%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWX190-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 11:02:31 AM UTC 2026
% Result : Unsatisfiable 260.45s 43.65s
% Output : CNFRefutation 260.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 91
% Syntax : Number of formulae : 470 ( 458 unt; 0 typ; 0 def)
% Number of atoms : 1282 ( 888 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 3143 ( 43 ~; 40 |; 0 &;3060 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 6 con; 0-3 aty)
% Number of variables : 1034 ( 0 ^;1034 !; 0 ?;1034 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_addNat,type,
addNat: $i > $i > $i ).
thf(tp_aux,type,
aux: $i > $i > $i > $i ).
thf(tp_bfalse,type,
bfalse: $i ).
thf(tp_btrue,type,
btrue: $i ).
thf(tp_d,type,
d: $i > $i ).
thf(tp_eq,type,
eq: $i > $i > $i ).
thf(tp_eq2,type,
eq2: $i > $i > $i ).
thf(tp_eq3,type,
eq3: $i > $i > $i ).
thf(tp_fail,type,
fail: $i > $i > $i ).
thf(tp_fail1,type,
fail1: $i > $i > $i ).
thf(tp_fail12,type,
fail12: $i > $i > $i ).
thf(tp_fail2,type,
fail2: $i > $i > $i ).
thf(tp_fail22,type,
fail22: $i > $i > $i ).
thf(tp_fail3,type,
fail3: $i > $i > $i ).
thf(tp_fail32,type,
fail32: $i > $i > $i ).
thf(tp_fail4,type,
fail4: $i > $i > $i ).
thf(tp_mulNat,type,
mulNat: $i > $i > $i ).
thf(tp_n,type,
n: $i > $i ).
thf(tp_opt,type,
opt: $i > $i ).
thf(tp_prop4,type,
prop4: $i > $i ).
thf(tp_s,type,
s: $i > $i ).
thf(tp_x,type,
x: $i > $i > $i ).
thf(tp_x2,type,
x2: $i ).
thf(tp_y,type,
y: $i > $i > $i ).
thf(tp_z,type,
z: $i ).
thf(1,axiom,
! [X: $i] :
( ( eq3 @ X @ X )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_088) ).
thf(2,axiom,
! [X: $i] :
( ( eq2 @ X @ X )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_087) ).
thf(3,axiom,
! [X: $i] :
( ( eq @ X @ X )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_086) ).
thf(4,axiom,
! [X: $i] :
( ( eq @ z @ ( s @ X ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_085) ).
thf(5,axiom,
! [X: $i] :
( ( eq @ ( s @ X ) @ z )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_084) ).
thf(6,axiom,
! [X: $i,Y: $i] :
( ( eq @ ( s @ X ) @ ( s @ Y ) )
= ( eq @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_083) ).
thf(7,axiom,
! [X: $i,Y: $i] :
( ( eq2 @ x2 @ ( y @ X @ Y ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_082) ).
thf(8,axiom,
! [X: $i,Y: $i] :
( ( eq2 @ x2 @ ( x @ X @ Y ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_081) ).
thf(9,axiom,
! [X: $i] :
( ( eq2 @ x2 @ ( n @ X ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_080) ).
thf(10,axiom,
! [X: $i,Y: $i] :
( ( eq2 @ ( y @ X @ Y ) @ x2 )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_079) ).
thf(11,axiom,
! [X: $i,Y: $i,Z: $i,X2: $i] :
( ( eq2 @ ( y @ X @ Y ) @ ( x @ Z @ X2 ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_078) ).
thf(12,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( eq2 @ ( y @ X @ Y ) @ ( n @ Z ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_077) ).
thf(13,axiom,
! [X: $i,Y: $i] :
( ( eq2 @ ( x @ X @ Y ) @ x2 )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_076) ).
thf(14,axiom,
! [X: $i,Y: $i,Z: $i,X2: $i] :
( ( eq2 @ ( x @ X @ Y ) @ ( y @ Z @ X2 ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_075) ).
thf(15,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( eq2 @ ( x @ X @ Y ) @ ( n @ Z ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_074) ).
thf(16,axiom,
! [X: $i] :
( ( eq2 @ ( n @ X ) @ x2 )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_073) ).
thf(17,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( eq2 @ ( n @ X ) @ ( y @ Y @ Z ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_072) ).
thf(18,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( eq2 @ ( n @ X ) @ ( x @ Y @ Z ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_071) ).
thf(19,axiom,
! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq2 @ X @ Z )
!= btrue )
| ( ( eq2 @ ( y @ X @ Y ) @ ( y @ Z @ X2 ) )
= ( eq2 @ Y @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_070) ).
thf(20,axiom,
! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq2 @ X @ Z )
!= bfalse )
| ( ( eq2 @ ( y @ X @ Y ) @ ( y @ Z @ X2 ) )
= bfalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_069) ).
thf(21,axiom,
! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq2 @ X @ Z )
!= btrue )
| ( ( eq2 @ ( x @ X @ Y ) @ ( x @ Z @ X2 ) )
= ( eq2 @ Y @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_068) ).
thf(22,axiom,
! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq2 @ X @ Z )
!= bfalse )
| ( ( eq2 @ ( x @ X @ Y ) @ ( x @ Z @ X2 ) )
= bfalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_067) ).
thf(23,axiom,
! [X: $i,Y: $i] :
( ( eq2 @ ( n @ X ) @ ( n @ Y ) )
= ( eq @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_066) ).
thf(24,axiom,
( ( eq3 @ btrue @ bfalse )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_065) ).
thf(25,axiom,
( ( eq3 @ bfalse @ btrue )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_064) ).
thf(26,axiom,
! [X: $i] :
( ( prop4 @ X )
= ( eq2 @ ( opt @ ( d @ X ) ) @ ( opt @ ( d @ ( opt @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_063) ).
thf(27,axiom,
( ( opt @ x2 )
= x2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_062) ).
thf(28,axiom,
! [X: $i] :
( ( opt @ ( n @ X ) )
= ( n @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_061) ).
thf(29,axiom,
! [E2: $i] :
( ( opt @ ( y @ x2 @ E2 ) )
= ( fail3 @ x2 @ E2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_060) ).
thf(30,axiom,
! [X: $i,X2: $i,E2: $i] :
( ( opt @ ( y @ ( y @ X @ X2 ) @ E2 ) )
= ( fail3 @ ( y @ X @ X2 ) @ E2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_059) ).
thf(31,axiom,
! [X: $i,X2: $i,E2: $i] :
( ( opt @ ( y @ ( x @ X @ X2 ) @ E2 ) )
= ( fail3 @ ( x @ X @ X2 ) @ E2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_058) ).
thf(32,axiom,
! [E2: $i] :
( ( opt @ ( y @ ( n @ z ) @ E2 ) )
= ( n @ z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_057) ).
thf(33,axiom,
! [X15: $i,E2: $i] :
( ( opt @ ( y @ ( n @ ( s @ X15 ) ) @ E2 ) )
= ( fail3 @ ( n @ ( s @ X15 ) ) @ E2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_056) ).
thf(34,axiom,
! [E: $i] :
( ( opt @ ( x @ x2 @ E ) )
= ( fail @ x2 @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_055) ).
thf(35,axiom,
! [X: $i,X2: $i,E: $i] :
( ( opt @ ( x @ ( y @ X @ X2 ) @ E ) )
= ( fail @ ( y @ X @ X2 ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_054) ).
thf(36,axiom,
! [X: $i,X2: $i,E: $i] :
( ( opt @ ( x @ ( x @ X @ X2 ) @ E ) )
= ( fail @ ( x @ X @ X2 ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_053) ).
thf(37,axiom,
! [E: $i] :
( ( opt @ ( x @ ( n @ z ) @ E ) )
= E ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_052) ).
thf(38,axiom,
! [X4: $i,E: $i] :
( ( opt @ ( x @ ( n @ ( s @ X4 ) ) @ E ) )
= ( fail @ ( n @ ( s @ X4 ) ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_051) ).
thf(39,axiom,
! [Y: $i] :
( ( mulNat @ z @ Y )
= z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_050) ).
thf(40,axiom,
! [Z: $i,Y: $i] :
( ( mulNat @ ( s @ Z ) @ Y )
= ( addNat @ Y @ ( mulNat @ Z @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_049) ).
thf(41,axiom,
! [Y: $i] :
( ( addNat @ z @ Y )
= Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_048) ).
thf(42,axiom,
! [Z: $i,Y: $i] :
( ( addNat @ ( s @ Z ) @ Y )
= ( s @ ( addNat @ Z @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_047) ).
thf(43,axiom,
( ( d @ x2 )
= ( n @ ( s @ z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_046) ).
thf(44,axiom,
! [H: $i,G2: $i] :
( ( d @ ( y @ H @ G2 ) )
= ( x @ ( y @ ( d @ H ) @ G2 ) @ ( y @ H @ ( d @ G2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_045) ).
thf(45,axiom,
! [F: $i,G: $i] :
( ( d @ ( x @ F @ G ) )
= ( x @ ( d @ F ) @ ( d @ G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_044) ).
thf(46,axiom,
! [Y: $i] :
( ( d @ ( n @ Y ) )
= ( n @ z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_043) ).
thf(47,axiom,
! [X5: $i] :
( ( fail3 @ X5 @ x2 )
= ( fail12 @ X5 @ x2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_042) ).
thf(48,axiom,
! [X5: $i,X: $i,X2: $i] :
( ( fail3 @ X5 @ ( y @ X @ X2 ) )
= ( fail12 @ X5 @ ( y @ X @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_041) ).
thf(49,axiom,
! [X5: $i,X: $i,X2: $i] :
( ( fail3 @ X5 @ ( x @ X @ X2 ) )
= ( fail12 @ X5 @ ( x @ X @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_040) ).
thf(50,axiom,
! [X5: $i] :
( ( fail3 @ X5 @ ( n @ z ) )
= ( n @ z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_039) ).
thf(51,axiom,
! [X5: $i,X13: $i] :
( ( fail3 @ X5 @ ( n @ ( s @ X13 ) ) )
= ( fail12 @ X5 @ ( n @ ( s @ X13 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_038) ).
thf(52,axiom,
! [E2: $i] :
( ( fail12 @ x2 @ E2 )
= ( fail22 @ x2 @ E2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_037) ).
thf(53,axiom,
! [X: $i,X2: $i,E2: $i] :
( ( fail12 @ ( y @ X @ X2 ) @ E2 )
= ( fail22 @ ( y @ X @ X2 ) @ E2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_036) ).
thf(54,axiom,
! [X: $i,X2: $i,E2: $i] :
( ( fail12 @ ( x @ X @ X2 ) @ E2 )
= ( fail22 @ ( x @ X @ X2 ) @ E2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_035) ).
thf(55,axiom,
! [E2: $i] :
( ( fail12 @ ( n @ z ) @ E2 )
= ( fail22 @ ( n @ z ) @ E2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_034) ).
thf(56,axiom,
! [E2: $i] :
( ( fail12 @ ( n @ ( s @ z ) ) @ E2 )
= E2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_033) ).
thf(57,axiom,
! [X11: $i,E2: $i] :
( ( fail12 @ ( n @ ( s @ ( s @ X11 ) ) ) @ E2 )
= ( fail22 @ ( n @ ( s @ ( s @ X11 ) ) ) @ E2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_032) ).
thf(58,axiom,
! [X5: $i] :
( ( fail22 @ X5 @ x2 )
= ( fail32 @ X5 @ x2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_031) ).
thf(59,axiom,
! [X5: $i,X: $i,X2: $i] :
( ( fail22 @ X5 @ ( y @ X @ X2 ) )
= ( fail32 @ X5 @ ( y @ X @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_030) ).
thf(60,axiom,
! [X5: $i,X: $i,X2: $i] :
( ( fail22 @ X5 @ ( x @ X @ X2 ) )
= ( fail32 @ X5 @ ( x @ X @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_029) ).
