TSTP Solution File: SEU188+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU188+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 : n007.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 12:07:52 EDT 2022
% Result : Theorem 0.19s 0.50s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 58
% Syntax : Number of formulae : 331 ( 182 unt; 24 typ; 0 def)
% Number of atoms : 1823 ( 611 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 3214 ( 522 ~; 513 |; 41 &;2096 @)
% ( 8 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 8 con; 0-3 aty)
% Number of variables : 571 ( 0 ^ 557 !; 14 ?; 571 :)
% 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_in,type,
in: $i > $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_sK10_C,type,
sK10_C: $i > $i > $i ).
thf(tp_sK11_SY45,type,
sK11_SY45: $i > $i > $i ).
thf(tp_sK12_D,type,
sK12_D: $i > $i > $i > $i ).
thf(tp_sK13_C,type,
sK13_C: $i > $i > $i ).
thf(tp_sK14_SY47,type,
sK14_SY47: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_B,type,
sK2_B: $i > $i ).
thf(tp_sK3_SY43,type,
sK3_SY43: $i > $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_sK6_A,type,
sK6_A: $i ).
thf(tp_sK7_A,type,
sK7_A: $i ).
thf(tp_sK8_B,type,
sK8_B: $i > $i ).
thf(tp_sK9_D,type,
sK9_D: $i > $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(3,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(4,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_relat_1) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(7,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(8,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(9,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(10,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(11,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(12,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(13,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(14,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(15,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(16,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(17,axiom,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(18,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(19,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(20,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(21,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(22,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(23,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(24,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(25,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(26,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(27,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(29,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
thf(30,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(32,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(34,conjecture,
! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_relat_1) ).
thf(35,negated_conjecture,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[34]) ).
thf(36,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[35]) ).
thf(37,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(39,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(40,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(41,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(42,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(43,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(44,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(45,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(46,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(47,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(48,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(49,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(50,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(51,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(52,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(53,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(54,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(55,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(56,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(57,plain,
$true = $true,
inference(unfold_def,[status(thm)],[21]) ).
thf(58,plain,
$true = $true,
inference(unfold_def,[status(thm)],[22]) ).
thf(59,plain,
$true = $true,
inference(unfold_def,[status(thm)],[23]) ).
thf(60,plain,
$true = $true,
inference(unfold_def,[status(thm)],[24]) ).
thf(61,plain,
$true = $true,
inference(unfold_def,[status(thm)],[25]) ).
thf(62,plain,
$true = $true,
inference(unfold_def,[status(thm)],[26]) ).
thf(63,plain,
$true = $true,
inference(unfold_def,[status(thm)],[27]) ).
thf(64,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(65,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(66,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(67,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(68,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(69,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(70,plain,
( ( ( relation @ sK1_A )
=> ( ( ( ( relation_dom @ sK1_A )
= empty_set )
| ( ( relation_rng @ sK1_A )
= empty_set ) )
=> ( sK1_A = empty_set ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[36]) ).
thf(71,plain,
( ( relation @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[70]) ).
thf(72,plain,
( ( ( ( relation_dom @ sK1_A )
= empty_set )
| ( ( relation_rng @ sK1_A )
= empty_set ) )
= $true ),
inference(standard_cnf,[status(thm)],[70]) ).
thf(73,plain,
( ( sK1_A = empty_set )
= $false ),
inference(standard_cnf,[status(thm)],[70]) ).
thf(74,plain,
( ( ( sK1_A != empty_set ) )
= $true ),
inference(polarity_switch,[status(thm)],[73]) ).
thf(75,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(76,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(77,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(78,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK2_B @ A ) @ ( sK3_SY43 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(79,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(80,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(81,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(82,plain,
( ( ~ ( empty @ sK5_A )
& ( relation @ sK5_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(83,plain,
( ( empty @ sK6_A )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(84,plain,
( ( ( empty @ sK7_A )
& ( relation @ sK7_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(85,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(86,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(87,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(88,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(89,plain,
( ( ! [A: $i] : ( element @ ( sK8_B @ A ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[56]) ).
thf(90,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY44: $i] :
~ ( in @ ( ordered_pair @ SY44 @ ( sK10_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK10_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK11_SY45 @ B @ A ) @ ( sK10_C @ B @ A ) ) @ A )
| ( in @ ( sK10_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_rng @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_rng @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ ( sK9_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[65]) ).
thf(91,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY46: $i] :
~ ( in @ ( ordered_pair @ ( sK13_C @ B @ A ) @ SY46 ) @ A )
| ~ ( in @ ( sK13_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK13_C @ B @ A ) @ ( sK14_SY47 @ B @ A ) ) @ A )
| ( in @ ( sK13_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_dom @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_dom @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ C @ ( sK12_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[66]) ).
thf(92,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[68]) ).
thf(93,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[69]) ).
thf(94,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(95,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(96,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(97,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY46: $i] :
~ ( in @ ( ordered_pair @ ( sK13_C @ B @ A ) @ SY46 ) @ A )
| ~ ( in @ ( sK13_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK13_C @ B @ A ) @ ( sK14_SY47 @ B @ A ) ) @ A )
| ( in @ ( sK13_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_dom @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_dom @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ C @ ( sK12_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(98,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY44: $i] :
~ ( in @ ( ordered_pair @ SY44 @ ( sK10_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK10_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK11_SY45 @ B @ A ) @ ( sK10_C @ B @ A ) ) @ A )
| ( in @ ( sK10_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_rng @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_rng @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ ( sK9_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(99,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(100,plain,
$true = $true,
inference(copy,[status(thm)],[63]) ).
thf(101,plain,
$true = $true,
inference(copy,[status(thm)],[62]) ).
thf(102,plain,
$true = $true,
inference(copy,[status(thm)],[61]) ).
thf(103,plain,
$true = $true,
inference(copy,[status(thm)],[60]) ).
thf(104,plain,
$true = $true,
inference(copy,[status(thm)],[59]) ).
thf(105,plain,
$true = $true,
inference(copy,[status(thm)],[58]) ).
thf(106,plain,
$true = $true,
inference(copy,[status(thm)],[57]) ).
