TSTP Solution File: SET955+1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET955+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 03:06:32 EDT 2022
% Result : Theorem 0.90s 1.07s
% Output : CNFRefutation 0.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 27
% Syntax : Number of formulae : 169 ( 75 unt; 18 typ; 0 def)
% Number of atoms : 1168 ( 474 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 3358 ( 518 ~; 416 |; 22 &;2377 @)
% ( 14 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 8 con; 0-4 aty)
% Number of variables : 530 ( 0 ^ 522 !; 8 ?; 530 :)
% 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_D,type,
sK10_D: $i > $i > $i > $i ).
thf(tp_sK11_SY42,type,
sK11_SY42: $i > $i > $i > $i ).
thf(tp_sK12_SY44,type,
sK12_SY44: $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY25,type,
sK2_SY25: $i ).
thf(tp_sK3_SY30,type,
sK3_SY30: $i ).
thf(tp_sK4_SY34,type,
sK4_SY34: $i ).
thf(tp_sK5_C,type,
sK5_C: $i > $i > $i ).
thf(tp_sK6_A,type,
sK6_A: $i ).
thf(tp_sK7_A,type,
sK7_A: $i ).
thf(tp_sK8_E,type,
sK8_E: $i > $i > $i > $i > $i ).
thf(tp_sK9_SY39,type,
sK9_SY39: $i > $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/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(2,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(3,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(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/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/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/sandbox2/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] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(14,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(16,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(17,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(18,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(19,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(20,plain,
( ( ! [SY25: $i,SY26: $i,SY27: $i] :
( ! [SY28: $i,SY29: $i] :
( ( in @ ( ordered_pair @ SY28 @ SY29 ) @ ( cartesian_product2 @ sK1_A @ SY25 ) )
<=> ( in @ ( ordered_pair @ SY28 @ SY29 ) @ ( cartesian_product2 @ SY26 @ SY27 ) ) )
=> ( ( cartesian_product2 @ sK1_A @ SY25 )
= ( cartesian_product2 @ SY26 @ SY27 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(21,plain,
( ( ! [SY30: $i,SY31: $i] :
( ! [SY32: $i,SY33: $i] :
( ( in @ ( ordered_pair @ SY32 @ SY33 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY25 ) )
<=> ( in @ ( ordered_pair @ SY32 @ SY33 ) @ ( cartesian_product2 @ SY30 @ SY31 ) ) )
=> ( ( cartesian_product2 @ sK1_A @ sK2_SY25 )
= ( cartesian_product2 @ SY30 @ SY31 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[20]) ).
thf(22,plain,
( ( ! [SY34: $i] :
( ! [SY35: $i,SY36: $i] :
( ( in @ ( ordered_pair @ SY35 @ SY36 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY25 ) )
<=> ( in @ ( ordered_pair @ SY35 @ SY36 ) @ ( cartesian_product2 @ sK3_SY30 @ SY34 ) ) )
=> ( ( cartesian_product2 @ sK1_A @ sK2_SY25 )
= ( cartesian_product2 @ sK3_SY30 @ SY34 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(23,plain,
( ( ! [SY37: $i,SY38: $i] :
( ( in @ ( ordered_pair @ SY37 @ SY38 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY25 ) )
<=> ( in @ ( ordered_pair @ SY37 @ SY38 ) @ ( cartesian_product2 @ sK3_SY30 @ sK4_SY34 ) ) )
=> ( ( cartesian_product2 @ sK1_A @ sK2_SY25 )
= ( cartesian_product2 @ sK3_SY30 @ sK4_SY34 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[22]) ).
thf(24,plain,
( ( ! [SY37: $i,SY38: $i] :
( ( in @ ( ordered_pair @ SY37 @ SY38 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY25 ) )
<=> ( in @ ( ordered_pair @ SY37 @ SY38 ) @ ( cartesian_product2 @ sK3_SY30 @ sK4_SY34 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[23]) ).
thf(25,plain,
( ( ( cartesian_product2 @ sK1_A @ sK2_SY25 )
= ( cartesian_product2 @ sK3_SY30 @ sK4_SY34 ) )
= $false ),
inference(standard_cnf,[status(thm)],[23]) ).
thf(26,plain,
( ( ( ( cartesian_product2 @ sK1_A @ sK2_SY25 )
!= ( cartesian_product2 @ sK3_SY30 @ sK4_SY34 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[25]) ).
thf(27,plain,
( ( ! [SY37: $i,SY38: $i] :
( ~ ( in @ ( ordered_pair @ SY37 @ SY38 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY25 ) )
| ( in @ ( ordered_pair @ SY37 @ SY38 ) @ ( cartesian_product2 @ sK3_SY30 @ sK4_SY34 ) ) )
& ! [SY37: $i,SY38: $i] :
( ~ ( in @ ( ordered_pair @ SY37 @ SY38 ) @ ( cartesian_product2 @ sK3_SY30 @ sK4_SY34 ) )
| ( in @ ( ordered_pair @ SY37 @ SY38 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY25 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(28,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK5_C @ B @ A ) @ A )
| ~ ( in @ ( sK5_C @ B @ A ) @ B ) )
& ( ( in @ ( sK5_C @ B @ A ) @ A )
| ( in @ ( sK5_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(29,plain,
( ( ~ ( empty @ sK6_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(30,plain,
( ( empty @ sK7_A )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(31,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY40: $i,SY41: $i] :
( ~ ( in @ SY40 @ A )
| ~ ( in @ SY41 @ B )
| ( ( sK10_D @ C @ B @ A )
!= ( ordered_pair @ SY40 @ SY41 ) ) )
| ~ ( in @ ( sK10_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK11_SY42 @ C @ B @ A ) @ A )
& ( in @ ( sK12_SY44 @ C @ B @ A ) @ B )
& ( ( sK10_D @ C @ B @ A )
= ( ordered_pair @ ( sK11_SY42 @ C @ B @ A ) @ ( sK12_SY44 @ C @ B @ A ) ) ) )
| ( in @ ( sK10_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( cartesian_product2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( cartesian_product2 @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i,F: $i] :
( ~ ( in @ E @ A )
| ~ ( in @ F @ B )
| ( D
!= ( ordered_pair @ E @ F ) ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( sK8_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK9_SY39 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK8_E @ D @ C @ B @ A ) @ ( sK9_SY39 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(32,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(33,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(34,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(35,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY40: $i,SY41: $i] :
