%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWX223+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 11:02:36 AM UTC 2026
% Result : Theorem 1.49s 0.55s
% Output : CNFRefutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 36
% Syntax : Number of formulae : 302 ( 231 unt; 0 typ; 0 def)
% Number of atoms : 1317 ( 595 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 2774 ( 512 ~; 275 |; 11 &;1949 @)
% ( 15 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 8 con; 0-3 aty)
% Number of variables : 775 ( 0 ^; 770 !; 5 ?; 775 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_app,type,
app: $i > $i > $i > $i ).
thf(tp_arr,type,
arr: $i > $i > $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_cons,type,
cons: $i > $i > $i ).
thf(tp_head,type,
head: $i > $i ).
thf(tp_index,type,
index: $i > $i > $i ).
thf(tp_just,type,
just: $i > $i ).
thf(tp_lam,type,
lam: $i > $i ).
thf(tp_nf,type,
nf: $i > $o ).
thf(tp_nil,type,
nil: $i ).
thf(tp_nothing,type,
nothing: $i ).
thf(tp_proj1App,type,
proj1App: $i > $i ).
thf(tp_proj1Arr,type,
proj1Arr: $i > $i ).
thf(tp_proj1Just,type,
proj1Just: $i > $i ).
thf(tp_proj1Lam,type,
proj1Lam: $i > $i ).
thf(tp_proj1Suc,type,
proj1Suc: $i > $i ).
thf(tp_proj1Var,type,
proj1Var: $i > $i ).
thf(tp_proj2App,type,
proj2App: $i > $i ).
thf(tp_proj2Arr,type,
proj2Arr: $i > $i ).
thf(tp_proj3App,type,
proj3App: $i > $i ).
thf(tp_suc,type,
suc: $i > $i ).
thf(tp_tail,type,
tail: $i > $i ).
thf(tp_tc,type,
tc: $i > $i > $i > $o ).
thf(tp_var,type,
var: $i > $i ).
thf(tp_zero,type,
zero: $i ).
thf(1,axiom,
! [X: $i,Z: $i,X3: $i,Tx3: $i] :
( ( ( index @ X @ X3 )
= ( just @ Tx3 ) )
=> ( ( tc @ X @ ( var @ X3 ) @ Z )
<=> ( Tx3 = Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_035) ).
thf(2,axiom,
! [X: $i,Z: $i,X3: $i] :
( ( ( index @ X @ X3 )
= nothing )
=> ~ ( tc @ X @ ( var @ X3 ) @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_034) ).
thf(3,axiom,
! [X: $i,E: $i,Tx2: $i,T1: $i] :
( ( tc @ X @ ( lam @ E ) @ ( arr @ Tx2 @ T1 ) )
<=> ( tc @ ( cons @ Tx2 @ X ) @ E @ T1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_033) ).
thf(4,axiom,
! [X: $i,Z: $i,E: $i] :
( ( Z
!= ( arr @ ( proj1Arr @ Z ) @ ( proj2Arr @ Z ) ) )
=> ~ ( tc @ X @ ( lam @ E ) @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_032) ).
thf(5,axiom,
! [X: $i,Z: $i,F: $i,X2: $i,Tx: $i] :
( ( tc @ X @ ( app @ F @ X2 @ Tx ) @ Z )
<=> ( ( tc @ X @ F @ ( arr @ Tx @ Z ) )
& ( tc @ X @ X2 @ Tx ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_031) ).
thf(6,axiom,
! [Z: $i,Xs: $i,N: $i] :
( ( index @ ( cons @ Z @ Xs ) @ ( suc @ N ) )
= ( index @ Xs @ N ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_030) ).
thf(7,axiom,
! [Z: $i,Xs: $i] :
( ( index @ ( cons @ Z @ Xs ) @ zero )
= ( just @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_029) ).
thf(8,axiom,
! [Y: $i] :
( ( index @ nil @ Y )
= nothing ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_028) ).
thf(9,axiom,
! [X4: $i] : ( nf @ ( var @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_027) ).
thf(10,axiom,
! [E: $i] :
( ( nf @ ( lam @ E ) )
<=> ( nf @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_026) ).
thf(11,axiom,
! [Z: $i,X2: $i,X3: $i] :
~ ( nf @ ( app @ ( lam @ X3 ) @ Z @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_025) ).
thf(12,axiom,
! [Y: $i,Z: $i,X2: $i] :
( ( Y
!= ( lam @ ( proj1Lam @ Y ) ) )
=> ( ( nf @ ( app @ Y @ Z @ X2 ) )
<=> ( ( nf @ Y )
& ( nf @ Z ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_024) ).
thf(13,axiom,
! [X: $i,X2: $i] :
( ( lam @ X )
!= ( var @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_023) ).
thf(14,axiom,
! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( app @ X @ X2 @ X3 )
!= ( var @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_022) ).
thf(15,axiom,
! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( app @ X @ X2 @ X3 )
!= ( lam @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_021) ).
thf(16,axiom,
! [X: $i] :
( ( proj1Var @ ( var @ X ) )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_020) ).
thf(17,axiom,
! [X: $i] :
( ( proj1Lam @ ( lam @ X ) )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_019) ).
thf(18,axiom,
! [X: $i,X2: $i,X3: $i] :
( ( proj3App @ ( app @ X @ X2 @ X3 ) )
= X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_018) ).
thf(19,axiom,
! [X: $i,X2: $i,X3: $i] :
( ( proj2App @ ( app @ X @ X2 @ X3 ) )
= X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_017) ).
thf(20,axiom,
! [X: $i,X2: $i,X3: $i] :
( ( proj1App @ ( app @ X @ X2 @ X3 ) )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_016) ).
thf(21,axiom,
! [X: $i] :
( nothing
!= ( just @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_015) ).
thf(22,axiom,
! [X: $i] :
( ( proj1Just @ ( just @ X ) )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_014) ).
thf(23,axiom,
! [X: $i] :
( zero
!= ( suc @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_013) ).
thf(24,axiom,
! [X: $i] :
( ( proj1Suc @ ( suc @ X ) )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_012) ).
thf(25,axiom,
b != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_011) ).
thf(26,axiom,
a != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
thf(27,axiom,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
thf(28,axiom,
! [X: $i,X2: $i] :
( ( arr @ X @ X2 )
!= c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
thf(29,axiom,
! [X: $i,X2: $i] :
( ( arr @ X @ X2 )
!= b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
thf(30,axiom,
! [X: $i,X2: $i] :
( ( arr @ X @ X2 )
!= a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
thf(31,axiom,
! [X: $i,X2: $i] :
( ( proj2Arr @ ( arr @ X @ X2 ) )
= X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
thf(32,axiom,
! [X: $i,X2: $i] :
( ( proj1Arr @ ( arr @ X @ X2 ) )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
thf(33,axiom,
! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
thf(34,axiom,
! [X: $i,X2: $i] :
( ( tail @ ( cons @ X @ X2 ) )
= X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
thf(35,axiom,
! [X: $i,X2: $i] :
( ( head @ ( cons @ X @ X2 ) )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
thf(36,conjecture,
? [E: $i] :
( ( nf @ E )
& ( tc @ nil @ E @ ( arr @ ( arr @ a @ ( arr @ a @ b ) ) @ ( arr @ a @ b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_036) ).
thf(37,negated_conjecture,
( ( ? [E: $i] :
( ( nf @ E )
& ( tc @ nil @ E @ ( arr @ ( arr @ a @ ( arr @ a @ b ) ) @ ( arr @ a @ b ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[36]) ).
thf(38,plain,
( ( ? [E: $i] :
( ( nf @ E )
& ( tc @ nil @ E @ ( arr @ ( arr @ a @ ( arr @ a @ b ) ) @ ( arr @ a @ b ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[37]) ).
