%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP130^1 : TPTP v9.3.1. Released v7.5.0.
% 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 : n013.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 10:24:13 AM UTC 2026
% Result : Theorem 32.97s 5.74s
% Output : CNFRefutation 32.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 167
% Syntax : Number of formulae : 2905 ( 956 unt; 0 typ; 0 def)
% Number of atoms : 20607 (8001 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 39556 (7412 ~;6658 |; 72 &;24856 @)
% ( 0 <=>; 558 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 918 ( 918 >; 0 *; 0 +; 0 <<)
% Number of symbols : 105 ( 102 usr; 12 con; 0-3 aty)
% Number of variables : 7608 ( 15 ^;7530 !; 63 ?;7608 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_int,type,
int: $tType ).
thf(tp_nat,type,
nat: $tType ).
thf(tp_real,type,
real: $tType ).
thf(tp_divide_divide_int,type,
divide_divide_int: int > int > int ).
thf(tp_divide_divide_nat,type,
divide_divide_nat: nat > nat > nat ).
thf(tp_divide_divide_real,type,
divide_divide_real: real > real > real ).
thf(tp_na,type,
na: int ).
thf(tp_nthRoo1352626670d_root,type,
nthRoo1352626670d_root: nat > nat > $o ).
thf(tp_ny,type,
ny: real ).
thf(tp_ord_less_eq_int,type,
ord_less_eq_int: int > int > $o ).
thf(tp_ord_less_eq_nat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(tp_ord_less_eq_real,type,
ord_less_eq_real: real > real > $o ).
thf(tp_ord_less_int,type,
ord_less_int: int > int > $o ).
thf(tp_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(tp_ord_less_real,type,
ord_less_real: real > real > $o ).
thf(tp_p,type,
p: nat ).
thf(tp_pm,type,
pm: nat ).
thf(tp_power_power_int,type,
power_power_int: int > nat > int ).
thf(tp_power_power_nat,type,
power_power_nat: nat > nat > nat ).
thf(tp_power_power_real,type,
power_power_real: real > nat > real ).
thf(tp_ring_1_of_int_int,type,
ring_1_of_int_int: int > int ).
thf(tp_ring_1_of_int_real,type,
ring_1_of_int_real: int > real ).
thf(tp_sK10_SY444,type,
sK10_SY444: nat > nat > ( nat > nat ) > nat ).
thf(tp_sK11_SY449,type,
sK11_SY449: nat > nat > ( nat > int ) > nat ).
thf(tp_sK12_SY457,type,
sK12_SY457: nat > nat > ( nat > nat ) > nat ).
thf(tp_sK13_SY627,type,
sK13_SY627: real > nat > real ).
thf(tp_sK14_SY628,type,
sK14_SY628: nat > nat > nat ).
thf(tp_sK15_SY475,type,
sK15_SY475: nat > nat ).
thf(tp_sK16_SY478,type,
sK16_SY478: nat > nat > ( nat > nat ) > nat ).
thf(tp_sK17_SY486,type,
sK17_SY486: nat > nat > ( nat > nat > $o ) > nat ).
thf(tp_sK18_SY492,type,
sK18_SY492: nat > nat > ( nat > int ) > nat ).
thf(tp_sK19_SY498,type,
sK19_SY498: nat > nat > ( nat > real ) > nat ).
thf(tp_sK1_SY431,type,
sK1_SY431: real > real ).
thf(tp_sK20_SY503,type,
sK20_SY503: nat > nat > ( nat > int ) > nat ).
thf(tp_sK21_SY523,type,
sK21_SY523: nat > nat > ( nat > real ) > nat ).
thf(tp_sK22_SY667,type,
sK22_SY667: nat > nat > nat ).
thf(tp_sK23_SY546,type,
sK23_SY546: nat > nat > ( nat > real ) > nat ).
thf(tp_sK24_SY549,type,
sK24_SY549: nat > nat > ( nat > nat ) > nat ).
thf(tp_sK25_SY591,type,
sK25_SY591: nat > nat ).
thf(tp_sK26_SY453,type,
sK26_SY453: nat > ( nat > $o ) > nat ).
thf(tp_sK27_SY649,type,
sK27_SY649: ( nat > $o ) > nat > nat ).
thf(tp_sK28_SY525,type,
sK28_SY525: nat > ( nat > $o ) > nat ).
thf(tp_sK29_SY528,type,
sK29_SY528: nat > ( nat > $o ) > nat ).
thf(tp_sK2_SY526,type,
sK2_SY526: real > int ).
thf(tp_sK30_SY669,type,
sK30_SY669: ( nat > $o ) > nat > nat ).
thf(tp_sK31_SY616,type,
sK31_SY616: real > nat > real ).
thf(tp_sK32_SY699,type,
sK32_SY699: nat > ( nat > $o ) > nat > nat ).
thf(tp_sK33_SY701,type,
sK33_SY701: nat > nat > ( nat > nat > $o ) > nat ).
thf(tp_sK34_SY718,type,
sK34_SY718: nat > nat > ( nat > nat > $o ) > nat ).
thf(tp_sK35_SY687,type,
sK35_SY687: real > nat > real ).
thf(tp_sK36_SY623,type,
sK36_SY623: nat > nat > nat ).
thf(tp_sK37_SY487,type,
sK37_SY487: nat > nat > ( nat > nat > $o ) > nat ).
thf(tp_sK38_SY677,type,
sK38_SY677: ( nat > $o ) > nat > nat ).
thf(tp_sK39_SY405,type,
sK39_SY405: nat > nat ).
thf(tp_sK3_SY570,type,
sK3_SY570: real > int ).
thf(tp_sK40_SY692,type,
sK40_SY692: nat > ( nat > $o ) > nat > nat ).
thf(tp_sK41_SY706,type,
sK41_SY706: ( nat > $o ) > nat > nat > nat ).
thf(tp_sK42_SY724,type,
sK42_SY724: ( nat > $o ) > nat > nat > nat ).
thf(tp_sK43_SY702,type,
sK43_SY702: nat > nat > ( nat > nat > $o ) > nat ).
thf(tp_sK44_SY650,type,
sK44_SY650: ( nat > $o ) > nat > nat ).
thf(tp_sK45_SY536,type,
sK45_SY536: nat > ( nat > $o ) > nat ).
thf(tp_sK46_SY670,type,
sK46_SY670: ( nat > $o ) > nat > nat ).
thf(tp_sK47_SY679,type,
sK47_SY679: nat > nat > nat ).
thf(tp_sK48_SY719,type,
sK48_SY719: nat > nat > ( nat > nat > $o ) > nat ).