thf(107,plain,
( ( ! [A: $i] : ( element @ ( sK8_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(108,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(109,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(110,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(111,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(112,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(113,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(114,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(115,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(116,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(117,plain,
( ( ( empty @ sK7_A )
& ( relation @ sK7_A ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(118,plain,
( ( empty @ sK6_A )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(119,plain,
( ( ~ ( empty @ sK5_A )
& ( relation @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(120,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(121,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(122,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(123,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK2_B @ A ) @ ( sK3_SY43 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(124,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(125,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(126,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(127,plain,
( ( ( ( relation_dom @ sK1_A )
= empty_set )
| ( ( relation_rng @ sK1_A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(128,plain,
( ( relation @ sK1_A )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(129,plain,
( ( ( sK1_A != empty_set ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(130,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(131,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ ( sK13_C @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SX1 @ SX0 ) @ ( sK14_SY47 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( relation_dom @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( relation_dom @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( ordered_pair @ SX2 @ ( sK12_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(132,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(133,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(134,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ SX2 @ ( sK10_C @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY45 @ SX1 @ SX0 ) @ ( sK10_C @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( relation_rng @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( relation_rng @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( ordered_pair @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(135,plain,
( ( ~ ( ~ ~ ( empty @ sK5_A )
| ~ ( relation @ sK5_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(136,plain,
( ( ~ ( ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(137,plain,
! [SV1: $i] :
( ( ! [SY48: $i] :
( ~ ( in @ SV1 @ SY48 )
| ~ ( in @ SY48 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(138,plain,
! [SV2: $i] :
( ( ~ ( empty @ SV2 )
| ( relation @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(139,plain,
! [SV3: $i] :
( ( ! [SY49: $i] :
( ( unordered_pair @ SV3 @ SY49 )
= ( unordered_pair @ SY49 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(140,plain,
! [SV4: $i] :
( ( ! [SY50: $i] :
( ( ordered_pair @ SV4 @ SY50 )
= ( unordered_pair @ ( unordered_pair @ SV4 @ SY50 ) @ ( singleton @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(141,plain,
! [SV5: $i] :
( ( element @ ( sK8_B @ SV5 ) @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(142,plain,
! [SV6: $i] :
( ( ! [SY51: $i] :
~ ( empty @ ( ordered_pair @ SV6 @ SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(143,plain,
! [SV7: $i] :
( ( ~ ( empty @ ( singleton @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(144,plain,
! [SV8: $i] :
( ( ! [SY52: $i] :
~ ( empty @ ( unordered_pair @ SV8 @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(145,plain,
! [SV9: $i] :
( ( ( empty @ SV9 )
| ~ ( relation @ SV9 )
| ~ ( empty @ ( relation_dom @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(146,plain,
! [SV10: $i] :
( ( ( empty @ SV10 )
| ~ ( relation @ SV10 )
| ~ ( empty @ ( relation_rng @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(147,plain,
( ( empty @ sK4_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(148,plain,
! [SV11: $i] :
( ( ! [SY53: $i] :
( ~ ( in @ SV11 @ SY53 )
| ( element @ SV11 @ SY53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(149,plain,
! [SV12: $i] :
( ( ! [SY54: $i] :
( ~ ( element @ SV12 @ SY54 )
| ( empty @ SY54 )
| ( in @ SV12 @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(150,plain,
! [SV13: $i] :
( ( ~ ( relation @ SV13 )
| ( in @ ( ordered_pair @ ( sK2_B @ SV13 ) @ ( sK3_SY43 @ SV13 ) ) @ SV13 )
| ( SV13 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(151,plain,
! [SV14: $i] :
( ( ~ ( empty @ SV14 )
| ( SV14 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(152,plain,
! [SV15: $i] :
( ( ! [SY55: $i] :
( ~ ( empty @ SY55 )
| ~ ( in @ SV15 @ SY55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(153,plain,
! [SV16: $i] :
( ( ! [SY56: $i] :
( ( SV16 = SY56 )
| ~ ( empty @ SV16 )
| ~ ( empty @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(154,plain,
( ( ( ( relation_dom @ sK1_A )
= empty_set )
= $true )
| ( ( ( relation_rng @ sK1_A )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(155,plain,
( ( sK1_A = empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(156,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(157,plain,
! [SV17: $i] :
( ( ~ ( relation @ SV17 )
| ~ ( ~ ! [SY57: $i] :
( ~ ( ~ ( ! [SY58: $i] :
~ ( in @ ( ordered_pair @ ( sK13_C @ SY57 @ SV17 ) @ SY58 ) @ SV17 )
| ~ ( in @ ( sK13_C @ SY57 @ SV17 ) @ SY57 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY57 @ SV17 ) @ ( sK14_SY47 @ SY57 @ SV17 ) ) @ SV17 )
| ( in @ ( sK13_C @ SY57 @ SV17 ) @ SY57 ) ) )
| ( SY57
= ( relation_dom @ SV17 ) ) )
| ~ ! [SY59: $i] :
( ( SY59
!= ( relation_dom @ SV17 ) )
| ~ ( ~ ! [SY60: $i] :
( ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV17 )
| ( in @ SY60 @ SY59 ) )
| ~ ! [SY62: $i] :
( ~ ( in @ SY62 @ SY59 )
| ( in @ ( ordered_pair @ SY62 @ ( sK12_D @ SY62 @ SY59 @ SV17 ) ) @ SV17 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(158,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(159,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(160,plain,
! [SV18: $i] :
( ( ~ ( relation @ SV18 )
| ~ ( ~ ! [SY63: $i] :
( ~ ( ~ ( ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY64 @ ( sK10_C @ SY63 @ SV18 ) ) @ SV18 )
| ~ ( in @ ( sK10_C @ SY63 @ SV18 ) @ SY63 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY45 @ SY63 @ SV18 ) @ ( sK10_C @ SY63 @ SV18 ) ) @ SV18 )
| ( in @ ( sK10_C @ SY63 @ SV18 ) @ SY63 ) ) )
| ( SY63
= ( relation_rng @ SV18 ) ) )
| ~ ! [SY65: $i] :
( ( SY65
!= ( relation_rng @ SV18 ) )
| ~ ( ~ ! [SY66: $i] :
( ! [SY67: $i] :
~ ( in @ ( ordered_pair @ SY67 @ SY66 ) @ SV18 )
| ( in @ SY66 @ SY65 ) )
| ~ ! [SY68: $i] :
( ~ ( in @ SY68 @ SY65 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY68 @ SY65 @ SV18 ) @ SY68 ) @ SV18 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(161,plain,
( ( ~ ~ ( empty @ sK5_A )
| ~ ( relation @ sK5_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(162,plain,
( ( ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(163,plain,
! [SV19: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV19 )
| ~ ( in @ SV19 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(164,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(165,plain,
! [SV20: $i,SV3: $i] :
( ( ( unordered_pair @ SV3 @ SV20 )
= ( unordered_pair @ SV20 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(166,plain,
! [SV21: $i,SV4: $i] :
( ( ( ordered_pair @ SV4 @ SV21 )