thf(39,plain,
( ( ! [X: $i,Z: $i,X3: $i,Tx3: $i] :
( ( ( index @ X @ X3 )
= ( just @ Tx3 ) )
=> ( ( tc @ X @ ( var @ X3 ) @ Z )
<=> ( Tx3 = Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(40,plain,
( ( ! [X: $i,Z: $i,X3: $i] :
( ( ( index @ X @ X3 )
= nothing )
=> ~ ( tc @ X @ ( var @ X3 ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(41,plain,
( ( ! [X: $i,E: $i,Tx2: $i,T1: $i] :
( ( tc @ X @ ( lam @ E ) @ ( arr @ Tx2 @ T1 ) )
<=> ( tc @ ( cons @ Tx2 @ X ) @ E @ T1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(42,plain,
( ( ! [X: $i,Z: $i,E: $i] :
( ( Z
!= ( arr @ ( proj1Arr @ Z ) @ ( proj2Arr @ Z ) ) )
=> ~ ( tc @ X @ ( lam @ E ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(43,plain,
( ( ! [X: $i,Z: $i,F: $i,X2: $i,Tx: $i] :
( ( tc @ X @ ( app @ F @ X2 @ Tx ) @ Z )
<=> ( ( tc @ X @ F @ ( arr @ Tx @ Z ) )
& ( tc @ X @ X2 @ Tx ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(44,plain,
( ( ! [Z: $i,Xs: $i,N: $i] :
( ( index @ ( cons @ Z @ Xs ) @ ( suc @ N ) )
= ( index @ Xs @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(45,plain,
( ( ! [Z: $i,Xs: $i] :
( ( index @ ( cons @ Z @ Xs ) @ zero )
= ( just @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(46,plain,
( ( ! [Y: $i] :
( ( index @ nil @ Y )
= nothing ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(47,plain,
( ( ! [X4: $i] : ( nf @ ( var @ X4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(48,plain,
( ( ! [E: $i] :
( ( nf @ ( lam @ E ) )
<=> ( nf @ E ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(49,plain,
( ( ! [Z: $i,X2: $i,X3: $i] :
~ ( nf @ ( app @ ( lam @ X3 ) @ Z @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(50,plain,
( ( ! [Y: $i,Z: $i,X2: $i] :
( ( Y
!= ( lam @ ( proj1Lam @ Y ) ) )
=> ( ( nf @ ( app @ Y @ Z @ X2 ) )
<=> ( ( nf @ Y )
& ( nf @ Z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(51,plain,
( ( ! [X: $i,X2: $i] :
( ( lam @ X )
!= ( var @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(52,plain,
( ( ! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( app @ X @ X2 @ X3 )
!= ( var @ X4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(53,plain,
( ( ! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( app @ X @ X2 @ X3 )
!= ( lam @ X4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(54,plain,
( ( ! [X: $i] :
( ( proj1Var @ ( var @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(55,plain,
( ( ! [X: $i] :
( ( proj1Lam @ ( lam @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(56,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( proj3App @ ( app @ X @ X2 @ X3 ) )
= X3 ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(57,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( proj2App @ ( app @ X @ X2 @ X3 ) )
= X2 ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(58,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( proj1App @ ( app @ X @ X2 @ X3 ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(59,plain,
( ( ! [X: $i] :
( nothing
!= ( just @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(60,plain,
( ( ! [X: $i] :
( ( proj1Just @ ( just @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(61,plain,
( ( ! [X: $i] :
( zero
!= ( suc @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(62,plain,
( ( ! [X: $i] :
( ( proj1Suc @ ( suc @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(63,plain,
( ( b != c )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(64,plain,
( ( a != c )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(65,plain,
( ( a != b )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(66,plain,
( ( ! [X: $i,X2: $i] :
( ( arr @ X @ X2 )
!= c ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(67,plain,
( ( ! [X: $i,X2: $i] :
( ( arr @ X @ X2 )
!= b ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(68,plain,
( ( ! [X: $i,X2: $i] :
( ( arr @ X @ X2 )
!= a ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(69,plain,
( ( ! [X: $i,X2: $i] :
( ( proj2Arr @ ( arr @ X @ X2 ) )
= X2 ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(70,plain,
( ( ! [X: $i,X2: $i] :
( ( proj1Arr @ ( arr @ X @ X2 ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(71,plain,
( ( ! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(72,plain,
( ( ! [X: $i,X2: $i] :
( ( tail @ ( cons @ X @ X2 ) )
= X2 ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(73,plain,
( ( ! [X: $i,X2: $i] :
( ( head @ ( cons @ X @ X2 ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(74,plain,
( ( ~ ? [E: $i] :
( ( nf @ E )
& ( tc @ nil @ E @ ( arr @ ( arr @ a @ ( arr @ a @ b ) ) @ ( arr @ a @ b ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[38]) ).
thf(75,plain,
( ( ! [X: $i,X2: $i] :
( ( head @ ( cons @ X @ X2 ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(76,plain,
( ( ! [X: $i,X2: $i] :
( ( tail @ ( cons @ X @ X2 ) )
= X2 ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(77,plain,
( ( ! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(78,plain,
( ( ! [X: $i,X2: $i] :
( ( proj1Arr @ ( arr @ X @ X2 ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(79,plain,
( ( ! [X: $i,X2: $i] :
( ( proj2Arr @ ( arr @ X @ X2 ) )
= X2 ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(80,plain,
( ( ! [X: $i,X2: $i] :
( ( arr @ X @ X2 )
!= a ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(81,plain,
( ( ! [X: $i,X2: $i] :
( ( arr @ X @ X2 )
!= b ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(82,plain,
( ( ! [X: $i,X2: $i] :
( ( arr @ X @ X2 )
!= c ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(83,plain,
( ( a != b )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(84,plain,
( ( a != c )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(85,plain,
( ( b != c )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(86,plain,
( ( ! [X: $i] :
( ( proj1Suc @ ( suc @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(87,plain,
( ( ! [X: $i] :
( zero
!= ( suc @ X ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(88,plain,
( ( ! [X: $i] :
( ( proj1Just @ ( just @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(89,plain,
( ( ! [X: $i] :
( nothing
!= ( just @ X ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(90,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( proj1App @ ( app @ X @ X2 @ X3 ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(91,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( proj2App @ ( app @ X @ X2 @ X3 ) )
= X2 ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(92,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( proj3App @ ( app @ X @ X2 @ X3 ) )
= X3 ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(93,plain,
( ( ! [X: $i] :
( ( proj1Lam @ ( lam @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(94,plain,
( ( ! [X: $i] :
( ( proj1Var @ ( var @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(95,plain,
( ( ! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( app @ X @ X2 @ X3 )
!= ( lam @ X4 ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(96,plain,
( ( ! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( app @ X @ X2 @ X3 )
!= ( var @ X4 ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(97,plain,
( ( ! [X: $i,X2: $i] :
( ( lam @ X )
!= ( var @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(98,plain,
( ( ! [Y: $i,Z: $i,X2: $i] :
( ( Y
!= ( lam @ ( proj1Lam @ Y ) ) )
=> ( ( nf @ ( app @ Y @ Z @ X2 ) )
<=> ( ( nf @ Y )
& ( nf @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(99,plain,
( ( ! [Z: $i,X2: $i,X3: $i] :
~ ( nf @ ( app @ ( lam @ X3 ) @ Z @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(100,plain,
( ( ! [E: $i] :
( ( nf @ ( lam @ E ) )
<=> ( nf @ E ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(101,plain,
