%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET955+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 10:42:38 AM UTC 2026
% Result : Theorem 2.64s 0.69s
% Output : CNFRefutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 5
% Syntax : Number of formulae : 182 ( 49 unt; 0 typ; 0 def)
% Number of atoms : 1871 ( 787 equ; 0 cnn)
% Maximal formula atoms : 5 ( 10 avg)
% Number of connectives : 5069 (1423 ~; 706 |; 6 &;2903 @)
% ( 18 <=>; 13 =>; 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 : 21 ( 18 usr; 6 con; 0-5 aty)
% Number of variables : 833 ( 0 ^; 827 !; 6 ?; 833 :)
% 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_SY83,type,
sK10_SY83: $i > $i > $i > $i ).
thf(tp_sK11_SY78,type,
sK11_SY78: $i > $i > $i > $i > $i > $i ).
thf(tp_sK12_SY84,type,
sK12_SY84: $i > $i > $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY19,type,
sK2_SY19: $i ).
thf(tp_sK3_SY24,type,
sK3_SY24: $i ).
thf(tp_sK4_SY28,type,
sK4_SY28: $i ).
thf(tp_sK5_SY50,type,
sK5_SY50: $i > $i > $i ).
thf(tp_sK6_SY67,type,
sK6_SY67: $i > $i > $i > $i ).
thf(tp_sK7_SY72,type,
sK7_SY72: $i > $i > $i > $i > $i ).
thf(tp_sK8_SY81,type,
sK8_SY81: $i > $i > $i > $i > $i ).
thf(tp_sK9_SY78,type,
sK9_SY78: $i > $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(6,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/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(9,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( in @ ( ordered_pair @ E @ F ) @ ( cartesian_product2 @ A @ B ) )
<=> ( in @ ( ordered_pair @ E @ F ) @ ( cartesian_product2 @ C @ D ) ) )
=> ( ( cartesian_product2 @ A @ B )
= ( cartesian_product2 @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_zfmisc_1) ).
thf(10,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( in @ ( ordered_pair @ E @ F ) @ ( cartesian_product2 @ A @ B ) )
<=> ( in @ ( ordered_pair @ E @ F ) @ ( cartesian_product2 @ C @ D ) ) )
=> ( ( cartesian_product2 @ A @ B )
= ( cartesian_product2 @ C @ D ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[9]) ).
thf(11,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( in @ ( ordered_pair @ E @ F ) @ ( cartesian_product2 @ A @ B ) )
<=> ( in @ ( ordered_pair @ E @ F ) @ ( cartesian_product2 @ C @ D ) ) )
=> ( ( cartesian_product2 @ A @ B )
= ( cartesian_product2 @ C @ D ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(13,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(14,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)],[6]) ).
thf(15,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(16,plain,
( ( ! [SY19: $i,SY20: $i,SY21: $i] :
( ! [SY22: $i,SY23: $i] :
( ( in @ ( ordered_pair @ SY22 @ SY23 ) @ ( cartesian_product2 @ sK1_A @ SY19 ) )
<=> ( in @ ( ordered_pair @ SY22 @ SY23 ) @ ( cartesian_product2 @ SY20 @ SY21 ) ) )
=> ( ( cartesian_product2 @ sK1_A @ SY19 )
= ( cartesian_product2 @ SY20 @ SY21 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(17,plain,
( ( ! [SY24: $i,SY25: $i] :
( ! [SY26: $i,SY27: $i] :
( ( in @ ( ordered_pair @ SY26 @ SY27 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY19 ) )
<=> ( in @ ( ordered_pair @ SY26 @ SY27 ) @ ( cartesian_product2 @ SY24 @ SY25 ) ) )
=> ( ( cartesian_product2 @ sK1_A @ sK2_SY19 )
= ( cartesian_product2 @ SY24 @ SY25 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(18,plain,
( ( ! [SY28: $i] :
( ! [SY29: $i,SY30: $i] :
( ( in @ ( ordered_pair @ SY29 @ SY30 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY19 ) )
<=> ( in @ ( ordered_pair @ SY29 @ SY30 ) @ ( cartesian_product2 @ sK3_SY24 @ SY28 ) ) )
=> ( ( cartesian_product2 @ sK1_A @ sK2_SY19 )
= ( cartesian_product2 @ sK3_SY24 @ SY28 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(19,plain,
( ( ! [SY31: $i,SY32: $i] :
( ( in @ ( ordered_pair @ SY31 @ SY32 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY19 ) )
<=> ( in @ ( ordered_pair @ SY31 @ SY32 ) @ ( cartesian_product2 @ sK3_SY24 @ sK4_SY28 ) ) )
=> ( ( cartesian_product2 @ sK1_A @ sK2_SY19 )
= ( cartesian_product2 @ sK3_SY24 @ sK4_SY28 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(20,plain,
( ( ! [SY31: $i,SY32: $i] :
( ( in @ ( ordered_pair @ SY31 @ SY32 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY19 ) )
<=> ( in @ ( ordered_pair @ SY31 @ SY32 ) @ ( cartesian_product2 @ sK3_SY24 @ sK4_SY28 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[19]) ).
thf(21,plain,
( ( ( cartesian_product2 @ sK1_A @ sK2_SY19 )
= ( cartesian_product2 @ sK3_SY24 @ sK4_SY28 ) )
= $false ),
inference(standard_cnf,[status(thm)],[19]) ).
thf(22,plain,
( ( ( cartesian_product2 @ sK1_A @ sK2_SY19 )
!= ( cartesian_product2 @ sK3_SY24 @ sK4_SY28 ) )
= $true ),
inference(polarity_switch,[status(thm)],[21]) ).
thf(23,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(24,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)],[14]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(26,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(27,plain,
( ( ! [SY31: $i,SY32: $i] :
( ( in @ ( ordered_pair @ SY31 @ SY32 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY19 ) )
<=> ( in @ ( ordered_pair @ SY31 @ SY32 ) @ ( cartesian_product2 @ sK3_SY24 @ sK4_SY28 ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(28,plain,
( ( ( cartesian_product2 @ sK1_A @ sK2_SY19 )
!= ( cartesian_product2 @ sK3_SY24 @ sK4_SY28 ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(29,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(30,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY19 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ sK3_SY24 @ sK4_SY28 ) ) )
| ~ ( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ sK3_SY24 @ sK4_SY28 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY19 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
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)],[24]) ).
