TSTP Solution File: SET949+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET949+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n023.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 03:06:30 EDT 2022
% Result : Theorem 0.21s 0.50s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 24
% Syntax : Number of formulae : 140 ( 63 unt; 16 typ; 0 def)
% Number of atoms : 977 ( 418 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 2766 ( 482 ~; 354 |; 27 &;1897 @)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 7 con; 0-4 aty)
% Number of variables : 464 ( 0 ^ 456 !; 8 ?; 464 :)
% 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_SY35,type,
sK10_SY35: $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY21,type,
sK2_SY21: $i ).
thf(tp_sK3_SY25,type,
sK3_SY25: $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_sK6_E,type,
sK6_E: $i > $i > $i > $i > $i ).
thf(tp_sK7_SY30,type,
sK7_SY30: $i > $i > $i > $i > $i ).
thf(tp_sK8_D,type,
sK8_D: $i > $i > $i > $i ).
thf(tp_sK9_SY33,type,
sK9_SY33: $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] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(2,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(4,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(5,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(6,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(8,conjecture,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ ( cartesian_product2 @ B @ C ) )
& ! [D: $i,E: $i] :
( ( ordered_pair @ D @ E )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_zfmisc_1) ).
thf(9,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ ( cartesian_product2 @ B @ C ) )
& ! [D: $i,E: $i] :
( ( ordered_pair @ D @ E )
!= A ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[8]) ).
thf(10,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ ( cartesian_product2 @ B @ C ) )
& ! [D: $i,E: $i] :
( ( ordered_pair @ D @ E )
!= A ) ) )
= $false ),
inference(unfold_def,[status(thm)],[9]) ).
thf(11,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(12,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(13,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(14,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(15,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(16,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(18,plain,
( ( ! [SY21: $i,SY22: $i] :
~ ( ( in @ sK1_A @ ( cartesian_product2 @ SY21 @ SY22 ) )
& ! [SY23: $i,SY24: $i] :
( ( ordered_pair @ SY23 @ SY24 )
!= sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(19,plain,
( ( ! [SY25: $i] :
~ ( ( in @ sK1_A @ ( cartesian_product2 @ sK2_SY21 @ SY25 ) )
& ! [SY23: $i,SY24: $i] :
( ( ordered_pair @ SY23 @ SY24 )
!= sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(20,plain,
( ( ~ ( ( in @ sK1_A @ ( cartesian_product2 @ sK2_SY21 @ sK3_SY25 ) )
& ! [SY23: $i,SY24: $i] :
( ( ordered_pair @ SY23 @ SY24 )
!= sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(21,plain,
( ( ( in @ sK1_A @ ( cartesian_product2 @ sK2_SY21 @ sK3_SY25 ) )
& ! [SY23: $i,SY24: $i] :
( ( ordered_pair @ SY23 @ SY24 )
!= sK1_A ) )
= $true ),
inference(polarity_switch,[status(thm)],[20]) ).
thf(22,plain,
( ( ! [SY23: $i,SY24: $i] :
( ( ordered_pair @ SY23 @ SY24 )
!= sK1_A )
& ( in @ sK1_A @ ( cartesian_product2 @ sK2_SY21 @ sK3_SY25 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(23,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(24,plain,
( ( empty @ sK5_A )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(25,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY31: $i,SY32: $i] :
( ~ ( in @ SY31 @ A )
| ~ ( in @ SY32 @ B )
| ( ( sK8_D @ C @ B @ A )
!= ( ordered_pair @ SY31 @ SY32 ) ) )
| ~ ( in @ ( sK8_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK9_SY33 @ C @ B @ A ) @ A )
& ( in @ ( sK10_SY35 @ C @ B @ A ) @ B )
& ( ( sK8_D @ C @ B @ A )
= ( ordered_pair @ ( sK9_SY33 @ C @ B @ A ) @ ( sK10_SY35 @ C @ B @ A ) ) ) )
| ( in @ ( sK8_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 @ ( sK6_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK7_SY30 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK6_E @ D @ C @ B @ A ) @ ( sK7_SY30 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(26,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(27,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(28,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(29,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY31: $i,SY32: $i] :
( ~ ( in @ SY31 @ A )
| ~ ( in @ SY32 @ B )
| ( ( sK8_D @ C @ B @ A )
!= ( ordered_pair @ SY31 @ SY32 ) ) )
| ~ ( in @ ( sK8_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK9_SY33 @ C @ B @ A ) @ A )
& ( in @ ( sK10_SY35 @ C @ B @ A ) @ B )
& ( ( sK8_D @ C @ B @ A )
= ( ordered_pair @ ( sK9_SY33 @ C @ B @ A ) @ ( sK10_SY35 @ C @ B @ A ) ) ) )
| ( in @ ( sK8_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 @ ( sK6_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK7_SY30 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK6_E @ D @ C @ B @ A ) @ ( sK7_SY30 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(30,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(31,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(32,plain,
