%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU166+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:43:12 AM UTC 2026
% Result : Theorem 1.67s 0.48s
% Output : CNFRefutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 4
% Syntax : Number of formulae : 303 ( 68 unt; 0 typ; 0 def)
% Number of atoms : 3356 (1400 equ; 0 cnn)
% Maximal formula atoms : 5 ( 11 avg)
% Number of connectives : 9121 (2740 ~;1328 |; 15 &;5016 @)
% ( 12 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 5 con; 0-5 aty)
% Number of variables : 1518 ( 0 ^;1510 !; 8 ?;1518 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_sK10_SY62,type,
sK10_SY62: $i > $i > $i > $i > $i > $i ).
thf(tp_sK11_SY68,type,
sK11_SY68: $i > $i > $i > $i > $i > $i ).
thf(tp_sK12_SY97,type,
sK12_SY97: $i > $i > $i ).
thf(tp_sK13_SY103,type,
sK13_SY103: $i > $i > $i > $i ).
thf(tp_sK14_SY108,type,
sK14_SY108: $i > $i > $i > $i > $i ).
thf(tp_sK15_SY117,type,
sK15_SY117: $i > $i > $i > $i > $i ).
thf(tp_sK16_SY114,type,
sK16_SY114: $i > $i > $i > $i ).
thf(tp_sK17_SY119,type,
sK17_SY119: $i > $i > $i > $i ).
thf(tp_sK18_SY114,type,
sK18_SY114: $i > $i > $i > $i > $i > $i ).
thf(tp_sK19_SY120,type,
sK19_SY120: $i > $i > $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY14,type,
sK2_SY14: $i ).
thf(tp_sK3_SY16,type,
sK3_SY16: $i ).
thf(tp_sK4_SY34,type,
sK4_SY34: $i > $i > $i ).
thf(tp_sK5_SY51,type,
sK5_SY51: $i > $i > $i > $i ).
thf(tp_sK6_SY56,type,
sK6_SY56: $i > $i > $i > $i > $i ).
thf(tp_sK7_SY65,type,
sK7_SY65: $i > $i > $i > $i > $i ).
thf(tp_sK8_SY62,type,
sK8_SY62: $i > $i > $i > $i ).
thf(tp_sK9_SY67,type,
sK9_SY67: $i > $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(10,conjecture,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(11,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[10]) ).
thf(12,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(14,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(15,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(16,plain,
( ( ! [SY14: $i,SY15: $i] :
( ( subset @ sK1_A @ SY14 )
=> ( ( subset @ ( cartesian_product2 @ sK1_A @ SY15 ) @ ( cartesian_product2 @ SY14 @ SY15 ) )
& ( subset @ ( cartesian_product2 @ SY15 @ sK1_A ) @ ( cartesian_product2 @ SY15 @ SY14 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(17,plain,
( ( ! [SY16: $i] :
( ( subset @ sK1_A @ sK2_SY14 )
=> ( ( subset @ ( cartesian_product2 @ sK1_A @ SY16 ) @ ( cartesian_product2 @ sK2_SY14 @ SY16 ) )
& ( subset @ ( cartesian_product2 @ SY16 @ sK1_A ) @ ( cartesian_product2 @ SY16 @ sK2_SY14 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(18,plain,
( ( ( subset @ sK1_A @ sK2_SY14 )
=> ( ( subset @ ( cartesian_product2 @ sK1_A @ sK3_SY16 ) @ ( cartesian_product2 @ sK2_SY14 @ sK3_SY16 ) )
& ( subset @ ( cartesian_product2 @ sK3_SY16 @ sK1_A ) @ ( cartesian_product2 @ sK3_SY16 @ sK2_SY14 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(19,plain,
( ( subset @ sK1_A @ sK2_SY14 )
= $true ),
inference(standard_cnf,[status(thm)],[18]) ).
thf(20,plain,
( ( ( subset @ ( cartesian_product2 @ sK1_A @ sK3_SY16 ) @ ( cartesian_product2 @ sK2_SY14 @ sK3_SY16 ) )
& ( subset @ ( cartesian_product2 @ sK3_SY16 @ sK1_A ) @ ( cartesian_product2 @ sK3_SY16 @ sK2_SY14 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[18]) ).
thf(21,plain,
( ( subset @ ( cartesian_product2 @ sK1_A @ sK3_SY16 ) @ ( cartesian_product2 @ sK2_SY14 @ sK3_SY16 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[20]) ).
thf(22,plain,
( ( subset @ ( cartesian_product2 @ sK3_SY16 @ sK1_A ) @ ( cartesian_product2 @ sK3_SY16 @ sK2_SY14 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[20]) ).
thf(23,plain,
( ( ~ ( subset @ ( cartesian_product2 @ sK1_A @ sK3_SY16 ) @ ( cartesian_product2 @ sK2_SY14 @ sK3_SY16 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[21]) ).
thf(24,plain,
( ( ~ ( subset @ ( cartesian_product2 @ sK3_SY16 @ sK1_A ) @ ( cartesian_product2 @ sK3_SY16 @ sK2_SY14 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(25,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(26,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(27,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(28,plain,
( ( subset @ sK1_A @ sK2_SY14 )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(29,plain,
( ( ~ ( subset @ ( cartesian_product2 @ sK1_A @ sK3_SY16 ) @ ( cartesian_product2 @ sK2_SY14 @ sK3_SY16 ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(30,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(31,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( cartesian_product2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( cartesian_product2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(32,plain,
! [SV1: $i] :
( ( ! [SY17: $i] : ( subset @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(33,plain,
( ( subset @ ( cartesian_product2 @ sK1_A @ sK3_SY16 ) @ ( cartesian_product2 @ sK2_SY14 @ sK3_SY16 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV2: $i] :
( ( ! [SY18: $i] :
~ ( ~ ( ~ ( subset @ SV2 @ SY18 )
| ! [SY19: $i] :
( ~ ( in @ SY19 @ SV2 )
| ( in @ SY19 @ SY18 ) ) )
| ~ ( ~ ! [SY20: $i] :
( ~ ( in @ SY20 @ SV2 )
| ( in @ SY20 @ SY18 ) )
| ( subset @ SV2 @ SY18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV3: $i] :
( ( ! [SY21: $i,SY22: $i] :
~ ( ~ ( ( SY22
!= ( cartesian_product2 @ SV3 @ SY21 ) )
| ! [SY23: $i] :
~ ( ~ ( ~ ( in @ SY23 @ SY22 )
| ~ ! [SY24: $i] :
~ ~ ! [SY25: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY24 @ SV3 )
| ~ ( in @ SY25 @ SY21 ) )
| ( SY23
!= ( ordered_pair @ SY24 @ SY25 ) ) ) )
| ~ ( ~ ~ ! [SY26: $i] :
~ ~ ! [SY27: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY26 @ SV3 )
| ~ ( in @ SY27 @ SY21 ) )
| ( SY23
!= ( ordered_pair @ SY26 @ SY27 ) ) )
| ( in @ SY23 @ SY22 ) ) ) )
| ~ ( ~ ! [SY28: $i] :
~ ( ~ ( ~ ( in @ SY28 @ SY22 )
| ~ ! [SY29: $i] :
~ ~ ! [SY30: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY29 @ SV3 )
| ~ ( in @ SY30 @ SY21 ) )
| ( SY28
!= ( ordered_pair @ SY29 @ SY30 ) ) ) )
| ~ ( ~ ~ ! [SY31: $i] :
~ ~ ! [SY32: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY31 @ SV3 )
| ~ ( in @ SY32 @ SY21 ) )
| ( SY28
!= ( ordered_pair @ SY31 @ SY32 ) ) )
| ( in @ SY28 @ SY22 ) ) )
| ( SY22
= ( cartesian_product2 @ SV3 @ SY21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV1: $i] :
( ( subset @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV2 @ SV5 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ SV2 )
| ( in @ SY33 @ SV5 ) ) )
| ~ ( ~ ! [SY34: $i] :
( ~ ( in @ SY34 @ SV2 )
| ( in @ SY34 @ SV5 ) )
| ( subset @ SV2 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV6: $i,SV3: $i] :
( ( ! [SY35: $i] :
~ ( ~ ( ( SY35
!= ( cartesian_product2 @ SV3 @ SV6 ) )
| ! [SY36: $i] :
~ ( ~ ( ~ ( in @ SY36 @ SY35 )
| ~ ! [SY37: $i] :
~ ~ ! [SY38: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY37 @ SV3 )
| ~ ( in @ SY38 @ SV6 ) )
| ( SY36
!= ( ordered_pair @ SY37 @ SY38 ) ) ) )
| ~ ( ~ ~ ! [SY39: $i] :
~ ~ ! [SY40: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY39 @ SV3 )
| ~ ( in @ SY40 @ SV6 ) )
| ( SY36
!= ( ordered_pair @ SY39 @ SY40 ) ) )
| ( in @ SY36 @ SY35 ) ) ) )
| ~ ( ~ ! [SY41: $i] :
~ ( ~ ( ~ ( in @ SY41 @ SY35 )
| ~ ! [SY42: $i] :
~ ~ ! [SY43: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY42 @ SV3 )
| ~ ( in @ SY43 @ SV6 ) )
| ( SY41
!= ( ordered_pair @ SY42 @ SY43 ) ) ) )
| ~ ( ~ ~ ! [SY44: $i] :
~ ~ ! [SY45: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY44 @ SV3 )
| ~ ( in @ SY45 @ SV6 ) )
| ( SY41
!= ( ordered_pair @ SY44 @ SY45 ) ) )
| ( in @ SY41 @ SY35 ) ) )
| ( SY35
= ( cartesian_product2 @ SV3 @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( ~ ( subset @ SV2 @ SV5 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ SV2 )
| ( in @ SY33 @ SV5 ) ) )
| ~ ( ~ ! [SY34: $i] :
( ~ ( in @ SY34 @ SV2 )
| ( in @ SY34 @ SV5 ) )
| ( subset @ SV2 @ SV5 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ~ ( ~ ( ( SV7
!= ( cartesian_product2 @ SV3 @ SV6 ) )
| ! [SY46: $i] :
~ ( ~ ( ~ ( in @ SY46 @ SV7 )
| ~ ! [SY37: $i] :
~ ~ ! [SY38: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY37 @ SV3 )
| ~ ( in @ SY38 @ SV6 ) )
| ( SY46
!= ( ordered_pair @ SY37 @ SY38 ) ) ) )
| ~ ( ~ ~ ! [SY39: $i] :
~ ~ ! [SY40: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY39 @ SV3 )
| ~ ( in @ SY40 @ SV6 ) )
| ( SY46
!= ( ordered_pair @ SY39 @ SY40 ) ) )
| ( in @ SY46 @ SV7 ) ) ) )
| ~ ( ~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SV7 )
| ~ ! [SY42: $i] :
~ ~ ! [SY43: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY42 @ SV3 )
| ~ ( in @ SY43 @ SV6 ) )
| ( SY51
!= ( ordered_pair @ SY42 @ SY43 ) ) ) )
| ~ ( ~ ~ ! [SY44: $i] :
~ ~ ! [SY45: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY44 @ SV3 )
| ~ ( in @ SY45 @ SV6 ) )
| ( SY51
!= ( ordered_pair @ SY44 @ SY45 ) ) )
| ( in @ SY51 @ SV7 ) ) )
| ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(41,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( ~ ( subset @ SV2 @ SV5 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ SV2 )
| ( in @ SY33 @ SV5 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(42,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( ~ ! [SY34: $i] :
( ~ ( in @ SY34 @ SV2 )
| ( in @ SY34 @ SV5 ) )
| ( subset @ SV2 @ SV5 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(43,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ~ ( ( SV7
!= ( cartesian_product2 @ SV3 @ SV6 ) )
| ! [SY46: $i] :
~ ( ~ ( ~ ( in @ SY46 @ SV7 )
| ~ ! [SY37: $i] :
~ ~ ! [SY38: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY37 @ SV3 )
| ~ ( in @ SY38 @ SV6 ) )
| ( SY46
!= ( ordered_pair @ SY37 @ SY38 ) ) ) )
| ~ ( ~ ~ ! [SY39: $i] :
~ ~ ! [SY40: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY39 @ SV3 )
| ~ ( in @ SY40 @ SV6 ) )
| ( SY46
!= ( ordered_pair @ SY39 @ SY40 ) ) )
| ( in @ SY46 @ SV7 ) ) ) )
| ~ ( ~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SV7 )
| ~ ! [SY42: $i] :
~ ~ ! [SY43: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY42 @ SV3 )
| ~ ( in @ SY43 @ SV6 ) )
| ( SY51
!= ( ordered_pair @ SY42 @ SY43 ) ) ) )
| ~ ( ~ ~ ! [SY44: $i] :
~ ~ ! [SY45: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY44 @ SV3 )
| ~ ( in @ SY45 @ SV6 ) )
| ( SY51
!= ( ordered_pair @ SY44 @ SY45 ) ) )
| ( in @ SY51 @ SV7 ) ) )
| ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(44,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( subset @ SV2 @ SV5 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ SV2 )
| ( in @ SY33 @ SV5 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(45,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ! [SY34: $i] :
( ~ ( in @ SY34 @ SV2 )
| ( in @ SY34 @ SV5 ) )
| ( subset @ SV2 @ SV5 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(46,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ~ ( ( SV7
!= ( cartesian_product2 @ SV3 @ SV6 ) )
| ! [SY46: $i] :
~ ( ~ ( ~ ( in @ SY46 @ SV7 )
| ~ ! [SY37: $i] :
~ ~ ! [SY38: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY37 @ SV3 )
| ~ ( in @ SY38 @ SV6 ) )
| ( SY46
!= ( ordered_pair @ SY37 @ SY38 ) ) ) )
| ~ ( ~ ~ ! [SY39: $i] :
~ ~ ! [SY40: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY39 @ SV3 )
| ~ ( in @ SY40 @ SV6 ) )
| ( SY46
!= ( ordered_pair @ SY39 @ SY40 ) ) )
| ( in @ SY46 @ SV7 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(47,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ~ ( ~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SV7 )
| ~ ! [SY42: $i] :
~ ~ ! [SY43: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY42 @ SV3 )
| ~ ( in @ SY43 @ SV6 ) )
| ( SY51
!= ( ordered_pair @ SY42 @ SY43 ) ) ) )
| ~ ( ~ ~ ! [SY44: $i] :
~ ~ ! [SY45: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY44 @ SV3 )
| ~ ( in @ SY45 @ SV6 ) )
| ( SY51
!= ( ordered_pair @ SY44 @ SY45 ) ) )
| ( in @ SY51 @ SV7 ) ) )
| ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(48,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ( subset @ SV2 @ SV5 ) )
= $true )
| ( ( ! [SY33: $i] :
( ~ ( in @ SY33 @ SV2 )
| ( in @ SY33 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ! [SY34: $i] :
( ~ ( in @ SY34 @ SV2 )
| ( in @ SY34 @ SV5 ) ) )
= $true )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(50,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ( SV7