= ( unordered_pair @ ( unordered_pair @ SV4 @ SV21 ) @ ( singleton @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(167,plain,
! [SV22: $i,SV6: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV6 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(168,plain,
! [SV7: $i] :
( ( empty @ ( singleton @ SV7 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(169,plain,
! [SV23: $i,SV8: $i] :
( ( ~ ( empty @ ( unordered_pair @ SV8 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(170,plain,
! [SV9: $i] :
( ( ( ( empty @ SV9 )
| ~ ( relation @ SV9 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(171,plain,
! [SV10: $i] :
( ( ( ( empty @ SV10 )
| ~ ( relation @ SV10 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(172,plain,
! [SV24: $i,SV11: $i] :
( ( ~ ( in @ SV11 @ SV24 )
| ( element @ SV11 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(173,plain,
! [SV25: $i,SV12: $i] :
( ( ~ ( element @ SV12 @ SV25 )
| ( empty @ SV25 )
| ( in @ SV12 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(174,plain,
! [SV13: $i] :
( ( ( ~ ( relation @ SV13 ) )
= $true )
| ( ( ( in @ ( ordered_pair @ ( sK2_B @ SV13 ) @ ( sK3_SY43 @ SV13 ) ) @ SV13 )
| ( SV13 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(175,plain,
! [SV14: $i] :
( ( ( ~ ( empty @ SV14 ) )
= $true )
| ( ( SV14 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(176,plain,
! [SV15: $i,SV26: $i] :
( ( ~ ( empty @ SV26 )
| ~ ( in @ SV15 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(177,plain,
! [SV27: $i,SV16: $i] :
( ( ( SV16 = SV27 )
| ~ ( empty @ SV16 )
| ~ ( empty @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(178,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(179,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(180,plain,
! [SV17: $i] :
( ( ( ~ ( relation @ SV17 ) )
= $true )
| ( ( ~ ( ~ ! [SY57: $i] :
( ~ ( ~ ( ! [SY58: $i] :
~ ( in @ ( ordered_pair @ ( sK13_C @ SY57 @ SV17 ) @ SY58 ) @ SV17 )
| ~ ( in @ ( sK13_C @ SY57 @ SV17 ) @ SY57 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY57 @ SV17 ) @ ( sK14_SY47 @ SY57 @ SV17 ) ) @ SV17 )
| ( in @ ( sK13_C @ SY57 @ SV17 ) @ SY57 ) ) )
| ( SY57
= ( relation_dom @ SV17 ) ) )
| ~ ! [SY59: $i] :
( ( SY59
!= ( relation_dom @ SV17 ) )
| ~ ( ~ ! [SY60: $i] :
( ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV17 )
| ( in @ SY60 @ SY59 ) )
| ~ ! [SY62: $i] :
( ~ ( in @ SY62 @ SY59 )
| ( in @ ( ordered_pair @ SY62 @ ( sK12_D @ SY62 @ SY59 @ SV17 ) ) @ SV17 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(181,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(182,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(183,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(184,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(185,plain,
! [SV18: $i] :
( ( ( ~ ( relation @ SV18 ) )
= $true )
| ( ( ~ ( ~ ! [SY63: $i] :
( ~ ( ~ ( ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY64 @ ( sK10_C @ SY63 @ SV18 ) ) @ SV18 )
| ~ ( in @ ( sK10_C @ SY63 @ SV18 ) @ SY63 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY45 @ SY63 @ SV18 ) @ ( sK10_C @ SY63 @ SV18 ) ) @ SV18 )
| ( in @ ( sK10_C @ SY63 @ SV18 ) @ SY63 ) ) )
| ( SY63
= ( relation_rng @ SV18 ) ) )
| ~ ! [SY65: $i] :
( ( SY65
!= ( relation_rng @ SV18 ) )
| ~ ( ~ ! [SY66: $i] :
( ! [SY67: $i] :
~ ( in @ ( ordered_pair @ SY67 @ SY66 ) @ SV18 )
| ( in @ SY66 @ SY65 ) )
| ~ ! [SY68: $i] :
( ~ ( in @ SY68 @ SY65 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY68 @ SY65 @ SV18 ) @ SY68 ) @ SV18 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(186,plain,
( ( ~ ~ ( empty @ sK5_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(187,plain,
( ( ~ ( relation @ sK5_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(188,plain,
( ( ~ ( empty @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[162]) ).
thf(189,plain,
( ( ~ ( relation @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[162]) ).
thf(190,plain,
! [SV19: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV19 ) )
= $true )
| ( ( ~ ( in @ SV19 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(191,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
= $false )
| ( ( relation @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(192,plain,
! [SV22: $i,SV6: $i] :
( ( empty @ ( ordered_pair @ SV6 @ SV22 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(193,plain,
! [SV23: $i,SV8: $i] :
( ( empty @ ( unordered_pair @ SV8 @ SV23 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(194,plain,
! [SV9: $i] :
( ( ( empty @ SV9 )
= $true )
| ( ( ~ ( relation @ SV9 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(195,plain,
! [SV10: $i] :
( ( ( empty @ SV10 )
= $true )
| ( ( ~ ( relation @ SV10 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(196,plain,
! [SV24: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV24 ) )
= $true )
| ( ( element @ SV11 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(197,plain,
! [SV25: $i,SV12: $i] :
( ( ( ~ ( element @ SV12 @ SV25 ) )
= $true )
| ( ( ( empty @ SV25 )
| ( in @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(198,plain,
! [SV13: $i] :
( ( ( relation @ SV13 )
= $false )
| ( ( ( in @ ( ordered_pair @ ( sK2_B @ SV13 ) @ ( sK3_SY43 @ SV13 ) ) @ SV13 )
| ( SV13 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(199,plain,
! [SV14: $i] :
( ( ( empty @ SV14 )
= $false )
| ( ( SV14 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(200,plain,
! [SV15: $i,SV26: $i] :
( ( ( ~ ( empty @ SV26 ) )
= $true )
| ( ( ~ ( in @ SV15 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(201,plain,
! [SV27: $i,SV16: $i] :
( ( ( ( SV16 = SV27 )
| ~ ( empty @ SV16 ) )
= $true )
| ( ( ~ ( empty @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(202,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(203,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(204,plain,
! [SV17: $i] :
( ( ( relation @ SV17 )
= $false )
| ( ( ~ ( ~ ! [SY57: $i] :
( ~ ( ~ ( ! [SY58: $i] :
~ ( in @ ( ordered_pair @ ( sK13_C @ SY57 @ SV17 ) @ SY58 ) @ SV17 )
| ~ ( in @ ( sK13_C @ SY57 @ SV17 ) @ SY57 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY57 @ SV17 ) @ ( sK14_SY47 @ SY57 @ SV17 ) ) @ SV17 )
| ( in @ ( sK13_C @ SY57 @ SV17 ) @ SY57 ) ) )
| ( SY57
= ( relation_dom @ SV17 ) ) )
| ~ ! [SY59: $i] :
( ( SY59
!= ( relation_dom @ SV17 ) )
| ~ ( ~ ! [SY60: $i] :
( ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV17 )
| ( in @ SY60 @ SY59 ) )
| ~ ! [SY62: $i] :
( ~ ( in @ SY62 @ SY59 )
| ( in @ ( ordered_pair @ SY62 @ ( sK12_D @ SY62 @ SY59 @ SV17 ) ) @ SV17 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(205,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(206,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(207,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(208,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(209,plain,
! [SV18: $i] :
( ( ( relation @ SV18 )
= $false )
| ( ( ~ ( ~ ! [SY63: $i] :
( ~ ( ~ ( ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY64 @ ( sK10_C @ SY63 @ SV18 ) ) @ SV18 )
| ~ ( in @ ( sK10_C @ SY63 @ SV18 ) @ SY63 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY45 @ SY63 @ SV18 ) @ ( sK10_C @ SY63 @ SV18 ) ) @ SV18 )
| ( in @ ( sK10_C @ SY63 @ SV18 ) @ SY63 ) ) )
| ( SY63
= ( relation_rng @ SV18 ) ) )
| ~ ! [SY65: $i] :
( ( SY65
!= ( relation_rng @ SV18 ) )
| ~ ( ~ ! [SY66: $i] :
( ! [SY67: $i] :
~ ( in @ ( ordered_pair @ SY67 @ SY66 ) @ SV18 )
| ( in @ SY66 @ SY65 ) )
| ~ ! [SY68: $i] :
( ~ ( in @ SY68 @ SY65 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY68 @ SY65 @ SV18 ) @ SY68 ) @ SV18 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(210,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(211,plain,
( ( relation @ sK5_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(212,plain,
( ( empty @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[188]) ).