thf(tp_sK49_SY601,type,
sK49_SY601: ( nat > $o ) > nat > nat ).
thf(tp_sK4_SY582,type,
sK4_SY582: real > int ).
thf(tp_sK50_SY700,type,
sK50_SY700: nat > ( nat > $o ) > nat > nat ).
thf(tp_sK51_SY728,type,
sK51_SY728: ( nat > nat > $o ) > nat > nat > nat ).
thf(tp_sK52_SY488,type,
sK52_SY488: nat > nat > ( nat > nat > $o ) > nat ).
thf(tp_sK53_SY665,type,
sK53_SY665: ( nat > $o ) > nat > nat ).
thf(tp_sK54_SY730,type,
sK54_SY730: nat > nat > ( nat > nat > $o ) > nat ).
thf(tp_sK55_SY686,type,
sK55_SY686: nat > nat > nat ).
thf(tp_sK56_SY405,type,
sK56_SY405: nat > nat > nat ).
thf(tp_sK57_SY602,type,
sK57_SY602: ( nat > $o ) > nat > nat ).
thf(tp_sK58_SY700,type,
sK58_SY700: nat > ( nat > $o ) > nat > nat ).
thf(tp_sK59_SY732,type,
sK59_SY732: ( nat > nat > $o ) > nat > nat > nat ).
thf(tp_sK5_SY587,type,
sK5_SY587: real > real ).
thf(tp_sK60_SY733,type,
sK60_SY733: nat > nat > ( nat > nat > $o ) > nat ).
thf(tp_sK61_SY666,type,
sK61_SY666: ( nat > $o ) > nat > nat ).
thf(tp_sK62_SY734,type,
sK62_SY734: nat > nat > ( nat > nat > $o ) > nat ).
thf(tp_sK63_SY686,type,
sK63_SY686: nat > nat > nat ).
thf(tp_sK64_SY601,type,
sK64_SY601: nat > ( nat > $o ) > nat > nat ).
thf(tp_sK65_SY665,type,
sK65_SY665: nat > ( nat > $o ) > nat > nat ).
thf(tp_sK66_SY679,type,
sK66_SY679: nat > nat > nat > nat ).
thf(tp_sK67_SY722,type,
sK67_SY722: nat > nat > ( nat > nat > $o ) > nat ).
thf(tp_sK68_SY722,type,
sK68_SY722: nat > nat > ( nat > nat > $o ) > nat ).
thf(tp_sK69_SY602,type,
sK69_SY602: nat > ( nat > $o ) > nat > nat ).
thf(tp_sK6_SY421,type,
sK6_SY421: nat > ( nat > $o ) > nat ).
thf(tp_sK70_SY601,type,
sK70_SY601: nat > ( nat > $o ) > nat > nat ).
thf(tp_sK71_SY666,type,
sK71_SY666: nat > ( nat > $o ) > nat > nat ).
thf(tp_sK72_SY665,type,
sK72_SY665: nat > ( nat > $o ) > nat > nat ).
thf(tp_sK73_SY722,type,
sK73_SY722: nat > nat > ( nat > nat > $o ) > nat ).
thf(tp_sK74_SY602,type,
sK74_SY602: nat > ( nat > $o ) > nat > nat ).
thf(tp_sK75_SY666,type,
sK75_SY666: nat > ( nat > $o ) > nat > nat ).
thf(tp_sK76_SY686,type,
sK76_SY686: nat > nat > nat > nat ).
thf(tp_sK7_SY559,type,
sK7_SY559: nat > nat ).
thf(tp_sK8_SY428,type,
sK8_SY428: nat > nat > ( nat > int ) > nat ).
thf(tp_sK9_SY434,type,
sK9_SY434: nat > nat > ( nat > real ) > nat ).
thf(tp_suc,type,
suc: nat > nat ).
thf(tp_x,type,
x: int ).
thf(tp_y,type,
y: int ).
thf(tp_ya,type,
ya: int ).
thf(tp_zero_zero_int,type,
zero_zero_int: int ).
thf(tp_zero_zero_nat,type,
zero_zero_nat: nat ).
thf(tp_zero_zero_real,type,
zero_zero_real: real ).
thf(16,axiom,
! [X: real,Y: real] :
( ( X != Y )
=> ( ~ ( ord_less_real @ X @ Y )
=> ( ord_less_real @ Y @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_linorder__neqE__linordered__idom) ).
thf(25,axiom,
! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ ( divide_divide_nat @ ( suc @ M ) @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_Suc__div__le__mono) ).
thf(30,axiom,
! [M: nat] :
( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
= M ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_div__by__Suc__0) ).
thf(34,axiom,
! [X: real,Y: real] :
( ( ord_less_eq_real @ X @ zero_zero_real )
=> ( ( ord_less_real @ zero_zero_real @ Y )
=> ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_divide__nonpos__pos) ).
thf(35,axiom,
! [X: real,Y: real] :
( ( ord_less_eq_real @ X @ zero_zero_real )
=> ( ( ord_less_real @ Y @ zero_zero_real )
=> ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_divide__nonpos__neg) ).
thf(36,axiom,
! [X: real,Y: real] :
( ( ord_less_eq_real @ zero_zero_real @ X )
=> ( ( ord_less_real @ zero_zero_real @ Y )
=> ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_divide__nonneg__pos) ).
thf(37,axiom,
! [X: real,Y: real] :
( ( ord_less_eq_real @ zero_zero_real @ X )
=> ( ( ord_less_real @ Y @ zero_zero_real )
=> ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_divide__nonneg__neg) ).
thf(38,axiom,
! [A: real,C: real,B: real] :
( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
= ( ( ( ord_less_real @ zero_zero_real @ C )
=> ( ord_less_eq_real @ A @ B ) )
& ( ( ord_less_real @ C @ zero_zero_real )
=> ( ord_less_eq_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_divide__le__cancel) ).
thf(39,axiom,
! [X: real,Y: real,W: real,Z: real] :
( ( ord_less_real @ zero_zero_real @ X )
=> ( ( ord_less_eq_real @ X @ Y )
=> ( ( ord_less_real @ zero_zero_real @ W )
=> ( ( ord_less_real @ W @ Z )
=> ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_frac__less2) ).
thf(40,axiom,
! [X: real,Y: real,W: real,Z: real] :
( ( ord_less_eq_real @ zero_zero_real @ X )
=> ( ( ord_less_real @ X @ Y )
=> ( ( ord_less_real @ zero_zero_real @ W )
=> ( ( ord_less_eq_real @ W @ Z )
=> ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_frac__less) ).