( ( ! [X4: $i] : ( nf @ ( var @ X4 ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(102,plain,
( ( ! [Y: $i] :
( ( index @ nil @ Y )
= nothing ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(103,plain,
( ( ! [Z: $i,Xs: $i] :
( ( index @ ( cons @ Z @ Xs ) @ zero )
= ( just @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(104,plain,
( ( ! [Z: $i,Xs: $i,N: $i] :
( ( index @ ( cons @ Z @ Xs ) @ ( suc @ N ) )
= ( index @ Xs @ N ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(105,plain,
( ( ! [X: $i,Z: $i,F: $i,X2: $i,Tx: $i] :
( ( tc @ X @ ( app @ F @ X2 @ Tx ) @ Z )
<=> ( ( tc @ X @ F @ ( arr @ Tx @ Z ) )
& ( tc @ X @ X2 @ Tx ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(106,plain,
( ( ! [X: $i,Z: $i,E: $i] :
( ( Z
!= ( arr @ ( proj1Arr @ Z ) @ ( proj2Arr @ Z ) ) )
=> ~ ( tc @ X @ ( lam @ E ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(107,plain,
( ( ! [X: $i,E: $i,Tx2: $i,T1: $i] :
( ( tc @ X @ ( lam @ E ) @ ( arr @ Tx2 @ T1 ) )
<=> ( tc @ ( cons @ Tx2 @ X ) @ E @ T1 ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(108,plain,
( ( ! [X: $i,Z: $i,X3: $i] :
( ( ( index @ X @ X3 )
= nothing )
=> ~ ( tc @ X @ ( var @ X3 ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(109,plain,
( ( ! [X: $i,Z: $i,X3: $i,Tx3: $i] :
( ( ( index @ X @ X3 )
= ( just @ Tx3 ) )
=> ( ( tc @ X @ ( var @ X3 ) @ Z )
<=> ( Tx3 = Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(110,plain,
( ( ~ ? [E: $i] :
( ( nf @ E )
& ( tc @ nil @ E @ ( arr @ ( arr @ a @ ( arr @ a @ b ) ) @ ( arr @ a @ b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(111,plain,
( ( a != b )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(112,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( app @ SX0 @ SX1 @ SX2 )
!= ( lam @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(113,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( lam @ SX0 )
!= ( var @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(114,plain,
( ( a != c )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(115,plain,
( ( ! [SX0: $i] :
( zero
!= ( suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(116,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( nf @ SX0 )
| ~ ( tc @ nil @ SX0 @ ( arr @ ( arr @ a @ ( arr @ a @ b ) ) @ ( arr @ a @ b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(117,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( tc @ SX0 @ ( lam @ SX1 ) @ ( arr @ SX2 @ SX3 ) )
| ( tc @ ( cons @ SX2 @ SX0 ) @ SX1 @ SX3 ) )
| ~ ( ~ ( tc @ ( cons @ SX2 @ SX0 ) @ SX1 @ SX3 )
| ( tc @ SX0 @ ( lam @ SX1 ) @ ( arr @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(118,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( tc @ SX0 @ ( app @ SX2 @ SX3 @ SX4 ) @ SX1 )
| ~ ( ~ ( tc @ SX0 @ SX2 @ ( arr @ SX4 @ SX1 ) )
| ~ ( tc @ SX0 @ SX3 @ SX4 ) ) )
| ~ ( ~ ~ ( ~ ( tc @ SX0 @ SX2 @ ( arr @ SX4 @ SX1 ) )
| ~ ( tc @ SX0 @ SX3 @ SX4 ) )
| ( tc @ SX0 @ ( app @ SX2 @ SX3 @ SX4 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(119,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ( SX0
!= ( lam @ ( proj1Lam @ SX0 ) ) ) )
| ~ ( ~ ( ~ ( nf @ ( app @ SX0 @ SX1 @ SX2 ) )
| ~ ( ~ ( nf @ SX0 )
| ~ ( nf @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( nf @ SX0 )
| ~ ( nf @ SX1 ) )
| ( nf @ ( app @ SX0 @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(120,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( nf @ ( lam @ SX0 ) )
| ( nf @ SX0 ) )
| ~ ( ~ ( nf @ SX0 )
| ( nf @ ( lam @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(121,plain,
( ( b != c )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(122,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( index @ SX0 @ SX2 )
!= ( just @ SX3 ) )
| ~ ( ~ ( ~ ( tc @ SX0 @ ( var @ SX2 ) @ SX1 )
| ( SX3 = SX1 ) )
| ~ ( ( SX3 != SX1 )
| ( tc @ SX0 @ ( var @ SX2 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(123,plain,
( ( ! [SX0: $i,SX1: $i] :
( nil
!= ( cons @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(124,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( arr @ SX0 @ SX1 )
!= b ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(125,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( app @ SX0 @ SX1 @ SX2 )
!= ( var @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(126,plain,
( ( ! [SX0: $i] :
( nothing
!= ( just @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(127,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( arr @ SX0 @ SX1 )
!= c ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(128,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ( SX1
!= ( arr @ ( proj1Arr @ SX1 ) @ ( proj2Arr @ SX1 ) ) ) )
| ~ ( tc @ SX0 @ ( lam @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(129,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( index @ SX0 @ SX2 )
!= nothing )
| ~ ( tc @ SX0 @ ( var @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(130,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( arr @ SX0 @ SX1 )
!= a ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(131,plain,
! [SV1: $i] :
( ( ! [SY75: $i] :
( ( head @ ( cons @ SV1 @ SY75 ) )
= SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(132,plain,
! [SV2: $i] :
( ( ! [SY76: $i] :
( ( tail @ ( cons @ SV2 @ SY76 ) )
= SY76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(133,plain,
! [SV3: $i] :
( ( ! [SY77: $i] :
( ( proj1Arr @ ( arr @ SV3 @ SY77 ) )
= SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(134,plain,
! [SV4: $i] :
( ( ! [SY78: $i] :
( ( proj2Arr @ ( arr @ SV4 @ SY78 ) )
= SY78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(135,plain,
! [SV5: $i] :
( ( ( proj1Suc @ ( suc @ SV5 ) )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(136,plain,
! [SV6: $i] :
( ( ( proj1Just @ ( just @ SV6 ) )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(137,plain,
! [SV7: $i] :
( ( ! [SY79: $i,SY80: $i] :
( ( proj1App @ ( app @ SV7 @ SY79 @ SY80 ) )
= SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(138,plain,
! [SV8: $i] :
( ( ! [SY81: $i,SY82: $i] :
( ( proj2App @ ( app @ SV8 @ SY81 @ SY82 ) )
= SY81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(139,plain,
! [SV9: $i] :
( ( ! [SY83: $i,SY84: $i] :
( ( proj3App @ ( app @ SV9 @ SY83 @ SY84 ) )
= SY84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(140,plain,
! [SV10: $i] :
( ( ( proj1Lam @ ( lam @ SV10 ) )
= SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(141,plain,
! [SV11: $i] :
( ( ( proj1Var @ ( var @ SV11 ) )
= SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(142,plain,
! [SV12: $i] :
( ( ! [SY85: $i,SY86: $i] :
~ ( nf @ ( app @ ( lam @ SY86 ) @ SV12 @ SY85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(143,plain,
! [SV13: $i] :
( ( nf @ ( var @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(144,plain,
! [SV14: $i] :
( ( ( index @ nil @ SV14 )
= nothing )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(145,plain,
! [SV15: $i] :
( ( ! [SY87: $i] :
( ( index @ ( cons @ SV15 @ SY87 ) @ zero )
= ( just @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(146,plain,
! [SV16: $i] :
( ( ! [SY88: $i,SY89: $i] :
( ( index @ ( cons @ SV16 @ SY88 ) @ ( suc @ SY89 ) )
= ( index @ SY88 @ SY89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(147,plain,
( ( a = b )
= $false ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(148,plain,
! [SV17: $i] :
( ( ! [SY90: $i,SY91: $i,SY92: $i] :
( ( app @ SV17 @ SY90 @ SY91 )
!= ( lam @ SY92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(149,plain,
! [SV18: $i] :
( ( ! [SY93: $i] :
( ( lam @ SV18 )
!= ( var @ SY93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(150,plain,
( ( a = c )
= $false ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(151,plain,
! [SV19: $i] :