thf(61,axiom,
! [X5: $i] :
( ( fail22 @ X5 @ ( n @ z ) )
= ( fail32 @ X5 @ ( n @ z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_028) ).
thf(62,axiom,
! [X5: $i] :
( ( fail22 @ X5 @ ( n @ ( s @ z ) ) )
= X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_027) ).
thf(63,axiom,
! [X5: $i,X8: $i] :
( ( fail22 @ X5 @ ( n @ ( s @ ( s @ X8 ) ) ) )
= ( fail32 @ X5 @ ( n @ ( s @ ( s @ X8 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_026) ).
thf(64,axiom,
! [E2: $i] :
( ( fail32 @ x2 @ E2 )
= ( fail4 @ x2 @ E2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_025) ).
thf(65,axiom,
! [X: $i,X2: $i,E2: $i] :
( ( fail32 @ ( x @ X @ X2 ) @ E2 )
= ( fail4 @ ( x @ X @ X2 ) @ E2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_024) ).
thf(66,axiom,
! [A4: $i,B4: $i,E2: $i] :
( ( fail32 @ ( y @ A4 @ B4 ) @ E2 )
= ( opt @ ( y @ A4 @ ( y @ B4 @ E2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_023) ).
thf(67,axiom,
! [A3: $i] :
( ( fail32 @ ( n @ A3 ) @ x2 )
= ( fail4 @ ( n @ A3 ) @ x2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_022) ).
thf(68,axiom,
! [A3: $i,X: $i,X2: $i] :
( ( fail32 @ ( n @ A3 ) @ ( y @ X @ X2 ) )
= ( fail4 @ ( n @ A3 ) @ ( y @ X @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_021) ).
thf(69,axiom,
! [A3: $i,X: $i,X2: $i] :
( ( fail32 @ ( n @ A3 ) @ ( x @ X @ X2 ) )
= ( fail4 @ ( n @ A3 ) @ ( x @ X @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_020) ).
thf(70,axiom,
! [A3: $i,B3: $i] :
( ( fail32 @ ( n @ A3 ) @ ( n @ B3 ) )
= ( n @ ( mulNat @ A3 @ B3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_019) ).
thf(71,axiom,
! [X5: $i,E2: $i] :
( ( fail4 @ X5 @ E2 )
= ( y @ ( opt @ X5 ) @ ( opt @ E2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_018) ).
thf(72,axiom,
! [Y: $i] :
( ( fail @ Y @ x2 )
= ( fail1 @ Y @ x2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_017) ).
thf(73,axiom,
! [Y: $i,X: $i,X2: $i] :
( ( fail @ Y @ ( y @ X @ X2 ) )
= ( fail1 @ Y @ ( y @ X @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_016) ).
thf(74,axiom,
! [Y: $i,X: $i,X2: $i] :
( ( fail @ Y @ ( x @ X @ X2 ) )
= ( fail1 @ Y @ ( x @ X @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_015) ).
thf(75,axiom,
! [Y: $i] :
( ( fail @ Y @ ( n @ z ) )
= Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_014) ).
thf(76,axiom,
! [Y: $i,X2: $i] :
( ( fail @ Y @ ( n @ ( s @ X2 ) ) )
= ( fail1 @ Y @ ( n @ ( s @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_013) ).
thf(77,axiom,
! [E: $i] :
( ( fail1 @ x2 @ E )
= ( fail2 @ x2 @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_012) ).
thf(78,axiom,
! [X: $i,X2: $i,E: $i] :
( ( fail1 @ ( y @ X @ X2 ) @ E )
= ( fail2 @ ( y @ X @ X2 ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_011) ).
thf(79,axiom,
! [X: $i,X2: $i,E: $i] :
( ( fail1 @ ( x @ X @ X2 ) @ E )
= ( fail2 @ ( x @ X @ X2 ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
thf(80,axiom,
! [A2: $i] :
( ( fail1 @ ( n @ A2 ) @ x2 )
= ( fail2 @ ( n @ A2 ) @ x2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
thf(81,axiom,
! [A2: $i,X: $i,X2: $i] :
( ( fail1 @ ( n @ A2 ) @ ( y @ X @ X2 ) )
= ( fail2 @ ( n @ A2 ) @ ( y @ X @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
thf(82,axiom,
! [A2: $i,X: $i,X2: $i] :
( ( fail1 @ ( n @ A2 ) @ ( x @ X @ X2 ) )
= ( fail2 @ ( n @ A2 ) @ ( x @ X @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
thf(83,axiom,
! [A2: $i,B2: $i] :
( ( fail1 @ ( n @ A2 ) @ ( n @ B2 ) )
= ( n @ ( addNat @ A2 @ B2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
thf(84,axiom,
! [Y: $i,E: $i] :
( ( fail2 @ Y @ E )
= ( aux @ Y @ E @ ( eq2 @ Y @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
thf(85,axiom,
! [E: $i] :
( ( aux @ x2 @ E @ bfalse )
= ( x @ ( opt @ x2 ) @ ( opt @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
thf(86,axiom,
! [X: $i,X2: $i,E: $i] :
( ( aux @ ( y @ X @ X2 ) @ E @ bfalse )
= ( x @ ( opt @ ( y @ X @ X2 ) ) @ ( opt @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
thf(87,axiom,
! [X: $i,E: $i] :
( ( aux @ ( n @ X ) @ E @ bfalse )
= ( x @ ( opt @ ( n @ X ) ) @ ( opt @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
thf(88,axiom,
! [B: $i,C: $i,E: $i] :
( ( aux @ ( x @ B @ C ) @ E @ bfalse )
= ( opt @ ( x @ B @ ( x @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
thf(89,axiom,
! [Y: $i,E: $i] :
( ( aux @ Y @ E @ btrue )
= ( y @ ( n @ ( s @ ( s @ z ) ) ) @ ( opt @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom) ).
thf(90,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(91,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[90]) ).
thf(92,negated_conjecture,
! [X: $i] :
( ( eq3 @ ( prop4 @ X ) @ bfalse )
!= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
thf(93,plain,
$false = $false,
inference(unfold_def,[status(thm)],[91]) ).
thf(94,plain,
( ( ! [X: $i] :
( ( eq3 @ X @ X )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(95,plain,
( ( ! [X: $i] :
( ( eq2 @ X @ X )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(96,plain,
( ( ! [X: $i] :
( ( eq @ X @ X )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(97,plain,
( ( ! [X: $i] :
( ( eq @ z @ ( s @ X ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(98,plain,
( ( ! [X: $i] :
( ( eq @ ( s @ X ) @ z )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(99,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ ( s @ X ) @ ( s @ Y ) )
= ( eq @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(100,plain,
( ( ! [X: $i,Y: $i] :
( ( eq2 @ x2 @ ( y @ X @ Y ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(101,plain,
( ( ! [X: $i,Y: $i] :
( ( eq2 @ x2 @ ( x @ X @ Y ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(102,plain,
( ( ! [X: $i] :
( ( eq2 @ x2 @ ( n @ X ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(103,plain,
( ( ! [X: $i,Y: $i] :
( ( eq2 @ ( y @ X @ Y ) @ x2 )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(104,plain,
( ( ! [X: $i,Y: $i,Z: $i,X2: $i] :
( ( eq2 @ ( y @ X @ Y ) @ ( x @ Z @ X2 ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(105,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( eq2 @ ( y @ X @ Y ) @ ( n @ Z ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(106,plain,
( ( ! [X: $i,Y: $i] :
( ( eq2 @ ( x @ X @ Y ) @ x2 )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(107,plain,
( ( ! [X: $i,Y: $i,Z: $i,X2: $i] :
( ( eq2 @ ( x @ X @ Y ) @ ( y @ Z @ X2 ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(108,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( eq2 @ ( x @ X @ Y ) @ ( n @ Z ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(109,plain,
( ( ! [X: $i] :
( ( eq2 @ ( n @ X ) @ x2 )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(110,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( eq2 @ ( n @ X ) @ ( y @ Y @ Z ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(111,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( eq2 @ ( n @ X ) @ ( x @ Y @ Z ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(112,plain,
( ( ! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq2 @ X @ Z )
!= btrue )
| ( ( eq2 @ ( y @ X @ Y ) @ ( y @ Z @ X2 ) )
= ( eq2 @ Y @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(113,plain,
( ( ! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq2 @ X @ Z )
!= bfalse )
| ( ( eq2 @ ( y @ X @ Y ) @ ( y @ Z @ X2 ) )
= bfalse ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(114,plain,
( ( ! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq2 @ X @ Z )
!= btrue )
| ( ( eq2 @ ( x @ X @ Y ) @ ( x @ Z @ X2 ) )
= ( eq2 @ Y @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(115,plain,
( ( ! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq2 @ X @ Z )
!= bfalse )
| ( ( eq2 @ ( x @ X @ Y ) @ ( x @ Z @ X2 ) )
= bfalse ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(116,plain,
( ( ! [X: $i,Y: $i] :
( ( eq2 @ ( n @ X ) @ ( n @ Y ) )
= ( eq @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(117,plain,
( ( ( eq3 @ btrue @ bfalse )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(118,plain,
( ( ( eq3 @ bfalse @ btrue )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(119,plain,
( ( ! [X: $i] :
( ( prop4 @ X )
= ( eq2 @ ( opt @ ( d @ X ) ) @ ( opt @ ( d @ ( opt @ X ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(120,plain,
( ( ( opt @ x2 )
= x2 )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(121,plain,
( ( ! [X: $i] :
( ( opt @ ( n @ X ) )
= ( n @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(122,plain,
( ( ! [E2: $i] :
( ( opt @ ( y @ x2 @ E2 ) )
= ( fail3 @ x2 @ E2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(123,plain,
( ( ! [X: $i,X2: $i,E2: $i] :
( ( opt @ ( y @ ( y @ X @ X2 ) @ E2 ) )
= ( fail3 @ ( y @ X @ X2 ) @ E2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(124,plain,
( ( ! [X: $i,X2: $i,E2: $i] :
( ( opt @ ( y @ ( x @ X @ X2 ) @ E2 ) )
= ( fail3 @ ( x @ X @ X2 ) @ E2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(125,plain,
( ( ! [E2: $i] :
( ( opt @ ( y @ ( n @ z ) @ E2 ) )
= ( n @ z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(126,plain,
( ( ! [X15: $i,E2: $i] :
( ( opt @ ( y @ ( n @ ( s @ X15 ) ) @ E2 ) )
= ( fail3 @ ( n @ ( s @ X15 ) ) @ E2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(127,plain,
( ( ! [E: $i] :
( ( opt @ ( x @ x2 @ E ) )
= ( fail @ x2 @ E ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(128,plain,
( ( ! [X: $i,X2: $i,E: $i] :
( ( opt @ ( x @ ( y @ X @ X2 ) @ E ) )
= ( fail @ ( y @ X @ X2 ) @ E ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(129,plain,
( ( ! [X: $i,X2: $i,E: $i] :
( ( opt @ ( x @ ( x @ X @ X2 ) @ E ) )
= ( fail @ ( x @ X @ X2 ) @ E ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(130,plain,
( ( ! [E: $i] :
( ( opt @ ( x @ ( n @ z ) @ E ) )
= E ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(131,plain,
( ( ! [X4: $i,E: $i] :
( ( opt @ ( x @ ( n @ ( s @ X4 ) ) @ E ) )