thf(41,axiom,
! [Y: real,X: real,W: real,Z: real] :
( ( ord_less_eq_real @ zero_zero_real @ Y )
=> ( ( ord_less_eq_real @ X @ Y )
=> ( ( ord_less_real @ zero_zero_real @ W )
=> ( ( ord_less_eq_real @ W @ Z )
=> ( ord_less_eq_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_frac__le) ).
thf(42,axiom,
! [B: real,A: real,C: real] :
( ( ord_less_real @ B @ A )
=> ( ( ord_less_real @ C @ zero_zero_real )
=> ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_divide__strict__right__mono__neg) ).
thf(43,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ zero_zero_real @ C )
=> ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_divide__strict__right__mono) ).
thf(44,axiom,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
= ( ( ( ord_less_real @ zero_zero_real @ A )
& ( ord_less_real @ zero_zero_real @ B ) )
| ( ( ord_less_real @ A @ zero_zero_real )
& ( ord_less_real @ B @ zero_zero_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_zero__less__divide__iff) ).
thf(45,axiom,
! [A: real,C: real,B: real] :
( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
= ( ( ( ord_less_real @ zero_zero_real @ C )
=> ( ord_less_real @ A @ B ) )
& ( ( ord_less_real @ C @ zero_zero_real )
=> ( ord_less_real @ B @ A ) )
& ( C != zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_divide__less__cancel) ).
thf(46,axiom,
! [A: real,B: real] :
( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
= ( ( ( ord_less_real @ zero_zero_real @ A )
& ( ord_less_real @ B @ zero_zero_real ) )
| ( ( ord_less_real @ A @ zero_zero_real )
& ( ord_less_real @ zero_zero_real @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_divide__less__0__iff) ).
thf(47,axiom,
! [X: real,Y: real] :
( ( ord_less_real @ zero_zero_real @ X )
=> ( ( ord_less_real @ zero_zero_real @ Y )
=> ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_divide__pos__pos) ).
thf(48,axiom,
! [X: real,Y: real] :
( ( ord_less_real @ zero_zero_real @ X )
=> ( ( ord_less_real @ Y @ zero_zero_real )
=> ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_divide__pos__neg) ).
thf(49,axiom,
! [X: real,Y: real] :
( ( ord_less_real @ X @ zero_zero_real )
=> ( ( ord_less_real @ zero_zero_real @ Y )
=> ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_divide__neg__pos) ).
thf(50,axiom,
! [X: real,Y: real] :
( ( ord_less_real @ X @ zero_zero_real )
=> ( ( ord_less_real @ Y @ zero_zero_real )
=> ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_divide__neg__neg) ).
thf(59,axiom,
! [P: nat > $o,N: nat] :
( ( P @ N )
=> ( ~ ( P @ zero_zero_nat )
=> ? [K: nat] :
( ( ord_less_nat @ K @ N )
& ! [I4: nat] :
( ( ord_less_eq_nat @ I4 @ K )
=> ~ ( P @ I4 ) )
& ( P @ ( suc @ K ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_ex__least__nat__less) ).
thf(60,axiom,
! [X4: real] :
? [Y3: real] : ( ord_less_real @ Y3 @ X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_linordered__field__no__lb) ).
thf(61,axiom,
! [X4: real] :
? [X_12: real] : ( ord_less_real @ X4 @ X_12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_linordered__field__no__ub) ).
thf(62,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ord_less_nat @ M @ ( suc @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_le__imp__less__Suc) ).
thf(63,axiom,
( ord_less_nat
= ( ^ [N4: nat] : ( ord_less_eq_nat @ ( suc @ N4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_less__eq__Suc__le) ).
thf(64,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
= ( ord_less_eq_nat @ M @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_less__Suc__eq__le) ).
thf(65,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( ord_less_nat @ N @ ( suc @ M ) )
= ( N = M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_le__less__Suc__eq) ).
thf(66,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ ( suc @ M ) @ N )
=> ( ord_less_nat @ M @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_Suc__le__lessD) ).
thf(67,axiom,
! [I: nat,J: nat,P: nat > $o] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( P @ J )
=> ( ! [N2: nat] :
( ( ord_less_eq_nat @ I @ N2 )
=> ( ( ord_less_nat @ N2 @ J )
=> ( ( P @ ( suc @ N2 ) )
=> ( P @ N2 ) ) ) )
=> ( P @ I ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_inc__induct) ).
thf(68,axiom,
! [I: nat,J: nat,P: nat > $o] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( P @ I )
=> ( ! [N2: nat] :
( ( ord_less_eq_nat @ I @ N2 )
=> ( ( ord_less_nat @ N2 @ J )
=> ( ( P @ N2 )
=> ( P @ ( suc @ N2 ) ) ) ) )
=> ( P @ J ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_dec__induct) ).
thf(69,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ ( suc @ M ) @ N )
= ( ord_less_nat @ M @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_Suc__le__eq) ).
thf(70,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_eq_nat @ ( suc @ M ) @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_Suc__leI) ).
thf(72,axiom,
! [I: nat,N: nat] :
( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
=> ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_nat__one__le__power) ).
thf(73,axiom,
! [P2: nat,Pm: nat] :
( ( nthRoo1352626670d_root @ P2 @ Pm )
=> ( P2
= ( suc @ Pm ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_fixed__root_Op) ).
thf(74,axiom,
( nthRoo1352626670d_root
= ( ^ [P3: nat,Pm2: nat] :
( P3
= ( suc @ Pm2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_fixed__root__def) ).
thf(75,axiom,
! [P2: nat,Pm: nat] :
( ( P2
= ( suc @ Pm ) )
=> ( nthRoo1352626670d_root @ P2 @ Pm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_fixed__root_Ointro) ).
thf(83,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ ( suc @ M ) @ N )
=> ( ord_less_eq_nat @ M @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_Suc__leD) ).
thf(84,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ ( suc @ N ) )
=> ( ~ ( ord_less_eq_nat @ M @ N )
=> ( M
= ( suc @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_le__SucE) ).
thf(85,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ord_less_eq_nat @ M @ ( suc @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_le__SucI) ).
thf(86,axiom,
! [N: nat,M6: nat] :
( ( ord_less_eq_nat @ ( suc @ N ) @ M6 )
=> ? [M4: nat] :
( M6
= ( suc @ M4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_Suc__le__D) ).
thf(87,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ ( suc @ N ) )
= ( ( ord_less_eq_nat @ M @ N )
| ( M
= ( suc @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_le__Suc__eq) ).
thf(88,axiom,
! [N: nat] :
~ ( ord_less_eq_nat @ ( suc @ N ) @ N ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_Suc__n__not__le__n) ).
