%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWX224+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 : n006.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 16.03s 2.95s
% Output : CNFRefutation 16.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 32
% Syntax : Number of formulae : 245 ( 205 unt; 0 typ; 0 def)
% Number of atoms : 928 ( 470 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 2026 ( 322 ~; 154 |; 3 &;1529 @)
% ( 9 <=>; 9 =>; 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 : 29 ( 26 usr; 8 con; 0-3 aty)
% Number of variables : 648 ( 0 ^; 643 !; 5 ?; 648 :)
% 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_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_031) ).
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_030) ).
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_029) ).
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_028) ).
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_027) ).
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_026) ).
thf(7,axiom,
! [Z: $i,Xs: $i] :
( ( index @ ( cons @ Z @ Xs ) @ zero )
= ( just @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_025) ).
thf(8,axiom,
! [Y: $i] :
( ( index @ nil @ Y )
= nothing ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_024) ).
thf(9,axiom,
! [X: $i,X2: $i] :
( ( lam @ X )
!= ( var @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_023) ).
thf(10,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(11,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(12,axiom,
! [X: $i] :
( ( proj1Var @ ( var @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
thf(13,axiom,
! [X: $i] :
( ( proj1Lam @ ( lam @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
thf(14,axiom,
! [X: $i,X2: $i,X3: $i] :
( ( proj3App @ ( app @ X @ X2 @ X3 ) )
= X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_018) ).
thf(15,axiom,
! [X: $i,X2: $i,X3: $i] :
( ( proj2App @ ( app @ X @ X2 @ X3 ) )
= X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_017) ).
thf(16,axiom,
! [X: $i,X2: $i,X3: $i] :
( ( proj1App @ ( app @ X @ X2 @ X3 ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
thf(17,axiom,
! [X: $i] :
( nothing
!= ( just @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
thf(18,axiom,
! [X: $i] :
( ( proj1Just @ ( just @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
thf(19,axiom,
! [X: $i] :
( zero
!= ( suc @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_013) ).
thf(20,axiom,
! [X: $i] :
( ( proj1Suc @ ( suc @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
thf(21,axiom,
b != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
thf(22,axiom,
a != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
thf(23,axiom,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
thf(24,axiom,
! [X: $i,X2: $i] :
( ( arr @ X @ X2 )
!= c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
thf(25,axiom,
! [X: $i,X2: $i] :
( ( arr @ X @ X2 )
!= b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
thf(26,axiom,
! [X: $i,X2: $i] :
( ( arr @ X @ X2 )
!= a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
thf(27,axiom,
! [X: $i,X2: $i] :
( ( proj2Arr @ ( arr @ X @ X2 ) )
= X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
thf(28,axiom,
! [X: $i,X2: $i] :
( ( proj1Arr @ ( arr @ X @ X2 ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
thf(29,axiom,
! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
thf(30,axiom,
! [X: $i,X2: $i] :
( ( tail @ ( cons @ X @ X2 ) )
= X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
thf(31,axiom,
! [X: $i,X2: $i] :
( ( head @ ( cons @ X @ X2 ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
thf(32,conjecture,
? [E: $i] : ( tc @ nil @ E @ ( arr @ ( arr @ a @ ( arr @ a @ b ) ) @ ( arr @ a @ b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_032) ).
thf(33,negated_conjecture,
( ( ? [E: $i] : ( tc @ nil @ E @ ( arr @ ( arr @ a @ ( arr @ a @ b ) ) @ ( arr @ a @ b ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[32]) ).
thf(34,plain,
( ( ? [E: $i] : ( tc @ nil @ E @ ( arr @ ( arr @ a @ ( arr @ a @ b ) ) @ ( arr @ a @ b ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[33]) ).
thf(35,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(36,plain,
( ( ! [X: $i,Z: $i,X3: $i] :
( ( ( index @ X @ X3 )
= nothing )
=> ~ ( tc @ X @ ( var @ X3 ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(37,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(38,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(39,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(40,plain,
( ( ! [Z: $i,Xs: $i,N: $i] :
( ( index @ ( cons @ Z @ Xs ) @ ( suc @ N ) )
= ( index @ Xs @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(41,plain,
( ( ! [Z: $i,Xs: $i] :
( ( index @ ( cons @ Z @ Xs ) @ zero )
= ( just @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(42,plain,
( ( ! [Y: $i] :
( ( index @ nil @ Y )
= nothing ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(43,plain,
( ( ! [X: $i,X2: $i] :
( ( lam @ X )
!= ( var @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(44,plain,
( ( ! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( app @ X @ X2 @ X3 )
!= ( var @ X4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(45,plain,
( ( ! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( app @ X @ X2 @ X3 )
!= ( lam @ X4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(46,plain,
( ( ! [X: $i] :
( ( proj1Var @ ( var @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(47,plain,
( ( ! [X: $i] :
( ( proj1Lam @ ( lam @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(48,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( proj3App @ ( app @ X @ X2 @ X3 ) )
= X3 ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(49,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( proj2App @ ( app @ X @ X2 @ X3 ) )
= X2 ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(50,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( proj1App @ ( app @ X @ X2 @ X3 ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(51,plain,
( ( ! [X: $i] :
( nothing
!= ( just @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(52,plain,
( ( ! [X: $i] :
( ( proj1Just @ ( just @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(53,plain,
( ( ! [X: $i] :
( zero
!= ( suc @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(54,plain,
( ( ! [X: $i] :
( ( proj1Suc @ ( suc @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(55,plain,
( ( b != c )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(56,plain,
( ( a != c )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(57,plain,
( ( a != b )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(58,plain,
( ( ! [X: $i,X2: $i] :
( ( arr @ X @ X2 )
!= c ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(59,plain,
( ( ! [X: $i,X2: $i] :
( ( arr @ X @ X2 )
!= b ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(60,plain,
( ( ! [X: $i,X2: $i] :
( ( arr @ X @ X2 )
!= a ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(61,plain,
( ( ! [X: $i,X2: $i] :
( ( proj2Arr @ ( arr @ X @ X2 ) )
= X2 ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(62,plain,
( ( ! [X: $i,X2: $i] :
( ( proj1Arr @ ( arr @ X @ X2 ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(63,plain,
( ( ! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(64,plain,
( ( ! [X: $i,X2: $i] :
( ( tail @ ( cons @ X @ X2 ) )
= X2 ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(65,plain,
( ( ! [X: $i,X2: $i] :
( ( head @ ( cons @ X @ X2 ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(66,plain,
( ( ~ ? [E: $i] : ( tc @ nil @ E @ ( arr @ ( arr @ a @ ( arr @ a @ b ) ) @ ( arr @ a @ b ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[34]) ).