= ( fail @ ( n @ ( s @ X4 ) ) @ E ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(132,plain,
( ( ! [Y: $i] :
( ( mulNat @ z @ Y )
= z ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(133,plain,
( ( ! [Z: $i,Y: $i] :
( ( mulNat @ ( s @ Z ) @ Y )
= ( addNat @ Y @ ( mulNat @ Z @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(134,plain,
( ( ! [Y: $i] :
( ( addNat @ z @ Y )
= Y ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(135,plain,
( ( ! [Z: $i,Y: $i] :
( ( addNat @ ( s @ Z ) @ Y )
= ( s @ ( addNat @ Z @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(136,plain,
( ( ( d @ x2 )
= ( n @ ( s @ z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(137,plain,
( ( ! [H: $i,G2: $i] :
( ( d @ ( y @ H @ G2 ) )
= ( x @ ( y @ ( d @ H ) @ G2 ) @ ( y @ H @ ( d @ G2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(138,plain,
( ( ! [F: $i,G: $i] :
( ( d @ ( x @ F @ G ) )
= ( x @ ( d @ F ) @ ( d @ G ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(139,plain,
( ( ! [Y: $i] :
( ( d @ ( n @ Y ) )
= ( n @ z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(140,plain,
( ( ! [X5: $i] :
( ( fail3 @ X5 @ x2 )
= ( fail12 @ X5 @ x2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(141,plain,
( ( ! [X5: $i,X: $i,X2: $i] :
( ( fail3 @ X5 @ ( y @ X @ X2 ) )
= ( fail12 @ X5 @ ( y @ X @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(142,plain,
( ( ! [X5: $i,X: $i,X2: $i] :
( ( fail3 @ X5 @ ( x @ X @ X2 ) )
= ( fail12 @ X5 @ ( x @ X @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(143,plain,
( ( ! [X5: $i] :
( ( fail3 @ X5 @ ( n @ z ) )
= ( n @ z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(144,plain,
( ( ! [X5: $i,X13: $i] :
( ( fail3 @ X5 @ ( n @ ( s @ X13 ) ) )
= ( fail12 @ X5 @ ( n @ ( s @ X13 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(145,plain,
( ( ! [E2: $i] :
( ( fail12 @ x2 @ E2 )
= ( fail22 @ x2 @ E2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(146,plain,
( ( ! [X: $i,X2: $i,E2: $i] :
( ( fail12 @ ( y @ X @ X2 ) @ E2 )
= ( fail22 @ ( y @ X @ X2 ) @ E2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(147,plain,
( ( ! [X: $i,X2: $i,E2: $i] :
( ( fail12 @ ( x @ X @ X2 ) @ E2 )
= ( fail22 @ ( x @ X @ X2 ) @ E2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(148,plain,
( ( ! [E2: $i] :
( ( fail12 @ ( n @ z ) @ E2 )
= ( fail22 @ ( n @ z ) @ E2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(149,plain,
( ( ! [E2: $i] :
( ( fail12 @ ( n @ ( s @ z ) ) @ E2 )
= E2 ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(150,plain,
( ( ! [X11: $i,E2: $i] :
( ( fail12 @ ( n @ ( s @ ( s @ X11 ) ) ) @ E2 )
= ( fail22 @ ( n @ ( s @ ( s @ X11 ) ) ) @ E2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(151,plain,
( ( ! [X5: $i] :
( ( fail22 @ X5 @ x2 )
= ( fail32 @ X5 @ x2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(152,plain,
( ( ! [X5: $i,X: $i,X2: $i] :
( ( fail22 @ X5 @ ( y @ X @ X2 ) )
= ( fail32 @ X5 @ ( y @ X @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(153,plain,
( ( ! [X5: $i,X: $i,X2: $i] :
( ( fail22 @ X5 @ ( x @ X @ X2 ) )
= ( fail32 @ X5 @ ( x @ X @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(154,plain,
( ( ! [X5: $i] :
( ( fail22 @ X5 @ ( n @ z ) )
= ( fail32 @ X5 @ ( n @ z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(155,plain,
( ( ! [X5: $i] :
( ( fail22 @ X5 @ ( n @ ( s @ z ) ) )
= X5 ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(156,plain,
( ( ! [X5: $i,X8: $i] :
( ( fail22 @ X5 @ ( n @ ( s @ ( s @ X8 ) ) ) )
= ( fail32 @ X5 @ ( n @ ( s @ ( s @ X8 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(157,plain,
( ( ! [E2: $i] :
( ( fail32 @ x2 @ E2 )
= ( fail4 @ x2 @ E2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(158,plain,
( ( ! [X: $i,X2: $i,E2: $i] :
( ( fail32 @ ( x @ X @ X2 ) @ E2 )
= ( fail4 @ ( x @ X @ X2 ) @ E2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(159,plain,
( ( ! [A4: $i,B4: $i,E2: $i] :
( ( fail32 @ ( y @ A4 @ B4 ) @ E2 )
= ( opt @ ( y @ A4 @ ( y @ B4 @ E2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(160,plain,
( ( ! [A3: $i] :
( ( fail32 @ ( n @ A3 ) @ x2 )
= ( fail4 @ ( n @ A3 ) @ x2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(161,plain,
( ( ! [A3: $i,X: $i,X2: $i] :
( ( fail32 @ ( n @ A3 ) @ ( y @ X @ X2 ) )
= ( fail4 @ ( n @ A3 ) @ ( y @ X @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(162,plain,
( ( ! [A3: $i,X: $i,X2: $i] :
( ( fail32 @ ( n @ A3 ) @ ( x @ X @ X2 ) )
= ( fail4 @ ( n @ A3 ) @ ( x @ X @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(163,plain,
( ( ! [A3: $i,B3: $i] :
( ( fail32 @ ( n @ A3 ) @ ( n @ B3 ) )
= ( n @ ( mulNat @ A3 @ B3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(164,plain,
( ( ! [X5: $i,E2: $i] :
( ( fail4 @ X5 @ E2 )
= ( y @ ( opt @ X5 ) @ ( opt @ E2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(165,plain,
( ( ! [Y: $i] :
( ( fail @ Y @ x2 )
= ( fail1 @ Y @ x2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(166,plain,
( ( ! [Y: $i,X: $i,X2: $i] :
( ( fail @ Y @ ( y @ X @ X2 ) )
= ( fail1 @ Y @ ( y @ X @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(167,plain,
( ( ! [Y: $i,X: $i,X2: $i] :
( ( fail @ Y @ ( x @ X @ X2 ) )
= ( fail1 @ Y @ ( x @ X @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(168,plain,
( ( ! [Y: $i] :
( ( fail @ Y @ ( n @ z ) )
= Y ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(169,plain,
( ( ! [Y: $i,X2: $i] :
( ( fail @ Y @ ( n @ ( s @ X2 ) ) )
= ( fail1 @ Y @ ( n @ ( s @ X2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(170,plain,
( ( ! [E: $i] :
( ( fail1 @ x2 @ E )
= ( fail2 @ x2 @ E ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(171,plain,
( ( ! [X: $i,X2: $i,E: $i] :
( ( fail1 @ ( y @ X @ X2 ) @ E )
= ( fail2 @ ( y @ X @ X2 ) @ E ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(172,plain,
( ( ! [X: $i,X2: $i,E: $i] :
( ( fail1 @ ( x @ X @ X2 ) @ E )
= ( fail2 @ ( x @ X @ X2 ) @ E ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(173,plain,
( ( ! [A2: $i] :
( ( fail1 @ ( n @ A2 ) @ x2 )
= ( fail2 @ ( n @ A2 ) @ x2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(174,plain,
( ( ! [A2: $i,X: $i,X2: $i] :
( ( fail1 @ ( n @ A2 ) @ ( y @ X @ X2 ) )
= ( fail2 @ ( n @ A2 ) @ ( y @ X @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(175,plain,
( ( ! [A2: $i,X: $i,X2: $i] :
( ( fail1 @ ( n @ A2 ) @ ( x @ X @ X2 ) )
= ( fail2 @ ( n @ A2 ) @ ( x @ X @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(176,plain,
( ( ! [A2: $i,B2: $i] :
( ( fail1 @ ( n @ A2 ) @ ( n @ B2 ) )
= ( n @ ( addNat @ A2 @ B2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(177,plain,
( ( ! [Y: $i,E: $i] :
( ( fail2 @ Y @ E )
= ( aux @ Y @ E @ ( eq2 @ Y @ E ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(178,plain,
( ( ! [E: $i] :
( ( aux @ x2 @ E @ bfalse )
= ( x @ ( opt @ x2 ) @ ( opt @ E ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(179,plain,
( ( ! [X: $i,X2: $i,E: $i] :
( ( aux @ ( y @ X @ X2 ) @ E @ bfalse )
= ( x @ ( opt @ ( y @ X @ X2 ) ) @ ( opt @ E ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(180,plain,
( ( ! [X: $i,E: $i] :
( ( aux @ ( n @ X ) @ E @ bfalse )
= ( x @ ( opt @ ( n @ X ) ) @ ( opt @ E ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(181,plain,
( ( ! [B: $i,C: $i,E: $i] :
( ( aux @ ( x @ B @ C ) @ E @ bfalse )
= ( opt @ ( x @ B @ ( x @ C @ E ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(182,plain,
( ( ! [Y: $i,E: $i] :
( ( aux @ Y @ E @ btrue )
= ( y @ ( n @ ( s @ ( s @ z ) ) ) @ ( opt @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(183,plain,
( ( ! [X: $i] :
( ( eq3 @ ( prop4 @ X ) @ bfalse )
!= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(184,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[93]) ).
thf(185,plain,
( ( ! [X: $i] :
( ( eq3 @ ( prop4 @ X ) @ bfalse )
!= btrue ) )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(186,plain,
( ( ! [Y: $i,E: $i] :
( ( aux @ Y @ E @ btrue )
= ( y @ ( n @ ( s @ ( s @ z ) ) ) @ ( opt @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(187,plain,
( ( ! [B: $i,C: $i,E: $i] :
( ( aux @ ( x @ B @ C ) @ E @ bfalse )
= ( opt @ ( x @ B @ ( x @ C @ E ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[181]) ).
thf(188,plain,
( ( ! [X: $i,E: $i] :
( ( aux @ ( n @ X ) @ E @ bfalse )
= ( x @ ( opt @ ( n @ X ) ) @ ( opt @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[180]) ).
thf(189,plain,
( ( ! [X: $i,X2: $i,E: $i] :
( ( aux @ ( y @ X @ X2 ) @ E @ bfalse )
= ( x @ ( opt @ ( y @ X @ X2 ) ) @ ( opt @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[179]) ).
thf(190,plain,
( ( ! [E: $i] :
( ( aux @ x2 @ E @ bfalse )
= ( x @ ( opt @ x2 ) @ ( opt @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(191,plain,
( ( ! [Y: $i,E: $i] :
( ( fail2 @ Y @ E )
= ( aux @ Y @ E @ ( eq2 @ Y @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(192,plain,
( ( ! [A2: $i,B2: $i] :
( ( fail1 @ ( n @ A2 ) @ ( n @ B2 ) )
= ( n @ ( addNat @ A2 @ B2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(193,plain,
( ( ! [A2: $i,X: $i,X2: $i] :
( ( fail1 @ ( n @ A2 ) @ ( x @ X @ X2 ) )
= ( fail2 @ ( n @ A2 ) @ ( x @ X @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[175]) ).
thf(194,plain,
( ( ! [A2: $i,X: $i,X2: $i] :
( ( fail1 @ ( n @ A2 ) @ ( y @ X @ X2 ) )
= ( fail2 @ ( n @ A2 ) @ ( y @ X @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(195,plain,
( ( ! [A2: $i] :
( ( fail1 @ ( n @ A2 ) @ x2 )
= ( fail2 @ ( n @ A2 ) @ x2 ) ) )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(196,plain,
( ( ! [X: $i,X2: $i,E: $i] :
( ( fail1 @ ( x @ X @ X2 ) @ E )
= ( fail2 @ ( x @ X @ X2 ) @ E ) ) )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(197,plain,
( ( ! [X: $i,X2: $i,E: $i] :
( ( fail1 @ ( y @ X @ X2 ) @ E )
= ( fail2 @ ( y @ X @ X2 ) @ E ) ) )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(198,plain,
( ( ! [E: $i] :
( ( fail1 @ x2 @ E )
= ( fail2 @ x2 @ E ) ) )
= $true ),
inference(copy,[status(thm)],[170]) ).