( ~ ( in @ SY40 @ A )
| ~ ( in @ SY41 @ B )
| ( ( sK10_D @ C @ B @ A )
!= ( ordered_pair @ SY40 @ SY41 ) ) )
| ~ ( in @ ( sK10_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK11_SY42 @ C @ B @ A ) @ A )
& ( in @ ( sK12_SY44 @ C @ B @ A ) @ B )
& ( ( sK10_D @ C @ B @ A )
= ( ordered_pair @ ( sK11_SY42 @ C @ B @ A ) @ ( sK12_SY44 @ C @ B @ A ) ) ) )
| ( in @ ( sK10_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( cartesian_product2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( cartesian_product2 @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i,F: $i] :
( ~ ( in @ E @ A )
| ~ ( in @ F @ B )
| ( D
!= ( ordered_pair @ E @ F ) ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( sK8_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK9_SY39 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK8_E @ D @ C @ B @ A ) @ ( sK9_SY39 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(36,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(37,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(38,plain,
( ( empty @ sK7_A )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(39,plain,
( ( ~ ( empty @ sK6_A ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(40,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK5_C @ B @ A ) @ A )
| ~ ( in @ ( sK5_C @ B @ A ) @ B ) )
& ( ( in @ ( sK5_C @ B @ A ) @ A )
| ( in @ ( sK5_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(41,plain,
( ( ! [SY37: $i,SY38: $i] :
( ~ ( in @ ( ordered_pair @ SY37 @ SY38 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY25 ) )
| ( in @ ( ordered_pair @ SY37 @ SY38 ) @ ( cartesian_product2 @ sK3_SY30 @ sK4_SY34 ) ) )
& ! [SY37: $i,SY38: $i] :
( ~ ( in @ ( ordered_pair @ SY37 @ SY38 ) @ ( cartesian_product2 @ sK3_SY30 @ sK4_SY34 ) )
| ( in @ ( ordered_pair @ SY37 @ SY38 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY25 ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(42,plain,
( ( ( ( cartesian_product2 @ sK1_A @ sK2_SY25 )
!= ( cartesian_product2 @ sK3_SY30 @ sK4_SY34 ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(43,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX4 @ SX1 )
| ( ( sK10_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ SX3 @ SX4 ) ) )
| ~ ( in @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK11_SY42 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK12_SY44 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK10_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ ( sK11_SY42 @ SX2 @ SX1 @ SX0 ) @ ( sK12_SY44 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( in @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ( SX2
= ( cartesian_product2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( cartesian_product2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i,SX5: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ~ ( ~ ( in @ ( sK8_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK9_SY39 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( ordered_pair @ ( sK8_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK9_SY39 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(44,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY25 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ sK3_SY30 @ sK4_SY34 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ sK3_SY30 @ sK4_SY34 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY25 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(45,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(46,plain,
! [SV1: $i] :
( ( ! [SY45: $i] :
( ~ ( in @ SV1 @ SY45 )
| ~ ( in @ SY45 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(47,plain,
! [SV2: $i] :
( ( ! [SY46: $i] :
( ( unordered_pair @ SV2 @ SY46 )
= ( unordered_pair @ SY46 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(48,plain,
! [SV3: $i] :
( ( ! [SY47: $i] :
( ( ordered_pair @ SV3 @ SY47 )
= ( unordered_pair @ ( unordered_pair @ SV3 @ SY47 ) @ ( singleton @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(49,plain,
! [SV4: $i] :
( ( ! [SY48: $i] :
~ ( empty @ ( ordered_pair @ SV4 @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(50,plain,
( ( empty @ sK6_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(51,plain,
( ( ( cartesian_product2 @ sK1_A @ sK2_SY25 )
= ( cartesian_product2 @ sK3_SY30 @ sK4_SY34 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(52,plain,
! [SV5: $i] :
( ( ~ ( ~ ! [SY49: $i,SY50: $i] :
( ~ ( ~ ( ! [SY51: $i,SY52: $i] :
( ~ ( in @ SY51 @ SV5 )
| ~ ( in @ SY52 @ SY49 )
| ( ( sK10_D @ SY50 @ SY49 @ SV5 )
!= ( ordered_pair @ SY51 @ SY52 ) ) )
| ~ ( in @ ( sK10_D @ SY50 @ SY49 @ SV5 ) @ SY50 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK11_SY42 @ SY50 @ SY49 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK12_SY44 @ SY50 @ SY49 @ SV5 ) @ SY49 ) )
| ( ( sK10_D @ SY50 @ SY49 @ SV5 )
!= ( ordered_pair @ ( sK11_SY42 @ SY50 @ SY49 @ SV5 ) @ ( sK12_SY44 @ SY50 @ SY49 @ SV5 ) ) ) )
| ( in @ ( sK10_D @ SY50 @ SY49 @ SV5 ) @ SY50 ) ) )
| ( SY50
= ( cartesian_product2 @ SV5 @ SY49 ) ) )
| ~ ! [SY53: $i,SY54: $i] :
( ( SY54
!= ( cartesian_product2 @ SV5 @ SY53 ) )
| ~ ( ~ ! [SY55: $i] :
( ! [SY56: $i,SY57: $i] :
( ~ ( in @ SY56 @ SV5 )
| ~ ( in @ SY57 @ SY53 )
| ( SY55
!= ( ordered_pair @ SY56 @ SY57 ) ) )
| ( in @ SY55 @ SY54 ) )
| ~ ! [SY58: $i] :
( ~ ( in @ SY58 @ SY54 )
| ~ ( ~ ~ ( ~ ( in @ ( sK8_E @ SY58 @ SY54 @ SY53 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK9_SY39 @ SY58 @ SY54 @ SY53 @ SV5 ) @ SY53 ) )
| ( SY58
!= ( ordered_pair @ ( sK8_E @ SY58 @ SY54 @ SY53 @ SV5 ) @ ( sK9_SY39 @ SY58 @ SY54 @ SY53 @ SV5 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(53,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY25 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ sK3_SY30 @ sK4_SY34 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ sK3_SY30 @ sK4_SY34 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY25 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(54,plain,