thf(89,axiom,
! [M: nat,N: nat] :
( ( ~ ( ord_less_eq_nat @ M @ N ) )
= ( ord_less_eq_nat @ ( suc @ N ) @ M ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_not__less__eq__eq) ).
thf(90,axiom,
! [P: nat > $o,N: nat] :
( ! [N2: nat] :
( ! [M3: nat] :
( ( ord_less_eq_nat @ ( suc @ M3 ) @ N2 )
=> ( P @ M3 ) )
=> ( P @ N2 ) )
=> ( P @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_full__nat__induct) ).
thf(91,axiom,
! [M: nat,N: nat,P: nat > $o] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( P @ M )
=> ( ! [N2: nat] :
( ( ord_less_eq_nat @ M @ N2 )
=> ( ( P @ N2 )
=> ( P @ ( suc @ N2 ) ) ) )
=> ( P @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_nat__induct__at__least) ).
thf(92,axiom,
! [M: nat,N: nat,R2: nat > nat > $o] :
( ( ord_less_eq_nat @ M @ N )
=> ( ! [X3: nat] : ( R2 @ X3 @ X3 )
=> ( ! [X3: nat,Y3: nat,Z2: nat] :
( ( R2 @ X3 @ Y3 )
=> ( ( R2 @ Y3 @ Z2 )
=> ( R2 @ X3 @ Z2 ) ) )
=> ( ! [N2: nat] : ( R2 @ N2 @ ( suc @ N2 ) )
=> ( R2 @ M @ N ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_transitive__stepwise__le) ).
thf(103,axiom,
! [N: nat,M: nat] :
( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
= ( ord_less_eq_nat @ N @ M ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_Suc__le__mono) ).
thf(122,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( power_power_real @ zero_zero_real @ N )
= zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_zero__power) ).
thf(125,axiom,
! [A: real,N: nat] :
( ( A != zero_zero_real )
=> ( ( power_power_real @ A @ N )
!= zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_power__not__zero) ).
thf(133,axiom,
! [N: nat,A: real] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ? [X3: real] :
( ( ord_less_real @ zero_zero_real @ X3 )
& ( ( power_power_real @ X3 @ N )
= A )
& ! [Y4: real] :
( ( ( ord_less_real @ zero_zero_real @ Y4 )
& ( ( power_power_real @ Y4 @ N )
= A ) )
=> ( Y4 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_realpow__pos__nth__unique) ).
thf(134,axiom,
! [N: nat,A: real] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ? [R: real] :
( ( ord_less_real @ zero_zero_real @ R )
& ( ( power_power_real @ R @ N )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_realpow__pos__nth) ).
thf(135,axiom,
! [A: nat,N: nat,B: nat] :
( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_power__le__imp__le__base) ).
thf(136,axiom,
! [A: int,N: nat,B: int] :
( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B @ ( suc @ N ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_power__le__imp__le__base) ).
thf(137,axiom,
! [A: real,N: nat,B: real] :
( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ ( power_power_real @ B @ ( suc @ N ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_power__le__imp__le__base) ).
thf(138,axiom,
! [A: nat,N: nat,B: nat] :
( ( ( power_power_nat @ A @ ( suc @ N ) )
= ( power_power_nat @ B @ ( suc @ N ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_power__inject__base) ).
thf(139,axiom,
! [A: int,N: nat,B: int] :
( ( ( power_power_int @ A @ ( suc @ N ) )
= ( power_power_int @ B @ ( suc @ N ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_power__inject__base) ).
thf(140,axiom,
! [A: real,N: nat,B: real] :
( ( ( power_power_real @ A @ ( suc @ N ) )
= ( power_power_real @ B @ ( suc @ N ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_power__inject__base) ).
thf(146,axiom,
! [A: real,N: nat,B: real] :
( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_power__less__imp__less__base) ).
thf(151,axiom,
! [A: real,B: real,N: nat] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_power__mono) ).
thf(154,axiom,
! [A: real,N: nat] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_zero__le__power) ).
thf(161,axiom,
! [N: nat,P: nat > $o] :
( ( ? [I3: nat] :
( ( ord_less_nat @ I3 @ ( suc @ N ) )
& ( P @ I3 ) ) )
= ( ( P @ zero_zero_nat )
| ? [I3: nat] :
( ( ord_less_nat @ I3 @ N )
& ( P @ ( suc @ I3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_Ex__less__Suc2) ).
thf(162,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( ? [M5: nat] :
( N
= ( suc @ M5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_gr0__conv__Suc) ).
thf(163,axiom,
! [N: nat,P: nat > $o] :
( ( ! [I3: nat] :
( ( ord_less_nat @ I3 @ ( suc @ N ) )
=> ( P @ I3 ) ) )
= ( ( P @ zero_zero_nat )
& ! [I3: nat] :
( ( ord_less_nat @ I3 @ N )
=> ( P @ ( suc @ I3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_All__less__Suc2) ).
thf(164,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ? [M4: nat] :
( N
= ( suc @ M4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_gr0__implies__Suc) ).
thf(165,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
= ( ( M = zero_zero_nat )
| ? [J3: nat] :
( ( M
= ( suc @ J3 ) )
& ( ord_less_nat @ J3 @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_less__Suc__eq__0__disj) ).
thf(166,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ? [M4: nat] :
( N
= ( suc @ M4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_not0__implies__Suc) ).
thf(167,axiom,
! [P: nat > $o,Nat: nat] :
( ( P @ zero_zero_nat )
=> ( ! [Nat3: nat] :
( ( P @ Nat3 )
=> ( P @ ( suc @ Nat3 ) ) )
=> ( P @ Nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_old_Onat_Oinducts) ).
thf(168,axiom,
! [Y: nat] :
( ( Y != zero_zero_nat )
=> ~ ! [Nat3: nat] :
( Y
!= ( suc @ Nat3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_old_Onat_Oexhaust) ).
thf(169,axiom,
! [M: nat] :
( zero_zero_nat
!= ( suc @ M ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_Zero__not__Suc) ).
thf(170,axiom,
! [M: nat] :
( zero_zero_nat
!= ( suc @ M ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_Zero__neq__Suc) ).
thf(171,axiom,
! [M: nat] :
( ( suc @ M )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_Suc__neq__Zero) ).
thf(172,axiom,
! [P: nat > $o,K2: nat] :
( ( P @ K2 )
=> ( ! [N2: nat] :
( ( P @ ( suc @ N2 ) )
=> ( P @ N2 ) )
=> ( P @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_zero__induct) ).
thf(173,axiom,
! [P: nat > nat > $o,M: nat,N: nat] :
( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
=> ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
=> ( ! [X3: nat,Y3: nat] :
( ( P @ X3 @ Y3 )
=> ( P @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
=> ( P @ M @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_diff__induct) ).