( ( zero
!= ( suc @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(152,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( nf @ SX0 )
| ~ ( tc @ nil @ SX0 @ ( arr @ ( arr @ a @ ( arr @ a @ b ) ) @ ( arr @ a @ b ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(153,plain,
! [SV20: $i] :
( ( ! [SY94: $i,SY95: $i,SY96: $i] :
~ ( ~ ( ~ ( tc @ SV20 @ ( lam @ SY94 ) @ ( arr @ SY95 @ SY96 ) )
| ( tc @ ( cons @ SY95 @ SV20 ) @ SY94 @ SY96 ) )
| ~ ( ~ ( tc @ ( cons @ SY95 @ SV20 ) @ SY94 @ SY96 )
| ( tc @ SV20 @ ( lam @ SY94 ) @ ( arr @ SY95 @ SY96 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(154,plain,
! [SV21: $i] :
( ( ! [SY97: $i,SY98: $i,SY99: $i,SY100: $i] :
~ ( ~ ( ~ ( tc @ SV21 @ ( app @ SY98 @ SY99 @ SY100 ) @ SY97 )
| ~ ( ~ ( tc @ SV21 @ SY98 @ ( arr @ SY100 @ SY97 ) )
| ~ ( tc @ SV21 @ SY99 @ SY100 ) ) )
| ~ ( ~ ~ ( ~ ( tc @ SV21 @ SY98 @ ( arr @ SY100 @ SY97 ) )
| ~ ( tc @ SV21 @ SY99 @ SY100 ) )
| ( tc @ SV21 @ ( app @ SY98 @ SY99 @ SY100 ) @ SY97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(155,plain,
! [SV22: $i] :
( ( ! [SY101: $i,SY102: $i] :
( ~ ( ( SV22
!= ( lam @ ( proj1Lam @ SV22 ) ) ) )
| ~ ( ~ ( ~ ( nf @ ( app @ SV22 @ SY101 @ SY102 ) )
| ~ ( ~ ( nf @ SV22 )
| ~ ( nf @ SY101 ) ) )
| ~ ( ~ ~ ( ~ ( nf @ SV22 )
| ~ ( nf @ SY101 ) )
| ( nf @ ( app @ SV22 @ SY101 @ SY102 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(156,plain,
! [SV23: $i] :
( ( ~ ( ~ ( ~ ( nf @ ( lam @ SV23 ) )
| ( nf @ SV23 ) )
| ~ ( ~ ( nf @ SV23 )
| ( nf @ ( lam @ SV23 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(157,plain,
( ( b = c )
= $false ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(158,plain,
! [SV24: $i] :
( ( ! [SY103: $i,SY104: $i,SY105: $i] :
( ( ( index @ SV24 @ SY104 )
!= ( just @ SY105 ) )
| ~ ( ~ ( ~ ( tc @ SV24 @ ( var @ SY104 ) @ SY103 )
| ( SY105 = SY103 ) )
| ~ ( ( SY105 != SY103 )
| ( tc @ SV24 @ ( var @ SY104 ) @ SY103 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(159,plain,
! [SV25: $i] :
( ( ! [SY106: $i] :
( nil
!= ( cons @ SV25 @ SY106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(160,plain,
! [SV26: $i] :
( ( ! [SY107: $i] :
( ( arr @ SV26 @ SY107 )
!= b ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(161,plain,
! [SV27: $i] :
( ( ! [SY108: $i,SY109: $i,SY110: $i] :
( ( app @ SV27 @ SY108 @ SY109 )
!= ( var @ SY110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(162,plain,
! [SV28: $i] :
( ( nothing
!= ( just @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(163,plain,
! [SV29: $i] :
( ( ! [SY111: $i] :
( ( arr @ SV29 @ SY111 )
!= c ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(164,plain,
! [SV30: $i] :
( ( ! [SY112: $i,SY113: $i] :
( ~ ( ( SY112
!= ( arr @ ( proj1Arr @ SY112 ) @ ( proj2Arr @ SY112 ) ) ) )
| ~ ( tc @ SV30 @ ( lam @ SY113 ) @ SY112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(165,plain,
! [SV31: $i] :
( ( ! [SY114: $i,SY115: $i] :
( ( ( index @ SV31 @ SY115 )
!= nothing )
| ~ ( tc @ SV31 @ ( var @ SY115 ) @ SY114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(166,plain,
! [SV32: $i] :
( ( ! [SY116: $i] :
( ( arr @ SV32 @ SY116 )
!= a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(167,plain,
! [SV33: $i,SV1: $i] :
( ( ( head @ ( cons @ SV1 @ SV33 ) )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(168,plain,
! [SV34: $i,SV2: $i] :
( ( ( tail @ ( cons @ SV2 @ SV34 ) )
= SV34 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(169,plain,
! [SV35: $i,SV3: $i] :
( ( ( proj1Arr @ ( arr @ SV3 @ SV35 ) )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(170,plain,
! [SV36: $i,SV4: $i] :
( ( ( proj2Arr @ ( arr @ SV4 @ SV36 ) )
= SV36 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(171,plain,
! [SV37: $i,SV7: $i] :
( ( ! [SY117: $i] :
( ( proj1App @ ( app @ SV7 @ SV37 @ SY117 ) )
= SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(172,plain,
! [SV38: $i,SV8: $i] :
( ( ! [SY118: $i] :
( ( proj2App @ ( app @ SV8 @ SV38 @ SY118 ) )
= SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(173,plain,
! [SV39: $i,SV9: $i] :
( ( ! [SY119: $i] :
( ( proj3App @ ( app @ SV9 @ SV39 @ SY119 ) )
= SY119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(174,plain,
! [SV40: $i,SV12: $i] :
( ( ! [SY120: $i] :
~ ( nf @ ( app @ ( lam @ SY120 ) @ SV12 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(175,plain,
! [SV41: $i,SV15: $i] :
( ( ( index @ ( cons @ SV15 @ SV41 ) @ zero )
= ( just @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(176,plain,
! [SV42: $i,SV16: $i] :
( ( ! [SY121: $i] :
( ( index @ ( cons @ SV16 @ SV42 ) @ ( suc @ SY121 ) )
= ( index @ SV42 @ SY121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(177,plain,
! [SV43: $i,SV17: $i] :
( ( ! [SY122: $i,SY123: $i] :
( ( app @ SV17 @ SV43 @ SY122 )
!= ( lam @ SY123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(178,plain,
! [SV44: $i,SV18: $i] :
( ( ( lam @ SV18 )
!= ( var @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(179,plain,
! [SV19: $i] :
( ( zero
= ( suc @ SV19 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(180,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( nf @ SX0 )
| ~ ( tc @ nil @ SX0 @ ( arr @ ( arr @ a @ ( arr @ a @ b ) ) @ ( arr @ a @ b ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(181,plain,
! [SV45: $i,SV20: $i] :
( ( ! [SY124: $i,SY125: $i] :
~ ( ~ ( ~ ( tc @ SV20 @ ( lam @ SV45 ) @ ( arr @ SY124 @ SY125 ) )
| ( tc @ ( cons @ SY124 @ SV20 ) @ SV45 @ SY125 ) )
| ~ ( ~ ( tc @ ( cons @ SY124 @ SV20 ) @ SV45 @ SY125 )
| ( tc @ SV20 @ ( lam @ SV45 ) @ ( arr @ SY124 @ SY125 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(182,plain,
! [SV46: $i,SV21: $i] :
( ( ! [SY126: $i,SY127: $i,SY128: $i] :
~ ( ~ ( ~ ( tc @ SV21 @ ( app @ SY126 @ SY127 @ SY128 ) @ SV46 )
| ~ ( ~ ( tc @ SV21 @ SY126 @ ( arr @ SY128 @ SV46 ) )
| ~ ( tc @ SV21 @ SY127 @ SY128 ) ) )
| ~ ( ~ ~ ( ~ ( tc @ SV21 @ SY126 @ ( arr @ SY128 @ SV46 ) )
| ~ ( tc @ SV21 @ SY127 @ SY128 ) )
| ( tc @ SV21 @ ( app @ SY126 @ SY127 @ SY128 ) @ SV46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(183,plain,
! [SV47: $i,SV22: $i] :
( ( ! [SY129: $i] :
( ~ ( ( SV22
!= ( lam @ ( proj1Lam @ SV22 ) ) ) )
| ~ ( ~ ( ~ ( nf @ ( app @ SV22 @ SV47 @ SY129 ) )
| ~ ( ~ ( nf @ SV22 )
| ~ ( nf @ SV47 ) ) )
| ~ ( ~ ~ ( ~ ( nf @ SV22 )
| ~ ( nf @ SV47 ) )
| ( nf @ ( app @ SV22 @ SV47 @ SY129 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(184,plain,
! [SV23: $i] :
( ( ~ ( ~ ( nf @ ( lam @ SV23 ) )
| ( nf @ SV23 ) )
| ~ ( ~ ( nf @ SV23 )
| ( nf @ ( lam @ SV23 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(185,plain,
! [SV48: $i,SV24: $i] :
( ( ! [SY130: $i,SY131: $i] :
( ( ( index @ SV24 @ SY130 )
!= ( just @ SY131 ) )
| ~ ( ~ ( ~ ( tc @ SV24 @ ( var @ SY130 ) @ SV48 )
| ( SY131 = SV48 ) )
| ~ ( ( SY131 != SV48 )
| ( tc @ SV24 @ ( var @ SY130 ) @ SV48 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(186,plain,
! [SV49: $i,SV25: $i] :
( ( nil
!= ( cons @ SV25 @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(187,plain,
! [SV50: $i,SV26: $i] :
( ( ( arr @ SV26 @ SV50 )
!= b )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(188,plain,
! [SV51: $i,SV27: $i] :
( ( ! [SY132: $i,SY133: $i] :
( ( app @ SV27 @ SV51 @ SY132 )
!= ( var @ SY133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(189,plain,
! [SV28: $i] :
( ( nothing
= ( just @ SV28 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(190,plain,
! [SV52: $i,SV29: $i] :
( ( ( arr @ SV29 @ SV52 )
!= c )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(191,plain,
! [SV30: $i,SV53: $i] :
( ( ! [SY134: $i] :
( ~ ( ( SV53
!= ( arr @ ( proj1Arr @ SV53 ) @ ( proj2Arr @ SV53 ) ) ) )
| ~ ( tc @ SV30 @ ( lam @ SY134 ) @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(192,plain,