! [SV6: $i] :
( ( ! [SY59: $i] :
( ~ ( ~ ( ~ ( in @ ( sK5_C @ SY59 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK5_C @ SY59 @ SV6 ) @ SY59 ) )
| ~ ( ( in @ ( sK5_C @ SY59 @ SV6 ) @ SV6 )
| ( in @ ( sK5_C @ SY59 @ SV6 ) @ SY59 ) ) )
| ( SV6 = SY59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(55,plain,
! [SV7: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV7 )
| ~ ( in @ SV7 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(56,plain,
! [SV8: $i,SV2: $i] :
( ( ( unordered_pair @ SV2 @ SV8 )
= ( unordered_pair @ SV8 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(57,plain,
! [SV9: $i,SV3: $i] :
( ( ( ordered_pair @ SV3 @ SV9 )
= ( unordered_pair @ ( unordered_pair @ SV3 @ SV9 ) @ ( singleton @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(58,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV4 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(59,plain,
! [SV5: $i] :
( ( ~ ! [SY49: $i,SY50: $i] :
( ~ ( ~ ( ! [SY51: $i,SY52: $i] :
( ~ ( in @ SY51 @ SV5 )
| ~ ( in @ SY52 @ SY49 )
| ( ( sK10_D @ SY50 @ SY49 @ SV5 )
!= ( ordered_pair @ SY51 @ SY52 ) ) )
| ~ ( in @ ( sK10_D @ SY50 @ SY49 @ SV5 ) @ SY50 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK11_SY42 @ SY50 @ SY49 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK12_SY44 @ SY50 @ SY49 @ SV5 ) @ SY49 ) )
| ( ( sK10_D @ SY50 @ SY49 @ SV5 )
!= ( ordered_pair @ ( sK11_SY42 @ SY50 @ SY49 @ SV5 ) @ ( sK12_SY44 @ SY50 @ SY49 @ SV5 ) ) ) )
| ( in @ ( sK10_D @ SY50 @ SY49 @ SV5 ) @ SY50 ) ) )
| ( SY50
= ( cartesian_product2 @ SV5 @ SY49 ) ) )
| ~ ! [SY53: $i,SY54: $i] :
( ( SY54
!= ( cartesian_product2 @ SV5 @ SY53 ) )
| ~ ( ~ ! [SY55: $i] :
( ! [SY56: $i,SY57: $i] :
( ~ ( in @ SY56 @ SV5 )
| ~ ( in @ SY57 @ SY53 )
| ( SY55
!= ( ordered_pair @ SY56 @ SY57 ) ) )
| ( in @ SY55 @ SY54 ) )
| ~ ! [SY58: $i] :
( ~ ( in @ SY58 @ SY54 )
| ~ ( ~ ~ ( ~ ( in @ ( sK8_E @ SY58 @ SY54 @ SY53 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK9_SY39 @ SY58 @ SY54 @ SY53 @ SV5 ) @ SY53 ) )
| ( SY58
!= ( ordered_pair @ ( sK8_E @ SY58 @ SY54 @ SY53 @ SV5 ) @ ( sK9_SY39 @ SY58 @ SY54 @ SY53 @ SV5 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(60,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY25 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ sK3_SY30 @ sK4_SY34 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(61,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ sK3_SY30 @ sK4_SY34 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY25 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(62,plain,
! [SV6: $i,SV11: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK5_C @ SV11 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK5_C @ SV11 @ SV6 ) @ SV11 ) )
| ~ ( ( in @ ( sK5_C @ SV11 @ SV6 ) @ SV6 )
| ( in @ ( sK5_C @ SV11 @ SV6 ) @ SV11 ) ) )
| ( SV6 = SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(63,plain,
! [SV7: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV7 ) )
= $true )
| ( ( ~ ( in @ SV7 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(64,plain,
! [SV10: $i,SV4: $i] :
( ( empty @ ( ordered_pair @ SV4 @ SV10 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(65,plain,
! [SV5: $i] :
( ( ~ ! [SY49: $i,SY50: $i] :
( ~ ( ~ ( ! [SY51: $i,SY52: $i] :
( ~ ( in @ SY51 @ SV5 )
| ~ ( in @ SY52 @ SY49 )
| ( ( sK10_D @ SY50 @ SY49 @ SV5 )
!= ( ordered_pair @ SY51 @ SY52 ) ) )
| ~ ( in @ ( sK10_D @ SY50 @ SY49 @ SV5 ) @ SY50 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK11_SY42 @ SY50 @ SY49 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK12_SY44 @ SY50 @ SY49 @ SV5 ) @ SY49 ) )
| ( ( sK10_D @ SY50 @ SY49 @ SV5 )
!= ( ordered_pair @ ( sK11_SY42 @ SY50 @ SY49 @ SV5 ) @ ( sK12_SY44 @ SY50 @ SY49 @ SV5 ) ) ) )
| ( in @ ( sK10_D @ SY50 @ SY49 @ SV5 ) @ SY50 ) ) )
| ( SY50
= ( cartesian_product2 @ SV5 @ SY49 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[59]) ).
thf(66,plain,
! [SV5: $i] :
( ( ~ ! [SY53: $i,SY54: $i] :
( ( SY54
!= ( cartesian_product2 @ SV5 @ SY53 ) )
| ~ ( ~ ! [SY55: $i] :
( ! [SY56: $i,SY57: $i] :
( ~ ( in @ SY56 @ SV5 )
| ~ ( in @ SY57 @ SY53 )
| ( SY55
!= ( ordered_pair @ SY56 @ SY57 ) ) )
| ( in @ SY55 @ SY54 ) )
| ~ ! [SY58: $i] :
( ~ ( in @ SY58 @ SY54 )
| ~ ( ~ ~ ( ~ ( in @ ( sK8_E @ SY58 @ SY54 @ SY53 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK9_SY39 @ SY58 @ SY54 @ SY53 @ SV5 ) @ SY53 ) )
| ( SY58
!= ( ordered_pair @ ( sK8_E @ SY58 @ SY54 @ SY53 @ SV5 ) @ ( sK9_SY39 @ SY58 @ SY54 @ SY53 @ SV5 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[59]) ).
thf(67,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY25 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ sK3_SY30 @ sK4_SY34 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(68,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ sK3_SY30 @ sK4_SY34 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY25 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(69,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK5_C @ SV11 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK5_C @ SV11 @ SV6 ) @ SV11 ) )
| ~ ( ( in @ ( sK5_C @ SV11 @ SV6 ) @ SV6 )
| ( in @ ( sK5_C @ SV11 @ SV6 ) @ SV11 ) ) ) )
= $true )
| ( ( SV6 = SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(70,plain,
! [SV7: $i,SV1: $i] :
( ( ( in @ SV1 @ SV7 )
= $false )
| ( ( ~ ( in @ SV7 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(71,plain,
! [SV5: $i] :
( ( ! [SY49: $i,SY50: $i] :
( ~ ( ~ ( ! [SY51: $i,SY52: $i] :
( ~ ( in @ SY51 @ SV5 )
| ~ ( in @ SY52 @ SY49 )
| ( ( sK10_D @ SY50 @ SY49 @ SV5 )
!= ( ordered_pair @ SY51 @ SY52 ) ) )
| ~ ( in @ ( sK10_D @ SY50 @ SY49 @ SV5 ) @ SY50 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK11_SY42 @ SY50 @ SY49 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK12_SY44 @ SY50 @ SY49 @ SV5 ) @ SY49 ) )
| ( ( sK10_D @ SY50 @ SY49 @ SV5 )
!= ( ordered_pair @ ( sK11_SY42 @ SY50 @ SY49 @ SV5 ) @ ( sK12_SY44 @ SY50 @ SY49 @ SV5 ) ) ) )
