TSTP Solution File: SEU355+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU355+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:11:02 EDT 2022
% Result : Theorem 0.20s 0.49s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 43
% Syntax : Number of formulae : 236 ( 111 unt; 21 typ; 0 def)
% Number of atoms : 1539 ( 401 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 3100 ( 515 ~; 484 |; 30 &;2029 @)
% ( 4 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 10 con; 0-3 aty)
% Number of variables : 449 ( 0 ^ 437 !; 12 ?; 449 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_finite,type,
finite: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_one_sorted_str,type,
one_sorted_str: $i > $o ).
thf(tp_rel_str,type,
rel_str: $i > $o ).
thf(tp_related,type,
related: $i > $i > $i > $o ).
thf(tp_relstr_element_smaller,type,
relstr_element_smaller: $i > $i > $i > $o ).
thf(tp_relstr_set_smaller,type,
relstr_set_smaller: $i > $i > $i > $o ).
thf(tp_sK10_D,type,
sK10_D: $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY30,type,
sK2_SY30: $i ).
thf(tp_sK3_A,type,
sK3_A: $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_sK6_B,type,
sK6_B: $i > $i ).
thf(tp_sK7_A,type,
sK7_A: $i ).
thf(tp_sK8_A,type,
sK8_A: $i ).
thf(tp_sK9_D,type,
sK9_D: $i > $i > $i > $i ).
thf(tp_the_carrier,type,
the_carrier: $i > $i ).
thf(1,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(3,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(6,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(7,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(8,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(9,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(10,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(11,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(12,axiom,
? [A: $i] : ( rel_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(13,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(14,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(15,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(16,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(17,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(18,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ C )
<=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ B )
=> ( related @ A @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_lattice3) ).
thf(19,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( relstr_element_smaller @ A @ B @ C )
<=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ B )
=> ( related @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_lattice3) ).
thf(20,axiom,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(22,conjecture,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ empty_set @ B )
& ( relstr_element_smaller @ A @ empty_set @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_yellow_0) ).
thf(23,negated_conjecture,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ empty_set @ B )
& ( relstr_element_smaller @ A @ empty_set @ B ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[22]) ).
thf(24,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ empty_set @ B )
& ( relstr_element_smaller @ A @ empty_set @ B ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[23]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(26,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(27,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(28,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(29,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(30,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(31,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(32,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(33,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(34,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(35,plain,
( ( ? [A: $i] : ( one_sorted_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(36,plain,
( ( ? [A: $i] : ( rel_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(37,plain,
$true = $true,
inference(unfold_def,[status(thm)],[13]) ).
thf(38,plain,
$true = $true,
inference(unfold_def,[status(thm)],[14]) ).
thf(39,plain,
$true = $true,
inference(unfold_def,[status(thm)],[15]) ).
thf(40,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(41,plain,
$true = $true,
inference(unfold_def,[status(thm)],[17]) ).
thf(42,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ C )
<=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ B )
=> ( related @ A @ D @ C ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(43,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( relstr_element_smaller @ A @ B @ C )
<=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ B )
=> ( related @ A @ C @ D ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(44,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(45,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(46,plain,
( ( ( rel_str @ sK1_A )
=> ! [SY30: $i] :
( ( element @ SY30 @ ( the_carrier @ sK1_A ) )
=> ( ( relstr_set_smaller @ sK1_A @ empty_set @ SY30 )
& ( relstr_element_smaller @ sK1_A @ empty_set @ SY30 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[24]) ).
thf(47,plain,
( ( rel_str @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[46]) ).
thf(48,plain,
( ( ! [SY30: $i] :
( ( element @ SY30 @ ( the_carrier @ sK1_A ) )
=> ( ( relstr_set_smaller @ sK1_A @ empty_set @ SY30 )
& ( relstr_element_smaller @ sK1_A @ empty_set @ SY30 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[46]) ).
thf(49,plain,
( ( ~ ! [SY30: $i] :
( ( element @ SY30 @ ( the_carrier @ sK1_A ) )
=> ( ( relstr_set_smaller @ sK1_A @ empty_set @ SY30 )
& ( relstr_element_smaller @ sK1_A @ empty_set @ SY30 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[48]) ).
thf(50,plain,
( ( ( element @ sK2_SY30 @ ( the_carrier @ sK1_A ) )
& ( ~ ( relstr_element_smaller @ sK1_A @ empty_set @ sK2_SY30 )
| ~ ( relstr_set_smaller @ sK1_A @ empty_set @ sK2_SY30 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(51,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(52,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(53,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(54,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(55,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(56,plain,
( ( ~ ( empty @ sK3_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(57,plain,
( ( empty @ sK4_A )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(58,plain,
( ( ~ ( empty @ sK5_A )
& ( finite @ sK5_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(59,plain,
( ( ! [A: $i] : ( element @ ( sK6_B @ A ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(60,plain,
( ( one_sorted_str @ sK7_A )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(61,plain,
( ( rel_str @ sK8_A )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(62,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(63,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( ! [B: $i,C: $i] :
( ~ ( element @ C @ ( the_carrier @ A ) )
| ( ( element @ ( sK9_D @ C @ B @ A ) @ ( the_carrier @ A ) )
& ( in @ ( sK9_D @ C @ B @ A ) @ B )
& ~ ( related @ A @ ( sK9_D @ C @ B @ A ) @ C ) )
| ( relstr_set_smaller @ A @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( element @ C @ ( the_carrier @ A ) )
| ~ ( relstr_set_smaller @ A @ B @ C )
| ! [D: $i] :
( ~ ( element @ D @ ( the_carrier @ A ) )
| ~ ( in @ D @ B )
| ( related @ A @ D @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(64,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( ! [B: $i,C: $i] :
( ~ ( element @ C @ ( the_carrier @ A ) )
| ( ( element @ ( sK10_D @ C @ B @ A ) @ ( the_carrier @ A ) )
& ( in @ ( sK10_D @ C @ B @ A ) @ B )
& ~ ( related @ A @ C @ ( sK10_D @ C @ B @ A ) ) )
| ( relstr_element_smaller @ A @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( element @ C @ ( the_carrier @ A ) )
| ~ ( relstr_element_smaller @ A @ B @ C )
| ! [D: $i] :
( ~ ( element @ D @ ( the_carrier @ A ) )
| ~ ( in @ D @ B )
| ( related @ A @ C @ D ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(65,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( finite @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(66,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(67,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(68,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(69,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( ! [B: $i,C: $i] :
( ~ ( element @ C @ ( the_carrier @ A ) )
| ( ( element @ ( sK10_D @ C @ B @ A ) @ ( the_carrier @ A ) )
& ( in @ ( sK10_D @ C @ B @ A ) @ B )
& ~ ( related @ A @ C @ ( sK10_D @ C @ B @ A ) ) )
| ( relstr_element_smaller @ A @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( element @ C @ ( the_carrier @ A ) )
| ~ ( relstr_element_smaller @ A @ B @ C )
| ! [D: $i] :
( ~ ( element @ D @ ( the_carrier @ A ) )
| ~ ( in @ D @ B )
| ( related @ A @ C @ D ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(70,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( ! [B: $i,C: $i] :
( ~ ( element @ C @ ( the_carrier @ A ) )
| ( ( element @ ( sK9_D @ C @ B @ A ) @ ( the_carrier @ A ) )
& ( in @ ( sK9_D @ C @ B @ A ) @ B )
& ~ ( related @ A @ ( sK9_D @ C @ B @ A ) @ C ) )
| ( relstr_set_smaller @ A @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( element @ C @ ( the_carrier @ A ) )
| ~ ( relstr_set_smaller @ A @ B @ C )
| ! [D: $i] :
( ~ ( element @ D @ ( the_carrier @ A ) )
| ~ ( in @ D @ B )
| ( related @ A @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(71,plain,
$true = $true,
inference(copy,[status(thm)],[41]) ).