!= ( cartesian_product2 @ SV3 @ SV6 ) )
| ! [SY46: $i] :
~ ( ~ ( ~ ( in @ SY46 @ SV7 )
| ~ ! [SY37: $i] :
~ ~ ! [SY38: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY37 @ SV3 )
| ~ ( in @ SY38 @ SV6 ) )
| ( SY46
!= ( ordered_pair @ SY37 @ SY38 ) ) ) )
| ~ ( ~ ~ ! [SY39: $i] :
~ ~ ! [SY40: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY39 @ SV3 )
| ~ ( in @ SY40 @ SV6 ) )
| ( SY46
!= ( ordered_pair @ SY39 @ SY40 ) ) )
| ( in @ SY46 @ SV7 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(51,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SV7 )
| ~ ! [SY42: $i] :
~ ~ ! [SY43: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY42 @ SV3 )
| ~ ( in @ SY43 @ SV6 ) )
| ( SY51
!= ( ordered_pair @ SY42 @ SY43 ) ) ) )
| ~ ( ~ ~ ! [SY44: $i] :
~ ~ ! [SY45: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY44 @ SV3 )
| ~ ( in @ SY45 @ SV6 ) )
| ( SY51
!= ( ordered_pair @ SY44 @ SY45 ) ) )
| ( in @ SY51 @ SV7 ) ) )
| ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(52,plain,
! [SV5: $i,SV2: $i] :
( ( ( subset @ SV2 @ SV5 )
= $false )
| ( ( ! [SY33: $i] :
( ~ ( in @ SY33 @ SV2 )
| ( in @ SY33 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV5: $i,SV2: $i] :
( ( ( ! [SY34: $i] :
( ~ ( in @ SY34 @ SV2 )
| ( in @ SY34 @ SV5 ) ) )
= $false )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(54,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ( SV7
!= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true )
| ( ( ! [SY46: $i] :
~ ( ~ ( ~ ( in @ SY46 @ SV7 )
| ~ ! [SY37: $i] :
~ ~ ! [SY38: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY37 @ SV3 )
| ~ ( in @ SY38 @ SV6 ) )
| ( SY46
!= ( ordered_pair @ SY37 @ SY38 ) ) ) )
| ~ ( ~ ~ ! [SY39: $i] :
~ ~ ! [SY40: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY39 @ SV3 )
| ~ ( in @ SY40 @ SV6 ) )
| ( SY46
!= ( ordered_pair @ SY39 @ SY40 ) ) )
| ( in @ SY46 @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(55,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ( ~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SV7 )
| ~ ! [SY42: $i] :
~ ~ ! [SY43: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY42 @ SV3 )
| ~ ( in @ SY43 @ SV6 ) )
| ( SY51
!= ( ordered_pair @ SY42 @ SY43 ) ) ) )
| ~ ( ~ ~ ! [SY44: $i] :
~ ~ ! [SY45: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY44 @ SV3 )
| ~ ( in @ SY45 @ SV6 ) )
| ( SY51
!= ( ordered_pair @ SY44 @ SY45 ) ) )
| ( in @ SY51 @ SV7 ) ) ) )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(56,plain,
! [SV5: $i,SV2: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV2 )
| ( in @ SV8 @ SV5 ) )
= $true )
| ( ( subset @ SV2 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(57,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK4_SY34 @ SV5 @ SV2 ) @ SV2 )
| ( in @ ( sK4_SY34 @ SV5 @ SV2 ) @ SV5 ) )
= $false )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[53]) ).
thf(58,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false )
| ( ( ! [SY46: $i] :
~ ( ~ ( ~ ( in @ SY46 @ SV7 )
| ~ ! [SY37: $i] :
~ ~ ! [SY38: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY37 @ SV3 )
| ~ ( in @ SY38 @ SV6 ) )
| ( SY46
!= ( ordered_pair @ SY37 @ SY38 ) ) ) )
| ~ ( ~ ~ ! [SY39: $i] :
~ ~ ! [SY40: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY39 @ SV3 )
| ~ ( in @ SY40 @ SV6 ) )
| ( SY46
!= ( ordered_pair @ SY39 @ SY40 ) ) )
| ( in @ SY46 @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(59,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ( ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SV7 )
| ~ ! [SY42: $i] :
~ ~ ! [SY43: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY42 @ SV3 )
| ~ ( in @ SY43 @ SV6 ) )
| ( SY51
!= ( ordered_pair @ SY42 @ SY43 ) ) ) )
| ~ ( ~ ~ ! [SY44: $i] :
~ ~ ! [SY45: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY44 @ SV3 )
| ~ ( in @ SY45 @ SV6 ) )
| ( SY51
!= ( ordered_pair @ SY44 @ SY45 ) ) )
| ( in @ SY51 @ SV7 ) ) ) )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(60,plain,
! [SV5: $i,SV2: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV2 ) )
= $true )
| ( ( in @ SV8 @ SV5 )
= $true )
| ( ( subset @ SV2 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(61,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK4_SY34 @ SV5 @ SV2 ) @ SV2 ) )
= $false )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(62,plain,
! [SV2: $i,SV5: $i] :
( ( ( in @ ( sK4_SY34 @ SV5 @ SV2 ) @ SV5 )
= $false )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(63,plain,
! [SV6: $i,SV3: $i,SV7: $i,SV9: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV9 @ SV7 )
| ~ ! [SY56: $i] :
~ ~ ! [SY57: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY56 @ SV3 )
| ~ ( in @ SY57 @ SV6 ) )
| ( SV9
!= ( ordered_pair @ SY56 @ SY57 ) ) ) )
| ~ ( ~ ~ ! [SY58: $i] :
~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY58 @ SV3 )
| ~ ( in @ SY59 @ SV6 ) )
| ( SV9
!= ( ordered_pair @ SY58 @ SY59 ) ) )
| ( in @ SV9 @ SV7 ) ) ) )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(64,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 )
| ~ ! [SY60: $i] :
~ ~ ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY60 @ SV3 )
| ~ ( in @ SY61 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY60 @ SY61 ) ) ) )
| ~ ( ~ ~ ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) )
| ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) ) )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[59]) ).
thf(65,plain,
! [SV5: $i,SV2: $i,SV8: $i] :
( ( ( in @ SV8 @ SV2 )
= $false )
| ( ( in @ SV8 @ SV5 )
= $true )
| ( ( subset @ SV2 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(66,plain,
! [SV2: $i,SV5: $i] :
( ( ( in @ ( sK4_SY34 @ SV5 @ SV2 ) @ SV2 )
= $true )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(67,plain,
! [SV6: $i,SV3: $i,SV7: $i,SV9: $i] :
( ( ( ~ ( ~ ( in @ SV9 @ SV7 )
| ~ ! [SY56: $i] :
~ ~ ! [SY57: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY56 @ SV3 )
| ~ ( in @ SY57 @ SV6 ) )
| ( SV9
!= ( ordered_pair @ SY56 @ SY57 ) ) ) )
| ~ ( ~ ~ ! [SY58: $i] :
~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY58 @ SV3 )
| ~ ( in @ SY59 @ SV6 ) )
| ( SV9
!= ( ordered_pair @ SY58 @ SY59 ) ) )
| ( in @ SV9 @ SV7 ) ) )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(68,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 )
| ~ ! [SY60: $i] :
~ ~ ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY60 @ SV3 )
| ~ ( in @ SY61 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY60 @ SY61 ) ) ) )
| ~ ( ~ ~ ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) )
| ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(69,plain,
! [SV6: $i,SV3: $i,SV7: $i,SV9: $i] :
( ( ( ~ ( ~ ( in @ SV9 @ SV7 )
| ~ ! [SY56: $i] :
~ ~ ! [SY57: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY56 @ SV3 )
| ~ ( in @ SY57 @ SV6 ) )
| ( SV9
!= ( ordered_pair @ SY56 @ SY57 ) ) ) ) )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(70,plain,
! [SV7: $i,SV9: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ! [SY58: $i] :
~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY58 @ SV3 )
| ~ ( in @ SY59 @ SV6 ) )
| ( SV9
!= ( ordered_pair @ SY58 @ SY59 ) ) )
| ( in @ SV9 @ SV7 ) ) )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(71,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 )
| ~ ! [SY60: $i] :
~ ~ ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY60 @ SV3 )
| ~ ( in @ SY61 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY60 @ SY61 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) )
| ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(72,plain,
! [SV6: $i,SV3: $i,SV7: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV7 )
| ~ ! [SY56: $i] :
~ ~ ! [SY57: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY56 @ SV3 )
| ~ ( in @ SY57 @ SV6 ) )
| ( SV9
!= ( ordered_pair @ SY56 @ SY57 ) ) ) )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(73,plain,
! [SV7: $i,SV9: $i,SV6: $i,SV3: $i] :
( ( ( ~ ~ ! [SY58: $i] :
~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY58 @ SV3 )
| ~ ( in @ SY59 @ SV6 ) )
| ( SV9
!= ( ordered_pair @ SY58 @ SY59 ) ) )
| ( in @ SV9 @ SV7 ) )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(74,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 )
| ~ ! [SY60: $i] :
~ ~ ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY60 @ SV3 )
| ~ ( in @ SY61 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY60 @ SY61 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) )
| ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(75,plain,
! [SV6: $i,SV3: $i,SV7: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV7 ) )
= $true )
| ( ( ~ ! [SY56: $i] :
~ ~ ! [SY57: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY56 @ SV3 )
| ~ ( in @ SY57 @ SV6 ) )
| ( SV9
!= ( ordered_pair @ SY56 @ SY57 ) ) ) )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(76,plain,
! [SV7: $i,SV9: $i,SV6: $i,SV3: $i] :
( ( ( ~ ~ ! [SY58: $i] :
~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY58 @ SV3 )
| ~ ( in @ SY59 @ SV6 ) )
| ( SV9
!= ( ordered_pair @ SY58 @ SY59 ) ) ) )
= $true )
| ( ( in @ SV9 @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(77,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) )
| ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(78,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ! [SY60: $i] :
~ ~ ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY60 @ SV3 )
| ~ ( in @ SY61 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY60 @ SY61 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) )
| ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(79,plain,
! [SV6: $i,SV3: $i,SV7: $i,SV9: $i] :
( ( ( in @ SV9 @ SV7 )
= $false )
| ( ( ~ ! [SY56: $i] :
~ ~ ! [SY57: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY56 @ SV3 )
| ~ ( in @ SY57 @ SV6 ) )
| ( SV9
!= ( ordered_pair @ SY56 @ SY57 ) ) ) )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(80,plain,
! [SV7: $i,SV9: $i,SV6: $i,SV3: $i] :
( ( ( ~ ! [SY58: $i] :
~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY58 @ SV3 )
| ~ ( in @ SY59 @ SV6 ) )
| ( SV9
!= ( ordered_pair @ SY58 @ SY59 ) ) ) )
= $false )
| ( ( in @ SV9 @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(81,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( ~ ( ~ ~ ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) )
| ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(82,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ! [SY60: $i] :
~ ~ ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY60 @ SV3 )
| ~ ( in @ SY61 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY60 @ SY61 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) )
| ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(83,plain,
! [SV7: $i,SV9: $i,SV6: $i,SV3: $i] :
( ( ( ! [SY56: $i] :
~ ~ ! [SY57: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY56 @ SV3 )
| ~ ( in @ SY57 @ SV6 ) )
| ( SV9
!= ( ordered_pair @ SY56 @ SY57 ) ) ) )
= $false )
| ( ( in @ SV9 @ SV7 )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(84,plain,
! [SV7: $i,SV9: $i,SV6: $i,SV3: $i] :
( ( ( ! [SY58: $i] :
~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY58 @ SV3 )
| ~ ( in @ SY59 @ SV6 ) )
| ( SV9
!= ( ordered_pair @ SY58 @ SY59 ) ) ) )
= $true )
| ( ( in @ SV9 @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(85,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ~ ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) )
| ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 ) )
= $false )
| ( ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(86,plain,
! [SV7: $i,SV6: $i,SV3: $i,SV10: $i] :
( ( ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV10 @ SV3 )
| ~ ( in @ SY64 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SV10 @ SY64 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) )
| ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(87,plain,
! [SV3: $i,SV6: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK6_SY56 @ SV7 @ SV9 @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ SY65 @ SV6 ) )
| ( SV9
!= ( ordered_pair @ ( sK6_SY56 @ SV7 @ SV9 @ SV6 @ SV3 ) @ SY65 ) ) ) )
= $false )
| ( ( in @ SV9 @ SV7 )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[83]) ).