| ( in @ ( sK10_D @ SY50 @ SY49 @ SV5 ) @ SY50 ) ) )
| ( SY50
= ( cartesian_product2 @ SV5 @ SY49 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(72,plain,
! [SV5: $i] :
( ( ! [SY53: $i,SY54: $i] :
( ( SY54
!= ( cartesian_product2 @ SV5 @ SY53 ) )
| ~ ( ~ ! [SY55: $i] :
( ! [SY56: $i,SY57: $i] :
( ~ ( in @ SY56 @ SV5 )
| ~ ( in @ SY57 @ SY53 )
| ( SY55
!= ( ordered_pair @ SY56 @ SY57 ) ) )
| ( in @ SY55 @ SY54 ) )
| ~ ! [SY58: $i] :
( ~ ( in @ SY58 @ SY54 )
| ~ ( ~ ~ ( ~ ( in @ ( sK8_E @ SY58 @ SY54 @ SY53 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK9_SY39 @ SY58 @ SY54 @ SY53 @ SV5 ) @ SY53 ) )
| ( SY58
!= ( ordered_pair @ ( sK8_E @ SY58 @ SY54 @ SY53 @ SV5 ) @ ( sK9_SY39 @ SY58 @ SY54 @ SY53 @ SV5 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(73,plain,
! [SV12: $i] :
( ( ! [SY60: $i] :
( ~ ( in @ ( ordered_pair @ SV12 @ SY60 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY25 ) )
| ( in @ ( ordered_pair @ SV12 @ SY60 ) @ ( cartesian_product2 @ sK3_SY30 @ sK4_SY34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(74,plain,
! [SV13: $i] :
( ( ! [SY61: $i] :
( ~ ( in @ ( ordered_pair @ SV13 @ SY61 ) @ ( cartesian_product2 @ sK3_SY30 @ sK4_SY34 ) )
| ( in @ ( ordered_pair @ SV13 @ SY61 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(75,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_C @ SV11 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK5_C @ SV11 @ SV6 ) @ SV11 ) )
| ~ ( ( in @ ( sK5_C @ SV11 @ SV6 ) @ SV6 )
| ( in @ ( sK5_C @ SV11 @ SV6 ) @ SV11 ) ) )
= $false )
| ( ( SV6 = SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(76,plain,
! [SV1: $i,SV7: $i] :
( ( ( in @ SV7 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(77,plain,
! [SV14: $i,SV5: $i] :
( ( ! [SY62: $i] :
( ~ ( ~ ( ! [SY63: $i,SY64: $i] :
( ~ ( in @ SY63 @ SV5 )
| ~ ( in @ SY64 @ SV14 )
| ( ( sK10_D @ SY62 @ SV14 @ SV5 )
!= ( ordered_pair @ SY63 @ SY64 ) ) )
| ~ ( in @ ( sK10_D @ SY62 @ SV14 @ SV5 ) @ SY62 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK11_SY42 @ SY62 @ SV14 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK12_SY44 @ SY62 @ SV14 @ SV5 ) @ SV14 ) )
| ( ( sK10_D @ SY62 @ SV14 @ SV5 )
!= ( ordered_pair @ ( sK11_SY42 @ SY62 @ SV14 @ SV5 ) @ ( sK12_SY44 @ SY62 @ SV14 @ SV5 ) ) ) )
| ( in @ ( sK10_D @ SY62 @ SV14 @ SV5 ) @ SY62 ) ) )
| ( SY62
= ( cartesian_product2 @ SV5 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(78,plain,
! [SV15: $i,SV5: $i] :
( ( ! [SY65: $i] :
( ( SY65
!= ( cartesian_product2 @ SV5 @ SV15 ) )
| ~ ( ~ ! [SY66: $i] :
( ! [SY67: $i,SY68: $i] :
( ~ ( in @ SY67 @ SV5 )
| ~ ( in @ SY68 @ SV15 )
| ( SY66
!= ( ordered_pair @ SY67 @ SY68 ) ) )
| ( in @ SY66 @ SY65 ) )
| ~ ! [SY69: $i] :
( ~ ( in @ SY69 @ SY65 )
| ~ ( ~ ~ ( ~ ( in @ ( sK8_E @ SY69 @ SY65 @ SV15 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK9_SY39 @ SY69 @ SY65 @ SV15 @ SV5 ) @ SV15 ) )
| ( SY69
!= ( ordered_pair @ ( sK8_E @ SY69 @ SY65 @ SV15 @ SV5 ) @ ( sK9_SY39 @ SY69 @ SY65 @ SV15 @ SV5 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(79,plain,
! [SV16: $i,SV12: $i] :
( ( ~ ( in @ ( ordered_pair @ SV12 @ SV16 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY25 ) )
| ( in @ ( ordered_pair @ SV12 @ SV16 ) @ ( cartesian_product2 @ sK3_SY30 @ sK4_SY34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(80,plain,
! [SV17: $i,SV13: $i] :
( ( ~ ( in @ ( ordered_pair @ SV13 @ SV17 ) @ ( cartesian_product2 @ sK3_SY30 @ sK4_SY34 ) )
| ( in @ ( ordered_pair @ SV13 @ SV17 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(81,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_C @ SV11 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK5_C @ SV11 @ SV6 ) @ SV11 ) ) )
= $false )
| ( ( SV6 = SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(82,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ( ( in @ ( sK5_C @ SV11 @ SV6 ) @ SV6 )
| ( in @ ( sK5_C @ SV11 @ SV6 ) @ SV11 ) ) )
= $false )
| ( ( SV6 = SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(83,plain,
! [SV18: $i,SV14: $i,SV5: $i] :
( ( ~ ( ~ ( ! [SY70: $i,SY71: $i] :
( ~ ( in @ SY70 @ SV5 )
| ~ ( in @ SY71 @ SV14 )
| ( ( sK10_D @ SV18 @ SV14 @ SV5 )
!= ( ordered_pair @ SY70 @ SY71 ) ) )
| ~ ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK11_SY42 @ SV18 @ SV14 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK12_SY44 @ SV18 @ SV14 @ SV5 ) @ SV14 ) )
| ( ( sK10_D @ SV18 @ SV14 @ SV5 )
!= ( ordered_pair @ ( sK11_SY42 @ SV18 @ SV14 @ SV5 ) @ ( sK12_SY44 @ SV18 @ SV14 @ SV5 ) ) ) )
| ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 ) ) )
| ( SV18
= ( cartesian_product2 @ SV5 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(84,plain,
! [SV15: $i,SV5: $i,SV19: $i] :
( ( ( SV19
!= ( cartesian_product2 @ SV5 @ SV15 ) )
| ~ ( ~ ! [SY72: $i] :
( ! [SY67: $i,SY68: $i] :
( ~ ( in @ SY67 @ SV5 )
| ~ ( in @ SY68 @ SV15 )
| ( SY72
!= ( ordered_pair @ SY67 @ SY68 ) ) )
| ( in @ SY72 @ SV19 ) )
| ~ ! [SY75: $i] :
( ~ ( in @ SY75 @ SV19 )
| ~ ( ~ ~ ( ~ ( in @ ( sK8_E @ SY75 @ SV19 @ SV15 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK9_SY39 @ SY75 @ SV19 @ SV15 @ SV5 ) @ SV15 ) )
| ( SY75
!= ( ordered_pair @ ( sK8_E @ SY75 @ SV19 @ SV15 @ SV5 ) @ ( sK9_SY39 @ SY75 @ SV19 @ SV15 @ SV5 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(85,plain,
! [SV16: $i,SV12: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV12 @ SV16 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY25 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV12 @ SV16 ) @ ( cartesian_product2 @ sK3_SY30 @ sK4_SY34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(86,plain,
! [SV17: $i,SV13: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV13 @ SV17 ) @ ( cartesian_product2 @ sK3_SY30 @ sK4_SY34 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV13 @ SV17 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(87,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ( in @ ( sK5_C @ SV11 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK5_C @ SV11 @ SV6 ) @ SV11 ) )