thf(199,plain,
( ( ! [Y: $i,X2: $i] :
( ( fail @ Y @ ( n @ ( s @ X2 ) ) )
= ( fail1 @ Y @ ( n @ ( s @ X2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(200,plain,
( ( ! [Y: $i] :
( ( fail @ Y @ ( n @ z ) )
= Y ) )
= $true ),
inference(copy,[status(thm)],[168]) ).
thf(201,plain,
( ( ! [Y: $i,X: $i,X2: $i] :
( ( fail @ Y @ ( x @ X @ X2 ) )
= ( fail1 @ Y @ ( x @ X @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[167]) ).
thf(202,plain,
( ( ! [Y: $i,X: $i,X2: $i] :
( ( fail @ Y @ ( y @ X @ X2 ) )
= ( fail1 @ Y @ ( y @ X @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(203,plain,
( ( ! [Y: $i] :
( ( fail @ Y @ x2 )
= ( fail1 @ Y @ x2 ) ) )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(204,plain,
( ( ! [X5: $i,E2: $i] :
( ( fail4 @ X5 @ E2 )
= ( y @ ( opt @ X5 ) @ ( opt @ E2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[164]) ).
thf(205,plain,
( ( ! [A3: $i,B3: $i] :
( ( fail32 @ ( n @ A3 ) @ ( n @ B3 ) )
= ( n @ ( mulNat @ A3 @ B3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[163]) ).
thf(206,plain,
( ( ! [A3: $i,X: $i,X2: $i] :
( ( fail32 @ ( n @ A3 ) @ ( x @ X @ X2 ) )
= ( fail4 @ ( n @ A3 ) @ ( x @ X @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(207,plain,
( ( ! [A3: $i,X: $i,X2: $i] :
( ( fail32 @ ( n @ A3 ) @ ( y @ X @ X2 ) )
= ( fail4 @ ( n @ A3 ) @ ( y @ X @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[161]) ).
thf(208,plain,
( ( ! [A3: $i] :
( ( fail32 @ ( n @ A3 ) @ x2 )
= ( fail4 @ ( n @ A3 ) @ x2 ) ) )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(209,plain,
( ( ! [A4: $i,B4: $i,E2: $i] :
( ( fail32 @ ( y @ A4 @ B4 ) @ E2 )
= ( opt @ ( y @ A4 @ ( y @ B4 @ E2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(210,plain,
( ( ! [X: $i,X2: $i,E2: $i] :
( ( fail32 @ ( x @ X @ X2 ) @ E2 )
= ( fail4 @ ( x @ X @ X2 ) @ E2 ) ) )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(211,plain,
( ( ! [E2: $i] :
( ( fail32 @ x2 @ E2 )
= ( fail4 @ x2 @ E2 ) ) )
= $true ),
inference(copy,[status(thm)],[157]) ).
thf(212,plain,
( ( ! [X5: $i,X8: $i] :
( ( fail22 @ X5 @ ( n @ ( s @ ( s @ X8 ) ) ) )
= ( fail32 @ X5 @ ( n @ ( s @ ( s @ X8 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(213,plain,
( ( ! [X5: $i] :
( ( fail22 @ X5 @ ( n @ ( s @ z ) ) )
= X5 ) )
= $true ),
inference(copy,[status(thm)],[155]) ).
thf(214,plain,
( ( ! [X5: $i] :
( ( fail22 @ X5 @ ( n @ z ) )
= ( fail32 @ X5 @ ( n @ z ) ) ) )
= $true ),
inference(copy,[status(thm)],[154]) ).
thf(215,plain,
( ( ! [X5: $i,X: $i,X2: $i] :
( ( fail22 @ X5 @ ( x @ X @ X2 ) )
= ( fail32 @ X5 @ ( x @ X @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(216,plain,
( ( ! [X5: $i,X: $i,X2: $i] :
( ( fail22 @ X5 @ ( y @ X @ X2 ) )
= ( fail32 @ X5 @ ( y @ X @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(217,plain,
( ( ! [X5: $i] :
( ( fail22 @ X5 @ x2 )
= ( fail32 @ X5 @ x2 ) ) )
= $true ),
inference(copy,[status(thm)],[151]) ).
thf(218,plain,
( ( ! [X11: $i,E2: $i] :
( ( fail12 @ ( n @ ( s @ ( s @ X11 ) ) ) @ E2 )
= ( fail22 @ ( n @ ( s @ ( s @ X11 ) ) ) @ E2 ) ) )
= $true ),
inference(copy,[status(thm)],[150]) ).
thf(219,plain,
( ( ! [E2: $i] :
( ( fail12 @ ( n @ ( s @ z ) ) @ E2 )
= E2 ) )
= $true ),
inference(copy,[status(thm)],[149]) ).
thf(220,plain,
( ( ! [E2: $i] :
( ( fail12 @ ( n @ z ) @ E2 )
= ( fail22 @ ( n @ z ) @ E2 ) ) )
= $true ),
inference(copy,[status(thm)],[148]) ).
thf(221,plain,
( ( ! [X: $i,X2: $i,E2: $i] :
( ( fail12 @ ( x @ X @ X2 ) @ E2 )
= ( fail22 @ ( x @ X @ X2 ) @ E2 ) ) )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(222,plain,
( ( ! [X: $i,X2: $i,E2: $i] :
( ( fail12 @ ( y @ X @ X2 ) @ E2 )
= ( fail22 @ ( y @ X @ X2 ) @ E2 ) ) )
= $true ),
inference(copy,[status(thm)],[146]) ).
thf(223,plain,
( ( ! [E2: $i] :
( ( fail12 @ x2 @ E2 )
= ( fail22 @ x2 @ E2 ) ) )
= $true ),
inference(copy,[status(thm)],[145]) ).
thf(224,plain,
( ( ! [X5: $i,X13: $i] :
( ( fail3 @ X5 @ ( n @ ( s @ X13 ) ) )
= ( fail12 @ X5 @ ( n @ ( s @ X13 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[144]) ).
thf(225,plain,
( ( ! [X5: $i] :
( ( fail3 @ X5 @ ( n @ z ) )
= ( n @ z ) ) )
= $true ),
inference(copy,[status(thm)],[143]) ).
thf(226,plain,
( ( ! [X5: $i,X: $i,X2: $i] :
( ( fail3 @ X5 @ ( x @ X @ X2 ) )
= ( fail12 @ X5 @ ( x @ X @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(227,plain,
( ( ! [X5: $i,X: $i,X2: $i] :
( ( fail3 @ X5 @ ( y @ X @ X2 ) )
= ( fail12 @ X5 @ ( y @ X @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(228,plain,
( ( ! [X5: $i] :
( ( fail3 @ X5 @ x2 )
= ( fail12 @ X5 @ x2 ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(229,plain,
( ( ! [Y: $i] :
( ( d @ ( n @ Y ) )
= ( n @ z ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(230,plain,
( ( ! [F: $i,G: $i] :
( ( d @ ( x @ F @ G ) )
= ( x @ ( d @ F ) @ ( d @ G ) ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(231,plain,
( ( ! [H: $i,G2: $i] :
( ( d @ ( y @ H @ G2 ) )
= ( x @ ( y @ ( d @ H ) @ G2 ) @ ( y @ H @ ( d @ G2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(232,plain,
( ( ( d @ x2 )
= ( n @ ( s @ z ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(233,plain,
( ( ! [Z: $i,Y: $i] :
( ( addNat @ ( s @ Z ) @ Y )
= ( s @ ( addNat @ Z @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(234,plain,
( ( ! [Y: $i] :
( ( addNat @ z @ Y )
= Y ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(235,plain,
( ( ! [Z: $i,Y: $i] :
( ( mulNat @ ( s @ Z ) @ Y )
= ( addNat @ Y @ ( mulNat @ Z @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(236,plain,
( ( ! [Y: $i] :
( ( mulNat @ z @ Y )
= z ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(237,plain,
( ( ! [X4: $i,E: $i] :
( ( opt @ ( x @ ( n @ ( s @ X4 ) ) @ E ) )
= ( fail @ ( n @ ( s @ X4 ) ) @ E ) ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(238,plain,
( ( ! [E: $i] :
( ( opt @ ( x @ ( n @ z ) @ E ) )
= E ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(239,plain,
( ( ! [X: $i,X2: $i,E: $i] :
( ( opt @ ( x @ ( x @ X @ X2 ) @ E ) )
= ( fail @ ( x @ X @ X2 ) @ E ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(240,plain,
( ( ! [X: $i,X2: $i,E: $i] :
( ( opt @ ( x @ ( y @ X @ X2 ) @ E ) )
= ( fail @ ( y @ X @ X2 ) @ E ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(241,plain,
( ( ! [E: $i] :
( ( opt @ ( x @ x2 @ E ) )
= ( fail @ x2 @ E ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(242,plain,
( ( ! [X15: $i,E2: $i] :
( ( opt @ ( y @ ( n @ ( s @ X15 ) ) @ E2 ) )
= ( fail3 @ ( n @ ( s @ X15 ) ) @ E2 ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(243,plain,
( ( ! [E2: $i] :
( ( opt @ ( y @ ( n @ z ) @ E2 ) )
= ( n @ z ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(244,plain,
( ( ! [X: $i,X2: $i,E2: $i] :
( ( opt @ ( y @ ( x @ X @ X2 ) @ E2 ) )
= ( fail3 @ ( x @ X @ X2 ) @ E2 ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(245,plain,
( ( ! [X: $i,X2: $i,E2: $i] :
( ( opt @ ( y @ ( y @ X @ X2 ) @ E2 ) )
= ( fail3 @ ( y @ X @ X2 ) @ E2 ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(246,plain,
( ( ! [E2: $i] :
( ( opt @ ( y @ x2 @ E2 ) )
= ( fail3 @ x2 @ E2 ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(247,plain,
( ( ! [X: $i] :
( ( opt @ ( n @ X ) )
= ( n @ X ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(248,plain,
( ( ( opt @ x2 )
= x2 )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(249,plain,
( ( ! [X: $i] :
( ( prop4 @ X )
= ( eq2 @ ( opt @ ( d @ X ) ) @ ( opt @ ( d @ ( opt @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(250,plain,
( ( ( eq3 @ bfalse @ btrue )
= bfalse )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(251,plain,
( ( ( eq3 @ btrue @ bfalse )
= bfalse )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(252,plain,
( ( ! [X: $i,Y: $i] :
( ( eq2 @ ( n @ X ) @ ( n @ Y ) )
= ( eq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(253,plain,
( ( ! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq2 @ X @ Z )
!= bfalse )
| ( ( eq2 @ ( x @ X @ Y ) @ ( x @ Z @ X2 ) )
= bfalse ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(254,plain,
( ( ! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq2 @ X @ Z )
!= btrue )
| ( ( eq2 @ ( x @ X @ Y ) @ ( x @ Z @ X2 ) )
= ( eq2 @ Y @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(255,plain,
( ( ! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq2 @ X @ Z )
!= bfalse )
| ( ( eq2 @ ( y @ X @ Y ) @ ( y @ Z @ X2 ) )
= bfalse ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(256,plain,
( ( ! [X: $i,Z: $i,Y: $i,X2: $i] :
( ( ( eq2 @ X @ Z )
!= btrue )
| ( ( eq2 @ ( y @ X @ Y ) @ ( y @ Z @ X2 ) )
= ( eq2 @ Y @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(257,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( eq2 @ ( n @ X ) @ ( x @ Y @ Z ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(258,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( eq2 @ ( n @ X ) @ ( y @ Y @ Z ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(259,plain,
( ( ! [X: $i] :
( ( eq2 @ ( n @ X ) @ x2 )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(260,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( eq2 @ ( x @ X @ Y ) @ ( n @ Z ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(261,plain,
( ( ! [X: $i,Y: $i,Z: $i,X2: $i] :
( ( eq2 @ ( x @ X @ Y ) @ ( y @ Z @ X2 ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(262,plain,
( ( ! [X: $i,Y: $i] :
( ( eq2 @ ( x @ X @ Y ) @ x2 )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(263,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( eq2 @ ( y @ X @ Y ) @ ( n @ Z ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(264,plain,
( ( ! [X: $i,Y: $i,Z: $i,X2: $i] :
( ( eq2 @ ( y @ X @ Y ) @ ( x @ Z @ X2 ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(265,plain,
( ( ! [X: $i,Y: $i] :
( ( eq2 @ ( y @ X @ Y ) @ x2 )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(266,plain,
( ( ! [X: $i] :
( ( eq2 @ x2 @ ( n @ X ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(267,plain,
( ( ! [X: $i,Y: $i] :
( ( eq2 @ x2 @ ( x @ X @ Y ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(268,plain,
( ( ! [X: $i,Y: $i] :
( ( eq2 @ x2 @ ( y @ X @ Y ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(269,plain,
( ( ! [X: $i,Y: $i] :
( ( eq @ ( s @ X ) @ ( s @ Y ) )
= ( eq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(270,plain,
( ( ! [X: $i] :
( ( eq @ ( s @ X ) @ z )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(271,plain,
( ( ! [X: $i] :
( ( eq @ z @ ( s @ X ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(272,plain,
( ( ! [X: $i] :
( ( eq @ X @ X )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(273,plain,
( ( ! [X: $i] :
( ( eq2 @ X @ X )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(274,plain,
( ( ! [X: $i] :
( ( eq3 @ X @ X )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(275,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[184]) ).