thf(32,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(33,plain,
! [SV1: $i] :
( ( ! [SY33: $i] :
~ ( empty @ ( ordered_pair @ SV1 @ SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(34,plain,
( ( ( cartesian_product2 @ sK1_A @ sK2_SY19 )
= ( cartesian_product2 @ sK3_SY24 @ sK4_SY28 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(35,plain,
! [SV2: $i] :
( ( ! [SY34: $i] :
( ~ ! [SY35: $i] :
~ ( ~ ( ~ ( in @ SY35 @ SV2 )
| ( in @ SY35 @ SY34 ) )
| ~ ( ~ ( in @ SY35 @ SY34 )
| ( in @ SY35 @ SV2 ) ) )
| ( SV2 = SY34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(36,plain,
! [SV3: $i] :
( ( ! [SY36: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV3 @ SY36 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY19 ) )
| ( in @ ( ordered_pair @ SV3 @ SY36 ) @ ( cartesian_product2 @ sK3_SY24 @ sK4_SY28 ) ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV3 @ SY36 ) @ ( cartesian_product2 @ sK3_SY24 @ sK4_SY28 ) )
| ( in @ ( ordered_pair @ SV3 @ SY36 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(37,plain,
! [SV4: $i] :
( ( ! [SY37: $i,SY38: $i] :
~ ( ~ ( ( SY38
!= ( cartesian_product2 @ SV4 @ SY37 ) )
| ! [SY39: $i] :
~ ( ~ ( ~ ( in @ SY39 @ SY38 )
| ~ ! [SY40: $i] :
~ ~ ! [SY41: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY40 @ SV4 )
| ~ ( in @ SY41 @ SY37 ) )
| ( SY39
!= ( ordered_pair @ SY40 @ SY41 ) ) ) )
| ~ ( ~ ~ ! [SY42: $i] :
~ ~ ! [SY43: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY42 @ SV4 )
| ~ ( in @ SY43 @ SY37 ) )
| ( SY39
!= ( ordered_pair @ SY42 @ SY43 ) ) )
| ( in @ SY39 @ SY38 ) ) ) )
| ~ ( ~ ! [SY44: $i] :
~ ( ~ ( ~ ( in @ SY44 @ SY38 )
| ~ ! [SY45: $i] :
~ ~ ! [SY46: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY45 @ SV4 )
| ~ ( in @ SY46 @ SY37 ) )
| ( SY44
!= ( ordered_pair @ SY45 @ SY46 ) ) ) )
| ~ ( ~ ~ ! [SY47: $i] :
~ ~ ! [SY48: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY47 @ SV4 )
| ~ ( in @ SY48 @ SY37 ) )
| ( SY44
!= ( ordered_pair @ SY47 @ SY48 ) ) )
| ( in @ SY44 @ SY38 ) ) )
| ( SY38
= ( cartesian_product2 @ SV4 @ SY37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(38,plain,
! [SV5: $i] :
( ( ! [SY49: $i] :
( ~ ( in @ SV5 @ SY49 )
| ~ ( in @ SY49 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(39,plain,
! [SV6: $i,SV1: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV1 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(40,plain,
! [SV7: $i,SV2: $i] :
( ( ~ ! [SY50: $i] :
~ ( ~ ( ~ ( in @ SY50 @ SV2 )
| ( in @ SY50 @ SV7 ) )
| ~ ( ~ ( in @ SY50 @ SV7 )
| ( in @ SY50 @ SV2 ) ) )
| ( SV2 = SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(41,plain,
! [SV8: $i,SV3: $i] :
( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV3 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY19 ) )
| ( in @ ( ordered_pair @ SV3 @ SV8 ) @ ( cartesian_product2 @ sK3_SY24 @ sK4_SY28 ) ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV3 @ SV8 ) @ ( cartesian_product2 @ sK3_SY24 @ sK4_SY28 ) )
| ( in @ ( ordered_pair @ SV3 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(42,plain,
! [SV9: $i,SV4: $i] :
( ( ! [SY51: $i] :
~ ( ~ ( ( SY51
!= ( cartesian_product2 @ SV4 @ SV9 ) )
| ! [SY52: $i] :
~ ( ~ ( ~ ( in @ SY52 @ SY51 )
| ~ ! [SY53: $i] :
~ ~ ! [SY54: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ SV4 )
| ~ ( in @ SY54 @ SV9 ) )
| ( SY52
!= ( ordered_pair @ SY53 @ SY54 ) ) ) )
| ~ ( ~ ~ ! [SY55: $i] :
~ ~ ! [SY56: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY55 @ SV4 )
| ~ ( in @ SY56 @ SV9 ) )
| ( SY52
!= ( ordered_pair @ SY55 @ SY56 ) ) )
| ( in @ SY52 @ SY51 ) ) ) )
| ~ ( ~ ! [SY57: $i] :
~ ( ~ ( ~ ( in @ SY57 @ SY51 )
| ~ ! [SY58: $i] :
~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY58 @ SV4 )
| ~ ( in @ SY59 @ SV9 ) )
| ( SY57
!= ( ordered_pair @ SY58 @ SY59 ) ) ) )
| ~ ( ~ ~ ! [SY60: $i] :
~ ~ ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY60 @ SV4 )
| ~ ( in @ SY61 @ SV9 ) )
| ( SY57
!= ( ordered_pair @ SY60 @ SY61 ) ) )
| ( in @ SY57 @ SY51 ) ) )
| ( SY51
= ( cartesian_product2 @ SV4 @ SV9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(43,plain,
! [SV10: $i,SV5: $i] :
( ( ~ ( in @ SV5 @ SV10 )
| ~ ( in @ SV10 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(44,plain,
! [SV6: $i,SV1: $i] :
( ( empty @ ( ordered_pair @ SV1 @ SV6 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(45,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ! [SY50: $i] :
~ ( ~ ( ~ ( in @ SY50 @ SV2 )
| ( in @ SY50 @ SV7 ) )
| ~ ( ~ ( in @ SY50 @ SV7 )
| ( in @ SY50 @ SV2 ) ) ) )
= $true )
| ( ( SV2 = SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(46,plain,
! [SV8: $i,SV3: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV3 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY19 ) )
| ( in @ ( ordered_pair @ SV3 @ SV8 ) @ ( cartesian_product2 @ sK3_SY24 @ sK4_SY28 ) ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV3 @ SV8 ) @ ( cartesian_product2 @ sK3_SY24 @ sK4_SY28 ) )
| ( in @ ( ordered_pair @ SV3 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY19 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(47,plain,
! [SV9: $i,SV4: $i,SV11: $i] :
( ( ~ ( ~ ( ( SV11
!= ( cartesian_product2 @ SV4 @ SV9 ) )
| ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SV11 )
| ~ ! [SY53: $i] :
~ ~ ! [SY54: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ SV4 )
| ~ ( in @ SY54 @ SV9 ) )
| ( SY62
!= ( ordered_pair @ SY53 @ SY54 ) ) ) )
| ~ ( ~ ~ ! [SY55: $i] :
~ ~ ! [SY56: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY55 @ SV4 )
| ~ ( in @ SY56 @ SV9 ) )
| ( SY62
!= ( ordered_pair @ SY55 @ SY56 ) ) )
| ( in @ SY62 @ SV11 ) ) ) )
| ~ ( ~ ! [SY67: $i] :
~ ( ~ ( ~ ( in @ SY67 @ SV11 )
| ~ ! [SY58: $i] :
~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY58 @ SV4 )
| ~ ( in @ SY59 @ SV9 ) )
| ( SY67
!= ( ordered_pair @ SY58 @ SY59 ) ) ) )
| ~ ( ~ ~ ! [SY60: $i] :
~ ~ ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY60 @ SV4 )
| ~ ( in @ SY61 @ SV9 ) )
| ( SY67
!= ( ordered_pair @ SY60 @ SY61 ) ) )
| ( in @ SY67 @ SV11 ) ) )
| ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(48,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ SV10 ) )
= $true )
| ( ( ~ ( in @ SV10 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(49,plain,
! [SV7: $i,SV2: $i] :
( ( ( ! [SY50: $i] :
~ ( ~ ( ~ ( in @ SY50 @ SV2 )
| ( in @ SY50 @ SV7 ) )
| ~ ( ~ ( in @ SY50 @ SV7 )
| ( in @ SY50 @ SV2 ) ) ) )
= $false )
| ( ( SV2 = SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(50,plain,
! [SV8: $i,SV3: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV3 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY19 ) )
| ( in @ ( ordered_pair @ SV3 @ SV8 ) @ ( cartesian_product2 @ sK3_SY24 @ sK4_SY28 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(51,plain,
! [SV8: $i,SV3: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV3 @ SV8 ) @ ( cartesian_product2 @ sK3_SY24 @ sK4_SY28 ) )
| ( in @ ( ordered_pair @ SV3 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY19 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(52,plain,
! [SV9: $i,SV4: $i,SV11: $i] :
( ( ~ ( ( SV11
!= ( cartesian_product2 @ SV4 @ SV9 ) )
| ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SV11 )
| ~ ! [SY53: $i] :
~ ~ ! [SY54: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ SV4 )
| ~ ( in @ SY54 @ SV9 ) )
| ( SY62
!= ( ordered_pair @ SY53 @ SY54 ) ) ) )
| ~ ( ~ ~ ! [SY55: $i] :
~ ~ ! [SY56: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY55 @ SV4 )
| ~ ( in @ SY56 @ SV9 ) )
| ( SY62
!= ( ordered_pair @ SY55 @ SY56 ) ) )
| ( in @ SY62 @ SV11 ) ) ) )
| ~ ( ~ ! [SY67: $i] :
~ ( ~ ( ~ ( in @ SY67 @ SV11 )
| ~ ! [SY58: $i] :
~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY58 @ SV4 )
| ~ ( in @ SY59 @ SV9 ) )
| ( SY67
!= ( ordered_pair @ SY58 @ SY59 ) ) ) )
| ~ ( ~ ~ ! [SY60: $i] :
~ ~ ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY60 @ SV4 )
| ~ ( in @ SY61 @ SV9 ) )
| ( SY67
!= ( ordered_pair @ SY60 @ SY61 ) ) )
| ( in @ SY67 @ SV11 ) ) )
| ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(53,plain,
! [SV10: $i,SV5: $i] :
( ( ( in @ SV5 @ SV10 )
= $false )
| ( ( ~ ( in @ SV10 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(54,plain,
! [SV2: $i,SV7: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV2 )
| ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV7 ) )
| ~ ( ~ ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV7 )
| ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV2 ) ) ) )
= $false )
| ( ( SV2 = SV7 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[49]) ).