thf(67,plain,
( ( ! [X: $i,X2: $i] :
( ( head @ ( cons @ X @ X2 ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(68,plain,
( ( ! [X: $i,X2: $i] :
( ( tail @ ( cons @ X @ X2 ) )
= X2 ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(69,plain,
( ( ! [X: $i,X2: $i] :
( nil
!= ( cons @ X @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(70,plain,
( ( ! [X: $i,X2: $i] :
( ( proj1Arr @ ( arr @ X @ X2 ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(71,plain,
( ( ! [X: $i,X2: $i] :
( ( proj2Arr @ ( arr @ X @ X2 ) )
= X2 ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(72,plain,
( ( ! [X: $i,X2: $i] :
( ( arr @ X @ X2 )
!= a ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(73,plain,
( ( ! [X: $i,X2: $i] :
( ( arr @ X @ X2 )
!= b ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(74,plain,
( ( ! [X: $i,X2: $i] :
( ( arr @ X @ X2 )
!= c ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(75,plain,
( ( a != b )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(76,plain,
( ( a != c )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(77,plain,
( ( b != c )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(78,plain,
( ( ! [X: $i] :
( ( proj1Suc @ ( suc @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(79,plain,
( ( ! [X: $i] :
( zero
!= ( suc @ X ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(80,plain,
( ( ! [X: $i] :
( ( proj1Just @ ( just @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(81,plain,
( ( ! [X: $i] :
( nothing
!= ( just @ X ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(82,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( proj1App @ ( app @ X @ X2 @ X3 ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(83,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( proj2App @ ( app @ X @ X2 @ X3 ) )
= X2 ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(84,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( proj3App @ ( app @ X @ X2 @ X3 ) )
= X3 ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(85,plain,
( ( ! [X: $i] :
( ( proj1Lam @ ( lam @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(86,plain,
( ( ! [X: $i] :
( ( proj1Var @ ( var @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(87,plain,
( ( ! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( app @ X @ X2 @ X3 )
!= ( lam @ X4 ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(88,plain,
( ( ! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( app @ X @ X2 @ X3 )
!= ( var @ X4 ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(89,plain,
( ( ! [X: $i,X2: $i] :
( ( lam @ X )
!= ( var @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(90,plain,
( ( ! [Y: $i] :
( ( index @ nil @ Y )
= nothing ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(91,plain,
( ( ! [Z: $i,Xs: $i] :
( ( index @ ( cons @ Z @ Xs ) @ zero )
= ( just @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(92,plain,
( ( ! [Z: $i,Xs: $i,N: $i] :
( ( index @ ( cons @ Z @ Xs ) @ ( suc @ N ) )
= ( index @ Xs @ N ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(93,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)],[39]) ).
thf(94,plain,
( ( ! [X: $i,Z: $i,E: $i] :
( ( Z
!= ( arr @ ( proj1Arr @ Z ) @ ( proj2Arr @ Z ) ) )
=> ~ ( tc @ X @ ( lam @ E ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(95,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)],[37]) ).
thf(96,plain,
( ( ! [X: $i,Z: $i,X3: $i] :
( ( ( index @ X @ X3 )
= nothing )
=> ~ ( tc @ X @ ( var @ X3 ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(97,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)],[35]) ).
thf(98,plain,
( ( ~ ? [E: $i] : ( tc @ nil @ E @ ( arr @ ( arr @ a @ ( arr @ a @ b ) ) @ ( arr @ a @ b ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(99,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( app @ SX0 @ SX1 @ SX2 )
!= ( var @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(100,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)],[95]) ).
thf(101,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)],[93]) ).
thf(102,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( arr @ SX0 @ SX1 )
!= a ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(103,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)],[97]) ).
thf(104,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( arr @ SX0 @ SX1 )
!= b ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(105,plain,
( ( a != b )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(106,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( arr @ SX0 @ SX1 )
!= c ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(107,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( app @ SX0 @ SX1 @ SX2 )
!= ( lam @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(108,plain,