! [SV54: $i,SV31: $i] :
( ( ! [SY135: $i] :
( ( ( index @ SV31 @ SY135 )
!= nothing )
| ~ ( tc @ SV31 @ ( var @ SY135 ) @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(193,plain,
! [SV55: $i,SV32: $i] :
( ( ( arr @ SV32 @ SV55 )
!= a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(194,plain,
! [SV56: $i,SV37: $i,SV7: $i] :
( ( ( proj1App @ ( app @ SV7 @ SV37 @ SV56 ) )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(195,plain,
! [SV57: $i,SV38: $i,SV8: $i] :
( ( ( proj2App @ ( app @ SV8 @ SV38 @ SV57 ) )
= SV38 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(196,plain,
! [SV58: $i,SV39: $i,SV9: $i] :
( ( ( proj3App @ ( app @ SV9 @ SV39 @ SV58 ) )
= SV58 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(197,plain,
! [SV40: $i,SV12: $i,SV59: $i] :
( ( ~ ( nf @ ( app @ ( lam @ SV59 ) @ SV12 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(198,plain,
! [SV60: $i,SV42: $i,SV16: $i] :
( ( ( index @ ( cons @ SV16 @ SV42 ) @ ( suc @ SV60 ) )
= ( index @ SV42 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(199,plain,
! [SV61: $i,SV43: $i,SV17: $i] :
( ( ! [SY136: $i] :
( ( app @ SV17 @ SV43 @ SV61 )
!= ( lam @ SY136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(200,plain,
! [SV44: $i,SV18: $i] :
( ( ( lam @ SV18 )
= ( var @ SV44 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(201,plain,
! [SV62: $i] :
( ( ~ ~ ( ~ ( nf @ SV62 )
| ~ ( tc @ nil @ SV62 @ ( arr @ ( arr @ a @ ( arr @ a @ b ) ) @ ( arr @ a @ b ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(202,plain,
! [SV63: $i,SV45: $i,SV20: $i] :
( ( ! [SY137: $i] :
~ ( ~ ( ~ ( tc @ SV20 @ ( lam @ SV45 ) @ ( arr @ SV63 @ SY137 ) )
| ( tc @ ( cons @ SV63 @ SV20 ) @ SV45 @ SY137 ) )
| ~ ( ~ ( tc @ ( cons @ SV63 @ SV20 ) @ SV45 @ SY137 )
| ( tc @ SV20 @ ( lam @ SV45 ) @ ( arr @ SV63 @ SY137 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(203,plain,
! [SV46: $i,SV64: $i,SV21: $i] :
( ( ! [SY138: $i,SY139: $i] :
~ ( ~ ( ~ ( tc @ SV21 @ ( app @ SV64 @ SY138 @ SY139 ) @ SV46 )
| ~ ( ~ ( tc @ SV21 @ SV64 @ ( arr @ SY139 @ SV46 ) )
| ~ ( tc @ SV21 @ SY138 @ SY139 ) ) )
| ~ ( ~ ~ ( ~ ( tc @ SV21 @ SV64 @ ( arr @ SY139 @ SV46 ) )
| ~ ( tc @ SV21 @ SY138 @ SY139 ) )
| ( tc @ SV21 @ ( app @ SV64 @ SY138 @ SY139 ) @ SV46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(204,plain,
! [SV65: $i,SV47: $i,SV22: $i] :
( ( ~ ( ( SV22
!= ( lam @ ( proj1Lam @ SV22 ) ) ) )
| ~ ( ~ ( ~ ( nf @ ( app @ SV22 @ SV47 @ SV65 ) )
| ~ ( ~ ( nf @ SV22 )
| ~ ( nf @ SV47 ) ) )
| ~ ( ~ ~ ( ~ ( nf @ SV22 )
| ~ ( nf @ SV47 ) )
| ( nf @ ( app @ SV22 @ SV47 @ SV65 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(205,plain,
! [SV23: $i] :
( ( ~ ( ~ ( nf @ ( lam @ SV23 ) )
| ( nf @ SV23 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(206,plain,
! [SV23: $i] :
( ( ~ ( ~ ( nf @ SV23 )
| ( nf @ ( lam @ SV23 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(207,plain,
! [SV48: $i,SV66: $i,SV24: $i] :
( ( ! [SY140: $i] :
( ( ( index @ SV24 @ SV66 )
!= ( just @ SY140 ) )
| ~ ( ~ ( ~ ( tc @ SV24 @ ( var @ SV66 ) @ SV48 )
| ( SY140 = SV48 ) )
| ~ ( ( SY140 != SV48 )
| ( tc @ SV24 @ ( var @ SV66 ) @ SV48 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(208,plain,
! [SV49: $i,SV25: $i] :
( ( nil
= ( cons @ SV25 @ SV49 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(209,plain,
! [SV50: $i,SV26: $i] :
( ( ( arr @ SV26 @ SV50 )
= b )
= $false ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(210,plain,
! [SV67: $i,SV51: $i,SV27: $i] :
( ( ! [SY141: $i] :
( ( app @ SV27 @ SV51 @ SV67 )
!= ( var @ SY141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(211,plain,
! [SV52: $i,SV29: $i] :
( ( ( arr @ SV29 @ SV52 )
= c )
= $false ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(212,plain,
! [SV68: $i,SV30: $i,SV53: $i] :
( ( ~ ( ( SV53
!= ( arr @ ( proj1Arr @ SV53 ) @ ( proj2Arr @ SV53 ) ) ) )
| ~ ( tc @ SV30 @ ( lam @ SV68 ) @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(213,plain,
! [SV54: $i,SV69: $i,SV31: $i] :
( ( ( ( index @ SV31 @ SV69 )
!= nothing )
| ~ ( tc @ SV31 @ ( var @ SV69 ) @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(214,plain,
! [SV55: $i,SV32: $i] :
( ( ( arr @ SV32 @ SV55 )
= a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(215,plain,
! [SV40: $i,SV12: $i,SV59: $i] :
( ( nf @ ( app @ ( lam @ SV59 ) @ SV12 @ SV40 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(216,plain,
! [SV70: $i,SV61: $i,SV43: $i,SV17: $i] :
( ( ( app @ SV17 @ SV43 @ SV61 )
!= ( lam @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(217,plain,
! [SV62: $i] :
( ( ~ ( ~ ( nf @ SV62 )
| ~ ( tc @ nil @ SV62 @ ( arr @ ( arr @ a @ ( arr @ a @ b ) ) @ ( arr @ a @ b ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(218,plain,
! [SV71: $i,SV63: $i,SV45: $i,SV20: $i] :
( ( ~ ( ~ ( ~ ( tc @ SV20 @ ( lam @ SV45 ) @ ( arr @ SV63 @ SV71 ) )
| ( tc @ ( cons @ SV63 @ SV20 ) @ SV45 @ SV71 ) )
| ~ ( ~ ( tc @ ( cons @ SV63 @ SV20 ) @ SV45 @ SV71 )
| ( tc @ SV20 @ ( lam @ SV45 ) @ ( arr @ SV63 @ SV71 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(219,plain,
! [SV46: $i,SV72: $i,SV64: $i,SV21: $i] :
( ( ! [SY142: $i] :
~ ( ~ ( ~ ( tc @ SV21 @ ( app @ SV64 @ SV72 @ SY142 ) @ SV46 )
| ~ ( ~ ( tc @ SV21 @ SV64 @ ( arr @ SY142 @ SV46 ) )
| ~ ( tc @ SV21 @ SV72 @ SY142 ) ) )
| ~ ( ~ ~ ( ~ ( tc @ SV21 @ SV64 @ ( arr @ SY142 @ SV46 ) )
| ~ ( tc @ SV21 @ SV72 @ SY142 ) )
| ( tc @ SV21 @ ( app @ SV64 @ SV72 @ SY142 ) @ SV46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(220,plain,
! [SV65: $i,SV47: $i,SV22: $i] :
( ( ( ~ ( ( SV22
!= ( lam @ ( proj1Lam @ SV22 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( nf @ ( app @ SV22 @ SV47 @ SV65 ) )
| ~ ( ~ ( nf @ SV22 )
| ~ ( nf @ SV47 ) ) )
| ~ ( ~ ~ ( ~ ( nf @ SV22 )
| ~ ( nf @ SV47 ) )
| ( nf @ ( app @ SV22 @ SV47 @ SV65 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(221,plain,
! [SV23: $i] :
( ( ~ ( nf @ ( lam @ SV23 ) )
| ( nf @ SV23 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(222,plain,
! [SV23: $i] :
( ( ~ ( nf @ SV23 )
| ( nf @ ( lam @ SV23 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(223,plain,
! [SV48: $i,SV73: $i,SV66: $i,SV24: $i] :
( ( ( ( index @ SV24 @ SV66 )
!= ( just @ SV73 ) )
| ~ ( ~ ( ~ ( tc @ SV24 @ ( var @ SV66 ) @ SV48 )
| ( SV73 = SV48 ) )
| ~ ( ( SV73 != SV48 )
| ( tc @ SV24 @ ( var @ SV66 ) @ SV48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(224,plain,
! [SV74: $i,SV67: $i,SV51: $i,SV27: $i] :
( ( ( app @ SV27 @ SV51 @ SV67 )
!= ( var @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(225,plain,
! [SV68: $i,SV30: $i,SV53: $i] :
( ( ( ~ ( ( SV53
!= ( arr @ ( proj1Arr @ SV53 ) @ ( proj2Arr @ SV53 ) ) ) ) )
= $true )
| ( ( ~ ( tc @ SV30 @ ( lam @ SV68 ) @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(226,plain,
! [SV54: $i,SV69: $i,SV31: $i] :
( ( ( ( index @ SV31 @ SV69 )
!= nothing )
= $true )
| ( ( ~ ( tc @ SV31 @ ( var @ SV69 ) @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(227,plain,
! [SV70: $i,SV61: $i,SV43: $i,SV17: $i] :
( ( ( app @ SV17 @ SV43 @ SV61 )
= ( lam @ SV70 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(228,plain,
! [SV62: $i] :
( ( ~ ( nf @ SV62 )
| ~ ( tc @ nil @ SV62 @ ( arr @ ( arr @ a @ ( arr @ a @ b ) ) @ ( arr @ a @ b ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(229,plain,
! [SV71: $i,SV63: $i,SV45: $i,SV20: $i] :
( ( ~ ( ~ ( tc @ SV20 @ ( lam @ SV45 ) @ ( arr @ SV63 @ SV71 ) )
| ( tc @ ( cons @ SV63 @ SV20 ) @ SV45 @ SV71 ) )
| ~ ( ~ ( tc @ ( cons @ SV63 @ SV20 ) @ SV45 @ SV71 )
| ( tc @ SV20 @ ( lam @ SV45 ) @ ( arr @ SV63 @ SV71 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(230,plain,
! [SV46: $i,SV75: $i,SV72: $i,SV64: $i,SV21: $i] :