= $true )
| ( ( SV6 = SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(88,plain,
! [SV6: $i,SV11: $i] :
( ( ( ( in @ ( sK5_C @ SV11 @ SV6 ) @ SV6 )
| ( in @ ( sK5_C @ SV11 @ SV6 ) @ SV11 ) )
= $true )
| ( ( SV6 = SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(89,plain,
! [SV18: $i,SV14: $i,SV5: $i] :
( ( ( ~ ( ~ ( ! [SY70: $i,SY71: $i] :
( ~ ( in @ SY70 @ SV5 )
| ~ ( in @ SY71 @ SV14 )
| ( ( sK10_D @ SV18 @ SV14 @ SV5 )
!= ( ordered_pair @ SY70 @ SY71 ) ) )
| ~ ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK11_SY42 @ SV18 @ SV14 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK12_SY44 @ SV18 @ SV14 @ SV5 ) @ SV14 ) )
| ( ( sK10_D @ SV18 @ SV14 @ SV5 )
!= ( ordered_pair @ ( sK11_SY42 @ SV18 @ SV14 @ SV5 ) @ ( sK12_SY44 @ SV18 @ SV14 @ SV5 ) ) ) )
| ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 ) ) ) )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV5 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(90,plain,
! [SV15: $i,SV5: $i,SV19: $i] :
( ( ( ( SV19
!= ( cartesian_product2 @ SV5 @ SV15 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY72: $i] :
( ! [SY67: $i,SY68: $i] :
( ~ ( in @ SY67 @ SV5 )
| ~ ( in @ SY68 @ SV15 )
| ( SY72
!= ( ordered_pair @ SY67 @ SY68 ) ) )
| ( in @ SY72 @ SV19 ) )
| ~ ! [SY75: $i] :
( ~ ( in @ SY75 @ SV19 )
| ~ ( ~ ~ ( ~ ( in @ ( sK8_E @ SY75 @ SV19 @ SV15 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK9_SY39 @ SY75 @ SV19 @ SV15 @ SV5 ) @ SV15 ) )
| ( SY75
!= ( ordered_pair @ ( sK8_E @ SY75 @ SV19 @ SV15 @ SV5 ) @ ( sK9_SY39 @ SY75 @ SV19 @ SV15 @ SV5 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(91,plain,
! [SV16: $i,SV12: $i] :
( ( ( in @ ( ordered_pair @ SV12 @ SV16 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY25 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV12 @ SV16 ) @ ( cartesian_product2 @ sK3_SY30 @ sK4_SY34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(92,plain,
! [SV17: $i,SV13: $i] :
( ( ( in @ ( ordered_pair @ SV13 @ SV17 ) @ ( cartesian_product2 @ sK3_SY30 @ sK4_SY34 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV13 @ SV17 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(93,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ( in @ ( sK5_C @ SV11 @ SV6 ) @ SV6 ) )
= $true )
| ( ( ~ ( in @ ( sK5_C @ SV11 @ SV6 ) @ SV11 ) )
= $true )
| ( ( SV6 = SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(94,plain,
! [SV6: $i,SV11: $i] :
( ( ( in @ ( sK5_C @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( in @ ( sK5_C @ SV11 @ SV6 ) @ SV11 )
= $true )
| ( ( SV6 = SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(95,plain,
! [SV18: $i,SV14: $i,SV5: $i] :
( ( ( ~ ( ! [SY70: $i,SY71: $i] :
( ~ ( in @ SY70 @ SV5 )
| ~ ( in @ SY71 @ SV14 )
| ( ( sK10_D @ SV18 @ SV14 @ SV5 )
!= ( ordered_pair @ SY70 @ SY71 ) ) )
| ~ ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK11_SY42 @ SV18 @ SV14 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK12_SY44 @ SV18 @ SV14 @ SV5 ) @ SV14 ) )
| ( ( sK10_D @ SV18 @ SV14 @ SV5 )
!= ( ordered_pair @ ( sK11_SY42 @ SV18 @ SV14 @ SV5 ) @ ( sK12_SY44 @ SV18 @ SV14 @ SV5 ) ) ) )
| ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 ) ) )
= $false )
| ( ( SV18
= ( cartesian_product2 @ SV5 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(96,plain,
! [SV15: $i,SV5: $i,SV19: $i] :
( ( ( SV19
= ( cartesian_product2 @ SV5 @ SV15 ) )
= $false )
| ( ( ~ ( ~ ! [SY72: $i] :
( ! [SY67: $i,SY68: $i] :
( ~ ( in @ SY67 @ SV5 )
| ~ ( in @ SY68 @ SV15 )
| ( SY72
!= ( ordered_pair @ SY67 @ SY68 ) ) )
| ( in @ SY72 @ SV19 ) )
| ~ ! [SY75: $i] :
( ~ ( in @ SY75 @ SV19 )
| ~ ( ~ ~ ( ~ ( in @ ( sK8_E @ SY75 @ SV19 @ SV15 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK9_SY39 @ SY75 @ SV19 @ SV15 @ SV5 ) @ SV15 ) )
| ( SY75
!= ( ordered_pair @ ( sK8_E @ SY75 @ SV19 @ SV15 @ SV5 ) @ ( sK9_SY39 @ SY75 @ SV19 @ SV15 @ SV5 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(97,plain,
! [SV6: $i,SV11: $i] :
( ( ( in @ ( sK5_C @ SV11 @ SV6 ) @ SV6 )
= $false )
| ( ( ~ ( in @ ( sK5_C @ SV11 @ SV6 ) @ SV11 ) )
= $true )
| ( ( SV6 = SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(98,plain,
! [SV18: $i,SV14: $i,SV5: $i] :
( ( ( ~ ( ! [SY70: $i,SY71: $i] :
( ~ ( in @ SY70 @ SV5 )
| ~ ( in @ SY71 @ SV14 )
| ( ( sK10_D @ SV18 @ SV14 @ SV5 )
!= ( ordered_pair @ SY70 @ SY71 ) ) )
| ~ ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 ) ) )
= $false )
| ( ( SV18
= ( cartesian_product2 @ SV5 @ SV14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(99,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK11_SY42 @ SV18 @ SV14 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK12_SY44 @ SV18 @ SV14 @ SV5 ) @ SV14 ) )
| ( ( sK10_D @ SV18 @ SV14 @ SV5 )
!= ( ordered_pair @ ( sK11_SY42 @ SV18 @ SV14 @ SV5 ) @ ( sK12_SY44 @ SV18 @ SV14 @ SV5 ) ) ) )
| ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 ) ) )
= $false )
| ( ( SV18
= ( cartesian_product2 @ SV5 @ SV14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(100,plain,
! [SV19: $i,SV15: $i,SV5: $i] :
( ( ( ~ ! [SY72: $i] :
( ! [SY67: $i,SY68: $i] :
( ~ ( in @ SY67 @ SV5 )
| ~ ( in @ SY68 @ SV15 )
| ( SY72
!= ( ordered_pair @ SY67 @ SY68 ) ) )
| ( in @ SY72 @ SV19 ) )
| ~ ! [SY75: $i] :
( ~ ( in @ SY75 @ SV19 )
| ~ ( ~ ~ ( ~ ( in @ ( sK8_E @ SY75 @ SV19 @ SV15 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK9_SY39 @ SY75 @ SV19 @ SV15 @ SV5 ) @ SV15 ) )
| ( SY75
!= ( ordered_pair @ ( sK8_E @ SY75 @ SV19 @ SV15 @ SV5 ) @ ( sK9_SY39 @ SY75 @ SV19 @ SV15 @ SV5 ) ) ) ) ) )
= $false )
| ( ( SV19
= ( cartesian_product2 @ SV5 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(101,plain,
! [SV6: $i,SV11: $i] :
( ( ( in @ ( sK5_C @ SV11 @ SV6 ) @ SV11 )
= $false )
| ( ( in @ ( sK5_C @ SV11 @ SV6 ) @ SV6 )
= $false )
| ( ( SV6 = SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(102,plain,
! [SV18: $i,SV14: $i,SV5: $i] :
( ( ( ! [SY70: $i,SY71: $i] :
( ~ ( in @ SY70 @ SV5 )
| ~ ( in @ SY71 @ SV14 )
| ( ( sK10_D @ SV18 @ SV14 @ SV5 )
!= ( ordered_pair @ SY70 @ SY71 ) ) )