thf(72,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(73,plain,
$true = $true,
inference(copy,[status(thm)],[39]) ).
thf(74,plain,
$true = $true,
inference(copy,[status(thm)],[38]) ).
thf(75,plain,
$true = $true,
inference(copy,[status(thm)],[37]) ).
thf(76,plain,
( ( rel_str @ sK8_A )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(77,plain,
( ( one_sorted_str @ sK7_A )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(78,plain,
( ( ! [A: $i] : ( element @ ( sK6_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(79,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(80,plain,
( ( ~ ( empty @ sK5_A )
& ( finite @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(81,plain,
( ( empty @ sK4_A )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(82,plain,
( ( ~ ( empty @ sK3_A ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(83,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(84,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(85,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(86,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(87,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(88,plain,
( ( rel_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(89,plain,
( ( ( element @ sK2_SY30 @ ( the_carrier @ sK1_A ) )
& ( ~ ( relstr_element_smaller @ sK1_A @ empty_set @ sK2_SY30 )
| ~ ( relstr_set_smaller @ sK1_A @ empty_set @ sK2_SY30 ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(90,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( ~ ( element @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ~ ( ~ ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( related @ SX0 @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ( relstr_set_smaller @ SX0 @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_set_smaller @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( element @ SX3 @ ( the_carrier @ SX0 ) )
| ~ ( in @ SX3 @ SX1 )
| ( related @ SX0 @ SX3 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(91,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( ~ ( element @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ~ ( ~ ( in @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( related @ SX0 @ SX2 @ ( sK10_D @ SX2 @ SX1 @ SX0 ) ) ) )
| ( relstr_element_smaller @ SX0 @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( element @ SX3 @ ( the_carrier @ SX0 ) )
| ~ ( in @ SX3 @ SX1 )
| ( related @ SX0 @ SX2 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(92,plain,
( ( ~ ( ~ ( element @ sK2_SY30 @ ( the_carrier @ sK1_A ) )
| ~ ( ~ ( relstr_element_smaller @ sK1_A @ empty_set @ sK2_SY30 )
| ~ ( relstr_set_smaller @ sK1_A @ empty_set @ sK2_SY30 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(93,plain,
( ( ~ ( ~ ~ ( empty @ sK5_A )
| ~ ( finite @ sK5_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(94,plain,
! [SV1: $i] :
( ( ! [SY31: $i] :
( ~ ( in @ SV1 @ SY31 )
| ~ ( in @ SY31 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(95,plain,
! [SV2: $i] :
( ( ~ ( empty @ SV2 )
| ( finite @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(96,plain,
! [SV3: $i] :
( ( ~ ( rel_str @ SV3 )
| ( one_sorted_str @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(97,plain,
! [SV4: $i] :
( ( element @ ( sK6_B @ SV4 ) @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(98,plain,
( ( empty @ sK3_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(99,plain,
! [SV5: $i] :
( ( ! [SY32: $i] :
( ~ ( in @ SV5 @ SY32 )
| ( element @ SV5 @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(100,plain,
! [SV6: $i] :
( ( ! [SY33: $i] :
( ~ ( element @ SV6 @ SY33 )
| ( empty @ SY33 )
| ( in @ SV6 @ SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(101,plain,
! [SV7: $i] :
( ( ~ ( empty @ SV7 )
| ( SV7 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(102,plain,
! [SV8: $i] :
( ( ! [SY34: $i] :
( ~ ( empty @ SY34 )
| ~ ( in @ SV8 @ SY34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(103,plain,
! [SV9: $i] :
( ( ! [SY35: $i] :
( ( SV9 = SY35 )
| ~ ( empty @ SV9 )
| ~ ( empty @ SY35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(104,plain,
! [SV10: $i] :
( ( ~ ( rel_str @ SV10 )
| ~ ( ~ ! [SY36: $i,SY37: $i] :
( ~ ( element @ SY37 @ ( the_carrier @ SV10 ) )
| ~ ( ~ ( element @ ( sK9_D @ SY37 @ SY36 @ SV10 ) @ ( the_carrier @ SV10 ) )
| ~ ~ ( ~ ( in @ ( sK9_D @ SY37 @ SY36 @ SV10 ) @ SY36 )
| ~ ~ ( related @ SV10 @ ( sK9_D @ SY37 @ SY36 @ SV10 ) @ SY37 ) ) )
| ( relstr_set_smaller @ SV10 @ SY36 @ SY37 ) )
| ~ ! [SY38: $i,SY39: $i] :
( ~ ( element @ SY39 @ ( the_carrier @ SV10 ) )
| ~ ( relstr_set_smaller @ SV10 @ SY38 @ SY39 )
| ! [SY40: $i] :
( ~ ( element @ SY40 @ ( the_carrier @ SV10 ) )
| ~ ( in @ SY40 @ SY38 )
| ( related @ SV10 @ SY40 @ SY39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(105,plain,
! [SV11: $i] :
( ( ~ ( rel_str @ SV11 )
| ~ ( ~ ! [SY41: $i,SY42: $i] :
( ~ ( element @ SY42 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( element @ ( sK10_D @ SY42 @ SY41 @ SV11 ) @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( in @ ( sK10_D @ SY42 @ SY41 @ SV11 ) @ SY41 )
| ~ ~ ( related @ SV11 @ SY42 @ ( sK10_D @ SY42 @ SY41 @ SV11 ) ) ) )
| ( relstr_element_smaller @ SV11 @ SY41 @ SY42 ) )