thf(55,plain,
! [SV8: $i,SV3: $i] :
( ( ~ ( in @ ( ordered_pair @ SV3 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY19 ) )
| ( in @ ( ordered_pair @ SV3 @ SV8 ) @ ( cartesian_product2 @ sK3_SY24 @ sK4_SY28 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(56,plain,
! [SV8: $i,SV3: $i] :
( ( ~ ( in @ ( ordered_pair @ SV3 @ SV8 ) @ ( cartesian_product2 @ sK3_SY24 @ sK4_SY28 ) )
| ( in @ ( ordered_pair @ SV3 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY19 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(57,plain,
! [SV9: $i,SV4: $i,SV11: $i] :
( ( ~ ( ( SV11
!= ( cartesian_product2 @ SV4 @ SV9 ) )
| ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SV11 )
| ~ ! [SY53: $i] :
~ ~ ! [SY54: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ SV4 )
| ~ ( in @ SY54 @ SV9 ) )
| ( SY62
!= ( ordered_pair @ SY53 @ SY54 ) ) ) )
| ~ ( ~ ~ ! [SY55: $i] :
~ ~ ! [SY56: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY55 @ SV4 )
| ~ ( in @ SY56 @ SV9 ) )
| ( SY62
!= ( ordered_pair @ SY55 @ SY56 ) ) )
| ( in @ SY62 @ SV11 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(58,plain,
! [SV9: $i,SV4: $i,SV11: $i] :
( ( ~ ( ~ ! [SY67: $i] :
~ ( ~ ( ~ ( in @ SY67 @ SV11 )
| ~ ! [SY58: $i] :
~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY58 @ SV4 )
| ~ ( in @ SY59 @ SV9 ) )
| ( SY67
!= ( ordered_pair @ SY58 @ SY59 ) ) ) )
| ~ ( ~ ~ ! [SY60: $i] :
~ ~ ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY60 @ SV4 )
| ~ ( in @ SY61 @ SV9 ) )
| ( SY67
!= ( ordered_pair @ SY60 @ SY61 ) ) )
| ( in @ SY67 @ SV11 ) ) )
| ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(59,plain,
! [SV5: $i,SV10: $i] :
( ( ( in @ SV10 @ SV5 )
= $false )
| ( ( in @ SV5 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(60,plain,
! [SV2: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV2 )
| ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV7 ) )
| ~ ( ~ ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV7 )
| ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV2 ) ) )
= $true )
| ( ( SV2 = SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(61,plain,
! [SV8: $i,SV3: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV3 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY19 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV3 @ SV8 ) @ ( cartesian_product2 @ sK3_SY24 @ sK4_SY28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(62,plain,
! [SV8: $i,SV3: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV3 @ SV8 ) @ ( cartesian_product2 @ sK3_SY24 @ sK4_SY28 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV3 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(63,plain,
! [SV9: $i,SV4: $i,SV11: $i] :
( ( ( SV11
!= ( cartesian_product2 @ SV4 @ SV9 ) )
| ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SV11 )
| ~ ! [SY53: $i] :
~ ~ ! [SY54: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ SV4 )
| ~ ( in @ SY54 @ SV9 ) )
| ( SY62
!= ( ordered_pair @ SY53 @ SY54 ) ) ) )
| ~ ( ~ ~ ! [SY55: $i] :
~ ~ ! [SY56: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY55 @ SV4 )
| ~ ( in @ SY56 @ SV9 ) )
| ( SY62
!= ( ordered_pair @ SY55 @ SY56 ) ) )
| ( in @ SY62 @ SV11 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(64,plain,
! [SV9: $i,SV4: $i,SV11: $i] :
( ( ~ ! [SY67: $i] :
~ ( ~ ( ~ ( in @ SY67 @ SV11 )
| ~ ! [SY58: $i] :
~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY58 @ SV4 )
| ~ ( in @ SY59 @ SV9 ) )
| ( SY67
!= ( ordered_pair @ SY58 @ SY59 ) ) ) )
| ~ ( ~ ~ ! [SY60: $i] :
~ ~ ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY60 @ SV4 )
| ~ ( in @ SY61 @ SV9 ) )
| ( SY67
!= ( ordered_pair @ SY60 @ SY61 ) ) )
| ( in @ SY67 @ SV11 ) ) )
| ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(65,plain,
! [SV2: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV2 )
| ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV7 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV7 )
| ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV2 ) ) )
= $true )
| ( ( SV2 = SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(66,plain,
! [SV8: $i,SV3: $i] :
( ( ( in @ ( ordered_pair @ SV3 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY19 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV3 @ SV8 ) @ ( cartesian_product2 @ sK3_SY24 @ sK4_SY28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(67,plain,
! [SV8: $i,SV3: $i] :
( ( ( in @ ( ordered_pair @ SV3 @ SV8 ) @ ( cartesian_product2 @ sK3_SY24 @ sK4_SY28 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV3 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(68,plain,
! [SV9: $i,SV4: $i,SV11: $i] :
( ( ( SV11
!= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true )
| ( ( ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SV11 )
| ~ ! [SY53: $i] :
~ ~ ! [SY54: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ SV4 )
| ~ ( in @ SY54 @ SV9 ) )
| ( SY62
!= ( ordered_pair @ SY53 @ SY54 ) ) ) )
| ~ ( ~ ~ ! [SY55: $i] :
~ ~ ! [SY56: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY55 @ SV4 )
| ~ ( in @ SY56 @ SV9 ) )
| ( SY62
!= ( ordered_pair @ SY55 @ SY56 ) ) )
| ( in @ SY62 @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(69,plain,
! [SV9: $i,SV4: $i,SV11: $i] :
( ( ( ~ ! [SY67: $i] :
~ ( ~ ( ~ ( in @ SY67 @ SV11 )
| ~ ! [SY58: $i] :
~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY58 @ SV4 )
| ~ ( in @ SY59 @ SV9 ) )
| ( SY67
!= ( ordered_pair @ SY58 @ SY59 ) ) ) )
| ~ ( ~ ~ ! [SY60: $i] :
~ ~ ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY60 @ SV4 )
| ~ ( in @ SY61 @ SV9 ) )
| ( SY67
!= ( ordered_pair @ SY60 @ SY61 ) ) )
| ( in @ SY67 @ SV11 ) ) ) )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(70,plain,
! [SV2: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV2 )
| ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV7 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV7 )
| ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV2 ) ) )
= $true )
| ( ( SV2 = SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(71,plain,
! [SV9: $i,SV4: $i,SV11: $i] :
( ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false )
| ( ( ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SV11 )
| ~ ! [SY53: $i] :
~ ~ ! [SY54: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY53 @ SV4 )
| ~ ( in @ SY54 @ SV9 ) )
| ( SY62
!= ( ordered_pair @ SY53 @ SY54 ) ) ) )
| ~ ( ~ ~ ! [SY55: $i] :
~ ~ ! [SY56: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY55 @ SV4 )
| ~ ( in @ SY56 @ SV9 ) )
| ( SY62
!= ( ordered_pair @ SY55 @ SY56 ) ) )
| ( in @ SY62 @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(72,plain,
! [SV9: $i,SV4: $i,SV11: $i] :
( ( ( ! [SY67: $i] :
~ ( ~ ( ~ ( in @ SY67 @ SV11 )
| ~ ! [SY58: $i] :
~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY58 @ SV4 )
| ~ ( in @ SY59 @ SV9 ) )
| ( SY67
!= ( ordered_pair @ SY58 @ SY59 ) ) ) )
| ~ ( ~ ~ ! [SY60: $i] :
~ ~ ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY60 @ SV4 )
| ~ ( in @ SY61 @ SV9 ) )
| ( SY67
!= ( ordered_pair @ SY60 @ SY61 ) ) )
| ( in @ SY67 @ SV11 ) ) ) )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(73,plain,
! [SV2: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV2 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV7 )
| ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV2 ) ) )
= $true )
| ( ( SV2 = SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(74,plain,
! [SV2: $i,SV7: $i] :
( ( ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV7 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV7 )
| ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV2 ) ) )
= $true )
| ( ( SV2 = SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(75,plain,
! [SV9: $i,SV4: $i,SV11: $i,SV12: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV12 @ SV11 )
| ~ ! [SY72: $i] :
~ ~ ! [SY73: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ SV4 )
| ~ ( in @ SY73 @ SV9 ) )
| ( SV12
!= ( ordered_pair @ SY72 @ SY73 ) ) ) )
| ~ ( ~ ~ ! [SY74: $i] :
~ ~ ! [SY75: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY74 @ SV4 )
| ~ ( in @ SY75 @ SV9 ) )
| ( SV12
!= ( ordered_pair @ SY74 @ SY75 ) ) )
| ( in @ SV12 @ SV11 ) ) ) )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(76,plain,
! [SV11: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 )
| ~ ! [SY76: $i] :
~ ~ ! [SY77: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY76 @ SV4 )
| ~ ( in @ SY77 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY76 @ SY77 ) ) ) )
| ~ ( ~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) )
| ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 ) ) ) )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[72]) ).