( ( ~ ~ ! [SX0: $i] :
~ ( tc @ nil @ SX0 @ ( arr @ ( arr @ a @ ( arr @ a @ b ) ) @ ( arr @ a @ b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(109,plain,
( ( a != c )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(110,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ( SX1
!= ( arr @ ( proj1Arr @ SX1 ) @ ( proj2Arr @ SX1 ) ) ) )
| ~ ( tc @ SX0 @ ( lam @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(111,plain,
( ( b != c )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(112,plain,
( ( ! [SX0: $i] :
( nothing
!= ( just @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(113,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( index @ SX0 @ SX2 )
!= nothing )
| ~ ( tc @ SX0 @ ( var @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(114,plain,
( ( ! [SX0: $i,SX1: $i] :
( nil
!= ( cons @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(115,plain,
( ( ! [SX0: $i] :
( zero
!= ( suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(116,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( lam @ SX0 )
!= ( var @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(117,plain,
! [SV1: $i] :
( ( ! [SY67: $i] :
( ( head @ ( cons @ SV1 @ SY67 ) )
= SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(118,plain,
! [SV2: $i] :
( ( ! [SY68: $i] :
( ( tail @ ( cons @ SV2 @ SY68 ) )
= SY68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(119,plain,
! [SV3: $i] :
( ( ! [SY69: $i] :
( ( proj1Arr @ ( arr @ SV3 @ SY69 ) )
= SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(120,plain,
! [SV4: $i] :
( ( ! [SY70: $i] :
( ( proj2Arr @ ( arr @ SV4 @ SY70 ) )
= SY70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(121,plain,
! [SV5: $i] :
( ( ( proj1Suc @ ( suc @ SV5 ) )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(122,plain,
! [SV6: $i] :
( ( ( proj1Just @ ( just @ SV6 ) )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(123,plain,
! [SV7: $i] :
( ( ! [SY71: $i,SY72: $i] :
( ( proj1App @ ( app @ SV7 @ SY71 @ SY72 ) )
= SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(124,plain,
! [SV8: $i] :
( ( ! [SY73: $i,SY74: $i] :
( ( proj2App @ ( app @ SV8 @ SY73 @ SY74 ) )
= SY73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(125,plain,
! [SV9: $i] :
( ( ! [SY75: $i,SY76: $i] :
( ( proj3App @ ( app @ SV9 @ SY75 @ SY76 ) )
= SY76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(126,plain,
! [SV10: $i] :
( ( ( proj1Lam @ ( lam @ SV10 ) )
= SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(127,plain,
! [SV11: $i] :
( ( ( proj1Var @ ( var @ SV11 ) )
= SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(128,plain,
! [SV12: $i] :
( ( ( index @ nil @ SV12 )
= nothing )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(129,plain,
! [SV13: $i] :
( ( ! [SY77: $i] :
( ( index @ ( cons @ SV13 @ SY77 ) @ zero )
= ( just @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(130,plain,
! [SV14: $i] :
( ( ! [SY78: $i,SY79: $i] :
( ( index @ ( cons @ SV14 @ SY78 ) @ ( suc @ SY79 ) )
= ( index @ SY78 @ SY79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(131,plain,
! [SV15: $i] :
( ( ! [SY80: $i,SY81: $i,SY82: $i] :
( ( app @ SV15 @ SY80 @ SY81 )
!= ( var @ SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(132,plain,
! [SV16: $i] :
( ( ! [SY83: $i,SY84: $i,SY85: $i] :
~ ( ~ ( ~ ( tc @ SV16 @ ( lam @ SY83 ) @ ( arr @ SY84 @ SY85 ) )
| ( tc @ ( cons @ SY84 @ SV16 ) @ SY83 @ SY85 ) )
| ~ ( ~ ( tc @ ( cons @ SY84 @ SV16 ) @ SY83 @ SY85 )
| ( tc @ SV16 @ ( lam @ SY83 ) @ ( arr @ SY84 @ SY85 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(133,plain,
! [SV17: $i] :
( ( ! [SY86: $i,SY87: $i,SY88: $i,SY89: $i] :
~ ( ~ ( ~ ( tc @ SV17 @ ( app @ SY87 @ SY88 @ SY89 ) @ SY86 )
| ~ ( ~ ( tc @ SV17 @ SY87 @ ( arr @ SY89 @ SY86 ) )
| ~ ( tc @ SV17 @ SY88 @ SY89 ) ) )
| ~ ( ~ ~ ( ~ ( tc @ SV17 @ SY87 @ ( arr @ SY89 @ SY86 ) )
| ~ ( tc @ SV17 @ SY88 @ SY89 ) )
| ( tc @ SV17 @ ( app @ SY87 @ SY88 @ SY89 ) @ SY86 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(134,plain,
! [SV18: $i] :
( ( ! [SY90: $i] :
( ( arr @ SV18 @ SY90 )
!= a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(135,plain,
! [SV19: $i] :
( ( ! [SY91: $i,SY92: $i,SY93: $i] :
( ( ( index @ SV19 @ SY92 )
!= ( just @ SY93 ) )
| ~ ( ~ ( ~ ( tc @ SV19 @ ( var @ SY92 ) @ SY91 )
| ( SY93 = SY91 ) )
| ~ ( ( SY93 != SY91 )
| ( tc @ SV19 @ ( var @ SY92 ) @ SY91 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(136,plain,
! [SV20: $i] :
( ( ! [SY94: $i] :
( ( arr @ SV20 @ SY94 )
!= b ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(137,plain,
( ( a = b )
= $false ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(138,plain,
! [SV21: $i] :
( ( ! [SY95: $i] :
( ( arr @ SV21 @ SY95 )
