%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ALG227+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 10:08:31 AM UTC 2026
% Result : Theorem 0.64s 0.42s
% Output : CNFRefutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 23
% Syntax : Number of formulae : 259 ( 143 unt; 0 typ; 0 def)
% Number of atoms : 1748 ( 686 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 2969 ( 847 ~; 493 |; 21 &;1541 @)
% ( 9 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 9 con; 0-3 aty)
% Number of variables : 512 ( 0 ^; 494 !; 18 ?; 512 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a_2_0_closure3,type,
a_2_0_closure3: $i > $i > $i ).
thf(tp_k1_closure3,type,
k1_closure3: $i > $i > $i ).
thf(tp_k1_funct_1,type,
k1_funct_1: $i > $i > $i ).
thf(tp_k1_xboole_0,type,
k1_xboole_0: $i ).
thf(tp_m1_pboole,type,
m1_pboole: $i > $i > $o ).
thf(tp_m1_subset_1,type,
m1_subset_1: $i > $i > $o ).
thf(tp_r2_hidden,type,
r2_hidden: $i > $i > $o ).
thf(tp_sK10_SY56,type,
sK10_SY56: $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SX0,type,
sK5_SX0: $i ).
thf(tp_sK6_SY39,type,
sK6_SY39: $i > $i ).
thf(tp_sK7_SY40,type,
sK7_SY40: $i > $i ).
thf(tp_sK8_SY55,type,
sK8_SY55: $i ).
thf(tp_sK9_SY51,type,
sK9_SY51: $i > $i > $i ).
thf(tp_v1_finset_1,type,
v1_finset_1: $i > $o ).
thf(tp_v1_fraenkel,type,
v1_fraenkel: $i > $o ).
thf(tp_v1_funct_1,type,
v1_funct_1: $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_v2_funct_1,type,
v2_funct_1: $i > $o ).
thf(1,axiom,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(3,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
<=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(8,axiom,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(10,axiom,
? [A: $i] : ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(12,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_pboole @ C @ B ) )
=> ( ( r2_hidden @ A @ ( a_2_0_closure3 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ( ( k1_funct_1 @ C @ D )
!= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_closure3) ).
thf(15,axiom,
v1_xboole_0 @ k1_xboole_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(16,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(17,axiom,
! [A: $i] :
? [B: $i] : ( m1_pboole @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_pboole) ).
thf(18,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(20,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(21,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_funct_1) ).
thf(22,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_closure3) ).
thf(23,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( C
= ( k1_closure3 @ A @ B ) )
<=> ( C
= ( a_2_0_closure3 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_closure3) ).
thf(25,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(26,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(27,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_fraenkel @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_closure2) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(29,conjecture,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ~ ( r2_hidden @ C @ ( k1_closure3 @ A @ B ) )
=> ( ( k1_funct_1 @ B @ C )
= k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_closure3) ).
thf(30,negated_conjecture,
( ( ! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ~ ( r2_hidden @ C @ ( k1_closure3 @ A @ B ) )
=> ( ( k1_funct_1 @ B @ C )
= k1_xboole_0 ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[29]) ).
thf(31,plain,
( ( ! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ~ ( r2_hidden @ C @ ( k1_closure3 @ A @ B ) )
=> ( ( k1_funct_1 @ B @ C )
= k1_xboole_0 ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[30]) ).
thf(32,plain,
( ( ! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(33,plain,
( ( ! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(34,plain,
( ( ! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(35,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
<=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(36,plain,
( ( ! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(37,plain,
( ( ! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(38,plain,
( ( ? [A: $i] :
~ ( v1_xboole_0 @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(39,plain,
( ( ? [A: $i] : ( v1_xboole_0 @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(40,plain,
( ( ? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(41,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_pboole @ C @ B ) )
=> ( ( r2_hidden @ A @ ( a_2_0_closure3 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ( ( k1_funct_1 @ C @ D )
!= k1_xboole_0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(42,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(43,plain,
( ( ! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(44,plain,
( ( ! [A: $i] :
? [B: $i] : ( m1_pboole @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(45,plain,
$true = $true,
inference(unfold_def,[status(thm)],[18]) ).
thf(46,plain,
$true = $true,
inference(unfold_def,[status(thm)],[20]) ).
thf(47,plain,
$true = $true,
inference(unfold_def,[status(thm)],[21]) ).
thf(48,plain,
$true = $true,
inference(unfold_def,[status(thm)],[22]) ).
thf(49,plain,
( ( ! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( C
= ( k1_closure3 @ A @ B ) )
<=> ( C
= ( a_2_0_closure3 @ A @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(50,plain,
( ( ! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(51,plain,
( ( ! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(52,plain,
( ( ! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_fraenkel @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(53,plain,
( ( ! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(54,plain,
( ( ~ ( v1_xboole_0 @ sK1_A )
=> ! [SY34: $i] :
( ( m1_pboole @ SY34 @ sK1_A )
=> ! [SY35: $i] :
( ( m1_subset_1 @ SY35 @ sK1_A )
=> ( ~ ( r2_hidden @ SY35 @ ( k1_closure3 @ sK1_A @ SY34 ) )
=> ( ( k1_funct_1 @ SY34 @ SY35 )
= k1_xboole_0 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[31]) ).
thf(55,plain,
( ( ~ ( v1_xboole_0 @ sK1_A ) )
= $true ),
inference(standard_cnf,[status(thm)],[54]) ).
thf(56,plain,
( ( ! [SY34: $i] :
( ( m1_pboole @ SY34 @ sK1_A )
=> ! [SY35: $i] :
( ( m1_subset_1 @ SY35 @ sK1_A )
=> ( ~ ( r2_hidden @ SY35 @ ( k1_closure3 @ sK1_A @ SY34 ) )
=> ( ( k1_funct_1 @ SY34 @ SY35 )
= k1_xboole_0 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[54]) ).
thf(57,plain,
( ( ~ ! [SY34: $i] :
( ( m1_pboole @ SY34 @ sK1_A )
=> ! [SY35: $i] :
( ( m1_subset_1 @ SY35 @ sK1_A )
=> ( ~ ( r2_hidden @ SY35 @ ( k1_closure3 @ sK1_A @ SY34 ) )
=> ( ( k1_funct_1 @ SY34 @ SY35 )
= k1_xboole_0 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[56]) ).
thf(58,plain,
( ( ! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(59,plain,
( ( ! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_fraenkel @ A ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(60,plain,
( ( ! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(61,plain,
( ( ! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(62,plain,
( ( ! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_pboole @ B @ A )
=> ! [C: $i] :
( ( C
= ( k1_closure3 @ A @ B ) )
<=> ( C
= ( a_2_0_closure3 @ A @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(63,plain,
$true = $true,
inference(copy,[status(thm)],[48]) ).
thf(64,plain,
$true = $true,
inference(copy,[status(thm)],[47]) ).
thf(65,plain,
$true = $true,
inference(copy,[status(thm)],[46]) ).
thf(66,plain,
$true = $true,
inference(copy,[status(thm)],[45]) ).