thf(213,plain,
( ( relation @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[189]) ).
thf(214,plain,
! [SV19: $i,SV1: $i] :
( ( ( in @ SV1 @ SV19 )
= $false )
| ( ( ~ ( in @ SV19 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(215,plain,
! [SV9: $i] :
( ( ( relation @ SV9 )
= $false )
| ( ( empty @ SV9 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(216,plain,
! [SV10: $i] :
( ( ( relation @ SV10 )
= $false )
| ( ( empty @ SV10 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(217,plain,
! [SV24: $i,SV11: $i] :
( ( ( in @ SV11 @ SV24 )
= $false )
| ( ( element @ SV11 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(218,plain,
! [SV25: $i,SV12: $i] :
( ( ( element @ SV12 @ SV25 )
= $false )
| ( ( ( empty @ SV25 )
| ( in @ SV12 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(219,plain,
! [SV13: $i] :
( ( ( in @ ( ordered_pair @ ( sK2_B @ SV13 ) @ ( sK3_SY43 @ SV13 ) ) @ SV13 )
= $true )
| ( ( SV13 = empty_set )
= $true )
| ( ( relation @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(220,plain,
! [SV15: $i,SV26: $i] :
( ( ( empty @ SV26 )
= $false )
| ( ( ~ ( in @ SV15 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(221,plain,
! [SV27: $i,SV16: $i] :
( ( ( SV16 = SV27 )
= $true )
| ( ( ~ ( empty @ SV16 ) )
= $true )
| ( ( ~ ( empty @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(222,plain,
! [SV28: $i] :
( ( ~ ( empty @ SV28 )
| ( empty @ ( relation_dom @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(223,plain,
! [SV29: $i] :
( ( ~ ( empty @ SV29 )
| ( relation @ ( relation_dom @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(224,plain,
! [SV17: $i] :
( ( ( ~ ! [SY57: $i] :
( ~ ( ~ ( ! [SY58: $i] :
~ ( in @ ( ordered_pair @ ( sK13_C @ SY57 @ SV17 ) @ SY58 ) @ SV17 )
| ~ ( in @ ( sK13_C @ SY57 @ SV17 ) @ SY57 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY57 @ SV17 ) @ ( sK14_SY47 @ SY57 @ SV17 ) ) @ SV17 )
| ( in @ ( sK13_C @ SY57 @ SV17 ) @ SY57 ) ) )
| ( SY57
= ( relation_dom @ SV17 ) ) )
| ~ ! [SY59: $i] :
( ( SY59
!= ( relation_dom @ SV17 ) )
| ~ ( ~ ! [SY60: $i] :
( ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV17 )
| ( in @ SY60 @ SY59 ) )
| ~ ! [SY62: $i] :
( ~ ( in @ SY62 @ SY59 )
| ( in @ ( ordered_pair @ SY62 @ ( sK12_D @ SY62 @ SY59 @ SV17 ) ) @ SV17 ) ) ) ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(225,plain,
! [SV30: $i] :
( ( ~ ( empty @ SV30 )
| ( empty @ ( relation_rng @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(226,plain,
! [SV31: $i] :
( ( ~ ( empty @ SV31 )
| ( relation @ ( relation_rng @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(227,plain,
! [SV18: $i] :
( ( ( ~ ! [SY63: $i] :
( ~ ( ~ ( ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY64 @ ( sK10_C @ SY63 @ SV18 ) ) @ SV18 )
| ~ ( in @ ( sK10_C @ SY63 @ SV18 ) @ SY63 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY45 @ SY63 @ SV18 ) @ ( sK10_C @ SY63 @ SV18 ) ) @ SV18 )
| ( in @ ( sK10_C @ SY63 @ SV18 ) @ SY63 ) ) )
| ( SY63
= ( relation_rng @ SV18 ) ) )
| ~ ! [SY65: $i] :
( ( SY65
!= ( relation_rng @ SV18 ) )
| ~ ( ~ ! [SY66: $i] :
( ! [SY67: $i] :
~ ( in @ ( ordered_pair @ SY67 @ SY66 ) @ SV18 )
| ( in @ SY66 @ SY65 ) )
| ~ ! [SY68: $i] :
( ~ ( in @ SY68 @ SY65 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY68 @ SY65 @ SV18 ) @ SY68 ) @ SV18 ) ) ) ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(228,plain,
( ( empty @ sK5_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(229,plain,
! [SV1: $i,SV19: $i] :
( ( ( in @ SV19 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(230,plain,
! [SV9: $i] :
( ( ( empty @ ( relation_dom @ SV9 ) )
= $false )
| ( ( empty @ SV9 )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(231,plain,
! [SV10: $i] :
( ( ( empty @ ( relation_rng @ SV10 ) )
= $false )
| ( ( empty @ SV10 )
= $true )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(232,plain,
! [SV12: $i,SV25: $i] :
( ( ( empty @ SV25 )
= $true )
| ( ( in @ SV12 @ SV25 )
= $true )
| ( ( element @ SV12 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(233,plain,
! [SV26: $i,SV15: $i] :
( ( ( in @ SV15 @ SV26 )
= $false )
| ( ( empty @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(234,plain,
! [SV27: $i,SV16: $i] :
( ( ( empty @ SV16 )
= $false )
| ( ( SV16 = SV27 )
= $true )
| ( ( ~ ( empty @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(235,plain,
! [SV28: $i] :
( ( ( ~ ( empty @ SV28 ) )
= $true )
| ( ( empty @ ( relation_dom @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(236,plain,
! [SV29: $i] :
( ( ( ~ ( empty @ SV29 ) )
= $true )
| ( ( relation @ ( relation_dom @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(237,plain,
! [SV17: $i] :
( ( ( ~ ! [SY57: $i] :
( ~ ( ~ ( ! [SY58: $i] :
~ ( in @ ( ordered_pair @ ( sK13_C @ SY57 @ SV17 ) @ SY58 ) @ SV17 )
| ~ ( in @ ( sK13_C @ SY57 @ SV17 ) @ SY57 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY57 @ SV17 ) @ ( sK14_SY47 @ SY57 @ SV17 ) ) @ SV17 )
| ( in @ ( sK13_C @ SY57 @ SV17 ) @ SY57 ) ) )
| ( SY57
= ( relation_dom @ SV17 ) ) ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(238,plain,
! [SV17: $i] :
( ( ( ~ ! [SY59: $i] :
( ( SY59
!= ( relation_dom @ SV17 ) )
| ~ ( ~ ! [SY60: $i] :
( ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV17 )
| ( in @ SY60 @ SY59 ) )
| ~ ! [SY62: $i] :
( ~ ( in @ SY62 @ SY59 )
| ( in @ ( ordered_pair @ SY62 @ ( sK12_D @ SY62 @ SY59 @ SV17 ) ) @ SV17 ) ) ) ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(239,plain,
! [SV30: $i] :