thf(174,axiom,
! [P: nat > $o,N: nat] :
( ( P @ zero_zero_nat )
=> ( ! [N2: nat] :
( ( P @ N2 )
=> ( P @ ( suc @ N2 ) ) )
=> ( P @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_nat__induct) ).
thf(175,axiom,
! [Nat: nat,X2: nat] :
( ( Nat
= ( suc @ X2 ) )
=> ( Nat != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_nat_OdiscI) ).
thf(176,axiom,
! [Nat2: nat] :
( zero_zero_nat
!= ( suc @ Nat2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_old_Onat_Odistinct_I1_J) ).
thf(177,axiom,
! [Nat2: nat] :
( ( suc @ Nat2 )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_old_Onat_Odistinct_I2_J) ).
thf(178,axiom,
! [X2: nat] :
( zero_zero_nat
!= ( suc @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_nat_Odistinct_I1_J) ).
thf(180,axiom,
! [N: nat,K2: nat] :
( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
=> ( ord_less_nat @ K2 @ ( power_power_nat @ N @ K2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_power__gt__expt) ).
thf(181,axiom,
! [P: nat > $o] :
( ~ ( P @ zero_zero_nat )
=> ( ? [X_1: nat] : ( P @ X_1 )
=> ? [N2: nat] :
( ~ ( P @ N2 )
& ( P @ ( suc @ N2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_exists__least__lemma) ).
thf(182,axiom,
! [X: real] :
? [Z2: int] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_ex__le__of__int) ).
thf(183,axiom,
! [A: real,B: real,N: nat] :
( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N )
= ( divide_divide_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_power__divide) ).
thf(185,axiom,
! [F: nat > nat,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_eq_nat @ N @ N3 )
=> ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_lift__Suc__mono__le) ).
thf(186,axiom,
! [F: nat > int,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_eq_nat @ N @ N3 )
=> ( ord_less_eq_int @ ( F @ N ) @ ( F @ N3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_lift__Suc__mono__le) ).
thf(187,axiom,
! [F: nat > real,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_eq_nat @ N @ N3 )
=> ( ord_less_eq_real @ ( F @ N ) @ ( F @ N3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_lift__Suc__mono__le) ).
thf(188,axiom,
! [F: nat > nat,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
=> ( ( ord_less_eq_nat @ N @ N3 )
=> ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_lift__Suc__antimono__le) ).
thf(189,axiom,
! [F: nat > int,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
=> ( ( ord_less_eq_nat @ N @ N3 )
=> ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_lift__Suc__antimono__le) ).
thf(190,axiom,
! [F: nat > real,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_eq_real @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
=> ( ( ord_less_eq_nat @ N @ N3 )
=> ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_lift__Suc__antimono__le) ).
thf(208,axiom,
! [X: int,B: int,W: nat] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
= ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_of__int__power__le__of__int__cancel__iff) ).
thf(210,axiom,
! [B: int,W: nat,X: int] :
( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X ) )
= ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_of__int__le__of__int__power__cancel__iff) ).
thf(219,axiom,
! [W: int,Z: int] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
= ( ord_less_eq_int @ W @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_of__int__le__iff) ).
thf(220,axiom,
! [N: nat] :
( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
= ( N = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_less__Suc0) ).
thf(221,axiom,
! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_zero__less__Suc) ).
thf(222,axiom,
! [A: nat] :
( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_power__Suc0__right) ).
thf(223,axiom,
! [A: int] :
( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_power__Suc0__right) ).
thf(224,axiom,
! [A: real] :
( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_power__Suc0__right) ).
thf(229,axiom,
! [N: nat] :
( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
= ( suc @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_power__Suc__0) ).
thf(230,axiom,
! [X: nat,M: nat] :
( ( ( power_power_nat @ X @ M )
= ( suc @ zero_zero_nat ) )
= ( ( M = zero_zero_nat )
| ( X
= ( suc @ zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_nat__power__eq__Suc__0__iff) ).
thf(232,axiom,
nthRoo1352626670d_root @ p @ pm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_fixed__root__axioms) ).
thf(233,axiom,
( p
= ( suc @ pm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_p) ).
thf(234,axiom,
ord_less_eq_int @ na @ ( power_power_int @ ya @ p ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85__C1_Oprems_C_I1_J) ).
thf(235,axiom,
ord_less_nat @ zero_zero_nat @ pm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_pm0) ).
thf(237,axiom,
pm != zero_zero_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82__092_060open_062pm_A_061_A0_A_092_060Longrightarrow_062_AFalse_092_060close_062) ).
thf(238,axiom,
ord_less_int @ na @ ( power_power_int @ ya @ p ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_yyn) ).
thf(239,axiom,
! [X: real] :
? [Z2: int] : ( ord_less_real @ X @ ( ring_1_of_int_real @ Z2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_ex__less__of__int) ).
thf(240,axiom,
! [X: real] :
? [Z2: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z2 ) @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_ex__of__int__less) ).
thf(241,axiom,
( ny
= ( divide_divide_real @ ( ring_1_of_int_real @ na ) @ ( power_power_real @ ( ring_1_of_int_real @ ya ) @ pm ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_NY__def) ).
thf(244,axiom,
! [A: real,N: nat] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_zero__less__power) ).
thf(245,axiom,
! [A: real,N: nat] :
( ( ord_less_real @ zero_zero_real @ A )
=> ? [R: real] :
( ( ord_less_real @ zero_zero_real @ R )
& ( ( power_power_real @ R @ ( suc @ N ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_realpow__pos__nth2) ).
thf(249,axiom,
! [A: real,N: nat] :
( ( ( power_power_real @ A @ N )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( ord_less_nat @ zero_zero_nat @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_power__eq__0__iff) ).
thf(250,axiom,
ord_less_real @ zero_zero_real @ ny,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_NY0) ).
thf(251,axiom,
! [N: nat] :
( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_power__0__Suc) ).
thf(252,axiom,
! [N: nat] :
( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_power__0__Suc) ).
thf(253,axiom,
! [N: nat] :
( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_power__0__Suc) ).
thf(254,axiom,
! [F: nat > nat,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_nat @ N @ N3 )
=> ( ord_less_nat @ ( F @ N ) @ ( F @ N3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_lift__Suc__mono__less) ).
thf(255,axiom,
! [F: nat > int,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_nat @ N @ N3 )
=> ( ord_less_int @ ( F @ N ) @ ( F @ N3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_lift__Suc__mono__less) ).