thf(276,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( eq2 @ SX0 @ SX1 )
!= bfalse )
| ( ( eq2 @ ( y @ SX0 @ SX2 ) @ ( y @ SX1 @ SX3 ) )
= bfalse ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(277,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( eq2 @ SX0 @ SX1 )
!= btrue )
| ( ( eq2 @ ( x @ SX0 @ SX2 ) @ ( x @ SX1 @ SX3 ) )
= ( eq2 @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(278,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( eq2 @ SX0 @ SX1 )
!= bfalse )
| ( ( eq2 @ ( x @ SX0 @ SX2 ) @ ( x @ SX1 @ SX3 ) )
= bfalse ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(279,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( eq2 @ SX0 @ SX1 )
!= btrue )
| ( ( eq2 @ ( y @ SX0 @ SX2 ) @ ( y @ SX1 @ SX3 ) )
= ( eq2 @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(280,plain,
( ( ! [SX0: $i] :
( ( eq3 @ ( prop4 @ SX0 ) @ bfalse )
!= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(281,plain,
! [SV1: $i] :
( ( ! [SY178: $i] :
( ( aux @ SV1 @ SY178 @ btrue )
= ( y @ ( n @ ( s @ ( s @ z ) ) ) @ ( opt @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(282,plain,
! [SV2: $i] :
( ( ! [SY179: $i,SY180: $i] :
( ( aux @ ( x @ SV2 @ SY179 ) @ SY180 @ bfalse )
= ( opt @ ( x @ SV2 @ ( x @ SY179 @ SY180 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(283,plain,
! [SV3: $i] :
( ( ! [SY181: $i] :
( ( aux @ ( n @ SV3 ) @ SY181 @ bfalse )
= ( x @ ( opt @ ( n @ SV3 ) ) @ ( opt @ SY181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(284,plain,
! [SV4: $i] :
( ( ! [SY182: $i,SY183: $i] :
( ( aux @ ( y @ SV4 @ SY182 ) @ SY183 @ bfalse )
= ( x @ ( opt @ ( y @ SV4 @ SY182 ) ) @ ( opt @ SY183 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(285,plain,
! [SV5: $i] :
( ( ( aux @ x2 @ SV5 @ bfalse )
= ( x @ ( opt @ x2 ) @ ( opt @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(286,plain,
! [SV6: $i] :
( ( ! [SY184: $i] :
( ( fail2 @ SV6 @ SY184 )
= ( aux @ SV6 @ SY184 @ ( eq2 @ SV6 @ SY184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(287,plain,
! [SV7: $i] :
( ( ! [SY185: $i] :
( ( fail1 @ ( n @ SV7 ) @ ( n @ SY185 ) )
= ( n @ ( addNat @ SV7 @ SY185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(288,plain,
! [SV8: $i] :
( ( ! [SY186: $i,SY187: $i] :
( ( fail1 @ ( n @ SV8 ) @ ( x @ SY186 @ SY187 ) )
= ( fail2 @ ( n @ SV8 ) @ ( x @ SY186 @ SY187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(289,plain,
! [SV9: $i] :
( ( ! [SY188: $i,SY189: $i] :
( ( fail1 @ ( n @ SV9 ) @ ( y @ SY188 @ SY189 ) )
= ( fail2 @ ( n @ SV9 ) @ ( y @ SY188 @ SY189 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(290,plain,
! [SV10: $i] :
( ( ( fail1 @ ( n @ SV10 ) @ x2 )
= ( fail2 @ ( n @ SV10 ) @ x2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(291,plain,
! [SV11: $i] :
( ( ! [SY190: $i,SY191: $i] :
( ( fail1 @ ( x @ SV11 @ SY190 ) @ SY191 )
= ( fail2 @ ( x @ SV11 @ SY190 ) @ SY191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(292,plain,
! [SV12: $i] :
( ( ! [SY192: $i,SY193: $i] :
( ( fail1 @ ( y @ SV12 @ SY192 ) @ SY193 )
= ( fail2 @ ( y @ SV12 @ SY192 ) @ SY193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(293,plain,
! [SV13: $i] :
( ( ( fail1 @ x2 @ SV13 )
= ( fail2 @ x2 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(294,plain,
! [SV14: $i] :
( ( ! [SY194: $i] :
( ( fail @ SV14 @ ( n @ ( s @ SY194 ) ) )
= ( fail1 @ SV14 @ ( n @ ( s @ SY194 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(295,plain,
! [SV15: $i] :
( ( ( fail @ SV15 @ ( n @ z ) )
= SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(296,plain,
! [SV16: $i] :
( ( ! [SY195: $i,SY196: $i] :
( ( fail @ SV16 @ ( x @ SY195 @ SY196 ) )
= ( fail1 @ SV16 @ ( x @ SY195 @ SY196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(297,plain,
! [SV17: $i] :
( ( ! [SY197: $i,SY198: $i] :
( ( fail @ SV17 @ ( y @ SY197 @ SY198 ) )
= ( fail1 @ SV17 @ ( y @ SY197 @ SY198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(298,plain,
! [SV18: $i] :
( ( ( fail @ SV18 @ x2 )
= ( fail1 @ SV18 @ x2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(299,plain,
! [SV19: $i] :
( ( ! [SY199: $i] :
( ( fail4 @ SV19 @ SY199 )
= ( y @ ( opt @ SV19 ) @ ( opt @ SY199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(300,plain,
! [SV20: $i] :
( ( ! [SY200: $i] :
( ( fail32 @ ( n @ SV20 ) @ ( n @ SY200 ) )
= ( n @ ( mulNat @ SV20 @ SY200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(301,plain,
! [SV21: $i] :
( ( ! [SY201: $i,SY202: $i] :
( ( fail32 @ ( n @ SV21 ) @ ( x @ SY201 @ SY202 ) )
= ( fail4 @ ( n @ SV21 ) @ ( x @ SY201 @ SY202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(302,plain,
! [SV22: $i] :
( ( ! [SY203: $i,SY204: $i] :
( ( fail32 @ ( n @ SV22 ) @ ( y @ SY203 @ SY204 ) )
= ( fail4 @ ( n @ SV22 ) @ ( y @ SY203 @ SY204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(303,plain,
! [SV23: $i] :
( ( ( fail32 @ ( n @ SV23 ) @ x2 )
= ( fail4 @ ( n @ SV23 ) @ x2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(304,plain,
! [SV24: $i] :
( ( ! [SY205: $i,SY206: $i] :
( ( fail32 @ ( y @ SV24 @ SY205 ) @ SY206 )
= ( opt @ ( y @ SV24 @ ( y @ SY205 @ SY206 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(305,plain,
! [SV25: $i] :
( ( ! [SY207: $i,SY208: $i] :
( ( fail32 @ ( x @ SV25 @ SY207 ) @ SY208 )
= ( fail4 @ ( x @ SV25 @ SY207 ) @ SY208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(306,plain,
! [SV26: $i] :
( ( ( fail32 @ x2 @ SV26 )
= ( fail4 @ x2 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(307,plain,
! [SV27: $i] :
( ( ! [SY209: $i] :
( ( fail22 @ SV27 @ ( n @ ( s @ ( s @ SY209 ) ) ) )
= ( fail32 @ SV27 @ ( n @ ( s @ ( s @ SY209 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(308,plain,
! [SV28: $i] :
( ( ( fail22 @ SV28 @ ( n @ ( s @ z ) ) )
= SV28 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(309,plain,
! [SV29: $i] :
( ( ( fail22 @ SV29 @ ( n @ z ) )
= ( fail32 @ SV29 @ ( n @ z ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(310,plain,
! [SV30: $i] :
( ( ! [SY210: $i,SY211: $i] :
( ( fail22 @ SV30 @ ( x @ SY210 @ SY211 ) )
= ( fail32 @ SV30 @ ( x @ SY210 @ SY211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(311,plain,
! [SV31: $i] :
( ( ! [SY212: $i,SY213: $i] :
( ( fail22 @ SV31 @ ( y @ SY212 @ SY213 ) )
= ( fail32 @ SV31 @ ( y @ SY212 @ SY213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(312,plain,
! [SV32: $i] :
( ( ( fail22 @ SV32 @ x2 )
= ( fail32 @ SV32 @ x2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(313,plain,
! [SV33: $i] :
( ( ! [SY214: $i] :
( ( fail12 @ ( n @ ( s @ ( s @ SV33 ) ) ) @ SY214 )
= ( fail22 @ ( n @ ( s @ ( s @ SV33 ) ) ) @ SY214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(314,plain,
! [SV34: $i] :
( ( ( fail12 @ ( n @ ( s @ z ) ) @ SV34 )
= SV34 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(315,plain,
! [SV35: $i] :
( ( ( fail12 @ ( n @ z ) @ SV35 )
= ( fail22 @ ( n @ z ) @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(316,plain,
! [SV36: $i] :
( ( ! [SY215: $i,SY216: $i] :
( ( fail12 @ ( x @ SV36 @ SY215 ) @ SY216 )
= ( fail22 @ ( x @ SV36 @ SY215 ) @ SY216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(317,plain,
! [SV37: $i] :
( ( ! [SY217: $i,SY218: $i] :
( ( fail12 @ ( y @ SV37 @ SY217 ) @ SY218 )
= ( fail22 @ ( y @ SV37 @ SY217 ) @ SY218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(318,plain,
! [SV38: $i] :
( ( ( fail12 @ x2 @ SV38 )
= ( fail22 @ x2 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(319,plain,
! [SV39: $i] :
( ( ! [SY219: $i] :
( ( fail3 @ SV39 @ ( n @ ( s @ SY219 ) ) )
= ( fail12 @ SV39 @ ( n @ ( s @ SY219 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(320,plain,
! [SV40: $i] :
( ( ( fail3 @ SV40 @ ( n @ z ) )
= ( n @ z ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(321,plain,
! [SV41: $i] :
( ( ! [SY220: $i,SY221: $i] :
( ( fail3 @ SV41 @ ( x @ SY220 @ SY221 ) )
= ( fail12 @ SV41 @ ( x @ SY220 @ SY221 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(322,plain,
! [SV42: $i] :
( ( ! [SY222: $i,SY223: $i] :
( ( fail3 @ SV42 @ ( y @ SY222 @ SY223 ) )
= ( fail12 @ SV42 @ ( y @ SY222 @ SY223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(323,plain,
! [SV43: $i] :
( ( ( fail3 @ SV43 @ x2 )
= ( fail12 @ SV43 @ x2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(324,plain,
! [SV44: $i] :
( ( ( d @ ( n @ SV44 ) )
= ( n @ z ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(325,plain,
! [SV45: $i] :
( ( ! [SY224: $i] :
( ( d @ ( x @ SV45 @ SY224 ) )
= ( x @ ( d @ SV45 ) @ ( d @ SY224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(326,plain,
! [SV46: $i] :
( ( ! [SY225: $i] :
( ( d @ ( y @ SV46 @ SY225 ) )
= ( x @ ( y @ ( d @ SV46 ) @ SY225 ) @ ( y @ SV46 @ ( d @ SY225 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(327,plain,
! [SV47: $i] :
( ( ! [SY226: $i] :
( ( addNat @ ( s @ SV47 ) @ SY226 )
= ( s @ ( addNat @ SV47 @ SY226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(328,plain,
! [SV48: $i] :