( ( ( ~ ( empty @ SV30 ) )
= $true )
| ( ( empty @ ( relation_rng @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(240,plain,
! [SV31: $i] :
( ( ( ~ ( empty @ SV31 ) )
= $true )
| ( ( relation @ ( relation_rng @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(241,plain,
! [SV18: $i] :
( ( ( ~ ! [SY63: $i] :
( ~ ( ~ ( ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY64 @ ( sK10_C @ SY63 @ SV18 ) ) @ SV18 )
| ~ ( in @ ( sK10_C @ SY63 @ SV18 ) @ SY63 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY45 @ SY63 @ SV18 ) @ ( sK10_C @ SY63 @ SV18 ) ) @ SV18 )
| ( in @ ( sK10_C @ SY63 @ SV18 ) @ SY63 ) ) )
| ( SY63
= ( relation_rng @ SV18 ) ) ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(242,plain,
! [SV18: $i] :
( ( ( ~ ! [SY65: $i] :
( ( SY65
!= ( relation_rng @ SV18 ) )
| ~ ( ~ ! [SY66: $i] :
( ! [SY67: $i] :
~ ( in @ ( ordered_pair @ SY67 @ SY66 ) @ SV18 )
| ( in @ SY66 @ SY65 ) )
| ~ ! [SY68: $i] :
( ~ ( in @ SY68 @ SY65 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY68 @ SY65 @ SV18 ) @ SY68 ) @ SV18 ) ) ) ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(243,plain,
! [SV16: $i,SV27: $i] :
( ( ( empty @ SV27 )
= $false )
| ( ( SV16 = SV27 )
= $true )
| ( ( empty @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(244,plain,
! [SV28: $i] :
( ( ( empty @ SV28 )
= $false )
| ( ( empty @ ( relation_dom @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(245,plain,
! [SV29: $i] :
( ( ( empty @ SV29 )
= $false )
| ( ( relation @ ( relation_dom @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(246,plain,
! [SV17: $i] :
( ( ( ! [SY57: $i] :
( ~ ( ~ ( ! [SY58: $i] :
~ ( in @ ( ordered_pair @ ( sK13_C @ SY57 @ SV17 ) @ SY58 ) @ SV17 )
| ~ ( in @ ( sK13_C @ SY57 @ SV17 ) @ SY57 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY57 @ SV17 ) @ ( sK14_SY47 @ SY57 @ SV17 ) ) @ SV17 )
| ( in @ ( sK13_C @ SY57 @ SV17 ) @ SY57 ) ) )
| ( SY57
= ( relation_dom @ SV17 ) ) ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(247,plain,
! [SV17: $i] :
( ( ( ! [SY59: $i] :
( ( SY59
!= ( relation_dom @ SV17 ) )
| ~ ( ~ ! [SY60: $i] :
( ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV17 )
| ( in @ SY60 @ SY59 ) )
| ~ ! [SY62: $i] :
( ~ ( in @ SY62 @ SY59 )
| ( in @ ( ordered_pair @ SY62 @ ( sK12_D @ SY62 @ SY59 @ SV17 ) ) @ SV17 ) ) ) ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(248,plain,
! [SV30: $i] :
( ( ( empty @ SV30 )
= $false )
| ( ( empty @ ( relation_rng @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(249,plain,
! [SV31: $i] :
( ( ( empty @ SV31 )
= $false )
| ( ( relation @ ( relation_rng @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(250,plain,
! [SV18: $i] :
( ( ( ! [SY63: $i] :
( ~ ( ~ ( ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY64 @ ( sK10_C @ SY63 @ SV18 ) ) @ SV18 )
| ~ ( in @ ( sK10_C @ SY63 @ SV18 ) @ SY63 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY45 @ SY63 @ SV18 ) @ ( sK10_C @ SY63 @ SV18 ) ) @ SV18 )
| ( in @ ( sK10_C @ SY63 @ SV18 ) @ SY63 ) ) )
| ( SY63
= ( relation_rng @ SV18 ) ) ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(251,plain,
! [SV18: $i] :
( ( ( ! [SY65: $i] :
( ( SY65
!= ( relation_rng @ SV18 ) )
| ~ ( ~ ! [SY66: $i] :
( ! [SY67: $i] :
~ ( in @ ( ordered_pair @ SY67 @ SY66 ) @ SV18 )
| ( in @ SY66 @ SY65 ) )
| ~ ! [SY68: $i] :
( ~ ( in @ SY68 @ SY65 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY68 @ SY65 @ SV18 ) @ SY68 ) @ SV18 ) ) ) ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(252,plain,
! [SV17: $i,SV32: $i] :
( ( ( ~ ( ~ ( ! [SY69: $i] :
~ ( in @ ( ordered_pair @ ( sK13_C @ SV32 @ SV17 ) @ SY69 ) @ SV17 )
| ~ ( in @ ( sK13_C @ SV32 @ SV17 ) @ SV32 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SV32 @ SV17 ) @ ( sK14_SY47 @ SV32 @ SV17 ) ) @ SV17 )
| ( in @ ( sK13_C @ SV32 @ SV17 ) @ SV32 ) ) )
| ( SV32
= ( relation_dom @ SV17 ) ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(253,plain,
! [SV17: $i,SV33: $i] :
( ( ( ( SV33
!= ( relation_dom @ SV17 ) )
| ~ ( ~ ! [SY70: $i] :
( ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY70 @ SY61 ) @ SV17 )
| ( in @ SY70 @ SV33 ) )
| ~ ! [SY72: $i] :
( ~ ( in @ SY72 @ SV33 )
| ( in @ ( ordered_pair @ SY72 @ ( sK12_D @ SY72 @ SV33 @ SV17 ) ) @ SV17 ) ) ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(254,plain,
! [SV18: $i,SV34: $i] :
( ( ( ~ ( ~ ( ! [SY73: $i] :
~ ( in @ ( ordered_pair @ SY73 @ ( sK10_C @ SV34 @ SV18 ) ) @ SV18 )
| ~ ( in @ ( sK10_C @ SV34 @ SV18 ) @ SV34 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY45 @ SV34 @ SV18 ) @ ( sK10_C @ SV34 @ SV18 ) ) @ SV18 )
| ( in @ ( sK10_C @ SV34 @ SV18 ) @ SV34 ) ) )
| ( SV34
= ( relation_rng @ SV18 ) ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(255,plain,
! [SV18: $i,SV35: $i] :
( ( ( ( SV35
!= ( relation_rng @ SV18 ) )
| ~ ( ~ ! [SY74: $i] :
( ! [SY67: $i] :
~ ( in @ ( ordered_pair @ SY67 @ SY74 ) @ SV18 )
| ( in @ SY74 @ SV35 ) )
| ~ ! [SY76: $i] :
( ~ ( in @ SY76 @ SV35 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY76 @ SV35 @ SV18 ) @ SY76 ) @ SV18 ) ) ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(256,plain,
! [SV17: $i,SV32: $i] :
( ( ( ~ ( ~ ( ! [SY69: $i] :
~ ( in @ ( ordered_pair @ ( sK13_C @ SV32 @ SV17 ) @ SY69 ) @ SV17 )
| ~ ( in @ ( sK13_C @ SV32 @ SV17 ) @ SV32 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SV32 @ SV17 ) @ ( sK14_SY47 @ SV32 @ SV17 ) ) @ SV17 )
| ( in @ ( sK13_C @ SV32 @ SV17 ) @ SV32 ) ) ) )
= $true )
| ( ( SV32