!= c ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(139,plain,
! [SV22: $i] :
( ( ! [SY96: $i,SY97: $i,SY98: $i] :
( ( app @ SV22 @ SY96 @ SY97 )
!= ( lam @ SY98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(140,plain,
( ( ~ ! [SX0: $i] :
~ ( tc @ nil @ SX0 @ ( arr @ ( arr @ a @ ( arr @ a @ b ) ) @ ( arr @ a @ b ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(141,plain,
( ( a = c )
= $false ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(142,plain,
! [SV23: $i] :
( ( ! [SY99: $i,SY100: $i] :
( ~ ( ( SY99
!= ( arr @ ( proj1Arr @ SY99 ) @ ( proj2Arr @ SY99 ) ) ) )
| ~ ( tc @ SV23 @ ( lam @ SY100 ) @ SY99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(143,plain,
( ( b = c )
= $false ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(144,plain,
! [SV24: $i] :
( ( nothing
!= ( just @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(145,plain,
! [SV25: $i] :
( ( ! [SY101: $i,SY102: $i] :
( ( ( index @ SV25 @ SY102 )
!= nothing )
| ~ ( tc @ SV25 @ ( var @ SY102 ) @ SY101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(146,plain,
! [SV26: $i] :
( ( ! [SY103: $i] :
( nil
!= ( cons @ SV26 @ SY103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(147,plain,
! [SV27: $i] :
( ( zero
!= ( suc @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(148,plain,
! [SV28: $i] :
( ( ! [SY104: $i] :
( ( lam @ SV28 )
!= ( var @ SY104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(149,plain,
! [SV29: $i,SV1: $i] :
( ( ( head @ ( cons @ SV1 @ SV29 ) )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(150,plain,
! [SV30: $i,SV2: $i] :
( ( ( tail @ ( cons @ SV2 @ SV30 ) )
= SV30 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(151,plain,
! [SV31: $i,SV3: $i] :
( ( ( proj1Arr @ ( arr @ SV3 @ SV31 ) )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(152,plain,
! [SV32: $i,SV4: $i] :
( ( ( proj2Arr @ ( arr @ SV4 @ SV32 ) )
= SV32 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(153,plain,
! [SV33: $i,SV7: $i] :
( ( ! [SY105: $i] :
( ( proj1App @ ( app @ SV7 @ SV33 @ SY105 ) )
= SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(154,plain,
! [SV34: $i,SV8: $i] :
( ( ! [SY106: $i] :
( ( proj2App @ ( app @ SV8 @ SV34 @ SY106 ) )
= SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(155,plain,
! [SV35: $i,SV9: $i] :
( ( ! [SY107: $i] :
( ( proj3App @ ( app @ SV9 @ SV35 @ SY107 ) )
= SY107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(156,plain,
! [SV36: $i,SV13: $i] :
( ( ( index @ ( cons @ SV13 @ SV36 ) @ zero )
= ( just @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(157,plain,
! [SV37: $i,SV14: $i] :
( ( ! [SY108: $i] :
( ( index @ ( cons @ SV14 @ SV37 ) @ ( suc @ SY108 ) )
= ( index @ SV37 @ SY108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(158,plain,
! [SV38: $i,SV15: $i] :
( ( ! [SY109: $i,SY110: $i] :
( ( app @ SV15 @ SV38 @ SY109 )
!= ( var @ SY110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(159,plain,
! [SV39: $i,SV16: $i] :
( ( ! [SY111: $i,SY112: $i] :
~ ( ~ ( ~ ( tc @ SV16 @ ( lam @ SV39 ) @ ( arr @ SY111 @ SY112 ) )
| ( tc @ ( cons @ SY111 @ SV16 ) @ SV39 @ SY112 ) )
| ~ ( ~ ( tc @ ( cons @ SY111 @ SV16 ) @ SV39 @ SY112 )
| ( tc @ SV16 @ ( lam @ SV39 ) @ ( arr @ SY111 @ SY112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(160,plain,
! [SV40: $i,SV17: $i] :
( ( ! [SY113: $i,SY114: $i,SY115: $i] :
~ ( ~ ( ~ ( tc @ SV17 @ ( app @ SY113 @ SY114 @ SY115 ) @ SV40 )
| ~ ( ~ ( tc @ SV17 @ SY113 @ ( arr @ SY115 @ SV40 ) )
| ~ ( tc @ SV17 @ SY114 @ SY115 ) ) )
| ~ ( ~ ~ ( ~ ( tc @ SV17 @ SY113 @ ( arr @ SY115 @ SV40 ) )
| ~ ( tc @ SV17 @ SY114 @ SY115 ) )
| ( tc @ SV17 @ ( app @ SY113 @ SY114 @ SY115 ) @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(161,plain,
! [SV41: $i,SV18: $i] :
( ( ( arr @ SV18 @ SV41 )
!= a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(162,plain,
! [SV42: $i,SV19: $i] :
( ( ! [SY116: $i,SY117: $i] :
( ( ( index @ SV19 @ SY116 )
!= ( just @ SY117 ) )
| ~ ( ~ ( ~ ( tc @ SV19 @ ( var @ SY116 ) @ SV42 )
| ( SY117 = SV42 ) )
| ~ ( ( SY117 != SV42 )
| ( tc @ SV19 @ ( var @ SY116 ) @ SV42 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(163,plain,
! [SV43: $i,SV20: $i] :
( ( ( arr @ SV20 @ SV43 )
!= b )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(164,plain,
! [SV44: $i,SV21: $i] :
( ( ( arr @ SV21 @ SV44 )
!= c )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(165,plain,
! [SV45: $i,SV22: $i] :
( ( ! [SY118: $i,SY119: $i] :
( ( app @ SV22 @ SV45 @ SY118 )
!= ( lam @ SY119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(166,plain,
( ( ! [SX0: $i] :
~ ( tc @ nil @ SX0 @ ( arr @ ( arr @ a @ ( arr @ a @ b ) ) @ ( arr @ a @ b ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(167,plain,
! [SV23: $i,SV46: $i] :
