%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWX221+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 11:02:35 AM UTC 2026
% Result : Theorem 7.21s 1.66s
% Output : CNFRefutation 7.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 36
% Syntax : Number of formulae : 316 ( 258 unt; 0 typ; 0 def)
% Number of atoms : 1375 ( 626 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 2923 ( 408 ~; 315 |; 22 &;2160 @)
% ( 10 <=>; 8 =>; 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 : 927 ( 0 ^; 923 !; 4 ?; 927 :)
% 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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',axiom_030) ).
thf(7,axiom,
! [Z: $i,Xs: $i] :
( ( index @ ( cons @ Z @ Xs ) @ zero )
= ( just @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_029) ).
thf(8,axiom,
! [Y: $i] :
( ( index @ nil @ Y )
= nothing ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_028) ).
thf(9,axiom,
! [X4: $i] : ( nf @ ( var @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_027) ).
thf(10,axiom,
! [E: $i] :
( ( nf @ ( lam @ E ) )
<=> ( nf @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_026) ).
thf(11,axiom,
! [Z: $i,X2: $i,X3: $i] :
~ ( nf @ ( app @ ( lam @ X3 ) @ Z @ X2 ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',axiom_024) ).
thf(13,axiom,
! [X: $i,X2: $i] :
( ( lam @ X )
!= ( var @ X2 ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',axiom_021) ).
thf(16,axiom,
! [X: $i] :
( ( proj1Var @ ( var @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
thf(17,axiom,
! [X: $i] :
( ( proj1Lam @ ( lam @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
thf(18,axiom,
! [X: $i,X2: $i,X3: $i] :
( ( proj3App @ ( app @ X @ X2 @ X3 ) )
= X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_018) ).
thf(19,axiom,
! [X: $i,X2: $i,X3: $i] :
( ( proj2App @ ( app @ X @ X2 @ X3 ) )
= X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_017) ).
thf(20,axiom,
! [X: $i,X2: $i,X3: $i] :
( ( proj1App @ ( app @ X @ X2 @ X3 ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
thf(21,axiom,
! [X: $i] :
( nothing
!= ( just @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
thf(22,axiom,
! [X: $i] :
( ( proj1Just @ ( just @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
thf(23,axiom,
! [X: $i] :
( zero
!= ( suc @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_013) ).
thf(24,axiom,
! [X: $i] :
( ( proj1Suc @ ( suc @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
thf(25,axiom,
b != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
thf(26,axiom,
a != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
thf(27,axiom,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
thf(28,axiom,
! [X: $i,X2: $i] :
( ( arr @ X @ X2 )
!= c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
thf(29,axiom,
! [X: $i,X2: $i] :
( ( arr @ X @ X2 )
!= b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
thf(30,axiom,
! [X: $i,X2: $i] :
( ( arr @ X @ X2 )
!= a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
thf(31,axiom,
! [X: $i,X2: $i] :
( ( proj2Arr @ ( arr @ X @ X2 ) )
= X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
thf(32,axiom,
! [X: $i,X2: $i] :
( ( proj1Arr @ ( arr @ X @ X2 ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
thf(33,axiom,
! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
thf(34,axiom,
! [X: $i,X2: $i] :
( ( tail @ ( cons @ X @ X2 ) )
= X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
thf(35,axiom,
! [X: $i,X2: $i] :
( ( head @ ( cons @ X @ X2 ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
thf(36,conjecture,
? [E: $i] :
( ( nf @ E )
& ( tc @ nil @ E @ ( arr @ ( arr @ a @ ( arr @ b @ c ) ) @ ( arr @ b @ ( arr @ a @ c ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_036) ).
thf(37,negated_conjecture,
( ( ? [E: $i] :
( ( nf @ E )
& ( tc @ nil @ E @ ( arr @ ( arr @ a @ ( arr @ b @ c ) ) @ ( arr @ b @ ( arr @ a @ c ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[36]) ).
thf(38,plain,
( ( ? [E: $i] :
( ( nf @ E )
& ( tc @ nil @ E @ ( arr @ ( arr @ a @ ( arr @ b @ c ) ) @ ( arr @ b @ ( arr @ a @ c ) ) ) ) ) )
= $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 @ b @ c ) ) @ ( arr @ b @ ( arr @ a @ c ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[38]) ).
thf(75,plain,
( ( ! [E: $i] :
( ~ ( nf @ E )
| ~ ( tc @ nil @ E @ ( arr @ ( arr @ a @ ( arr @ b @ c ) ) @ ( arr @ b @ ( arr @ a @ c ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[74]) ).
thf(76,plain,
( ( ! [X: $i,Z: $i] :
( ! [X3: $i,Tx3: $i] :
( ( ( index @ X @ X3 )
!= ( just @ Tx3 ) )
| ( Tx3 != Z )
| ( tc @ X @ ( var @ X3 ) @ Z ) )
& ! [X3: $i,Tx3: $i] :
( ( ( index @ X @ X3 )
!= ( just @ Tx3 ) )
| ~ ( tc @ X @ ( var @ X3 ) @ Z )
| ( Tx3 = Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(77,plain,
( ( ! [X: $i,Z: $i,X3: $i] :
( ( ( index @ X @ X3 )
!= nothing )
| ~ ( tc @ X @ ( var @ X3 ) @ Z ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(78,plain,
( ( ! [X: $i,E: $i] :
( ! [Tx2: $i,T1: $i] :
( ~ ( tc @ X @ ( lam @ E ) @ ( arr @ Tx2 @ T1 ) )
| ( tc @ ( cons @ Tx2 @ X ) @ E @ T1 ) )
& ! [Tx2: $i,T1: $i] :
( ~ ( tc @ ( cons @ Tx2 @ X ) @ E @ T1 )
| ( tc @ X @ ( lam @ E ) @ ( arr @ Tx2 @ T1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(79,plain,
( ( ! [X: $i,Z: $i] :
( ( Z
= ( arr @ ( proj1Arr @ Z ) @ ( proj2Arr @ Z ) ) )
| ! [E: $i] :
~ ( tc @ X @ ( lam @ E ) @ Z ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(80,plain,
( ( ! [X: $i,Z: $i,F: $i] :
( ! [X2: $i,Tx: $i] :
( ~ ( tc @ X @ F @ ( arr @ Tx @ Z ) )
| ~ ( tc @ X @ X2 @ Tx )
| ( tc @ X @ ( app @ F @ X2 @ Tx ) @ Z ) )
& ! [X2: $i,Tx: $i] :
( ~ ( tc @ X @ ( app @ F @ X2 @ Tx ) @ Z )
| ( tc @ X @ F @ ( arr @ Tx @ Z ) ) )
& ! [X2: $i,Tx: $i] :
( ~ ( tc @ X @ ( app @ F @ X2 @ Tx ) @ Z )
| ( tc @ X @ X2 @ Tx ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(81,plain,
( ( ! [E: $i] :
( ~ ( nf @ ( lam @ E ) )
| ( nf @ E ) )
& ! [E: $i] :
( ~ ( nf @ E )
| ( nf @ ( lam @ E ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(82,plain,
( ( ! [Y: $i] :
( ( ( Y
= ( lam @ ( proj1Lam @ Y ) ) )
| ! [Z: $i] :
( ~ ( nf @ Y )
| ~ ( nf @ Z )
| ! [X2: $i] : ( nf @ ( app @ Y @ Z @ X2 ) ) ) )
& ( ( Y
= ( lam @ ( proj1Lam @ Y ) ) )
| ! [Z: $i,X2: $i] :
~ ( nf @ ( app @ Y @ Z @ X2 ) )
| ( nf @ Y ) )
& ( ( Y
= ( lam @ ( proj1Lam @ Y ) ) )
| ! [Z: $i] :
( ! [X2: $i] :
~ ( nf @ ( app @ Y @ Z @ X2 ) )
| ( nf @ Z ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(83,plain,
( ( ! [X: $i,X2: $i] :
( ( lam @ X )
!= ( var @ X2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(84,plain,
( ( ! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( app @ X @ X2 @ X3 )
!= ( var @ X4 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(85,plain,
( ( ! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( app @ X @ X2 @ X3 )
!= ( lam @ X4 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(86,plain,
( ( ! [X: $i] :
( nothing
!= ( just @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[59]) ).
thf(87,plain,
( ( ! [X: $i] :
( zero
!= ( suc @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[61]) ).
thf(88,plain,
( ( b != c )
= $true ),
inference(extcnf_combined,[status(esa)],[63]) ).
thf(89,plain,
( ( a != c )
= $true ),
inference(extcnf_combined,[status(esa)],[64]) ).
thf(90,plain,
( ( a != b )
= $true ),
inference(extcnf_combined,[status(esa)],[65]) ).