| ~ ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 ) )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV5 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(103,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK11_SY42 @ SV18 @ SV14 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK12_SY44 @ SV18 @ SV14 @ SV5 ) @ SV14 ) )
| ( ( sK10_D @ SV18 @ SV14 @ SV5 )
!= ( ordered_pair @ ( sK11_SY42 @ SV18 @ SV14 @ SV5 ) @ ( sK12_SY44 @ SV18 @ SV14 @ SV5 ) ) ) )
| ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 ) )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV5 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(104,plain,
! [SV19: $i,SV15: $i,SV5: $i] :
( ( ( ~ ! [SY72: $i] :
( ! [SY67: $i,SY68: $i] :
( ~ ( in @ SY67 @ SV5 )
| ~ ( in @ SY68 @ SV15 )
| ( SY72
!= ( ordered_pair @ SY67 @ SY68 ) ) )
| ( in @ SY72 @ SV19 ) ) )
= $false )
| ( ( SV19
= ( cartesian_product2 @ SV5 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(105,plain,
! [SV5: $i,SV15: $i,SV19: $i] :
( ( ( ~ ! [SY75: $i] :
( ~ ( in @ SY75 @ SV19 )
| ~ ( ~ ~ ( ~ ( in @ ( sK8_E @ SY75 @ SV19 @ SV15 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK9_SY39 @ SY75 @ SV19 @ SV15 @ SV5 ) @ SV15 ) )
| ( SY75
!= ( ordered_pair @ ( sK8_E @ SY75 @ SV19 @ SV15 @ SV5 ) @ ( sK9_SY39 @ SY75 @ SV19 @ SV15 @ SV5 ) ) ) ) ) )
= $false )
| ( ( SV19
= ( cartesian_product2 @ SV5 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(106,plain,
! [SV18: $i,SV14: $i,SV5: $i] :
( ( ( ! [SY70: $i,SY71: $i] :
( ~ ( in @ SY70 @ SV5 )
| ~ ( in @ SY71 @ SV14 )
| ( ( sK10_D @ SV18 @ SV14 @ SV5 )
!= ( ordered_pair @ SY70 @ SY71 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 ) )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV5 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(107,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK11_SY42 @ SV18 @ SV14 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK12_SY44 @ SV18 @ SV14 @ SV5 ) @ SV14 ) )
| ( ( sK10_D @ SV18 @ SV14 @ SV5 )
!= ( ordered_pair @ ( sK11_SY42 @ SV18 @ SV14 @ SV5 ) @ ( sK12_SY44 @ SV18 @ SV14 @ SV5 ) ) ) ) )
= $true )
| ( ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV5 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(108,plain,
! [SV19: $i,SV15: $i,SV5: $i] :
( ( ( ! [SY72: $i] :
( ! [SY67: $i,SY68: $i] :
( ~ ( in @ SY67 @ SV5 )
| ~ ( in @ SY68 @ SV15 )
| ( SY72
!= ( ordered_pair @ SY67 @ SY68 ) ) )
| ( in @ SY72 @ SV19 ) ) )
= $true )
| ( ( SV19
= ( cartesian_product2 @ SV5 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(109,plain,
! [SV5: $i,SV15: $i,SV19: $i] :
( ( ( ! [SY75: $i] :
( ~ ( in @ SY75 @ SV19 )
| ~ ( ~ ~ ( ~ ( in @ ( sK8_E @ SY75 @ SV19 @ SV15 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK9_SY39 @ SY75 @ SV19 @ SV15 @ SV5 ) @ SV15 ) )
| ( SY75
!= ( ordered_pair @ ( sK8_E @ SY75 @ SV19 @ SV15 @ SV5 ) @ ( sK9_SY39 @ SY75 @ SV19 @ SV15 @ SV5 ) ) ) ) ) )
= $true )
| ( ( SV19
= ( cartesian_product2 @ SV5 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(110,plain,
! [SV18: $i,SV14: $i,SV5: $i,SV20: $i] :
( ( ( ! [SY76: $i] :
( ~ ( in @ SV20 @ SV5 )
| ~ ( in @ SY76 @ SV14 )
| ( ( sK10_D @ SV18 @ SV14 @ SV5 )
!= ( ordered_pair @ SV20 @ SY76 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 ) )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV5 @ SV14 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(111,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK11_SY42 @ SV18 @ SV14 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK12_SY44 @ SV18 @ SV14 @ SV5 ) @ SV14 ) )
| ( ( sK10_D @ SV18 @ SV14 @ SV5 )
!= ( ordered_pair @ ( sK11_SY42 @ SV18 @ SV14 @ SV5 ) @ ( sK12_SY44 @ SV18 @ SV14 @ SV5 ) ) ) )
= $false )
| ( ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV5 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(112,plain,
! [SV19: $i,SV21: $i,SV15: $i,SV5: $i] :
( ( ( ! [SY77: $i,SY78: $i] :
( ~ ( in @ SY77 @ SV5 )
| ~ ( in @ SY78 @ SV15 )
| ( SV21
!= ( ordered_pair @ SY77 @ SY78 ) ) )
| ( in @ SV21 @ SV19 ) )
= $true )
| ( ( SV19
= ( cartesian_product2 @ SV5 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(113,plain,
! [SV5: $i,SV15: $i,SV19: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ SV19 )
| ~ ( ~ ~ ( ~ ( in @ ( sK8_E @ SV22 @ SV19 @ SV15 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK9_SY39 @ SV22 @ SV19 @ SV15 @ SV5 ) @ SV15 ) )
| ( SV22
!= ( ordered_pair @ ( sK8_E @ SV22 @ SV19 @ SV15 @ SV5 ) @ ( sK9_SY39 @ SV22 @ SV19 @ SV15 @ SV5 ) ) ) ) )
= $true )
| ( ( SV19
= ( cartesian_product2 @ SV5 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(114,plain,
! [SV18: $i,SV14: $i,SV23: $i,SV5: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ SV5 )
| ~ ( in @ SV23 @ SV14 )
| ( ( sK10_D @ SV18 @ SV14 @ SV5 )
!= ( ordered_pair @ SV20 @ SV23 ) ) )
= $true )
| ( ( ~ ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 ) )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV5 @ SV14 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(115,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK11_SY42 @ SV18 @ SV14 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK12_SY44 @ SV18 @ SV14 @ SV5 ) @ SV14 ) ) )
= $false )
| ( ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV5 @ SV14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(116,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ( ( sK10_D @ SV18 @ SV14 @ SV5 )
!= ( ordered_pair @ ( sK11_SY42 @ SV18 @ SV14 @ SV5 ) @ ( sK12_SY44 @ SV18 @ SV14 @ SV5 ) ) ) )
= $false )
| ( ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV5 @ SV14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(117,plain,
! [SV19: $i,SV21: $i,SV15: $i,SV5: $i] :
( ( ( ! [SY77: $i,SY78: $i] :
( ~ ( in @ SY77 @ SV5 )
| ~ ( in @ SY78 @ SV15 )
| ( SV21
!= ( ordered_pair @ SY77 @ SY78 ) ) ) )
= $true )
| ( ( in @ SV21 @ SV19 )
= $true )
| ( ( SV19
= ( cartesian_product2 @ SV5 @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(118,plain,