| ~ ! [SY43: $i,SY44: $i] :
( ~ ( element @ SY44 @ ( the_carrier @ SV11 ) )
| ~ ( relstr_element_smaller @ SV11 @ SY43 @ SY44 )
| ! [SY45: $i] :
( ~ ( element @ SY45 @ ( the_carrier @ SV11 ) )
| ~ ( in @ SY45 @ SY43 )
| ( related @ SV11 @ SY44 @ SY45 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(106,plain,
( ( ~ ( element @ sK2_SY30 @ ( the_carrier @ sK1_A ) )
| ~ ( ~ ( relstr_element_smaller @ sK1_A @ empty_set @ sK2_SY30 )
| ~ ( relstr_set_smaller @ sK1_A @ empty_set @ sK2_SY30 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(107,plain,
( ( ~ ~ ( empty @ sK5_A )
| ~ ( finite @ sK5_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(108,plain,
! [SV12: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV12 )
| ~ ( in @ SV12 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(109,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ SV2 ) )
= $true )
| ( ( finite @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(110,plain,
! [SV3: $i] :
( ( ( ~ ( rel_str @ SV3 ) )
= $true )
| ( ( one_sorted_str @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(111,plain,
! [SV13: $i,SV5: $i] :
( ( ~ ( in @ SV5 @ SV13 )
| ( element @ SV5 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(112,plain,
! [SV14: $i,SV6: $i] :
( ( ~ ( element @ SV6 @ SV14 )
| ( empty @ SV14 )
| ( in @ SV6 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(113,plain,
! [SV7: $i] :
( ( ( ~ ( empty @ SV7 ) )
= $true )
| ( ( SV7 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(114,plain,
! [SV8: $i,SV15: $i] :
( ( ~ ( empty @ SV15 )
| ~ ( in @ SV8 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(115,plain,
! [SV16: $i,SV9: $i] :
( ( ( SV9 = SV16 )
| ~ ( empty @ SV9 )
| ~ ( empty @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(116,plain,
! [SV10: $i] :
( ( ( ~ ( rel_str @ SV10 ) )
= $true )
| ( ( ~ ( ~ ! [SY36: $i,SY37: $i] :
( ~ ( element @ SY37 @ ( the_carrier @ SV10 ) )
| ~ ( ~ ( element @ ( sK9_D @ SY37 @ SY36 @ SV10 ) @ ( the_carrier @ SV10 ) )
| ~ ~ ( ~ ( in @ ( sK9_D @ SY37 @ SY36 @ SV10 ) @ SY36 )
| ~ ~ ( related @ SV10 @ ( sK9_D @ SY37 @ SY36 @ SV10 ) @ SY37 ) ) )
| ( relstr_set_smaller @ SV10 @ SY36 @ SY37 ) )
| ~ ! [SY38: $i,SY39: $i] :
( ~ ( element @ SY39 @ ( the_carrier @ SV10 ) )
| ~ ( relstr_set_smaller @ SV10 @ SY38 @ SY39 )
| ! [SY40: $i] :
( ~ ( element @ SY40 @ ( the_carrier @ SV10 ) )
| ~ ( in @ SY40 @ SY38 )
| ( related @ SV10 @ SY40 @ SY39 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(117,plain,
! [SV11: $i] :
( ( ( ~ ( rel_str @ SV11 ) )
= $true )
| ( ( ~ ( ~ ! [SY41: $i,SY42: $i] :
( ~ ( element @ SY42 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( element @ ( sK10_D @ SY42 @ SY41 @ SV11 ) @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( in @ ( sK10_D @ SY42 @ SY41 @ SV11 ) @ SY41 )
| ~ ~ ( related @ SV11 @ SY42 @ ( sK10_D @ SY42 @ SY41 @ SV11 ) ) ) )
| ( relstr_element_smaller @ SV11 @ SY41 @ SY42 ) )
| ~ ! [SY43: $i,SY44: $i] :
( ~ ( element @ SY44 @ ( the_carrier @ SV11 ) )
| ~ ( relstr_element_smaller @ SV11 @ SY43 @ SY44 )
| ! [SY45: $i] :
( ~ ( element @ SY45 @ ( the_carrier @ SV11 ) )
| ~ ( in @ SY45 @ SY43 )
| ( related @ SV11 @ SY44 @ SY45 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(118,plain,
( ( ~ ( element @ sK2_SY30 @ ( the_carrier @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[106]) ).
thf(119,plain,
( ( ~ ( ~ ( relstr_element_smaller @ sK1_A @ empty_set @ sK2_SY30 )
| ~ ( relstr_set_smaller @ sK1_A @ empty_set @ sK2_SY30 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[106]) ).
thf(120,plain,
( ( ~ ~ ( empty @ sK5_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(121,plain,
( ( ~ ( finite @ sK5_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(122,plain,
! [SV12: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV12 ) )
= $true )
| ( ( ~ ( in @ SV12 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(123,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
= $false )
| ( ( finite @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(124,plain,
! [SV3: $i] :
( ( ( rel_str @ SV3 )
= $false )
| ( ( one_sorted_str @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(125,plain,
! [SV13: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ SV13 ) )
= $true )
| ( ( element @ SV5 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(126,plain,
! [SV14: $i,SV6: $i] :
( ( ( ~ ( element @ SV6 @ SV14 ) )
= $true )
| ( ( ( empty @ SV14 )
| ( in @ SV6 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(127,plain,
! [SV7: $i] :
( ( ( empty @ SV7 )
= $false )
| ( ( SV7 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(128,plain,
! [SV8: $i,SV15: $i] :
( ( ( ~ ( empty @ SV15 ) )
= $true )
| ( ( ~ ( in @ SV8 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(129,plain,
! [SV16: $i,SV9: $i] :
( ( ( ( SV9 = SV16 )
| ~ ( empty @ SV9 ) )
= $true )
| ( ( ~ ( empty @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(130,plain,
! [SV10: $i] :
( ( ( rel_str @ SV10 )
= $false )
| ( ( ~ ( ~ ! [SY36: $i,SY37: $i] :
( ~ ( element @ SY37 @ ( the_carrier @ SV10 ) )
| ~ ( ~ ( element @ ( sK9_D @ SY37 @ SY36 @ SV10 ) @ ( the_carrier @ SV10 ) )
| ~ ~ ( ~ ( in @ ( sK9_D @ SY37 @ SY36 @ SV10 ) @ SY36 )