= ( relation_dom @ SV17 ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(257,plain,
! [SV17: $i,SV33: $i] :
( ( ( ( SV33
!= ( relation_dom @ SV17 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY70: $i] :
( ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY70 @ SY61 ) @ SV17 )
| ( in @ SY70 @ SV33 ) )
| ~ ! [SY72: $i] :
( ~ ( in @ SY72 @ SV33 )
| ( in @ ( ordered_pair @ SY72 @ ( sK12_D @ SY72 @ SV33 @ SV17 ) ) @ SV17 ) ) ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(258,plain,
! [SV18: $i,SV34: $i] :
( ( ( ~ ( ~ ( ! [SY73: $i] :
~ ( in @ ( ordered_pair @ SY73 @ ( sK10_C @ SV34 @ SV18 ) ) @ SV18 )
| ~ ( in @ ( sK10_C @ SV34 @ SV18 ) @ SV34 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY45 @ SV34 @ SV18 ) @ ( sK10_C @ SV34 @ SV18 ) ) @ SV18 )
| ( in @ ( sK10_C @ SV34 @ SV18 ) @ SV34 ) ) ) )
= $true )
| ( ( SV34
= ( relation_rng @ SV18 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(259,plain,
! [SV18: $i,SV35: $i] :
( ( ( ( SV35
!= ( relation_rng @ SV18 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY74: $i] :
( ! [SY67: $i] :
~ ( in @ ( ordered_pair @ SY67 @ SY74 ) @ SV18 )
| ( in @ SY74 @ SV35 ) )
| ~ ! [SY76: $i] :
( ~ ( in @ SY76 @ SV35 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY76 @ SV35 @ SV18 ) @ SY76 ) @ SV18 ) ) ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[255]) ).
thf(260,plain,
! [SV17: $i,SV32: $i] :
( ( ( ~ ( ! [SY69: $i] :
~ ( in @ ( ordered_pair @ ( sK13_C @ SV32 @ SV17 ) @ SY69 ) @ SV17 )
| ~ ( in @ ( sK13_C @ SV32 @ SV17 ) @ SV32 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SV32 @ SV17 ) @ ( sK14_SY47 @ SV32 @ SV17 ) ) @ SV17 )
| ( in @ ( sK13_C @ SV32 @ SV17 ) @ SV32 ) ) )
= $false )
| ( ( SV32
= ( relation_dom @ SV17 ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(261,plain,
! [SV17: $i,SV33: $i] :
( ( ( SV33
= ( relation_dom @ SV17 ) )
= $false )
| ( ( ~ ( ~ ! [SY70: $i] :
( ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY70 @ SY61 ) @ SV17 )
| ( in @ SY70 @ SV33 ) )
| ~ ! [SY72: $i] :
( ~ ( in @ SY72 @ SV33 )
| ( in @ ( ordered_pair @ SY72 @ ( sK12_D @ SY72 @ SV33 @ SV17 ) ) @ SV17 ) ) ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(262,plain,
! [SV18: $i,SV34: $i] :
( ( ( ~ ( ! [SY73: $i] :
~ ( in @ ( ordered_pair @ SY73 @ ( sK10_C @ SV34 @ SV18 ) ) @ SV18 )
| ~ ( in @ ( sK10_C @ SV34 @ SV18 ) @ SV34 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_SY45 @ SV34 @ SV18 ) @ ( sK10_C @ SV34 @ SV18 ) ) @ SV18 )
| ( in @ ( sK10_C @ SV34 @ SV18 ) @ SV34 ) ) )
= $false )
| ( ( SV34
= ( relation_rng @ SV18 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(263,plain,
! [SV18: $i,SV35: $i] :
( ( ( SV35
= ( relation_rng @ SV18 ) )
= $false )
| ( ( ~ ( ~ ! [SY74: $i] :
( ! [SY67: $i] :
~ ( in @ ( ordered_pair @ SY67 @ SY74 ) @ SV18 )
| ( in @ SY74 @ SV35 ) )
| ~ ! [SY76: $i] :
( ~ ( in @ SY76 @ SV35 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY76 @ SV35 @ SV18 ) @ SY76 ) @ SV18 ) ) ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(264,plain,
! [SV17: $i,SV32: $i] :
( ( ( ~ ( ! [SY69: $i] :
~ ( in @ ( ordered_pair @ ( sK13_C @ SV32 @ SV17 ) @ SY69 ) @ SV17 )
| ~ ( in @ ( sK13_C @ SV32 @ SV17 ) @ SV32 ) ) )
= $false )
| ( ( SV32
= ( relation_dom @ SV17 ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[260]) ).
thf(265,plain,
! [SV17: $i,SV32: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SV32 @ SV17 ) @ ( sK14_SY47 @ SV32 @ SV17 ) ) @ SV17 )
| ( in @ ( sK13_C @ SV32 @ SV17 ) @ SV32 ) ) )
= $false )
| ( ( SV32
= ( relation_dom @ SV17 ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[260]) ).
thf(266,plain,
! [SV33: $i,SV17: $i] :
( ( ( ~ ! [SY70: $i] :
( ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY70 @ SY61 ) @ SV17 )
| ( in @ SY70 @ SV33 ) )
| ~ ! [SY72: $i] :
( ~ ( in @ SY72 @ SV33 )
| ( in @ ( ordered_pair @ SY72 @ ( sK12_D @ SY72 @ SV33 @ SV17 ) ) @ SV17 ) ) )
= $false )
| ( ( SV33
= ( relation_dom @ SV17 ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(267,plain,
! [SV18: $i,SV34: $i] :
( ( ( ~ ( ! [SY73: $i] :
~ ( in @ ( ordered_pair @ SY73 @ ( sK10_C @ SV34 @ SV18 ) ) @ SV18 )
| ~ ( in @ ( sK10_C @ SV34 @ SV18 ) @ SV34 ) ) )
= $false )
| ( ( SV34
= ( relation_rng @ SV18 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(268,plain,
! [SV18: $i,SV34: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK11_SY45 @ SV34 @ SV18 ) @ ( sK10_C @ SV34 @ SV18 ) ) @ SV18 )
| ( in @ ( sK10_C @ SV34 @ SV18 ) @ SV34 ) ) )
= $false )
| ( ( SV34
= ( relation_rng @ SV18 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(269,plain,
! [SV35: $i,SV18: $i] :
( ( ( ~ ! [SY74: $i] :
( ! [SY67: $i] :
~ ( in @ ( ordered_pair @ SY67 @ SY74 ) @ SV18 )
| ( in @ SY74 @ SV35 ) )
| ~ ! [SY76: $i] :
( ~ ( in @ SY76 @ SV35 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY76 @ SV35 @ SV18 ) @ SY76 ) @ SV18 ) ) )
= $false )
| ( ( SV35
= ( relation_rng @ SV18 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(270,plain,
! [SV17: $i,SV32: $i] :
( ( ( ! [SY69: $i] :
~ ( in @ ( ordered_pair @ ( sK13_C @ SV32 @ SV17 ) @ SY69 ) @ SV17 )
| ~ ( in @ ( sK13_C @ SV32 @ SV17 ) @ SV32 ) )
= $true )
| ( ( SV32
= ( relation_dom @ SV17 ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(271,plain,
! [SV17: $i,SV32: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK13_C @ SV32 @ SV17 ) @ ( sK14_SY47 @ SV32 @ SV17 ) ) @ SV17 )
| ( in @ ( sK13_C @ SV32 @ SV17 ) @ SV32 ) )
= $true )
| ( ( SV32
= ( relation_dom @ SV17 ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[265]) ).