thf(67,plain,
( ( ! [A: $i] :
? [B: $i] : ( m1_pboole @ B @ A ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(68,plain,
( ( ! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(69,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(70,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_pboole @ C @ B ) )
=> ( ( r2_hidden @ A @ ( a_2_0_closure3 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ B )
& ( A = D )
& ( ( k1_funct_1 @ C @ D )
!= k1_xboole_0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(71,plain,
( ( ? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(72,plain,
( ( ? [A: $i] : ( v1_xboole_0 @ A ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(73,plain,
( ( ? [A: $i] :
~ ( v1_xboole_0 @ A ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(74,plain,
( ( ! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(75,plain,
( ( ! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(76,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
<=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(77,plain,
( ( ! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(78,plain,
( ( ! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(79,plain,
( ( ! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(80,plain,
( ( ~ ( v1_xboole_0 @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(81,plain,
( ( ~ ! [SY34: $i] :
( ( m1_pboole @ SY34 @ sK1_A )
=> ! [SY35: $i] :
( ( m1_subset_1 @ SY35 @ sK1_A )
=> ( ~ ( r2_hidden @ SY35 @ ( k1_closure3 @ sK1_A @ SY34 ) )
=> ( ( k1_funct_1 @ SY34 @ SY35 )
= k1_xboole_0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(82,plain,
( ( ~ ! [SX0: $i] :
~ ( v1_xboole_0 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(83,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( v1_xboole_0 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(84,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( v1_xboole_0 @ SX0 )
| ~ ( v1_finset_1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(85,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( m1_subset_1 @ SX0 @ SX1 )
| ( v1_xboole_0 @ SX1 )
| ( r2_hidden @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(86,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( r2_hidden @ SX0 @ SX1 )
| ( m1_subset_1 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(87,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( r2_hidden @ SX0 @ SX1 )
| ~ ( r2_hidden @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(88,plain,
( ( ! [SX0: $i] :
( ~ ( v1_xboole_0 @ SX0 )
| ( v1_funct_1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(89,plain,
( ( ! [SX0: $i] :
( ~ ( v1_xboole_0 @ SX0 )
| ( v1_fraenkel @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(90,plain,
( ( ! [SX0: $i] :
( ~ ( v1_xboole_0 @ SX0 )
| ( v1_finset_1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(91,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( m1_pboole @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(92,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( m1_subset_1 @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(93,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( r2_hidden @ SX2 @ SX0 )
| ( r2_hidden @ SX2 @ SX1 ) )
| ~ ( ~ ( r2_hidden @ SX2 @ SX1 )
| ( r2_hidden @ SX2 @ SX0 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(94,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( v1_xboole_0 @ SX1 )
| ~ ( m1_pboole @ SX2 @ SX1 ) )
| ~ ( ~ ( ~ ( r2_hidden @ SX0 @ ( a_2_0_closure3 @ SX1 @ SX2 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SX3 @ SX1 )
| ( SX0 != SX3 ) )
| ~ ( ( ( k1_funct_1 @ SX2 @ SX3 )
!= k1_xboole_0 ) ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SX3 @ SX1 )
| ( SX0 != SX3 ) )
| ~ ( ( ( k1_funct_1 @ SX2 @ SX3 )
!= k1_xboole_0 ) ) )
| ( r2_hidden @ SX0 @ ( a_2_0_closure3 @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(95,plain,
( ( ! [SX0: $i] :
( ~ ( v1_xboole_0 @ SX0 )
| ( SX0 = k1_xboole_0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(96,plain,
( ( ~ ! [SX0: $i] :
( ~ ( m1_pboole @ SX0 @ sK1_A )
| ! [SX1: $i] :
( ~ ( m1_subset_1 @ SX1 @ sK1_A )
| ~ ~ ( r2_hidden @ SX1 @ ( k1_closure3 @ sK1_A @ SX0 ) )
| ( ( k1_funct_1 @ SX0 @ SX1 )
= k1_xboole_0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(97,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( r2_hidden @ SX0 @ SX1 )
| ~ ( v1_xboole_0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(98,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ~ ( ~ ( v1_xboole_0 @ SX0 )
| ~ ( ( SX0 != SX1 ) ) )
| ~ ( v1_xboole_0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(99,plain,
( ( ! [SX0: $i] :
( ~ ~ ( v1_xboole_0 @ SX0 )
| ! [SX1: $i] :
( ~ ( m1_pboole @ SX1 @ SX0 )
| ! [SX2: $i] :
~ ( ~ ( ( SX2
!= ( k1_closure3 @ SX0 @ SX1 ) )
| ( SX2
= ( a_2_0_closure3 @ SX0 @ SX1 ) ) )
| ~ ( ( SX2
!= ( a_2_0_closure3 @ SX0 @ SX1 ) )
| ( SX2
= ( k1_closure3 @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(100,plain,
( ( v1_xboole_0 @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(101,plain,
( ( ! [SX0: $i] :
~ ( v1_xboole_0 @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(102,plain,
( ( ! [SX0: $i] :
~ ~ ( v1_xboole_0 @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(103,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( v1_xboole_0 @ SX0 )
| ~ ( v1_finset_1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(104,plain,
! [SV1: $i] :
( ( ! [SY36: $i] :
( ~ ( m1_subset_1 @ SV1 @ SY36 )
| ( v1_xboole_0 @ SY36 )
| ( r2_hidden @ SV1 @ SY36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(105,plain,
! [SV2: $i] :
( ( ! [SY37: $i] :
( ~ ( r2_hidden @ SV2 @ SY37 )
| ( m1_subset_1 @ SV2 @ SY37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(106,plain,
! [SV3: $i] :
( ( ! [SY38: $i] :
( ~ ( r2_hidden @ SV3 @ SY38 )
| ~ ( r2_hidden @ SY38 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(107,plain,
! [SV4: $i] :
( ( ~ ( v1_xboole_0 @ SV4 )
| ( v1_funct_1 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(108,plain,
! [SV5: $i] :
( ( ~ ( v1_xboole_0 @ SV5 )
| ( v1_fraenkel @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(109,plain,
! [SV6: $i] :
( ( ~ ( v1_xboole_0 @ SV6 )
| ( v1_finset_1 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(110,plain,
! [SV7: $i] :
( ( ~ ! [SY39: $i] :
~ ( m1_pboole @ SY39 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(111,plain,
! [SV8: $i] :
( ( ~ ! [SY40: $i] :
~ ( m1_subset_1 @ SY40 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(112,plain,
! [SV9: $i] :
( ( ! [SY41: $i] :
( ~ ! [SY42: $i] :
~ ( ~ ( ~ ( r2_hidden @ SY42 @ SV9 )
| ( r2_hidden @ SY42 @ SY41 ) )
| ~ ( ~ ( r2_hidden @ SY42 @ SY41 )
| ( r2_hidden @ SY42 @ SV9 ) ) )
| ( SV9 = SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(113,plain,
! [SV10: $i] :
( ( ! [SY43: $i,SY44: $i] :
( ~ ~ ( ~ ~ ( v1_xboole_0 @ SY43 )
| ~ ( m1_pboole @ SY44 @ SY43 ) )
| ~ ( ~ ( ~ ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SY43 @ SY44 ) )
| ~ ! [SY45: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY45 @ SY43 )
| ( SV10 != SY45 ) )
| ~ ( ( ( k1_funct_1 @ SY44 @ SY45 )
!= k1_xboole_0 ) ) ) )
| ~ ( ~ ~ ! [SY46: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY46 @ SY43 )
| ( SV10 != SY46 ) )
| ~ ( ( ( k1_funct_1 @ SY44 @ SY46 )
!= k1_xboole_0 ) ) )
| ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SY43 @ SY44 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(114,plain,
! [SV11: $i] :
( ( ~ ( v1_xboole_0 @ SV11 )
| ( SV11 = k1_xboole_0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(115,plain,
( ( ! [SX0: $i] :
( ~ ( m1_pboole @ SX0 @ sK1_A )
| ! [SX1: $i] :
( ~ ( m1_subset_1 @ SX1 @ sK1_A )
| ~ ~ ( r2_hidden @ SX1 @ ( k1_closure3 @ sK1_A @ SX0 ) )
| ( ( k1_funct_1 @ SX0 @ SX1 )
= k1_xboole_0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(116,plain,
! [SV12: $i] :
( ( ! [SY47: $i] :
~ ~ ( ~ ( r2_hidden @ SV12 @ SY47 )
| ~ ( v1_xboole_0 @ SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(117,plain,
! [SV13: $i] :
( ( ! [SY48: $i] :
~ ~ ( ~ ~ ( ~ ( v1_xboole_0 @ SV13 )
| ~ ( ( SV13 != SY48 ) ) )
| ~ ( v1_xboole_0 @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(118,plain,
! [SV14: $i] :
( ( ~ ~ ( v1_xboole_0 @ SV14 )
| ! [SY49: $i] :
( ~ ( m1_pboole @ SY49 @ SV14 )
| ! [SY50: $i] :
~ ( ~ ( ( SY50
!= ( k1_closure3 @ SV14 @ SY49 ) )
| ( SY50
= ( a_2_0_closure3 @ SV14 @ SY49 ) ) )
| ~ ( ( SY50
!= ( a_2_0_closure3 @ SV14 @ SY49 ) )
| ( SY50
= ( k1_closure3 @ SV14 @ SY49 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(119,plain,
( ( ~ ( v1_xboole_0 @ sK2_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[101]) ).