( ( ~ ( ~ ( ~ ( tc @ SV21 @ ( app @ SV64 @ SV72 @ SV75 ) @ SV46 )
| ~ ( ~ ( tc @ SV21 @ SV64 @ ( arr @ SV75 @ SV46 ) )
| ~ ( tc @ SV21 @ SV72 @ SV75 ) ) )
| ~ ( ~ ~ ( ~ ( tc @ SV21 @ SV64 @ ( arr @ SV75 @ SV46 ) )
| ~ ( tc @ SV21 @ SV72 @ SV75 ) )
| ( tc @ SV21 @ ( app @ SV64 @ SV72 @ SV75 ) @ SV46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(231,plain,
! [SV65: $i,SV47: $i,SV22: $i] :
( ( ( SV22
!= ( lam @ ( proj1Lam @ SV22 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( nf @ ( app @ SV22 @ SV47 @ SV65 ) )
| ~ ( ~ ( nf @ SV22 )
| ~ ( nf @ SV47 ) ) )
| ~ ( ~ ~ ( ~ ( nf @ SV22 )
| ~ ( nf @ SV47 ) )
| ( nf @ ( app @ SV22 @ SV47 @ SV65 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(232,plain,
! [SV23: $i] :
( ( ( ~ ( nf @ ( lam @ SV23 ) ) )
= $true )
| ( ( nf @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(233,plain,
! [SV23: $i] :
( ( ( ~ ( nf @ SV23 ) )
= $true )
| ( ( nf @ ( lam @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(234,plain,
! [SV48: $i,SV73: $i,SV66: $i,SV24: $i] :
( ( ( ( index @ SV24 @ SV66 )
!= ( just @ SV73 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( tc @ SV24 @ ( var @ SV66 ) @ SV48 )
| ( SV73 = SV48 ) )
| ~ ( ( SV73 != SV48 )
| ( tc @ SV24 @ ( var @ SV66 ) @ SV48 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(235,plain,
! [SV74: $i,SV67: $i,SV51: $i,SV27: $i] :
( ( ( app @ SV27 @ SV51 @ SV67 )
= ( var @ SV74 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(236,plain,
! [SV68: $i,SV30: $i,SV53: $i] :
( ( ( SV53
!= ( arr @ ( proj1Arr @ SV53 ) @ ( proj2Arr @ SV53 ) ) )
= $false )
| ( ( ~ ( tc @ SV30 @ ( lam @ SV68 ) @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(237,plain,
! [SV54: $i,SV69: $i,SV31: $i] :
( ( ( ( index @ SV31 @ SV69 )
= nothing )
= $false )
| ( ( ~ ( tc @ SV31 @ ( var @ SV69 ) @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(238,plain,
! [SV62: $i] :
( ( ( ~ ( nf @ SV62 ) )
= $true )
| ( ( ~ ( tc @ nil @ SV62 @ ( arr @ ( arr @ a @ ( arr @ a @ b ) ) @ ( arr @ a @ b ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(239,plain,
! [SV71: $i,SV63: $i,SV45: $i,SV20: $i] :
( ( ~ ( ~ ( tc @ SV20 @ ( lam @ SV45 ) @ ( arr @ SV63 @ SV71 ) )
| ( tc @ ( cons @ SV63 @ SV20 ) @ SV45 @ SV71 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(240,plain,
! [SV71: $i,SV45: $i,SV20: $i,SV63: $i] :
( ( ~ ( ~ ( tc @ ( cons @ SV63 @ SV20 ) @ SV45 @ SV71 )
| ( tc @ SV20 @ ( lam @ SV45 ) @ ( arr @ SV63 @ SV71 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(241,plain,
! [SV46: $i,SV75: $i,SV72: $i,SV64: $i,SV21: $i] :
( ( ~ ( ~ ( tc @ SV21 @ ( app @ SV64 @ SV72 @ SV75 ) @ SV46 )
| ~ ( ~ ( tc @ SV21 @ SV64 @ ( arr @ SV75 @ SV46 ) )
| ~ ( tc @ SV21 @ SV72 @ SV75 ) ) )
| ~ ( ~ ~ ( ~ ( tc @ SV21 @ SV64 @ ( arr @ SV75 @ SV46 ) )
| ~ ( tc @ SV21 @ SV72 @ SV75 ) )
| ( tc @ SV21 @ ( app @ SV64 @ SV72 @ SV75 ) @ SV46 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(242,plain,
! [SV65: $i,SV47: $i,SV22: $i] :
( ( ( SV22
= ( lam @ ( proj1Lam @ SV22 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( nf @ ( app @ SV22 @ SV47 @ SV65 ) )
| ~ ( ~ ( nf @ SV22 )
| ~ ( nf @ SV47 ) ) )
| ~ ( ~ ~ ( ~ ( nf @ SV22 )
| ~ ( nf @ SV47 ) )
| ( nf @ ( app @ SV22 @ SV47 @ SV65 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(243,plain,
! [SV23: $i] :
( ( ( nf @ ( lam @ SV23 ) )
= $false )
| ( ( nf @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(244,plain,
! [SV23: $i] :
( ( ( nf @ SV23 )
= $false )
| ( ( nf @ ( lam @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(245,plain,
! [SV48: $i,SV73: $i,SV66: $i,SV24: $i] :
( ( ( ( index @ SV24 @ SV66 )
= ( just @ SV73 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( tc @ SV24 @ ( var @ SV66 ) @ SV48 )
| ( SV73 = SV48 ) )
| ~ ( ( SV73 != SV48 )
| ( tc @ SV24 @ ( var @ SV66 ) @ SV48 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(246,plain,
! [SV68: $i,SV30: $i,SV53: $i] :
( ( ( SV53
= ( arr @ ( proj1Arr @ SV53 ) @ ( proj2Arr @ SV53 ) ) )
= $true )
| ( ( ~ ( tc @ SV30 @ ( lam @ SV68 ) @ SV53 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[236]) ).
thf(247,plain,
! [SV54: $i,SV69: $i,SV31: $i] :
( ( ( tc @ SV31 @ ( var @ SV69 ) @ SV54 )
= $false )
| ( ( ( index @ SV31 @ SV69 )
= nothing )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(248,plain,
! [SV62: $i] :
( ( ( nf @ SV62 )
= $false )
| ( ( ~ ( tc @ nil @ SV62 @ ( arr @ ( arr @ a @ ( arr @ a @ b ) ) @ ( arr @ a @ b ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(249,plain,
! [SV71: $i,SV63: $i,SV45: $i,SV20: $i] :
( ( ~ ( tc @ SV20 @ ( lam @ SV45 ) @ ( arr @ SV63 @ SV71 ) )
| ( tc @ ( cons @ SV63 @ SV20 ) @ SV45 @ SV71 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(250,plain,
! [SV71: $i,SV45: $i,SV20: $i,SV63: $i] :
( ( ~ ( tc @ ( cons @ SV63 @ SV20 ) @ SV45 @ SV71 )
| ( tc @ SV20 @ ( lam @ SV45 ) @ ( arr @ SV63 @ SV71 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(251,plain,
! [SV46: $i,SV75: $i,SV72: $i,SV64: $i,SV21: $i] :
( ( ~ ( ~ ( tc @ SV21 @ ( app @ SV64 @ SV72 @ SV75 ) @ SV46 )
| ~ ( ~ ( tc @ SV21 @ SV64 @ ( arr @ SV75 @ SV46 ) )
| ~ ( tc @ SV21 @ SV72 @ SV75 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(252,plain,
! [SV72: $i,SV46: $i,SV75: $i,SV64: $i,SV21: $i] :
( ( ~ ( ~ ~ ( ~ ( tc @ SV21 @ SV64 @ ( arr @ SV75 @ SV46 ) )
| ~ ( tc @ SV21 @ SV72 @ SV75 ) )
| ( tc @ SV21 @ ( app @ SV64 @ SV72 @ SV75 ) @ SV46 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(253,plain,
! [SV65: $i,SV47: $i,SV22: $i] :
( ( ( ~ ( ~ ( nf @ ( app @ SV22 @ SV47 @ SV65 ) )
| ~ ( ~ ( nf @ SV22 )
| ~ ( nf @ SV47 ) ) )
| ~ ( ~ ~ ( ~ ( nf @ SV22 )
| ~ ( nf @ SV47 ) )
| ( nf @ ( app @ SV22 @ SV47 @ SV65 ) ) ) )
= $false )
| ( ( SV22
= ( lam @ ( proj1Lam @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(254,plain,
! [SV73: $i,SV48: $i,SV66: $i,SV24: $i] :
( ( ( ~ ( ~ ( tc @ SV24 @ ( var @ SV66 ) @ SV48 )
| ( SV73 = SV48 ) )
| ~ ( ( SV73 != SV48 )
| ( tc @ SV24 @ ( var @ SV66 ) @ SV48 ) ) )
= $false )
| ( ( ( index @ SV24 @ SV66 )
= ( just @ SV73 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(255,plain,
! [SV53: $i,SV68: $i,SV30: $i] :
( ( ( tc @ SV30 @ ( lam @ SV68 ) @ SV53 )
= $false )
| ( ( SV53
= ( arr @ ( proj1Arr @ SV53 ) @ ( proj2Arr @ SV53 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(256,plain,
! [SV62: $i] :
( ( ( tc @ nil @ SV62 @ ( arr @ ( arr @ a @ ( arr @ a @ b ) ) @ ( arr @ a @ b ) ) )
= $false )
| ( ( nf @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(257,plain,
! [SV71: $i,SV63: $i,SV45: $i,SV20: $i] :
( ( ( ~ ( tc @ SV20 @ ( lam @ SV45 ) @ ( arr @ SV63 @ SV71 ) ) )
= $true )
| ( ( tc @ ( cons @ SV63 @ SV20 ) @ SV45 @ SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(258,plain,
! [SV71: $i,SV45: $i,SV20: $i,SV63: $i] :
( ( ( ~ ( tc @ ( cons @ SV63 @ SV20 ) @ SV45 @ SV71 ) )
= $true )
| ( ( tc @ SV20 @ ( lam @ SV45 ) @ ( arr @ SV63 @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(259,plain,
! [SV46: $i,SV75: $i,SV72: $i,SV64: $i,SV21: $i] :
( ( ~ ( tc @ SV21 @ ( app @ SV64 @ SV72 @ SV75 ) @ SV46 )
| ~ ( ~ ( tc @ SV21 @ SV64 @ ( arr @ SV75 @ SV46 ) )
| ~ ( tc @ SV21 @ SV72 @ SV75 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(260,plain,
! [SV72: $i,SV46: $i,SV75: $i,SV64: $i,SV21: $i] :
( ( ~ ~ ( ~ ( tc @ SV21 @ SV64 @ ( arr @ SV75 @ SV46 ) )
| ~ ( tc @ SV21 @ SV72 @ SV75 ) )
| ( tc @ SV21 @ ( app @ SV64 @ SV72 @ SV75 ) @ SV46 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(261,plain,
! [SV65: $i,SV47: $i,SV22: $i] :
( ( ( ~ ( ~ ( nf @ ( app @ SV22 @ SV47 @ SV65 ) )
| ~ ( ~ ( nf @ SV22 )
| ~ ( nf @ SV47 ) ) ) )
= $false )
| ( ( SV22
= ( lam @ ( proj1Lam @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[253]) ).