thf(272,plain,
! [SV33: $i,SV17: $i] :
( ( ( ~ ! [SY70: $i] :
( ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY70 @ SY61 ) @ SV17 )
| ( in @ SY70 @ SV33 ) ) )
= $false )
| ( ( SV33
= ( relation_dom @ SV17 ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[266]) ).
thf(273,plain,
! [SV17: $i,SV33: $i] :
( ( ( ~ ! [SY72: $i] :
( ~ ( in @ SY72 @ SV33 )
| ( in @ ( ordered_pair @ SY72 @ ( sK12_D @ SY72 @ SV33 @ SV17 ) ) @ SV17 ) ) )
= $false )
| ( ( SV33
= ( relation_dom @ SV17 ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[266]) ).
thf(274,plain,
! [SV18: $i,SV34: $i] :
( ( ( ! [SY73: $i] :
~ ( in @ ( ordered_pair @ SY73 @ ( sK10_C @ SV34 @ SV18 ) ) @ SV18 )
| ~ ( in @ ( sK10_C @ SV34 @ SV18 ) @ SV34 ) )
= $true )
| ( ( SV34
= ( relation_rng @ SV18 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[267]) ).
thf(275,plain,
! [SV18: $i,SV34: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK11_SY45 @ SV34 @ SV18 ) @ ( sK10_C @ SV34 @ SV18 ) ) @ SV18 )
| ( in @ ( sK10_C @ SV34 @ SV18 ) @ SV34 ) )
= $true )
| ( ( SV34
= ( relation_rng @ SV18 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(276,plain,
! [SV35: $i,SV18: $i] :
( ( ( ~ ! [SY74: $i] :
( ! [SY67: $i] :
~ ( in @ ( ordered_pair @ SY67 @ SY74 ) @ SV18 )
| ( in @ SY74 @ SV35 ) ) )
= $false )
| ( ( SV35
= ( relation_rng @ SV18 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[269]) ).
thf(277,plain,
! [SV18: $i,SV35: $i] :
( ( ( ~ ! [SY76: $i] :
( ~ ( in @ SY76 @ SV35 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY76 @ SV35 @ SV18 ) @ SY76 ) @ SV18 ) ) )
= $false )
| ( ( SV35
= ( relation_rng @ SV18 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[269]) ).
thf(278,plain,
! [SV17: $i,SV32: $i] :
( ( ( ! [SY69: $i] :
~ ( in @ ( ordered_pair @ ( sK13_C @ SV32 @ SV17 ) @ SY69 ) @ SV17 ) )
= $true )
| ( ( ~ ( in @ ( sK13_C @ SV32 @ SV17 ) @ SV32 ) )
= $true )
| ( ( SV32
= ( relation_dom @ SV17 ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(279,plain,
! [SV17: $i,SV32: $i] :
( ( ( in @ ( ordered_pair @ ( sK13_C @ SV32 @ SV17 ) @ ( sK14_SY47 @ SV32 @ SV17 ) ) @ SV17 )
= $true )
| ( ( in @ ( sK13_C @ SV32 @ SV17 ) @ SV32 )
= $true )
| ( ( SV32
= ( relation_dom @ SV17 ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(280,plain,
! [SV33: $i,SV17: $i] :
( ( ( ! [SY70: $i] :
( ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY70 @ SY61 ) @ SV17 )
| ( in @ SY70 @ SV33 ) ) )
= $true )
| ( ( SV33
= ( relation_dom @ SV17 ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(281,plain,
! [SV17: $i,SV33: $i] :
( ( ( ! [SY72: $i] :
( ~ ( in @ SY72 @ SV33 )
| ( in @ ( ordered_pair @ SY72 @ ( sK12_D @ SY72 @ SV33 @ SV17 ) ) @ SV17 ) ) )
= $true )
| ( ( SV33
= ( relation_dom @ SV17 ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(282,plain,
! [SV18: $i,SV34: $i] :
( ( ( ! [SY73: $i] :
~ ( in @ ( ordered_pair @ SY73 @ ( sK10_C @ SV34 @ SV18 ) ) @ SV18 ) )
= $true )
| ( ( ~ ( in @ ( sK10_C @ SV34 @ SV18 ) @ SV34 ) )
= $true )
| ( ( SV34
= ( relation_rng @ SV18 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(283,plain,
! [SV18: $i,SV34: $i] :
( ( ( in @ ( ordered_pair @ ( sK11_SY45 @ SV34 @ SV18 ) @ ( sK10_C @ SV34 @ SV18 ) ) @ SV18 )
= $true )
| ( ( in @ ( sK10_C @ SV34 @ SV18 ) @ SV34 )
= $true )
| ( ( SV34
= ( relation_rng @ SV18 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(284,plain,
! [SV35: $i,SV18: $i] :
( ( ( ! [SY74: $i] :
( ! [SY67: $i] :
~ ( in @ ( ordered_pair @ SY67 @ SY74 ) @ SV18 )
| ( in @ SY74 @ SV35 ) ) )
= $true )
| ( ( SV35
= ( relation_rng @ SV18 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[276]) ).
thf(285,plain,
! [SV18: $i,SV35: $i] :
( ( ( ! [SY76: $i] :
( ~ ( in @ SY76 @ SV35 )
| ( in @ ( ordered_pair @ ( sK9_D @ SY76 @ SV35 @ SV18 ) @ SY76 ) @ SV18 ) ) )
= $true )
| ( ( SV35
= ( relation_rng @ SV18 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[277]) ).