thf(88,plain,
! [SV7: $i,SV9: $i,SV6: $i,SV3: $i,SV11: $i] :
( ( ( ~ ~ ! [SY66: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV11 @ SV3 )
| ~ ( in @ SY66 @ SV6 ) )
| ( SV9
!= ( ordered_pair @ SV11 @ SY66 ) ) ) )
= $true )
| ( ( in @ SV9 @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(89,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ~ ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) ) )
= $false )
| ( ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(90,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $false )
| ( ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(91,plain,
! [SV7: $i,SV6: $i,SV3: $i,SV10: $i] :
( ( ( ~ ! [SY64: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV10 @ SV3 )
| ~ ( in @ SY64 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SV10 @ SY64 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) )
| ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(92,plain,
! [SV3: $i,SV6: $i,SV9: $i,SV7: $i] :
( ( ( ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK6_SY56 @ SV7 @ SV9 @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ SY65 @ SV6 ) )
| ( SV9
!= ( ordered_pair @ ( sK6_SY56 @ SV7 @ SV9 @ SV6 @ SV3 ) @ SY65 ) ) ) )
= $true )
| ( ( in @ SV9 @ SV7 )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(93,plain,
! [SV7: $i,SV9: $i,SV6: $i,SV3: $i,SV11: $i] :
( ( ( ~ ! [SY66: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV11 @ SV3 )
| ~ ( in @ SY66 @ SV6 ) )
| ( SV9
!= ( ordered_pair @ SV11 @ SY66 ) ) ) )
= $false )
| ( ( in @ SV9 @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(94,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) ) )
= $true )
| ( ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(95,plain,
! [SV7: $i,SV6: $i,SV3: $i,SV10: $i] :
( ( ( ! [SY64: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV10 @ SV3 )
| ~ ( in @ SY64 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SV10 @ SY64 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) )
| ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(96,plain,
! [SV3: $i,SV6: $i,SV9: $i,SV7: $i] :
( ( ( ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK6_SY56 @ SV7 @ SV9 @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ SY65 @ SV6 ) )
| ( SV9
!= ( ordered_pair @ ( sK6_SY56 @ SV7 @ SV9 @ SV6 @ SV3 ) @ SY65 ) ) ) )
= $false )
| ( ( in @ SV9 @ SV7 )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(97,plain,
! [SV7: $i,SV9: $i,SV6: $i,SV3: $i,SV11: $i] :
( ( ( ! [SY66: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV11 @ SV3 )
| ~ ( in @ SY66 @ SV6 ) )
| ( SV9
!= ( ordered_pair @ SV11 @ SY66 ) ) ) )
= $true )
| ( ( in @ SV9 @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(98,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) ) )
= $false )
| ( ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(99,plain,
! [SV7: $i,SV6: $i,SV12: $i,SV3: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV10 @ SV3 )
| ~ ( in @ SV12 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SV10 @ SV12 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) )
| ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(100,plain,
! [SV3: $i,SV6: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK6_SY56 @ SV7 @ SV9 @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ ( sK7_SY65 @ SV3 @ SV6 @ SV9 @ SV7 ) @ SV6 ) )
| ( SV9
!= ( ordered_pair @ ( sK6_SY56 @ SV7 @ SV9 @ SV6 @ SV3 ) @ ( sK7_SY65 @ SV3 @ SV6 @ SV9 @ SV7 ) ) ) ) )
= $false )
| ( ( in @ SV9 @ SV7 )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[96]) ).
thf(101,plain,
! [SV7: $i,SV9: $i,SV6: $i,SV13: $i,SV3: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV11 @ SV3 )
| ~ ( in @ SV13 @ SV6 ) )
| ( SV9
!= ( ordered_pair @ SV11 @ SV13 ) ) ) )
= $true )
| ( ( in @ SV9 @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(102,plain,
! [SV3: $i,SV6: $i,SV7: $i] :
( ( ( ~ ~ ! [SY67: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK8_SY62 @ SV7 @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ SY67 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ ( sK8_SY62 @ SV7 @ SV6 @ SV3 ) @ SY67 ) ) ) )
= $false )
| ( ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[98]) ).
thf(103,plain,
! [SV7: $i,SV6: $i,SV12: $i,SV3: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV10 @ SV3 )
| ~ ( in @ SV12 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SV10 @ SV12 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) )
| ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(104,plain,
! [SV3: $i,SV6: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK6_SY56 @ SV7 @ SV9 @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ ( sK7_SY65 @ SV3 @ SV6 @ SV9 @ SV7 ) @ SV6 ) )
| ( SV9
!= ( ordered_pair @ ( sK6_SY56 @ SV7 @ SV9 @ SV6 @ SV3 ) @ ( sK7_SY65 @ SV3 @ SV6 @ SV9 @ SV7 ) ) ) ) )
= $true )
| ( ( in @ SV9 @ SV7 )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(105,plain,
! [SV7: $i,SV9: $i,SV6: $i,SV13: $i,SV3: $i,SV11: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV11 @ SV3 )
| ~ ( in @ SV13 @ SV6 ) )
| ( SV9
!= ( ordered_pair @ SV11 @ SV13 ) ) ) )
= $false )
| ( ( in @ SV9 @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(106,plain,
! [SV3: $i,SV6: $i,SV7: $i] :
( ( ( ~ ! [SY67: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK8_SY62 @ SV7 @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ SY67 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ ( sK8_SY62 @ SV7 @ SV6 @ SV3 ) @ SY67 ) ) ) )
= $true )
| ( ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(107,plain,
! [SV7: $i,SV6: $i,SV12: $i,SV3: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( in @ SV10 @ SV3 )
| ~ ( in @ SV12 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SV10 @ SV12 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) )
| ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(108,plain,
! [SV3: $i,SV6: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK6_SY56 @ SV7 @ SV9 @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ ( sK7_SY65 @ SV3 @ SV6 @ SV9 @ SV7 ) @ SV6 ) )
| ( SV9
!= ( ordered_pair @ ( sK6_SY56 @ SV7 @ SV9 @ SV6 @ SV3 ) @ ( sK7_SY65 @ SV3 @ SV6 @ SV9 @ SV7 ) ) ) )
= $false )
| ( ( in @ SV9 @ SV7 )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(109,plain,
! [SV7: $i,SV9: $i,SV6: $i,SV13: $i,SV3: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( in @ SV11 @ SV3 )
| ~ ( in @ SV13 @ SV6 ) )
| ( SV9
!= ( ordered_pair @ SV11 @ SV13 ) ) )
= $true )
| ( ( in @ SV9 @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(110,plain,
! [SV3: $i,SV6: $i,SV7: $i] :
( ( ( ! [SY67: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK8_SY62 @ SV7 @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ SY67 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ ( sK8_SY62 @ SV7 @ SV6 @ SV3 ) @ SY67 ) ) ) )
= $false )
| ( ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(111,plain,
! [SV7: $i,SV6: $i,SV12: $i,SV3: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( in @ SV10 @ SV3 )
| ~ ( in @ SV12 @ SV6 ) ) )
= $true )
| ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SV10 @ SV12 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) )
| ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(112,plain,
! [SV3: $i,SV6: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK6_SY56 @ SV7 @ SV9 @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ ( sK7_SY65 @ SV3 @ SV6 @ SV9 @ SV7 ) @ SV6 ) ) )
= $false )
| ( ( in @ SV9 @ SV7 )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(113,plain,
! [SV3: $i,SV6: $i,SV7: $i,SV9: $i] :
( ( ( SV9
!= ( ordered_pair @ ( sK6_SY56 @ SV7 @ SV9 @ SV6 @ SV3 ) @ ( sK7_SY65 @ SV3 @ SV6 @ SV9 @ SV7 ) ) )
= $false )
| ( ( in @ SV9 @ SV7 )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(114,plain,
! [SV7: $i,SV9: $i,SV6: $i,SV13: $i,SV3: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( in @ SV11 @ SV3 )
| ~ ( in @ SV13 @ SV6 ) ) )
= $true )
| ( ( SV9
!= ( ordered_pair @ SV11 @ SV13 ) )
= $true )
| ( ( in @ SV9 @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(115,plain,
! [SV3: $i,SV6: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK8_SY62 @ SV7 @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ ( sK9_SY67 @ SV3 @ SV6 @ SV7 ) @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ ( sK8_SY62 @ SV7 @ SV6 @ SV3 ) @ ( sK9_SY67 @ SV3 @ SV6 @ SV7 ) ) ) ) )
= $false )
| ( ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[110]) ).
thf(116,plain,
! [SV7: $i,SV6: $i,SV12: $i,SV3: $i,SV10: $i] :
( ( ( ~ ( ~ ( in @ SV10 @ SV3 )
| ~ ( in @ SV12 @ SV6 ) ) )
= $false )
| ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SV10 @ SV12 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) )
| ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(117,plain,
! [SV3: $i,SV6: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_SY56 @ SV7 @ SV9 @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ ( sK7_SY65 @ SV3 @ SV6 @ SV9 @ SV7 ) @ SV6 ) ) )
= $true )
| ( ( in @ SV9 @ SV7 )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(118,plain,
! [SV3: $i,SV6: $i,SV7: $i,SV9: $i] :
( ( ( SV9
= ( ordered_pair @ ( sK6_SY56 @ SV7 @ SV9 @ SV6 @ SV3 ) @ ( sK7_SY65 @ SV3 @ SV6 @ SV9 @ SV7 ) ) )
= $true )
| ( ( in @ SV9 @ SV7 )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(119,plain,
! [SV7: $i,SV9: $i,SV6: $i,SV13: $i,SV3: $i,SV11: $i] :
( ( ( ~ ( ~ ( in @ SV11 @ SV3 )
| ~ ( in @ SV13 @ SV6 ) ) )
= $false )
| ( ( SV9
!= ( ordered_pair @ SV11 @ SV13 ) )
= $true )
| ( ( in @ SV9 @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(120,plain,
! [SV3: $i,SV6: $i,SV7: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK8_SY62 @ SV7 @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ ( sK9_SY67 @ SV3 @ SV6 @ SV7 ) @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ ( sK8_SY62 @ SV7 @ SV6 @ SV3 ) @ ( sK9_SY67 @ SV3 @ SV6 @ SV7 ) ) ) ) )
= $true )
| ( ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(121,plain,
! [SV7: $i,SV6: $i,SV12: $i,SV3: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV3 )
| ~ ( in @ SV12 @ SV6 ) )
= $true )
| ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SV10 @ SV12 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) )
| ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(122,plain,
! [SV3: $i,SV6: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK6_SY56 @ SV7 @ SV9 @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ ( sK7_SY65 @ SV3 @ SV6 @ SV9 @ SV7 ) @ SV6 ) )
= $false )
| ( ( in @ SV9 @ SV7 )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(123,plain,
! [SV7: $i,SV9: $i,SV6: $i,SV13: $i,SV3: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV3 )
| ~ ( in @ SV13 @ SV6 ) )
= $true )
| ( ( SV9
!= ( ordered_pair @ SV11 @ SV13 ) )
= $true )
| ( ( in @ SV9 @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(124,plain,
! [SV3: $i,SV6: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK8_SY62 @ SV7 @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ ( sK9_SY67 @ SV3 @ SV6 @ SV7 ) @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ ( sK8_SY62 @ SV7 @ SV6 @ SV3 ) @ ( sK9_SY67 @ SV3 @ SV6 @ SV7 ) ) ) )
= $false )
| ( ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(125,plain,
! [SV7: $i,SV6: $i,SV12: $i,SV3: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV3 ) )
= $true )
| ( ( ~ ( in @ SV12 @ SV6 ) )
= $true )
| ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SV10 @ SV12 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) )
| ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(126,plain,
! [SV3: $i,SV6: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK6_SY56 @ SV7 @ SV9 @ SV6 @ SV3 ) @ SV3 ) )
= $false )
| ( ( in @ SV9 @ SV7 )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(127,plain,
! [SV7: $i,SV9: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( in @ ( sK7_SY65 @ SV3 @ SV6 @ SV9 @ SV7 ) @ SV6 ) )
= $false )
| ( ( in @ SV9 @ SV7 )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(128,plain,
! [SV7: $i,SV9: $i,SV6: $i,SV13: $i,SV3: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV3 ) )
= $true )
| ( ( ~ ( in @ SV13 @ SV6 ) )
= $true )
| ( ( SV9
!= ( ordered_pair @ SV11 @ SV13 ) )
= $true )
| ( ( in @ SV9 @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(129,plain,
! [SV3: $i,SV6: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK8_SY62 @ SV7 @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ ( sK9_SY67 @ SV3 @ SV6 @ SV7 ) @ SV6 ) ) )
= $false )
| ( ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(130,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ ( sK8_SY62 @ SV7 @ SV6 @ SV3 ) @ ( sK9_SY67 @ SV3 @ SV6 @ SV7 ) ) )
= $false )
| ( ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(131,plain,
! [SV7: $i,SV6: $i,SV12: $i,SV3: $i,SV10: $i] :
( ( ( in @ SV10 @ SV3 )
= $false )
| ( ( ~ ( in @ SV12 @ SV6 ) )
= $true )
| ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SV10 @ SV12 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) )
| ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(132,plain,
! [SV3: $i,SV6: $i,SV9: $i,SV7: $i] :
( ( ( in @ ( sK6_SY56 @ SV7 @ SV9 @ SV6 @ SV3 ) @ SV3 )
= $true )
| ( ( in @ SV9 @ SV7 )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(133,plain,
! [SV7: $i,SV9: $i,SV6: $i,SV3: $i] :
( ( ( in @ ( sK7_SY65 @ SV3 @ SV6 @ SV9 @ SV7 ) @ SV6 )
= $true )
| ( ( in @ SV9 @ SV7 )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(134,plain,
! [SV7: $i,SV9: $i,SV6: $i,SV13: $i,SV3: $i,SV11: $i] :
( ( ( in @ SV11 @ SV3 )
= $false )
| ( ( ~ ( in @ SV13 @ SV6 ) )
= $true )
| ( ( SV9
!= ( ordered_pair @ SV11 @ SV13 ) )
= $true )
| ( ( in @ SV9 @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(135,plain,
! [SV3: $i,SV6: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY62 @ SV7 @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ ( sK9_SY67 @ SV3 @ SV6 @ SV7 ) @ SV6 ) ) )
= $true )
| ( ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(136,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
= ( ordered_pair @ ( sK8_SY62 @ SV7 @ SV6 @ SV3 ) @ ( sK9_SY67 @ SV3 @ SV6 @ SV7 ) ) )
= $true )
| ( ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(137,plain,
! [SV7: $i,SV3: $i,SV10: $i,SV6: $i,SV12: $i] :
( ( ( in @ SV12 @ SV6 )
= $false )
| ( ( in @ SV10 @ SV3 )
= $false )
| ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SV10 @ SV12 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) )
| ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(138,plain,
! [SV7: $i,SV9: $i,SV3: $i,SV11: $i,SV6: $i,SV13: $i] :
( ( ( in @ SV13 @ SV6 )
= $false )
| ( ( in @ SV11 @ SV3 )
= $false )
| ( ( SV9
!= ( ordered_pair @ SV11 @ SV13 ) )
= $true )
| ( ( in @ SV9 @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(139,plain,
! [SV3: $i,SV6: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK8_SY62 @ SV7 @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ ( sK9_SY67 @ SV3 @ SV6 @ SV7 ) @ SV6 ) )
= $false )
| ( ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(140,plain,
! [SV12: $i,SV10: $i,SV7: $i,SV3: $i,SV6: $i] :
( ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
= ( ordered_pair @ SV10 @ SV12 ) )
= $false )
| ( ( in @ SV10 @ SV3 )
= $false )
| ( ( in @ SV12 @ SV6 )
= $false )
| ( ( ~ ( ~ ~ ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) )
| ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(141,plain,
! [SV7: $i,SV6: $i,SV3: $i,SV13: $i,SV11: $i,SV9: $i] :
( ( ( SV9
= ( ordered_pair @ SV11 @ SV13 ) )
= $false )
| ( ( in @ SV11 @ SV3 )
= $false )
| ( ( in @ SV13 @ SV6 )
= $false )
| ( ( in @ SV9 @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(142,plain,
! [SV3: $i,SV6: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK8_SY62 @ SV7 @ SV6 @ SV3 ) @ SV3 ) )
= $false )
| ( ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(143,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( in @ ( sK9_SY67 @ SV3 @ SV6 @ SV7 ) @ SV6 ) )
= $false )
| ( ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(144,plain,
! [SV10: $i,SV12: $i,SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ~ ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) )
| ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 ) )
= $false )
| ( ( in @ SV12 @ SV6 )
= $false )
| ( ( in @ SV10 @ SV3 )
= $false )
| ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
= ( ordered_pair @ SV10 @ SV12 ) )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(145,plain,
! [SV3: $i,SV6: $i,SV7: $i] :
( ( ( in @ ( sK8_SY62 @ SV7 @ SV6 @ SV3 ) @ SV3 )
= $true )
| ( ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(146,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( in @ ( sK9_SY67 @ SV3 @ SV6 @ SV7 ) @ SV6 )
= $true )
| ( ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(147,plain,
! [SV10: $i,SV12: $i,SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ~ ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) ) )
= $false )
| ( ( in @ SV12 @ SV6 )
= $false )
| ( ( in @ SV10 @ SV3 )
= $false )
| ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
= ( ordered_pair @ SV10 @ SV12 ) )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(148,plain,
! [SV10: $i,SV12: $i,SV7: $i,SV3: $i,SV6: $i] :
( ( ( in @ ( sK5_SY51 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $false )
| ( ( in @ SV12 @ SV6 )
= $false )
| ( ( in @ SV10 @ SV3 )
= $false )
| ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
= ( ordered_pair @ SV10 @ SV12 ) )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(149,plain,
! [SV10: $i,SV12: $i,SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) ) )
= $true )
| ( ( in @ SV12 @ SV6 )
= $false )
| ( ( in @ SV10 @ SV3 )
= $false )
| ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
= ( ordered_pair @ SV10 @ SV12 ) )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(150,plain,
! [SV10: $i,SV12: $i,SV7: $i,SV6: $i,SV3: $i] :
( ( ( ! [SY62: $i] :
~ ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY62 @ SV3 )
| ~ ( in @ SY63 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ SY62 @ SY63 ) ) ) )
= $false )
| ( ( in @ SV12 @ SV6 )
= $false )
| ( ( in @ SV10 @ SV3 )
= $false )
| ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
= ( ordered_pair @ SV10 @ SV12 ) )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(151,plain,
! [SV3: $i,SV6: $i,SV7: $i,SV12: $i,SV10: $i] :
( ( ( ~ ~ ! [SY68: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK10_SY62 @ SV10 @ SV12 @ SV7 @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ SY68 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ ( sK10_SY62 @ SV10 @ SV12 @ SV7 @ SV6 @ SV3 ) @ SY68 ) ) ) )
= $false )
| ( ( in @ SV12 @ SV6 )
= $false )
| ( ( in @ SV10 @ SV3 )
= $false )
| ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
= ( ordered_pair @ SV10 @ SV12 ) )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[150]) ).
thf(152,plain,
! [SV3: $i,SV6: $i,SV7: $i,SV12: $i,SV10: $i] :
( ( ( ~ ! [SY68: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK10_SY62 @ SV10 @ SV12 @ SV7 @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ SY68 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ ( sK10_SY62 @ SV10 @ SV12 @ SV7 @ SV6 @ SV3 ) @ SY68 ) ) ) )
= $true )
| ( ( in @ SV12 @ SV6 )
= $false )
| ( ( in @ SV10 @ SV3 )
= $false )
| ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
= ( ordered_pair @ SV10 @ SV12 ) )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(153,plain,
! [SV3: $i,SV6: $i,SV7: $i,SV12: $i,SV10: $i] :
( ( ( ! [SY68: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK10_SY62 @ SV10 @ SV12 @ SV7 @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ SY68 @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ ( sK10_SY62 @ SV10 @ SV12 @ SV7 @ SV6 @ SV3 ) @ SY68 ) ) ) )
= $false )
| ( ( in @ SV12 @ SV6 )
= $false )
| ( ( in @ SV10 @ SV3 )
= $false )
| ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
= ( ordered_pair @ SV10 @ SV12 ) )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(154,plain,
! [SV3: $i,SV6: $i,SV7: $i,SV12: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_SY62 @ SV10 @ SV12 @ SV7 @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ ( sK11_SY68 @ SV3 @ SV6 @ SV7 @ SV12 @ SV10 ) @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ ( sK10_SY62 @ SV10 @ SV12 @ SV7 @ SV6 @ SV3 ) @ ( sK11_SY68 @ SV3 @ SV6 @ SV7 @ SV12 @ SV10 ) ) ) ) )
= $false )
| ( ( in @ SV12 @ SV6 )
= $false )
| ( ( in @ SV10 @ SV3 )
= $false )
| ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
= ( ordered_pair @ SV10 @ SV12 ) )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[153]) ).
thf(155,plain,
! [SV3: $i,SV6: $i,SV7: $i,SV12: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY62 @ SV10 @ SV12 @ SV7 @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ ( sK11_SY68 @ SV3 @ SV6 @ SV7 @ SV12 @ SV10 ) @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ ( sK10_SY62 @ SV10 @ SV12 @ SV7 @ SV6 @ SV3 ) @ ( sK11_SY68 @ SV3 @ SV6 @ SV7 @ SV12 @ SV10 ) ) ) ) )
= $true )
| ( ( in @ SV12 @ SV6 )
= $false )
| ( ( in @ SV10 @ SV3 )
= $false )
| ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
= ( ordered_pair @ SV10 @ SV12 ) )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(156,plain,
! [SV3: $i,SV6: $i,SV7: $i,SV12: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK10_SY62 @ SV10 @ SV12 @ SV7 @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ ( sK11_SY68 @ SV3 @ SV6 @ SV7 @ SV12 @ SV10 ) @ SV6 ) )
| ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ ( sK10_SY62 @ SV10 @ SV12 @ SV7 @ SV6 @ SV3 ) @ ( sK11_SY68 @ SV3 @ SV6 @ SV7 @ SV12 @ SV10 ) ) ) )
= $false )
| ( ( in @ SV12 @ SV6 )
= $false )
| ( ( in @ SV10 @ SV3 )
= $false )
| ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
= ( ordered_pair @ SV10 @ SV12 ) )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(157,plain,
! [SV3: $i,SV6: $i,SV7: $i,SV12: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK10_SY62 @ SV10 @ SV12 @ SV7 @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ ( sK11_SY68 @ SV3 @ SV6 @ SV7 @ SV12 @ SV10 ) @ SV6 ) ) )
= $false )
| ( ( in @ SV12 @ SV6 )
= $false )
| ( ( in @ SV10 @ SV3 )
= $false )
| ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
= ( ordered_pair @ SV10 @ SV12 ) )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(158,plain,
! [SV12: $i,SV10: $i,SV7: $i,SV3: $i,SV6: $i] :
( ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
!= ( ordered_pair @ ( sK10_SY62 @ SV10 @ SV12 @ SV7 @ SV6 @ SV3 ) @ ( sK11_SY68 @ SV3 @ SV6 @ SV7 @ SV12 @ SV10 ) ) )
= $false )
| ( ( in @ SV12 @ SV6 )
= $false )
| ( ( in @ SV10 @ SV3 )
= $false )
| ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
= ( ordered_pair @ SV10 @ SV12 ) )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(159,plain,
! [SV3: $i,SV6: $i,SV7: $i,SV12: $i,SV10: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY62 @ SV10 @ SV12 @ SV7 @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ ( sK11_SY68 @ SV3 @ SV6 @ SV7 @ SV12 @ SV10 ) @ SV6 ) ) )
= $true )
| ( ( in @ SV12 @ SV6 )
= $false )
| ( ( in @ SV10 @ SV3 )
= $false )
| ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
= ( ordered_pair @ SV10 @ SV12 ) )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(160,plain,
! [SV12: $i,SV10: $i,SV7: $i,SV3: $i,SV6: $i] :
( ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
= ( ordered_pair @ ( sK10_SY62 @ SV10 @ SV12 @ SV7 @ SV6 @ SV3 ) @ ( sK11_SY68 @ SV3 @ SV6 @ SV7 @ SV12 @ SV10 ) ) )
= $true )
| ( ( in @ SV12 @ SV6 )
= $false )
| ( ( in @ SV10 @ SV3 )
= $false )
| ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
= ( ordered_pair @ SV10 @ SV12 ) )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(161,plain,
! [SV3: $i,SV6: $i,SV7: $i,SV12: $i,SV10: $i] :
( ( ( ~ ( in @ ( sK10_SY62 @ SV10 @ SV12 @ SV7 @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ ( sK11_SY68 @ SV3 @ SV6 @ SV7 @ SV12 @ SV10 ) @ SV6 ) )
= $false )
| ( ( in @ SV12 @ SV6 )
= $false )
| ( ( in @ SV10 @ SV3 )
= $false )
| ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
= ( ordered_pair @ SV10 @ SV12 ) )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(162,plain,
! [SV3: $i,SV6: $i,SV7: $i,SV12: $i,SV10: $i] :
( ( ( ~ ( in @ ( sK10_SY62 @ SV10 @ SV12 @ SV7 @ SV6 @ SV3 ) @ SV3 ) )
= $false )
| ( ( in @ SV12 @ SV6 )
= $false )
| ( ( in @ SV10 @ SV3 )
= $false )
| ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
= ( ordered_pair @ SV10 @ SV12 ) )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(163,plain,
! [SV10: $i,SV12: $i,SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( in @ ( sK11_SY68 @ SV3 @ SV6 @ SV7 @ SV12 @ SV10 ) @ SV6 ) )
= $false )
| ( ( in @ SV12 @ SV6 )
= $false )
| ( ( in @ SV10 @ SV3 )
= $false )
| ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
= ( ordered_pair @ SV10 @ SV12 ) )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(164,plain,
! [SV3: $i,SV6: $i,SV7: $i,SV12: $i,SV10: $i] :
( ( ( in @ ( sK10_SY62 @ SV10 @ SV12 @ SV7 @ SV6 @ SV3 ) @ SV3 )
= $true )
| ( ( in @ SV12 @ SV6 )
= $false )
| ( ( in @ SV10 @ SV3 )
= $false )
| ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
= ( ordered_pair @ SV10 @ SV12 ) )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(165,plain,
! [SV10: $i,SV12: $i,SV7: $i,SV6: $i,SV3: $i] :
( ( ( in @ ( sK11_SY68 @ SV3 @ SV6 @ SV7 @ SV12 @ SV10 ) @ SV6 )
= $true )
| ( ( in @ SV12 @ SV6 )
= $false )
| ( ( in @ SV10 @ SV3 )
= $false )
| ( ( ( sK5_SY51 @ SV6 @ SV3 @ SV7 )
= ( ordered_pair @ SV10 @ SV12 ) )
= $false )
| ( ( SV7
= ( cartesian_product2 @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(166,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[28,165,164,160,148,146,145,141,136,133,132,118,90,66,65,62,36,33]) ).