( ( ( addNat @ z @ SV48 )
= SV48 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(329,plain,
! [SV49: $i] :
( ( ! [SY227: $i] :
( ( mulNat @ ( s @ SV49 ) @ SY227 )
= ( addNat @ SY227 @ ( mulNat @ SV49 @ SY227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(330,plain,
! [SV50: $i] :
( ( ( mulNat @ z @ SV50 )
= z )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(331,plain,
! [SV51: $i] :
( ( ! [SY228: $i] :
( ( opt @ ( x @ ( n @ ( s @ SV51 ) ) @ SY228 ) )
= ( fail @ ( n @ ( s @ SV51 ) ) @ SY228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(332,plain,
! [SV52: $i] :
( ( ( opt @ ( x @ ( n @ z ) @ SV52 ) )
= SV52 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(333,plain,
! [SV53: $i] :
( ( ! [SY229: $i,SY230: $i] :
( ( opt @ ( x @ ( x @ SV53 @ SY229 ) @ SY230 ) )
= ( fail @ ( x @ SV53 @ SY229 ) @ SY230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(334,plain,
! [SV54: $i] :
( ( ! [SY231: $i,SY232: $i] :
( ( opt @ ( x @ ( y @ SV54 @ SY231 ) @ SY232 ) )
= ( fail @ ( y @ SV54 @ SY231 ) @ SY232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(335,plain,
! [SV55: $i] :
( ( ( opt @ ( x @ x2 @ SV55 ) )
= ( fail @ x2 @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(336,plain,
! [SV56: $i] :
( ( ! [SY233: $i] :
( ( opt @ ( y @ ( n @ ( s @ SV56 ) ) @ SY233 ) )
= ( fail3 @ ( n @ ( s @ SV56 ) ) @ SY233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(337,plain,
! [SV57: $i] :
( ( ( opt @ ( y @ ( n @ z ) @ SV57 ) )
= ( n @ z ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(338,plain,
! [SV58: $i] :
( ( ! [SY234: $i,SY235: $i] :
( ( opt @ ( y @ ( x @ SV58 @ SY234 ) @ SY235 ) )
= ( fail3 @ ( x @ SV58 @ SY234 ) @ SY235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(339,plain,
! [SV59: $i] :
( ( ! [SY236: $i,SY237: $i] :
( ( opt @ ( y @ ( y @ SV59 @ SY236 ) @ SY237 ) )
= ( fail3 @ ( y @ SV59 @ SY236 ) @ SY237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(340,plain,
! [SV60: $i] :
( ( ( opt @ ( y @ x2 @ SV60 ) )
= ( fail3 @ x2 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(341,plain,
! [SV61: $i] :
( ( ( opt @ ( n @ SV61 ) )
= ( n @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(342,plain,
! [SV62: $i] :
( ( ( prop4 @ SV62 )
= ( eq2 @ ( opt @ ( d @ SV62 ) ) @ ( opt @ ( d @ ( opt @ SV62 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(343,plain,
! [SV63: $i] :
( ( ! [SY238: $i] :
( ( eq2 @ ( n @ SV63 ) @ ( n @ SY238 ) )
= ( eq @ SV63 @ SY238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(344,plain,
! [SV64: $i] :
( ( ! [SY239: $i,SY240: $i] :
( ( eq2 @ ( n @ SV64 ) @ ( x @ SY239 @ SY240 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(345,plain,
! [SV65: $i] :
( ( ! [SY241: $i,SY242: $i] :
( ( eq2 @ ( n @ SV65 ) @ ( y @ SY241 @ SY242 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(346,plain,
! [SV66: $i] :
( ( ( eq2 @ ( n @ SV66 ) @ x2 )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(347,plain,
! [SV67: $i] :
( ( ! [SY243: $i,SY244: $i] :
( ( eq2 @ ( x @ SV67 @ SY243 ) @ ( n @ SY244 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(348,plain,
! [SV68: $i] :
( ( ! [SY245: $i,SY246: $i,SY247: $i] :
( ( eq2 @ ( x @ SV68 @ SY245 ) @ ( y @ SY246 @ SY247 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(349,plain,
! [SV69: $i] :
( ( ! [SY248: $i] :
( ( eq2 @ ( x @ SV69 @ SY248 ) @ x2 )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(350,plain,
! [SV70: $i] :
( ( ! [SY249: $i,SY250: $i] :
( ( eq2 @ ( y @ SV70 @ SY249 ) @ ( n @ SY250 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(351,plain,
! [SV71: $i] :
( ( ! [SY251: $i,SY252: $i,SY253: $i] :
( ( eq2 @ ( y @ SV71 @ SY251 ) @ ( x @ SY252 @ SY253 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(352,plain,
! [SV72: $i] :
( ( ! [SY254: $i] :
( ( eq2 @ ( y @ SV72 @ SY254 ) @ x2 )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(353,plain,
! [SV73: $i] :
( ( ( eq2 @ x2 @ ( n @ SV73 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(354,plain,
! [SV74: $i] :
( ( ! [SY255: $i] :
( ( eq2 @ x2 @ ( x @ SV74 @ SY255 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(355,plain,
! [SV75: $i] :
( ( ! [SY256: $i] :
( ( eq2 @ x2 @ ( y @ SV75 @ SY256 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(356,plain,
! [SV76: $i] :
( ( ! [SY257: $i] :
( ( eq @ ( s @ SV76 ) @ ( s @ SY257 ) )
= ( eq @ SV76 @ SY257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(357,plain,
! [SV77: $i] :
( ( ( eq @ ( s @ SV77 ) @ z )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(358,plain,
! [SV78: $i] :
( ( ( eq @ z @ ( s @ SV78 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(359,plain,
! [SV79: $i] :
( ( ( eq @ SV79 @ SV79 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(360,plain,
! [SV80: $i] :
( ( ( eq2 @ SV80 @ SV80 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(361,plain,
! [SV81: $i] :
( ( ( eq3 @ SV81 @ SV81 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(362,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(363,plain,
! [SV82: $i] :
( ( ! [SY258: $i,SY259: $i,SY260: $i] :
( ( ( eq2 @ SV82 @ SY258 )
!= bfalse )
| ( ( eq2 @ ( y @ SV82 @ SY259 ) @ ( y @ SY258 @ SY260 ) )
= bfalse ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(364,plain,
! [SV83: $i] :
( ( ! [SY261: $i,SY262: $i,SY263: $i] :
( ( ( eq2 @ SV83 @ SY261 )
!= btrue )
| ( ( eq2 @ ( x @ SV83 @ SY262 ) @ ( x @ SY261 @ SY263 ) )
= ( eq2 @ SY262 @ SY263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(365,plain,
! [SV84: $i] :
( ( ! [SY264: $i,SY265: $i,SY266: $i] :
( ( ( eq2 @ SV84 @ SY264 )
!= bfalse )
| ( ( eq2 @ ( x @ SV84 @ SY265 ) @ ( x @ SY264 @ SY266 ) )
= bfalse ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(366,plain,
! [SV85: $i] :
( ( ! [SY267: $i,SY268: $i,SY269: $i] :
( ( ( eq2 @ SV85 @ SY267 )
!= btrue )
| ( ( eq2 @ ( y @ SV85 @ SY268 ) @ ( y @ SY267 @ SY269 ) )
= ( eq2 @ SY268 @ SY269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(367,plain,
! [SV86: $i] :
( ( ( eq3 @ ( prop4 @ SV86 ) @ bfalse )
!= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(368,plain,
! [SV87: $i,SV1: $i] :
( ( ( aux @ SV1 @ SV87 @ btrue )
= ( y @ ( n @ ( s @ ( s @ z ) ) ) @ ( opt @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(369,plain,
! [SV88: $i,SV2: $i] :
( ( ! [SY270: $i] :
( ( aux @ ( x @ SV2 @ SV88 ) @ SY270 @ bfalse )
= ( opt @ ( x @ SV2 @ ( x @ SV88 @ SY270 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(370,plain,
! [SV89: $i,SV3: $i] :
( ( ( aux @ ( n @ SV3 ) @ SV89 @ bfalse )
= ( x @ ( opt @ ( n @ SV3 ) ) @ ( opt @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(371,plain,
! [SV90: $i,SV4: $i] :
( ( ! [SY271: $i] :
( ( aux @ ( y @ SV4 @ SV90 ) @ SY271 @ bfalse )
= ( x @ ( opt @ ( y @ SV4 @ SV90 ) ) @ ( opt @ SY271 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(372,plain,
! [SV91: $i,SV6: $i] :
( ( ( fail2 @ SV6 @ SV91 )
= ( aux @ SV6 @ SV91 @ ( eq2 @ SV6 @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(373,plain,
! [SV92: $i,SV7: $i] :
( ( ( fail1 @ ( n @ SV7 ) @ ( n @ SV92 ) )
= ( n @ ( addNat @ SV7 @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(374,plain,
! [SV93: $i,SV8: $i] :
( ( ! [SY272: $i] :
( ( fail1 @ ( n @ SV8 ) @ ( x @ SV93 @ SY272 ) )
= ( fail2 @ ( n @ SV8 ) @ ( x @ SV93 @ SY272 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(375,plain,
! [SV94: $i,SV9: $i] :
( ( ! [SY273: $i] :
( ( fail1 @ ( n @ SV9 ) @ ( y @ SV94 @ SY273 ) )
= ( fail2 @ ( n @ SV9 ) @ ( y @ SV94 @ SY273 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(376,plain,
! [SV95: $i,SV11: $i] :
( ( ! [SY274: $i] :
( ( fail1 @ ( x @ SV11 @ SV95 ) @ SY274 )
= ( fail2 @ ( x @ SV11 @ SV95 ) @ SY274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(377,plain,
! [SV96: $i,SV12: $i] :
( ( ! [SY275: $i] :
( ( fail1 @ ( y @ SV12 @ SV96 ) @ SY275 )
= ( fail2 @ ( y @ SV12 @ SV96 ) @ SY275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(378,plain,
! [SV97: $i,SV14: $i] :
( ( ( fail @ SV14 @ ( n @ ( s @ SV97 ) ) )
= ( fail1 @ SV14 @ ( n @ ( s @ SV97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(379,plain,
! [SV98: $i,SV16: $i] :
( ( ! [SY276: $i] :
( ( fail @ SV16 @ ( x @ SV98 @ SY276 ) )
= ( fail1 @ SV16 @ ( x @ SV98 @ SY276 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(380,plain,
! [SV99: $i,SV17: $i] :
( ( ! [SY277: $i] :
( ( fail @ SV17 @ ( y @ SV99 @ SY277 ) )
= ( fail1 @ SV17 @ ( y @ SV99 @ SY277 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(381,plain,
! [SV100: $i,SV19: $i] :
( ( ( fail4 @ SV19 @ SV100 )
= ( y @ ( opt @ SV19 ) @ ( opt @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(382,plain,
! [SV101: $i,SV20: $i] :
( ( ( fail32 @ ( n @ SV20 ) @ ( n @ SV101 ) )
= ( n @ ( mulNat @ SV20 @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(383,plain,
! [SV102: $i,SV21: $i] :
( ( ! [SY278: $i] :
( ( fail32 @ ( n @ SV21 ) @ ( x @ SV102 @ SY278 ) )
= ( fail4 @ ( n @ SV21 ) @ ( x @ SV102 @ SY278 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(384,plain,