( ( ! [SY120: $i] :
( ~ ( ( SV46
!= ( arr @ ( proj1Arr @ SV46 ) @ ( proj2Arr @ SV46 ) ) ) )
| ~ ( tc @ SV23 @ ( lam @ SY120 ) @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(168,plain,
! [SV24: $i] :
( ( nothing
= ( just @ SV24 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(169,plain,
! [SV47: $i,SV25: $i] :
( ( ! [SY121: $i] :
( ( ( index @ SV25 @ SY121 )
!= nothing )
| ~ ( tc @ SV25 @ ( var @ SY121 ) @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(170,plain,
! [SV48: $i,SV26: $i] :
( ( nil
!= ( cons @ SV26 @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(171,plain,
! [SV27: $i] :
( ( zero
= ( suc @ SV27 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(172,plain,
! [SV49: $i,SV28: $i] :
( ( ( lam @ SV28 )
!= ( var @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(173,plain,
! [SV50: $i,SV33: $i,SV7: $i] :
( ( ( proj1App @ ( app @ SV7 @ SV33 @ SV50 ) )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(174,plain,
! [SV51: $i,SV34: $i,SV8: $i] :
( ( ( proj2App @ ( app @ SV8 @ SV34 @ SV51 ) )
= SV34 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(175,plain,
! [SV52: $i,SV35: $i,SV9: $i] :
( ( ( proj3App @ ( app @ SV9 @ SV35 @ SV52 ) )
= SV52 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(176,plain,
! [SV53: $i,SV37: $i,SV14: $i] :
( ( ( index @ ( cons @ SV14 @ SV37 ) @ ( suc @ SV53 ) )
= ( index @ SV37 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(177,plain,
! [SV54: $i,SV38: $i,SV15: $i] :
( ( ! [SY122: $i] :
( ( app @ SV15 @ SV38 @ SV54 )
!= ( var @ SY122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(178,plain,
! [SV55: $i,SV39: $i,SV16: $i] :
( ( ! [SY123: $i] :
~ ( ~ ( ~ ( tc @ SV16 @ ( lam @ SV39 ) @ ( arr @ SV55 @ SY123 ) )
| ( tc @ ( cons @ SV55 @ SV16 ) @ SV39 @ SY123 ) )
| ~ ( ~ ( tc @ ( cons @ SV55 @ SV16 ) @ SV39 @ SY123 )
| ( tc @ SV16 @ ( lam @ SV39 ) @ ( arr @ SV55 @ SY123 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(179,plain,
! [SV40: $i,SV56: $i,SV17: $i] :
( ( ! [SY124: $i,SY125: $i] :
~ ( ~ ( ~ ( tc @ SV17 @ ( app @ SV56 @ SY124 @ SY125 ) @ SV40 )
| ~ ( ~ ( tc @ SV17 @ SV56 @ ( arr @ SY125 @ SV40 ) )
| ~ ( tc @ SV17 @ SY124 @ SY125 ) ) )
| ~ ( ~ ~ ( ~ ( tc @ SV17 @ SV56 @ ( arr @ SY125 @ SV40 ) )
| ~ ( tc @ SV17 @ SY124 @ SY125 ) )
| ( tc @ SV17 @ ( app @ SV56 @ SY124 @ SY125 ) @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(180,plain,
! [SV41: $i,SV18: $i] :
( ( ( arr @ SV18 @ SV41 )
= a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(181,plain,
! [SV42: $i,SV57: $i,SV19: $i] :
( ( ! [SY126: $i] :
( ( ( index @ SV19 @ SV57 )
!= ( just @ SY126 ) )
| ~ ( ~ ( ~ ( tc @ SV19 @ ( var @ SV57 ) @ SV42 )
| ( SY126 = SV42 ) )
| ~ ( ( SY126 != SV42 )
| ( tc @ SV19 @ ( var @ SV57 ) @ SV42 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(182,plain,
! [SV43: $i,SV20: $i] :
( ( ( arr @ SV20 @ SV43 )
= b )
= $false ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(183,plain,
! [SV44: $i,SV21: $i] :
( ( ( arr @ SV21 @ SV44 )
= c )
= $false ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(184,plain,
! [SV58: $i,SV45: $i,SV22: $i] :
( ( ! [SY127: $i] :
( ( app @ SV22 @ SV45 @ SV58 )
!= ( lam @ SY127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(185,plain,
! [SV59: $i] :
( ( ~ ( tc @ nil @ SV59 @ ( arr @ ( arr @ a @ ( arr @ a @ b ) ) @ ( arr @ a @ b ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(186,plain,
! [SV60: $i,SV23: $i,SV46: $i] :
( ( ~ ( ( SV46
!= ( arr @ ( proj1Arr @ SV46 ) @ ( proj2Arr @ SV46 ) ) ) )
| ~ ( tc @ SV23 @ ( lam @ SV60 ) @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(187,plain,
! [SV47: $i,SV61: $i,SV25: $i] :
( ( ( ( index @ SV25 @ SV61 )
!= nothing )
| ~ ( tc @ SV25 @ ( var @ SV61 ) @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(188,plain,
! [SV48: $i,SV26: $i] :
( ( nil
= ( cons @ SV26 @ SV48 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(189,plain,
! [SV49: $i,SV28: $i] :
( ( ( lam @ SV28 )
= ( var @ SV49 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(190,plain,
! [SV62: $i,SV54: $i,SV38: $i,SV15: $i] :
( ( ( app @ SV15 @ SV38 @ SV54 )
!= ( var @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(191,plain,
! [SV63: $i,SV55: $i,SV39: $i,SV16: $i] :
( ( ~ ( ~ ( ~ ( tc @ SV16 @ ( lam @ SV39 ) @ ( arr @ SV55 @ SV63 ) )
| ( tc @ ( cons @ SV55 @ SV16 ) @ SV39 @ SV63 ) )
| ~ ( ~ ( tc @ ( cons @ SV55 @ SV16 ) @ SV39 @ SV63 )
| ( tc @ SV16 @ ( lam @ SV39 ) @ ( arr @ SV55 @ SV63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(192,plain,
! [SV40: $i,SV64: $i,SV56: $i,SV17: $i] :
( ( ! [SY128: $i] :
~ ( ~ ( ~ ( tc @ SV17 @ ( app @ SV56 @ SV64 @ SY128 ) @ SV40 )
| ~ ( ~ ( tc @ SV17 @ SV56 @ ( arr @ SY128 @ SV40 ) )
| ~ ( tc @ SV17 @ SV64 @ SY128 ) ) )