| ~ ~ ( related @ SV10 @ ( sK9_D @ SY37 @ SY36 @ SV10 ) @ SY37 ) ) )
| ( relstr_set_smaller @ SV10 @ SY36 @ SY37 ) )
| ~ ! [SY38: $i,SY39: $i] :
( ~ ( element @ SY39 @ ( the_carrier @ SV10 ) )
| ~ ( relstr_set_smaller @ SV10 @ SY38 @ SY39 )
| ! [SY40: $i] :
( ~ ( element @ SY40 @ ( the_carrier @ SV10 ) )
| ~ ( in @ SY40 @ SY38 )
| ( related @ SV10 @ SY40 @ SY39 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(131,plain,
! [SV11: $i] :
( ( ( rel_str @ SV11 )
= $false )
| ( ( ~ ( ~ ! [SY41: $i,SY42: $i] :
( ~ ( element @ SY42 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( element @ ( sK10_D @ SY42 @ SY41 @ SV11 ) @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( in @ ( sK10_D @ SY42 @ SY41 @ SV11 ) @ SY41 )
| ~ ~ ( related @ SV11 @ SY42 @ ( sK10_D @ SY42 @ SY41 @ SV11 ) ) ) )
| ( relstr_element_smaller @ SV11 @ SY41 @ SY42 ) )
| ~ ! [SY43: $i,SY44: $i] :
( ~ ( element @ SY44 @ ( the_carrier @ SV11 ) )
| ~ ( relstr_element_smaller @ SV11 @ SY43 @ SY44 )
| ! [SY45: $i] :
( ~ ( element @ SY45 @ ( the_carrier @ SV11 ) )
| ~ ( in @ SY45 @ SY43 )
| ( related @ SV11 @ SY44 @ SY45 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(132,plain,
( ( element @ sK2_SY30 @ ( the_carrier @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(133,plain,
( ( ~ ( relstr_element_smaller @ sK1_A @ empty_set @ sK2_SY30 )
| ~ ( relstr_set_smaller @ sK1_A @ empty_set @ sK2_SY30 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(134,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(135,plain,
( ( finite @ sK5_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(136,plain,
! [SV12: $i,SV1: $i] :
( ( ( in @ SV1 @ SV12 )
= $false )
| ( ( ~ ( in @ SV12 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(137,plain,
! [SV13: $i,SV5: $i] :
( ( ( in @ SV5 @ SV13 )
= $false )
| ( ( element @ SV5 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(138,plain,
! [SV14: $i,SV6: $i] :
( ( ( element @ SV6 @ SV14 )
= $false )
| ( ( ( empty @ SV14 )
| ( in @ SV6 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(139,plain,
! [SV8: $i,SV15: $i] :
( ( ( empty @ SV15 )
= $false )
| ( ( ~ ( in @ SV8 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(140,plain,
! [SV16: $i,SV9: $i] :
( ( ( SV9 = SV16 )
= $true )
| ( ( ~ ( empty @ SV9 ) )
= $true )
| ( ( ~ ( empty @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(141,plain,
! [SV10: $i] :
( ( ( ~ ! [SY36: $i,SY37: $i] :
( ~ ( element @ SY37 @ ( the_carrier @ SV10 ) )
| ~ ( ~ ( element @ ( sK9_D @ SY37 @ SY36 @ SV10 ) @ ( the_carrier @ SV10 ) )
| ~ ~ ( ~ ( in @ ( sK9_D @ SY37 @ SY36 @ SV10 ) @ SY36 )
| ~ ~ ( related @ SV10 @ ( sK9_D @ SY37 @ SY36 @ SV10 ) @ SY37 ) ) )
| ( relstr_set_smaller @ SV10 @ SY36 @ SY37 ) )
| ~ ! [SY38: $i,SY39: $i] :
( ~ ( element @ SY39 @ ( the_carrier @ SV10 ) )
| ~ ( relstr_set_smaller @ SV10 @ SY38 @ SY39 )
| ! [SY40: $i] :
( ~ ( element @ SY40 @ ( the_carrier @ SV10 ) )
| ~ ( in @ SY40 @ SY38 )
| ( related @ SV10 @ SY40 @ SY39 ) ) ) )
= $false )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(142,plain,
! [SV11: $i] :
( ( ( ~ ! [SY41: $i,SY42: $i] :
( ~ ( element @ SY42 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( element @ ( sK10_D @ SY42 @ SY41 @ SV11 ) @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( in @ ( sK10_D @ SY42 @ SY41 @ SV11 ) @ SY41 )
| ~ ~ ( related @ SV11 @ SY42 @ ( sK10_D @ SY42 @ SY41 @ SV11 ) ) ) )
| ( relstr_element_smaller @ SV11 @ SY41 @ SY42 ) )
| ~ ! [SY43: $i,SY44: $i] :
( ~ ( element @ SY44 @ ( the_carrier @ SV11 ) )
| ~ ( relstr_element_smaller @ SV11 @ SY43 @ SY44 )
| ! [SY45: $i] :
( ~ ( element @ SY45 @ ( the_carrier @ SV11 ) )
| ~ ( in @ SY45 @ SY43 )
| ( related @ SV11 @ SY44 @ SY45 ) ) ) )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(143,plain,
( ( ( ~ ( relstr_element_smaller @ sK1_A @ empty_set @ sK2_SY30 ) )
= $true )
| ( ( ~ ( relstr_set_smaller @ sK1_A @ empty_set @ sK2_SY30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(144,plain,
( ( empty @ sK5_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(145,plain,
! [SV1: $i,SV12: $i] :
( ( ( in @ SV12 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(146,plain,
! [SV6: $i,SV14: $i] :
( ( ( empty @ SV14 )
= $true )
| ( ( in @ SV6 @ SV14 )
= $true )
| ( ( element @ SV6 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(147,plain,
! [SV15: $i,SV8: $i] :
( ( ( in @ SV8 @ SV15 )
= $false )
| ( ( empty @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(148,plain,
! [SV16: $i,SV9: $i] :
( ( ( empty @ SV9 )
= $false )
| ( ( SV9 = SV16 )
= $true )
| ( ( ~ ( empty @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(149,plain,
! [SV10: $i] :
( ( ( ~ ! [SY36: $i,SY37: $i] :
( ~ ( element @ SY37 @ ( the_carrier @ SV10 ) )
| ~ ( ~ ( element @ ( sK9_D @ SY37 @ SY36 @ SV10 ) @ ( the_carrier @ SV10 ) )
| ~ ~ ( ~ ( in @ ( sK9_D @ SY37 @ SY36 @ SV10 ) @ SY36 )
| ~ ~ ( related @ SV10 @ ( sK9_D @ SY37 @ SY36 @ SV10 ) @ SY37 ) ) )
| ( relstr_set_smaller @ SV10 @ SY36 @ SY37 ) ) )
= $false )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(150,plain,
! [SV10: $i] :
( ( ( ~ ! [SY38: $i,SY39: $i] :
( ~ ( element @ SY39 @ ( the_carrier @ SV10 ) )
| ~ ( relstr_set_smaller @ SV10 @ SY38 @ SY39 )
| ! [SY40: $i] :