( ( empty @ sK5_A )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(33,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(34,plain,
( ( ! [SY23: $i,SY24: $i] :
( ( ordered_pair @ SY23 @ SY24 )
!= sK1_A )
& ( in @ sK1_A @ ( cartesian_product2 @ sK2_SY21 @ sK3_SY25 ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(35,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX4 @ SX1 )
| ( ( sK8_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ SX3 @ SX4 ) ) )
| ~ ( in @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY33 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK10_SY35 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK8_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ ( sK9_SY33 @ SX2 @ SX1 @ SX0 ) @ ( sK10_SY35 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( in @ ( sK8_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 @ ( sK6_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK7_SY30 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( ordered_pair @ ( sK6_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK7_SY30 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(36,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ordered_pair @ SX0 @ SX1 )
!= sK1_A )
| ~ ( in @ sK1_A @ ( cartesian_product2 @ sK2_SY21 @ sK3_SY25 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(37,plain,
! [SV1: $i] :
( ( ! [SY36: $i] :
( ~ ( in @ SV1 @ SY36 )
| ~ ( in @ SY36 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(38,plain,
! [SV2: $i] :
( ( ! [SY37: $i] :
( ( unordered_pair @ SV2 @ SY37 )
= ( unordered_pair @ SY37 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(39,plain,
! [SV3: $i] :
( ( ! [SY38: $i] :
( ( ordered_pair @ SV3 @ SY38 )
= ( unordered_pair @ ( unordered_pair @ SV3 @ SY38 ) @ ( singleton @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(40,plain,
! [SV4: $i] :
( ( ! [SY39: $i] :
~ ( empty @ ( ordered_pair @ SV4 @ SY39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(41,plain,
( ( empty @ sK4_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(42,plain,
! [SV5: $i] :
( ( ~ ( ~ ! [SY40: $i,SY41: $i] :
( ~ ( ~ ( ! [SY42: $i,SY43: $i] :
( ~ ( in @ SY42 @ SV5 )
| ~ ( in @ SY43 @ SY40 )
| ( ( sK8_D @ SY41 @ SY40 @ SV5 )
!= ( ordered_pair @ SY42 @ SY43 ) ) )
| ~ ( in @ ( sK8_D @ SY41 @ SY40 @ SV5 ) @ SY41 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY33 @ SY41 @ SY40 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK10_SY35 @ SY41 @ SY40 @ SV5 ) @ SY40 ) )
| ( ( sK8_D @ SY41 @ SY40 @ SV5 )
!= ( ordered_pair @ ( sK9_SY33 @ SY41 @ SY40 @ SV5 ) @ ( sK10_SY35 @ SY41 @ SY40 @ SV5 ) ) ) )
| ( in @ ( sK8_D @ SY41 @ SY40 @ SV5 ) @ SY41 ) ) )
| ( SY41
= ( cartesian_product2 @ SV5 @ SY40 ) ) )
| ~ ! [SY44: $i,SY45: $i] :
( ( SY45
!= ( cartesian_product2 @ SV5 @ SY44 ) )
| ~ ( ~ ! [SY46: $i] :
( ! [SY47: $i,SY48: $i] :
( ~ ( in @ SY47 @ SV5 )
| ~ ( in @ SY48 @ SY44 )
| ( SY46
!= ( ordered_pair @ SY47 @ SY48 ) ) )
| ( in @ SY46 @ SY45 ) )
| ~ ! [SY49: $i] :
( ~ ( in @ SY49 @ SY45 )
| ~ ( ~ ~ ( ~ ( in @ ( sK6_E @ SY49 @ SY45 @ SY44 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK7_SY30 @ SY49 @ SY45 @ SY44 @ SV5 ) @ SY44 ) )
| ( SY49
!= ( ordered_pair @ ( sK6_E @ SY49 @ SY45 @ SY44 @ SV5 ) @ ( sK7_SY30 @ SY49 @ SY45 @ SY44 @ SV5 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(43,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ordered_pair @ SX0 @ SX1 )
!= sK1_A )
| ~ ( in @ sK1_A @ ( cartesian_product2 @ sK2_SY21 @ sK3_SY25 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(44,plain,
! [SV6: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV6 )
| ~ ( in @ SV6 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(45,plain,
! [SV7: $i,SV2: $i] :
( ( ( unordered_pair @ SV2 @ SV7 )
= ( unordered_pair @ SV7 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(46,plain,
! [SV8: $i,SV3: $i] :
( ( ( ordered_pair @ SV3 @ SV8 )
= ( unordered_pair @ ( unordered_pair @ SV3 @ SV8 ) @ ( singleton @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(47,plain,
! [SV9: $i,SV4: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV4 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(48,plain,
! [SV5: $i] :
( ( ~ ! [SY40: $i,SY41: $i] :
( ~ ( ~ ( ! [SY42: $i,SY43: $i] :
( ~ ( in @ SY42 @ SV5 )
| ~ ( in @ SY43 @ SY40 )
| ( ( sK8_D @ SY41 @ SY40 @ SV5 )
!= ( ordered_pair @ SY42 @ SY43 ) ) )
| ~ ( in @ ( sK8_D @ SY41 @ SY40 @ SV5 ) @ SY41 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY33 @ SY41 @ SY40 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK10_SY35 @ SY41 @ SY40 @ SV5 ) @ SY40 ) )
| ( ( sK8_D @ SY41 @ SY40 @ SV5 )
!= ( ordered_pair @ ( sK9_SY33 @ SY41 @ SY40 @ SV5 ) @ ( sK10_SY35 @ SY41 @ SY40 @ SV5 ) ) ) )
| ( in @ ( sK8_D @ SY41 @ SY40 @ SV5 ) @ SY41 ) ) )
| ( SY41
= ( cartesian_product2 @ SV5 @ SY40 ) ) )
| ~ ! [SY44: $i,SY45: $i] :