thf(91,plain,
( ( ! [X: $i,X2: $i] :
( ( arr @ X @ X2 )
!= c ) )
= $true ),
inference(extcnf_combined,[status(esa)],[66]) ).
thf(92,plain,
( ( ! [X: $i,X2: $i] :
( ( arr @ X @ X2 )
!= b ) )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
thf(93,plain,
( ( ! [X: $i,X2: $i] :
( ( arr @ X @ X2 )
!= a ) )
= $true ),
inference(extcnf_combined,[status(esa)],[68]) ).
thf(94,plain,
( ( ! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[71]) ).
thf(95,plain,
( ( ! [X: $i,X2: $i] :
( ( head @ ( cons @ X @ X2 ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(96,plain,
( ( ! [X: $i,X2: $i] :
( ( tail @ ( cons @ X @ X2 ) )
= X2 ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(97,plain,
( ( ! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(98,plain,
( ( ! [X: $i,X2: $i] :
( ( proj1Arr @ ( arr @ X @ X2 ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(99,plain,
( ( ! [X: $i,X2: $i] :
( ( proj2Arr @ ( arr @ X @ X2 ) )
= X2 ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(100,plain,
( ( ! [X: $i,X2: $i] :
( ( arr @ X @ X2 )
!= a ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(101,plain,
( ( ! [X: $i,X2: $i] :
( ( arr @ X @ X2 )
!= b ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(102,plain,
( ( ! [X: $i,X2: $i] :
( ( arr @ X @ X2 )
!= c ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(103,plain,
( ( a != b )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(104,plain,
( ( a != c )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(105,plain,
( ( b != c )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(106,plain,
( ( ! [X: $i] :
( ( proj1Suc @ ( suc @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(107,plain,
( ( ! [X: $i] :
( zero
!= ( suc @ X ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(108,plain,
( ( ! [X: $i] :
( ( proj1Just @ ( just @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(109,plain,
( ( ! [X: $i] :
( nothing
!= ( just @ X ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(110,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( proj1App @ ( app @ X @ X2 @ X3 ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(111,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( proj2App @ ( app @ X @ X2 @ X3 ) )
= X2 ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(112,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( proj3App @ ( app @ X @ X2 @ X3 ) )
= X3 ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(113,plain,
( ( ! [X: $i] :
( ( proj1Lam @ ( lam @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(114,plain,
( ( ! [X: $i] :
( ( proj1Var @ ( var @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(115,plain,
( ( ! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( app @ X @ X2 @ X3 )
!= ( lam @ X4 ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(116,plain,
( ( ! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( app @ X @ X2 @ X3 )
!= ( var @ X4 ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(117,plain,
( ( ! [X: $i,X2: $i] :
( ( lam @ X )
!= ( var @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(118,plain,
( ( ! [Y: $i] :
( ( ( Y
= ( lam @ ( proj1Lam @ Y ) ) )
| ! [Z: $i] :
( ~ ( nf @ Y )
| ~ ( nf @ Z )
| ! [X2: $i] : ( nf @ ( app @ Y @ Z @ X2 ) ) ) )
& ( ( Y
= ( lam @ ( proj1Lam @ Y ) ) )
| ! [Z: $i,X2: $i] :
~ ( nf @ ( app @ Y @ Z @ X2 ) )
| ( nf @ Y ) )
& ( ( Y
= ( lam @ ( proj1Lam @ Y ) ) )
| ! [Z: $i] :
( ! [X2: $i] :
~ ( nf @ ( app @ Y @ Z @ X2 ) )
| ( nf @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(119,plain,
( ( ! [Z: $i,X2: $i,X3: $i] :
~ ( nf @ ( app @ ( lam @ X3 ) @ Z @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(120,plain,
( ( ! [E: $i] :
( ~ ( nf @ ( lam @ E ) )
| ( nf @ E ) )
& ! [E: $i] :
( ~ ( nf @ E )
| ( nf @ ( lam @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(121,plain,
( ( ! [X4: $i] : ( nf @ ( var @ X4 ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(122,plain,
( ( ! [Y: $i] :
( ( index @ nil @ Y )
= nothing ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(123,plain,
( ( ! [Z: $i,Xs: $i] :
( ( index @ ( cons @ Z @ Xs ) @ zero )
= ( just @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(124,plain,
( ( ! [Z: $i,Xs: $i,N: $i] :
( ( index @ ( cons @ Z @ Xs ) @ ( suc @ N ) )
= ( index @ Xs @ N ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(125,plain,
( ( ! [X: $i,Z: $i,F: $i] :
( ! [X2: $i,Tx: $i] :
( ~ ( tc @ X @ F @ ( arr @ Tx @ Z ) )
| ~ ( tc @ X @ X2 @ Tx )
| ( tc @ X @ ( app @ F @ X2 @ Tx ) @ Z ) )
& ! [X2: $i,Tx: $i] :
( ~ ( tc @ X @ ( app @ F @ X2 @ Tx ) @ Z )
| ( tc @ X @ F @ ( arr @ Tx @ Z ) ) )
& ! [X2: $i,Tx: $i] :
( ~ ( tc @ X @ ( app @ F @ X2 @ Tx ) @ Z )
| ( tc @ X @ X2 @ Tx ) ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(126,plain,
( ( ! [X: $i,Z: $i] :
( ( Z
= ( arr @ ( proj1Arr @ Z ) @ ( proj2Arr @ Z ) ) )
| ! [E: $i] :
~ ( tc @ X @ ( lam @ E ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(127,plain,
( ( ! [X: $i,E: $i] :
( ! [Tx2: $i,T1: $i] :
( ~ ( tc @ X @ ( lam @ E ) @ ( arr @ Tx2 @ T1 ) )
| ( tc @ ( cons @ Tx2 @ X ) @ E @ T1 ) )
& ! [Tx2: $i,T1: $i] :
( ~ ( tc @ ( cons @ Tx2 @ X ) @ E @ T1 )
| ( tc @ X @ ( lam @ E ) @ ( arr @ Tx2 @ T1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(128,plain,
( ( ! [X: $i,Z: $i,X3: $i] :
( ( ( index @ X @ X3 )
!= nothing )
| ~ ( tc @ X @ ( var @ X3 ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(129,plain,
( ( ! [X: $i,Z: $i] :
( ! [X3: $i,Tx3: $i] :
( ( ( index @ X @ X3 )
!= ( just @ Tx3 ) )
| ( Tx3 != Z )
| ( tc @ X @ ( var @ X3 ) @ Z ) )
& ! [X3: $i,Tx3: $i] :
( ( ( index @ X @ X3 )
!= ( just @ Tx3 ) )
| ~ ( tc @ X @ ( var @ X3 ) @ Z )
| ( Tx3 = Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(130,plain,
( ( ! [E: $i] :
( ~ ( nf @ E )
| ~ ( tc @ nil @ E @ ( arr @ ( arr @ a @ ( arr @ b @ c ) ) @ ( arr @ b @ ( arr @ a @ c ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(131,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( SX0
= ( lam @ ( proj1Lam @ SX0 ) ) )
| ! [SX1: $i] :
( ~ ( nf @ SX0 )
| ~ ( nf @ SX1 )
| ! [SX2: $i] : ( nf @ ( app @ SX0 @ SX1 @ SX2 ) ) ) )
| ~ ~ ( ~ ( ( SX0
= ( lam @ ( proj1Lam @ SX0 ) ) )
| ! [SX1: $i,SX2: $i] :
~ ( nf @ ( app @ SX0 @ SX1 @ SX2 ) )
| ( nf @ SX0 ) )
| ~ ( ( SX0
= ( lam @ ( proj1Lam @ SX0 ) ) )
| ! [SX1: $i] :
( ! [SX2: $i] :
~ ( nf @ ( app @ SX0 @ SX1 @ SX2 ) )
| ( nf @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(132,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ( ( index @ SX0 @ SX2 )
!= ( just @ SX3 ) )
| ( SX3 != SX1 )
| ( tc @ SX0 @ ( var @ SX2 ) @ SX1 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( ( index @ SX0 @ SX2 )
!= ( just @ SX3 ) )
| ~ ( tc @ SX0 @ ( var @ SX2 ) @ SX1 )