! [SV103: $i,SV22: $i] :
( ( ! [SY279: $i] :
( ( fail32 @ ( n @ SV22 ) @ ( y @ SV103 @ SY279 ) )
= ( fail4 @ ( n @ SV22 ) @ ( y @ SV103 @ SY279 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(385,plain,
! [SV104: $i,SV24: $i] :
( ( ! [SY280: $i] :
( ( fail32 @ ( y @ SV24 @ SV104 ) @ SY280 )
= ( opt @ ( y @ SV24 @ ( y @ SV104 @ SY280 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(386,plain,
! [SV105: $i,SV25: $i] :
( ( ! [SY281: $i] :
( ( fail32 @ ( x @ SV25 @ SV105 ) @ SY281 )
= ( fail4 @ ( x @ SV25 @ SV105 ) @ SY281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(387,plain,
! [SV106: $i,SV27: $i] :
( ( ( fail22 @ SV27 @ ( n @ ( s @ ( s @ SV106 ) ) ) )
= ( fail32 @ SV27 @ ( n @ ( s @ ( s @ SV106 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(388,plain,
! [SV107: $i,SV30: $i] :
( ( ! [SY282: $i] :
( ( fail22 @ SV30 @ ( x @ SV107 @ SY282 ) )
= ( fail32 @ SV30 @ ( x @ SV107 @ SY282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(389,plain,
! [SV108: $i,SV31: $i] :
( ( ! [SY283: $i] :
( ( fail22 @ SV31 @ ( y @ SV108 @ SY283 ) )
= ( fail32 @ SV31 @ ( y @ SV108 @ SY283 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(390,plain,
! [SV109: $i,SV33: $i] :
( ( ( fail12 @ ( n @ ( s @ ( s @ SV33 ) ) ) @ SV109 )
= ( fail22 @ ( n @ ( s @ ( s @ SV33 ) ) ) @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(391,plain,
! [SV110: $i,SV36: $i] :
( ( ! [SY284: $i] :
( ( fail12 @ ( x @ SV36 @ SV110 ) @ SY284 )
= ( fail22 @ ( x @ SV36 @ SV110 ) @ SY284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(392,plain,
! [SV111: $i,SV37: $i] :
( ( ! [SY285: $i] :
( ( fail12 @ ( y @ SV37 @ SV111 ) @ SY285 )
= ( fail22 @ ( y @ SV37 @ SV111 ) @ SY285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(393,plain,
! [SV112: $i,SV39: $i] :
( ( ( fail3 @ SV39 @ ( n @ ( s @ SV112 ) ) )
= ( fail12 @ SV39 @ ( n @ ( s @ SV112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(394,plain,
! [SV113: $i,SV41: $i] :
( ( ! [SY286: $i] :
( ( fail3 @ SV41 @ ( x @ SV113 @ SY286 ) )
= ( fail12 @ SV41 @ ( x @ SV113 @ SY286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(395,plain,
! [SV114: $i,SV42: $i] :
( ( ! [SY287: $i] :
( ( fail3 @ SV42 @ ( y @ SV114 @ SY287 ) )
= ( fail12 @ SV42 @ ( y @ SV114 @ SY287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(396,plain,
! [SV115: $i,SV45: $i] :
( ( ( d @ ( x @ SV45 @ SV115 ) )
= ( x @ ( d @ SV45 ) @ ( d @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(397,plain,
! [SV116: $i,SV46: $i] :
( ( ( d @ ( y @ SV46 @ SV116 ) )
= ( x @ ( y @ ( d @ SV46 ) @ SV116 ) @ ( y @ SV46 @ ( d @ SV116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(398,plain,
! [SV117: $i,SV47: $i] :
( ( ( addNat @ ( s @ SV47 ) @ SV117 )
= ( s @ ( addNat @ SV47 @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(399,plain,
! [SV118: $i,SV49: $i] :
( ( ( mulNat @ ( s @ SV49 ) @ SV118 )
= ( addNat @ SV118 @ ( mulNat @ SV49 @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(400,plain,
! [SV119: $i,SV51: $i] :
( ( ( opt @ ( x @ ( n @ ( s @ SV51 ) ) @ SV119 ) )
= ( fail @ ( n @ ( s @ SV51 ) ) @ SV119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(401,plain,
! [SV120: $i,SV53: $i] :
( ( ! [SY288: $i] :
( ( opt @ ( x @ ( x @ SV53 @ SV120 ) @ SY288 ) )
= ( fail @ ( x @ SV53 @ SV120 ) @ SY288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(402,plain,
! [SV121: $i,SV54: $i] :
( ( ! [SY289: $i] :
( ( opt @ ( x @ ( y @ SV54 @ SV121 ) @ SY289 ) )
= ( fail @ ( y @ SV54 @ SV121 ) @ SY289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(403,plain,
! [SV122: $i,SV56: $i] :
( ( ( opt @ ( y @ ( n @ ( s @ SV56 ) ) @ SV122 ) )
= ( fail3 @ ( n @ ( s @ SV56 ) ) @ SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(404,plain,
! [SV123: $i,SV58: $i] :
( ( ! [SY290: $i] :
( ( opt @ ( y @ ( x @ SV58 @ SV123 ) @ SY290 ) )
= ( fail3 @ ( x @ SV58 @ SV123 ) @ SY290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(405,plain,
! [SV124: $i,SV59: $i] :
( ( ! [SY291: $i] :
( ( opt @ ( y @ ( y @ SV59 @ SV124 ) @ SY291 ) )
= ( fail3 @ ( y @ SV59 @ SV124 ) @ SY291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(406,plain,
! [SV125: $i,SV63: $i] :
( ( ( eq2 @ ( n @ SV63 ) @ ( n @ SV125 ) )
= ( eq @ SV63 @ SV125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(407,plain,
! [SV126: $i,SV64: $i] :
( ( ! [SY292: $i] :
( ( eq2 @ ( n @ SV64 ) @ ( x @ SV126 @ SY292 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(408,plain,
! [SV127: $i,SV65: $i] :
( ( ! [SY293: $i] :
( ( eq2 @ ( n @ SV65 ) @ ( y @ SV127 @ SY293 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(409,plain,
! [SV128: $i,SV67: $i] :
( ( ! [SY294: $i] :
( ( eq2 @ ( x @ SV67 @ SV128 ) @ ( n @ SY294 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(410,plain,
! [SV129: $i,SV68: $i] :
( ( ! [SY295: $i,SY296: $i] :
( ( eq2 @ ( x @ SV68 @ SV129 ) @ ( y @ SY295 @ SY296 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(411,plain,
! [SV130: $i,SV69: $i] :
( ( ( eq2 @ ( x @ SV69 @ SV130 ) @ x2 )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(412,plain,
! [SV131: $i,SV70: $i] :
( ( ! [SY297: $i] :
( ( eq2 @ ( y @ SV70 @ SV131 ) @ ( n @ SY297 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(413,plain,
! [SV132: $i,SV71: $i] :
( ( ! [SY298: $i,SY299: $i] :
( ( eq2 @ ( y @ SV71 @ SV132 ) @ ( x @ SY298 @ SY299 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(414,plain,
! [SV133: $i,SV72: $i] :
( ( ( eq2 @ ( y @ SV72 @ SV133 ) @ x2 )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(415,plain,
! [SV134: $i,SV74: $i] :
( ( ( eq2 @ x2 @ ( x @ SV74 @ SV134 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(416,plain,
! [SV135: $i,SV75: $i] :
( ( ( eq2 @ x2 @ ( y @ SV75 @ SV135 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(417,plain,
! [SV136: $i,SV76: $i] :
( ( ( eq @ ( s @ SV76 ) @ ( s @ SV136 ) )
= ( eq @ SV76 @ SV136 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(418,plain,
! [SV137: $i,SV82: $i] :
( ( ! [SY300: $i,SY301: $i] :
( ( ( eq2 @ SV82 @ SV137 )
!= bfalse )
| ( ( eq2 @ ( y @ SV82 @ SY300 ) @ ( y @ SV137 @ SY301 ) )
= bfalse ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(419,plain,
! [SV138: $i,SV83: $i] :
( ( ! [SY302: $i,SY303: $i] :
( ( ( eq2 @ SV83 @ SV138 )
!= btrue )
| ( ( eq2 @ ( x @ SV83 @ SY302 ) @ ( x @ SV138 @ SY303 ) )
= ( eq2 @ SY302 @ SY303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(420,plain,
! [SV139: $i,SV84: $i] :
( ( ! [SY304: $i,SY305: $i] :
( ( ( eq2 @ SV84 @ SV139 )
!= bfalse )
| ( ( eq2 @ ( x @ SV84 @ SY304 ) @ ( x @ SV139 @ SY305 ) )
= bfalse ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(421,plain,
! [SV140: $i,SV85: $i] :
( ( ! [SY306: $i,SY307: $i] :
( ( ( eq2 @ SV85 @ SV140 )
!= btrue )
| ( ( eq2 @ ( y @ SV85 @ SY306 ) @ ( y @ SV140 @ SY307 ) )
= ( eq2 @ SY306 @ SY307 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(422,plain,
! [SV86: $i] :
( ( ( eq3 @ ( prop4 @ SV86 ) @ bfalse )
= btrue )
= $false ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(423,plain,
! [SV141: $i,SV88: $i,SV2: $i] :
( ( ( aux @ ( x @ SV2 @ SV88 ) @ SV141 @ bfalse )
= ( opt @ ( x @ SV2 @ ( x @ SV88 @ SV141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(424,plain,
! [SV142: $i,SV90: $i,SV4: $i] :
( ( ( aux @ ( y @ SV4 @ SV90 ) @ SV142 @ bfalse )
= ( x @ ( opt @ ( y @ SV4 @ SV90 ) ) @ ( opt @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(425,plain,
! [SV143: $i,SV93: $i,SV8: $i] :
( ( ( fail1 @ ( n @ SV8 ) @ ( x @ SV93 @ SV143 ) )
= ( fail2 @ ( n @ SV8 ) @ ( x @ SV93 @ SV143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(426,plain,
! [SV144: $i,SV94: $i,SV9: $i] :
( ( ( fail1 @ ( n @ SV9 ) @ ( y @ SV94 @ SV144 ) )
= ( fail2 @ ( n @ SV9 ) @ ( y @ SV94 @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(427,plain,
! [SV145: $i,SV95: $i,SV11: $i] :
( ( ( fail1 @ ( x @ SV11 @ SV95 ) @ SV145 )
= ( fail2 @ ( x @ SV11 @ SV95 ) @ SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(428,plain,
! [SV146: $i,SV96: $i,SV12: $i] :
( ( ( fail1 @ ( y @ SV12 @ SV96 ) @ SV146 )
= ( fail2 @ ( y @ SV12 @ SV96 ) @ SV146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(429,plain,
! [SV147: $i,SV98: $i,SV16: $i] :
( ( ( fail @ SV16 @ ( x @ SV98 @ SV147 ) )
= ( fail1 @ SV16 @ ( x @ SV98 @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(430,plain,
! [SV148: $i,SV99: $i,SV17: $i] :
( ( ( fail @ SV17 @ ( y @ SV99 @ SV148 ) )
= ( fail1 @ SV17 @ ( y @ SV99 @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(431,plain,
! [SV149: $i,SV102: $i,SV21: $i] :
( ( ( fail32 @ ( n @ SV21 ) @ ( x @ SV102 @ SV149 ) )
= ( fail4 @ ( n @ SV21 ) @ ( x @ SV102 @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(432,plain,
! [SV150: $i,SV103: $i,SV22: $i] :
( ( ( fail32 @ ( n @ SV22 ) @ ( y @ SV103 @ SV150 ) )
= ( fail4 @ ( n @ SV22 ) @ ( y @ SV103 @ SV150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(433,plain,
! [SV151: $i,SV104: $i,SV24: $i] :
( ( ( fail32 @ ( y @ SV24 @ SV104 ) @ SV151 )