( ( SY45
!= ( cartesian_product2 @ SV5 @ SY44 ) )
| ~ ( ~ ! [SY46: $i] :
( ! [SY47: $i,SY48: $i] :
( ~ ( in @ SY47 @ SV5 )
| ~ ( in @ SY48 @ SY44 )
| ( SY46
!= ( ordered_pair @ SY47 @ SY48 ) ) )
| ( in @ SY46 @ SY45 ) )
| ~ ! [SY49: $i] :
( ~ ( in @ SY49 @ SY45 )
| ~ ( ~ ~ ( ~ ( in @ ( sK6_E @ SY49 @ SY45 @ SY44 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK7_SY30 @ SY49 @ SY45 @ SY44 @ SV5 ) @ SY44 ) )
| ( SY49
!= ( ordered_pair @ ( sK6_E @ SY49 @ SY45 @ SY44 @ SV5 ) @ ( sK7_SY30 @ SY49 @ SY45 @ SY44 @ SV5 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(49,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ordered_pair @ SX0 @ SX1 )
!= sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(50,plain,
( ( ~ ( in @ sK1_A @ ( cartesian_product2 @ sK2_SY21 @ sK3_SY25 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(51,plain,
! [SV6: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV6 ) )
= $true )
| ( ( ~ ( in @ SV6 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(52,plain,
! [SV9: $i,SV4: $i] :
( ( empty @ ( ordered_pair @ SV4 @ SV9 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(53,plain,
! [SV5: $i] :
( ( ~ ! [SY40: $i,SY41: $i] :
( ~ ( ~ ( ! [SY42: $i,SY43: $i] :
( ~ ( in @ SY42 @ SV5 )
| ~ ( in @ SY43 @ SY40 )
| ( ( sK8_D @ SY41 @ SY40 @ SV5 )
!= ( ordered_pair @ SY42 @ SY43 ) ) )
| ~ ( in @ ( sK8_D @ SY41 @ SY40 @ SV5 ) @ SY41 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY33 @ SY41 @ SY40 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK10_SY35 @ SY41 @ SY40 @ SV5 ) @ SY40 ) )
| ( ( sK8_D @ SY41 @ SY40 @ SV5 )
!= ( ordered_pair @ ( sK9_SY33 @ SY41 @ SY40 @ SV5 ) @ ( sK10_SY35 @ SY41 @ SY40 @ SV5 ) ) ) )
| ( in @ ( sK8_D @ SY41 @ SY40 @ SV5 ) @ SY41 ) ) )
| ( SY41
= ( cartesian_product2 @ SV5 @ SY40 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(54,plain,
! [SV5: $i] :
( ( ~ ! [SY44: $i,SY45: $i] :
( ( SY45
!= ( cartesian_product2 @ SV5 @ SY44 ) )
| ~ ( ~ ! [SY46: $i] :
( ! [SY47: $i,SY48: $i] :
( ~ ( in @ SY47 @ SV5 )
| ~ ( in @ SY48 @ SY44 )
| ( SY46
!= ( ordered_pair @ SY47 @ SY48 ) ) )
| ( in @ SY46 @ SY45 ) )
| ~ ! [SY49: $i] :
( ~ ( in @ SY49 @ SY45 )
| ~ ( ~ ~ ( ~ ( in @ ( sK6_E @ SY49 @ SY45 @ SY44 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK7_SY30 @ SY49 @ SY45 @ SY44 @ SV5 ) @ SY44 ) )
| ( SY49
!= ( ordered_pair @ ( sK6_E @ SY49 @ SY45 @ SY44 @ SV5 ) @ ( sK7_SY30 @ SY49 @ SY45 @ SY44 @ SV5 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(55,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ordered_pair @ SX0 @ SX1 )
!= sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(56,plain,
( ( in @ sK1_A @ ( cartesian_product2 @ sK2_SY21 @ sK3_SY25 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(57,plain,
! [SV6: $i,SV1: $i] :
( ( ( in @ SV1 @ SV6 )
= $false )
| ( ( ~ ( in @ SV6 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(58,plain,
! [SV5: $i] :
( ( ! [SY40: $i,SY41: $i] :
( ~ ( ~ ( ! [SY42: $i,SY43: $i] :
( ~ ( in @ SY42 @ SV5 )
| ~ ( in @ SY43 @ SY40 )
| ( ( sK8_D @ SY41 @ SY40 @ SV5 )
!= ( ordered_pair @ SY42 @ SY43 ) ) )
| ~ ( in @ ( sK8_D @ SY41 @ SY40 @ SV5 ) @ SY41 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY33 @ SY41 @ SY40 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK10_SY35 @ SY41 @ SY40 @ SV5 ) @ SY40 ) )
| ( ( sK8_D @ SY41 @ SY40 @ SV5 )
!= ( ordered_pair @ ( sK9_SY33 @ SY41 @ SY40 @ SV5 ) @ ( sK10_SY35 @ SY41 @ SY40 @ SV5 ) ) ) )
| ( in @ ( sK8_D @ SY41 @ SY40 @ SV5 ) @ SY41 ) ) )
| ( SY41
= ( cartesian_product2 @ SV5 @ SY40 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(59,plain,
! [SV5: $i] :
( ( ! [SY44: $i,SY45: $i] :
( ( SY45
!= ( cartesian_product2 @ SV5 @ SY44 ) )
| ~ ( ~ ! [SY46: $i] :
( ! [SY47: $i,SY48: $i] :
( ~ ( in @ SY47 @ SV5 )
| ~ ( in @ SY48 @ SY44 )
| ( SY46
!= ( ordered_pair @ SY47 @ SY48 ) ) )
| ( in @ SY46 @ SY45 ) )
| ~ ! [SY49: $i] :
( ~ ( in @ SY49 @ SY45 )
| ~ ( ~ ~ ( ~ ( in @ ( sK6_E @ SY49 @ SY45 @ SY44 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK7_SY30 @ SY49 @ SY45 @ SY44 @ SV5 ) @ SY44 ) )
| ( SY49
!= ( ordered_pair @ ( sK6_E @ SY49 @ SY45 @ SY44 @ SV5 ) @ ( sK7_SY30 @ SY49 @ SY45 @ SY44 @ SV5 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(60,plain,
! [SV10: $i] :
( ( ! [SY50: $i] :
( ( ordered_pair @ SV10 @ SY50 )
!= sK1_A ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(61,plain,
! [SV1: $i,SV6: $i] :
( ( ( in @ SV6 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(62,plain,
! [SV11: $i,SV5: $i] :
( ( ! [SY51: $i] :
( ~ ( ~ ( ! [SY52: $i,SY53: $i] :
( ~ ( in @ SY52 @ SV5 )
| ~ ( in @ SY53 @ SV11 )
| ( ( sK8_D @ SY51 @ SV11 @ SV5 )
!= ( ordered_pair @ SY52 @ SY53 ) ) )
| ~ ( in @ ( sK8_D @ SY51 @ SV11 @ SV5 ) @ SY51 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY33 @ SY51 @ SV11 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK10_SY35 @ SY51 @ SV11 @ SV5 ) @ SV11 ) )
| ( ( sK8_D @ SY51 @ SV11 @ SV5 )
!= ( ordered_pair @ ( sK9_SY33 @ SY51 @ SV11 @ SV5 ) @ ( sK10_SY35 @ SY51 @ SV11 @ SV5 ) ) ) )
| ( in @ ( sK8_D @ SY51 @ SV11 @ SV5 ) @ SY51 ) ) )