| ( SX3 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(133,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( nf @ ( lam @ SX0 ) )
| ( nf @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( nf @ SX0 )
| ( nf @ ( lam @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(134,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( tc @ SX0 @ ( lam @ SX1 ) @ ( arr @ SX2 @ SX3 ) )
| ( tc @ ( cons @ SX2 @ SX0 ) @ SX1 @ SX3 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( tc @ ( cons @ SX2 @ SX0 ) @ SX1 @ SX3 )
| ( tc @ SX0 @ ( lam @ SX1 ) @ ( arr @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(135,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( tc @ SX0 @ SX2 @ ( arr @ SX4 @ SX1 ) )
| ~ ( tc @ SX0 @ SX3 @ SX4 )
| ( tc @ SX0 @ ( app @ SX2 @ SX3 @ SX4 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( tc @ SX0 @ ( app @ SX2 @ SX3 @ SX4 ) @ SX1 )
| ( tc @ SX0 @ SX2 @ ( arr @ SX4 @ SX1 ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( tc @ SX0 @ ( app @ SX2 @ SX3 @ SX4 ) @ SX1 )
| ( tc @ SX0 @ SX3 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(136,plain,
! [SV1: $i] :
( ( ! [SY75: $i] :
( ( head @ ( cons @ SV1 @ SY75 ) )
= SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(137,plain,
! [SV2: $i] :
( ( ! [SY76: $i] :
( ( tail @ ( cons @ SV2 @ SY76 ) )
= SY76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(138,plain,
! [SV3: $i] :
( ( ! [SY77: $i] :
( nil
!= ( cons @ SV3 @ SY77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(139,plain,
! [SV4: $i] :
( ( ! [SY78: $i] :
( ( proj1Arr @ ( arr @ SV4 @ SY78 ) )
= SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(140,plain,
! [SV5: $i] :
( ( ! [SY79: $i] :
( ( proj2Arr @ ( arr @ SV5 @ SY79 ) )
= SY79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(141,plain,
! [SV6: $i] :
( ( ! [SY80: $i] :
( ( arr @ SV6 @ SY80 )
!= a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(142,plain,
! [SV7: $i] :
( ( ! [SY81: $i] :
( ( arr @ SV7 @ SY81 )
!= b ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(143,plain,
! [SV8: $i] :
( ( ! [SY82: $i] :
( ( arr @ SV8 @ SY82 )
!= c ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(144,plain,
( ( a = b )
= $false ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(145,plain,
( ( a = c )
= $false ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(146,plain,
( ( b = c )
= $false ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(147,plain,
! [SV9: $i] :
( ( ( proj1Suc @ ( suc @ SV9 ) )
= SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(148,plain,
! [SV10: $i] :
( ( zero
!= ( suc @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(149,plain,
! [SV11: $i] :
( ( ( proj1Just @ ( just @ SV11 ) )
= SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(150,plain,
! [SV12: $i] :
( ( nothing
!= ( just @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(151,plain,
! [SV13: $i] :
( ( ! [SY83: $i,SY84: $i] :
( ( proj1App @ ( app @ SV13 @ SY83 @ SY84 ) )
= SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(152,plain,
! [SV14: $i] :
( ( ! [SY85: $i,SY86: $i] :
( ( proj2App @ ( app @ SV14 @ SY85 @ SY86 ) )
= SY85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(153,plain,
! [SV15: $i] :
( ( ! [SY87: $i,SY88: $i] :
( ( proj3App @ ( app @ SV15 @ SY87 @ SY88 ) )
= SY88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(154,plain,
! [SV16: $i] :
( ( ( proj1Lam @ ( lam @ SV16 ) )
= SV16 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(155,plain,
! [SV17: $i] :
( ( ( proj1Var @ ( var @ SV17 ) )
= SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(156,plain,
! [SV18: $i] :
( ( ! [SY89: $i,SY90: $i,SY91: $i] :
( ( app @ SV18 @ SY89 @ SY90 )
!= ( lam @ SY91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(157,plain,
! [SV19: $i] :
( ( ! [SY92: $i,SY93: $i,SY94: $i] :
( ( app @ SV19 @ SY92 @ SY93 )
!= ( var @ SY94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(158,plain,
! [SV20: $i] :
( ( ! [SY95: $i] :
( ( lam @ SV20 )
!= ( var @ SY95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(159,plain,
! [SV21: $i] :
( ( ! [SY96: $i,SY97: $i] :
~ ( nf @ ( app @ ( lam @ SY97 ) @ SV21 @ SY96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(160,plain,
! [SV22: $i] :
( ( nf @ ( var @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(161,plain,
! [SV23: $i] :
( ( ( index @ nil @ SV23 )
= nothing )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(162,plain,
! [SV24: $i] :
( ( ! [SY98: $i] :
( ( index @ ( cons @ SV24 @ SY98 ) @ zero )
= ( just @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(163,plain,
! [SV25: $i] :
( ( ! [SY99: $i,SY100: $i] :
( ( index @ ( cons @ SV25 @ SY99 ) @ ( suc @ SY100 ) )
= ( index @ SY99 @ SY100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(164,plain,
! [SV26: $i] :
( ( ! [SY101: $i] :
( ( SY101
= ( arr @ ( proj1Arr @ SY101 ) @ ( proj2Arr @ SY101 ) ) )
| ! [SY102: $i] :
~ ( tc @ SV26 @ ( lam @ SY102 ) @ SY101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(165,plain,
! [SV27: $i] :
( ( ! [SY103: $i,SY104: $i] :
( ( ( index @ SV27 @ SY104 )
!= nothing )
| ~ ( tc @ SV27 @ ( var @ SY104 ) @ SY103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(166,plain,
! [SV28: $i] :
( ( ~ ( nf @ SV28 )
| ~ ( tc @ nil @ SV28 @ ( arr @ ( arr @ a @ ( arr @ b @ c ) ) @ ( arr @ b @ ( arr @ a @ c ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(167,plain,
! [SV29: $i] :
( ( ~ ( ~ ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
| ! [SY105: $i] :
( ~ ( nf @ SV29 )
| ~ ( nf @ SY105 )
| ! [SY106: $i] : ( nf @ ( app @ SV29 @ SY105 @ SY106 ) ) ) )
| ~ ~ ( ~ ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
| ! [SY107: $i,SY108: $i] :
~ ( nf @ ( app @ SV29 @ SY107 @ SY108 ) )
| ( nf @ SV29 ) )
| ~ ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
| ! [SY109: $i] :
( ! [SY110: $i] :
~ ( nf @ ( app @ SV29 @ SY109 @ SY110 ) )
| ( nf @ SY109 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(168,plain,
! [SV30: $i] :
( ( ! [SY111: $i] :
~ ( ~ ! [SY112: $i,SY113: $i] :
( ( ( index @ SV30 @ SY112 )
!= ( just @ SY113 ) )
| ( SY113 != SY111 )
| ( tc @ SV30 @ ( var @ SY112 ) @ SY111 ) )
| ~ ! [SY114: $i,SY115: $i] :
( ( ( index @ SV30 @ SY114 )
!= ( just @ SY115 ) )
| ~ ( tc @ SV30 @ ( var @ SY114 ) @ SY111 )
| ( SY115 = SY111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(169,plain,
( ( ~ ! [SX0: $i] :
( ~ ( nf @ ( lam @ SX0 ) )
| ( nf @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( nf @ SX0 )
| ( nf @ ( lam @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(170,plain,
! [SV31: $i] :
( ( ! [SY116: $i] :
~ ( ~ ! [SY117: $i,SY118: $i] :
( ~ ( tc @ SV31 @ ( lam @ SY116 ) @ ( arr @ SY117 @ SY118 ) )
| ( tc @ ( cons @ SY117 @ SV31 ) @ SY116 @ SY118 ) )
| ~ ! [SY119: $i,SY120: $i] :