thf(262,plain,
! [SV65: $i,SV47: $i,SV22: $i] :
( ( ( ~ ( ~ ~ ( ~ ( nf @ SV22 )
| ~ ( nf @ SV47 ) )
| ( nf @ ( app @ SV22 @ SV47 @ SV65 ) ) ) )
= $false )
| ( ( SV22
= ( lam @ ( proj1Lam @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[253]) ).
thf(263,plain,
! [SV73: $i,SV48: $i,SV66: $i,SV24: $i] :
( ( ( ~ ( ~ ( tc @ SV24 @ ( var @ SV66 ) @ SV48 )
| ( SV73 = SV48 ) ) )
= $false )
| ( ( ( index @ SV24 @ SV66 )
= ( just @ SV73 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[254]) ).
thf(264,plain,
! [SV66: $i,SV24: $i,SV48: $i,SV73: $i] :
( ( ( ~ ( ( SV73 != SV48 )
| ( tc @ SV24 @ ( var @ SV66 ) @ SV48 ) ) )
= $false )
| ( ( ( index @ SV24 @ SV66 )
= ( just @ SV73 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[254]) ).
thf(265,plain,
! [SV71: $i,SV63: $i,SV45: $i,SV20: $i] :
( ( ( tc @ SV20 @ ( lam @ SV45 ) @ ( arr @ SV63 @ SV71 ) )
= $false )
| ( ( tc @ ( cons @ SV63 @ SV20 ) @ SV45 @ SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(266,plain,
! [SV71: $i,SV45: $i,SV20: $i,SV63: $i] :
( ( ( tc @ ( cons @ SV63 @ SV20 ) @ SV45 @ SV71 )
= $false )
| ( ( tc @ SV20 @ ( lam @ SV45 ) @ ( arr @ SV63 @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(267,plain,
! [SV46: $i,SV75: $i,SV72: $i,SV64: $i,SV21: $i] :
( ( ( ~ ( tc @ SV21 @ ( app @ SV64 @ SV72 @ SV75 ) @ SV46 ) )
= $true )
| ( ( ~ ( ~ ( tc @ SV21 @ SV64 @ ( arr @ SV75 @ SV46 ) )
| ~ ( tc @ SV21 @ SV72 @ SV75 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(268,plain,
! [SV72: $i,SV46: $i,SV75: $i,SV64: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( tc @ SV21 @ SV64 @ ( arr @ SV75 @ SV46 ) )
| ~ ( tc @ SV21 @ SV72 @ SV75 ) ) )
= $true )
| ( ( tc @ SV21 @ ( app @ SV64 @ SV72 @ SV75 ) @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(269,plain,
! [SV65: $i,SV47: $i,SV22: $i] :
( ( ( ~ ( nf @ ( app @ SV22 @ SV47 @ SV65 ) )
| ~ ( ~ ( nf @ SV22 )
| ~ ( nf @ SV47 ) ) )
= $true )
| ( ( SV22
= ( lam @ ( proj1Lam @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(270,plain,
! [SV65: $i,SV47: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( nf @ SV22 )
| ~ ( nf @ SV47 ) )
| ( nf @ ( app @ SV22 @ SV47 @ SV65 ) ) )
= $true )
| ( ( SV22
= ( lam @ ( proj1Lam @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(271,plain,
! [SV73: $i,SV48: $i,SV66: $i,SV24: $i] :
( ( ( ~ ( tc @ SV24 @ ( var @ SV66 ) @ SV48 )
| ( SV73 = SV48 ) )
= $true )
| ( ( ( index @ SV24 @ SV66 )
= ( just @ SV73 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[263]) ).
thf(272,plain,
! [SV66: $i,SV24: $i,SV48: $i,SV73: $i] :
( ( ( ( SV73 != SV48 )
| ( tc @ SV24 @ ( var @ SV66 ) @ SV48 ) )
= $true )
| ( ( ( index @ SV24 @ SV66 )
= ( just @ SV73 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(273,plain,
! [SV46: $i,SV75: $i,SV72: $i,SV64: $i,SV21: $i] :
( ( ( tc @ SV21 @ ( app @ SV64 @ SV72 @ SV75 ) @ SV46 )
= $false )
| ( ( ~ ( ~ ( tc @ SV21 @ SV64 @ ( arr @ SV75 @ SV46 ) )
| ~ ( tc @ SV21 @ SV72 @ SV75 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(274,plain,
! [SV72: $i,SV46: $i,SV75: $i,SV64: $i,SV21: $i] :
( ( ( ~ ( ~ ( tc @ SV21 @ SV64 @ ( arr @ SV75 @ SV46 ) )
| ~ ( tc @ SV21 @ SV72 @ SV75 ) ) )
= $false )
| ( ( tc @ SV21 @ ( app @ SV64 @ SV72 @ SV75 ) @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(275,plain,
! [SV65: $i,SV47: $i,SV22: $i] :
( ( ( ~ ( nf @ ( app @ SV22 @ SV47 @ SV65 ) ) )
= $true )
| ( ( ~ ( ~ ( nf @ SV22 )
| ~ ( nf @ SV47 ) ) )
= $true )
| ( ( SV22
= ( lam @ ( proj1Lam @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[269]) ).