thf(77,plain,
! [SV2: $i,SV7: $i] :
( ( ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV2 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV7 )
| ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV2 ) ) )
= $true )
| ( ( SV2 = SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(78,plain,
! [SV2: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV7 )
| ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV2 ) )
= $false )
| ( ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV7 )
= $false )
| ( ( SV2 = SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(79,plain,
! [SV9: $i,SV4: $i,SV11: $i,SV12: $i] :
( ( ( ~ ( ~ ( in @ SV12 @ SV11 )
| ~ ! [SY72: $i] :
~ ~ ! [SY73: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ SV4 )
| ~ ( in @ SY73 @ SV9 ) )
| ( SV12
!= ( ordered_pair @ SY72 @ SY73 ) ) ) )
| ~ ( ~ ~ ! [SY74: $i] :
~ ~ ! [SY75: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY74 @ SV4 )
| ~ ( in @ SY75 @ SV9 ) )
| ( SV12
!= ( ordered_pair @ SY74 @ SY75 ) ) )
| ( in @ SV12 @ SV11 ) ) )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(80,plain,
! [SV11: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 )
| ~ ! [SY76: $i] :
~ ~ ! [SY77: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY76 @ SV4 )
| ~ ( in @ SY77 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY76 @ SY77 ) ) ) )
| ~ ( ~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) )
| ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(81,plain,
! [SV2: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV7 )
| ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV2 ) )
= $false )
| ( ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV2 )
= $true )
| ( ( SV2 = SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(82,plain,
! [SV2: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV7 ) )
= $false )
| ( ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV7 )
= $false )
| ( ( SV2 = SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(83,plain,
! [SV2: $i,SV7: $i] :
( ( ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV2 )
= $false )
| ( ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV7 )
= $false )
| ( ( SV2 = SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(84,plain,
! [SV9: $i,SV4: $i,SV11: $i,SV12: $i] :
( ( ( ~ ( ~ ( in @ SV12 @ SV11 )
| ~ ! [SY72: $i] :
~ ~ ! [SY73: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ SV4 )
| ~ ( in @ SY73 @ SV9 ) )
| ( SV12
!= ( ordered_pair @ SY72 @ SY73 ) ) ) ) )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(85,plain,
! [SV11: $i,SV12: $i,SV9: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ! [SY74: $i] :
~ ~ ! [SY75: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY74 @ SV4 )
| ~ ( in @ SY75 @ SV9 ) )
| ( SV12
!= ( ordered_pair @ SY74 @ SY75 ) ) )
| ( in @ SV12 @ SV11 ) ) )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(86,plain,
! [SV11: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 )
| ~ ! [SY76: $i] :
~ ~ ! [SY77: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY76 @ SV4 )
| ~ ( in @ SY77 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY76 @ SY77 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) )
| ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(87,plain,
! [SV2: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV7 ) )
= $false )
| ( ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV2 )
= $true )
| ( ( SV2 = SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(88,plain,
! [SV2: $i,SV7: $i] :
( ( ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV2 )
= $false )
| ( ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV2 )
= $true )
| ( ( SV2 = SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(89,plain,
! [SV2: $i,SV7: $i] :
( ( ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV7 )
= $true )
| ( ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV7 )
= $false )
| ( ( SV2 = SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(90,plain,
! [SV9: $i,SV4: $i,SV11: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV11 )
| ~ ! [SY72: $i] :
~ ~ ! [SY73: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ SV4 )
| ~ ( in @ SY73 @ SV9 ) )
| ( SV12
!= ( ordered_pair @ SY72 @ SY73 ) ) ) )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(91,plain,
! [SV11: $i,SV12: $i,SV9: $i,SV4: $i] :
( ( ( ~ ~ ! [SY74: $i] :
~ ~ ! [SY75: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY74 @ SV4 )
| ~ ( in @ SY75 @ SV9 ) )
| ( SV12
!= ( ordered_pair @ SY74 @ SY75 ) ) )
| ( in @ SV12 @ SV11 ) )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(92,plain,
! [SV11: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 )
| ~ ! [SY76: $i] :
~ ~ ! [SY77: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY76 @ SV4 )
| ~ ( in @ SY77 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY76 @ SY77 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) )
| ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(93,plain,
! [SV2: $i,SV7: $i] :
( ( ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV7 )
= $true )
| ( ( in @ ( sK5_SY50 @ SV7 @ SV2 ) @ SV2 )
= $true )
| ( ( SV2 = SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(94,plain,
! [SV9: $i,SV4: $i,SV11: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV11 ) )
= $true )
| ( ( ~ ! [SY72: $i] :
~ ~ ! [SY73: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ SV4 )
| ~ ( in @ SY73 @ SV9 ) )
| ( SV12
!= ( ordered_pair @ SY72 @ SY73 ) ) ) )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(95,plain,
! [SV11: $i,SV12: $i,SV9: $i,SV4: $i] :
( ( ( ~ ~ ! [SY74: $i] :
~ ~ ! [SY75: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY74 @ SV4 )
| ~ ( in @ SY75 @ SV9 ) )
| ( SV12
!= ( ordered_pair @ SY74 @ SY75 ) ) ) )
= $true )
| ( ( in @ SV12 @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(96,plain,
! [SV11: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) )
| ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(97,plain,
! [SV11: $i,SV9: $i,SV4: $i] :
( ( ( ~ ! [SY76: $i] :
~ ~ ! [SY77: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY76 @ SV4 )
| ~ ( in @ SY77 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY76 @ SY77 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) )
| ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(98,plain,
! [SV9: $i,SV4: $i,SV11: $i,SV12: $i] :
( ( ( in @ SV12 @ SV11 )
= $false )
| ( ( ~ ! [SY72: $i] :
~ ~ ! [SY73: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ SV4 )
| ~ ( in @ SY73 @ SV9 ) )
| ( SV12
!= ( ordered_pair @ SY72 @ SY73 ) ) ) )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(99,plain,
! [SV11: $i,SV12: $i,SV9: $i,SV4: $i] :
( ( ( ~ ! [SY74: $i] :
~ ~ ! [SY75: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY74 @ SV4 )
| ~ ( in @ SY75 @ SV9 ) )
| ( SV12
!= ( ordered_pair @ SY74 @ SY75 ) ) ) )
= $false )
| ( ( in @ SV12 @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(100,plain,
! [SV11: $i,SV4: $i,SV9: $i] :
( ( ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 )
= $true )
| ( ( ~ ( ~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) )
| ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(101,plain,
! [SV11: $i,SV9: $i,SV4: $i] :
( ( ( ! [SY76: $i] :
~ ~ ! [SY77: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY76 @ SV4 )
| ~ ( in @ SY77 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY76 @ SY77 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) )
| ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(102,plain,
! [SV11: $i,SV12: $i,SV9: $i,SV4: $i] :
( ( ( ! [SY72: $i] :
~ ~ ! [SY73: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ SV4 )
| ~ ( in @ SY73 @ SV9 ) )
| ( SV12
!= ( ordered_pair @ SY72 @ SY73 ) ) ) )
= $false )
| ( ( in @ SV12 @ SV11 )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(103,plain,
! [SV11: $i,SV12: $i,SV9: $i,SV4: $i] :
( ( ( ! [SY74: $i] :
~ ~ ! [SY75: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY74 @ SV4 )
| ~ ( in @ SY75 @ SV9 ) )
| ( SV12
!= ( ordered_pair @ SY74 @ SY75 ) ) ) )
= $true )
| ( ( in @ SV12 @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(104,plain,
! [SV11: $i,SV9: $i,SV4: $i] :
( ( ( ~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) )
| ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 ) )
= $false )
| ( ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(105,plain,
! [SV11: $i,SV9: $i,SV4: $i,SV13: $i] :
( ( ( ~ ~ ! [SY80: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV13 @ SV4 )
| ~ ( in @ SY80 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SV13 @ SY80 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) )
| ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(106,plain,
! [SV4: $i,SV9: $i,SV12: $i,SV11: $i] :
( ( ( ~ ~ ! [SY81: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK7_SY72 @ SV11 @ SV12 @ SV9 @ SV4 ) @ SV4 )
| ~ ( in @ SY81 @ SV9 ) )
| ( SV12
!= ( ordered_pair @ ( sK7_SY72 @ SV11 @ SV12 @ SV9 @ SV4 ) @ SY81 ) ) ) )
= $false )
| ( ( in @ SV12 @ SV11 )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[102]) ).