| ~ ( ~ ~ ( ~ ( tc @ SV17 @ SV56 @ ( arr @ SY128 @ SV40 ) )
| ~ ( tc @ SV17 @ SV64 @ SY128 ) )
| ( tc @ SV17 @ ( app @ SV56 @ SV64 @ SY128 ) @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(193,plain,
! [SV42: $i,SV65: $i,SV57: $i,SV19: $i] :
( ( ( ( index @ SV19 @ SV57 )
!= ( just @ SV65 ) )
| ~ ( ~ ( ~ ( tc @ SV19 @ ( var @ SV57 ) @ SV42 )
| ( SV65 = SV42 ) )
| ~ ( ( SV65 != SV42 )
| ( tc @ SV19 @ ( var @ SV57 ) @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(194,plain,
! [SV66: $i,SV58: $i,SV45: $i,SV22: $i] :
( ( ( app @ SV22 @ SV45 @ SV58 )
!= ( lam @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(195,plain,
! [SV59: $i] :
( ( tc @ nil @ SV59 @ ( arr @ ( arr @ a @ ( arr @ a @ b ) ) @ ( arr @ a @ b ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(196,plain,
! [SV60: $i,SV23: $i,SV46: $i] :
( ( ( ~ ( ( SV46
!= ( arr @ ( proj1Arr @ SV46 ) @ ( proj2Arr @ SV46 ) ) ) ) )
= $true )
| ( ( ~ ( tc @ SV23 @ ( lam @ SV60 ) @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(197,plain,
! [SV47: $i,SV61: $i,SV25: $i] :
( ( ( ( index @ SV25 @ SV61 )
!= nothing )
= $true )
| ( ( ~ ( tc @ SV25 @ ( var @ SV61 ) @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(198,plain,
! [SV62: $i,SV54: $i,SV38: $i,SV15: $i] :
( ( ( app @ SV15 @ SV38 @ SV54 )
= ( var @ SV62 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(199,plain,
! [SV63: $i,SV55: $i,SV39: $i,SV16: $i] :
( ( ~ ( ~ ( tc @ SV16 @ ( lam @ SV39 ) @ ( arr @ SV55 @ SV63 ) )
| ( tc @ ( cons @ SV55 @ SV16 ) @ SV39 @ SV63 ) )
| ~ ( ~ ( tc @ ( cons @ SV55 @ SV16 ) @ SV39 @ SV63 )
| ( tc @ SV16 @ ( lam @ SV39 ) @ ( arr @ SV55 @ SV63 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(200,plain,
! [SV40: $i,SV67: $i,SV64: $i,SV56: $i,SV17: $i] :
( ( ~ ( ~ ( ~ ( tc @ SV17 @ ( app @ SV56 @ SV64 @ SV67 ) @ SV40 )
| ~ ( ~ ( tc @ SV17 @ SV56 @ ( arr @ SV67 @ SV40 ) )
| ~ ( tc @ SV17 @ SV64 @ SV67 ) ) )
| ~ ( ~ ~ ( ~ ( tc @ SV17 @ SV56 @ ( arr @ SV67 @ SV40 ) )
| ~ ( tc @ SV17 @ SV64 @ SV67 ) )
| ( tc @ SV17 @ ( app @ SV56 @ SV64 @ SV67 ) @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(201,plain,
! [SV42: $i,SV65: $i,SV57: $i,SV19: $i] :
( ( ( ( index @ SV19 @ SV57 )
!= ( just @ SV65 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( tc @ SV19 @ ( var @ SV57 ) @ SV42 )
| ( SV65 = SV42 ) )
| ~ ( ( SV65 != SV42 )
| ( tc @ SV19 @ ( var @ SV57 ) @ SV42 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(202,plain,
! [SV66: $i,SV58: $i,SV45: $i,SV22: $i] :
( ( ( app @ SV22 @ SV45 @ SV58 )
= ( lam @ SV66 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(203,plain,
! [SV60: $i,SV23: $i,SV46: $i] :
( ( ( SV46
!= ( arr @ ( proj1Arr @ SV46 ) @ ( proj2Arr @ SV46 ) ) )
= $false )
| ( ( ~ ( tc @ SV23 @ ( lam @ SV60 ) @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(204,plain,
! [SV47: $i,SV61: $i,SV25: $i] :
( ( ( ( index @ SV25 @ SV61 )
= nothing )
= $false )
| ( ( ~ ( tc @ SV25 @ ( var @ SV61 ) @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(205,plain,
! [SV63: $i,SV55: $i,SV39: $i,SV16: $i] :
( ( ~ ( ~ ( tc @ SV16 @ ( lam @ SV39 ) @ ( arr @ SV55 @ SV63 ) )
| ( tc @ ( cons @ SV55 @ SV16 ) @ SV39 @ SV63 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(206,plain,
! [SV63: $i,SV39: $i,SV16: $i,SV55: $i] :
( ( ~ ( ~ ( tc @ ( cons @ SV55 @ SV16 ) @ SV39 @ SV63 )
| ( tc @ SV16 @ ( lam @ SV39 ) @ ( arr @ SV55 @ SV63 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(207,plain,
! [SV40: $i,SV67: $i,SV64: $i,SV56: $i,SV17: $i] :
( ( ~ ( ~ ( tc @ SV17 @ ( app @ SV56 @ SV64 @ SV67 ) @ SV40 )
| ~ ( ~ ( tc @ SV17 @ SV56 @ ( arr @ SV67 @ SV40 ) )
| ~ ( tc @ SV17 @ SV64 @ SV67 ) ) )
| ~ ( ~ ~ ( ~ ( tc @ SV17 @ SV56 @ ( arr @ SV67 @ SV40 ) )
| ~ ( tc @ SV17 @ SV64 @ SV67 ) )
| ( tc @ SV17 @ ( app @ SV56 @ SV64 @ SV67 ) @ SV40 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(208,plain,
! [SV42: $i,SV65: $i,SV57: $i,SV19: $i] :
( ( ( ( index @ SV19 @ SV57 )
= ( just @ SV65 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( tc @ SV19 @ ( var @ SV57 ) @ SV42 )
| ( SV65 = SV42 ) )
| ~ ( ( SV65 != SV42 )
| ( tc @ SV19 @ ( var @ SV57 ) @ SV42 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(209,plain,
! [SV60: $i,SV23: $i,SV46: $i] :
( ( ( SV46
= ( arr @ ( proj1Arr @ SV46 ) @ ( proj2Arr @ SV46 ) ) )
= $true )
| ( ( ~ ( tc @ SV23 @ ( lam @ SV60 ) @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(210,plain,
! [SV47: $i,SV61: $i,SV25: $i] :
( ( ( tc @ SV25 @ ( var @ SV61 ) @ SV47 )
= $false )
| ( ( ( index @ SV25 @ SV61 )
= nothing )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(211,plain,
! [SV63: $i,SV55: $i,SV39: $i,SV16: $i] :
( ( ~ ( tc @ SV16 @ ( lam @ SV39 ) @ ( arr @ SV55 @ SV63 ) )
| ( tc @ ( cons @ SV55 @ SV16 ) @ SV39 @ SV63 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(212,plain,