| ( SY51
= ( cartesian_product2 @ SV5 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV12: $i,SV5: $i] :
( ( ! [SY54: $i] :
( ( SY54
!= ( cartesian_product2 @ SV5 @ SV12 ) )
| ~ ( ~ ! [SY55: $i] :
( ! [SY56: $i,SY57: $i] :
( ~ ( in @ SY56 @ SV5 )
| ~ ( in @ SY57 @ SV12 )
| ( SY55
!= ( ordered_pair @ SY56 @ SY57 ) ) )
| ( in @ SY55 @ SY54 ) )
| ~ ! [SY58: $i] :
( ~ ( in @ SY58 @ SY54 )
| ~ ( ~ ~ ( ~ ( in @ ( sK6_E @ SY58 @ SY54 @ SV12 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK7_SY30 @ SY58 @ SY54 @ SV12 @ SV5 ) @ SV12 ) )
| ( SY58
!= ( ordered_pair @ ( sK6_E @ SY58 @ SY54 @ SV12 @ SV5 ) @ ( sK7_SY30 @ SY58 @ SY54 @ SV12 @ SV5 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(64,plain,
! [SV13: $i,SV10: $i] :
( ( ( ( ordered_pair @ SV10 @ SV13 )
!= sK1_A ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(65,plain,
! [SV14: $i,SV11: $i,SV5: $i] :
( ( ~ ( ~ ( ! [SY59: $i,SY60: $i] :
( ~ ( in @ SY59 @ SV5 )
| ~ ( in @ SY60 @ SV11 )
| ( ( sK8_D @ SV14 @ SV11 @ SV5 )
!= ( ordered_pair @ SY59 @ SY60 ) ) )
| ~ ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY33 @ SV14 @ SV11 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK10_SY35 @ SV14 @ SV11 @ SV5 ) @ SV11 ) )
| ( ( sK8_D @ SV14 @ SV11 @ SV5 )
!= ( ordered_pair @ ( sK9_SY33 @ SV14 @ SV11 @ SV5 ) @ ( sK10_SY35 @ SV14 @ SV11 @ SV5 ) ) ) )
| ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 ) ) )
| ( SV14
= ( cartesian_product2 @ SV5 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(66,plain,
! [SV12: $i,SV5: $i,SV15: $i] :
( ( ( SV15
!= ( cartesian_product2 @ SV5 @ SV12 ) )
| ~ ( ~ ! [SY61: $i] :
( ! [SY56: $i,SY57: $i] :
( ~ ( in @ SY56 @ SV5 )
| ~ ( in @ SY57 @ SV12 )
| ( SY61
!= ( ordered_pair @ SY56 @ SY57 ) ) )
| ( in @ SY61 @ SV15 ) )
| ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SV15 )
| ~ ( ~ ~ ( ~ ( in @ ( sK6_E @ SY64 @ SV15 @ SV12 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK7_SY30 @ SY64 @ SV15 @ SV12 @ SV5 ) @ SV12 ) )
| ( SY64
!= ( ordered_pair @ ( sK6_E @ SY64 @ SV15 @ SV12 @ SV5 ) @ ( sK7_SY30 @ SY64 @ SV15 @ SV12 @ SV5 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(67,plain,
! [SV13: $i,SV10: $i] :
( ( ( ordered_pair @ SV10 @ SV13 )
= sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(68,plain,
! [SV14: $i,SV11: $i,SV5: $i] :
( ( ( ~ ( ~ ( ! [SY59: $i,SY60: $i] :
( ~ ( in @ SY59 @ SV5 )
| ~ ( in @ SY60 @ SV11 )
| ( ( sK8_D @ SV14 @ SV11 @ SV5 )
!= ( ordered_pair @ SY59 @ SY60 ) ) )
| ~ ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY33 @ SV14 @ SV11 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK10_SY35 @ SV14 @ SV11 @ SV5 ) @ SV11 ) )
| ( ( sK8_D @ SV14 @ SV11 @ SV5 )
!= ( ordered_pair @ ( sK9_SY33 @ SV14 @ SV11 @ SV5 ) @ ( sK10_SY35 @ SV14 @ SV11 @ SV5 ) ) ) )
| ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 ) ) ) )
= $true )
| ( ( SV14
= ( cartesian_product2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(69,plain,
! [SV12: $i,SV5: $i,SV15: $i] :
( ( ( ( SV15
!= ( cartesian_product2 @ SV5 @ SV12 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY61: $i] :
( ! [SY56: $i,SY57: $i] :
( ~ ( in @ SY56 @ SV5 )
| ~ ( in @ SY57 @ SV12 )
| ( SY61
!= ( ordered_pair @ SY56 @ SY57 ) ) )
| ( in @ SY61 @ SV15 ) )
| ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SV15 )
| ~ ( ~ ~ ( ~ ( in @ ( sK6_E @ SY64 @ SV15 @ SV12 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK7_SY30 @ SY64 @ SV15 @ SV12 @ SV5 ) @ SV12 ) )
| ( SY64
!= ( ordered_pair @ ( sK6_E @ SY64 @ SV15 @ SV12 @ SV5 ) @ ( sK7_SY30 @ SY64 @ SV15 @ SV12 @ SV5 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(70,plain,
! [SV14: $i,SV11: $i,SV5: $i] :
( ( ( ~ ( ! [SY59: $i,SY60: $i] :
( ~ ( in @ SY59 @ SV5 )
| ~ ( in @ SY60 @ SV11 )
| ( ( sK8_D @ SV14 @ SV11 @ SV5 )
!= ( ordered_pair @ SY59 @ SY60 ) ) )
| ~ ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY33 @ SV14 @ SV11 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK10_SY35 @ SV14 @ SV11 @ SV5 ) @ SV11 ) )
| ( ( sK8_D @ SV14 @ SV11 @ SV5 )
!= ( ordered_pair @ ( sK9_SY33 @ SV14 @ SV11 @ SV5 ) @ ( sK10_SY35 @ SV14 @ SV11 @ SV5 ) ) ) )
| ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 ) ) )
= $false )
| ( ( SV14
= ( cartesian_product2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(71,plain,
! [SV12: $i,SV5: $i,SV15: $i] :
( ( ( SV15
= ( cartesian_product2 @ SV5 @ SV12 ) )
= $false )
| ( ( ~ ( ~ ! [SY61: $i] :
( ! [SY56: $i,SY57: $i] :
( ~ ( in @ SY56 @ SV5 )
| ~ ( in @ SY57 @ SV12 )
| ( SY61
!= ( ordered_pair @ SY56 @ SY57 ) ) )
| ( in @ SY61 @ SV15 ) )
| ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SV15 )
| ~ ( ~ ~ ( ~ ( in @ ( sK6_E @ SY64 @ SV15 @ SV12 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK7_SY30 @ SY64 @ SV15 @ SV12 @ SV5 ) @ SV12 ) )
| ( SY64
!= ( ordered_pair @ ( sK6_E @ SY64 @ SV15 @ SV12 @ SV5 ) @ ( sK7_SY30 @ SY64 @ SV15 @ SV12 @ SV5 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(72,plain,
! [SV14: $i,SV11: $i,SV5: $i] :
( ( ( ~ ( ! [SY59: $i,SY60: $i] :
( ~ ( in @ SY59 @ SV5 )