( ~ ( tc @ ( cons @ SY119 @ SV31 ) @ SY116 @ SY120 )
| ( tc @ SV31 @ ( lam @ SY116 ) @ ( arr @ SY119 @ SY120 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(171,plain,
! [SV32: $i] :
( ( ! [SY121: $i,SY122: $i] :
~ ( ~ ! [SY123: $i,SY124: $i] :
( ~ ( tc @ SV32 @ SY122 @ ( arr @ SY124 @ SY121 ) )
| ~ ( tc @ SV32 @ SY123 @ SY124 )
| ( tc @ SV32 @ ( app @ SY122 @ SY123 @ SY124 ) @ SY121 ) )
| ~ ~ ( ~ ! [SY125: $i,SY126: $i] :
( ~ ( tc @ SV32 @ ( app @ SY122 @ SY125 @ SY126 ) @ SY121 )
| ( tc @ SV32 @ SY122 @ ( arr @ SY126 @ SY121 ) ) )
| ~ ! [SY127: $i,SY128: $i] :
( ~ ( tc @ SV32 @ ( app @ SY122 @ SY127 @ SY128 ) @ SY121 )
| ( tc @ SV32 @ SY127 @ SY128 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(172,plain,
! [SV33: $i,SV1: $i] :
( ( ( head @ ( cons @ SV1 @ SV33 ) )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(173,plain,
! [SV34: $i,SV2: $i] :
( ( ( tail @ ( cons @ SV2 @ SV34 ) )
= SV34 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(174,plain,
! [SV35: $i,SV3: $i] :
( ( nil
!= ( cons @ SV3 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(175,plain,
! [SV36: $i,SV4: $i] :
( ( ( proj1Arr @ ( arr @ SV4 @ SV36 ) )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(176,plain,
! [SV37: $i,SV5: $i] :
( ( ( proj2Arr @ ( arr @ SV5 @ SV37 ) )
= SV37 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(177,plain,
! [SV38: $i,SV6: $i] :
( ( ( arr @ SV6 @ SV38 )
!= a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(178,plain,
! [SV39: $i,SV7: $i] :
( ( ( arr @ SV7 @ SV39 )
!= b )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(179,plain,
! [SV40: $i,SV8: $i] :
( ( ( arr @ SV8 @ SV40 )
!= c )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(180,plain,
! [SV10: $i] :
( ( zero
= ( suc @ SV10 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(181,plain,
! [SV12: $i] :
( ( nothing
= ( just @ SV12 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(182,plain,
! [SV41: $i,SV13: $i] :
( ( ! [SY129: $i] :
( ( proj1App @ ( app @ SV13 @ SV41 @ SY129 ) )
= SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(183,plain,
! [SV42: $i,SV14: $i] :
( ( ! [SY130: $i] :
( ( proj2App @ ( app @ SV14 @ SV42 @ SY130 ) )
= SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(184,plain,
! [SV43: $i,SV15: $i] :
( ( ! [SY131: $i] :
( ( proj3App @ ( app @ SV15 @ SV43 @ SY131 ) )
= SY131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(185,plain,
! [SV44: $i,SV18: $i] :
( ( ! [SY132: $i,SY133: $i] :
( ( app @ SV18 @ SV44 @ SY132 )
!= ( lam @ SY133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(186,plain,
! [SV45: $i,SV19: $i] :
( ( ! [SY134: $i,SY135: $i] :
( ( app @ SV19 @ SV45 @ SY134 )
!= ( var @ SY135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(187,plain,
! [SV46: $i,SV20: $i] :
( ( ( lam @ SV20 )
!= ( var @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(188,plain,
! [SV47: $i,SV21: $i] :
( ( ! [SY136: $i] :
~ ( nf @ ( app @ ( lam @ SY136 ) @ SV21 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(189,plain,
! [SV48: $i,SV24: $i] :
( ( ( index @ ( cons @ SV24 @ SV48 ) @ zero )
= ( just @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(190,plain,
! [SV49: $i,SV25: $i] :
( ( ! [SY137: $i] :
( ( index @ ( cons @ SV25 @ SV49 ) @ ( suc @ SY137 ) )
= ( index @ SV49 @ SY137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(191,plain,
! [SV26: $i,SV50: $i] :
( ( ( SV50
= ( arr @ ( proj1Arr @ SV50 ) @ ( proj2Arr @ SV50 ) ) )
| ! [SY138: $i] :
~ ( tc @ SV26 @ ( lam @ SY138 ) @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(192,plain,
! [SV51: $i,SV27: $i] :
( ( ! [SY139: $i] :
( ( ( index @ SV27 @ SY139 )
!= nothing )
| ~ ( tc @ SV27 @ ( var @ SY139 ) @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(193,plain,
! [SV28: $i] :
( ( ( ~ ( nf @ SV28 ) )
= $true )
| ( ( ~ ( tc @ nil @ SV28 @ ( arr @ ( arr @ a @ ( arr @ b @ c ) ) @ ( arr @ b @ ( arr @ a @ c ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(194,plain,
! [SV29: $i] :
( ( ~ ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
| ! [SY105: $i] :
( ~ ( nf @ SV29 )
| ~ ( nf @ SY105 )
| ! [SY106: $i] : ( nf @ ( app @ SV29 @ SY105 @ SY106 ) ) ) )
| ~ ~ ( ~ ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
| ! [SY107: $i,SY108: $i] :
~ ( nf @ ( app @ SV29 @ SY107 @ SY108 ) )
| ( nf @ SV29 ) )
| ~ ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
| ! [SY109: $i] :
( ! [SY110: $i] :
~ ( nf @ ( app @ SV29 @ SY109 @ SY110 ) )
| ( nf @ SY109 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(195,plain,
! [SV52: $i,SV30: $i] :
( ( ~ ( ~ ! [SY140: $i,SY141: $i] :
( ( ( index @ SV30 @ SY140 )
!= ( just @ SY141 ) )
| ( SY141 != SV52 )
| ( tc @ SV30 @ ( var @ SY140 ) @ SV52 ) )
| ~ ! [SY142: $i,SY143: $i] :
( ( ( index @ SV30 @ SY142 )
!= ( just @ SY143 ) )
| ~ ( tc @ SV30 @ ( var @ SY142 ) @ SV52 )
| ( SY143 = SV52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(196,plain,
( ( ~ ! [SX0: $i] :
( ~ ( nf @ ( lam @ SX0 ) )
| ( nf @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[169]) ).
thf(197,plain,
( ( ~ ! [SX0: $i] :
( ~ ( nf @ SX0 )
| ( nf @ ( lam @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[169]) ).
thf(198,plain,
! [SV53: $i,SV31: $i] :
( ( ~ ( ~ ! [SY144: $i,SY145: $i] :
( ~ ( tc @ SV31 @ ( lam @ SV53 ) @ ( arr @ SY144 @ SY145 ) )
| ( tc @ ( cons @ SY144 @ SV31 ) @ SV53 @ SY145 ) )
| ~ ! [SY146: $i,SY147: $i] :
( ~ ( tc @ ( cons @ SY146 @ SV31 ) @ SV53 @ SY147 )
| ( tc @ SV31 @ ( lam @ SV53 ) @ ( arr @ SY146 @ SY147 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(199,plain,
! [SV54: $i,SV32: $i] :
( ( ! [SY148: $i] :
~ ( ~ ! [SY149: $i,SY150: $i] :
( ~ ( tc @ SV32 @ SY148 @ ( arr @ SY150 @ SV54 ) )
| ~ ( tc @ SV32 @ SY149 @ SY150 )
| ( tc @ SV32 @ ( app @ SY148 @ SY149 @ SY150 ) @ SV54 ) )
| ~ ~ ( ~ ! [SY151: $i,SY152: $i] :
( ~ ( tc @ SV32 @ ( app @ SY148 @ SY151 @ SY152 ) @ SV54 )
| ( tc @ SV32 @ SY148 @ ( arr @ SY152 @ SV54 ) ) )
| ~ ! [SY153: $i,SY154: $i] :
( ~ ( tc @ SV32 @ ( app @ SY148 @ SY153 @ SY154 ) @ SV54 )
| ( tc @ SV32 @ SY153 @ SY154 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(200,plain,
! [SV35: $i,SV3: $i] :
( ( nil
= ( cons @ SV3 @ SV35 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(201,plain,
! [SV38: $i,SV6: $i] :
( ( ( arr @ SV6 @ SV38 )
= a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(202,plain,
! [SV39: $i,SV7: $i] :
( ( ( arr @ SV7 @ SV39 )
= b )
= $false ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(203,plain,
! [SV40: $i,SV8: $i] :
( ( ( arr @ SV8 @ SV40 )
= c )
= $false ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(204,plain,
! [SV55: $i,SV41: $i,SV13: $i] :
( ( ( proj1App @ ( app @ SV13 @ SV41 @ SV55 ) )
= SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(205,plain,