thf(107,plain,
! [SV11: $i,SV12: $i,SV9: $i,SV4: $i,SV14: $i] :
( ( ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV14 @ SV4 )
| ~ ( in @ SY82 @ SV9 ) )
| ( SV12
!= ( ordered_pair @ SV14 @ SY82 ) ) ) )
= $true )
| ( ( in @ SV12 @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(108,plain,
! [SV11: $i,SV9: $i,SV4: $i] :
( ( ( ~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) ) )
= $false )
| ( ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[104]) ).
thf(109,plain,
! [SV11: $i,SV4: $i,SV9: $i] :
( ( ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[104]) ).
thf(110,plain,
! [SV11: $i,SV9: $i,SV4: $i,SV13: $i] :
( ( ( ~ ! [SY80: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV13 @ SV4 )
| ~ ( in @ SY80 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SV13 @ SY80 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) )
| ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(111,plain,
! [SV4: $i,SV9: $i,SV12: $i,SV11: $i] :
( ( ( ~ ! [SY81: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK7_SY72 @ SV11 @ SV12 @ SV9 @ SV4 ) @ SV4 )
| ~ ( in @ SY81 @ SV9 ) )
| ( SV12
!= ( ordered_pair @ ( sK7_SY72 @ SV11 @ SV12 @ SV9 @ SV4 ) @ SY81 ) ) ) )
= $true )
| ( ( in @ SV12 @ SV11 )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(112,plain,
! [SV11: $i,SV12: $i,SV9: $i,SV4: $i,SV14: $i] :
( ( ( ~ ! [SY82: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV14 @ SV4 )
| ~ ( in @ SY82 @ SV9 ) )
| ( SV12
!= ( ordered_pair @ SV14 @ SY82 ) ) ) )
= $false )
| ( ( in @ SV12 @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(113,plain,
! [SV11: $i,SV9: $i,SV4: $i] :
( ( ( ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) ) )
= $true )
| ( ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(114,plain,
! [SV11: $i,SV9: $i,SV4: $i,SV13: $i] :
( ( ( ! [SY80: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV13 @ SV4 )
| ~ ( in @ SY80 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SV13 @ SY80 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) )
| ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(115,plain,
! [SV4: $i,SV9: $i,SV12: $i,SV11: $i] :
( ( ( ! [SY81: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK7_SY72 @ SV11 @ SV12 @ SV9 @ SV4 ) @ SV4 )
| ~ ( in @ SY81 @ SV9 ) )
| ( SV12
!= ( ordered_pair @ ( sK7_SY72 @ SV11 @ SV12 @ SV9 @ SV4 ) @ SY81 ) ) ) )
= $false )
| ( ( in @ SV12 @ SV11 )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(116,plain,
! [SV11: $i,SV12: $i,SV9: $i,SV4: $i,SV14: $i] :
( ( ( ! [SY82: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV14 @ SV4 )
| ~ ( in @ SY82 @ SV9 ) )
| ( SV12
!= ( ordered_pair @ SV14 @ SY82 ) ) ) )
= $true )
| ( ( in @ SV12 @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(117,plain,
! [SV11: $i,SV9: $i,SV4: $i] :
( ( ( ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) ) )
= $false )
| ( ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(118,plain,
! [SV11: $i,SV9: $i,SV15: $i,SV4: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV13 @ SV4 )
| ~ ( in @ SV15 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SV13 @ SV15 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) )
| ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(119,plain,
! [SV4: $i,SV9: $i,SV12: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK7_SY72 @ SV11 @ SV12 @ SV9 @ SV4 ) @ SV4 )
| ~ ( in @ ( sK8_SY81 @ SV4 @ SV9 @ SV12 @ SV11 ) @ SV9 ) )
| ( SV12
!= ( ordered_pair @ ( sK7_SY72 @ SV11 @ SV12 @ SV9 @ SV4 ) @ ( sK8_SY81 @ SV4 @ SV9 @ SV12 @ SV11 ) ) ) ) )
= $false )
| ( ( in @ SV12 @ SV11 )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[115]) ).
thf(120,plain,
! [SV11: $i,SV12: $i,SV9: $i,SV16: $i,SV4: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV14 @ SV4 )
| ~ ( in @ SV16 @ SV9 ) )
| ( SV12
!= ( ordered_pair @ SV14 @ SV16 ) ) ) )
= $true )
| ( ( in @ SV12 @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(121,plain,
! [SV4: $i,SV9: $i,SV11: $i] :
( ( ( ~ ~ ! [SY83: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK9_SY78 @ SV11 @ SV9 @ SV4 ) @ SV4 )
| ~ ( in @ SY83 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ ( sK9_SY78 @ SV11 @ SV9 @ SV4 ) @ SY83 ) ) ) )
= $false )
| ( ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[117]) ).