thf(120,plain,
( ( ~ ~ ( v1_xboole_0 @ sK3_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[102]) ).
thf(121,plain,
( ( ~ ~ ( ~ ~ ( v1_xboole_0 @ sK4_SX0 )
| ~ ( v1_finset_1 @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[103]) ).
thf(122,plain,
! [SV15: $i,SV1: $i] :
( ( ~ ( m1_subset_1 @ SV1 @ SV15 )
| ( v1_xboole_0 @ SV15 )
| ( r2_hidden @ SV1 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(123,plain,
! [SV16: $i,SV2: $i] :
( ( ~ ( r2_hidden @ SV2 @ SV16 )
| ( m1_subset_1 @ SV2 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(124,plain,
! [SV17: $i,SV3: $i] :
( ( ~ ( r2_hidden @ SV3 @ SV17 )
| ~ ( r2_hidden @ SV17 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(125,plain,
! [SV4: $i] :
( ( ( ~ ( v1_xboole_0 @ SV4 ) )
= $true )
| ( ( v1_funct_1 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(126,plain,
! [SV5: $i] :
( ( ( ~ ( v1_xboole_0 @ SV5 ) )
= $true )
| ( ( v1_fraenkel @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(127,plain,
! [SV6: $i] :
( ( ( ~ ( v1_xboole_0 @ SV6 ) )
= $true )
| ( ( v1_finset_1 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(128,plain,
! [SV7: $i] :
( ( ! [SY39: $i] :
~ ( m1_pboole @ SY39 @ SV7 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(129,plain,
! [SV8: $i] :
( ( ! [SY40: $i] :
~ ( m1_subset_1 @ SY40 @ SV8 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(130,plain,
! [SV18: $i,SV9: $i] :
( ( ~ ! [SY51: $i] :
~ ( ~ ( ~ ( r2_hidden @ SY51 @ SV9 )
| ( r2_hidden @ SY51 @ SV18 ) )
| ~ ( ~ ( r2_hidden @ SY51 @ SV18 )
| ( r2_hidden @ SY51 @ SV9 ) ) )
| ( SV9 = SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(131,plain,
! [SV10: $i,SV19: $i] :
( ( ! [SY52: $i] :
( ~ ~ ( ~ ~ ( v1_xboole_0 @ SV19 )
| ~ ( m1_pboole @ SY52 @ SV19 ) )
| ~ ( ~ ( ~ ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SY52 ) )
| ~ ! [SY53: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY53 @ SV19 )
| ( SV10 != SY53 ) )
| ~ ( ( ( k1_funct_1 @ SY52 @ SY53 )
!= k1_xboole_0 ) ) ) )
| ~ ( ~ ~ ! [SY54: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY54 @ SV19 )
| ( SV10 != SY54 ) )
| ~ ( ( ( k1_funct_1 @ SY52 @ SY54 )
!= k1_xboole_0 ) ) )
| ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SY52 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(132,plain,
! [SV11: $i] :
( ( ( ~ ( v1_xboole_0 @ SV11 ) )
= $true )
| ( ( SV11 = k1_xboole_0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(133,plain,
( ( ~ ( m1_pboole @ sK5_SX0 @ sK1_A )
| ! [SY55: $i] :
( ~ ( m1_subset_1 @ SY55 @ sK1_A )
| ~ ~ ( r2_hidden @ SY55 @ ( k1_closure3 @ sK1_A @ sK5_SX0 ) )
| ( ( k1_funct_1 @ sK5_SX0 @ SY55 )
= k1_xboole_0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[115]) ).
thf(134,plain,
! [SV20: $i,SV12: $i] :
( ( ~ ~ ( ~ ( r2_hidden @ SV12 @ SV20 )
| ~ ( v1_xboole_0 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(135,plain,
! [SV21: $i,SV13: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( v1_xboole_0 @ SV13 )
| ~ ( ( SV13 != SV21 ) ) )
| ~ ( v1_xboole_0 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(136,plain,
! [SV14: $i] :
( ( ( ~ ~ ( v1_xboole_0 @ SV14 ) )
= $true )
| ( ( ! [SY49: $i] :
( ~ ( m1_pboole @ SY49 @ SV14 )
| ! [SY50: $i] :
~ ( ~ ( ( SY50
!= ( k1_closure3 @ SV14 @ SY49 ) )
| ( SY50
= ( a_2_0_closure3 @ SV14 @ SY49 ) ) )
| ~ ( ( SY50
!= ( a_2_0_closure3 @ SV14 @ SY49 ) )
| ( SY50
= ( k1_closure3 @ SV14 @ SY49 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(137,plain,
( ( v1_xboole_0 @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(138,plain,
( ( ~ ( v1_xboole_0 @ sK3_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(139,plain,
( ( ~ ( ~ ~ ( v1_xboole_0 @ sK4_SX0 )
| ~ ( v1_finset_1 @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(140,plain,
! [SV15: $i,SV1: $i] :
( ( ( ~ ( m1_subset_1 @ SV1 @ SV15 ) )
= $true )
| ( ( ( v1_xboole_0 @ SV15 )
| ( r2_hidden @ SV1 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(141,plain,
! [SV16: $i,SV2: $i] :
( ( ( ~ ( r2_hidden @ SV2 @ SV16 ) )
= $true )
| ( ( m1_subset_1 @ SV2 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(142,plain,
! [SV17: $i,SV3: $i] :
( ( ( ~ ( r2_hidden @ SV3 @ SV17 ) )
= $true )
| ( ( ~ ( r2_hidden @ SV17 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(143,plain,
! [SV4: $i] :
( ( ( v1_xboole_0 @ SV4 )
= $false )
| ( ( v1_funct_1 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(144,plain,
! [SV5: $i] :
( ( ( v1_xboole_0 @ SV5 )
= $false )
| ( ( v1_fraenkel @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(145,plain,
! [SV6: $i] :
( ( ( v1_xboole_0 @ SV6 )
= $false )
| ( ( v1_finset_1 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(146,plain,
! [SV7: $i] :
( ( ~ ( m1_pboole @ ( sK6_SY39 @ SV7 ) @ SV7 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[128]) ).