! [SV5: $i,SV15: $i,SV19: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ SV19 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK8_E @ SV22 @ SV19 @ SV15 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK9_SY39 @ SV22 @ SV19 @ SV15 @ SV5 ) @ SV15 ) )
| ( SV22
!= ( ordered_pair @ ( sK8_E @ SV22 @ SV19 @ SV15 @ SV5 ) @ ( sK9_SY39 @ SV22 @ SV19 @ SV15 @ SV5 ) ) ) ) )
= $true )
| ( ( SV19
= ( cartesian_product2 @ SV5 @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(119,plain,
! [SV18: $i,SV14: $i,SV23: $i,SV5: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ SV5 )
| ~ ( in @ SV23 @ SV14 ) )
= $true )
| ( ( ( ( sK10_D @ SV18 @ SV14 @ SV5 )
!= ( ordered_pair @ SV20 @ SV23 ) ) )
= $true )
| ( ( ~ ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 ) )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV5 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(120,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_SY42 @ SV18 @ SV14 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK12_SY44 @ SV18 @ SV14 @ SV5 ) @ SV14 ) ) )
= $true )
| ( ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV5 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(121,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ( sK10_D @ SV18 @ SV14 @ SV5 )
= ( ordered_pair @ ( sK11_SY42 @ SV18 @ SV14 @ SV5 ) @ ( sK12_SY44 @ SV18 @ SV14 @ SV5 ) ) )
= $true )
| ( ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV5 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(122,plain,
! [SV19: $i,SV21: $i,SV15: $i,SV5: $i,SV24: $i] :
( ( ( ! [SY79: $i] :
( ~ ( in @ SV24 @ SV5 )
| ~ ( in @ SY79 @ SV15 )
| ( SV21
!= ( ordered_pair @ SV24 @ SY79 ) ) ) )
= $true )
| ( ( in @ SV21 @ SV19 )
= $true )
| ( ( SV19
= ( cartesian_product2 @ SV5 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(123,plain,
! [SV5: $i,SV15: $i,SV19: $i,SV22: $i] :
( ( ( in @ SV22 @ SV19 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK8_E @ SV22 @ SV19 @ SV15 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK9_SY39 @ SV22 @ SV19 @ SV15 @ SV5 ) @ SV15 ) )
| ( SV22
!= ( ordered_pair @ ( sK8_E @ SV22 @ SV19 @ SV15 @ SV5 ) @ ( sK9_SY39 @ SV22 @ SV19 @ SV15 @ SV5 ) ) ) ) )
= $true )
| ( ( SV19
= ( cartesian_product2 @ SV5 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(124,plain,
! [SV18: $i,SV14: $i,SV23: $i,SV5: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ SV5 ) )
= $true )
| ( ( ~ ( in @ SV23 @ SV14 ) )
= $true )
| ( ( ( ( sK10_D @ SV18 @ SV14 @ SV5 )
!= ( ordered_pair @ SV20 @ SV23 ) ) )
= $true )
| ( ( ~ ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 ) )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV5 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(125,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK11_SY42 @ SV18 @ SV14 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK12_SY44 @ SV18 @ SV14 @ SV5 ) @ SV14 ) )
= $false )
| ( ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV5 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(126,plain,
! [SV19: $i,SV21: $i,SV15: $i,SV25: $i,SV5: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV5 )
| ~ ( in @ SV25 @ SV15 )
| ( SV21
!= ( ordered_pair @ SV24 @ SV25 ) ) )
= $true )
| ( ( in @ SV21 @ SV19 )
= $true )
| ( ( SV19
= ( cartesian_product2 @ SV5 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(127,plain,
! [SV5: $i,SV15: $i,SV19: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK8_E @ SV22 @ SV19 @ SV15 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK9_SY39 @ SV22 @ SV19 @ SV15 @ SV5 ) @ SV15 ) )
| ( SV22
!= ( ordered_pair @ ( sK8_E @ SV22 @ SV19 @ SV15 @ SV5 ) @ ( sK9_SY39 @ SV22 @ SV19 @ SV15 @ SV5 ) ) ) )
= $false )
| ( ( in @ SV22 @ SV19 )
= $false )
| ( ( SV19
= ( cartesian_product2 @ SV5 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(128,plain,
! [SV18: $i,SV14: $i,SV23: $i,SV5: $i,SV20: $i] :
( ( ( in @ SV20 @ SV5 )
= $false )
| ( ( ~ ( in @ SV23 @ SV14 ) )
= $true )
| ( ( ( ( sK10_D @ SV18 @ SV14 @ SV5 )
!= ( ordered_pair @ SV20 @ SV23 ) ) )
= $true )
| ( ( ~ ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 ) )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV5 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(129,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK11_SY42 @ SV18 @ SV14 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV5 @ SV14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(130,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK12_SY44 @ SV18 @ SV14 @ SV5 ) @ SV14 ) )
= $false )
| ( ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV5 @ SV14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(131,plain,
! [SV19: $i,SV21: $i,SV15: $i,SV25: $i,SV5: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV5 )
| ~ ( in @ SV25 @ SV15 ) )
= $true )
| ( ( ( SV21
!= ( ordered_pair @ SV24 @ SV25 ) ) )
= $true )
| ( ( in @ SV21 @ SV19 )
= $true )
| ( ( SV19
= ( cartesian_product2 @ SV5 @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(132,plain,
! [SV5: $i,SV15: $i,SV19: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK8_E @ SV22 @ SV19 @ SV15 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK9_SY39 @ SV22 @ SV19 @ SV15 @ SV5 ) @ SV15 ) ) )
= $false )
| ( ( in @ SV22 @ SV19 )
= $false )
| ( ( SV19
= ( cartesian_product2 @ SV5 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(133,plain,
! [SV5: $i,SV15: $i,SV19: $i,SV22: $i] :
( ( ( ( SV22
!= ( ordered_pair @ ( sK8_E @ SV22 @ SV19 @ SV15 @ SV5 ) @ ( sK9_SY39 @ SV22 @ SV19 @ SV15 @ SV5 ) ) ) )
= $false )
| ( ( in @ SV22 @ SV19 )
= $false )
| ( ( SV19
= ( cartesian_product2 @ SV5 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(134,plain,
! [SV18: $i,SV5: $i,SV20: $i,SV14: $i,SV23: $i] :
( ( ( in @ SV23 @ SV14 )
= $false )
| ( ( in @ SV20 @ SV5 )
= $false )
| ( ( ( ( sK10_D @ SV18 @ SV14 @ SV5 )
!= ( ordered_pair @ SV20 @ SV23 ) ) )
= $true )
| ( ( ~ ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 ) )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV5 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(135,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( in @ ( sK11_SY42 @ SV18 @ SV14 @ SV5 ) @ SV5 )
