SV28 ) )
= $false )
| ( ( r1_tarski @ SV16 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(220,plain,
! [SV28: $i,SV16: $i] :
( ( ( r1_tarski @ SV16 @ SV28 )
= $false )
| ( ( m1_subset_1 @ SV16 @ ( k1_zfmisc_1 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(221,plain,
! [SV21: $i,SV6: $i] :
( ( ( v1_xboole_0 @ SV6 )
= $true )
| ( ( ~ ~ ( v1_xboole_0 @ SV21 ) )
= $true )
| ( ( ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ SV6 @ SV21 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(222,plain,
! [SV32: $i,SV24: $i,SV9: $i] :
( ( ( r2_hidden @ SV9 @ SV24 )
= $false )
| ( ( ~ ( m1_subset_1 @ SV24 @ ( k1_zfmisc_1 @ SV32 ) ) )
= $true )
| ( ( m1_subset_1 @ SV9 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(223,plain,
! [SV10: $i] :
( ( ( ~ ( m1_subset_1 @ ( sK9_SY73 @ SV10 ) @ ( k1_zfmisc_1 @ SV10 ) )
| ~ ~ ( v1_xboole_0 @ ( sK9_SY73 @ SV10 ) ) )
= $false )
| ( ( v1_xboole_0 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(224,plain,
! [SV25: $i,SV36: $i,SV13: $i,SV33: $i] :
( ( ( ~ ( m1_subset_1 @ SV33 @ ( k1_zfmisc_1 @ SV13 ) ) )
= $true )
| ( ( ~ ( m1_subset_1 @ SV36 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV13 @ SV25 ) ) ) )
= $true )
| ( ( m1_subset_1 @ ( k8_relset_2 @ SV13 @ SV25 @ SV33 @ SV36 ) @ ( k1_zfmisc_1 @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(225,plain,
! [SV38: $i,SV37: $i,SV39: $i,SV26: $i,SV14: $i,SV34: $i] :
( ( ( ~ ( ~ ( m1_subset_1 @ SV34 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV14 @ SV26 ) ) ) )
| ~ ( m1_subset_1 @ SV39 @ ( k1_zfmisc_1 @ SV37 ) ) ) )
= $false )
| ( ( m1_subset_1 @ ( a_6_0_relset_2 @ SV14 @ SV26 @ SV34 @ SV37 @ SV38 @ SV39 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SV38 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(226,plain,
! [SV6: $i,SV21: $i] :
( ( ( ~ ( v1_xboole_0 @ SV21 ) )
= $false )
| ( ( v1_xboole_0 @ SV6 )
= $true )
| ( ( ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ SV6 @ SV21 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(227,plain,
! [SV9: $i,SV32: $i,SV24: $i] :
( ( ( m1_subset_1 @ SV24 @ ( k1_zfmisc_1 @ SV32 ) )
= $false )
| ( ( r2_hidden @ SV9 @ SV24 )
= $false )
| ( ( m1_subset_1 @ SV9 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(228,plain,
! [SV10: $i] :
( ( ( ~ ( m1_subset_1 @ ( sK9_SY73 @ SV10 ) @ ( k1_zfmisc_1 @ SV10 ) ) )
= $false )
| ( ( v1_xboole_0 @ SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[223]) ).
thf(229,plain,
! [SV10: $i] :
( ( ( ~ ~ ( v1_xboole_0 @ ( sK9_SY73 @ SV10 ) ) )
= $false )
| ( ( v1_xboole_0 @ SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[223]) ).