thf(147,plain,
! [SV8: $i] :
( ( ~ ( m1_subset_1 @ ( sK7_SY40 @ SV8 ) @ SV8 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[129]) ).
thf(148,plain,
! [SV18: $i,SV9: $i] :
( ( ( ~ ! [SY51: $i] :
~ ( ~ ( ~ ( r2_hidden @ SY51 @ SV9 )
| ( r2_hidden @ SY51 @ SV18 ) )
| ~ ( ~ ( r2_hidden @ SY51 @ SV18 )
| ( r2_hidden @ SY51 @ SV9 ) ) ) )
= $true )
| ( ( SV9 = SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(149,plain,
! [SV10: $i,SV22: $i,SV19: $i] :
( ( ~ ~ ( ~ ~ ( v1_xboole_0 @ SV19 )
| ~ ( m1_pboole @ SV22 @ SV19 ) )
| ~ ( ~ ( ~ ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
| ~ ! [SY56: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY56 @ SV19 )
| ( SV10 != SY56 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SY56 )
!= k1_xboole_0 ) ) ) )
| ~ ( ~ ~ ! [SY57: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY57 @ SV19 )
| ( SV10 != SY57 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SY57 )
!= k1_xboole_0 ) ) )
| ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(150,plain,
! [SV11: $i] :
( ( ( v1_xboole_0 @ SV11 )
= $false )
| ( ( SV11 = k1_xboole_0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(151,plain,
( ( ~ ( m1_pboole @ sK5_SX0 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(152,plain,
( ( ! [SY55: $i] :
( ~ ( m1_subset_1 @ SY55 @ sK1_A )
| ~ ~ ( r2_hidden @ SY55 @ ( k1_closure3 @ sK1_A @ sK5_SX0 ) )
| ( ( k1_funct_1 @ sK5_SX0 @ SY55 )
= k1_xboole_0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(153,plain,
! [SV20: $i,SV12: $i] :
( ( ~ ( ~ ( r2_hidden @ SV12 @ SV20 )
| ~ ( v1_xboole_0 @ SV20 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(154,plain,
! [SV21: $i,SV13: $i] :
( ( ~ ( ~ ~ ( ~ ( v1_xboole_0 @ SV13 )
| ~ ( ( SV13 != SV21 ) ) )
| ~ ( v1_xboole_0 @ SV21 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(155,plain,
! [SV14: $i] :
( ( ( ~ ( v1_xboole_0 @ SV14 ) )
= $false )
| ( ( ! [SY49: $i] :
( ~ ( m1_pboole @ SY49 @ SV14 )
| ! [SY50: $i] :
~ ( ~ ( ( SY50
!= ( k1_closure3 @ SV14 @ SY49 ) )
| ( SY50
= ( a_2_0_closure3 @ SV14 @ SY49 ) ) )
| ~ ( ( SY50
!= ( a_2_0_closure3 @ SV14 @ SY49 ) )
| ( SY50
= ( k1_closure3 @ SV14 @ SY49 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(156,plain,
( ( v1_xboole_0 @ sK3_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(157,plain,
( ( ~ ~ ( v1_xboole_0 @ sK4_SX0 )
| ~ ( v1_finset_1 @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(158,plain,
! [SV15: $i,SV1: $i] :
( ( ( m1_subset_1 @ SV1 @ SV15 )
= $false )
| ( ( ( v1_xboole_0 @ SV15 )
| ( r2_hidden @ SV1 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(159,plain,
! [SV16: $i,SV2: $i] :
( ( ( r2_hidden @ SV2 @ SV16 )
= $false )
| ( ( m1_subset_1 @ SV2 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(160,plain,
! [SV17: $i,SV3: $i] :
( ( ( r2_hidden @ SV3 @ SV17 )
= $false )
| ( ( ~ ( r2_hidden @ SV17 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(161,plain,
! [SV7: $i] :
( ( m1_pboole @ ( sK6_SY39 @ SV7 ) @ SV7 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(162,plain,
! [SV8: $i] :
( ( m1_subset_1 @ ( sK7_SY40 @ SV8 ) @ SV8 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(163,plain,
! [SV18: $i,SV9: $i] :
( ( ( ! [SY51: $i] :
~ ( ~ ( ~ ( r2_hidden @ SY51 @ SV9 )
| ( r2_hidden @ SY51 @ SV18 ) )
| ~ ( ~ ( r2_hidden @ SY51 @ SV18 )
| ( r2_hidden @ SY51 @ SV9 ) ) ) )
= $false )
| ( ( SV9 = SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(164,plain,
! [SV10: $i,SV22: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ~ ( v1_xboole_0 @ SV19 )
| ~ ( m1_pboole @ SV22 @ SV19 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
| ~ ! [SY56: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY56 @ SV19 )
| ( SV10 != SY56 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SY56 )
!= k1_xboole_0 ) ) ) )
| ~ ( ~ ~ ! [SY57: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY57 @ SV19 )
| ( SV10 != SY57 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SY57 )
!= k1_xboole_0 ) ) )
| ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(165,plain,
( ( m1_pboole @ sK5_SX0 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(166,plain,
( ( ~ ( m1_subset_1 @ sK8_SY55 @ sK1_A )
| ~ ~ ( r2_hidden @ sK8_SY55 @ ( k1_closure3 @ sK1_A @ sK5_SX0 ) )
| ( ( k1_funct_1 @ sK5_SX0 @ sK8_SY55 )
= k1_xboole_0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[152]) ).
thf(167,plain,
! [SV20: $i,SV12: $i] :
( ( ~ ( r2_hidden @ SV12 @ SV20 )
| ~ ( v1_xboole_0 @ SV20 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(168,plain,
! [SV21: $i,SV13: $i] :
( ( ~ ~ ( ~ ( v1_xboole_0 @ SV13 )
| ~ ( ( SV13 != SV21 ) ) )
| ~ ( v1_xboole_0 @ SV21 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(169,plain,
! [SV14: $i] :
( ( ( v1_xboole_0 @ SV14 )
= $true )
| ( ( ! [SY49: $i] :
( ~ ( m1_pboole @ SY49 @ SV14 )
| ! [SY50: $i] :
~ ( ~ ( ( SY50
!= ( k1_closure3 @ SV14 @ SY49 ) )
| ( SY50
= ( a_2_0_closure3 @ SV14 @ SY49 ) ) )
| ~ ( ( SY50
!= ( a_2_0_closure3 @ SV14 @ SY49 ) )
| ( SY50
= ( k1_closure3 @ SV14 @ SY49 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[155]) ).
thf(170,plain,
( ( ~ ~ ( v1_xboole_0 @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(171,plain,
( ( ~ ( v1_finset_1 @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(172,plain,
! [SV1: $i,SV15: $i] :
( ( ( v1_xboole_0 @ SV15 )
= $true )
| ( ( r2_hidden @ SV1 @ SV15 )
= $true )
| ( ( m1_subset_1 @ SV1 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(173,plain,
! [SV3: $i,SV17: $i] :
( ( ( r2_hidden @ SV17 @ SV3 )
= $false )
| ( ( r2_hidden @ SV3 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(174,plain,
! [SV9: $i,SV18: $i] :
( ( ( ~ ( ~ ( ~ ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV9 )
| ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV18 ) )
| ~ ( ~ ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV18 )
| ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV9 ) ) ) )
= $false )
| ( ( SV9 = SV18 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[163]) ).