| ~ ( in @ SY60 @ SV11 )
| ( ( sK8_D @ SV14 @ SV11 @ SV5 )
!= ( ordered_pair @ SY59 @ SY60 ) ) )
| ~ ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 ) ) )
= $false )
| ( ( SV14
= ( cartesian_product2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(73,plain,
! [SV5: $i,SV11: $i,SV14: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY33 @ SV14 @ SV11 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK10_SY35 @ SV14 @ SV11 @ SV5 ) @ SV11 ) )
| ( ( sK8_D @ SV14 @ SV11 @ SV5 )
!= ( ordered_pair @ ( sK9_SY33 @ SV14 @ SV11 @ SV5 ) @ ( sK10_SY35 @ SV14 @ SV11 @ SV5 ) ) ) )
| ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 ) ) )
= $false )
| ( ( SV14
= ( cartesian_product2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(74,plain,
! [SV15: $i,SV12: $i,SV5: $i] :
( ( ( ~ ! [SY61: $i] :
( ! [SY56: $i,SY57: $i] :
( ~ ( in @ SY56 @ SV5 )
| ~ ( in @ SY57 @ SV12 )
| ( SY61
!= ( ordered_pair @ SY56 @ SY57 ) ) )
| ( in @ SY61 @ SV15 ) )
| ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SV15 )
| ~ ( ~ ~ ( ~ ( in @ ( sK6_E @ SY64 @ SV15 @ SV12 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK7_SY30 @ SY64 @ SV15 @ SV12 @ SV5 ) @ SV12 ) )
| ( SY64
!= ( ordered_pair @ ( sK6_E @ SY64 @ SV15 @ SV12 @ SV5 ) @ ( sK7_SY30 @ SY64 @ SV15 @ SV12 @ SV5 ) ) ) ) ) )
= $false )
| ( ( SV15
= ( cartesian_product2 @ SV5 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(75,plain,
! [SV14: $i,SV11: $i,SV5: $i] :
( ( ( ! [SY59: $i,SY60: $i] :
( ~ ( in @ SY59 @ SV5 )
| ~ ( in @ SY60 @ SV11 )
| ( ( sK8_D @ SV14 @ SV11 @ SV5 )
!= ( ordered_pair @ SY59 @ SY60 ) ) )
| ~ ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 ) )
= $true )
| ( ( SV14
= ( cartesian_product2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(76,plain,
! [SV5: $i,SV11: $i,SV14: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY33 @ SV14 @ SV11 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK10_SY35 @ SV14 @ SV11 @ SV5 ) @ SV11 ) )
| ( ( sK8_D @ SV14 @ SV11 @ SV5 )
!= ( ordered_pair @ ( sK9_SY33 @ SV14 @ SV11 @ SV5 ) @ ( sK10_SY35 @ SV14 @ SV11 @ SV5 ) ) ) )
| ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 ) )
= $true )
| ( ( SV14
= ( cartesian_product2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(77,plain,
! [SV15: $i,SV12: $i,SV5: $i] :
( ( ( ~ ! [SY61: $i] :
( ! [SY56: $i,SY57: $i] :
( ~ ( in @ SY56 @ SV5 )
| ~ ( in @ SY57 @ SV12 )
| ( SY61
!= ( ordered_pair @ SY56 @ SY57 ) ) )
| ( in @ SY61 @ SV15 ) ) )
= $false )
| ( ( SV15
= ( cartesian_product2 @ SV5 @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(78,plain,
! [SV5: $i,SV12: $i,SV15: $i] :
( ( ( ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SV15 )
| ~ ( ~ ~ ( ~ ( in @ ( sK6_E @ SY64 @ SV15 @ SV12 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK7_SY30 @ SY64 @ SV15 @ SV12 @ SV5 ) @ SV12 ) )
| ( SY64
!= ( ordered_pair @ ( sK6_E @ SY64 @ SV15 @ SV12 @ SV5 ) @ ( sK7_SY30 @ SY64 @ SV15 @ SV12 @ SV5 ) ) ) ) ) )
= $false )
| ( ( SV15
= ( cartesian_product2 @ SV5 @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(79,plain,
! [SV14: $i,SV11: $i,SV5: $i] :
( ( ( ! [SY59: $i,SY60: $i] :
( ~ ( in @ SY59 @ SV5 )
| ~ ( in @ SY60 @ SV11 )
| ( ( sK8_D @ SV14 @ SV11 @ SV5 )
!= ( ordered_pair @ SY59 @ SY60 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 ) )
= $true )
| ( ( SV14
= ( cartesian_product2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(80,plain,
! [SV5: $i,SV11: $i,SV14: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY33 @ SV14 @ SV11 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK10_SY35 @ SV14 @ SV11 @ SV5 ) @ SV11 ) )
| ( ( sK8_D @ SV14 @ SV11 @ SV5 )
!= ( ordered_pair @ ( sK9_SY33 @ SV14 @ SV11 @ SV5 ) @ ( sK10_SY35 @ SV14 @ SV11 @ SV5 ) ) ) ) )
= $true )
| ( ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 )
= $true )
| ( ( SV14
= ( cartesian_product2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(81,plain,
! [SV15: $i,SV12: $i,SV5: $i] :
( ( ( ! [SY61: $i] :
( ! [SY56: $i,SY57: $i] :
( ~ ( in @ SY56 @ SV5 )
| ~ ( in @ SY57 @ SV12 )
| ( SY61
!= ( ordered_pair @ SY56 @ SY57 ) ) )
| ( in @ SY61 @ SV15 ) ) )
= $true )
| ( ( SV15
= ( cartesian_product2 @ SV5 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(82,plain,
! [SV5: $i,SV12: $i,SV15: $i] :
( ( ( ! [SY64: $i] :
( ~ ( in @ SY64 @ SV15 )
| ~ ( ~ ~ ( ~ ( in @ ( sK6_E @ SY64 @ SV15 @ SV12 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK7_SY30 @ SY64 @ SV15 @ SV12 @ SV5 ) @ SV12 ) )
| ( SY64
!= ( ordered_pair @ ( sK6_E @ SY64 @ SV15 @ SV12 @ SV5 ) @ ( sK7_SY30 @ SY64 @ SV15 @ SV12 @ SV5 ) ) ) ) ) )
= $true )
| ( ( SV15
= ( cartesian_product2 @ SV5 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(83,plain,
! [SV14: $i,SV11: $i,SV5: $i,SV16: $i] :
( ( ( ! [SY65: $i] :
( ~ ( in @ SV16 @ SV5 )
| ~ ( in @ SY65 @ SV11 )
| ( ( sK8_D @ SV14 @ SV11 @ SV5 )
!= ( ordered_pair @ SV16 @ SY65 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 ) )
= $true )
| ( ( SV14
= ( cartesian_product2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(84,plain,