! [SV63: $i,SV39: $i,SV16: $i,SV55: $i] :
( ( ~ ( tc @ ( cons @ SV55 @ SV16 ) @ SV39 @ SV63 )
| ( tc @ SV16 @ ( lam @ SV39 ) @ ( arr @ SV55 @ SV63 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(213,plain,
! [SV40: $i,SV67: $i,SV64: $i,SV56: $i,SV17: $i] :
( ( ~ ( ~ ( tc @ SV17 @ ( app @ SV56 @ SV64 @ SV67 ) @ SV40 )
| ~ ( ~ ( tc @ SV17 @ SV56 @ ( arr @ SV67 @ SV40 ) )
| ~ ( tc @ SV17 @ SV64 @ SV67 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(214,plain,
! [SV64: $i,SV40: $i,SV67: $i,SV56: $i,SV17: $i] :
( ( ~ ( ~ ~ ( ~ ( tc @ SV17 @ SV56 @ ( arr @ SV67 @ SV40 ) )
| ~ ( tc @ SV17 @ SV64 @ SV67 ) )
| ( tc @ SV17 @ ( app @ SV56 @ SV64 @ SV67 ) @ SV40 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(215,plain,
! [SV65: $i,SV42: $i,SV57: $i,SV19: $i] :
( ( ( ~ ( ~ ( tc @ SV19 @ ( var @ SV57 ) @ SV42 )
| ( SV65 = SV42 ) )
| ~ ( ( SV65 != SV42 )
| ( tc @ SV19 @ ( var @ SV57 ) @ SV42 ) ) )
= $false )
| ( ( ( index @ SV19 @ SV57 )
= ( just @ SV65 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(216,plain,
! [SV46: $i,SV60: $i,SV23: $i] :
( ( ( tc @ SV23 @ ( lam @ SV60 ) @ SV46 )
= $false )
| ( ( SV46
= ( arr @ ( proj1Arr @ SV46 ) @ ( proj2Arr @ SV46 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(217,plain,
! [SV63: $i,SV55: $i,SV39: $i,SV16: $i] :
( ( ( ~ ( tc @ SV16 @ ( lam @ SV39 ) @ ( arr @ SV55 @ SV63 ) ) )
= $true )
| ( ( tc @ ( cons @ SV55 @ SV16 ) @ SV39 @ SV63 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(218,plain,
! [SV63: $i,SV39: $i,SV16: $i,SV55: $i] :
( ( ( ~ ( tc @ ( cons @ SV55 @ SV16 ) @ SV39 @ SV63 ) )
= $true )
| ( ( tc @ SV16 @ ( lam @ SV39 ) @ ( arr @ SV55 @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(219,plain,
! [SV40: $i,SV67: $i,SV64: $i,SV56: $i,SV17: $i] :
( ( ~ ( tc @ SV17 @ ( app @ SV56 @ SV64 @ SV67 ) @ SV40 )
| ~ ( ~ ( tc @ SV17 @ SV56 @ ( arr @ SV67 @ SV40 ) )
| ~ ( tc @ SV17 @ SV64 @ SV67 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(220,plain,
! [SV64: $i,SV40: $i,SV67: $i,SV56: $i,SV17: $i] :
( ( ~ ~ ( ~ ( tc @ SV17 @ SV56 @ ( arr @ SV67 @ SV40 ) )
| ~ ( tc @ SV17 @ SV64 @ SV67 ) )
| ( tc @ SV17 @ ( app @ SV56 @ SV64 @ SV67 ) @ SV40 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(221,plain,
! [SV65: $i,SV42: $i,SV57: $i,SV19: $i] :
( ( ( ~ ( ~ ( tc @ SV19 @ ( var @ SV57 ) @ SV42 )
| ( SV65 = SV42 ) ) )
= $false )
| ( ( ( index @ SV19 @ SV57 )
= ( just @ SV65 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[215]) ).
thf(222,plain,
! [SV57: $i,SV19: $i,SV42: $i,SV65: $i] :
( ( ( ~ ( ( SV65 != SV42 )
| ( tc @ SV19 @ ( var @ SV57 ) @ SV42 ) ) )
= $false )
| ( ( ( index @ SV19 @ SV57 )
= ( just @ SV65 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[215]) ).
thf(223,plain,
! [SV63: $i,SV55: $i,SV39: $i,SV16: $i] :
( ( ( tc @ SV16 @ ( lam @ SV39 ) @ ( arr @ SV55 @ SV63 ) )
= $false )
| ( ( tc @ ( cons @ SV55 @ SV16 ) @ SV39 @ SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(224,plain,
! [SV63: $i,SV39: $i,SV16: $i,SV55: $i] :
( ( ( tc @ ( cons @ SV55 @ SV16 ) @ SV39 @ SV63 )
= $false )
| ( ( tc @ SV16 @ ( lam @ SV39 ) @ ( arr @ SV55 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(225,plain,
! [SV40: $i,SV67: $i,SV64: $i,SV56: $i,SV17: $i] :
( ( ( ~ ( tc @ SV17 @ ( app @ SV56 @ SV64 @ SV67 ) @ SV40 ) )
= $true )
| ( ( ~ ( ~ ( tc @ SV17 @ SV56 @ ( arr @ SV67 @ SV40 ) )
| ~ ( tc @ SV17 @ SV64 @ SV67 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(226,plain,
! [SV64: $i,SV40: $i,SV67: $i,SV56: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( tc @ SV17 @ SV56 @ ( arr @ SV67 @ SV40 ) )
| ~ ( tc @ SV17 @ SV64 @ SV67 ) ) )
= $true )
| ( ( tc @ SV17 @ ( app @ SV56 @ SV64 @ SV67 ) @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(227,plain,
! [SV65: $i,SV42: $i,SV57: $i,SV19: $i] :
( ( ( ~ ( tc @ SV19 @ ( var @ SV57 ) @ SV42 )
| ( SV65 = SV42 ) )
= $true )
| ( ( ( index @ SV19 @ SV57 )
= ( just @ SV65 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(228,plain,
! [SV57: $i,SV19: $i,SV42: $i,SV65: $i] :
( ( ( ( SV65 != SV42 )
| ( tc @ SV19 @ ( var @ SV57 ) @ SV42 ) )
= $true )
| ( ( ( index @ SV19 @ SV57 )
= ( just @ SV65 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(229,plain,
! [SV40: $i,SV67: $i,SV64: $i,SV56: $i,SV17: $i] :
( ( ( tc @ SV17 @ ( app @ SV56 @ SV64 @ SV67 ) @ SV40 )
= $false )
| ( ( ~ ( ~ ( tc @ SV17 @ SV56 @ ( arr @ SV67 @ SV40 ) )
| ~ ( tc @ SV17 @ SV64 @ SV67 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(230,plain,
! [SV64: $i,SV40: $i,SV67: $i,SV56: $i,SV17: $i] :
( ( ( ~ ( ~ ( tc @ SV17 @ SV56 @ ( arr @ SV67 @ SV40 ) )
| ~ ( tc @ SV17 @ SV64 @ SV67 ) ) )
= $false )
| ( ( tc @ SV17 @ ( app @ SV56 @ SV64 @ SV67 ) @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(231,plain,