thf(175,plain,
! [SV10: $i,SV22: $i,SV19: $i] :
( ( ( ~ ( ~ ~ ( v1_xboole_0 @ SV19 )
| ~ ( m1_pboole @ SV22 @ SV19 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
| ~ ! [SY56: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY56 @ SV19 )
| ( SV10 != SY56 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SY56 )
!= k1_xboole_0 ) ) ) )
| ~ ( ~ ~ ! [SY57: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY57 @ SV19 )
| ( SV10 != SY57 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SY57 )
!= k1_xboole_0 ) ) )
| ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(176,plain,
( ( ~ ( m1_subset_1 @ sK8_SY55 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(177,plain,
( ( ~ ~ ( r2_hidden @ sK8_SY55 @ ( k1_closure3 @ sK1_A @ sK5_SX0 ) )
| ( ( k1_funct_1 @ sK5_SX0 @ sK8_SY55 )
= k1_xboole_0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(178,plain,
! [SV20: $i,SV12: $i] :
( ( ( ~ ( r2_hidden @ SV12 @ SV20 ) )
= $true )
| ( ( ~ ( v1_xboole_0 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(179,plain,
! [SV21: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( v1_xboole_0 @ SV13 )
| ~ ( ( SV13 != SV21 ) ) ) )
= $true )
| ( ( ~ ( v1_xboole_0 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(180,plain,
! [SV14: $i,SV23: $i] :
( ( ( ~ ( m1_pboole @ SV23 @ SV14 )
| ! [SY58: $i] :
~ ( ~ ( ( SY58
!= ( k1_closure3 @ SV14 @ SV23 ) )
| ( SY58
= ( a_2_0_closure3 @ SV14 @ SV23 ) ) )
| ~ ( ( SY58
!= ( a_2_0_closure3 @ SV14 @ SV23 ) )
| ( SY58
= ( k1_closure3 @ SV14 @ SV23 ) ) ) ) )
= $true )
| ( ( v1_xboole_0 @ SV14 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(181,plain,
( ( ~ ( v1_xboole_0 @ sK4_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(182,plain,
( ( v1_finset_1 @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(183,plain,
! [SV9: $i,SV18: $i] :
( ( ( ~ ( ~ ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV9 )
| ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV18 ) )
| ~ ( ~ ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV18 )
| ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV9 ) ) )
= $true )
| ( ( SV9 = SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(184,plain,
! [SV10: $i,SV22: $i,SV19: $i] :
( ( ( ~ ~ ( v1_xboole_0 @ SV19 )
| ~ ( m1_pboole @ SV22 @ SV19 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
| ~ ! [SY56: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY56 @ SV19 )
| ( SV10 != SY56 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SY56 )
!= k1_xboole_0 ) ) ) )
| ~ ( ~ ~ ! [SY57: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY57 @ SV19 )
| ( SV10 != SY57 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SY57 )
!= k1_xboole_0 ) ) )
| ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(185,plain,
( ( m1_subset_1 @ sK8_SY55 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(186,plain,
( ( ~ ~ ( r2_hidden @ sK8_SY55 @ ( k1_closure3 @ sK1_A @ sK5_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(187,plain,
( ( ( k1_funct_1 @ sK5_SX0 @ sK8_SY55 )
= k1_xboole_0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(188,plain,
! [SV20: $i,SV12: $i] :
( ( ( r2_hidden @ SV12 @ SV20 )
= $false )
| ( ( ~ ( v1_xboole_0 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(189,plain,
! [SV21: $i,SV13: $i] :
( ( ( ~ ( ~ ( v1_xboole_0 @ SV13 )
| ~ ( ( SV13 != SV21 ) ) ) )
= $false )
| ( ( ~ ( v1_xboole_0 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(190,plain,
! [SV14: $i,SV23: $i] :
( ( ( ~ ( m1_pboole @ SV23 @ SV14 ) )
= $true )
| ( ( ! [SY58: $i] :
~ ( ~ ( ( SY58
!= ( k1_closure3 @ SV14 @ SV23 ) )
| ( SY58
= ( a_2_0_closure3 @ SV14 @ SV23 ) ) )
| ~ ( ( SY58
!= ( a_2_0_closure3 @ SV14 @ SV23 ) )
| ( SY58
= ( k1_closure3 @ SV14 @ SV23 ) ) ) ) )
= $true )
| ( ( v1_xboole_0 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(191,plain,
( ( v1_xboole_0 @ sK4_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(192,plain,
! [SV9: $i,SV18: $i] :
( ( ( ~ ( ~ ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV9 )
| ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV18 ) ) )
= $true )
| ( ( ~ ( ~ ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV18 )
| ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV9 ) ) )
= $true )
| ( ( SV9 = SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(193,plain,
! [SV10: $i,SV22: $i,SV19: $i] :
( ( ( ~ ~ ( v1_xboole_0 @ SV19 ) )
= $true )
| ( ( ~ ( m1_pboole @ SV22 @ SV19 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
| ~ ! [SY56: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY56 @ SV19 )
| ( SV10 != SY56 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SY56 )
!= k1_xboole_0 ) ) ) )
| ~ ( ~ ~ ! [SY57: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY57 @ SV19 )
| ( SV10 != SY57 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SY57 )
!= k1_xboole_0 ) ) )
| ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(194,plain,
( ( ~ ( r2_hidden @ sK8_SY55 @ ( k1_closure3 @ sK1_A @ sK5_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(195,plain,
! [SV12: $i,SV20: $i] :
( ( ( v1_xboole_0 @ SV20 )
= $false )
| ( ( r2_hidden @ SV12 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(196,plain,
! [SV21: $i,SV13: $i] :
( ( ( ~ ( v1_xboole_0 @ SV13 )
| ~ ( ( SV13 != SV21 ) ) )
= $true )
| ( ( ~ ( v1_xboole_0 @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[189]) ).