thf(167,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(168,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(169,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(170,plain,
( ( subset @ sK1_A @ sK2_SY14 )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(171,plain,
( ( ~ ( subset @ ( cartesian_product2 @ sK3_SY16 @ sK1_A ) @ ( cartesian_product2 @ sK3_SY16 @ sK2_SY14 ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(172,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( cartesian_product2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( cartesian_product2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(173,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(174,plain,
! [SV14: $i] :
( ( ! [SY69: $i] : ( subset @ SV14 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(175,plain,
( ( subset @ ( cartesian_product2 @ sK3_SY16 @ sK1_A ) @ ( cartesian_product2 @ sK3_SY16 @ sK2_SY14 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(176,plain,
! [SV15: $i] :
( ( ! [SY70: $i,SY71: $i] :
~ ( ~ ( ( SY71
!= ( cartesian_product2 @ SV15 @ SY70 ) )
| ! [SY72: $i] :
~ ( ~ ( ~ ( in @ SY72 @ SY71 )
| ~ ! [SY73: $i] :
~ ~ ! [SY74: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY73 @ SV15 )
| ~ ( in @ SY74 @ SY70 ) )
| ( SY72
!= ( ordered_pair @ SY73 @ SY74 ) ) ) )
| ~ ( ~ ~ ! [SY75: $i] :
~ ~ ! [SY76: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY75 @ SV15 )
| ~ ( in @ SY76 @ SY70 ) )
| ( SY72
!= ( ordered_pair @ SY75 @ SY76 ) ) )
| ( in @ SY72 @ SY71 ) ) ) )
| ~ ( ~ ! [SY77: $i] :
~ ( ~ ( ~ ( in @ SY77 @ SY71 )
| ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV15 )
| ~ ( in @ SY79 @ SY70 ) )
| ( SY77
!= ( ordered_pair @ SY78 @ SY79 ) ) ) )
| ~ ( ~ ~ ! [SY80: $i] :
~ ~ ! [SY81: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY80 @ SV15 )
| ~ ( in @ SY81 @ SY70 ) )
| ( SY77
!= ( ordered_pair @ SY80 @ SY81 ) ) )
| ( in @ SY77 @ SY71 ) ) )
| ( SY71
= ( cartesian_product2 @ SV15 @ SY70 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(177,plain,
! [SV16: $i] :
( ( ! [SY82: $i] :
~ ( ~ ( ~ ( subset @ SV16 @ SY82 )
| ! [SY83: $i] :
( ~ ( in @ SY83 @ SV16 )
| ( in @ SY83 @ SY82 ) ) )
| ~ ( ~ ! [SY84: $i] :
( ~ ( in @ SY84 @ SV16 )
| ( in @ SY84 @ SY82 ) )
| ( subset @ SV16 @ SY82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(178,plain,
! [SV14: $i] :
( ( subset @ SV14 @ SV14 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(179,plain,
! [SV18: $i,SV15: $i] :
( ( ! [SY85: $i] :
~ ( ~ ( ( SY85
!= ( cartesian_product2 @ SV15 @ SV18 ) )
| ! [SY86: $i] :
~ ( ~ ( ~ ( in @ SY86 @ SY85 )
| ~ ! [SY87: $i] :
~ ~ ! [SY88: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY87 @ SV15 )
| ~ ( in @ SY88 @ SV18 ) )
| ( SY86
!= ( ordered_pair @ SY87 @ SY88 ) ) ) )
| ~ ( ~ ~ ! [SY89: $i] :
~ ~ ! [SY90: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY89 @ SV15 )
| ~ ( in @ SY90 @ SV18 ) )
| ( SY86
!= ( ordered_pair @ SY89 @ SY90 ) ) )
| ( in @ SY86 @ SY85 ) ) ) )
| ~ ( ~ ! [SY91: $i] :
~ ( ~ ( ~ ( in @ SY91 @ SY85 )
| ~ ! [SY92: $i] :
~ ~ ! [SY93: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY92 @ SV15 )
| ~ ( in @ SY93 @ SV18 ) )
| ( SY91
!= ( ordered_pair @ SY92 @ SY93 ) ) ) )
| ~ ( ~ ~ ! [SY94: $i] :
~ ~ ! [SY95: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ SV15 )
| ~ ( in @ SY95 @ SV18 ) )
| ( SY91
!= ( ordered_pair @ SY94 @ SY95 ) ) )
| ( in @ SY91 @ SY85 ) ) )
| ( SY85
= ( cartesian_product2 @ SV15 @ SV18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(180,plain,
! [SV19: $i,SV16: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV16 @ SV19 )
| ! [SY96: $i] :
( ~ ( in @ SY96 @ SV16 )
| ( in @ SY96 @ SV19 ) ) )
| ~ ( ~ ! [SY97: $i] :
( ~ ( in @ SY97 @ SV16 )
| ( in @ SY97 @ SV19 ) )
| ( subset @ SV16 @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(181,plain,
! [SV18: $i,SV15: $i,SV20: $i] :
( ( ~ ( ~ ( ( SV20
!= ( cartesian_product2 @ SV15 @ SV18 ) )
| ! [SY98: $i] :
~ ( ~ ( ~ ( in @ SY98 @ SV20 )
| ~ ! [SY87: $i] :
~ ~ ! [SY88: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY87 @ SV15 )
| ~ ( in @ SY88 @ SV18 ) )
| ( SY98
!= ( ordered_pair @ SY87 @ SY88 ) ) ) )
| ~ ( ~ ~ ! [SY89: $i] :
~ ~ ! [SY90: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY89 @ SV15 )
| ~ ( in @ SY90 @ SV18 ) )
| ( SY98
!= ( ordered_pair @ SY89 @ SY90 ) ) )
| ( in @ SY98 @ SV20 ) ) ) )
| ~ ( ~ ! [SY103: $i] :
~ ( ~ ( ~ ( in @ SY103 @ SV20 )
| ~ ! [SY92: $i] :
~ ~ ! [SY93: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY92 @ SV15 )
| ~ ( in @ SY93 @ SV18 ) )
| ( SY103
!= ( ordered_pair @ SY92 @ SY93 ) ) ) )
| ~ ( ~ ~ ! [SY94: $i] :
~ ~ ! [SY95: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ SV15 )
| ~ ( in @ SY95 @ SV18 ) )
| ( SY103
!= ( ordered_pair @ SY94 @ SY95 ) ) )
| ( in @ SY103 @ SV20 ) ) )
| ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(182,plain,
! [SV19: $i,SV16: $i] :
( ( ~ ( ~ ( subset @ SV16 @ SV19 )
| ! [SY96: $i] :
( ~ ( in @ SY96 @ SV16 )
| ( in @ SY96 @ SV19 ) ) )
| ~ ( ~ ! [SY97: $i] :
( ~ ( in @ SY97 @ SV16 )
| ( in @ SY97 @ SV19 ) )
| ( subset @ SV16 @ SV19 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(183,plain,
! [SV18: $i,SV15: $i,SV20: $i] :
( ( ~ ( ( SV20
!= ( cartesian_product2 @ SV15 @ SV18 ) )
| ! [SY98: $i] :
~ ( ~ ( ~ ( in @ SY98 @ SV20 )
| ~ ! [SY87: $i] :
~ ~ ! [SY88: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY87 @ SV15 )
| ~ ( in @ SY88 @ SV18 ) )
| ( SY98
!= ( ordered_pair @ SY87 @ SY88 ) ) ) )
| ~ ( ~ ~ ! [SY89: $i] :
~ ~ ! [SY90: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY89 @ SV15 )
| ~ ( in @ SY90 @ SV18 ) )
| ( SY98
!= ( ordered_pair @ SY89 @ SY90 ) ) )
| ( in @ SY98 @ SV20 ) ) ) )
| ~ ( ~ ! [SY103: $i] :
~ ( ~ ( ~ ( in @ SY103 @ SV20 )
| ~ ! [SY92: $i] :
~ ~ ! [SY93: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY92 @ SV15 )
| ~ ( in @ SY93 @ SV18 ) )
| ( SY103
!= ( ordered_pair @ SY92 @ SY93 ) ) ) )
| ~ ( ~ ~ ! [SY94: $i] :
~ ~ ! [SY95: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ SV15 )
| ~ ( in @ SY95 @ SV18 ) )
| ( SY103
!= ( ordered_pair @ SY94 @ SY95 ) ) )
| ( in @ SY103 @ SV20 ) ) )
| ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(184,plain,
! [SV19: $i,SV16: $i] :
( ( ~ ( ~ ( subset @ SV16 @ SV19 )
| ! [SY96: $i] :
( ~ ( in @ SY96 @ SV16 )
| ( in @ SY96 @ SV19 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[182]) ).
thf(185,plain,
! [SV19: $i,SV16: $i] :
( ( ~ ( ~ ! [SY97: $i] :
( ~ ( in @ SY97 @ SV16 )
| ( in @ SY97 @ SV19 ) )
| ( subset @ SV16 @ SV19 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[182]) ).
thf(186,plain,
! [SV18: $i,SV15: $i,SV20: $i] :
( ( ~ ( ( SV20
!= ( cartesian_product2 @ SV15 @ SV18 ) )
| ! [SY98: $i] :
~ ( ~ ( ~ ( in @ SY98 @ SV20 )
| ~ ! [SY87: $i] :
~ ~ ! [SY88: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY87 @ SV15 )
| ~ ( in @ SY88 @ SV18 ) )
| ( SY98
!= ( ordered_pair @ SY87 @ SY88 ) ) ) )
| ~ ( ~ ~ ! [SY89: $i] :
~ ~ ! [SY90: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY89 @ SV15 )
| ~ ( in @ SY90 @ SV18 ) )
| ( SY98
!= ( ordered_pair @ SY89 @ SY90 ) ) )
| ( in @ SY98 @ SV20 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(187,plain,
! [SV18: $i,SV15: $i,SV20: $i] :
( ( ~ ( ~ ! [SY103: $i] :
~ ( ~ ( ~ ( in @ SY103 @ SV20 )
| ~ ! [SY92: $i] :
~ ~ ! [SY93: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY92 @ SV15 )
| ~ ( in @ SY93 @ SV18 ) )
| ( SY103
!= ( ordered_pair @ SY92 @ SY93 ) ) ) )
| ~ ( ~ ~ ! [SY94: $i] :
~ ~ ! [SY95: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ SV15 )
| ~ ( in @ SY95 @ SV18 ) )
| ( SY103
!= ( ordered_pair @ SY94 @ SY95 ) ) )
| ( in @ SY103 @ SV20 ) ) )
| ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(188,plain,
! [SV19: $i,SV16: $i] :
( ( ~ ( subset @ SV16 @ SV19 )
| ! [SY96: $i] :
( ~ ( in @ SY96 @ SV16 )
| ( in @ SY96 @ SV19 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(189,plain,
! [SV19: $i,SV16: $i] :
( ( ~ ! [SY97: $i] :
( ~ ( in @ SY97 @ SV16 )
| ( in @ SY97 @ SV19 ) )
| ( subset @ SV16 @ SV19 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(190,plain,
! [SV18: $i,SV15: $i,SV20: $i] :
( ( ( SV20
!= ( cartesian_product2 @ SV15 @ SV18 ) )
| ! [SY98: $i] :
~ ( ~ ( ~ ( in @ SY98 @ SV20 )
| ~ ! [SY87: $i] :
~ ~ ! [SY88: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY87 @ SV15 )
| ~ ( in @ SY88 @ SV18 ) )
| ( SY98
!= ( ordered_pair @ SY87 @ SY88 ) ) ) )
| ~ ( ~ ~ ! [SY89: $i] :
~ ~ ! [SY90: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY89 @ SV15 )
| ~ ( in @ SY90 @ SV18 ) )
| ( SY98
!= ( ordered_pair @ SY89 @ SY90 ) ) )
| ( in @ SY98 @ SV20 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(191,plain,
! [SV18: $i,SV15: $i,SV20: $i] :
( ( ~ ! [SY103: $i] :
~ ( ~ ( ~ ( in @ SY103 @ SV20 )
| ~ ! [SY92: $i] :
~ ~ ! [SY93: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY92 @ SV15 )
| ~ ( in @ SY93 @ SV18 ) )
| ( SY103
!= ( ordered_pair @ SY92 @ SY93 ) ) ) )
| ~ ( ~ ~ ! [SY94: $i] :
~ ~ ! [SY95: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ SV15 )
| ~ ( in @ SY95 @ SV18 ) )
| ( SY103
!= ( ordered_pair @ SY94 @ SY95 ) ) )
| ( in @ SY103 @ SV20 ) ) )
| ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(192,plain,
! [SV19: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV19 ) )
= $true )
| ( ( ! [SY96: $i] :
( ~ ( in @ SY96 @ SV16 )
| ( in @ SY96 @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(193,plain,
! [SV19: $i,SV16: $i] :
( ( ( ~ ! [SY97: $i] :
( ~ ( in @ SY97 @ SV16 )
| ( in @ SY97 @ SV19 ) ) )
= $true )
| ( ( subset @ SV16 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(194,plain,
! [SV18: $i,SV15: $i,SV20: $i] :
( ( ( SV20
!= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true )
| ( ( ! [SY98: $i] :
~ ( ~ ( ~ ( in @ SY98 @ SV20 )
| ~ ! [SY87: $i] :
~ ~ ! [SY88: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY87 @ SV15 )
| ~ ( in @ SY88 @ SV18 ) )
| ( SY98
!= ( ordered_pair @ SY87 @ SY88 ) ) ) )
| ~ ( ~ ~ ! [SY89: $i] :
~ ~ ! [SY90: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY89 @ SV15 )
| ~ ( in @ SY90 @ SV18 ) )
| ( SY98
!= ( ordered_pair @ SY89 @ SY90 ) ) )
| ( in @ SY98 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(195,plain,
! [SV18: $i,SV15: $i,SV20: $i] :
( ( ( ~ ! [SY103: $i] :
~ ( ~ ( ~ ( in @ SY103 @ SV20 )
| ~ ! [SY92: $i] :
~ ~ ! [SY93: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY92 @ SV15 )
| ~ ( in @ SY93 @ SV18 ) )
| ( SY103
!= ( ordered_pair @ SY92 @ SY93 ) ) ) )
| ~ ( ~ ~ ! [SY94: $i] :
~ ~ ! [SY95: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ SV15 )
| ~ ( in @ SY95 @ SV18 ) )
| ( SY103
!= ( ordered_pair @ SY94 @ SY95 ) ) )
| ( in @ SY103 @ SV20 ) ) ) )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(196,plain,
! [SV19: $i,SV16: $i] :
( ( ( subset @ SV16 @ SV19 )
= $false )
| ( ( ! [SY96: $i] :
( ~ ( in @ SY96 @ SV16 )
| ( in @ SY96 @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(197,plain,
! [SV19: $i,SV16: $i] :
( ( ( ! [SY97: $i] :
( ~ ( in @ SY97 @ SV16 )
| ( in @ SY97 @ SV19 ) ) )
= $false )
| ( ( subset @ SV16 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(198,plain,
! [SV18: $i,SV15: $i,SV20: $i] :
( ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false )
| ( ( ! [SY98: $i] :
~ ( ~ ( ~ ( in @ SY98 @ SV20 )
| ~ ! [SY87: $i] :
~ ~ ! [SY88: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY87 @ SV15 )
| ~ ( in @ SY88 @ SV18 ) )
| ( SY98
!= ( ordered_pair @ SY87 @ SY88 ) ) ) )
| ~ ( ~ ~ ! [SY89: $i] :
~ ~ ! [SY90: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY89 @ SV15 )
| ~ ( in @ SY90 @ SV18 ) )
| ( SY98
!= ( ordered_pair @ SY89 @ SY90 ) ) )
| ( in @ SY98 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(199,plain,
! [SV18: $i,SV15: $i,SV20: $i] :
( ( ( ! [SY103: $i] :
~ ( ~ ( ~ ( in @ SY103 @ SV20 )
| ~ ! [SY92: $i] :
~ ~ ! [SY93: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY92 @ SV15 )
| ~ ( in @ SY93 @ SV18 ) )
| ( SY103
!= ( ordered_pair @ SY92 @ SY93 ) ) ) )
| ~ ( ~ ~ ! [SY94: $i] :
~ ~ ! [SY95: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ SV15 )
| ~ ( in @ SY95 @ SV18 ) )
| ( SY103
!= ( ordered_pair @ SY94 @ SY95 ) ) )
| ( in @ SY103 @ SV20 ) ) ) )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(200,plain,
! [SV19: $i,SV16: $i,SV21: $i] :
( ( ( ~ ( in @ SV21 @ SV16 )
| ( in @ SV21 @ SV19 ) )
= $true )
| ( ( subset @ SV16 @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(201,plain,
! [SV16: $i,SV19: $i] :
( ( ( ~ ( in @ ( sK12_SY97 @ SV19 @ SV16 ) @ SV16 )
| ( in @ ( sK12_SY97 @ SV19 @ SV16 ) @ SV19 ) )
= $false )
| ( ( subset @ SV16 @ SV19 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[197]) ).