= ( opt @ ( y @ SV24 @ ( y @ SV104 @ SV151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(434,plain,
! [SV152: $i,SV105: $i,SV25: $i] :
( ( ( fail32 @ ( x @ SV25 @ SV105 ) @ SV152 )
= ( fail4 @ ( x @ SV25 @ SV105 ) @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(435,plain,
! [SV153: $i,SV107: $i,SV30: $i] :
( ( ( fail22 @ SV30 @ ( x @ SV107 @ SV153 ) )
= ( fail32 @ SV30 @ ( x @ SV107 @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(436,plain,
! [SV154: $i,SV108: $i,SV31: $i] :
( ( ( fail22 @ SV31 @ ( y @ SV108 @ SV154 ) )
= ( fail32 @ SV31 @ ( y @ SV108 @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(437,plain,
! [SV155: $i,SV110: $i,SV36: $i] :
( ( ( fail12 @ ( x @ SV36 @ SV110 ) @ SV155 )
= ( fail22 @ ( x @ SV36 @ SV110 ) @ SV155 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(438,plain,
! [SV156: $i,SV111: $i,SV37: $i] :
( ( ( fail12 @ ( y @ SV37 @ SV111 ) @ SV156 )
= ( fail22 @ ( y @ SV37 @ SV111 ) @ SV156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(439,plain,
! [SV157: $i,SV113: $i,SV41: $i] :
( ( ( fail3 @ SV41 @ ( x @ SV113 @ SV157 ) )
= ( fail12 @ SV41 @ ( x @ SV113 @ SV157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(440,plain,
! [SV158: $i,SV114: $i,SV42: $i] :
( ( ( fail3 @ SV42 @ ( y @ SV114 @ SV158 ) )
= ( fail12 @ SV42 @ ( y @ SV114 @ SV158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(441,plain,
! [SV159: $i,SV120: $i,SV53: $i] :
( ( ( opt @ ( x @ ( x @ SV53 @ SV120 ) @ SV159 ) )
= ( fail @ ( x @ SV53 @ SV120 ) @ SV159 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(442,plain,
! [SV160: $i,SV121: $i,SV54: $i] :
( ( ( opt @ ( x @ ( y @ SV54 @ SV121 ) @ SV160 ) )
= ( fail @ ( y @ SV54 @ SV121 ) @ SV160 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(443,plain,
! [SV161: $i,SV123: $i,SV58: $i] :
( ( ( opt @ ( y @ ( x @ SV58 @ SV123 ) @ SV161 ) )
= ( fail3 @ ( x @ SV58 @ SV123 ) @ SV161 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(444,plain,
! [SV162: $i,SV124: $i,SV59: $i] :
( ( ( opt @ ( y @ ( y @ SV59 @ SV124 ) @ SV162 ) )
= ( fail3 @ ( y @ SV59 @ SV124 ) @ SV162 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(445,plain,
! [SV163: $i,SV126: $i,SV64: $i] :
( ( ( eq2 @ ( n @ SV64 ) @ ( x @ SV126 @ SV163 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(446,plain,
! [SV164: $i,SV127: $i,SV65: $i] :
( ( ( eq2 @ ( n @ SV65 ) @ ( y @ SV127 @ SV164 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(447,plain,
! [SV165: $i,SV128: $i,SV67: $i] :
( ( ( eq2 @ ( x @ SV67 @ SV128 ) @ ( n @ SV165 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(448,plain,
! [SV166: $i,SV129: $i,SV68: $i] :
( ( ! [SY308: $i] :
( ( eq2 @ ( x @ SV68 @ SV129 ) @ ( y @ SV166 @ SY308 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(449,plain,
! [SV167: $i,SV131: $i,SV70: $i] :
( ( ( eq2 @ ( y @ SV70 @ SV131 ) @ ( n @ SV167 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(450,plain,
! [SV168: $i,SV132: $i,SV71: $i] :
( ( ! [SY309: $i] :
( ( eq2 @ ( y @ SV71 @ SV132 ) @ ( x @ SV168 @ SY309 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(451,plain,
! [SV169: $i,SV137: $i,SV82: $i] :
( ( ! [SY310: $i] :
( ( ( eq2 @ SV82 @ SV137 )
!= bfalse )
| ( ( eq2 @ ( y @ SV82 @ SV169 ) @ ( y @ SV137 @ SY310 ) )
= bfalse ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(452,plain,
! [SV170: $i,SV138: $i,SV83: $i] :
( ( ! [SY311: $i] :
( ( ( eq2 @ SV83 @ SV138 )
!= btrue )
| ( ( eq2 @ ( x @ SV83 @ SV170 ) @ ( x @ SV138 @ SY311 ) )
= ( eq2 @ SV170 @ SY311 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(453,plain,
! [SV171: $i,SV139: $i,SV84: $i] :
( ( ! [SY312: $i] :
( ( ( eq2 @ SV84 @ SV139 )
!= bfalse )
| ( ( eq2 @ ( x @ SV84 @ SV171 ) @ ( x @ SV139 @ SY312 ) )
= bfalse ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(454,plain,
! [SV172: $i,SV140: $i,SV85: $i] :
( ( ! [SY313: $i] :
( ( ( eq2 @ SV85 @ SV140 )
!= btrue )
| ( ( eq2 @ ( y @ SV85 @ SV172 ) @ ( y @ SV140 @ SY313 ) )
= ( eq2 @ SV172 @ SY313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(455,plain,
! [SV173: $i,SV166: $i,SV129: $i,SV68: $i] :
( ( ( eq2 @ ( x @ SV68 @ SV129 ) @ ( y @ SV166 @ SV173 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(456,plain,
! [SV174: $i,SV168: $i,SV132: $i,SV71: $i] :
( ( ( eq2 @ ( y @ SV71 @ SV132 ) @ ( x @ SV168 @ SV174 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(457,plain,
! [SV175: $i,SV169: $i,SV137: $i,SV82: $i] :
( ( ( ( eq2 @ SV82 @ SV137 )
!= bfalse )
| ( ( eq2 @ ( y @ SV82 @ SV169 ) @ ( y @ SV137 @ SV175 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(458,plain,
! [SV176: $i,SV170: $i,SV138: $i,SV83: $i] :
( ( ( ( eq2 @ SV83 @ SV138 )
!= btrue )
| ( ( eq2 @ ( x @ SV83 @ SV170 ) @ ( x @ SV138 @ SV176 ) )
= ( eq2 @ SV170 @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(459,plain,
! [SV177: $i,SV171: $i,SV139: $i,SV84: $i] :
( ( ( ( eq2 @ SV84 @ SV139 )
!= bfalse )
| ( ( eq2 @ ( x @ SV84 @ SV171 ) @ ( x @ SV139 @ SV177 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(460,plain,
! [SV178: $i,SV172: $i,SV140: $i,SV85: $i] :
( ( ( ( eq2 @ SV85 @ SV140 )
!= btrue )
| ( ( eq2 @ ( y @ SV85 @ SV172 ) @ ( y @ SV140 @ SV178 ) )
= ( eq2 @ SV172 @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(461,plain,
! [SV175: $i,SV169: $i,SV137: $i,SV82: $i] :
( ( ( ( eq2 @ SV82 @ SV137 )
!= bfalse )
= $true )
| ( ( ( eq2 @ ( y @ SV82 @ SV169 ) @ ( y @ SV137 @ SV175 ) )
= bfalse )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[457]) ).
thf(462,plain,
! [SV176: $i,SV170: $i,SV138: $i,SV83: $i] :
( ( ( ( eq2 @ SV83 @ SV138 )
!= btrue )
= $true )
| ( ( ( eq2 @ ( x @ SV83 @ SV170 ) @ ( x @ SV138 @ SV176 ) )
= ( eq2 @ SV170 @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[458]) ).
thf(463,plain,
! [SV177: $i,SV171: $i,SV139: $i,SV84: $i] :
( ( ( ( eq2 @ SV84 @ SV139 )
!= bfalse )
= $true )
| ( ( ( eq2 @ ( x @ SV84 @ SV171 ) @ ( x @ SV139 @ SV177 ) )
= bfalse )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[459]) ).
thf(464,plain,
! [SV178: $i,SV172: $i,SV140: $i,SV85: $i] :
( ( ( ( eq2 @ SV85 @ SV140 )
!= btrue )
= $true )
| ( ( ( eq2 @ ( y @ SV85 @ SV172 ) @ ( y @ SV140 @ SV178 ) )
= ( eq2 @ SV172 @ SV178 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[460]) ).
thf(465,plain,
! [SV175: $i,SV169: $i,SV137: $i,SV82: $i] :
( ( ( ( eq2 @ SV82 @ SV137 )
= bfalse )
= $false )
| ( ( ( eq2 @ ( y @ SV82 @ SV169 ) @ ( y @ SV137 @ SV175 ) )
= bfalse )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(466,plain,
! [SV176: $i,SV170: $i,SV138: $i,SV83: $i] :
( ( ( ( eq2 @ SV83 @ SV138 )
= btrue )
= $false )
| ( ( ( eq2 @ ( x @ SV83 @ SV170 ) @ ( x @ SV138 @ SV176 ) )
= ( eq2 @ SV170 @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(467,plain,
! [SV177: $i,SV171: $i,SV139: $i,SV84: $i] :
( ( ( ( eq2 @ SV84 @ SV139 )
= bfalse )
= $false )
| ( ( ( eq2 @ ( x @ SV84 @ SV171 ) @ ( x @ SV139 @ SV177 ) )
= bfalse )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(468,plain,
! [SV178: $i,SV172: $i,SV140: $i,SV85: $i] :
( ( ( ( eq2 @ SV85 @ SV140 )
= btrue )
= $false )
| ( ( ( eq2 @ ( y @ SV85 @ SV172 ) @ ( y @ SV140 @ SV178 ) )
= ( eq2 @ SV172 @ SV178 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(469,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[232,468,467,466,465,456,455,449,447,446,445,444,443,442,441,440,439,438,437,436,435,434,433,432,431,430,429,428,427,426,425,424,423,422,417,416,415,414,411,406,403,400,399,398,397,396,393,390,387,382,381,378,373,372,370,368,362,361,360,359,358,357,353,346,342,341,340,337,335,332,330,328,324,323,320,318,315,314,312,309,308,306,303,298,295,293,290,285,251,250,248]) ).
thf(470,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[469]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX190-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n004.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 17:11:09 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 260.45/43.65
% 260.45/43.65 No.of.Axioms: 90
% 260.45/43.65
% 260.45/43.65 Length.of.Defs: 0
% 260.45/43.65
% 260.45/43.65 Contains.Choice.Funs: false
% 260.45/43.65 ............
% 260.45/43.65
% 260.45/43.65 ********************************
% 260.45/43.65 * All subproblems solved! *
% 260.45/43.65 ********************************
% 260.45/43.65 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:90,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:469,loop_count:0,foatp_calls:1,translation:fof_full)
% 260.45/43.65
% 260.45/43.65 %**** Beginning of derivation protocol ****
% 260.45/43.65 % SZS output start CNFRefutation
% See solution above
% 260.45/43.65
% 260.45/43.65 %**** End of derivation protocol ****
% 260.45/43.65 %**** no. of clauses in derivation: 470 ****
% 260.45/43.65 %**** clause counter: 469 ****
% 260.45/43.65
% 260.45/43.65 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:90,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:469,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------