! [SV56: $i,SV42: $i,SV14: $i] :
( ( ( proj2App @ ( app @ SV14 @ SV42 @ SV56 ) )
= SV42 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(206,plain,
! [SV57: $i,SV43: $i,SV15: $i] :
( ( ( proj3App @ ( app @ SV15 @ SV43 @ SV57 ) )
= SV57 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(207,plain,
! [SV58: $i,SV44: $i,SV18: $i] :
( ( ! [SY155: $i] :
( ( app @ SV18 @ SV44 @ SV58 )
!= ( lam @ SY155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(208,plain,
! [SV59: $i,SV45: $i,SV19: $i] :
( ( ! [SY156: $i] :
( ( app @ SV19 @ SV45 @ SV59 )
!= ( var @ SY156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(209,plain,
! [SV46: $i,SV20: $i] :
( ( ( lam @ SV20 )
= ( var @ SV46 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(210,plain,
! [SV47: $i,SV21: $i,SV60: $i] :
( ( ~ ( nf @ ( app @ ( lam @ SV60 ) @ SV21 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(211,plain,
! [SV61: $i,SV49: $i,SV25: $i] :
( ( ( index @ ( cons @ SV25 @ SV49 ) @ ( suc @ SV61 ) )
= ( index @ SV49 @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(212,plain,
! [SV26: $i,SV50: $i] :
( ( ( SV50
= ( arr @ ( proj1Arr @ SV50 ) @ ( proj2Arr @ SV50 ) ) )
= $true )
| ( ( ! [SY138: $i] :
~ ( tc @ SV26 @ ( lam @ SY138 ) @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(213,plain,
! [SV51: $i,SV62: $i,SV27: $i] :
( ( ( ( index @ SV27 @ SV62 )
!= nothing )
| ~ ( tc @ SV27 @ ( var @ SV62 ) @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(214,plain,
! [SV28: $i] :
( ( ( nf @ SV28 )
= $false )
| ( ( ~ ( tc @ nil @ SV28 @ ( arr @ ( arr @ a @ ( arr @ b @ c ) ) @ ( arr @ b @ ( arr @ a @ c ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(215,plain,
! [SV29: $i] :
( ( ~ ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
| ! [SY105: $i] :
( ~ ( nf @ SV29 )
| ~ ( nf @ SY105 )
| ! [SY106: $i] : ( nf @ ( app @ SV29 @ SY105 @ SY106 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(216,plain,
! [SV29: $i] :
( ( ~ ~ ( ~ ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
| ! [SY107: $i,SY108: $i] :
~ ( nf @ ( app @ SV29 @ SY107 @ SY108 ) )
| ( nf @ SV29 ) )
| ~ ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
| ! [SY109: $i] :
( ! [SY110: $i] :
~ ( nf @ ( app @ SV29 @ SY109 @ SY110 ) )
| ( nf @ SY109 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(217,plain,
! [SV52: $i,SV30: $i] :
( ( ~ ! [SY140: $i,SY141: $i] :
( ( ( index @ SV30 @ SY140 )
!= ( just @ SY141 ) )
| ( SY141 != SV52 )
| ( tc @ SV30 @ ( var @ SY140 ) @ SV52 ) )
| ~ ! [SY142: $i,SY143: $i] :
( ( ( index @ SV30 @ SY142 )
!= ( just @ SY143 ) )
| ~ ( tc @ SV30 @ ( var @ SY142 ) @ SV52 )
| ( SY143 = SV52 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(218,plain,
( ( ! [SX0: $i] :
( ~ ( nf @ ( lam @ SX0 ) )
| ( nf @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(219,plain,
( ( ! [SX0: $i] :
( ~ ( nf @ SX0 )
| ( nf @ ( lam @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(220,plain,
! [SV53: $i,SV31: $i] :
( ( ~ ! [SY144: $i,SY145: $i] :
( ~ ( tc @ SV31 @ ( lam @ SV53 ) @ ( arr @ SY144 @ SY145 ) )
| ( tc @ ( cons @ SY144 @ SV31 ) @ SV53 @ SY145 ) )
| ~ ! [SY146: $i,SY147: $i] :
( ~ ( tc @ ( cons @ SY146 @ SV31 ) @ SV53 @ SY147 )
| ( tc @ SV31 @ ( lam @ SV53 ) @ ( arr @ SY146 @ SY147 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(221,plain,
! [SV54: $i,SV63: $i,SV32: $i] :
( ( ~ ( ~ ! [SY157: $i,SY158: $i] :
( ~ ( tc @ SV32 @ SV63 @ ( arr @ SY158 @ SV54 ) )
| ~ ( tc @ SV32 @ SY157 @ SY158 )
| ( tc @ SV32 @ ( app @ SV63 @ SY157 @ SY158 ) @ SV54 ) )
| ~ ~ ( ~ ! [SY159: $i,SY160: $i] :
( ~ ( tc @ SV32 @ ( app @ SV63 @ SY159 @ SY160 ) @ SV54 )
| ( tc @ SV32 @ SV63 @ ( arr @ SY160 @ SV54 ) ) )
| ~ ! [SY161: $i,SY162: $i] :
( ~ ( tc @ SV32 @ ( app @ SV63 @ SY161 @ SY162 ) @ SV54 )
| ( tc @ SV32 @ SY161 @ SY162 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(222,plain,
! [SV64: $i,SV58: $i,SV44: $i,SV18: $i] :
( ( ( app @ SV18 @ SV44 @ SV58 )
!= ( lam @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(223,plain,
! [SV65: $i,SV59: $i,SV45: $i,SV19: $i] :
( ( ( app @ SV19 @ SV45 @ SV59 )
!= ( var @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(224,plain,
! [SV47: $i,SV21: $i,SV60: $i] :
( ( nf @ ( app @ ( lam @ SV60 ) @ SV21 @ SV47 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(225,plain,
! [SV50: $i,SV66: $i,SV26: $i] :
( ( ( ~ ( tc @ SV26 @ ( lam @ SV66 ) @ SV50 ) )
= $true )
| ( ( SV50
= ( arr @ ( proj1Arr @ SV50 ) @ ( proj2Arr @ SV50 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(226,plain,
! [SV51: $i,SV62: $i,SV27: $i] :
( ( ( ( index @ SV27 @ SV62 )
!= nothing )
= $true )
| ( ( ~ ( tc @ SV27 @ ( var @ SV62 ) @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(227,plain,
! [SV28: $i] :
( ( ( tc @ nil @ SV28 @ ( arr @ ( arr @ a @ ( arr @ b @ c ) ) @ ( arr @ b @ ( arr @ a @ c ) ) ) )
= $false )
| ( ( nf @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(228,plain,
! [SV29: $i] :
( ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
| ! [SY105: $i] :
( ~ ( nf @ SV29 )
| ~ ( nf @ SY105 )
| ! [SY106: $i] : ( nf @ ( app @ SV29 @ SY105 @ SY106 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[215]) ).
thf(229,plain,
! [SV29: $i] :
( ( ~ ( ~ ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
| ! [SY107: $i,SY108: $i] :
~ ( nf @ ( app @ SV29 @ SY107 @ SY108 ) )
| ( nf @ SV29 ) )
| ~ ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
| ! [SY109: $i] :
( ! [SY110: $i] :
~ ( nf @ ( app @ SV29 @ SY109 @ SY110 ) )
| ( nf @ SY109 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(230,plain,
! [SV52: $i,SV30: $i] :
( ( ~ ! [SY140: $i,SY141: $i] :
( ( ( index @ SV30 @ SY140 )
!= ( just @ SY141 ) )
| ( SY141 != SV52 )
| ( tc @ SV30 @ ( var @ SY140 ) @ SV52 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(231,plain,
! [SV52: $i,SV30: $i] :
( ( ~ ! [SY142: $i,SY143: $i] :
( ( ( index @ SV30 @ SY142 )
!= ( just @ SY143 ) )
| ~ ( tc @ SV30 @ ( var @ SY142 ) @ SV52 )
| ( SY143 = SV52 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(232,plain,
! [SV67: $i] :
( ( ~ ( nf @ ( lam @ SV67 ) )
| ( nf @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(233,plain,
! [SV68: $i] :
( ( ~ ( nf @ SV68 )
| ( nf @ ( lam @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(234,plain,
! [SV53: $i,SV31: $i] :
( ( ~ ! [SY144: $i,SY145: $i] :
( ~ ( tc @ SV31 @ ( lam @ SV53 ) @ ( arr @ SY144 @ SY145 ) )
| ( tc @ ( cons @ SY144 @ SV31 ) @ SV53 @ SY145 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[220]) ).
thf(235,plain,
! [SV53: $i,SV31: $i] :
( ( ~ ! [SY146: $i,SY147: $i] :
( ~ ( tc @ ( cons @ SY146 @ SV31 ) @ SV53 @ SY147 )
| ( tc @ SV31 @ ( lam @ SV53 ) @ ( arr @ SY146 @ SY147 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[220]) ).