( ~ ( element @ SY40 @ ( the_carrier @ SV10 ) )
| ~ ( in @ SY40 @ SY38 )
| ( related @ SV10 @ SY40 @ SY39 ) ) ) )
= $false )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(151,plain,
! [SV11: $i] :
( ( ( ~ ! [SY41: $i,SY42: $i] :
( ~ ( element @ SY42 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( element @ ( sK10_D @ SY42 @ SY41 @ SV11 ) @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( in @ ( sK10_D @ SY42 @ SY41 @ SV11 ) @ SY41 )
| ~ ~ ( related @ SV11 @ SY42 @ ( sK10_D @ SY42 @ SY41 @ SV11 ) ) ) )
| ( relstr_element_smaller @ SV11 @ SY41 @ SY42 ) ) )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(152,plain,
! [SV11: $i] :
( ( ( ~ ! [SY43: $i,SY44: $i] :
( ~ ( element @ SY44 @ ( the_carrier @ SV11 ) )
| ~ ( relstr_element_smaller @ SV11 @ SY43 @ SY44 )
| ! [SY45: $i] :
( ~ ( element @ SY45 @ ( the_carrier @ SV11 ) )
| ~ ( in @ SY45 @ SY43 )
| ( related @ SV11 @ SY44 @ SY45 ) ) ) )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(153,plain,
( ( ( relstr_element_smaller @ sK1_A @ empty_set @ sK2_SY30 )
= $false )
| ( ( ~ ( relstr_set_smaller @ sK1_A @ empty_set @ sK2_SY30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(154,plain,
! [SV9: $i,SV16: $i] :
( ( ( empty @ SV16 )
= $false )
| ( ( SV9 = SV16 )
= $true )
| ( ( empty @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(155,plain,
! [SV10: $i] :
( ( ( ! [SY36: $i,SY37: $i] :
( ~ ( element @ SY37 @ ( the_carrier @ SV10 ) )
| ~ ( ~ ( element @ ( sK9_D @ SY37 @ SY36 @ SV10 ) @ ( the_carrier @ SV10 ) )
| ~ ~ ( ~ ( in @ ( sK9_D @ SY37 @ SY36 @ SV10 ) @ SY36 )
| ~ ~ ( related @ SV10 @ ( sK9_D @ SY37 @ SY36 @ SV10 ) @ SY37 ) ) )
| ( relstr_set_smaller @ SV10 @ SY36 @ SY37 ) ) )
= $true )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(156,plain,
! [SV10: $i] :
( ( ( ! [SY38: $i,SY39: $i] :
( ~ ( element @ SY39 @ ( the_carrier @ SV10 ) )
| ~ ( relstr_set_smaller @ SV10 @ SY38 @ SY39 )
| ! [SY40: $i] :
( ~ ( element @ SY40 @ ( the_carrier @ SV10 ) )
| ~ ( in @ SY40 @ SY38 )
| ( related @ SV10 @ SY40 @ SY39 ) ) ) )
= $true )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(157,plain,
! [SV11: $i] :
( ( ( ! [SY41: $i,SY42: $i] :
( ~ ( element @ SY42 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( element @ ( sK10_D @ SY42 @ SY41 @ SV11 ) @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( in @ ( sK10_D @ SY42 @ SY41 @ SV11 ) @ SY41 )
| ~ ~ ( related @ SV11 @ SY42 @ ( sK10_D @ SY42 @ SY41 @ SV11 ) ) ) )
| ( relstr_element_smaller @ SV11 @ SY41 @ SY42 ) ) )
= $true )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(158,plain,
! [SV11: $i] :
( ( ( ! [SY43: $i,SY44: $i] :
( ~ ( element @ SY44 @ ( the_carrier @ SV11 ) )
| ~ ( relstr_element_smaller @ SV11 @ SY43 @ SY44 )
| ! [SY45: $i] :
( ~ ( element @ SY45 @ ( the_carrier @ SV11 ) )
| ~ ( in @ SY45 @ SY43 )
| ( related @ SV11 @ SY44 @ SY45 ) ) ) )
= $true )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(159,plain,
( ( ( relstr_set_smaller @ sK1_A @ empty_set @ sK2_SY30 )
= $false )
| ( ( relstr_element_smaller @ sK1_A @ empty_set @ sK2_SY30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(160,plain,
! [SV17: $i,SV10: $i] :
( ( ( ! [SY46: $i] :
( ~ ( element @ SY46 @ ( the_carrier @ SV10 ) )
| ~ ( ~ ( element @ ( sK9_D @ SY46 @ SV17 @ SV10 ) @ ( the_carrier @ SV10 ) )
| ~ ~ ( ~ ( in @ ( sK9_D @ SY46 @ SV17 @ SV10 ) @ SV17 )
| ~ ~ ( related @ SV10 @ ( sK9_D @ SY46 @ SV17 @ SV10 ) @ SY46 ) ) )
| ( relstr_set_smaller @ SV10 @ SV17 @ SY46 ) ) )
= $true )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(161,plain,
! [SV18: $i,SV10: $i] :
( ( ( ! [SY47: $i] :
( ~ ( element @ SY47 @ ( the_carrier @ SV10 ) )
| ~ ( relstr_set_smaller @ SV10 @ SV18 @ SY47 )
| ! [SY48: $i] :
( ~ ( element @ SY48 @ ( the_carrier @ SV10 ) )
| ~ ( in @ SY48 @ SV18 )
| ( related @ SV10 @ SY48 @ SY47 ) ) ) )
= $true )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(162,plain,
! [SV19: $i,SV11: $i] :
( ( ( ! [SY49: $i] :
( ~ ( element @ SY49 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( element @ ( sK10_D @ SY49 @ SV19 @ SV11 ) @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( in @ ( sK10_D @ SY49 @ SV19 @ SV11 ) @ SV19 )
| ~ ~ ( related @ SV11 @ SY49 @ ( sK10_D @ SY49 @ SV19 @ SV11 ) ) ) )
| ( relstr_element_smaller @ SV11 @ SV19 @ SY49 ) ) )
= $true )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(163,plain,
! [SV20: $i,SV11: $i] :
( ( ( ! [SY50: $i] :
( ~ ( element @ SY50 @ ( the_carrier @ SV11 ) )
| ~ ( relstr_element_smaller @ SV11 @ SV20 @ SY50 )
| ! [SY51: $i] :
( ~ ( element @ SY51 @ ( the_carrier @ SV11 ) )
| ~ ( in @ SY51 @ SV20 )
| ( related @ SV11 @ SY50 @ SY51 ) ) ) )
= $true )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(164,plain,
! [SV17: $i,SV10: $i,SV21: $i] :
( ( ( ~ ( element @ SV21 @ ( the_carrier @ SV10 ) )
| ~ ( ~ ( element @ ( sK9_D @ SV21 @ SV17 @ SV10 ) @ ( the_carrier @ SV10 ) )
| ~ ~ ( ~ ( in @ ( sK9_D @ SV21 @ SV17 @ SV10 ) @ SV17 )
| ~ ~ ( related @ SV10 @ ( sK9_D @ SV21 @ SV17 @ SV10 ) @ SV21 ) ) )
| ( relstr_set_smaller @ SV10 @ SV17 @ SV21 ) )
= $true )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(165,plain,
! [SV18: $i,SV10: $i,SV22: $i] :
( ( ( ~ ( element @ SV22 @ ( the_carrier @ SV10 ) )