! [SV5: $i,SV11: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK9_SY33 @ SV14 @ SV11 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK10_SY35 @ SV14 @ SV11 @ SV5 ) @ SV11 ) )
| ( ( sK8_D @ SV14 @ SV11 @ SV5 )
!= ( ordered_pair @ ( sK9_SY33 @ SV14 @ SV11 @ SV5 ) @ ( sK10_SY35 @ SV14 @ SV11 @ SV5 ) ) ) )
= $false )
| ( ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 )
= $true )
| ( ( SV14
= ( cartesian_product2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(85,plain,
! [SV15: $i,SV17: $i,SV12: $i,SV5: $i] :
( ( ( ! [SY66: $i,SY67: $i] :
( ~ ( in @ SY66 @ SV5 )
| ~ ( in @ SY67 @ SV12 )
| ( SV17
!= ( ordered_pair @ SY66 @ SY67 ) ) )
| ( in @ SV17 @ SV15 ) )
= $true )
| ( ( SV15
= ( cartesian_product2 @ SV5 @ SV12 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(86,plain,
! [SV5: $i,SV12: $i,SV15: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ SV15 )
| ~ ( ~ ~ ( ~ ( in @ ( sK6_E @ SV18 @ SV15 @ SV12 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK7_SY30 @ SV18 @ SV15 @ SV12 @ SV5 ) @ SV12 ) )
| ( SV18
!= ( ordered_pair @ ( sK6_E @ SV18 @ SV15 @ SV12 @ SV5 ) @ ( sK7_SY30 @ SV18 @ SV15 @ SV12 @ SV5 ) ) ) ) )
= $true )
| ( ( SV15
= ( cartesian_product2 @ SV5 @ SV12 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(87,plain,
! [SV14: $i,SV11: $i,SV19: $i,SV5: $i,SV16: $i] :
( ( ( ~ ( in @ SV16 @ SV5 )
| ~ ( in @ SV19 @ SV11 )
| ( ( sK8_D @ SV14 @ SV11 @ SV5 )
!= ( ordered_pair @ SV16 @ SV19 ) ) )
= $true )
| ( ( ~ ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 ) )
= $true )
| ( ( SV14
= ( cartesian_product2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(88,plain,
! [SV5: $i,SV11: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK9_SY33 @ SV14 @ SV11 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK10_SY35 @ SV14 @ SV11 @ SV5 ) @ SV11 ) ) )
= $false )
| ( ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 )
= $true )
| ( ( SV14
= ( cartesian_product2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(89,plain,
! [SV5: $i,SV11: $i,SV14: $i] :
( ( ( ( ( sK8_D @ SV14 @ SV11 @ SV5 )
!= ( ordered_pair @ ( sK9_SY33 @ SV14 @ SV11 @ SV5 ) @ ( sK10_SY35 @ SV14 @ SV11 @ SV5 ) ) ) )
= $false )
| ( ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 )
= $true )
| ( ( SV14
= ( cartesian_product2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(90,plain,
! [SV15: $i,SV17: $i,SV12: $i,SV5: $i] :
( ( ( ! [SY66: $i,SY67: $i] :
( ~ ( in @ SY66 @ SV5 )
| ~ ( in @ SY67 @ SV12 )
| ( SV17
!= ( ordered_pair @ SY66 @ SY67 ) ) ) )
= $true )
| ( ( in @ SV17 @ SV15 )
= $true )
| ( ( SV15
= ( cartesian_product2 @ SV5 @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(91,plain,
! [SV5: $i,SV12: $i,SV15: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ SV15 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK6_E @ SV18 @ SV15 @ SV12 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK7_SY30 @ SV18 @ SV15 @ SV12 @ SV5 ) @ SV12 ) )
| ( SV18
!= ( ordered_pair @ ( sK6_E @ SV18 @ SV15 @ SV12 @ SV5 ) @ ( sK7_SY30 @ SV18 @ SV15 @ SV12 @ SV5 ) ) ) ) )
= $true )
| ( ( SV15
= ( cartesian_product2 @ SV5 @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(92,plain,
! [SV14: $i,SV11: $i,SV19: $i,SV5: $i,SV16: $i] :
( ( ( ~ ( in @ SV16 @ SV5 )
| ~ ( in @ SV19 @ SV11 ) )
= $true )
| ( ( ( ( sK8_D @ SV14 @ SV11 @ SV5 )
!= ( ordered_pair @ SV16 @ SV19 ) ) )
= $true )
| ( ( ~ ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 ) )
= $true )
| ( ( SV14
= ( cartesian_product2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(93,plain,
! [SV5: $i,SV11: $i,SV14: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_SY33 @ SV14 @ SV11 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK10_SY35 @ SV14 @ SV11 @ SV5 ) @ SV11 ) ) )
= $true )
| ( ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 )
= $true )
| ( ( SV14
= ( cartesian_product2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(94,plain,
! [SV5: $i,SV11: $i,SV14: $i] :
( ( ( ( sK8_D @ SV14 @ SV11 @ SV5 )
= ( ordered_pair @ ( sK9_SY33 @ SV14 @ SV11 @ SV5 ) @ ( sK10_SY35 @ SV14 @ SV11 @ SV5 ) ) )
= $true )
| ( ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 )
= $true )
| ( ( SV14
= ( cartesian_product2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(95,plain,
! [SV15: $i,SV17: $i,SV12: $i,SV5: $i,SV20: $i] :
( ( ( ! [SY68: $i] :
( ~ ( in @ SV20 @ SV5 )
| ~ ( in @ SY68 @ SV12 )
| ( SV17
!= ( ordered_pair @ SV20 @ SY68 ) ) ) )
= $true )
| ( ( in @ SV17 @ SV15 )
= $true )
| ( ( SV15
= ( cartesian_product2 @ SV5 @ SV12 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(96,plain,
! [SV5: $i,SV12: $i,SV15: $i,SV18: $i] :
( ( ( in @ SV18 @ SV15 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK6_E @ SV18 @ SV15 @ SV12 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK7_SY30 @ SV18 @ SV15 @ SV12 @ SV5 ) @ SV12 ) )
| ( SV18
!= ( ordered_pair @ ( sK6_E @ SV18 @ SV15 @ SV12 @ SV5 ) @ ( sK7_SY30 @ SV18 @ SV15 @ SV12 @ SV5 ) ) ) ) )
= $true )
| ( ( SV15
= ( cartesian_product2 @ SV5 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(97,plain,