thf(256,axiom,
! [F: nat > real,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_nat @ N @ N3 )
=> ( ord_less_real @ ( F @ N ) @ ( F @ N3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_lift__Suc__mono__less) ).
thf(257,axiom,
! [F: nat > nat,N: nat,M: nat] :
( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
= ( ord_less_nat @ N @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_lift__Suc__mono__less__iff) ).
thf(258,axiom,
! [F: nat > int,N: nat,M: nat] :
( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
= ( ord_less_nat @ N @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_lift__Suc__mono__less__iff) ).
thf(259,axiom,
! [F: nat > real,N: nat,M: nat] :
( ! [N2: nat] : ( ord_less_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_real @ ( F @ N ) @ ( F @ M ) )
= ( ord_less_nat @ N @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_lift__Suc__mono__less__iff) ).
thf(260,axiom,
! [X: nat,Y: nat] :
( ( ( suc @ X )
= ( suc @ Y ) )
=> ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_Suc__inject) ).
thf(261,axiom,
! [N: nat] :
( N
!= ( suc @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_n__not__Suc__n) ).
thf(263,axiom,
! [Z: int] :
( ( ord_less_int @ zero_zero_int @ Z )
=> ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_of__int__pos) ).
thf(264,axiom,
! [I: nat,K2: nat] :
( ( ord_less_nat @ I @ K2 )
=> ( ( K2
!= ( suc @ I ) )
=> ~ ! [J2: nat] :
( ( ord_less_nat @ I @ J2 )
=> ( K2
!= ( suc @ J2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Nat_OlessE) ).
thf(265,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ ( suc @ M ) @ N )
=> ( ord_less_nat @ M @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_Suc__lessD) ).
thf(266,axiom,
! [I: nat,K2: nat] :
( ( ord_less_nat @ ( suc @ I ) @ K2 )
=> ~ ! [J2: nat] :
( ( ord_less_nat @ I @ J2 )
=> ( K2
!= ( suc @ J2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_Suc__lessE) ).
thf(267,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ( ( suc @ M )
!= N )
=> ( ord_less_nat @ ( suc @ M ) @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_Suc__lessI) ).
thf(268,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
=> ( ~ ( ord_less_nat @ M @ N )
=> ( M = N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_less__SucE) ).
thf(269,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_nat @ M @ ( suc @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_less__SucI) ).
thf(270,axiom,
! [N: nat,P: nat > $o] :
( ( ? [I3: nat] :
( ( ord_less_nat @ I3 @ ( suc @ N ) )
& ( P @ I3 ) ) )
= ( ( P @ N )
| ? [I3: nat] :
( ( ord_less_nat @ I3 @ N )
& ( P @ I3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_Ex__less__Suc) ).
thf(271,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
= ( ( ord_less_nat @ M @ N )
| ( M = N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_less__Suc__eq) ).
thf(272,axiom,
! [M: nat,N: nat] :
( ( ~ ( ord_less_nat @ M @ N ) )
= ( ord_less_nat @ N @ ( suc @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_not__less__eq) ).
thf(273,axiom,
! [N: nat,P: nat > $o] :
( ( ! [I3: nat] :
( ( ord_less_nat @ I3 @ ( suc @ N ) )
=> ( P @ I3 ) ) )
= ( ( P @ N )
& ! [I3: nat] :
( ( ord_less_nat @ I3 @ N )
=> ( P @ I3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_All__less__Suc) ).
thf(274,axiom,
! [N: nat,M: nat] :
( ( ord_less_nat @ ( suc @ N ) @ M )
= ( ? [M2: nat] :
( ( M
= ( suc @ M2 ) )
& ( ord_less_nat @ N @ M2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_Suc__less__eq2) ).
thf(275,axiom,
! [N: nat,M: nat] :
( ~ ( ord_less_nat @ N @ M )
=> ( ( ord_less_nat @ N @ ( suc @ M ) )
=> ( M = N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_less__antisym) ).
thf(276,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
=> ( ord_less_nat @ M @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_Suc__less__SucD) ).
thf(277,axiom,
! [I: nat,J: nat,K2: nat] :
( ( ord_less_nat @ I @ J )
=> ( ( ord_less_nat @ J @ K2 )
=> ( ord_less_nat @ ( suc @ I ) @ K2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_less__trans__Suc) ).
thf(278,axiom,
! [I: nat,J: nat,P: nat > nat > $o] :
( ( ord_less_nat @ I @ J )
=> ( ! [I2: nat] : ( P @ I2 @ ( suc @ I2 ) )
=> ( ! [I2: nat,J2: nat,K: nat] :
( ( ord_less_nat @ I2 @ J2 )
=> ( ( ord_less_nat @ J2 @ K )
=> ( ( P @ I2 @ J2 )
=> ( ( P @ J2 @ K )
=> ( P @ I2 @ K ) ) ) ) )
=> ( P @ I @ J ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_less__Suc__induct) ).
thf(279,axiom,
! [I: nat,J: nat,P: nat > $o] :
( ( ord_less_nat @ I @ J )
=> ( ! [I2: nat] :
( ( J
= ( suc @ I2 ) )
=> ( P @ I2 ) )
=> ( ! [I2: nat] :
( ( ord_less_nat @ I2 @ J )
=> ( ( P @ ( suc @ I2 ) )
=> ( P @ I2 ) ) )
=> ( P @ I ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_strict__inc__induct) ).
thf(280,axiom,
! [N: nat,M: nat] :
( ~ ( ord_less_nat @ N @ M )
=> ( ( ord_less_nat @ N @ ( suc @ M ) )
= ( N = M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_not__less__less__Suc__eq) ).
thf(283,axiom,
! [Z: int] :
( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
= ( ord_less_int @ zero_zero_int @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_of__int__0__less__iff) ).
thf(285,axiom,
! [Z: int] :
( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
= ( ord_less_int @ Z @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_of__int__less__0__iff) ).
thf(287,axiom,
! [Z: int] :
( ( ( ring_1_of_int_real @ Z )
= zero_zero_real )
= ( Z = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_of__int__eq__0__iff) ).
thf(289,axiom,
! [Z: int] :
( ( zero_zero_real
= ( ring_1_of_int_real @ Z ) )
= ( Z = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_of__int__0__eq__iff) ).
thf(291,axiom,
( ( ring_1_of_int_real @ zero_zero_int )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_of__int__0) ).
thf(292,axiom,
ord_less_eq_int @ zero_zero_int @ na,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27__C1_Oprems_C_I3_J) ).
thf(293,axiom,
ord_less_eq_int @ zero_zero_int @ ya,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26__C1_Oprems_C_I2_J) ).