thf(236,plain,
! [SV54: $i,SV63: $i,SV32: $i] :
( ( ~ ! [SY157: $i,SY158: $i] :
( ~ ( tc @ SV32 @ SV63 @ ( arr @ SY158 @ SV54 ) )
| ~ ( tc @ SV32 @ SY157 @ SY158 )
| ( tc @ SV32 @ ( app @ SV63 @ SY157 @ SY158 ) @ SV54 ) )
| ~ ~ ( ~ ! [SY159: $i,SY160: $i] :
( ~ ( tc @ SV32 @ ( app @ SV63 @ SY159 @ SY160 ) @ SV54 )
| ( tc @ SV32 @ SV63 @ ( arr @ SY160 @ SV54 ) ) )
| ~ ! [SY161: $i,SY162: $i] :
( ~ ( tc @ SV32 @ ( app @ SV63 @ SY161 @ SY162 ) @ SV54 )
| ( tc @ SV32 @ SY161 @ SY162 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(237,plain,
! [SV64: $i,SV58: $i,SV44: $i,SV18: $i] :
( ( ( app @ SV18 @ SV44 @ SV58 )
= ( lam @ SV64 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(238,plain,
! [SV65: $i,SV59: $i,SV45: $i,SV19: $i] :
( ( ( app @ SV19 @ SV45 @ SV59 )
= ( var @ SV65 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(239,plain,
! [SV50: $i,SV66: $i,SV26: $i] :
( ( ( tc @ SV26 @ ( lam @ SV66 ) @ SV50 )
= $false )
| ( ( SV50
= ( arr @ ( proj1Arr @ SV50 ) @ ( proj2Arr @ SV50 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(240,plain,
! [SV51: $i,SV62: $i,SV27: $i] :
( ( ( ( index @ SV27 @ SV62 )
= nothing )
= $false )
| ( ( ~ ( tc @ SV27 @ ( var @ SV62 ) @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(241,plain,
! [SV29: $i] :
( ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
= $true )
| ( ( ! [SY105: $i] :
( ~ ( nf @ SV29 )
| ~ ( nf @ SY105 )
| ! [SY106: $i] : ( nf @ ( app @ SV29 @ SY105 @ SY106 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(242,plain,
! [SV29: $i] :
( ( ~ ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
| ! [SY107: $i,SY108: $i] :
~ ( nf @ ( app @ SV29 @ SY107 @ SY108 ) )
| ( nf @ SV29 ) )
| ~ ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
| ! [SY109: $i] :
( ! [SY110: $i] :
~ ( nf @ ( app @ SV29 @ SY109 @ SY110 ) )
| ( nf @ SY109 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(243,plain,
! [SV52: $i,SV30: $i] :
( ( ! [SY140: $i,SY141: $i] :
( ( ( index @ SV30 @ SY140 )
!= ( just @ SY141 ) )
| ( SY141 != SV52 )
| ( tc @ SV30 @ ( var @ SY140 ) @ SV52 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(244,plain,
! [SV52: $i,SV30: $i] :
( ( ! [SY142: $i,SY143: $i] :
( ( ( index @ SV30 @ SY142 )
!= ( just @ SY143 ) )
| ~ ( tc @ SV30 @ ( var @ SY142 ) @ SV52 )
| ( SY143 = SV52 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(245,plain,
! [SV67: $i] :
( ( ( ~ ( nf @ ( lam @ SV67 ) ) )
= $true )
| ( ( nf @ SV67 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(246,plain,
! [SV68: $i] :
( ( ( ~ ( nf @ SV68 ) )
= $true )
| ( ( nf @ ( lam @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(247,plain,
! [SV53: $i,SV31: $i] :
( ( ! [SY144: $i,SY145: $i] :
( ~ ( tc @ SV31 @ ( lam @ SV53 ) @ ( arr @ SY144 @ SY145 ) )
| ( tc @ ( cons @ SY144 @ SV31 ) @ SV53 @ SY145 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(248,plain,
! [SV53: $i,SV31: $i] :
( ( ! [SY146: $i,SY147: $i] :
( ~ ( tc @ ( cons @ SY146 @ SV31 ) @ SV53 @ SY147 )
| ( tc @ SV31 @ ( lam @ SV53 ) @ ( arr @ SY146 @ SY147 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(249,plain,
! [SV54: $i,SV63: $i,SV32: $i] :
( ( ~ ! [SY157: $i,SY158: $i] :
( ~ ( tc @ SV32 @ SV63 @ ( arr @ SY158 @ SV54 ) )
| ~ ( tc @ SV32 @ SY157 @ SY158 )
| ( tc @ SV32 @ ( app @ SV63 @ SY157 @ SY158 ) @ SV54 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(250,plain,
! [SV54: $i,SV63: $i,SV32: $i] :
( ( ~ ~ ( ~ ! [SY159: $i,SY160: $i] :
( ~ ( tc @ SV32 @ ( app @ SV63 @ SY159 @ SY160 ) @ SV54 )
| ( tc @ SV32 @ SV63 @ ( arr @ SY160 @ SV54 ) ) )
| ~ ! [SY161: $i,SY162: $i] :
( ~ ( tc @ SV32 @ ( app @ SV63 @ SY161 @ SY162 ) @ SV54 )
| ( tc @ SV32 @ SY161 @ SY162 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(251,plain,
! [SV51: $i,SV62: $i,SV27: $i] :
( ( ( tc @ SV27 @ ( var @ SV62 ) @ SV51 )
= $false )
| ( ( ( index @ SV27 @ SV62 )
= nothing )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(252,plain,
! [SV69: $i,SV29: $i] :
( ( ( ~ ( nf @ SV29 )
| ~ ( nf @ SV69 )
| ! [SY163: $i] : ( nf @ ( app @ SV29 @ SV69 @ SY163 ) ) )
= $true )
| ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(253,plain,
! [SV29: $i] :
( ( ~ ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
| ! [SY107: $i,SY108: $i] :
~ ( nf @ ( app @ SV29 @ SY107 @ SY108 ) )
| ( nf @ SV29 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(254,plain,
! [SV29: $i] :
( ( ~ ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
| ! [SY109: $i] :
( ! [SY110: $i] :
~ ( nf @ ( app @ SV29 @ SY109 @ SY110 ) )
| ( nf @ SY109 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(255,plain,
! [SV52: $i,SV70: $i,SV30: $i] :
( ( ! [SY164: $i] :
( ( ( index @ SV30 @ SV70 )
!= ( just @ SY164 ) )
| ( SY164 != SV52 )
| ( tc @ SV30 @ ( var @ SV70 ) @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(256,plain,
! [SV52: $i,SV71: $i,SV30: $i] :
( ( ! [SY165: $i] :
( ( ( index @ SV30 @ SV71 )
!= ( just @ SY165 ) )
| ~ ( tc @ SV30 @ ( var @ SV71 ) @ SV52 )
| ( SY165 = SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(257,plain,
! [SV67: $i] :
( ( ( nf @ ( lam @ SV67 ) )
= $false )
| ( ( nf @ SV67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(258,plain,
! [SV68: $i] :
( ( ( nf @ SV68 )
= $false )
| ( ( nf @ ( lam @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(259,plain,
! [SV72: $i,SV53: $i,SV31: $i] :
( ( ! [SY166: $i] :
( ~ ( tc @ SV31 @ ( lam @ SV53 ) @ ( arr @ SV72 @ SY166 ) )
| ( tc @ ( cons @ SV72 @ SV31 ) @ SV53 @ SY166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(260,plain,
! [SV53: $i,SV31: $i,SV73: $i] :
( ( ! [SY167: $i] :
( ~ ( tc @ ( cons @ SV73 @ SV31 ) @ SV53 @ SY167 )
| ( tc @ SV31 @ ( lam @ SV53 ) @ ( arr @ SV73 @ SY167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(261,plain,
! [SV54: $i,SV63: $i,SV32: $i] :
( ( ! [SY157: $i,SY158: $i] :
( ~ ( tc @ SV32 @ SV63 @ ( arr @ SY158 @ SV54 ) )
| ~ ( tc @ SV32 @ SY157 @ SY158 )
| ( tc @ SV32 @ ( app @ SV63 @ SY157 @ SY158 ) @ SV54 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(262,plain,
! [SV54: $i,SV63: $i,SV32: $i] :
( ( ~ ( ~ ! [SY159: $i,SY160: $i] :
( ~ ( tc @ SV32 @ ( app @ SV63 @ SY159 @ SY160 ) @ SV54 )
| ( tc @ SV32 @ SV63 @ ( arr @ SY160 @ SV54 ) ) )
| ~ ! [SY161: $i,SY162: $i] :
( ~ ( tc @ SV32 @ ( app @ SV63 @ SY161 @ SY162 ) @ SV54 )
| ( tc @ SV32 @ SY161 @ SY162 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(263,plain,
! [SV69: $i,SV29: $i] :
( ( ( ~ ( nf @ SV29 )
| ~ ( nf @ SV69 ) )
= $true )
| ( ( ! [SY163: $i] : ( nf @ ( app @ SV29 @ SV69 @ SY163 ) ) )
= $true )
| ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(264,plain,
! [SV29: $i] :
( ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
| ! [SY107: $i,SY108: $i] :
~ ( nf @ ( app @ SV29 @ SY107 @ SY108 ) )
| ( nf @ SV29 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(265,plain,
! [SV29: $i] :
( ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
| ! [SY109: $i] :
( ! [SY110: $i] :
~ ( nf @ ( app @ SV29 @ SY109 @ SY110 ) )
| ( nf @ SY109 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(266,plain,
! [SV52: $i,SV74: $i,SV70: $i,SV30: $i] :
( ( ( ( index @ SV30 @ SV70 )
!= ( just @ SV74 ) )
| ( SV74 != SV52 )
| ( tc @ SV30 @ ( var @ SV70 ) @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(267,plain,
! [SV52: $i,SV75: $i,SV71: $i,SV30: $i] :
( ( ( ( index @ SV30 @ SV71 )
!= ( just @ SV75 ) )
| ~ ( tc @ SV30 @ ( var @ SV71 ) @ SV52 )
| ( SV75 = SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(268,plain,
! [SV76: $i,SV72: $i,SV53: $i,SV31: $i] :
( ( ~ ( tc @ SV31 @ ( lam @ SV53 ) @ ( arr @ SV72 @ SV76 ) )
| ( tc @ ( cons @ SV72 @ SV31 ) @ SV53 @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(269,plain,
! [SV77: $i,SV53: $i,SV31: $i,SV73: $i] :
( ( ~ ( tc @ ( cons @ SV73 @ SV31 ) @ SV53 @ SV77 )
| ( tc @ SV31 @ ( lam @ SV53 ) @ ( arr @ SV73 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(270,plain,
! [SV78: $i,SV54: $i,SV63: $i,SV32: $i] :
( ( ! [SY168: $i] :
( ~ ( tc @ SV32 @ SV63 @ ( arr @ SY168 @ SV54 ) )
| ~ ( tc @ SV32 @ SV78 @ SY168 )
| ( tc @ SV32 @ ( app @ SV63 @ SV78 @ SY168 ) @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(271,plain,
! [SV54: $i,SV63: $i,SV32: $i] :
( ( ~ ! [SY159: $i,SY160: $i] :
( ~ ( tc @ SV32 @ ( app @ SV63 @ SY159 @ SY160 ) @ SV54 )
| ( tc @ SV32 @ SV63 @ ( arr @ SY160 @ SV54 ) ) )
| ~ ! [SY161: $i,SY162: $i] :
( ~ ( tc @ SV32 @ ( app @ SV63 @ SY161 @ SY162 ) @ SV54 )
| ( tc @ SV32 @ SY161 @ SY162 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(272,plain,
! [SV69: $i,SV29: $i] :
( ( ( ~ ( nf @ SV29 ) )
= $true )
| ( ( ~ ( nf @ SV69 ) )
= $true )
| ( ( ! [SY163: $i] : ( nf @ ( app @ SV29 @ SV69 @ SY163 ) ) )
= $true )
| ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[263]) ).