! [SV14: $i,SV11: $i,SV19: $i,SV5: $i,SV16: $i] :
( ( ( ~ ( in @ SV16 @ SV5 ) )
= $true )
| ( ( ~ ( in @ SV19 @ SV11 ) )
= $true )
| ( ( ( ( sK8_D @ SV14 @ SV11 @ SV5 )
!= ( ordered_pair @ SV16 @ SV19 ) ) )
= $true )
| ( ( ~ ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 ) )
= $true )
| ( ( SV14
= ( cartesian_product2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(98,plain,
! [SV5: $i,SV11: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK9_SY33 @ SV14 @ SV11 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK10_SY35 @ SV14 @ SV11 @ SV5 ) @ SV11 ) )
= $false )
| ( ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 )
= $true )
| ( ( SV14
= ( cartesian_product2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(99,plain,
! [SV15: $i,SV17: $i,SV12: $i,SV21: $i,SV5: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ SV5 )
| ~ ( in @ SV21 @ SV12 )
| ( SV17
!= ( ordered_pair @ SV20 @ SV21 ) ) )
= $true )
| ( ( in @ SV17 @ SV15 )
= $true )
| ( ( SV15
= ( cartesian_product2 @ SV5 @ SV12 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(100,plain,
! [SV5: $i,SV12: $i,SV15: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK6_E @ SV18 @ SV15 @ SV12 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK7_SY30 @ SV18 @ SV15 @ SV12 @ SV5 ) @ SV12 ) )
| ( SV18
!= ( ordered_pair @ ( sK6_E @ SV18 @ SV15 @ SV12 @ SV5 ) @ ( sK7_SY30 @ SV18 @ SV15 @ SV12 @ SV5 ) ) ) )
= $false )
| ( ( in @ SV18 @ SV15 )
= $false )
| ( ( SV15
= ( cartesian_product2 @ SV5 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(101,plain,
! [SV14: $i,SV11: $i,SV19: $i,SV5: $i,SV16: $i] :
( ( ( in @ SV16 @ SV5 )
= $false )
| ( ( ~ ( in @ SV19 @ SV11 ) )
= $true )
| ( ( ( ( sK8_D @ SV14 @ SV11 @ SV5 )
!= ( ordered_pair @ SV16 @ SV19 ) ) )
= $true )
| ( ( ~ ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 ) )
= $true )
| ( ( SV14
= ( cartesian_product2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(102,plain,
! [SV5: $i,SV11: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK9_SY33 @ SV14 @ SV11 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 )
= $true )
| ( ( SV14
= ( cartesian_product2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(103,plain,
! [SV5: $i,SV11: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK10_SY35 @ SV14 @ SV11 @ SV5 ) @ SV11 ) )
= $false )
| ( ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 )
= $true )
| ( ( SV14
= ( cartesian_product2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(104,plain,
! [SV15: $i,SV17: $i,SV12: $i,SV21: $i,SV5: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ SV5 )
| ~ ( in @ SV21 @ SV12 ) )
= $true )
| ( ( ( SV17
!= ( ordered_pair @ SV20 @ SV21 ) ) )
= $true )
| ( ( in @ SV17 @ SV15 )
= $true )
| ( ( SV15
= ( cartesian_product2 @ SV5 @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(105,plain,
! [SV5: $i,SV12: $i,SV15: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK6_E @ SV18 @ SV15 @ SV12 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK7_SY30 @ SV18 @ SV15 @ SV12 @ SV5 ) @ SV12 ) ) )
= $false )
| ( ( in @ SV18 @ SV15 )
= $false )
| ( ( SV15
= ( cartesian_product2 @ SV5 @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(106,plain,
! [SV5: $i,SV12: $i,SV15: $i,SV18: $i] :
( ( ( ( SV18
!= ( ordered_pair @ ( sK6_E @ SV18 @ SV15 @ SV12 @ SV5 ) @ ( sK7_SY30 @ SV18 @ SV15 @ SV12 @ SV5 ) ) ) )
= $false )
| ( ( in @ SV18 @ SV15 )
= $false )
| ( ( SV15
= ( cartesian_product2 @ SV5 @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(107,plain,
! [SV14: $i,SV5: $i,SV16: $i,SV11: $i,SV19: $i] :
( ( ( in @ SV19 @ SV11 )
= $false )
| ( ( in @ SV16 @ SV5 )
= $false )
| ( ( ( ( sK8_D @ SV14 @ SV11 @ SV5 )
!= ( ordered_pair @ SV16 @ SV19 ) ) )
= $true )
| ( ( ~ ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 ) )
= $true )
| ( ( SV14
= ( cartesian_product2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(108,plain,
! [SV5: $i,SV11: $i,SV14: $i] :
( ( ( in @ ( sK9_SY33 @ SV14 @ SV11 @ SV5 ) @ SV5 )
= $true )
| ( ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 )
= $true )
| ( ( SV14
= ( cartesian_product2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(109,plain,
! [SV5: $i,SV11: $i,SV14: $i] :
( ( ( in @ ( sK10_SY35 @ SV14 @ SV11 @ SV5 ) @ SV11 )
= $true )
| ( ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 )
= $true )
| ( ( SV14
= ( cartesian_product2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(110,plain,
! [SV15: $i,SV17: $i,SV12: $i,SV21: $i,SV5: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ SV5 ) )
= $true )
| ( ( ~ ( in @ SV21 @ SV12 ) )
= $true )
| ( ( ( SV17
!= ( ordered_pair @ SV20 @ SV21 ) ) )
= $true )
| ( ( in @ SV17 @ SV15 )
= $true )
| ( ( SV15
= ( cartesian_product2 @ SV5 @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(111,plain,
! [SV5: $i,SV12: $i,SV15: $i,SV18: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_E @ SV18 @ SV15 @ SV12 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK7_SY30 @ SV18 @ SV15 @ SV12 @ SV5 ) @ SV12 ) ) )