! [SV65: $i,SV42: $i,SV57: $i,SV19: $i] :
( ( ( ~ ( tc @ SV19 @ ( var @ SV57 ) @ SV42 ) )
= $true )
| ( ( SV65 = SV42 )
= $true )
| ( ( ( index @ SV19 @ SV57 )
= ( just @ SV65 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(232,plain,
! [SV57: $i,SV19: $i,SV42: $i,SV65: $i] :
( ( ( SV65 != SV42 )
= $true )
| ( ( tc @ SV19 @ ( var @ SV57 ) @ SV42 )
= $true )
| ( ( ( index @ SV19 @ SV57 )
= ( just @ SV65 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(233,plain,
! [SV64: $i,SV40: $i,SV67: $i,SV56: $i,SV17: $i] :
( ( ( ~ ( tc @ SV17 @ SV56 @ ( arr @ SV67 @ SV40 ) )
| ~ ( tc @ SV17 @ SV64 @ SV67 ) )
= $false )
| ( ( tc @ SV17 @ ( app @ SV56 @ SV64 @ SV67 ) @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(234,plain,
! [SV64: $i,SV40: $i,SV67: $i,SV56: $i,SV17: $i] :
( ( ( ~ ( tc @ SV17 @ SV56 @ ( arr @ SV67 @ SV40 ) )
| ~ ( tc @ SV17 @ SV64 @ SV67 ) )
= $true )
| ( ( tc @ SV17 @ ( app @ SV56 @ SV64 @ SV67 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(235,plain,
! [SV65: $i,SV42: $i,SV57: $i,SV19: $i] :
( ( ( tc @ SV19 @ ( var @ SV57 ) @ SV42 )
= $false )
| ( ( SV65 = SV42 )
= $true )
| ( ( ( index @ SV19 @ SV57 )
= ( just @ SV65 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(236,plain,
! [SV57: $i,SV19: $i,SV42: $i,SV65: $i] :
( ( ( SV65 = SV42 )
= $false )
| ( ( tc @ SV19 @ ( var @ SV57 ) @ SV42 )
= $true )
| ( ( ( index @ SV19 @ SV57 )
= ( just @ SV65 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(237,plain,
! [SV64: $i,SV40: $i,SV67: $i,SV56: $i,SV17: $i] :
( ( ( ~ ( tc @ SV17 @ SV56 @ ( arr @ SV67 @ SV40 ) ) )
= $false )
| ( ( tc @ SV17 @ ( app @ SV56 @ SV64 @ SV67 ) @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[233]) ).
thf(238,plain,
! [SV40: $i,SV56: $i,SV67: $i,SV64: $i,SV17: $i] :
( ( ( ~ ( tc @ SV17 @ SV64 @ SV67 ) )
= $false )
| ( ( tc @ SV17 @ ( app @ SV56 @ SV64 @ SV67 ) @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[233]) ).
thf(239,plain,
! [SV64: $i,SV40: $i,SV67: $i,SV56: $i,SV17: $i] :
( ( ( ~ ( tc @ SV17 @ SV56 @ ( arr @ SV67 @ SV40 ) ) )
= $true )
| ( ( ~ ( tc @ SV17 @ SV64 @ SV67 ) )
= $true )
| ( ( tc @ SV17 @ ( app @ SV56 @ SV64 @ SV67 ) @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(240,plain,
! [SV64: $i,SV40: $i,SV67: $i,SV56: $i,SV17: $i] :
( ( ( tc @ SV17 @ SV56 @ ( arr @ SV67 @ SV40 ) )
= $true )
| ( ( tc @ SV17 @ ( app @ SV56 @ SV64 @ SV67 ) @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(241,plain,
! [SV40: $i,SV56: $i,SV67: $i,SV64: $i,SV17: $i] :
( ( ( tc @ SV17 @ SV64 @ SV67 )
= $true )
| ( ( tc @ SV17 @ ( app @ SV56 @ SV64 @ SV67 ) @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(242,plain,
! [SV64: $i,SV40: $i,SV67: $i,SV56: $i,SV17: $i] :
( ( ( tc @ SV17 @ SV56 @ ( arr @ SV67 @ SV40 ) )
= $false )
| ( ( ~ ( tc @ SV17 @ SV64 @ SV67 ) )
= $true )
| ( ( tc @ SV17 @ ( app @ SV56 @ SV64 @ SV67 ) @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(243,plain,
! [SV40: $i,SV56: $i,SV67: $i,SV64: $i,SV17: $i] :
( ( ( tc @ SV17 @ SV64 @ SV67 )
= $false )
| ( ( tc @ SV17 @ SV56 @ ( arr @ SV67 @ SV40 ) )
= $false )
| ( ( tc @ SV17 @ ( app @ SV56 @ SV64 @ SV67 ) @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(244,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[121,243,241,240,236,235,224,223,216,210,202,198,195,189,188,183,182,180,176,175,174,173,171,168,156,152,151,150,149,143,141,137,128,127,126,122]) ).
thf(245,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[244]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX224+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
% 0.07/0.20 % Computer : n006.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Oct 6 17:12:07 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
% 16.03/2.95
% 16.03/2.95 No.of.Axioms: 31
% 16.03/2.95
% 16.03/2.95 Length.of.Defs: 0
% 16.03/2.95
% 16.03/2.95 Contains.Choice.Funs: false
% 16.03/2.95 .......
% 16.03/2.95
% 16.03/2.95 ********************************
% 16.03/2.95 * All subproblems solved! *
% 16.03/2.95 ********************************
% 16.03/2.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:31,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:244,loop_count:0,foatp_calls:1,translation:fof_full)
% 16.03/2.95
% 16.03/2.95 %**** Beginning of derivation protocol ****
% 16.03/2.95 % SZS output start CNFRefutation
% See solution above
% 16.03/2.95
% 16.03/2.95 %**** End of derivation protocol ****
% 16.03/2.95 %**** no. of clauses in derivation: 245 ****
% 16.03/2.95 %**** clause counter: 244 ****
% 16.03/2.95
% 16.03/2.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:31,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:244,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------