| ~ ( relstr_set_smaller @ SV10 @ SV18 @ SV22 )
| ! [SY52: $i] :
( ~ ( element @ SY52 @ ( the_carrier @ SV10 ) )
| ~ ( in @ SY52 @ SV18 )
| ( related @ SV10 @ SY52 @ SV22 ) ) )
= $true )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(166,plain,
! [SV19: $i,SV11: $i,SV23: $i] :
( ( ( ~ ( element @ SV23 @ ( the_carrier @ SV11 ) )
| ~ ( ~ ( element @ ( sK10_D @ SV23 @ SV19 @ SV11 ) @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( in @ ( sK10_D @ SV23 @ SV19 @ SV11 ) @ SV19 )
| ~ ~ ( related @ SV11 @ SV23 @ ( sK10_D @ SV23 @ SV19 @ SV11 ) ) ) )
| ( relstr_element_smaller @ SV11 @ SV19 @ SV23 ) )
= $true )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(167,plain,
! [SV20: $i,SV11: $i,SV24: $i] :
( ( ( ~ ( element @ SV24 @ ( the_carrier @ SV11 ) )
| ~ ( relstr_element_smaller @ SV11 @ SV20 @ SV24 )
| ! [SY53: $i] :
( ~ ( element @ SY53 @ ( the_carrier @ SV11 ) )
| ~ ( in @ SY53 @ SV20 )
| ( related @ SV11 @ SV24 @ SY53 ) ) )
= $true )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(168,plain,
! [SV17: $i,SV10: $i,SV21: $i] :
( ( ( ~ ( element @ SV21 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK9_D @ SV21 @ SV17 @ SV10 ) @ ( the_carrier @ SV10 ) )
| ~ ~ ( ~ ( in @ ( sK9_D @ SV21 @ SV17 @ SV10 ) @ SV17 )
| ~ ~ ( related @ SV10 @ ( sK9_D @ SV21 @ SV17 @ SV10 ) @ SV21 ) ) )
| ( relstr_set_smaller @ SV10 @ SV17 @ SV21 ) )
= $true )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(169,plain,
! [SV18: $i,SV10: $i,SV22: $i] :
( ( ( ~ ( element @ SV22 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ( relstr_set_smaller @ SV10 @ SV18 @ SV22 )
| ! [SY52: $i] :
( ~ ( element @ SY52 @ ( the_carrier @ SV10 ) )
| ~ ( in @ SY52 @ SV18 )
| ( related @ SV10 @ SY52 @ SV22 ) ) )
= $true )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(170,plain,
! [SV19: $i,SV11: $i,SV23: $i] :
( ( ( ~ ( element @ SV23 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK10_D @ SV23 @ SV19 @ SV11 ) @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( in @ ( sK10_D @ SV23 @ SV19 @ SV11 ) @ SV19 )
| ~ ~ ( related @ SV11 @ SV23 @ ( sK10_D @ SV23 @ SV19 @ SV11 ) ) ) )
| ( relstr_element_smaller @ SV11 @ SV19 @ SV23 ) )
= $true )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(171,plain,
! [SV20: $i,SV11: $i,SV24: $i] :
( ( ( ~ ( element @ SV24 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV11 @ SV20 @ SV24 )
| ! [SY53: $i] :
( ~ ( element @ SY53 @ ( the_carrier @ SV11 ) )
| ~ ( in @ SY53 @ SV20 )
| ( related @ SV11 @ SV24 @ SY53 ) ) )
= $true )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(172,plain,
! [SV17: $i,SV10: $i,SV21: $i] :
( ( ( element @ SV21 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK9_D @ SV21 @ SV17 @ SV10 ) @ ( the_carrier @ SV10 ) )
| ~ ~ ( ~ ( in @ ( sK9_D @ SV21 @ SV17 @ SV10 ) @ SV17 )
| ~ ~ ( related @ SV10 @ ( sK9_D @ SV21 @ SV17 @ SV10 ) @ SV21 ) ) )
| ( relstr_set_smaller @ SV10 @ SV17 @ SV21 ) )
= $true )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(173,plain,
! [SV18: $i,SV10: $i,SV22: $i] :
( ( ( element @ SV22 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( ~ ( relstr_set_smaller @ SV10 @ SV18 @ SV22 )
| ! [SY52: $i] :
( ~ ( element @ SY52 @ ( the_carrier @ SV10 ) )
| ~ ( in @ SY52 @ SV18 )
| ( related @ SV10 @ SY52 @ SV22 ) ) )
= $true )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(174,plain,
! [SV19: $i,SV11: $i,SV23: $i] :
( ( ( element @ SV23 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK10_D @ SV23 @ SV19 @ SV11 ) @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( in @ ( sK10_D @ SV23 @ SV19 @ SV11 ) @ SV19 )
| ~ ~ ( related @ SV11 @ SV23 @ ( sK10_D @ SV23 @ SV19 @ SV11 ) ) ) )
| ( relstr_element_smaller @ SV11 @ SV19 @ SV23 ) )
= $true )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(175,plain,
! [SV20: $i,SV11: $i,SV24: $i] :
( ( ( element @ SV24 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV11 @ SV20 @ SV24 )
| ! [SY53: $i] :
( ~ ( element @ SY53 @ ( the_carrier @ SV11 ) )
| ~ ( in @ SY53 @ SV20 )
| ( related @ SV11 @ SV24 @ SY53 ) ) )
= $true )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(176,plain,
! [SV10: $i,SV17: $i,SV21: $i] :
( ( ( ~ ( ~ ( element @ ( sK9_D @ SV21 @ SV17 @ SV10 ) @ ( the_carrier @ SV10 ) )
| ~ ~ ( ~ ( in @ ( sK9_D @ SV21 @ SV17 @ SV10 ) @ SV17 )
| ~ ~ ( related @ SV10 @ ( sK9_D @ SV21 @ SV17 @ SV10 ) @ SV21 ) ) ) )
= $true )
| ( ( relstr_set_smaller @ SV10 @ SV17 @ SV21 )
= $true )
| ( ( element @ SV21 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(177,plain,
! [SV22: $i,SV18: $i,SV10: $i] :
( ( ( ~ ( relstr_set_smaller @ SV10 @ SV18 @ SV22 ) )
= $true )
| ( ( ! [SY52: $i] :
( ~ ( element @ SY52 @ ( the_carrier @ SV10 ) )
| ~ ( in @ SY52 @ SV18 )
| ( related @ SV10 @ SY52 @ SV22 ) ) )
= $true )
| ( ( element @ SV22 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(178,plain,
! [SV11: $i,SV19: $i,SV23: $i] :
( ( ( ~ ( ~ ( element @ ( sK10_D @ SV23 @ SV19 @ SV11 ) @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( in @ ( sK10_D @ SV23 @ SV19 @ SV11 ) @ SV19 )
| ~ ~ ( related @ SV11 @ SV23 @ ( sK10_D @ SV23 @ SV19 @ SV11 ) ) ) ) )
= $true )
| ( ( relstr_element_smaller @ SV11 @ SV19 @ SV23 )
= $true )