thf(294,axiom,
~ ( ( ord_less_int @ ya @ zero_zero_int )
| ( ord_less_int @ na @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_not_I2_J) ).
thf(295,axiom,
~ ( ( ord_less_int @ ya @ zero_zero_int )
| ( ord_less_int @ na @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_not_I1_J) ).
thf(296,axiom,
! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_lessI) ).
thf(297,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_Suc__mono) ).
thf(298,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
= ( ord_less_nat @ M @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_Suc__less__eq) ).
thf(299,axiom,
( ( ord_less_int @ zero_zero_int @ ya )
| ( ya = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20__092_060open_0620_A_060_Ay_A_092_060or_062_Ay_A_061_A0_092_060close_062) ).
thf(300,axiom,
ya != zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_y00) ).
thf(301,axiom,
! [Nat: nat,Nat2: nat] :
( ( ( suc @ Nat )
= ( suc @ Nat2 ) )
= ( Nat = Nat2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_old_Onat_Oinject) ).
thf(302,axiom,
! [X2: nat,Y2: nat] :
( ( ( suc @ X2 )
= ( suc @ Y2 ) )
= ( X2 = Y2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_nat_Oinject) ).
thf(303,axiom,
! [W: int,Z: int] :
( ( ( ring_1_of_int_real @ W )
= ( ring_1_of_int_real @ Z ) )
= ( W = Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_of__int__eq__iff) ).
thf(305,axiom,
ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ ya ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_y0) ).
thf(306,axiom,
ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ na ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_n0) ).
thf(308,axiom,
! [W: int,Z: int] :
( ( ord_less_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
= ( ord_less_int @ W @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_of__int__less__iff) ).
thf(310,axiom,
! [X: int,B: int,W: nat] :
( ( ( ring_1_of_int_real @ X )
= ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
= ( X
= ( power_power_int @ B @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_of__int__power__eq__of__int__cancel__iff) ).
thf(312,axiom,
! [B: int,W: nat,X: int] :
( ( ( power_power_real @ ( ring_1_of_int_real @ B ) @ W )
= ( ring_1_of_int_real @ X ) )
= ( ( power_power_int @ B @ W )
= X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_of__int__eq__of__int__power__cancel__iff) ).
thf(314,axiom,
! [Z: int,N: nat] :
( ( ring_1_of_int_real @ ( power_power_int @ Z @ N ) )
= ( power_power_real @ ( ring_1_of_int_real @ Z ) @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_of__int__power) ).
thf(316,axiom,
! [X: int,B: int,W: nat] :
( ( ord_less_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
= ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_of__int__power__less__of__int__cancel__iff) ).
thf(318,axiom,
! [B: int,W: nat,X: int] :
( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X ) )
= ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_of__int__less__of__int__power__cancel__iff) ).
thf(319,axiom,
na != zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_n00) ).
thf(320,conjecture,
ord_less_real @ ( ring_1_of_int_real @ na ) @ ( power_power_real @ ( ring_1_of_int_real @ ya ) @ ( suc @ pm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(321,negated_conjecture,
( ( ord_less_real @ ( ring_1_of_int_real @ na ) @ ( power_power_real @ ( ring_1_of_int_real @ ya ) @ ( suc @ pm ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[320]) ).
thf(322,plain,
( ( ord_less_real @ ( ring_1_of_int_real @ na ) @ ( power_power_real @ ( ring_1_of_int_real @ ya ) @ ( suc @ pm ) ) )
= $false ),
inference(unfold_def,[status(thm)],[321]) ).
thf(323,plain,
( ( ! [X: real,Y: real] :
( ( X != Y )
=> ( ~ ( ord_less_real @ X @ Y )
=> ( ord_less_real @ Y @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(324,plain,
( ( ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ ( divide_divide_nat @ ( suc @ M ) @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(325,plain,
( ( ! [M: nat] :
( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
= M ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(326,plain,
( ( ! [X: real,Y: real] :
( ( ord_less_eq_real @ X @ zero_zero_real )
=> ( ( ord_less_real @ zero_zero_real @ Y )
=> ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(327,plain,
( ( ! [X: real,Y: real] :
( ( ord_less_eq_real @ X @ zero_zero_real )
=> ( ( ord_less_real @ Y @ zero_zero_real )
=> ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(328,plain,
( ( ! [X: real,Y: real] :
( ( ord_less_eq_real @ zero_zero_real @ X )
=> ( ( ord_less_real @ zero_zero_real @ Y )
=> ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(329,plain,
( ( ! [X: real,Y: real] :
( ( ord_less_eq_real @ zero_zero_real @ X )
=> ( ( ord_less_real @ Y @ zero_zero_real )
=> ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(330,plain,
( ( ! [A: real,C: real,B: real] :
( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
= ( ( ( ord_less_real @ zero_zero_real @ C )
=> ( ord_less_eq_real @ A @ B ) )
& ( ( ord_less_real @ C @ zero_zero_real )
=> ( ord_less_eq_real @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(331,plain,
( ( ! [X: real,Y: real,W: real,Z: real] :
( ( ord_less_real @ zero_zero_real @ X )
=> ( ( ord_less_eq_real @ X @ Y )
=> ( ( ord_less_real @ zero_zero_real @ W )
=> ( ( ord_less_real @ W @ Z )
=> ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(332,plain,
( ( ! [X: real,Y: real,W: real,Z: real] :
( ( ord_less_eq_real @ zero_zero_real @ X )
=> ( ( ord_less_real @ X @ Y )
=> ( ( ord_less_real @ zero_zero_real @ W )
=> ( ( ord_less_eq_real @ W @ Z )
=> ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(333,plain,
( ( ! [Y: real,X: real,W: real,Z: real] :
( ( ord_less_eq_real @ zero_zero_real @ Y )
=> ( ( ord_less_eq_real @ X @ Y )
=> ( ( ord_less_real @ zero_zero_real @ W )
=> ( ( ord_less_eq_real @ W @ Z )
=> ( ord_less_eq_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(334,plain,
( ( ! [B: real,A: real,C: real] :
( ( ord_less_real @ B @ A )
=> ( ( ord_less_real @ C @ zero_zero_real )
=> ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(335,plain,
( ( ! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ zero_zero_real @ C )
=> ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(336,plain,
( ( ! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
= ( ( ( ord_less_real @ zero_zero_real @ A )
& ( ord_less_real @ zero_zero_real @ B ) )
| ( ( ord_less_real @ A @ zero_zero_real )
& ( ord_less_real @ B @ zero_zero_real ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(337,plain,
( ( ! [A: real,C: real,B: real] :
( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