thf(202,plain,
! [SV18: $i,SV15: $i,SV20: $i,SV22: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV22 @ SV20 )
| ~ ! [SY108: $i] :
~ ~ ! [SY109: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY108 @ SV15 )
| ~ ( in @ SY109 @ SV18 ) )
| ( SV22
!= ( ordered_pair @ SY108 @ SY109 ) ) ) )
| ~ ( ~ ~ ! [SY110: $i] :
~ ~ ! [SY111: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY110 @ SV15 )
| ~ ( in @ SY111 @ SV18 ) )
| ( SV22
!= ( ordered_pair @ SY110 @ SY111 ) ) )
| ( in @ SV22 @ SV20 ) ) ) )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(203,plain,
! [SV20: $i,SV15: $i,SV18: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 )
| ~ ! [SY112: $i] :
~ ~ ! [SY113: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY112 @ SV15 )
| ~ ( in @ SY113 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY112 @ SY113 ) ) ) )
| ~ ( ~ ~ ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) )
| ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 ) ) ) )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[199]) ).
thf(204,plain,
! [SV19: $i,SV16: $i,SV21: $i] :
( ( ( ~ ( in @ SV21 @ SV16 ) )
= $true )
| ( ( in @ SV21 @ SV19 )
= $true )
| ( ( subset @ SV16 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(205,plain,
! [SV16: $i,SV19: $i] :
( ( ( ~ ( in @ ( sK12_SY97 @ SV19 @ SV16 ) @ SV16 ) )
= $false )
| ( ( subset @ SV16 @ SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(206,plain,
! [SV16: $i,SV19: $i] :
( ( ( in @ ( sK12_SY97 @ SV19 @ SV16 ) @ SV19 )
= $false )
| ( ( subset @ SV16 @ SV19 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(207,plain,
! [SV18: $i,SV15: $i,SV20: $i,SV22: $i] :
( ( ( ~ ( ~ ( in @ SV22 @ SV20 )
| ~ ! [SY108: $i] :
~ ~ ! [SY109: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY108 @ SV15 )
| ~ ( in @ SY109 @ SV18 ) )
| ( SV22
!= ( ordered_pair @ SY108 @ SY109 ) ) ) )
| ~ ( ~ ~ ! [SY110: $i] :
~ ~ ! [SY111: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY110 @ SV15 )
| ~ ( in @ SY111 @ SV18 ) )
| ( SV22
!= ( ordered_pair @ SY110 @ SY111 ) ) )
| ( in @ SV22 @ SV20 ) ) )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(208,plain,
! [SV20: $i,SV15: $i,SV18: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 )
| ~ ! [SY112: $i] :
~ ~ ! [SY113: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY112 @ SV15 )
| ~ ( in @ SY113 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY112 @ SY113 ) ) ) )
| ~ ( ~ ~ ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) )
| ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(209,plain,
! [SV19: $i,SV16: $i,SV21: $i] :
( ( ( in @ SV21 @ SV16 )
= $false )
| ( ( in @ SV21 @ SV19 )
= $true )
| ( ( subset @ SV16 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(210,plain,
! [SV16: $i,SV19: $i] :
( ( ( in @ ( sK12_SY97 @ SV19 @ SV16 ) @ SV16 )
= $true )
| ( ( subset @ SV16 @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(211,plain,
! [SV18: $i,SV15: $i,SV20: $i,SV22: $i] :
( ( ( ~ ( ~ ( in @ SV22 @ SV20 )
| ~ ! [SY108: $i] :
~ ~ ! [SY109: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY108 @ SV15 )
| ~ ( in @ SY109 @ SV18 ) )
| ( SV22
!= ( ordered_pair @ SY108 @ SY109 ) ) ) ) )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(212,plain,
! [SV20: $i,SV22: $i,SV18: $i,SV15: $i] :
( ( ( ~ ( ~ ~ ! [SY110: $i] :
~ ~ ! [SY111: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY110 @ SV15 )
| ~ ( in @ SY111 @ SV18 ) )
| ( SV22
!= ( ordered_pair @ SY110 @ SY111 ) ) )
| ( in @ SV22 @ SV20 ) ) )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(213,plain,
! [SV20: $i,SV15: $i,SV18: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 )
| ~ ! [SY112: $i] :
~ ~ ! [SY113: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY112 @ SV15 )
| ~ ( in @ SY113 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY112 @ SY113 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) )
| ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(214,plain,
! [SV18: $i,SV15: $i,SV20: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ SV20 )
| ~ ! [SY108: $i] :
~ ~ ! [SY109: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY108 @ SV15 )
| ~ ( in @ SY109 @ SV18 ) )
| ( SV22
!= ( ordered_pair @ SY108 @ SY109 ) ) ) )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(215,plain,
! [SV20: $i,SV22: $i,SV18: $i,SV15: $i] :
( ( ( ~ ~ ! [SY110: $i] :
~ ~ ! [SY111: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY110 @ SV15 )
| ~ ( in @ SY111 @ SV18 ) )
| ( SV22
!= ( ordered_pair @ SY110 @ SY111 ) ) )
| ( in @ SV22 @ SV20 ) )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(216,plain,
! [SV20: $i,SV15: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 )
| ~ ! [SY112: $i] :
~ ~ ! [SY113: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY112 @ SV15 )
| ~ ( in @ SY113 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY112 @ SY113 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) )
| ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(217,plain,
! [SV18: $i,SV15: $i,SV20: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ SV20 ) )
= $true )
| ( ( ~ ! [SY108: $i] :
~ ~ ! [SY109: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY108 @ SV15 )
| ~ ( in @ SY109 @ SV18 ) )
| ( SV22
!= ( ordered_pair @ SY108 @ SY109 ) ) ) )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(218,plain,
! [SV20: $i,SV22: $i,SV18: $i,SV15: $i] :
( ( ( ~ ~ ! [SY110: $i] :
~ ~ ! [SY111: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY110 @ SV15 )
| ~ ( in @ SY111 @ SV18 ) )
| ( SV22
!= ( ordered_pair @ SY110 @ SY111 ) ) ) )
= $true )
| ( ( in @ SV22 @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(219,plain,
! [SV20: $i,SV15: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) )
| ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[216]) ).
thf(220,plain,
! [SV20: $i,SV18: $i,SV15: $i] :
( ( ( ~ ! [SY112: $i] :
~ ~ ! [SY113: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY112 @ SV15 )
| ~ ( in @ SY113 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY112 @ SY113 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) )
| ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[216]) ).
thf(221,plain,
! [SV18: $i,SV15: $i,SV20: $i,SV22: $i] :
( ( ( in @ SV22 @ SV20 )
= $false )
| ( ( ~ ! [SY108: $i] :
~ ~ ! [SY109: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY108 @ SV15 )
| ~ ( in @ SY109 @ SV18 ) )
| ( SV22
!= ( ordered_pair @ SY108 @ SY109 ) ) ) )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(222,plain,
! [SV20: $i,SV22: $i,SV18: $i,SV15: $i] :
( ( ( ~ ! [SY110: $i] :
~ ~ ! [SY111: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY110 @ SV15 )
| ~ ( in @ SY111 @ SV18 ) )
| ( SV22
!= ( ordered_pair @ SY110 @ SY111 ) ) ) )
= $false )
| ( ( in @ SV22 @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(223,plain,
! [SV20: $i,SV15: $i,SV18: $i] :
( ( ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 )
= $true )
| ( ( ~ ( ~ ~ ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) )
| ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(224,plain,
! [SV20: $i,SV18: $i,SV15: $i] :
( ( ( ! [SY112: $i] :
~ ~ ! [SY113: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY112 @ SV15 )
| ~ ( in @ SY113 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY112 @ SY113 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) )
| ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(225,plain,
! [SV20: $i,SV22: $i,SV18: $i,SV15: $i] :
( ( ( ! [SY108: $i] :
~ ~ ! [SY109: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY108 @ SV15 )
| ~ ( in @ SY109 @ SV18 ) )
| ( SV22
!= ( ordered_pair @ SY108 @ SY109 ) ) ) )
= $false )
| ( ( in @ SV22 @ SV20 )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(226,plain,
! [SV20: $i,SV22: $i,SV18: $i,SV15: $i] :
( ( ( ! [SY110: $i] :
~ ~ ! [SY111: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY110 @ SV15 )
| ~ ( in @ SY111 @ SV18 ) )
| ( SV22
!= ( ordered_pair @ SY110 @ SY111 ) ) ) )
= $true )
| ( ( in @ SV22 @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(227,plain,
! [SV20: $i,SV18: $i,SV15: $i] :
( ( ( ~ ~ ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) )
| ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 ) )
= $false )
| ( ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(228,plain,
! [SV20: $i,SV18: $i,SV15: $i,SV23: $i] :
( ( ( ~ ~ ! [SY116: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV23 @ SV15 )
| ~ ( in @ SY116 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SV23 @ SY116 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) )
| ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(229,plain,
! [SV15: $i,SV18: $i,SV22: $i,SV20: $i] :
( ( ( ~ ~ ! [SY117: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY108 @ SV20 @ SV22 @ SV18 @ SV15 ) @ SV15 )
| ~ ( in @ SY117 @ SV18 ) )
| ( SV22
!= ( ordered_pair @ ( sK14_SY108 @ SV20 @ SV22 @ SV18 @ SV15 ) @ SY117 ) ) ) )
= $false )
| ( ( in @ SV22 @ SV20 )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[225]) ).
thf(230,plain,
! [SV20: $i,SV22: $i,SV18: $i,SV15: $i,SV24: $i] :
( ( ( ~ ~ ! [SY118: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV24 @ SV15 )
| ~ ( in @ SY118 @ SV18 ) )
| ( SV22
!= ( ordered_pair @ SV24 @ SY118 ) ) ) )
= $true )
| ( ( in @ SV22 @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(231,plain,
! [SV20: $i,SV18: $i,SV15: $i] :
( ( ( ~ ~ ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) ) )
= $false )
| ( ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(232,plain,
! [SV20: $i,SV15: $i,SV18: $i] :
( ( ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 )
= $false )
| ( ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(233,plain,
! [SV20: $i,SV18: $i,SV15: $i,SV23: $i] :
( ( ( ~ ! [SY116: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV23 @ SV15 )
| ~ ( in @ SY116 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SV23 @ SY116 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) )
| ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(234,plain,
! [SV15: $i,SV18: $i,SV22: $i,SV20: $i] :
( ( ( ~ ! [SY117: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY108 @ SV20 @ SV22 @ SV18 @ SV15 ) @ SV15 )
| ~ ( in @ SY117 @ SV18 ) )
| ( SV22
!= ( ordered_pair @ ( sK14_SY108 @ SV20 @ SV22 @ SV18 @ SV15 ) @ SY117 ) ) ) )
= $true )
| ( ( in @ SV22 @ SV20 )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(235,plain,
! [SV20: $i,SV22: $i,SV18: $i,SV15: $i,SV24: $i] :
( ( ( ~ ! [SY118: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV24 @ SV15 )
| ~ ( in @ SY118 @ SV18 ) )
| ( SV22
!= ( ordered_pair @ SV24 @ SY118 ) ) ) )
= $false )
| ( ( in @ SV22 @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(236,plain,
! [SV20: $i,SV18: $i,SV15: $i] :
( ( ( ~ ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) ) )
= $true )
| ( ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(237,plain,
! [SV20: $i,SV18: $i,SV15: $i,SV23: $i] :
( ( ( ! [SY116: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV23 @ SV15 )
| ~ ( in @ SY116 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SV23 @ SY116 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) )
| ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(238,plain,
! [SV15: $i,SV18: $i,SV22: $i,SV20: $i] :
( ( ( ! [SY117: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY108 @ SV20 @ SV22 @ SV18 @ SV15 ) @ SV15 )
| ~ ( in @ SY117 @ SV18 ) )
| ( SV22
!= ( ordered_pair @ ( sK14_SY108 @ SV20 @ SV22 @ SV18 @ SV15 ) @ SY117 ) ) ) )
= $false )
| ( ( in @ SV22 @ SV20 )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(239,plain,
! [SV20: $i,SV22: $i,SV18: $i,SV15: $i,SV24: $i] :
( ( ( ! [SY118: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV24 @ SV15 )
| ~ ( in @ SY118 @ SV18 ) )
| ( SV22
!= ( ordered_pair @ SV24 @ SY118 ) ) ) )
= $true )
| ( ( in @ SV22 @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(240,plain,
! [SV20: $i,SV18: $i,SV15: $i] :
( ( ( ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) ) )
= $false )
| ( ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(241,plain,
! [SV20: $i,SV18: $i,SV25: $i,SV15: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV23 @ SV15 )
| ~ ( in @ SV25 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SV23 @ SV25 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) )
| ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(242,plain,
! [SV15: $i,SV18: $i,SV22: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK14_SY108 @ SV20 @ SV22 @ SV18 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK15_SY117 @ SV15 @ SV18 @ SV22 @ SV20 ) @ SV18 ) )
| ( SV22
!= ( ordered_pair @ ( sK14_SY108 @ SV20 @ SV22 @ SV18 @ SV15 ) @ ( sK15_SY117 @ SV15 @ SV18 @ SV22 @ SV20 ) ) ) ) )
= $false )
| ( ( in @ SV22 @ SV20 )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[238]) ).