| ( ( element @ SV23 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(179,plain,
! [SV24: $i,SV20: $i,SV11: $i] :
( ( ( ~ ( relstr_element_smaller @ SV11 @ SV20 @ SV24 ) )
= $true )
| ( ( ! [SY53: $i] :
( ~ ( element @ SY53 @ ( the_carrier @ SV11 ) )
| ~ ( in @ SY53 @ SV20 )
| ( related @ SV11 @ SV24 @ SY53 ) ) )
= $true )
| ( ( element @ SV24 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(180,plain,
! [SV10: $i,SV17: $i,SV21: $i] :
( ( ( ~ ( element @ ( sK9_D @ SV21 @ SV17 @ SV10 ) @ ( the_carrier @ SV10 ) )
| ~ ~ ( ~ ( in @ ( sK9_D @ SV21 @ SV17 @ SV10 ) @ SV17 )
| ~ ~ ( related @ SV10 @ ( sK9_D @ SV21 @ SV17 @ SV10 ) @ SV21 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV10 @ SV17 @ SV21 )
= $true )
| ( ( element @ SV21 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(181,plain,
! [SV22: $i,SV18: $i,SV10: $i] :
( ( ( relstr_set_smaller @ SV10 @ SV18 @ SV22 )
= $false )
| ( ( ! [SY52: $i] :
( ~ ( element @ SY52 @ ( the_carrier @ SV10 ) )
| ~ ( in @ SY52 @ SV18 )
| ( related @ SV10 @ SY52 @ SV22 ) ) )
= $true )
| ( ( element @ SV22 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(182,plain,
! [SV11: $i,SV19: $i,SV23: $i] :
( ( ( ~ ( element @ ( sK10_D @ SV23 @ SV19 @ SV11 ) @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( in @ ( sK10_D @ SV23 @ SV19 @ SV11 ) @ SV19 )
| ~ ~ ( related @ SV11 @ SV23 @ ( sK10_D @ SV23 @ SV19 @ SV11 ) ) ) )
= $false )
| ( ( relstr_element_smaller @ SV11 @ SV19 @ SV23 )
= $true )
| ( ( element @ SV23 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(183,plain,
! [SV24: $i,SV20: $i,SV11: $i] :
( ( ( relstr_element_smaller @ SV11 @ SV20 @ SV24 )
= $false )
| ( ( ! [SY53: $i] :
( ~ ( element @ SY53 @ ( the_carrier @ SV11 ) )
| ~ ( in @ SY53 @ SV20 )
| ( related @ SV11 @ SV24 @ SY53 ) ) )
= $true )
| ( ( element @ SV24 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(184,plain,
! [SV10: $i,SV17: $i,SV21: $i] :
( ( ( ~ ( element @ ( sK9_D @ SV21 @ SV17 @ SV10 ) @ ( the_carrier @ SV10 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV10 @ SV17 @ SV21 )
= $true )
| ( ( element @ SV21 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(185,plain,
! [SV10: $i,SV17: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK9_D @ SV21 @ SV17 @ SV10 ) @ SV17 )
| ~ ~ ( related @ SV10 @ ( sK9_D @ SV21 @ SV17 @ SV10 ) @ SV21 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV10 @ SV17 @ SV21 )
= $true )
| ( ( element @ SV21 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(186,plain,
! [SV22: $i,SV18: $i,SV10: $i,SV25: $i] :
( ( ( ~ ( element @ SV25 @ ( the_carrier @ SV10 ) )
| ~ ( in @ SV25 @ SV18 )
| ( related @ SV10 @ SV25 @ SV22 ) )
= $true )
| ( ( relstr_set_smaller @ SV10 @ SV18 @ SV22 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(187,plain,
! [SV11: $i,SV19: $i,SV23: $i] :
( ( ( ~ ( element @ ( sK10_D @ SV23 @ SV19 @ SV11 ) @ ( the_carrier @ SV11 ) ) )
= $false )
| ( ( relstr_element_smaller @ SV11 @ SV19 @ SV23 )
= $true )
| ( ( element @ SV23 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[182]) ).
thf(188,plain,
! [SV11: $i,SV19: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK10_D @ SV23 @ SV19 @ SV11 ) @ SV19 )
| ~ ~ ( related @ SV11 @ SV23 @ ( sK10_D @ SV23 @ SV19 @ SV11 ) ) ) )
= $false )
| ( ( relstr_element_smaller @ SV11 @ SV19 @ SV23 )
= $true )
| ( ( element @ SV23 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[182]) ).
thf(189,plain,
! [SV24: $i,SV20: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( element @ SV26 @ ( the_carrier @ SV11 ) )
| ~ ( in @ SV26 @ SV20 )
| ( related @ SV11 @ SV24 @ SV26 ) )
= $true )
| ( ( relstr_element_smaller @ SV11 @ SV20 @ SV24 )
= $false )
| ( ( element @ SV24 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(190,plain,
! [SV10: $i,SV17: $i,SV21: $i] :
( ( ( element @ ( sK9_D @ SV21 @ SV17 @ SV10 ) @ ( the_carrier @ SV10 ) )
= $true )
| ( ( relstr_set_smaller @ SV10 @ SV17 @ SV21 )
= $true )
| ( ( element @ SV21 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(191,plain,
! [SV10: $i,SV17: $i,SV21: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_D @ SV21 @ SV17 @ SV10 ) @ SV17 )
| ~ ~ ( related @ SV10 @ ( sK9_D @ SV21 @ SV17 @ SV10 ) @ SV21 ) ) )
= $true )
| ( ( relstr_set_smaller @ SV10 @ SV17 @ SV21 )
= $true )
| ( ( element @ SV21 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(192,plain,
! [SV22: $i,SV18: $i,SV10: $i,SV25: $i] :
( ( ( ~ ( element @ SV25 @ ( the_carrier @ SV10 ) ) )
= $true )
| ( ( ~ ( in @ SV25 @ SV18 )
| ( related @ SV10 @ SV25 @ SV22 ) )
= $true )
| ( ( relstr_set_smaller @ SV10 @ SV18 @ SV22 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(193,plain,
! [SV11: $i,SV19: $i,SV23: $i] :
( ( ( element @ ( sK10_D @ SV23 @ SV19 @ SV11 ) @ ( the_carrier @ SV11 ) )
= $true )
| ( ( relstr_element_smaller @ SV11 @ SV19 @ SV23 )
= $true )
| ( ( element @ SV23 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(194,plain,
! [SV11: $i,SV19: $i,SV23: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_D @ SV23 @ SV19 @ SV11 ) @ SV19 )
| ~ ~ ( related @ SV11 @ SV23 @ ( sK10_D @ SV23 @ SV19 @ SV11 ) ) ) )
= $true )
| ( ( relstr_element_smaller @ SV11 @ SV19 @ SV23 )
= $true )
| ( ( element @ SV23 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[188]) ).