thf(230,plain,
! [SV25: $i,SV36: $i,SV13: $i,SV33: $i] :
( ( ( m1_subset_1 @ SV33 @ ( k1_zfmisc_1 @ SV13 ) )
= $false )
| ( ( ~ ( m1_subset_1 @ SV36 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV13 @ SV25 ) ) ) )
= $true )
| ( ( m1_subset_1 @ ( k8_relset_2 @ SV13 @ SV25 @ SV33 @ SV36 ) @ ( k1_zfmisc_1 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(231,plain,
! [SV38: $i,SV37: $i,SV39: $i,SV26: $i,SV14: $i,SV34: $i] :
( ( ( ~ ( m1_subset_1 @ SV34 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV14 @ SV26 ) ) ) )
| ~ ( m1_subset_1 @ SV39 @ ( k1_zfmisc_1 @ SV37 ) ) )
= $true )
| ( ( m1_subset_1 @ ( a_6_0_relset_2 @ SV14 @ SV26 @ SV34 @ SV37 @ SV38 @ SV39 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SV38 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(232,plain,
! [SV6: $i,SV21: $i] :
( ( ( v1_xboole_0 @ SV21 )
= $true )
| ( ( v1_xboole_0 @ SV6 )
= $true )
| ( ( ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ SV6 @ SV21 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(233,plain,
! [SV10: $i] :
( ( ( m1_subset_1 @ ( sK9_SY73 @ SV10 ) @ ( k1_zfmisc_1 @ SV10 ) )
= $true )
| ( ( v1_xboole_0 @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(234,plain,
! [SV10: $i] :
( ( ( ~ ( v1_xboole_0 @ ( sK9_SY73 @ SV10 ) ) )
= $true )
| ( ( v1_xboole_0 @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(235,plain,
! [SV33: $i,SV25: $i,SV13: $i,SV36: $i] :
( ( ( m1_subset_1 @ SV36 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV13 @ SV25 ) ) )
= $false )
| ( ( m1_subset_1 @ SV33 @ ( k1_zfmisc_1 @ SV13 ) )
= $false )
| ( ( m1_subset_1 @ ( k8_relset_2 @ SV13 @ SV25 @ SV33 @ SV36 ) @ ( k1_zfmisc_1 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(236,plain,
! [SV38: $i,SV37: $i,SV39: $i,SV26: $i,SV14: $i,SV34: $i] :
( ( ( ~ ( m1_subset_1 @ SV34 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV14 @ SV26 ) ) ) ) )
= $true )
| ( ( ~ ( m1_subset_1 @ SV39 @ ( k1_zfmisc_1 @ SV37 ) ) )
= $true )
| ( ( m1_subset_1 @ ( a_6_0_relset_2 @ SV14 @ SV26 @ SV34 @ SV37 @ SV38 @ SV39 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SV38 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(237,plain,
! [SV21: $i,SV6: $i] :
( ( ( v1_xboole_0 @ ( k2_zfmisc_1 @ SV6 @ SV21 ) )
= $false )
| ( ( v1_xboole_0 @ SV6 )
= $true )
| ( ( v1_xboole_0 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(238,plain,
! [SV10: $i] :
( ( ( v1_xboole_0 @ ( sK9_SY73 @ SV10 ) )
= $false )
| ( ( v1_xboole_0 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(239,plain,
! [SV38: $i,SV37: $i,SV39: $i,SV26: $i,SV14: $i,SV34: $i] :
( ( ( m1_subset_1 @ SV34 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV14 @ SV26 ) ) ) )
= $false )
| ( ( ~ ( m1_subset_1 @ SV39 @ ( k1_zfmisc_1 @ SV37 ) ) )
= $true )
| ( ( m1_subset_1 @ ( a_6_0_relset_2 @ SV14 @ SV26 @ SV34 @ SV37 @ SV38 @ SV39 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SV38 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(240,plain,
! [SV38: $i,SV26: $i,SV14: $i,SV34: $i,SV37: $i,SV39: $i] :
( ( ( m1_subset_1 @ SV39 @ ( k1_zfmisc_1 @ SV37 ) )
= $false )
| ( ( m1_subset_1 @ SV34 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ SV14 @ SV26 ) ) ) )
= $false )
| ( ( m1_subset_1 @ ( a_6_0_relset_2 @ SV14 @ SV26 @ SV34 @ SV37 @ SV38 @ SV39 ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ SV38 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(241,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[84,240,238,237,235,233,227,220,219,216,215,203,202,193,189,188,185,181,177,173,141,140,106,94,93,91,88,86,85]) ).
thf(242,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[241]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU435+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.17 % Computer : n002.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Oct 6 15:25:57 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.26
% 0.10/0.26 No.of.Axioms: 23
% 0.10/0.26
% 0.10/0.26 Length.of.Defs: 0
% 0.10/0.26
% 0.10/0.26 Contains.Choice.Funs: false
% 0.10/0.26 ......
% 0.10/0.26
% 0.10/0.26 ********************************
% 0.10/0.26 * All subproblems solved! *
% 0.10/0.26 ********************************
% 0.10/0.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:24,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:241,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.26
% 0.10/0.26 %**** Beginning of derivation protocol ****
% 0.10/0.26 % SZS output start CNFRefutation
% See solution above
% 0.10/0.26
% 0.10/0.26 %**** End of derivation protocol ****
% 0.10/0.26 %**** no. of clauses in derivation: 215 ****
% 0.10/0.26 %**** clause counter: 241 ****
% 0.10/0.26
% 0.10/0.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:24,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:241,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------