thf(122,plain,
! [SV11: $i,SV9: $i,SV15: $i,SV4: $i,SV13: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV13 @ SV4 )
| ~ ( in @ SV15 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SV13 @ SV15 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) )
| ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(123,plain,
! [SV4: $i,SV9: $i,SV12: $i,SV11: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_SY72 @ SV11 @ SV12 @ SV9 @ SV4 ) @ SV4 )
| ~ ( in @ ( sK8_SY81 @ SV4 @ SV9 @ SV12 @ SV11 ) @ SV9 ) )
| ( SV12
!= ( ordered_pair @ ( sK7_SY72 @ SV11 @ SV12 @ SV9 @ SV4 ) @ ( sK8_SY81 @ SV4 @ SV9 @ SV12 @ SV11 ) ) ) ) )
= $true )
| ( ( in @ SV12 @ SV11 )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(124,plain,
! [SV11: $i,SV12: $i,SV9: $i,SV16: $i,SV4: $i,SV14: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV14 @ SV4 )
| ~ ( in @ SV16 @ SV9 ) )
| ( SV12
!= ( ordered_pair @ SV14 @ SV16 ) ) ) )
= $false )
| ( ( in @ SV12 @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(125,plain,
! [SV4: $i,SV9: $i,SV11: $i] :
( ( ( ~ ! [SY83: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK9_SY78 @ SV11 @ SV9 @ SV4 ) @ SV4 )
| ~ ( in @ SY83 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ ( sK9_SY78 @ SV11 @ SV9 @ SV4 ) @ SY83 ) ) ) )
= $true )
| ( ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(126,plain,
! [SV11: $i,SV9: $i,SV15: $i,SV4: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( in @ SV13 @ SV4 )
| ~ ( in @ SV15 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SV13 @ SV15 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) )
| ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(127,plain,
! [SV4: $i,SV9: $i,SV12: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK7_SY72 @ SV11 @ SV12 @ SV9 @ SV4 ) @ SV4 )
| ~ ( in @ ( sK8_SY81 @ SV4 @ SV9 @ SV12 @ SV11 ) @ SV9 ) )
| ( SV12
!= ( ordered_pair @ ( sK7_SY72 @ SV11 @ SV12 @ SV9 @ SV4 ) @ ( sK8_SY81 @ SV4 @ SV9 @ SV12 @ SV11 ) ) ) )
= $false )
| ( ( in @ SV12 @ SV11 )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(128,plain,
! [SV11: $i,SV12: $i,SV9: $i,SV16: $i,SV4: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( in @ SV14 @ SV4 )
| ~ ( in @ SV16 @ SV9 ) )
| ( SV12
!= ( ordered_pair @ SV14 @ SV16 ) ) )
= $true )
| ( ( in @ SV12 @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(129,plain,
! [SV4: $i,SV9: $i,SV11: $i] :
( ( ( ! [SY83: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK9_SY78 @ SV11 @ SV9 @ SV4 ) @ SV4 )
| ~ ( in @ SY83 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ ( sK9_SY78 @ SV11 @ SV9 @ SV4 ) @ SY83 ) ) ) )
= $false )
| ( ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(130,plain,
! [SV11: $i,SV9: $i,SV15: $i,SV4: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( in @ SV13 @ SV4 )
| ~ ( in @ SV15 @ SV9 ) ) )
= $true )
| ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SV13 @ SV15 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) )
| ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(131,plain,
! [SV4: $i,SV9: $i,SV12: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK7_SY72 @ SV11 @ SV12 @ SV9 @ SV4 ) @ SV4 )
| ~ ( in @ ( sK8_SY81 @ SV4 @ SV9 @ SV12 @ SV11 ) @ SV9 ) ) )
= $false )
| ( ( in @ SV12 @ SV11 )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(132,plain,
! [SV4: $i,SV9: $i,SV11: $i,SV12: $i] :
( ( ( SV12
!= ( ordered_pair @ ( sK7_SY72 @ SV11 @ SV12 @ SV9 @ SV4 ) @ ( sK8_SY81 @ SV4 @ SV9 @ SV12 @ SV11 ) ) )
= $false )
| ( ( in @ SV12 @ SV11 )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(133,plain,
! [SV11: $i,SV12: $i,SV9: $i,SV16: $i,SV4: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( in @ SV14 @ SV4 )
| ~ ( in @ SV16 @ SV9 ) ) )
= $true )
| ( ( SV12
!= ( ordered_pair @ SV14 @ SV16 ) )
= $true )
| ( ( in @ SV12 @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(134,plain,
! [SV4: $i,SV9: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK9_SY78 @ SV11 @ SV9 @ SV4 ) @ SV4 )
| ~ ( in @ ( sK10_SY83 @ SV4 @ SV9 @ SV11 ) @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ ( sK9_SY78 @ SV11 @ SV9 @ SV4 ) @ ( sK10_SY83 @ SV4 @ SV9 @ SV11 ) ) ) ) )
= $false )
| ( ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[129]) ).
thf(135,plain,
! [SV11: $i,SV9: $i,SV15: $i,SV4: $i,SV13: $i] :
( ( ( ~ ( ~ ( in @ SV13 @ SV4 )
| ~ ( in @ SV15 @ SV9 ) ) )
= $false )
| ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SV13 @ SV15 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) )
| ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(136,plain,
! [SV4: $i,SV9: $i,SV12: $i,SV11: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_SY72 @ SV11 @ SV12 @ SV9 @ SV4 ) @ SV4 )
| ~ ( in @ ( sK8_SY81 @ SV4 @ SV9 @ SV12 @ SV11 ) @ SV9 ) ) )
= $true )
| ( ( in @ SV12 @ SV11 )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(137,plain,
! [SV4: $i,SV9: $i,SV11: $i,SV12: $i] :
( ( ( SV12
= ( ordered_pair @ ( sK7_SY72 @ SV11 @ SV12 @ SV9 @ SV4 ) @ ( sK8_SY81 @ SV4 @ SV9 @ SV12 @ SV11 ) ) )
= $true )
| ( ( in @ SV12 @ SV11 )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(138,plain,
! [SV11: $i,SV12: $i,SV9: $i,SV16: $i,SV4: $i,SV14: $i] :
( ( ( ~ ( ~ ( in @ SV14 @ SV4 )
| ~ ( in @ SV16 @ SV9 ) ) )
= $false )
| ( ( SV12
!= ( ordered_pair @ SV14 @ SV16 ) )
= $true )
| ( ( in @ SV12 @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(139,plain,
! [SV4: $i,SV9: $i,SV11: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY78 @ SV11 @ SV9 @ SV4 ) @ SV4 )
| ~ ( in @ ( sK10_SY83 @ SV4 @ SV9 @ SV11 ) @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ ( sK9_SY78 @ SV11 @ SV9 @ SV4 ) @ ( sK10_SY83 @ SV4 @ SV9 @ SV11 ) ) ) ) )
= $true )
| ( ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(140,plain,
! [SV11: $i,SV9: $i,SV15: $i,SV4: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ SV4 )
| ~ ( in @ SV15 @ SV9 ) )
= $true )
| ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SV13 @ SV15 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) )
| ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(141,plain,
! [SV4: $i,SV9: $i,SV12: $i,SV11: $i] :
( ( ( ~ ( in @ ( sK7_SY72 @ SV11 @ SV12 @ SV9 @ SV4 ) @ SV4 )
| ~ ( in @ ( sK8_SY81 @ SV4 @ SV9 @ SV12 @ SV11 ) @ SV9 ) )
= $false )
| ( ( in @ SV12 @ SV11 )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(142,plain,
! [SV11: $i,SV12: $i,SV9: $i,SV16: $i,SV4: $i,SV14: $i] :
( ( ( ~ ( in @ SV14 @ SV4 )
| ~ ( in @ SV16 @ SV9 ) )
= $true )
| ( ( SV12
!= ( ordered_pair @ SV14 @ SV16 ) )
= $true )
| ( ( in @ SV12 @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(143,plain,
! [SV4: $i,SV9: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK9_SY78 @ SV11 @ SV9 @ SV4 ) @ SV4 )
| ~ ( in @ ( sK10_SY83 @ SV4 @ SV9 @ SV11 ) @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ ( sK9_SY78 @ SV11 @ SV9 @ SV4 ) @ ( sK10_SY83 @ SV4 @ SV9 @ SV11 ) ) ) )
= $false )
| ( ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(144,plain,
! [SV11: $i,SV9: $i,SV15: $i,SV4: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ SV4 ) )
= $true )
| ( ( ~ ( in @ SV15 @ SV9 ) )
= $true )
| ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SV13 @ SV15 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) )
| ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(145,plain,
! [SV4: $i,SV9: $i,SV12: $i,SV11: $i] :
( ( ( ~ ( in @ ( sK7_SY72 @ SV11 @ SV12 @ SV9 @ SV4 ) @ SV4 ) )
= $false )
| ( ( in @ SV12 @ SV11 )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(146,plain,
! [SV11: $i,SV12: $i,SV9: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK8_SY81 @ SV4 @ SV9 @ SV12 @ SV11 ) @ SV9 ) )
= $false )
| ( ( in @ SV12 @ SV11 )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(147,plain,
! [SV11: $i,SV12: $i,SV9: $i,SV16: $i,SV4: $i,SV14: $i] :
( ( ( ~ ( in @ SV14 @ SV4 ) )
= $true )
| ( ( ~ ( in @ SV16 @ SV9 ) )
= $true )
| ( ( SV12
!= ( ordered_pair @ SV14 @ SV16 ) )
= $true )
| ( ( in @ SV12 @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(148,plain,
! [SV4: $i,SV9: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK9_SY78 @ SV11 @ SV9 @ SV4 ) @ SV4 )
| ~ ( in @ ( sK10_SY83 @ SV4 @ SV9 @ SV11 ) @ SV9 ) ) )
= $false )
| ( ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(149,plain,
! [SV11: $i,SV4: $i,SV9: $i] :
( ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ ( sK9_SY78 @ SV11 @ SV9 @ SV4 ) @ ( sK10_SY83 @ SV4 @ SV9 @ SV11 ) ) )
= $false )
| ( ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(150,plain,
! [SV11: $i,SV9: $i,SV15: $i,SV4: $i,SV13: $i] :
( ( ( in @ SV13 @ SV4 )
= $false )
| ( ( ~ ( in @ SV15 @ SV9 ) )
= $true )
| ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SV13 @ SV15 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) )
| ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(151,plain,
! [SV4: $i,SV9: $i,SV12: $i,SV11: $i] :
( ( ( in @ ( sK7_SY72 @ SV11 @ SV12 @ SV9 @ SV4 ) @ SV4 )
= $true )
| ( ( in @ SV12 @ SV11 )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(152,plain,
! [SV11: $i,SV12: $i,SV9: $i,SV4: $i] :
( ( ( in @ ( sK8_SY81 @ SV4 @ SV9 @ SV12 @ SV11 ) @ SV9 )
= $true )
| ( ( in @ SV12 @ SV11 )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(153,plain,
! [SV11: $i,SV12: $i,SV9: $i,SV16: $i,SV4: $i,SV14: $i] :
( ( ( in @ SV14 @ SV4 )
= $false )
| ( ( ~ ( in @ SV16 @ SV9 ) )
= $true )
| ( ( SV12
!= ( ordered_pair @ SV14 @ SV16 ) )
= $true )
| ( ( in @ SV12 @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(154,plain,
! [SV4: $i,SV9: $i,SV11: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_SY78 @ SV11 @ SV9 @ SV4 ) @ SV4 )
| ~ ( in @ ( sK10_SY83 @ SV4 @ SV9 @ SV11 ) @ SV9 ) ) )
= $true )
| ( ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(155,plain,
! [SV11: $i,SV4: $i,SV9: $i] :
( ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
= ( ordered_pair @ ( sK9_SY78 @ SV11 @ SV9 @ SV4 ) @ ( sK10_SY83 @ SV4 @ SV9 @ SV11 ) ) )
= $true )
| ( ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(156,plain,
! [SV11: $i,SV4: $i,SV13: $i,SV9: $i,SV15: $i] :
( ( ( in @ SV15 @ SV9 )
= $false )
| ( ( in @ SV13 @ SV4 )
= $false )
| ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SV13 @ SV15 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) )
| ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(157,plain,
! [SV11: $i,SV12: $i,SV4: $i,SV14: $i,SV9: $i,SV16: $i] :
( ( ( in @ SV16 @ SV9 )
= $false )
| ( ( in @ SV14 @ SV4 )
= $false )
| ( ( SV12
!= ( ordered_pair @ SV14 @ SV16 ) )
= $true )
| ( ( in @ SV12 @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(158,plain,
! [SV4: $i,SV9: $i,SV11: $i] :
( ( ( ~ ( in @ ( sK9_SY78 @ SV11 @ SV9 @ SV4 ) @ SV4 )
| ~ ( in @ ( sK10_SY83 @ SV4 @ SV9 @ SV11 ) @ SV9 ) )
= $false )
| ( ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(159,plain,
! [SV15: $i,SV13: $i,SV11: $i,SV4: $i,SV9: $i] :
( ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
= ( ordered_pair @ SV13 @ SV15 ) )
= $false )
| ( ( in @ SV13 @ SV4 )
= $false )
| ( ( in @ SV15 @ SV9 )
= $false )
| ( ( ~ ( ~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) )
| ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 ) ) )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(160,plain,
! [SV11: $i,SV9: $i,SV4: $i,SV16: $i,SV14: $i,SV12: $i] :
( ( ( SV12
= ( ordered_pair @ SV14 @ SV16 ) )
= $false )
| ( ( in @ SV14 @ SV4 )
= $false )
| ( ( in @ SV16 @ SV9 )
= $false )
| ( ( in @ SV12 @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(161,plain,
! [SV4: $i,SV9: $i,SV11: $i] :
( ( ( ~ ( in @ ( sK9_SY78 @ SV11 @ SV9 @ SV4 ) @ SV4 ) )
= $false )
| ( ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(162,plain,
! [SV11: $i,SV9: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK10_SY83 @ SV4 @ SV9 @ SV11 ) @ SV9 ) )
= $false )
| ( ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(163,plain,
! [SV13: $i,SV15: $i,SV11: $i,SV9: $i,SV4: $i] :
( ( ( ~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) )
| ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 ) )
= $false )
| ( ( in @ SV15 @ SV9 )
= $false )
| ( ( in @ SV13 @ SV4 )
= $false )
| ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
= ( ordered_pair @ SV13 @ SV15 ) )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(164,plain,
! [SV4: $i,SV9: $i,SV11: $i] :
( ( ( in @ ( sK9_SY78 @ SV11 @ SV9 @ SV4 ) @ SV4 )
= $true )
| ( ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(165,plain,
! [SV11: $i,SV9: $i,SV4: $i] :
( ( ( in @ ( sK10_SY83 @ SV4 @ SV9 @ SV11 ) @ SV9 )
= $true )
| ( ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 )
= $true )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(166,plain,
! [SV13: $i,SV15: $i,SV11: $i,SV9: $i,SV4: $i] :
( ( ( ~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) ) )
= $false )
| ( ( in @ SV15 @ SV9 )
= $false )
| ( ( in @ SV13 @ SV4 )
= $false )
| ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
= ( ordered_pair @ SV13 @ SV15 ) )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(167,plain,
! [SV13: $i,SV15: $i,SV11: $i,SV4: $i,SV9: $i] :
( ( ( in @ ( sK6_SY67 @ SV9 @ SV4 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ SV15 @ SV9 )
= $false )
| ( ( in @ SV13 @ SV4 )
= $false )
| ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
= ( ordered_pair @ SV13 @ SV15 ) )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(168,plain,
! [SV13: $i,SV15: $i,SV11: $i,SV9: $i,SV4: $i] :
( ( ( ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) ) )
= $true )
| ( ( in @ SV15 @ SV9 )
= $false )
| ( ( in @ SV13 @ SV4 )
= $false )
| ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
= ( ordered_pair @ SV13 @ SV15 ) )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(169,plain,
! [SV13: $i,SV15: $i,SV11: $i,SV9: $i,SV4: $i] :
( ( ( ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY78 @ SV4 )
| ~ ( in @ SY79 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ SY78 @ SY79 ) ) ) )
= $false )
| ( ( in @ SV15 @ SV9 )
= $false )
| ( ( in @ SV13 @ SV4 )
= $false )
| ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
= ( ordered_pair @ SV13 @ SV15 ) )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(170,plain,
! [SV4: $i,SV9: $i,SV11: $i,SV15: $i,SV13: $i] :
( ( ( ~ ~ ! [SY84: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK11_SY78 @ SV13 @ SV15 @ SV11 @ SV9 @ SV4 ) @ SV4 )
| ~ ( in @ SY84 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ ( sK11_SY78 @ SV13 @ SV15 @ SV11 @ SV9 @ SV4 ) @ SY84 ) ) ) )
= $false )
| ( ( in @ SV15 @ SV9 )
= $false )
| ( ( in @ SV13 @ SV4 )
= $false )
| ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
= ( ordered_pair @ SV13 @ SV15 ) )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[169]) ).
thf(171,plain,
! [SV4: $i,SV9: $i,SV11: $i,SV15: $i,SV13: $i] :
( ( ( ~ ! [SY84: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK11_SY78 @ SV13 @ SV15 @ SV11 @ SV9 @ SV4 ) @ SV4 )
| ~ ( in @ SY84 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ ( sK11_SY78 @ SV13 @ SV15 @ SV11 @ SV9 @ SV4 ) @ SY84 ) ) ) )
= $true )
| ( ( in @ SV15 @ SV9 )
= $false )
| ( ( in @ SV13 @ SV4 )
= $false )
| ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
= ( ordered_pair @ SV13 @ SV15 ) )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(172,plain,
! [SV4: $i,SV9: $i,SV11: $i,SV15: $i,SV13: $i] :
( ( ( ! [SY84: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK11_SY78 @ SV13 @ SV15 @ SV11 @ SV9 @ SV4 ) @ SV4 )
| ~ ( in @ SY84 @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ ( sK11_SY78 @ SV13 @ SV15 @ SV11 @ SV9 @ SV4 ) @ SY84 ) ) ) )
= $false )
| ( ( in @ SV15 @ SV9 )
= $false )
| ( ( in @ SV13 @ SV4 )
= $false )
| ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
= ( ordered_pair @ SV13 @ SV15 ) )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(173,plain,
! [SV4: $i,SV9: $i,SV11: $i,SV15: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_SY78 @ SV13 @ SV15 @ SV11 @ SV9 @ SV4 ) @ SV4 )
| ~ ( in @ ( sK12_SY84 @ SV4 @ SV9 @ SV11 @ SV15 @ SV13 ) @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ ( sK11_SY78 @ SV13 @ SV15 @ SV11 @ SV9 @ SV4 ) @ ( sK12_SY84 @ SV4 @ SV9 @ SV11 @ SV15 @ SV13 ) ) ) ) )
= $false )
| ( ( in @ SV15 @ SV9 )
= $false )
| ( ( in @ SV13 @ SV4 )
= $false )
| ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
= ( ordered_pair @ SV13 @ SV15 ) )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[172]) ).