thf(195,plain,
! [SV24: $i,SV20: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( element @ SV26 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ~ ( in @ SV26 @ SV20 )
| ( related @ SV11 @ SV24 @ SV26 ) )
= $true )
| ( ( relstr_element_smaller @ SV11 @ SV20 @ SV24 )
= $false )
| ( ( element @ SV24 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(196,plain,
! [SV10: $i,SV17: $i,SV21: $i] :
( ( ( ~ ( in @ ( sK9_D @ SV21 @ SV17 @ SV10 ) @ SV17 )
| ~ ~ ( related @ SV10 @ ( sK9_D @ SV21 @ SV17 @ SV10 ) @ SV21 ) )
= $false )
| ( ( relstr_set_smaller @ SV10 @ SV17 @ SV21 )
= $true )
| ( ( element @ SV21 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(197,plain,
! [SV22: $i,SV18: $i,SV10: $i,SV25: $i] :
( ( ( element @ SV25 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( ~ ( in @ SV25 @ SV18 )
| ( related @ SV10 @ SV25 @ SV22 ) )
= $true )
| ( ( relstr_set_smaller @ SV10 @ SV18 @ SV22 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(198,plain,
! [SV11: $i,SV19: $i,SV23: $i] :
( ( ( ~ ( in @ ( sK10_D @ SV23 @ SV19 @ SV11 ) @ SV19 )
| ~ ~ ( related @ SV11 @ SV23 @ ( sK10_D @ SV23 @ SV19 @ SV11 ) ) )
= $false )
| ( ( relstr_element_smaller @ SV11 @ SV19 @ SV23 )
= $true )
| ( ( element @ SV23 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(199,plain,
! [SV24: $i,SV20: $i,SV11: $i,SV26: $i] :
( ( ( element @ SV26 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( ~ ( in @ SV26 @ SV20 )
| ( related @ SV11 @ SV24 @ SV26 ) )
= $true )
| ( ( relstr_element_smaller @ SV11 @ SV20 @ SV24 )
= $false )
| ( ( element @ SV24 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(200,plain,
! [SV10: $i,SV17: $i,SV21: $i] :
( ( ( ~ ( in @ ( sK9_D @ SV21 @ SV17 @ SV10 ) @ SV17 ) )
= $false )
| ( ( relstr_set_smaller @ SV10 @ SV17 @ SV21 )
= $true )
| ( ( element @ SV21 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(201,plain,
! [SV17: $i,SV21: $i,SV10: $i] :
( ( ( ~ ~ ( related @ SV10 @ ( sK9_D @ SV21 @ SV17 @ SV10 ) @ SV21 ) )
= $false )
| ( ( relstr_set_smaller @ SV10 @ SV17 @ SV21 )
= $true )
| ( ( element @ SV21 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(202,plain,
! [SV22: $i,SV10: $i,SV18: $i,SV25: $i] :
( ( ( ~ ( in @ SV25 @ SV18 ) )
= $true )
| ( ( related @ SV10 @ SV25 @ SV22 )
= $true )
| ( ( element @ SV25 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( relstr_set_smaller @ SV10 @ SV18 @ SV22 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(203,plain,
! [SV11: $i,SV19: $i,SV23: $i] :
( ( ( ~ ( in @ ( sK10_D @ SV23 @ SV19 @ SV11 ) @ SV19 ) )
= $false )
| ( ( relstr_element_smaller @ SV11 @ SV19 @ SV23 )
= $true )
| ( ( element @ SV23 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[198]) ).
thf(204,plain,
! [SV19: $i,SV23: $i,SV11: $i] :
( ( ( ~ ~ ( related @ SV11 @ SV23 @ ( sK10_D @ SV23 @ SV19 @ SV11 ) ) )
= $false )
| ( ( relstr_element_smaller @ SV11 @ SV19 @ SV23 )
= $true )
| ( ( element @ SV23 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[198]) ).
thf(205,plain,
! [SV24: $i,SV11: $i,SV20: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ SV20 ) )
= $true )
| ( ( related @ SV11 @ SV24 @ SV26 )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( relstr_element_smaller @ SV11 @ SV20 @ SV24 )
= $false )
| ( ( element @ SV24 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(206,plain,
! [SV10: $i,SV17: $i,SV21: $i] :
( ( ( in @ ( sK9_D @ SV21 @ SV17 @ SV10 ) @ SV17 )
= $true )
| ( ( relstr_set_smaller @ SV10 @ SV17 @ SV21 )
= $true )
| ( ( element @ SV21 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(207,plain,
! [SV17: $i,SV21: $i,SV10: $i] :
( ( ( ~ ( related @ SV10 @ ( sK9_D @ SV21 @ SV17 @ SV10 ) @ SV21 ) )
= $true )
| ( ( relstr_set_smaller @ SV10 @ SV17 @ SV21 )
= $true )
| ( ( element @ SV21 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(208,plain,
! [SV22: $i,SV10: $i,SV18: $i,SV25: $i] :
( ( ( in @ SV25 @ SV18 )
= $false )
| ( ( related @ SV10 @ SV25 @ SV22 )
= $true )
| ( ( element @ SV25 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( relstr_set_smaller @ SV10 @ SV18 @ SV22 )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(209,plain,
! [SV11: $i,SV19: $i,SV23: $i] :
( ( ( in @ ( sK10_D @ SV23 @ SV19 @ SV11 ) @ SV19 )
= $true )
| ( ( relstr_element_smaller @ SV11 @ SV19 @ SV23 )
= $true )
| ( ( element @ SV23 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(210,plain,
! [SV19: $i,SV23: $i,SV11: $i] :
( ( ( ~ ( related @ SV11 @ SV23 @ ( sK10_D @ SV23 @ SV19 @ SV11 ) ) )
= $true )
| ( ( relstr_element_smaller @ SV11 @ SV19 @ SV23 )
= $true )
| ( ( element @ SV23 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(211,plain,
! [SV24: $i,SV11: $i,SV20: $i,SV26: $i] :
( ( ( in @ SV26 @ SV20 )
= $false )
| ( ( related @ SV11 @ SV24 @ SV26 )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( relstr_element_smaller @ SV11 @ SV20 @ SV24 )
= $false )
| ( ( element @ SV24 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(212,plain,
! [SV17: $i,SV21: $i,SV10: $i] :
( ( ( related @ SV10 @ ( sK9_D @ SV21 @ SV17 @ SV10 ) @ SV21 )
= $false )
| ( ( relstr_set_smaller @ SV10 @ SV17 @ SV21 )
= $true )
| ( ( element @ SV21 @ ( the_carrier @ SV10 ) )
= $false )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(213,plain,
! [SV19: $i,SV23: $i,SV11: $i] :
( ( ( related @ SV11 @ SV23 @ ( sK10_D @ SV23 @ SV19 @ SV11 ) )
= $false )
| ( ( relstr_element_smaller @ SV11 @ SV19 @ SV23 )
= $true )
| ( ( element @ SV23 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(214,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[71,213,212,211,209,208,206,193,190,159,154,147,146,145,144,137,135,132,127,124,123,98,97,88,81,79,77,76,75,74,73]) ).
thf(215,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[214]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU355+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 10:38:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.35
% 0.20/0.35 No.of.Axioms: 21
% 0.20/0.35
% 0.20/0.35 Length.of.Defs: 0
% 0.20/0.35
% 0.20/0.35 Contains.Choice.Funs: false
% 0.20/0.36 (rf:0,axioms:21,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:23,loop_count:0,foatp_calls:0,translation:fof_full)...........
% 0.20/0.49
% 0.20/0.49 ********************************
% 0.20/0.49 * All subproblems solved! *
% 0.20/0.49 ********************************
% 0.20/0.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:22,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:214,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.51
% 0.20/0.51 %**** Beginning of derivation protocol ****
% 0.20/0.51 % SZS output start CNFRefutation
% See solution above
% 0.20/0.51
% 0.20/0.51 %**** End of derivation protocol ****
% 0.20/0.51 %**** no. of clauses in derivation: 215 ****
% 0.20/0.51 %**** clause counter: 214 ****
% 0.20/0.51
% 0.20/0.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:22,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:214,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------