= $true )
| ( ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV5 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(136,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( in @ ( sK12_SY44 @ SV18 @ SV14 @ SV5 ) @ SV14 )
= $true )
| ( ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV5 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(137,plain,
! [SV19: $i,SV21: $i,SV15: $i,SV25: $i,SV5: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV5 ) )
= $true )
| ( ( ~ ( in @ SV25 @ SV15 ) )
= $true )
| ( ( ( SV21
!= ( ordered_pair @ SV24 @ SV25 ) ) )
= $true )
| ( ( in @ SV21 @ SV19 )
= $true )
| ( ( SV19
= ( cartesian_product2 @ SV5 @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(138,plain,
! [SV5: $i,SV15: $i,SV19: $i,SV22: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_E @ SV22 @ SV19 @ SV15 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK9_SY39 @ SV22 @ SV19 @ SV15 @ SV5 ) @ SV15 ) ) )
= $true )
| ( ( in @ SV22 @ SV19 )
= $false )
| ( ( SV19
= ( cartesian_product2 @ SV5 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(139,plain,
! [SV5: $i,SV15: $i,SV19: $i,SV22: $i] :
( ( ( SV22
= ( ordered_pair @ ( sK8_E @ SV22 @ SV19 @ SV15 @ SV5 ) @ ( sK9_SY39 @ SV22 @ SV19 @ SV15 @ SV5 ) ) )
= $true )
| ( ( in @ SV22 @ SV19 )
= $false )
| ( ( SV19
= ( cartesian_product2 @ SV5 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(140,plain,
! [SV23: $i,SV20: $i,SV5: $i,SV14: $i,SV18: $i] :
( ( ( ( sK10_D @ SV18 @ SV14 @ SV5 )
= ( ordered_pair @ SV20 @ SV23 ) )
= $false )
| ( ( in @ SV20 @ SV5 )
= $false )
| ( ( in @ SV23 @ SV14 )
= $false )
| ( ( ~ ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 ) )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV5 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(141,plain,
! [SV19: $i,SV21: $i,SV15: $i,SV25: $i,SV5: $i,SV24: $i] :
( ( ( in @ SV24 @ SV5 )
= $false )
| ( ( ~ ( in @ SV25 @ SV15 ) )
= $true )
| ( ( ( SV21
!= ( ordered_pair @ SV24 @ SV25 ) ) )
= $true )
| ( ( in @ SV21 @ SV19 )
= $true )
| ( ( SV19
= ( cartesian_product2 @ SV5 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(142,plain,
! [SV5: $i,SV15: $i,SV19: $i,SV22: $i] :
( ( ( ~ ( in @ ( sK8_E @ SV22 @ SV19 @ SV15 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK9_SY39 @ SV22 @ SV19 @ SV15 @ SV5 ) @ SV15 ) )
= $false )
| ( ( in @ SV22 @ SV19 )
= $false )
| ( ( SV19
= ( cartesian_product2 @ SV5 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(143,plain,
! [SV20: $i,SV23: $i,SV5: $i,SV14: $i,SV18: $i] :
( ( ( in @ ( sK10_D @ SV18 @ SV14 @ SV5 ) @ SV18 )
= $false )
| ( ( in @ SV23 @ SV14 )
= $false )
| ( ( in @ SV20 @ SV5 )
= $false )
| ( ( ( sK10_D @ SV18 @ SV14 @ SV5 )
= ( ordered_pair @ SV20 @ SV23 ) )
= $false )
| ( ( SV18
= ( cartesian_product2 @ SV5 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(144,plain,
! [SV19: $i,SV21: $i,SV5: $i,SV24: $i,SV15: $i,SV25: $i] :
( ( ( in @ SV25 @ SV15 )
= $false )
| ( ( in @ SV24 @ SV5 )
= $false )
| ( ( ( SV21
!= ( ordered_pair @ SV24 @ SV25 ) ) )
= $true )
| ( ( in @ SV21 @ SV19 )
= $true )
| ( ( SV19
= ( cartesian_product2 @ SV5 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(145,plain,
! [SV5: $i,SV15: $i,SV19: $i,SV22: $i] :
( ( ( ~ ( in @ ( sK8_E @ SV22 @ SV19 @ SV15 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ SV22 @ SV19 )
= $false )
| ( ( SV19
= ( cartesian_product2 @ SV5 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(146,plain,
! [SV5: $i,SV15: $i,SV19: $i,SV22: $i] :
( ( ( ~ ( in @ ( sK9_SY39 @ SV22 @ SV19 @ SV15 @ SV5 ) @ SV15 ) )
= $false )
| ( ( in @ SV22 @ SV19 )
= $false )
| ( ( SV19
= ( cartesian_product2 @ SV5 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(147,plain,
! [SV19: $i,SV15: $i,SV5: $i,SV25: $i,SV24: $i,SV21: $i] :
( ( ( SV21
= ( ordered_pair @ SV24 @ SV25 ) )
= $false )
| ( ( in @ SV24 @ SV5 )
= $false )
| ( ( in @ SV25 @ SV15 )
= $false )
| ( ( in @ SV21 @ SV19 )
= $true )
| ( ( SV19
= ( cartesian_product2 @ SV5 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(148,plain,
! [SV5: $i,SV15: $i,SV19: $i,SV22: $i] :
( ( ( in @ ( sK8_E @ SV22 @ SV19 @ SV15 @ SV5 ) @ SV5 )
= $true )
| ( ( in @ SV22 @ SV19 )
= $false )
| ( ( SV19
= ( cartesian_product2 @ SV5 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(149,plain,
! [SV5: $i,SV15: $i,SV19: $i,SV22: $i] :
( ( ( in @ ( sK9_SY39 @ SV22 @ SV19 @ SV15 @ SV5 ) @ SV15 )
= $true )
| ( ( in @ SV22 @ SV19 )
= $false )
| ( ( SV19
= ( cartesian_product2 @ SV5 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(150,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[38,149,148,147,143,139,136,135,121,101,94,92,91,76,64,57,56,51,50]) ).
thf(151,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET955+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.06/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jul 10 21:50:08 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35
% 0.14/0.35 No.of.Axioms: 8
% 0.14/0.35
% 0.14/0.35 Length.of.Defs: 0
% 0.14/0.35
% 0.14/0.35 Contains.Choice.Funs: false
% 0.14/0.35 (rf:0,axioms:8,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:10,loop_count:0,foatp_calls:0,translation:fof_full)............
% 0.90/1.07
% 0.90/1.07 ********************************
% 0.90/1.07 * All subproblems solved! *
% 0.90/1.07 ********************************
% 0.90/1.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:9,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:150,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.90/1.08
% 0.90/1.08 %**** Beginning of derivation protocol ****
% 0.90/1.08 % SZS output start CNFRefutation
% See solution above
% 0.90/1.08
% 0.90/1.08 %**** End of derivation protocol ****
% 0.90/1.08 %**** no. of clauses in derivation: 151 ****
% 0.90/1.08 %**** clause counter: 150 ****
% 0.90/1.08
% 0.90/1.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:9,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:150,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------