thf(197,plain,
! [SV14: $i,SV23: $i] :
( ( ( m1_pboole @ SV23 @ SV14 )
= $false )
| ( ( ! [SY58: $i] :
~ ( ~ ( ( SY58
!= ( k1_closure3 @ SV14 @ SV23 ) )
| ( SY58
= ( a_2_0_closure3 @ SV14 @ SV23 ) ) )
| ~ ( ( SY58
!= ( a_2_0_closure3 @ SV14 @ SV23 ) )
| ( SY58
= ( k1_closure3 @ SV14 @ SV23 ) ) ) ) )
= $true )
| ( ( v1_xboole_0 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(198,plain,
! [SV9: $i,SV18: $i] :
( ( ( ~ ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV9 )
| ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV18 ) )
= $false )
| ( ( ~ ( ~ ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV18 )
| ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV9 ) ) )
= $true )
| ( ( SV9 = SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(199,plain,
! [SV10: $i,SV22: $i,SV19: $i] :
( ( ( ~ ( v1_xboole_0 @ SV19 ) )
= $false )
| ( ( ~ ( m1_pboole @ SV22 @ SV19 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
| ~ ! [SY56: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY56 @ SV19 )
| ( SV10 != SY56 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SY56 )
!= k1_xboole_0 ) ) ) )
| ~ ( ~ ~ ! [SY57: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY57 @ SV19 )
| ( SV10 != SY57 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SY57 )
!= k1_xboole_0 ) ) )
| ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(200,plain,
( ( r2_hidden @ sK8_SY55 @ ( k1_closure3 @ sK1_A @ sK5_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(201,plain,
! [SV21: $i,SV13: $i] :
( ( ( ~ ( v1_xboole_0 @ SV13 ) )
= $true )
| ( ( ~ ( ( SV13 != SV21 ) ) )
= $true )
| ( ( ~ ( v1_xboole_0 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(202,plain,
! [SV23: $i,SV14: $i,SV24: $i] :
( ( ( ~ ( ~ ( ( SV24
!= ( k1_closure3 @ SV14 @ SV23 ) )
| ( SV24
= ( a_2_0_closure3 @ SV14 @ SV23 ) ) )
| ~ ( ( SV24
!= ( a_2_0_closure3 @ SV14 @ SV23 ) )
| ( SV24
= ( k1_closure3 @ SV14 @ SV23 ) ) ) ) )
= $true )
| ( ( m1_pboole @ SV23 @ SV14 )
= $false )
| ( ( v1_xboole_0 @ SV14 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(203,plain,
! [SV9: $i,SV18: $i] :
( ( ( ~ ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV9 ) )
= $false )
| ( ( ~ ( ~ ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV18 )
| ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV9 ) ) )
= $true )
| ( ( SV9 = SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[198]) ).
thf(204,plain,
! [SV9: $i,SV18: $i] :
( ( ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV18 )
= $false )
| ( ( ~ ( ~ ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV18 )
| ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV9 ) ) )
= $true )
| ( ( SV9 = SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[198]) ).
thf(205,plain,
! [SV10: $i,SV22: $i,SV19: $i] :
( ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( ~ ( m1_pboole @ SV22 @ SV19 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
| ~ ! [SY56: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY56 @ SV19 )
| ( SV10 != SY56 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SY56 )
!= k1_xboole_0 ) ) ) )
| ~ ( ~ ~ ! [SY57: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY57 @ SV19 )
| ( SV10 != SY57 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SY57 )
!= k1_xboole_0 ) ) )
| ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(206,plain,
! [SV21: $i,SV13: $i] :
( ( ( v1_xboole_0 @ SV13 )
= $false )
| ( ( ~ ( ( SV13 != SV21 ) ) )
= $true )
| ( ( ~ ( v1_xboole_0 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(207,plain,
! [SV23: $i,SV14: $i,SV24: $i] :
( ( ( ~ ( ( SV24
!= ( k1_closure3 @ SV14 @ SV23 ) )
| ( SV24
= ( a_2_0_closure3 @ SV14 @ SV23 ) ) )
| ~ ( ( SV24
!= ( a_2_0_closure3 @ SV14 @ SV23 ) )
| ( SV24
= ( k1_closure3 @ SV14 @ SV23 ) ) ) )
= $false )
| ( ( m1_pboole @ SV23 @ SV14 )
= $false )
| ( ( v1_xboole_0 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(208,plain,
! [SV9: $i,SV18: $i] :
( ( ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV9 )
= $true )
| ( ( ~ ( ~ ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV18 )
| ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV9 ) ) )
= $true )
| ( ( SV9 = SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(209,plain,
! [SV9: $i,SV18: $i] :
( ( ( ~ ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV18 )
| ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV9 ) )
= $false )
| ( ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV18 )
= $false )
| ( ( SV9 = SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(210,plain,
! [SV10: $i,SV19: $i,SV22: $i] :
( ( ( m1_pboole @ SV22 @ SV19 )
= $false )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( ~ ( ~ ( ~ ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
| ~ ! [SY56: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY56 @ SV19 )
| ( SV10 != SY56 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SY56 )
!= k1_xboole_0 ) ) ) )
| ~ ( ~ ~ ! [SY57: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY57 @ SV19 )
| ( SV10 != SY57 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SY57 )
!= k1_xboole_0 ) ) )
| ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(211,plain,
! [SV21: $i,SV13: $i] :
( ( ( SV13 != SV21 )
= $false )
| ( ( v1_xboole_0 @ SV13 )
= $false )
| ( ( ~ ( v1_xboole_0 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(212,plain,
! [SV23: $i,SV14: $i,SV24: $i] :
( ( ( ~ ( ( SV24
!= ( k1_closure3 @ SV14 @ SV23 ) )
| ( SV24
= ( a_2_0_closure3 @ SV14 @ SV23 ) ) ) )
= $false )
| ( ( m1_pboole @ SV23 @ SV14 )
= $false )
| ( ( v1_xboole_0 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(213,plain,
! [SV23: $i,SV14: $i,SV24: $i] :
( ( ( ~ ( ( SV24
!= ( a_2_0_closure3 @ SV14 @ SV23 ) )
| ( SV24
= ( k1_closure3 @ SV14 @ SV23 ) ) ) )
= $false )
| ( ( m1_pboole @ SV23 @ SV14 )
= $false )
| ( ( v1_xboole_0 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(214,plain,
! [SV9: $i,SV18: $i] :
( ( ( ~ ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV18 )
| ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV9 ) )
= $false )
| ( ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV9 )
= $true )
| ( ( SV9 = SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(215,plain,
! [SV9: $i,SV18: $i] :
( ( ( ~ ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV18 ) )
= $false )
| ( ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV18 )
= $false )
| ( ( SV9 = SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(216,plain,
! [SV9: $i,SV18: $i] :
( ( ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV9 )
= $false )
| ( ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV18 )
= $false )
| ( ( SV9 = SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(217,plain,
! [SV22: $i,SV19: $i,SV10: $i] :
( ( ( ~ ( ~ ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
| ~ ! [SY56: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY56 @ SV19 )
| ( SV10 != SY56 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SY56 )
!= k1_xboole_0 ) ) ) )
| ~ ( ~ ~ ! [SY57: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY57 @ SV19 )
| ( SV10 != SY57 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SY57 )
!= k1_xboole_0 ) ) )
| ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) ) ) )
= $false )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(218,plain,
! [SV21: $i,SV13: $i] :
( ( ( SV13 = SV21 )
= $true )
| ( ( v1_xboole_0 @ SV13 )
= $false )
| ( ( ~ ( v1_xboole_0 @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(219,plain,
! [SV23: $i,SV14: $i,SV24: $i] :
( ( ( ( SV24
!= ( k1_closure3 @ SV14 @ SV23 ) )
| ( SV24
= ( a_2_0_closure3 @ SV14 @ SV23 ) ) )
= $true )
| ( ( m1_pboole @ SV23 @ SV14 )
= $false )
| ( ( v1_xboole_0 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(220,plain,
! [SV23: $i,SV14: $i,SV24: $i] :
( ( ( ( SV24
!= ( a_2_0_closure3 @ SV14 @ SV23 ) )
| ( SV24
= ( k1_closure3 @ SV14 @ SV23 ) ) )
= $true )
| ( ( m1_pboole @ SV23 @ SV14 )
= $false )
| ( ( v1_xboole_0 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(221,plain,
! [SV9: $i,SV18: $i] :
( ( ( ~ ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV18 ) )
= $false )
| ( ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV9 )
= $true )
| ( ( SV9 = SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(222,plain,
! [SV9: $i,SV18: $i] :
( ( ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV9 )
= $false )
| ( ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV9 )
= $true )
| ( ( SV9 = SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(223,plain,
! [SV9: $i,SV18: $i] :
( ( ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV18 )
= $true )
| ( ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV18 )
= $false )
| ( ( SV9 = SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[215]) ).