thf(273,plain,
! [SV29: $i] :
( ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
= $true )
| ( ( ! [SY107: $i,SY108: $i] :
~ ( nf @ ( app @ SV29 @ SY107 @ SY108 ) )
| ( nf @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(274,plain,
! [SV29: $i] :
( ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
= $true )
| ( ( ! [SY109: $i] :
( ! [SY110: $i] :
~ ( nf @ ( app @ SV29 @ SY109 @ SY110 ) )
| ( nf @ SY109 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(275,plain,
! [SV52: $i,SV74: $i,SV70: $i,SV30: $i] :
( ( ( ( index @ SV30 @ SV70 )
!= ( just @ SV74 ) )
= $true )
| ( ( ( SV74 != SV52 )
| ( tc @ SV30 @ ( var @ SV70 ) @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(276,plain,
! [SV52: $i,SV75: $i,SV71: $i,SV30: $i] :
( ( ( ( index @ SV30 @ SV71 )
!= ( just @ SV75 ) )
= $true )
| ( ( ~ ( tc @ SV30 @ ( var @ SV71 ) @ SV52 )
| ( SV75 = SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[267]) ).
thf(277,plain,
! [SV76: $i,SV72: $i,SV53: $i,SV31: $i] :
( ( ( ~ ( tc @ SV31 @ ( lam @ SV53 ) @ ( arr @ SV72 @ SV76 ) ) )
= $true )
| ( ( tc @ ( cons @ SV72 @ SV31 ) @ SV53 @ SV76 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(278,plain,
! [SV77: $i,SV53: $i,SV31: $i,SV73: $i] :
( ( ( ~ ( tc @ ( cons @ SV73 @ SV31 ) @ SV53 @ SV77 ) )
= $true )
| ( ( tc @ SV31 @ ( lam @ SV53 ) @ ( arr @ SV73 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[269]) ).
thf(279,plain,
! [SV78: $i,SV54: $i,SV79: $i,SV63: $i,SV32: $i] :
( ( ~ ( tc @ SV32 @ SV63 @ ( arr @ SV79 @ SV54 ) )
| ~ ( tc @ SV32 @ SV78 @ SV79 )
| ( tc @ SV32 @ ( app @ SV63 @ SV78 @ SV79 ) @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(280,plain,
! [SV54: $i,SV63: $i,SV32: $i] :
( ( ~ ! [SY159: $i,SY160: $i] :
( ~ ( tc @ SV32 @ ( app @ SV63 @ SY159 @ SY160 ) @ SV54 )
| ( tc @ SV32 @ SV63 @ ( arr @ SY160 @ SV54 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[271]) ).
thf(281,plain,
! [SV54: $i,SV63: $i,SV32: $i] :
( ( ~ ! [SY161: $i,SY162: $i] :
( ~ ( tc @ SV32 @ ( app @ SV63 @ SY161 @ SY162 ) @ SV54 )
| ( tc @ SV32 @ SY161 @ SY162 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[271]) ).
thf(282,plain,
! [SV69: $i,SV29: $i] :
( ( ( nf @ SV29 )
= $false )
| ( ( ~ ( nf @ SV69 ) )
= $true )
| ( ( ! [SY163: $i] : ( nf @ ( app @ SV29 @ SV69 @ SY163 ) ) )
= $true )
| ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(283,plain,
! [SV29: $i] :
( ( ( ! [SY107: $i,SY108: $i] :
~ ( nf @ ( app @ SV29 @ SY107 @ SY108 ) ) )
= $true )
| ( ( nf @ SV29 )
= $true )
| ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(284,plain,
! [SV80: $i,SV29: $i] :
( ( ( ! [SY169: $i] :
~ ( nf @ ( app @ SV29 @ SV80 @ SY169 ) )
| ( nf @ SV80 ) )
= $true )
| ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(285,plain,
! [SV52: $i,SV74: $i,SV70: $i,SV30: $i] :
( ( ( ( index @ SV30 @ SV70 )
= ( just @ SV74 ) )
= $false )
| ( ( ( SV74 != SV52 )
| ( tc @ SV30 @ ( var @ SV70 ) @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(286,plain,
! [SV52: $i,SV75: $i,SV71: $i,SV30: $i] :
( ( ( ( index @ SV30 @ SV71 )
= ( just @ SV75 ) )
= $false )
| ( ( ~ ( tc @ SV30 @ ( var @ SV71 ) @ SV52 )
| ( SV75 = SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(287,plain,
! [SV76: $i,SV72: $i,SV53: $i,SV31: $i] :
( ( ( tc @ SV31 @ ( lam @ SV53 ) @ ( arr @ SV72 @ SV76 ) )
= $false )
| ( ( tc @ ( cons @ SV72 @ SV31 ) @ SV53 @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(288,plain,
! [SV77: $i,SV53: $i,SV31: $i,SV73: $i] :
( ( ( tc @ ( cons @ SV73 @ SV31 ) @ SV53 @ SV77 )
= $false )
| ( ( tc @ SV31 @ ( lam @ SV53 ) @ ( arr @ SV73 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(289,plain,
! [SV78: $i,SV54: $i,SV79: $i,SV63: $i,SV32: $i] :
( ( ( ~ ( tc @ SV32 @ SV63 @ ( arr @ SV79 @ SV54 ) )
| ~ ( tc @ SV32 @ SV78 @ SV79 ) )
= $true )
| ( ( tc @ SV32 @ ( app @ SV63 @ SV78 @ SV79 ) @ SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(290,plain,
! [SV54: $i,SV63: $i,SV32: $i] :
( ( ! [SY159: $i,SY160: $i] :
( ~ ( tc @ SV32 @ ( app @ SV63 @ SY159 @ SY160 ) @ SV54 )
| ( tc @ SV32 @ SV63 @ ( arr @ SY160 @ SV54 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(291,plain,
! [SV54: $i,SV63: $i,SV32: $i] :
( ( ! [SY161: $i,SY162: $i] :
( ~ ( tc @ SV32 @ ( app @ SV63 @ SY161 @ SY162 ) @ SV54 )
| ( tc @ SV32 @ SY161 @ SY162 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(292,plain,
! [SV29: $i,SV69: $i] :
( ( ( nf @ SV69 )
= $false )
| ( ( nf @ SV29 )
= $false )
| ( ( ! [SY163: $i] : ( nf @ ( app @ SV29 @ SV69 @ SY163 ) ) )
= $true )
| ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(293,plain,
! [SV81: $i,SV29: $i] :
( ( ( ! [SY170: $i] :
~ ( nf @ ( app @ SV29 @ SV81 @ SY170 ) ) )
= $true )
| ( ( nf @ SV29 )
= $true )
| ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(294,plain,
! [SV80: $i,SV29: $i] :
( ( ( ! [SY169: $i] :
~ ( nf @ ( app @ SV29 @ SV80 @ SY169 ) ) )
= $true )
| ( ( nf @ SV80 )
= $true )
| ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(295,plain,
! [SV70: $i,SV30: $i,SV52: $i,SV74: $i] :
( ( ( SV74 != SV52 )
= $true )
| ( ( tc @ SV30 @ ( var @ SV70 ) @ SV52 )
= $true )
| ( ( ( index @ SV30 @ SV70 )
= ( just @ SV74 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(296,plain,
! [SV75: $i,SV52: $i,SV71: $i,SV30: $i] :
( ( ( ~ ( tc @ SV30 @ ( var @ SV71 ) @ SV52 ) )
= $true )
| ( ( SV75 = SV52 )
= $true )
| ( ( ( index @ SV30 @ SV71 )
= ( just @ SV75 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(297,plain,
! [SV78: $i,SV54: $i,SV79: $i,SV63: $i,SV32: $i] :
( ( ( ~ ( tc @ SV32 @ SV63 @ ( arr @ SV79 @ SV54 ) ) )
= $true )
| ( ( ~ ( tc @ SV32 @ SV78 @ SV79 ) )
= $true )