thf(286,plain,
! [SV36: $i,SV17: $i,SV32: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV32 @ SV17 ) @ SV36 ) @ SV17 ) )
= $true )
| ( ( ~ ( in @ ( sK13_C @ SV32 @ SV17 ) @ SV32 ) )
= $true )
| ( ( SV32
= ( relation_dom @ SV17 ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(287,plain,
! [SV33: $i,SV17: $i,SV37: $i] :
( ( ( ! [SY77: $i] :
~ ( in @ ( ordered_pair @ SV37 @ SY77 ) @ SV17 )
| ( in @ SV37 @ SV33 ) )
= $true )
| ( ( SV33
= ( relation_dom @ SV17 ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(288,plain,
! [SV17: $i,SV33: $i,SV38: $i] :
( ( ( ~ ( in @ SV38 @ SV33 )
| ( in @ ( ordered_pair @ SV38 @ ( sK12_D @ SV38 @ SV33 @ SV17 ) ) @ SV17 ) )
= $true )
| ( ( SV33
= ( relation_dom @ SV17 ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(289,plain,
! [SV18: $i,SV34: $i,SV39: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV39 @ ( sK10_C @ SV34 @ SV18 ) ) @ SV18 ) )
= $true )
| ( ( ~ ( in @ ( sK10_C @ SV34 @ SV18 ) @ SV34 ) )
= $true )
| ( ( SV34
= ( relation_rng @ SV18 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(290,plain,
! [SV35: $i,SV18: $i,SV40: $i] :
( ( ( ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SY78 @ SV40 ) @ SV18 )
| ( in @ SV40 @ SV35 ) )
= $true )
| ( ( SV35
= ( relation_rng @ SV18 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(291,plain,
! [SV18: $i,SV35: $i,SV41: $i] :
( ( ( ~ ( in @ SV41 @ SV35 )
| ( in @ ( ordered_pair @ ( sK9_D @ SV41 @ SV35 @ SV18 ) @ SV41 ) @ SV18 ) )
= $true )
| ( ( SV35
= ( relation_rng @ SV18 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(292,plain,
! [SV36: $i,SV17: $i,SV32: $i] :
( ( ( in @ ( ordered_pair @ ( sK13_C @ SV32 @ SV17 ) @ SV36 ) @ SV17 )
= $false )
| ( ( ~ ( in @ ( sK13_C @ SV32 @ SV17 ) @ SV32 ) )
= $true )
| ( ( SV32
= ( relation_dom @ SV17 ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(293,plain,
! [SV33: $i,SV17: $i,SV37: $i] :
( ( ( ! [SY77: $i] :
~ ( in @ ( ordered_pair @ SV37 @ SY77 ) @ SV17 ) )
= $true )
| ( ( in @ SV37 @ SV33 )
= $true )
| ( ( SV33
= ( relation_dom @ SV17 ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(294,plain,
! [SV17: $i,SV33: $i,SV38: $i] :
( ( ( ~ ( in @ SV38 @ SV33 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV38 @ ( sK12_D @ SV38 @ SV33 @ SV17 ) ) @ SV17 )
= $true )
| ( ( SV33
= ( relation_dom @ SV17 ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(295,plain,
! [SV18: $i,SV34: $i,SV39: $i] :
( ( ( in @ ( ordered_pair @ SV39 @ ( sK10_C @ SV34 @ SV18 ) ) @ SV18 )
= $false )
| ( ( ~ ( in @ ( sK10_C @ SV34 @ SV18 ) @ SV34 ) )
= $true )
| ( ( SV34
= ( relation_rng @ SV18 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(296,plain,
! [SV35: $i,SV18: $i,SV40: $i] :
( ( ( ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SY78 @ SV40 ) @ SV18 ) )
= $true )
| ( ( in @ SV40 @ SV35 )
= $true )
| ( ( SV35
= ( relation_rng @ SV18 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(297,plain,
! [SV18: $i,SV35: $i,SV41: $i] :
( ( ( ~ ( in @ SV41 @ SV35 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK9_D @ SV41 @ SV35 @ SV18 ) @ SV41 ) @ SV18 )
= $true )
| ( ( SV35
= ( relation_rng @ SV18 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(298,plain,
! [SV36: $i,SV17: $i,SV32: $i] :
( ( ( in @ ( sK13_C @ SV32 @ SV17 ) @ SV32 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK13_C @ SV32 @ SV17 ) @ SV36 ) @ SV17 )
= $false )
| ( ( SV32
= ( relation_dom @ SV17 ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(299,plain,
! [SV33: $i,SV17: $i,SV42: $i,SV37: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV37 @ SV42 ) @ SV17 ) )
= $true )
| ( ( in @ SV37 @ SV33 )
= $true )
| ( ( SV33
= ( relation_dom @ SV17 ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(300,plain,
! [SV17: $i,SV33: $i,SV38: $i] :
( ( ( in @ SV38 @ SV33 )
= $false )
| ( ( in @ ( ordered_pair @ SV38 @ ( sK12_D @ SV38 @ SV33 @ SV17 ) ) @ SV17 )
= $true )
| ( ( SV33
= ( relation_dom @ SV17 ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(301,plain,
! [SV39: $i,SV18: $i,SV34: $i] :
( ( ( in @ ( sK10_C @ SV34 @ SV18 ) @ SV34 )
= $false )
| ( ( in @ ( ordered_pair @ SV39 @ ( sK10_C @ SV34 @ SV18 ) ) @ SV18 )
= $false )
| ( ( SV34
= ( relation_rng @ SV18 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(302,plain,
! [SV35: $i,SV18: $i,SV40: $i,SV43: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV43 @ SV40 ) @ SV18 ) )
= $true )
| ( ( in @ SV40 @ SV35 )
= $true )
| ( ( SV35
= ( relation_rng @ SV18 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(303,plain,
! [SV18: $i,SV35: $i,SV41: $i] :
( ( ( in @ SV41 @ SV35 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK9_D @ SV41 @ SV35 @ SV18 ) @ SV41 ) @ SV18 )
= $true )
| ( ( SV35
= ( relation_rng @ SV18 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(304,plain,
! [SV33: $i,SV17: $i,SV42: $i,SV37: $i] :
( ( ( in @ ( ordered_pair @ SV37 @ SV42 ) @ SV17 )
= $false )
| ( ( in @ SV37 @ SV33 )
= $true )
| ( ( SV33
= ( relation_dom @ SV17 ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(305,plain,
! [SV35: $i,SV18: $i,SV40: $i,SV43: $i] :
( ( ( in @ ( ordered_pair @ SV43 @ SV40 ) @ SV18 )
= $false )
| ( ( in @ SV40 @ SV35 )
= $true )
| ( ( SV35
= ( relation_rng @ SV18 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(306,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[100,305,304,303,301,300,298,283,279,249,248,245,244,243,233,232,231,230,229,228,219,217,213,212,211,206,205,199,193,192,191,168,166,165,155,154,147,141,128,118,108,106,105,104,103,102,101]) ).
thf(307,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[306]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU188+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n007.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 01:57:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 33
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.19/0.36 .
% 0.19/0.36 (rf:0,axioms:33,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:35,loop_count:0,foatp_calls:0,translation:fof_full).................
% 0.19/0.50
% 0.19/0.50 ********************************
% 0.19/0.50 * All subproblems solved! *
% 0.19/0.50 ********************************
% 0.19/0.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:35,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:306,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.54
% 0.19/0.54 %**** Beginning of derivation protocol ****
% 0.19/0.54 % SZS output start CNFRefutation
% See solution above
% 0.19/0.54
% 0.19/0.54 %**** End of derivation protocol ****
% 0.19/0.54 %**** no. of clauses in derivation: 307 ****
% 0.19/0.54 %**** clause counter: 306 ****
% 0.19/0.54
% 0.19/0.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:35,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:306,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------