thf(224,plain,
! [SV22: $i,SV19: $i,SV10: $i] :
( ( ( ~ ( ~ ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
| ~ ! [SY56: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY56 @ SV19 )
| ( SV10 != SY56 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SY56 )
!= k1_xboole_0 ) ) ) ) )
= $false )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(225,plain,
! [SV22: $i,SV10: $i,SV19: $i] :
( ( ( ~ ( ~ ~ ! [SY57: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY57 @ SV19 )
| ( SV10 != SY57 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SY57 )
!= k1_xboole_0 ) ) )
| ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) ) ) )
= $false )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(226,plain,
! [SV13: $i,SV21: $i] :
( ( ( v1_xboole_0 @ SV21 )
= $false )
| ( ( v1_xboole_0 @ SV13 )
= $false )
| ( ( SV13 = SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(227,plain,
! [SV23: $i,SV14: $i,SV24: $i] :
( ( ( SV24
!= ( k1_closure3 @ SV14 @ SV23 ) )
= $true )
| ( ( SV24
= ( a_2_0_closure3 @ SV14 @ SV23 ) )
= $true )
| ( ( m1_pboole @ SV23 @ SV14 )
= $false )
| ( ( v1_xboole_0 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(228,plain,
! [SV23: $i,SV14: $i,SV24: $i] :
( ( ( SV24
!= ( a_2_0_closure3 @ SV14 @ SV23 ) )
= $true )
| ( ( SV24
= ( k1_closure3 @ SV14 @ SV23 ) )
= $true )
| ( ( m1_pboole @ SV23 @ SV14 )
= $false )
| ( ( v1_xboole_0 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(229,plain,
! [SV9: $i,SV18: $i] :
( ( ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV18 )
= $true )
| ( ( r2_hidden @ ( sK9_SY51 @ SV18 @ SV9 ) @ SV9 )
= $true )
| ( ( SV9 = SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(230,plain,
! [SV22: $i,SV19: $i,SV10: $i] :
( ( ( ~ ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
| ~ ! [SY56: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY56 @ SV19 )
| ( SV10 != SY56 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SY56 )
!= k1_xboole_0 ) ) ) )
= $true )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[224]) ).
thf(231,plain,
! [SV22: $i,SV10: $i,SV19: $i] :
( ( ( ~ ~ ! [SY57: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY57 @ SV19 )
| ( SV10 != SY57 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SY57 )
!= k1_xboole_0 ) ) )
| ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) ) )
= $true )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(232,plain,
! [SV23: $i,SV14: $i,SV24: $i] :
( ( ( SV24
= ( k1_closure3 @ SV14 @ SV23 ) )
= $false )
| ( ( SV24
= ( a_2_0_closure3 @ SV14 @ SV23 ) )
= $true )
| ( ( m1_pboole @ SV23 @ SV14 )
= $false )
| ( ( v1_xboole_0 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(233,plain,
! [SV23: $i,SV14: $i,SV24: $i] :
( ( ( SV24
= ( a_2_0_closure3 @ SV14 @ SV23 ) )
= $false )
| ( ( SV24
= ( k1_closure3 @ SV14 @ SV23 ) )
= $true )
| ( ( m1_pboole @ SV23 @ SV14 )
= $false )
| ( ( v1_xboole_0 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(234,plain,
! [SV22: $i,SV19: $i,SV10: $i] :
( ( ( ~ ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) ) )
= $true )
| ( ( ~ ! [SY56: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY56 @ SV19 )
| ( SV10 != SY56 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SY56 )
!= k1_xboole_0 ) ) ) )
= $true )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(235,plain,
! [SV22: $i,SV10: $i,SV19: $i] :
( ( ( ~ ~ ! [SY57: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY57 @ SV19 )
| ( SV10 != SY57 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SY57 )
!= k1_xboole_0 ) ) ) )
= $true )
| ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $true )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(236,plain,
! [SV22: $i,SV19: $i,SV10: $i] :
( ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $false )
| ( ( ~ ! [SY56: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY56 @ SV19 )
| ( SV10 != SY56 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SY56 )
!= k1_xboole_0 ) ) ) )
= $true )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(237,plain,
! [SV22: $i,SV10: $i,SV19: $i] :
( ( ( ~ ! [SY57: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY57 @ SV19 )
| ( SV10 != SY57 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SY57 )
!= k1_xboole_0 ) ) ) )
= $false )
| ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $true )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(238,plain,
! [SV22: $i,SV10: $i,SV19: $i] :
( ( ( ! [SY56: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY56 @ SV19 )
| ( SV10 != SY56 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SY56 )
!= k1_xboole_0 ) ) ) )
= $false )
| ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $false )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(239,plain,
! [SV22: $i,SV10: $i,SV19: $i] :
( ( ( ! [SY57: $i] :
~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SY57 @ SV19 )
| ( SV10 != SY57 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SY57 )
!= k1_xboole_0 ) ) ) )
= $true )
| ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $true )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(240,plain,
! [SV19: $i,SV10: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ ( sK10_SY56 @ SV22 @ SV10 @ SV19 ) @ SV19 )
| ( SV10
!= ( sK10_SY56 @ SV22 @ SV10 @ SV19 ) ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ ( sK10_SY56 @ SV22 @ SV10 @ SV19 ) )
!= k1_xboole_0 ) ) ) )
= $false )
| ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $false )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[238]) ).
thf(241,plain,
! [SV22: $i,SV10: $i,SV19: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( m1_subset_1 @ SV25 @ SV19 )
| ( SV10 != SV25 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SV25 )
!= k1_xboole_0 ) ) ) )
= $true )
| ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $true )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(242,plain,
! [SV19: $i,SV10: $i,SV22: $i] :
( ( ( ~ ( ~ ~ ( ~ ( m1_subset_1 @ ( sK10_SY56 @ SV22 @ SV10 @ SV19 ) @ SV19 )
| ( SV10
!= ( sK10_SY56 @ SV22 @ SV10 @ SV19 ) ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ ( sK10_SY56 @ SV22 @ SV10 @ SV19 ) )
!= k1_xboole_0 ) ) ) )
= $true )
| ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $false )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(243,plain,
! [SV22: $i,SV10: $i,SV19: $i,SV25: $i] :
( ( ( ~ ( ~ ~ ( ~ ( m1_subset_1 @ SV25 @ SV19 )
| ( SV10 != SV25 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SV25 )
!= k1_xboole_0 ) ) ) )
= $false )
| ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $true )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(244,plain,
! [SV19: $i,SV10: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( m1_subset_1 @ ( sK10_SY56 @ SV22 @ SV10 @ SV19 ) @ SV19 )
| ( SV10
!= ( sK10_SY56 @ SV22 @ SV10 @ SV19 ) ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ ( sK10_SY56 @ SV22 @ SV10 @ SV19 ) )
!= k1_xboole_0 ) ) )
= $false )
| ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $false )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(245,plain,
! [SV22: $i,SV10: $i,SV19: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( m1_subset_1 @ SV25 @ SV19 )
| ( SV10 != SV25 ) )
| ~ ( ( ( k1_funct_1 @ SV22 @ SV25 )
!= k1_xboole_0 ) ) )
= $true )
| ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $true )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(246,plain,
! [SV19: $i,SV10: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( m1_subset_1 @ ( sK10_SY56 @ SV22 @ SV10 @ SV19 ) @ SV19 )
| ( SV10
!= ( sK10_SY56 @ SV22 @ SV10 @ SV19 ) ) ) )
= $false )
| ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $false )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[244]) ).