thf(243,plain,
! [SV20: $i,SV22: $i,SV18: $i,SV26: $i,SV15: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV24 @ SV15 )
| ~ ( in @ SV26 @ SV18 ) )
| ( SV22
!= ( ordered_pair @ SV24 @ SV26 ) ) ) )
= $true )
| ( ( in @ SV22 @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(244,plain,
! [SV15: $i,SV18: $i,SV20: $i] :
( ( ( ~ ~ ! [SY119: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK16_SY114 @ SV20 @ SV18 @ SV15 ) @ SV15 )
| ~ ( in @ SY119 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ ( sK16_SY114 @ SV20 @ SV18 @ SV15 ) @ SY119 ) ) ) )
= $false )
| ( ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[240]) ).
thf(245,plain,
! [SV20: $i,SV18: $i,SV25: $i,SV15: $i,SV23: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV23 @ SV15 )
| ~ ( in @ SV25 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SV23 @ SV25 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) )
| ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(246,plain,
! [SV15: $i,SV18: $i,SV22: $i,SV20: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK14_SY108 @ SV20 @ SV22 @ SV18 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK15_SY117 @ SV15 @ SV18 @ SV22 @ SV20 ) @ SV18 ) )
| ( SV22
!= ( ordered_pair @ ( sK14_SY108 @ SV20 @ SV22 @ SV18 @ SV15 ) @ ( sK15_SY117 @ SV15 @ SV18 @ SV22 @ SV20 ) ) ) ) )
= $true )
| ( ( in @ SV22 @ SV20 )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(247,plain,
! [SV20: $i,SV22: $i,SV18: $i,SV26: $i,SV15: $i,SV24: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV24 @ SV15 )
| ~ ( in @ SV26 @ SV18 ) )
| ( SV22
!= ( ordered_pair @ SV24 @ SV26 ) ) ) )
= $false )
| ( ( in @ SV22 @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(248,plain,
! [SV15: $i,SV18: $i,SV20: $i] :
( ( ( ~ ! [SY119: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK16_SY114 @ SV20 @ SV18 @ SV15 ) @ SV15 )
| ~ ( in @ SY119 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ ( sK16_SY114 @ SV20 @ SV18 @ SV15 ) @ SY119 ) ) ) )
= $true )
| ( ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(249,plain,
! [SV20: $i,SV18: $i,SV25: $i,SV15: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( in @ SV23 @ SV15 )
| ~ ( in @ SV25 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SV23 @ SV25 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) )
| ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(250,plain,
! [SV15: $i,SV18: $i,SV22: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK14_SY108 @ SV20 @ SV22 @ SV18 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK15_SY117 @ SV15 @ SV18 @ SV22 @ SV20 ) @ SV18 ) )
| ( SV22
!= ( ordered_pair @ ( sK14_SY108 @ SV20 @ SV22 @ SV18 @ SV15 ) @ ( sK15_SY117 @ SV15 @ SV18 @ SV22 @ SV20 ) ) ) )
= $false )
| ( ( in @ SV22 @ SV20 )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(251,plain,
! [SV20: $i,SV22: $i,SV18: $i,SV26: $i,SV15: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( in @ SV24 @ SV15 )
| ~ ( in @ SV26 @ SV18 ) )
| ( SV22
!= ( ordered_pair @ SV24 @ SV26 ) ) )
= $true )
| ( ( in @ SV22 @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(252,plain,
! [SV15: $i,SV18: $i,SV20: $i] :
( ( ( ! [SY119: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK16_SY114 @ SV20 @ SV18 @ SV15 ) @ SV15 )
| ~ ( in @ SY119 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ ( sK16_SY114 @ SV20 @ SV18 @ SV15 ) @ SY119 ) ) ) )
= $false )
| ( ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(253,plain,
! [SV20: $i,SV18: $i,SV25: $i,SV15: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( in @ SV23 @ SV15 )
| ~ ( in @ SV25 @ SV18 ) ) )
= $true )
| ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SV23 @ SV25 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) )
| ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(254,plain,
! [SV15: $i,SV18: $i,SV22: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK14_SY108 @ SV20 @ SV22 @ SV18 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK15_SY117 @ SV15 @ SV18 @ SV22 @ SV20 ) @ SV18 ) ) )
= $false )
| ( ( in @ SV22 @ SV20 )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[250]) ).
thf(255,plain,
! [SV15: $i,SV18: $i,SV20: $i,SV22: $i] :
( ( ( SV22
!= ( ordered_pair @ ( sK14_SY108 @ SV20 @ SV22 @ SV18 @ SV15 ) @ ( sK15_SY117 @ SV15 @ SV18 @ SV22 @ SV20 ) ) )
= $false )
| ( ( in @ SV22 @ SV20 )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[250]) ).
thf(256,plain,
! [SV20: $i,SV22: $i,SV18: $i,SV26: $i,SV15: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( in @ SV24 @ SV15 )
| ~ ( in @ SV26 @ SV18 ) ) )
= $true )
| ( ( SV22
!= ( ordered_pair @ SV24 @ SV26 ) )
= $true )
| ( ( in @ SV22 @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(257,plain,
! [SV15: $i,SV18: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK16_SY114 @ SV20 @ SV18 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK17_SY119 @ SV15 @ SV18 @ SV20 ) @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ ( sK16_SY114 @ SV20 @ SV18 @ SV15 ) @ ( sK17_SY119 @ SV15 @ SV18 @ SV20 ) ) ) ) )
= $false )
| ( ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[252]) ).
thf(258,plain,
! [SV20: $i,SV18: $i,SV25: $i,SV15: $i,SV23: $i] :
( ( ( ~ ( ~ ( in @ SV23 @ SV15 )
| ~ ( in @ SV25 @ SV18 ) ) )
= $false )
| ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SV23 @ SV25 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) )
| ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(259,plain,
! [SV15: $i,SV18: $i,SV22: $i,SV20: $i] :
( ( ( ~ ( ~ ( in @ ( sK14_SY108 @ SV20 @ SV22 @ SV18 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK15_SY117 @ SV15 @ SV18 @ SV22 @ SV20 ) @ SV18 ) ) )
= $true )
| ( ( in @ SV22 @ SV20 )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(260,plain,
! [SV15: $i,SV18: $i,SV20: $i,SV22: $i] :
( ( ( SV22
= ( ordered_pair @ ( sK14_SY108 @ SV20 @ SV22 @ SV18 @ SV15 ) @ ( sK15_SY117 @ SV15 @ SV18 @ SV22 @ SV20 ) ) )
= $true )
| ( ( in @ SV22 @ SV20 )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(261,plain,
! [SV20: $i,SV22: $i,SV18: $i,SV26: $i,SV15: $i,SV24: $i] :
( ( ( ~ ( ~ ( in @ SV24 @ SV15 )
| ~ ( in @ SV26 @ SV18 ) ) )
= $false )
| ( ( SV22
!= ( ordered_pair @ SV24 @ SV26 ) )
= $true )
| ( ( in @ SV22 @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(262,plain,
! [SV15: $i,SV18: $i,SV20: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK16_SY114 @ SV20 @ SV18 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK17_SY119 @ SV15 @ SV18 @ SV20 ) @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ ( sK16_SY114 @ SV20 @ SV18 @ SV15 ) @ ( sK17_SY119 @ SV15 @ SV18 @ SV20 ) ) ) ) )
= $true )
| ( ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(263,plain,
! [SV20: $i,SV18: $i,SV25: $i,SV15: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ SV15 )
| ~ ( in @ SV25 @ SV18 ) )
= $true )
| ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SV23 @ SV25 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) )
| ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[258]) ).
thf(264,plain,
! [SV15: $i,SV18: $i,SV22: $i,SV20: $i] :
( ( ( ~ ( in @ ( sK14_SY108 @ SV20 @ SV22 @ SV18 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK15_SY117 @ SV15 @ SV18 @ SV22 @ SV20 ) @ SV18 ) )
= $false )
| ( ( in @ SV22 @ SV20 )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(265,plain,
! [SV20: $i,SV22: $i,SV18: $i,SV26: $i,SV15: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV15 )
| ~ ( in @ SV26 @ SV18 ) )
= $true )
| ( ( SV22
!= ( ordered_pair @ SV24 @ SV26 ) )
= $true )
| ( ( in @ SV22 @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(266,plain,
! [SV15: $i,SV18: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK16_SY114 @ SV20 @ SV18 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK17_SY119 @ SV15 @ SV18 @ SV20 ) @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ ( sK16_SY114 @ SV20 @ SV18 @ SV15 ) @ ( sK17_SY119 @ SV15 @ SV18 @ SV20 ) ) ) )
= $false )
| ( ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(267,plain,
! [SV20: $i,SV18: $i,SV25: $i,SV15: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ SV15 ) )
= $true )
| ( ( ~ ( in @ SV25 @ SV18 ) )
= $true )
| ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SV23 @ SV25 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) )
| ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[263]) ).
thf(268,plain,
! [SV15: $i,SV18: $i,SV22: $i,SV20: $i] :
( ( ( ~ ( in @ ( sK14_SY108 @ SV20 @ SV22 @ SV18 @ SV15 ) @ SV15 ) )
= $false )
| ( ( in @ SV22 @ SV20 )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[264]) ).
thf(269,plain,
! [SV20: $i,SV22: $i,SV18: $i,SV15: $i] :
( ( ( ~ ( in @ ( sK15_SY117 @ SV15 @ SV18 @ SV22 @ SV20 ) @ SV18 ) )
= $false )
| ( ( in @ SV22 @ SV20 )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[264]) ).
thf(270,plain,
! [SV20: $i,SV22: $i,SV18: $i,SV26: $i,SV15: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV15 ) )
= $true )
| ( ( ~ ( in @ SV26 @ SV18 ) )
= $true )
| ( ( SV22
!= ( ordered_pair @ SV24 @ SV26 ) )
= $true )
| ( ( in @ SV22 @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(271,plain,
! [SV15: $i,SV18: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK16_SY114 @ SV20 @ SV18 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK17_SY119 @ SV15 @ SV18 @ SV20 ) @ SV18 ) ) )
= $false )
| ( ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[266]) ).
thf(272,plain,
! [SV20: $i,SV15: $i,SV18: $i] :
( ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ ( sK16_SY114 @ SV20 @ SV18 @ SV15 ) @ ( sK17_SY119 @ SV15 @ SV18 @ SV20 ) ) )
= $false )
| ( ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[266]) ).
thf(273,plain,
! [SV20: $i,SV18: $i,SV25: $i,SV15: $i,SV23: $i] :
( ( ( in @ SV23 @ SV15 )
= $false )
| ( ( ~ ( in @ SV25 @ SV18 ) )
= $true )
| ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SV23 @ SV25 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) )
| ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(274,plain,
! [SV15: $i,SV18: $i,SV22: $i,SV20: $i] :
( ( ( in @ ( sK14_SY108 @ SV20 @ SV22 @ SV18 @ SV15 ) @ SV15 )
= $true )
| ( ( in @ SV22 @ SV20 )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(275,plain,
! [SV20: $i,SV22: $i,SV18: $i,SV15: $i] :
( ( ( in @ ( sK15_SY117 @ SV15 @ SV18 @ SV22 @ SV20 ) @ SV18 )
= $true )
| ( ( in @ SV22 @ SV20 )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(276,plain,
! [SV20: $i,SV22: $i,SV18: $i,SV26: $i,SV15: $i,SV24: $i] :
( ( ( in @ SV24 @ SV15 )
= $false )
| ( ( ~ ( in @ SV26 @ SV18 ) )
= $true )
| ( ( SV22
!= ( ordered_pair @ SV24 @ SV26 ) )
= $true )
| ( ( in @ SV22 @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(277,plain,
! [SV15: $i,SV18: $i,SV20: $i] :
( ( ( ~ ( ~ ( in @ ( sK16_SY114 @ SV20 @ SV18 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK17_SY119 @ SV15 @ SV18 @ SV20 ) @ SV18 ) ) )
= $true )
| ( ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(278,plain,
! [SV20: $i,SV15: $i,SV18: $i] :
( ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
= ( ordered_pair @ ( sK16_SY114 @ SV20 @ SV18 @ SV15 ) @ ( sK17_SY119 @ SV15 @ SV18 @ SV20 ) ) )
= $true )
| ( ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(279,plain,
! [SV20: $i,SV15: $i,SV23: $i,SV18: $i,SV25: $i] :
( ( ( in @ SV25 @ SV18 )
= $false )
| ( ( in @ SV23 @ SV15 )
= $false )
| ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SV23 @ SV25 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) )
| ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(280,plain,
! [SV20: $i,SV22: $i,SV15: $i,SV24: $i,SV18: $i,SV26: $i] :
( ( ( in @ SV26 @ SV18 )
= $false )
| ( ( in @ SV24 @ SV15 )
= $false )
| ( ( SV22
!= ( ordered_pair @ SV24 @ SV26 ) )
= $true )
| ( ( in @ SV22 @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(281,plain,
! [SV15: $i,SV18: $i,SV20: $i] :
( ( ( ~ ( in @ ( sK16_SY114 @ SV20 @ SV18 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK17_SY119 @ SV15 @ SV18 @ SV20 ) @ SV18 ) )
= $false )
| ( ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(282,plain,
! [SV25: $i,SV23: $i,SV20: $i,SV15: $i,SV18: $i] :
( ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
= ( ordered_pair @ SV23 @ SV25 ) )
= $false )
| ( ( in @ SV23 @ SV15 )
= $false )
| ( ( in @ SV25 @ SV18 )
= $false )
| ( ( ~ ( ~ ~ ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) )
| ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(283,plain,
! [SV20: $i,SV18: $i,SV15: $i,SV26: $i,SV24: $i,SV22: $i] :
( ( ( SV22
= ( ordered_pair @ SV24 @ SV26 ) )
= $false )
| ( ( in @ SV24 @ SV15 )
= $false )
| ( ( in @ SV26 @ SV18 )
= $false )
| ( ( in @ SV22 @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(284,plain,
! [SV15: $i,SV18: $i,SV20: $i] :
( ( ( ~ ( in @ ( sK16_SY114 @ SV20 @ SV18 @ SV15 ) @ SV15 ) )
= $false )
| ( ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(285,plain,
! [SV20: $i,SV18: $i,SV15: $i] :
( ( ( ~ ( in @ ( sK17_SY119 @ SV15 @ SV18 @ SV20 ) @ SV18 ) )
= $false )
| ( ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(286,plain,
! [SV23: $i,SV25: $i,SV20: $i,SV18: $i,SV15: $i] :
( ( ( ~ ~ ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) )
| ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 ) )
= $false )
| ( ( in @ SV25 @ SV18 )
= $false )
| ( ( in @ SV23 @ SV15 )
= $false )
| ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
= ( ordered_pair @ SV23 @ SV25 ) )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(287,plain,
! [SV15: $i,SV18: $i,SV20: $i] :
( ( ( in @ ( sK16_SY114 @ SV20 @ SV18 @ SV15 ) @ SV15 )
= $true )
| ( ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(288,plain,
! [SV20: $i,SV18: $i,SV15: $i] :
( ( ( in @ ( sK17_SY119 @ SV15 @ SV18 @ SV20 ) @ SV18 )
= $true )
| ( ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 )
= $true )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(289,plain,
! [SV23: $i,SV25: $i,SV20: $i,SV18: $i,SV15: $i] :
( ( ( ~ ~ ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) ) )
= $false )
| ( ( in @ SV25 @ SV18 )
= $false )
| ( ( in @ SV23 @ SV15 )
= $false )
| ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
= ( ordered_pair @ SV23 @ SV25 ) )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[286]) ).