= $true )
| ( ( in @ SV18 @ SV15 )
= $false )
| ( ( SV15
= ( cartesian_product2 @ SV5 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(112,plain,
! [SV5: $i,SV12: $i,SV15: $i,SV18: $i] :
( ( ( SV18
= ( ordered_pair @ ( sK6_E @ SV18 @ SV15 @ SV12 @ SV5 ) @ ( sK7_SY30 @ SV18 @ SV15 @ SV12 @ SV5 ) ) )
= $true )
| ( ( in @ SV18 @ SV15 )
= $false )
| ( ( SV15
= ( cartesian_product2 @ SV5 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(113,plain,
! [SV19: $i,SV16: $i,SV5: $i,SV11: $i,SV14: $i] :
( ( ( ( sK8_D @ SV14 @ SV11 @ SV5 )
= ( ordered_pair @ SV16 @ SV19 ) )
= $false )
| ( ( in @ SV16 @ SV5 )
= $false )
| ( ( in @ SV19 @ SV11 )
= $false )
| ( ( ~ ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 ) )
= $true )
| ( ( SV14
= ( cartesian_product2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(114,plain,
! [SV15: $i,SV17: $i,SV12: $i,SV21: $i,SV5: $i,SV20: $i] :
( ( ( in @ SV20 @ SV5 )
= $false )
| ( ( ~ ( in @ SV21 @ SV12 ) )
= $true )
| ( ( ( SV17
!= ( ordered_pair @ SV20 @ SV21 ) ) )
= $true )
| ( ( in @ SV17 @ SV15 )
= $true )
| ( ( SV15
= ( cartesian_product2 @ SV5 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(115,plain,
! [SV5: $i,SV12: $i,SV15: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK6_E @ SV18 @ SV15 @ SV12 @ SV5 ) @ SV5 )
| ~ ( in @ ( sK7_SY30 @ SV18 @ SV15 @ SV12 @ SV5 ) @ SV12 ) )
= $false )
| ( ( in @ SV18 @ SV15 )
= $false )
| ( ( SV15
= ( cartesian_product2 @ SV5 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(116,plain,
! [SV16: $i,SV19: $i,SV5: $i,SV11: $i,SV14: $i] :
( ( ( in @ ( sK8_D @ SV14 @ SV11 @ SV5 ) @ SV14 )
= $false )
| ( ( in @ SV19 @ SV11 )
= $false )
| ( ( in @ SV16 @ SV5 )
= $false )
| ( ( ( sK8_D @ SV14 @ SV11 @ SV5 )
= ( ordered_pair @ SV16 @ SV19 ) )
= $false )
| ( ( SV14
= ( cartesian_product2 @ SV5 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(117,plain,
! [SV15: $i,SV17: $i,SV5: $i,SV20: $i,SV12: $i,SV21: $i] :
( ( ( in @ SV21 @ SV12 )
= $false )
| ( ( in @ SV20 @ SV5 )
= $false )
| ( ( ( SV17
!= ( ordered_pair @ SV20 @ SV21 ) ) )
= $true )
| ( ( in @ SV17 @ SV15 )
= $true )
| ( ( SV15
= ( cartesian_product2 @ SV5 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(118,plain,
! [SV5: $i,SV12: $i,SV15: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK6_E @ SV18 @ SV15 @ SV12 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ SV18 @ SV15 )
= $false )
| ( ( SV15
= ( cartesian_product2 @ SV5 @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(119,plain,
! [SV5: $i,SV12: $i,SV15: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK7_SY30 @ SV18 @ SV15 @ SV12 @ SV5 ) @ SV12 ) )
= $false )
| ( ( in @ SV18 @ SV15 )
= $false )
| ( ( SV15
= ( cartesian_product2 @ SV5 @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(120,plain,
! [SV15: $i,SV12: $i,SV5: $i,SV21: $i,SV20: $i,SV17: $i] :
( ( ( SV17
= ( ordered_pair @ SV20 @ SV21 ) )
= $false )
| ( ( in @ SV20 @ SV5 )
= $false )
| ( ( in @ SV21 @ SV12 )
= $false )
| ( ( in @ SV17 @ SV15 )
= $true )
| ( ( SV15
= ( cartesian_product2 @ SV5 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(121,plain,
! [SV5: $i,SV12: $i,SV15: $i,SV18: $i] :
( ( ( in @ ( sK6_E @ SV18 @ SV15 @ SV12 @ SV5 ) @ SV5 )
= $true )
| ( ( in @ SV18 @ SV15 )
= $false )
| ( ( SV15
= ( cartesian_product2 @ SV5 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(122,plain,
! [SV5: $i,SV12: $i,SV15: $i,SV18: $i] :
( ( ( in @ ( sK7_SY30 @ SV18 @ SV15 @ SV12 @ SV5 ) @ SV12 )
= $true )
| ( ( in @ SV18 @ SV15 )
= $false )
| ( ( SV15
= ( cartesian_product2 @ SV5 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(123,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[32,122,121,120,116,112,109,108,94,67,61,56,52,46,45,41]) ).
thf(124,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET949+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n023.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 13:40:40 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.36
% 0.21/0.36 No.of.Axioms: 7
% 0.21/0.36
% 0.21/0.36 Length.of.Defs: 0
% 0.21/0.36
% 0.21/0.36 Contains.Choice.Funs: false
% 0.21/0.36 (rf:0,axioms:7,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:9,loop_count:0,foatp_calls:0,translation:fof_full)..........
% 0.21/0.50
% 0.21/0.50 ********************************
% 0.21/0.50 * All subproblems solved! *
% 0.21/0.50 ********************************
% 0.21/0.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:7,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:123,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.21/0.51
% 0.21/0.51 %**** Beginning of derivation protocol ****
% 0.21/0.51 % SZS output start CNFRefutation
% See solution above
% 0.21/0.51
% 0.21/0.51 %**** End of derivation protocol ****
% 0.21/0.51 %**** no. of clauses in derivation: 124 ****
% 0.21/0.51 %**** clause counter: 123 ****
% 0.21/0.51
% 0.21/0.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:7,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:123,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------