thf(247,plain,
! [SV19: $i,SV10: $i,SV22: $i] :
( ( ( ~ ( ( ( k1_funct_1 @ SV22 @ ( sK10_SY56 @ SV22 @ SV10 @ SV19 ) )
!= k1_xboole_0 ) ) )
= $false )
| ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $false )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[244]) ).
thf(248,plain,
! [SV22: $i,SV10: $i,SV19: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( m1_subset_1 @ SV25 @ SV19 )
| ( SV10 != SV25 ) ) )
= $true )
| ( ( ~ ( ( ( k1_funct_1 @ SV22 @ SV25 )
!= k1_xboole_0 ) ) )
= $true )
| ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $true )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(249,plain,
! [SV19: $i,SV10: $i,SV22: $i] :
( ( ( ~ ( ~ ( m1_subset_1 @ ( sK10_SY56 @ SV22 @ SV10 @ SV19 ) @ SV19 )
| ( SV10
!= ( sK10_SY56 @ SV22 @ SV10 @ SV19 ) ) ) )
= $true )
| ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $false )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(250,plain,
! [SV19: $i,SV10: $i,SV22: $i] :
( ( ( ( k1_funct_1 @ SV22 @ ( sK10_SY56 @ SV22 @ SV10 @ SV19 ) )
!= k1_xboole_0 )
= $true )
| ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $false )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(251,plain,
! [SV22: $i,SV10: $i,SV19: $i,SV25: $i] :
( ( ( ~ ( ~ ( m1_subset_1 @ SV25 @ SV19 )
| ( SV10 != SV25 ) ) )
= $false )
| ( ( ~ ( ( ( k1_funct_1 @ SV22 @ SV25 )
!= k1_xboole_0 ) ) )
= $true )
| ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $true )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(252,plain,
! [SV19: $i,SV10: $i,SV22: $i] :
( ( ( ~ ( m1_subset_1 @ ( sK10_SY56 @ SV22 @ SV10 @ SV19 ) @ SV19 )
| ( SV10
!= ( sK10_SY56 @ SV22 @ SV10 @ SV19 ) ) )
= $false )
| ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $false )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(253,plain,
! [SV19: $i,SV10: $i,SV22: $i] :
( ( ( ( k1_funct_1 @ SV22 @ ( sK10_SY56 @ SV22 @ SV10 @ SV19 ) )
= k1_xboole_0 )
= $false )
| ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $false )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(254,plain,
! [SV22: $i,SV10: $i,SV19: $i,SV25: $i] :
( ( ( ~ ( m1_subset_1 @ SV25 @ SV19 )
| ( SV10 != SV25 ) )
= $true )
| ( ( ~ ( ( ( k1_funct_1 @ SV22 @ SV25 )
!= k1_xboole_0 ) ) )
= $true )
| ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $true )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(255,plain,
! [SV19: $i,SV10: $i,SV22: $i] :
( ( ( ~ ( m1_subset_1 @ ( sK10_SY56 @ SV22 @ SV10 @ SV19 ) @ SV19 ) )
= $false )
| ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $false )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[252]) ).
thf(256,plain,
! [SV19: $i,SV22: $i,SV10: $i] :
( ( ( SV10
!= ( sK10_SY56 @ SV22 @ SV10 @ SV19 ) )
= $false )
| ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $false )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[252]) ).
thf(257,plain,
! [SV22: $i,SV10: $i,SV19: $i,SV25: $i] :
( ( ( ~ ( m1_subset_1 @ SV25 @ SV19 ) )
= $true )
| ( ( SV10 != SV25 )
= $true )
| ( ( ~ ( ( ( k1_funct_1 @ SV22 @ SV25 )
!= k1_xboole_0 ) ) )
= $true )
| ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $true )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(258,plain,
! [SV19: $i,SV10: $i,SV22: $i] :
( ( ( m1_subset_1 @ ( sK10_SY56 @ SV22 @ SV10 @ SV19 ) @ SV19 )
= $true )
| ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $false )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(259,plain,
! [SV19: $i,SV22: $i,SV10: $i] :
( ( ( SV10
= ( sK10_SY56 @ SV22 @ SV10 @ SV19 ) )
= $true )
| ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $false )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(260,plain,
! [SV22: $i,SV10: $i,SV19: $i,SV25: $i] :
( ( ( m1_subset_1 @ SV25 @ SV19 )
= $false )
| ( ( SV10 != SV25 )
= $true )
| ( ( ~ ( ( ( k1_funct_1 @ SV22 @ SV25 )
!= k1_xboole_0 ) ) )
= $true )
| ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $true )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(261,plain,
! [SV22: $i,SV19: $i,SV25: $i,SV10: $i] :
( ( ( SV10 = SV25 )
= $false )
| ( ( m1_subset_1 @ SV25 @ SV19 )
= $false )
| ( ( ~ ( ( ( k1_funct_1 @ SV22 @ SV25 )
!= k1_xboole_0 ) ) )
= $true )
| ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $true )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(262,plain,
! [SV10: $i,SV19: $i,SV25: $i,SV22: $i] :
( ( ( ( k1_funct_1 @ SV22 @ SV25 )
!= k1_xboole_0 )
= $false )
| ( ( m1_subset_1 @ SV25 @ SV19 )
= $false )
| ( ( SV10 = SV25 )
= $false )
| ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $true )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(263,plain,
! [SV10: $i,SV19: $i,SV25: $i,SV22: $i] :
( ( ( ( k1_funct_1 @ SV22 @ SV25 )
= k1_xboole_0 )
= $true )
| ( ( m1_subset_1 @ SV25 @ SV19 )
= $false )
| ( ( SV10 = SV25 )
= $false )
| ( ( r2_hidden @ SV10 @ ( a_2_0_closure3 @ SV19 @ SV22 ) )
= $true )
| ( ( v1_xboole_0 @ SV19 )
= $true )
| ( ( m1_pboole @ SV22 @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(264,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[63,263,259,258,253,233,232,229,226,223,222,216,200,195,191,187,185,182,173,172,165,162,161,159,156,150,145,144,143,137,100,69,66,65,64]) ).
thf(265,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[264]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG227+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.20 % Computer : n016.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Oct 6 18:13:15 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.64/0.42
% 0.64/0.42 No.of.Axioms: 22
% 0.64/0.42
% 0.64/0.42 Length.of.Defs: 0
% 0.64/0.42
% 0.64/0.42 Contains.Choice.Funs: false
% 0.64/0.42 .......
% 0.64/0.42
% 0.64/0.42 ********************************
% 0.64/0.42 * All subproblems solved! *
% 0.64/0.42 ********************************
% 0.64/0.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:23,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:264,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.64/0.42
% 0.64/0.42 %**** Beginning of derivation protocol ****
% 0.64/0.42 % SZS output start CNFRefutation
% See solution above
% 0.64/0.42
% 0.64/0.42 %**** End of derivation protocol ****
% 0.64/0.42 %**** no. of clauses in derivation: 259 ****
% 0.64/0.42 %**** clause counter: 264 ****
% 0.64/0.42
% 0.64/0.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:23,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:264,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------