| ( ( tc @ SV32 @ ( app @ SV63 @ SV78 @ SV79 ) @ SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(298,plain,
! [SV54: $i,SV82: $i,SV63: $i,SV32: $i] :
( ( ! [SY171: $i] :
( ~ ( tc @ SV32 @ ( app @ SV63 @ SV82 @ SY171 ) @ SV54 )
| ( tc @ SV32 @ SV63 @ ( arr @ SY171 @ SV54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(299,plain,
! [SV54: $i,SV83: $i,SV63: $i,SV32: $i] :
( ( ! [SY172: $i] :
( ~ ( tc @ SV32 @ ( app @ SV63 @ SV83 @ SY172 ) @ SV54 )
| ( tc @ SV32 @ SV83 @ SY172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(300,plain,
! [SV84: $i,SV69: $i,SV29: $i] :
( ( ( nf @ ( app @ SV29 @ SV69 @ SV84 ) )
= $true )
| ( ( nf @ SV29 )
= $false )
| ( ( nf @ SV69 )
= $false )
| ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(301,plain,
! [SV85: $i,SV81: $i,SV29: $i] :
( ( ( ~ ( nf @ ( app @ SV29 @ SV81 @ SV85 ) ) )
= $true )
| ( ( nf @ SV29 )
= $true )
| ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(302,plain,
! [SV86: $i,SV80: $i,SV29: $i] :
( ( ( ~ ( nf @ ( app @ SV29 @ SV80 @ SV86 ) ) )
= $true )
| ( ( nf @ SV80 )
= $true )
| ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(303,plain,
! [SV70: $i,SV30: $i,SV52: $i,SV74: $i] :
( ( ( SV74 = SV52 )
= $false )
| ( ( tc @ SV30 @ ( var @ SV70 ) @ SV52 )
= $true )
| ( ( ( index @ SV30 @ SV70 )
= ( just @ SV74 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(304,plain,
! [SV75: $i,SV52: $i,SV71: $i,SV30: $i] :
( ( ( tc @ SV30 @ ( var @ SV71 ) @ SV52 )
= $false )
| ( ( SV75 = SV52 )
= $true )
| ( ( ( index @ SV30 @ SV71 )
= ( just @ SV75 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(305,plain,
! [SV78: $i,SV54: $i,SV79: $i,SV63: $i,SV32: $i] :
( ( ( tc @ SV32 @ SV63 @ ( arr @ SV79 @ SV54 ) )
= $false )
| ( ( ~ ( tc @ SV32 @ SV78 @ SV79 ) )
= $true )
| ( ( tc @ SV32 @ ( app @ SV63 @ SV78 @ SV79 ) @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(306,plain,
! [SV54: $i,SV87: $i,SV82: $i,SV63: $i,SV32: $i] :
( ( ~ ( tc @ SV32 @ ( app @ SV63 @ SV82 @ SV87 ) @ SV54 )
| ( tc @ SV32 @ SV63 @ ( arr @ SV87 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(307,plain,
! [SV54: $i,SV88: $i,SV83: $i,SV63: $i,SV32: $i] :
( ( ~ ( tc @ SV32 @ ( app @ SV63 @ SV83 @ SV88 ) @ SV54 )
| ( tc @ SV32 @ SV83 @ SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(308,plain,
! [SV85: $i,SV81: $i,SV29: $i] :
( ( ( nf @ ( app @ SV29 @ SV81 @ SV85 ) )
= $false )
| ( ( nf @ SV29 )
= $true )
| ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(309,plain,
! [SV86: $i,SV80: $i,SV29: $i] :
( ( ( nf @ ( app @ SV29 @ SV80 @ SV86 ) )
= $false )
| ( ( nf @ SV80 )
= $true )
| ( ( SV29
= ( lam @ ( proj1Lam @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(310,plain,
! [SV54: $i,SV63: $i,SV79: $i,SV78: $i,SV32: $i] :
( ( ( tc @ SV32 @ SV78 @ SV79 )
= $false )
| ( ( tc @ SV32 @ SV63 @ ( arr @ SV79 @ SV54 ) )
= $false )
| ( ( tc @ SV32 @ ( app @ SV63 @ SV78 @ SV79 ) @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(311,plain,
! [SV54: $i,SV87: $i,SV82: $i,SV63: $i,SV32: $i] :
( ( ( ~ ( tc @ SV32 @ ( app @ SV63 @ SV82 @ SV87 ) @ SV54 ) )
= $true )
| ( ( tc @ SV32 @ SV63 @ ( arr @ SV87 @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(312,plain,
! [SV54: $i,SV88: $i,SV83: $i,SV63: $i,SV32: $i] :
( ( ( ~ ( tc @ SV32 @ ( app @ SV63 @ SV83 @ SV88 ) @ SV54 ) )
= $true )
| ( ( tc @ SV32 @ SV83 @ SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[307]) ).
thf(313,plain,
! [SV54: $i,SV87: $i,SV82: $i,SV63: $i,SV32: $i] :
( ( ( tc @ SV32 @ ( app @ SV63 @ SV82 @ SV87 ) @ SV54 )
= $false )
| ( ( tc @ SV32 @ SV63 @ ( arr @ SV87 @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(314,plain,
! [SV54: $i,SV88: $i,SV83: $i,SV63: $i,SV32: $i] :
( ( ( tc @ SV32 @ ( app @ SV63 @ SV83 @ SV88 ) @ SV54 )
= $false )
| ( ( tc @ SV32 @ SV83 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(315,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[144,314,313,310,309,308,304,303,300,288,287,258,257,251,239,238,237,227,224,211,209,206,205,204,203,202,201,200,189,181,180,176,175,173,172,161,160,155,154,149,147,146,145]) ).
thf(316,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[315]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX221+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.21 % Computer : n020.cluster.edu
% 0.07/0.21 % Model : x86_64 x86_64
% 0.07/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.21 % Memory : 8046.5625MB
% 0.07/0.21 % OS : Linux 6.8.0-71-generic
% 0.07/0.21 % CPULimit : 300
% 0.07/0.21 % WCLimit : 300
% 0.07/0.21 % DateTime : Tue Oct 6 17:13:21 UTC 2026
% 0.07/0.21 % CPUTime :
% 0.07/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.21/1.66
% 7.21/1.66 No.of.Axioms: 35
% 7.21/1.66
% 7.21/1.66 Length.of.Defs: 0
% 7.21/1.66
% 7.21/1.66 Contains.Choice.Funs: false
% 7.21/1.66 ...........
% 7.21/1.66
% 7.21/1.66 ********************************
% 7.21/1.66 * All subproblems solved! *
% 7.21/1.66 ********************************
% 7.21/1.66 % SZS status Theorem for /export/starexec/sandbox/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:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:315,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 7.21/1.66
% 7.21/1.66 %**** Beginning of derivation protocol ****
% 7.21/1.66 % SZS output start CNFRefutation
% See solution above
% 7.21/1.66
% 7.21/1.66 %**** End of derivation protocol ****
% 7.21/1.66 %**** no. of clauses in derivation: 316 ****
% 7.21/1.66 %**** clause counter: 315 ****
% 7.21/1.66
% 7.21/1.66 % SZS status Theorem for /export/starexec/sandbox/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:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:315,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------