thf(276,plain,
! [SV65: $i,SV47: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( nf @ SV22 )
| ~ ( nf @ SV47 ) ) )
= $true )
| ( ( nf @ ( app @ SV22 @ SV47 @ SV65 ) )
= $true )
| ( ( SV22
= ( lam @ ( proj1Lam @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(277,plain,
! [SV73: $i,SV48: $i,SV66: $i,SV24: $i] :
( ( ( ~ ( tc @ SV24 @ ( var @ SV66 ) @ SV48 ) )
= $true )
| ( ( SV73 = SV48 )
= $true )
| ( ( ( index @ SV24 @ SV66 )
= ( just @ SV73 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(278,plain,
! [SV66: $i,SV24: $i,SV48: $i,SV73: $i] :
( ( ( SV73 != SV48 )
= $true )
| ( ( tc @ SV24 @ ( var @ SV66 ) @ SV48 )
= $true )
| ( ( ( index @ SV24 @ SV66 )
= ( just @ SV73 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(279,plain,
! [SV72: $i,SV46: $i,SV75: $i,SV64: $i,SV21: $i] :
( ( ( ~ ( tc @ SV21 @ SV64 @ ( arr @ SV75 @ SV46 ) )
| ~ ( tc @ SV21 @ SV72 @ SV75 ) )
= $false )
| ( ( tc @ SV21 @ ( app @ SV64 @ SV72 @ SV75 ) @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(280,plain,
! [SV72: $i,SV46: $i,SV75: $i,SV64: $i,SV21: $i] :
( ( ( ~ ( tc @ SV21 @ SV64 @ ( arr @ SV75 @ SV46 ) )
| ~ ( tc @ SV21 @ SV72 @ SV75 ) )
= $true )
| ( ( tc @ SV21 @ ( app @ SV64 @ SV72 @ SV75 ) @ SV46 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(281,plain,
! [SV65: $i,SV47: $i,SV22: $i] :
( ( ( nf @ ( app @ SV22 @ SV47 @ SV65 ) )
= $false )
| ( ( ~ ( ~ ( nf @ SV22 )
| ~ ( nf @ SV47 ) ) )
= $true )
| ( ( SV22
= ( lam @ ( proj1Lam @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(282,plain,
! [SV65: $i,SV47: $i,SV22: $i] :
( ( ( ~ ( ~ ( nf @ SV22 )
| ~ ( nf @ SV47 ) ) )
= $false )
| ( ( nf @ ( app @ SV22 @ SV47 @ SV65 ) )
= $true )
| ( ( SV22
= ( lam @ ( proj1Lam @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(283,plain,
! [SV73: $i,SV48: $i,SV66: $i,SV24: $i] :
( ( ( tc @ SV24 @ ( var @ SV66 ) @ SV48 )
= $false )
| ( ( SV73 = SV48 )
= $true )
| ( ( ( index @ SV24 @ SV66 )
= ( just @ SV73 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(284,plain,
! [SV66: $i,SV24: $i,SV48: $i,SV73: $i] :
( ( ( SV73 = SV48 )
= $false )
| ( ( tc @ SV24 @ ( var @ SV66 ) @ SV48 )
= $true )
| ( ( ( index @ SV24 @ SV66 )
= ( just @ SV73 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(285,plain,
! [SV72: $i,SV46: $i,SV75: $i,SV64: $i,SV21: $i] :
( ( ( ~ ( tc @ SV21 @ SV64 @ ( arr @ SV75 @ SV46 ) ) )
= $false )
| ( ( tc @ SV21 @ ( app @ SV64 @ SV72 @ SV75 ) @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[279]) ).
thf(286,plain,
! [SV46: $i,SV64: $i,SV75: $i,SV72: $i,SV21: $i] :
( ( ( ~ ( tc @ SV21 @ SV72 @ SV75 ) )
= $false )
| ( ( tc @ SV21 @ ( app @ SV64 @ SV72 @ SV75 ) @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[279]) ).
thf(287,plain,
! [SV72: $i,SV46: $i,SV75: $i,SV64: $i,SV21: $i] :
( ( ( ~ ( tc @ SV21 @ SV64 @ ( arr @ SV75 @ SV46 ) ) )
= $true )
| ( ( ~ ( tc @ SV21 @ SV72 @ SV75 ) )
= $true )
| ( ( tc @ SV21 @ ( app @ SV64 @ SV72 @ SV75 ) @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(288,plain,
! [SV65: $i,SV47: $i,SV22: $i] :
( ( ( ~ ( nf @ SV22 )
| ~ ( nf @ SV47 ) )
= $false )
| ( ( nf @ ( app @ SV22 @ SV47 @ SV65 ) )
= $false )
| ( ( SV22
= ( lam @ ( proj1Lam @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(289,plain,
! [SV65: $i,SV47: $i,SV22: $i] :
( ( ( ~ ( nf @ SV22 )
| ~ ( nf @ SV47 ) )
= $true )
| ( ( nf @ ( app @ SV22 @ SV47 @ SV65 ) )
= $true )
| ( ( SV22
= ( lam @ ( proj1Lam @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[282]) ).
thf(290,plain,
! [SV72: $i,SV46: $i,SV75: $i,SV64: $i,SV21: $i] :
( ( ( tc @ SV21 @ SV64 @ ( arr @ SV75 @ SV46 ) )
= $true )
| ( ( tc @ SV21 @ ( app @ SV64 @ SV72 @ SV75 ) @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(291,plain,
! [SV46: $i,SV64: $i,SV75: $i,SV72: $i,SV21: $i] :
( ( ( tc @ SV21 @ SV72 @ SV75 )
= $true )
| ( ( tc @ SV21 @ ( app @ SV64 @ SV72 @ SV75 ) @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(292,plain,
! [SV72: $i,SV46: $i,SV75: $i,SV64: $i,SV21: $i] :
( ( ( tc @ SV21 @ SV64 @ ( arr @ SV75 @ SV46 ) )
= $false )
| ( ( ~ ( tc @ SV21 @ SV72 @ SV75 ) )
= $true )
| ( ( tc @ SV21 @ ( app @ SV64 @ SV72 @ SV75 ) @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(293,plain,
! [SV65: $i,SV47: $i,SV22: $i] :
( ( ( ~ ( nf @ SV22 ) )
= $false )
| ( ( nf @ ( app @ SV22 @ SV47 @ SV65 ) )
= $false )
| ( ( SV22
= ( lam @ ( proj1Lam @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[288]) ).
thf(294,plain,
! [SV65: $i,SV22: $i,SV47: $i] :
( ( ( ~ ( nf @ SV47 ) )
= $false )
| ( ( nf @ ( app @ SV22 @ SV47 @ SV65 ) )
= $false )
| ( ( SV22
= ( lam @ ( proj1Lam @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[288]) ).
thf(295,plain,
! [SV65: $i,SV47: $i,SV22: $i] :
( ( ( ~ ( nf @ SV22 ) )
= $true )
| ( ( ~ ( nf @ SV47 ) )
= $true )
| ( ( nf @ ( app @ SV22 @ SV47 @ SV65 ) )
= $true )
| ( ( SV22
= ( lam @ ( proj1Lam @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(296,plain,
! [SV46: $i,SV64: $i,SV75: $i,SV72: $i,SV21: $i] :
( ( ( tc @ SV21 @ SV72 @ SV75 )
= $false )
| ( ( tc @ SV21 @ SV64 @ ( arr @ SV75 @ SV46 ) )
= $false )
| ( ( tc @ SV21 @ ( app @ SV64 @ SV72 @ SV75 ) @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(297,plain,
! [SV65: $i,SV47: $i,SV22: $i] :
( ( ( nf @ SV22 )
= $true )
| ( ( nf @ ( app @ SV22 @ SV47 @ SV65 ) )
= $false )
| ( ( SV22
= ( lam @ ( proj1Lam @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(298,plain,
! [SV65: $i,SV22: $i,SV47: $i] :
( ( ( nf @ SV47 )
= $true )
| ( ( nf @ ( app @ SV22 @ SV47 @ SV65 ) )
= $false )
| ( ( SV22
= ( lam @ ( proj1Lam @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[294]) ).
thf(299,plain,
! [SV65: $i,SV47: $i,SV22: $i] :
( ( ( nf @ SV22 )
= $false )
| ( ( ~ ( nf @ SV47 ) )
= $true )
| ( ( nf @ ( app @ SV22 @ SV47 @ SV65 ) )
= $true )
| ( ( SV22
= ( lam @ ( proj1Lam @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(300,plain,
! [SV65: $i,SV22: $i,SV47: $i] :
( ( ( nf @ SV47 )
= $false )
| ( ( nf @ SV22 )
= $false )
| ( ( nf @ ( app @ SV22 @ SV47 @ SV65 ) )
= $true )
| ( ( SV22
= ( lam @ ( proj1Lam @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(301,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[135,300,298,297,296,291,290,284,283,266,265,256,255,247,244,243,235,227,215,214,211,209,208,200,198,196,195,194,189,179,175,170,169,168,167,157,150,147,144,143,141,140,136]) ).
thf(302,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[301]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX223+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.22 % Computer : n026.cluster.edu
% 0.08/0.22 % Model : x86_64 x86_64
% 0.08/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.22 % Memory : 8046.5625MB
% 0.08/0.22 % OS : Linux 6.8.0-71-generic
% 0.08/0.22 % CPULimit : 300
% 0.08/0.22 % WCLimit : 300
% 0.08/0.22 % DateTime : Tue Oct 6 17:16:28 UTC 2026
% 0.08/0.22 % CPUTime :
% 0.08/0.22 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.49/0.55
% 1.49/0.55 No.of.Axioms: 35
% 1.49/0.55
% 1.49/0.55 Length.of.Defs: 0
% 1.49/0.55
% 1.49/0.55 Contains.Choice.Funs: false
% 1.49/0.55 .........
% 1.49/0.55
% 1.49/0.55 ********************************
% 1.49/0.55 * All subproblems solved! *
% 1.49/0.55 ********************************
% 1.49/0.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:35,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:301,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.49/0.55
% 1.49/0.55 %**** Beginning of derivation protocol ****
% 1.49/0.55 % SZS output start CNFRefutation
% See solution above
% 1.49/0.55
% 1.49/0.55 %**** End of derivation protocol ****
% 1.49/0.55 %**** no. of clauses in derivation: 302 ****
% 1.49/0.55 %**** clause counter: 301 ****
% 1.49/0.55
% 1.49/0.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:35,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:301,loop_count:0,foatp_calls:1,translation:fof_full)
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