thf(174,plain,
! [SV4: $i,SV9: $i,SV11: $i,SV15: $i,SV13: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK11_SY78 @ SV13 @ SV15 @ SV11 @ SV9 @ SV4 ) @ SV4 )
| ~ ( in @ ( sK12_SY84 @ SV4 @ SV9 @ SV11 @ SV15 @ SV13 ) @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ ( sK11_SY78 @ SV13 @ SV15 @ SV11 @ SV9 @ SV4 ) @ ( sK12_SY84 @ SV4 @ SV9 @ SV11 @ SV15 @ SV13 ) ) ) ) )
= $true )
| ( ( in @ SV15 @ SV9 )
= $false )
| ( ( in @ SV13 @ SV4 )
= $false )
| ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
= ( ordered_pair @ SV13 @ SV15 ) )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(175,plain,
! [SV4: $i,SV9: $i,SV11: $i,SV15: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK11_SY78 @ SV13 @ SV15 @ SV11 @ SV9 @ SV4 ) @ SV4 )
| ~ ( in @ ( sK12_SY84 @ SV4 @ SV9 @ SV11 @ SV15 @ SV13 ) @ SV9 ) )
| ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ ( sK11_SY78 @ SV13 @ SV15 @ SV11 @ SV9 @ SV4 ) @ ( sK12_SY84 @ SV4 @ SV9 @ SV11 @ SV15 @ SV13 ) ) ) )
= $false )
| ( ( in @ SV15 @ SV9 )
= $false )
| ( ( in @ SV13 @ SV4 )
= $false )
| ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
= ( ordered_pair @ SV13 @ SV15 ) )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(176,plain,
! [SV4: $i,SV9: $i,SV11: $i,SV15: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK11_SY78 @ SV13 @ SV15 @ SV11 @ SV9 @ SV4 ) @ SV4 )
| ~ ( in @ ( sK12_SY84 @ SV4 @ SV9 @ SV11 @ SV15 @ SV13 ) @ SV9 ) ) )
= $false )
| ( ( in @ SV15 @ SV9 )
= $false )
| ( ( in @ SV13 @ SV4 )
= $false )
| ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
= ( ordered_pair @ SV13 @ SV15 ) )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(177,plain,
! [SV15: $i,SV13: $i,SV11: $i,SV4: $i,SV9: $i] :
( ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
!= ( ordered_pair @ ( sK11_SY78 @ SV13 @ SV15 @ SV11 @ SV9 @ SV4 ) @ ( sK12_SY84 @ SV4 @ SV9 @ SV11 @ SV15 @ SV13 ) ) )
= $false )
| ( ( in @ SV15 @ SV9 )
= $false )
| ( ( in @ SV13 @ SV4 )
= $false )
| ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
= ( ordered_pair @ SV13 @ SV15 ) )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(178,plain,
! [SV4: $i,SV9: $i,SV11: $i,SV15: $i,SV13: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_SY78 @ SV13 @ SV15 @ SV11 @ SV9 @ SV4 ) @ SV4 )
| ~ ( in @ ( sK12_SY84 @ SV4 @ SV9 @ SV11 @ SV15 @ SV13 ) @ SV9 ) ) )
= $true )
| ( ( in @ SV15 @ SV9 )
= $false )
| ( ( in @ SV13 @ SV4 )
= $false )
| ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
= ( ordered_pair @ SV13 @ SV15 ) )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(179,plain,
! [SV15: $i,SV13: $i,SV11: $i,SV4: $i,SV9: $i] :
( ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
= ( ordered_pair @ ( sK11_SY78 @ SV13 @ SV15 @ SV11 @ SV9 @ SV4 ) @ ( sK12_SY84 @ SV4 @ SV9 @ SV11 @ SV15 @ SV13 ) ) )
= $true )
| ( ( in @ SV15 @ SV9 )
= $false )
| ( ( in @ SV13 @ SV4 )
= $false )
| ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
= ( ordered_pair @ SV13 @ SV15 ) )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(180,plain,
! [SV4: $i,SV9: $i,SV11: $i,SV15: $i,SV13: $i] :
( ( ( ~ ( in @ ( sK11_SY78 @ SV13 @ SV15 @ SV11 @ SV9 @ SV4 ) @ SV4 )
| ~ ( in @ ( sK12_SY84 @ SV4 @ SV9 @ SV11 @ SV15 @ SV13 ) @ SV9 ) )
= $false )
| ( ( in @ SV15 @ SV9 )
= $false )
| ( ( in @ SV13 @ SV4 )
= $false )
| ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
= ( ordered_pair @ SV13 @ SV15 ) )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(181,plain,
! [SV4: $i,SV9: $i,SV11: $i,SV15: $i,SV13: $i] :
( ( ( ~ ( in @ ( sK11_SY78 @ SV13 @ SV15 @ SV11 @ SV9 @ SV4 ) @ SV4 ) )
= $false )
| ( ( in @ SV15 @ SV9 )
= $false )
| ( ( in @ SV13 @ SV4 )
= $false )
| ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
= ( ordered_pair @ SV13 @ SV15 ) )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(182,plain,
! [SV13: $i,SV15: $i,SV11: $i,SV9: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK12_SY84 @ SV4 @ SV9 @ SV11 @ SV15 @ SV13 ) @ SV9 ) )
= $false )
| ( ( in @ SV15 @ SV9 )
= $false )
| ( ( in @ SV13 @ SV4 )
= $false )
| ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
= ( ordered_pair @ SV13 @ SV15 ) )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(183,plain,
! [SV4: $i,SV9: $i,SV11: $i,SV15: $i,SV13: $i] :
( ( ( in @ ( sK11_SY78 @ SV13 @ SV15 @ SV11 @ SV9 @ SV4 ) @ SV4 )
= $true )
| ( ( in @ SV15 @ SV9 )
= $false )
| ( ( in @ SV13 @ SV4 )
= $false )
| ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
= ( ordered_pair @ SV13 @ SV15 ) )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(184,plain,
! [SV13: $i,SV15: $i,SV11: $i,SV9: $i,SV4: $i] :
( ( ( in @ ( sK12_SY84 @ SV4 @ SV9 @ SV11 @ SV15 @ SV13 ) @ SV9 )
= $true )
| ( ( in @ SV15 @ SV9 )
= $false )
| ( ( in @ SV13 @ SV4 )
= $false )
| ( ( ( sK6_SY67 @ SV9 @ SV4 @ SV11 )
= ( ordered_pair @ SV13 @ SV15 ) )
= $false )
| ( ( SV11
= ( cartesian_product2 @ SV4 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(185,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[34,184,183,179,167,165,164,160,155,152,151,137,109,93,89,88,83,67,66,59,44]) ).
thf(186,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[185]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET955+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.18 % Computer : n026.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Oct 6 15:00:16 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.64/0.69
% 2.64/0.69 No.of.Axioms: 4
% 2.64/0.69
% 2.64/0.69 Length.of.Defs: 0
% 2.64/0.69
% 2.64/0.69 Contains.Choice.Funs: false
% 2.64/0.69 .......
% 2.64/0.69
% 2.64/0.69 ********************************
% 2.64/0.69 * All subproblems solved! *
% 2.64/0.69 ********************************
% 2.64/0.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:5,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:185,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.64/0.69
% 2.64/0.69 %**** Beginning of derivation protocol ****
% 2.64/0.69 % SZS output start CNFRefutation
% See solution above
% 2.64/0.69
% 2.64/0.69 %**** End of derivation protocol ****
% 2.64/0.69 %**** no. of clauses in derivation: 182 ****
% 2.64/0.69 %**** clause counter: 185 ****
% 2.64/0.69
% 2.64/0.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:5,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:185,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------