thf(290,plain,
! [SV23: $i,SV25: $i,SV20: $i,SV15: $i,SV18: $i] :
( ( ( in @ ( sK13_SY103 @ SV18 @ SV15 @ SV20 ) @ SV20 )
= $false )
| ( ( in @ SV25 @ SV18 )
= $false )
| ( ( in @ SV23 @ SV15 )
= $false )
| ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
= ( ordered_pair @ SV23 @ SV25 ) )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[286]) ).
thf(291,plain,
! [SV23: $i,SV25: $i,SV20: $i,SV18: $i,SV15: $i] :
( ( ( ~ ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) ) )
= $true )
| ( ( in @ SV25 @ SV18 )
= $false )
| ( ( in @ SV23 @ SV15 )
= $false )
| ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
= ( ordered_pair @ SV23 @ SV25 ) )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[289]) ).
thf(292,plain,
! [SV23: $i,SV25: $i,SV20: $i,SV18: $i,SV15: $i] :
( ( ( ! [SY114: $i] :
~ ~ ! [SY115: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY114 @ SV15 )
| ~ ( in @ SY115 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ SY114 @ SY115 ) ) ) )
= $false )
| ( ( in @ SV25 @ SV18 )
= $false )
| ( ( in @ SV23 @ SV15 )
= $false )
| ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
= ( ordered_pair @ SV23 @ SV25 ) )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(293,plain,
! [SV15: $i,SV18: $i,SV20: $i,SV25: $i,SV23: $i] :
( ( ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK18_SY114 @ SV23 @ SV25 @ SV20 @ SV18 @ SV15 ) @ SV15 )
| ~ ( in @ SY120 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ ( sK18_SY114 @ SV23 @ SV25 @ SV20 @ SV18 @ SV15 ) @ SY120 ) ) ) )
= $false )
| ( ( in @ SV25 @ SV18 )
= $false )
| ( ( in @ SV23 @ SV15 )
= $false )
| ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
= ( ordered_pair @ SV23 @ SV25 ) )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[292]) ).
thf(294,plain,
! [SV15: $i,SV18: $i,SV20: $i,SV25: $i,SV23: $i] :
( ( ( ~ ! [SY120: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK18_SY114 @ SV23 @ SV25 @ SV20 @ SV18 @ SV15 ) @ SV15 )
| ~ ( in @ SY120 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ ( sK18_SY114 @ SV23 @ SV25 @ SV20 @ SV18 @ SV15 ) @ SY120 ) ) ) )
= $true )
| ( ( in @ SV25 @ SV18 )
= $false )
| ( ( in @ SV23 @ SV15 )
= $false )
| ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
= ( ordered_pair @ SV23 @ SV25 ) )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(295,plain,
! [SV15: $i,SV18: $i,SV20: $i,SV25: $i,SV23: $i] :
( ( ( ! [SY120: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK18_SY114 @ SV23 @ SV25 @ SV20 @ SV18 @ SV15 ) @ SV15 )
| ~ ( in @ SY120 @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ ( sK18_SY114 @ SV23 @ SV25 @ SV20 @ SV18 @ SV15 ) @ SY120 ) ) ) )
= $false )
| ( ( in @ SV25 @ SV18 )
= $false )
| ( ( in @ SV23 @ SV15 )
= $false )
| ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
= ( ordered_pair @ SV23 @ SV25 ) )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(296,plain,
! [SV15: $i,SV18: $i,SV20: $i,SV25: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK18_SY114 @ SV23 @ SV25 @ SV20 @ SV18 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK19_SY120 @ SV15 @ SV18 @ SV20 @ SV25 @ SV23 ) @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ ( sK18_SY114 @ SV23 @ SV25 @ SV20 @ SV18 @ SV15 ) @ ( sK19_SY120 @ SV15 @ SV18 @ SV20 @ SV25 @ SV23 ) ) ) ) )
= $false )
| ( ( in @ SV25 @ SV18 )
= $false )
| ( ( in @ SV23 @ SV15 )
= $false )
| ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
= ( ordered_pair @ SV23 @ SV25 ) )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[295]) ).
thf(297,plain,
! [SV15: $i,SV18: $i,SV20: $i,SV25: $i,SV23: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY114 @ SV23 @ SV25 @ SV20 @ SV18 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK19_SY120 @ SV15 @ SV18 @ SV20 @ SV25 @ SV23 ) @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ ( sK18_SY114 @ SV23 @ SV25 @ SV20 @ SV18 @ SV15 ) @ ( sK19_SY120 @ SV15 @ SV18 @ SV20 @ SV25 @ SV23 ) ) ) ) )
= $true )
| ( ( in @ SV25 @ SV18 )
= $false )
| ( ( in @ SV23 @ SV15 )
= $false )
| ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
= ( ordered_pair @ SV23 @ SV25 ) )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(298,plain,
! [SV15: $i,SV18: $i,SV20: $i,SV25: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK18_SY114 @ SV23 @ SV25 @ SV20 @ SV18 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK19_SY120 @ SV15 @ SV18 @ SV20 @ SV25 @ SV23 ) @ SV18 ) )
| ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ ( sK18_SY114 @ SV23 @ SV25 @ SV20 @ SV18 @ SV15 ) @ ( sK19_SY120 @ SV15 @ SV18 @ SV20 @ SV25 @ SV23 ) ) ) )
= $false )
| ( ( in @ SV25 @ SV18 )
= $false )
| ( ( in @ SV23 @ SV15 )
= $false )
| ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
= ( ordered_pair @ SV23 @ SV25 ) )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(299,plain,
! [SV15: $i,SV18: $i,SV20: $i,SV25: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK18_SY114 @ SV23 @ SV25 @ SV20 @ SV18 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK19_SY120 @ SV15 @ SV18 @ SV20 @ SV25 @ SV23 ) @ SV18 ) ) )
= $false )
| ( ( in @ SV25 @ SV18 )
= $false )
| ( ( in @ SV23 @ SV15 )
= $false )
| ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
= ( ordered_pair @ SV23 @ SV25 ) )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[298]) ).
thf(300,plain,
! [SV25: $i,SV23: $i,SV20: $i,SV15: $i,SV18: $i] :
( ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
!= ( ordered_pair @ ( sK18_SY114 @ SV23 @ SV25 @ SV20 @ SV18 @ SV15 ) @ ( sK19_SY120 @ SV15 @ SV18 @ SV20 @ SV25 @ SV23 ) ) )
= $false )
| ( ( in @ SV25 @ SV18 )
= $false )
| ( ( in @ SV23 @ SV15 )
= $false )
| ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
= ( ordered_pair @ SV23 @ SV25 ) )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[298]) ).
thf(301,plain,
! [SV15: $i,SV18: $i,SV20: $i,SV25: $i,SV23: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_SY114 @ SV23 @ SV25 @ SV20 @ SV18 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK19_SY120 @ SV15 @ SV18 @ SV20 @ SV25 @ SV23 ) @ SV18 ) ) )
= $true )
| ( ( in @ SV25 @ SV18 )
= $false )
| ( ( in @ SV23 @ SV15 )
= $false )
| ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
= ( ordered_pair @ SV23 @ SV25 ) )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[299]) ).
thf(302,plain,
! [SV25: $i,SV23: $i,SV20: $i,SV15: $i,SV18: $i] :
( ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
= ( ordered_pair @ ( sK18_SY114 @ SV23 @ SV25 @ SV20 @ SV18 @ SV15 ) @ ( sK19_SY120 @ SV15 @ SV18 @ SV20 @ SV25 @ SV23 ) ) )
= $true )
| ( ( in @ SV25 @ SV18 )
= $false )
| ( ( in @ SV23 @ SV15 )
= $false )
| ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
= ( ordered_pair @ SV23 @ SV25 ) )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[300]) ).
thf(303,plain,
! [SV15: $i,SV18: $i,SV20: $i,SV25: $i,SV23: $i] :
( ( ( ~ ( in @ ( sK18_SY114 @ SV23 @ SV25 @ SV20 @ SV18 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK19_SY120 @ SV15 @ SV18 @ SV20 @ SV25 @ SV23 ) @ SV18 ) )
= $false )
| ( ( in @ SV25 @ SV18 )
= $false )
| ( ( in @ SV23 @ SV15 )
= $false )
| ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
= ( ordered_pair @ SV23 @ SV25 ) )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(304,plain,
! [SV15: $i,SV18: $i,SV20: $i,SV25: $i,SV23: $i] :
( ( ( ~ ( in @ ( sK18_SY114 @ SV23 @ SV25 @ SV20 @ SV18 @ SV15 ) @ SV15 ) )
= $false )
| ( ( in @ SV25 @ SV18 )
= $false )
| ( ( in @ SV23 @ SV15 )
= $false )
| ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
= ( ordered_pair @ SV23 @ SV25 ) )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(305,plain,
! [SV23: $i,SV25: $i,SV20: $i,SV18: $i,SV15: $i] :
( ( ( ~ ( in @ ( sK19_SY120 @ SV15 @ SV18 @ SV20 @ SV25 @ SV23 ) @ SV18 ) )
= $false )
| ( ( in @ SV25 @ SV18 )
= $false )
| ( ( in @ SV23 @ SV15 )
= $false )
| ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
= ( ordered_pair @ SV23 @ SV25 ) )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(306,plain,
! [SV15: $i,SV18: $i,SV20: $i,SV25: $i,SV23: $i] :
( ( ( in @ ( sK18_SY114 @ SV23 @ SV25 @ SV20 @ SV18 @ SV15 ) @ SV15 )
= $true )
| ( ( in @ SV25 @ SV18 )
= $false )
| ( ( in @ SV23 @ SV15 )
= $false )
| ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
= ( ordered_pair @ SV23 @ SV25 ) )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[304]) ).
thf(307,plain,
! [SV23: $i,SV25: $i,SV20: $i,SV18: $i,SV15: $i] :
( ( ( in @ ( sK19_SY120 @ SV15 @ SV18 @ SV20 @ SV25 @ SV23 ) @ SV18 )
= $true )
| ( ( in @ SV25 @ SV18 )
= $false )
| ( ( in @ SV23 @ SV15 )
= $false )
| ( ( ( sK13_SY103 @ SV18 @ SV15 @ SV20 )
= ( ordered_pair @ SV23 @ SV25 ) )
= $false )
| ( ( SV20
= ( cartesian_product2 @ SV15 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[305]) ).
thf(308,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[170,307,306,302,290,288,287,283,278,275,274,260,232,210,209,206,178,175]) ).
thf(309,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[308,166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU166+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.18 % Computer : n014.cluster.edu
% 0.12/0.18 % Model : x86_64 x86_64
% 0.12/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.18 % Memory : 8046.5625MB
% 0.12/0.18 % OS : Linux 6.8.0-71-generic
% 0.12/0.18 % CPULimit : 300
% 0.12/0.18 % WCLimit : 300
% 0.12/0.18 % DateTime : Tue Oct 6 15:02:26 UTC 2026
% 0.12/0.18 % CPUTime :
% 0.12/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.67/0.48
% 1.67/0.48 No.of.Axioms: 3
% 1.67/0.48
% 1.67/0.48 Length.of.Defs: 0
% 1.67/0.48
% 1.67/0.48 Contains.Choice.Funs: false
% 1.67/0.48 ............
% 1.67/0.48
% 1.67/0.48 ********************************
% 1.67/0.48 * All subproblems solved! *
% 1.67/0.48 ********************************
% 1.67/0.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:4,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:308,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.67/0.48
% 1.67/0.48 %**** Beginning of derivation protocol ****
% 1.67/0.48 % SZS output start CNFRefutation
% See solution above
% 1.67/0.48
% 1.67/0.48 %**** End of derivation protocol ****
% 1.67/0.48 %**** no. of clauses in derivation: 303 ****
% 1.67/0.48 %**** clause counter: 308 ****
% 1.67/0.48
% 1.67/0.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:4,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:308,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------