= ( ( ( ord_less_real @ zero_zero_real @ C )
=> ( ord_less_real @ A @ B ) )
& ( ( ord_less_real @ C @ zero_zero_real )
=> ( ord_less_real @ B @ A ) )
& ( C != zero_zero_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(338,plain,
( ( ! [A: real,B: real] :
( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
= ( ( ( ord_less_real @ zero_zero_real @ A )
& ( ord_less_real @ B @ zero_zero_real ) )
| ( ( ord_less_real @ A @ zero_zero_real )
& ( ord_less_real @ zero_zero_real @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(339,plain,
( ( ! [X: real,Y: real] :
( ( ord_less_real @ zero_zero_real @ X )
=> ( ( ord_less_real @ zero_zero_real @ Y )
=> ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(340,plain,
( ( ! [X: real,Y: real] :
( ( ord_less_real @ zero_zero_real @ X )
=> ( ( ord_less_real @ Y @ zero_zero_real )
=> ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(341,plain,
( ( ! [X: real,Y: real] :
( ( ord_less_real @ X @ zero_zero_real )
=> ( ( ord_less_real @ zero_zero_real @ Y )
=> ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(342,plain,
( ( ! [X: real,Y: real] :
( ( ord_less_real @ X @ zero_zero_real )
=> ( ( ord_less_real @ Y @ zero_zero_real )
=> ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(343,plain,
( ( ! [P: nat > $o,N: nat] :
( ( P @ N )
=> ( ~ ( P @ zero_zero_nat )
=> ? [K: nat] :
( ( ord_less_nat @ K @ N )
& ! [I4: nat] :
( ( ord_less_eq_nat @ I4 @ K )
=> ~ ( P @ I4 ) )
& ( P @ ( suc @ K ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(344,plain,
( ( ! [X4: real] :
? [Y3: real] : ( ord_less_real @ Y3 @ X4 ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(345,plain,
( ( ! [X4: real] :
? [X_12: real] : ( ord_less_real @ X4 @ X_12 ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(346,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ord_less_nat @ M @ ( suc @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(347,plain,
( ( ord_less_nat
= ( ^ [N4: nat] : ( ord_less_eq_nat @ ( suc @ N4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(348,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
= ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(349,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( ord_less_nat @ N @ ( suc @ M ) )
= ( N = M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(350,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ ( suc @ M ) @ N )
=> ( ord_less_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(351,plain,
( ( ! [I: nat,J: nat,P: nat > $o] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( P @ J )
=> ( ! [N2: nat] :
( ( ord_less_eq_nat @ I @ N2 )
=> ( ( ord_less_nat @ N2 @ J )
=> ( ( P @ ( suc @ N2 ) )
=> ( P @ N2 ) ) ) )
=> ( P @ I ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(352,plain,
( ( ! [I: nat,J: nat,P: nat > $o] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( P @ I )
=> ( ! [N2: nat] :
( ( ord_less_eq_nat @ I @ N2 )
=> ( ( ord_less_nat @ N2 @ J )
=> ( ( P @ N2 )
=> ( P @ ( suc @ N2 ) ) ) ) )
=> ( P @ J ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(353,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ ( suc @ M ) @ N )
= ( ord_less_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(354,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(355,plain,
( ( ! [I: nat,N: nat] :
( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
=> ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(356,plain,
( ( ! [P2: nat,Pm: nat] :
( ( nthRoo1352626670d_root @ P2 @ Pm )
=> ( P2
= ( suc @ Pm ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(357,plain,
( ( nthRoo1352626670d_root
= ( ^ [P3: nat,Pm2: nat] :
( P3
= ( suc @ Pm2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(358,plain,
( ( ! [P2: nat,Pm: nat] :
( ( P2
= ( suc @ Pm ) )
=> ( nthRoo1352626670d_root @ P2 @ Pm ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(359,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ ( suc @ M ) @ N )
=> ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(360,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ ( suc @ N ) )
=> ( ~ ( ord_less_eq_nat @ M @ N )
=> ( M
= ( suc @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(361,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(362,plain,
( ( ! [N: nat,M6: nat] :
( ( ord_less_eq_nat @ ( suc @ N ) @ M6 )
=> ? [M4: nat] :
( M6
= ( suc @ M4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(363,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ ( suc @ N ) )
= ( ( ord_less_eq_nat @ M @ N )
| ( M
= ( suc @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(364,plain,
( ( ! [N: nat] :
~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(365,plain,
( ( ! [M: nat,N: nat] :
( ( ~ ( ord_less_eq_nat @ M @ N ) )
= ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(366,plain,
( ( ! [P: nat > $o,N: nat] :
( ! [N2: nat] :
( ! [M3: nat] :
( ( ord_less_eq_nat @ ( suc @ M3 ) @ N2 )
=> ( P @ M3 ) )
=> ( P @ N2 ) )
=> ( P @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(367,plain,
( ( ! [M: nat,N: nat,P: nat > $o] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( P @ M )
=> ( ! [N2: nat] :
( ( ord_less_eq_nat @ M @ N2 )
=> ( ( P @ N2 )
=> ( P @ ( suc @ N2 ) ) ) )
=> ( P @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(368,plain,
( ( ! [M: nat,N: nat,R2: nat > nat > $o] :
( ( ord_less_eq_nat @ M @ N )
=> ( ! [X3: nat] : ( R2 @ X3 @ X3 )
=> ( ! [X3: nat,Y3: nat,Z2: nat] :
( ( R2 @ X3 @ Y3 )
=> ( ( R2 @ Y3 @ Z2 )
=> ( R2 @ X3 @ Z2 ) ) )
=> ( ! [N2: nat] : ( R2 @ N2 @ ( suc @ N2 ) )
=> ( R2 @ M @ N ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(369,plain,
( ( ! [N: nat,M: nat] :
( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
= ( ord_less_eq_nat @ N @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(370,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( power_power_real @ zero_zero_real @ N )
= zero_zero_real ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(371,plain,
( ( ! [A: real,N: nat] :
( ( A != zero_zero_real )
=> ( ( power_power_real @ A @ N )
!= zero_zero_real ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(372,plain,
( ( ! [N: nat,A: real] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ? [X3: real] :
( ( ord_less_real @ zero_zero_real @ X3 )
& ( ( power_power_real @ X3 @ N )
= A )
& ! [Y4: real] :
( ( ( ord_less_real @ zero_zero_real @ Y4 )
& ( ( power_power_real @ Y4 @ N )
= A ) )
=> ( Y4 = X3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(373,plain,
( ( ! [N: nat,A: real] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ? [R: real] :
( ( ord_less_real @ zero_zero_real @ R )
& ( ( power_power_real @ R @ N )
= A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(374,plain,
( ( ! [A: nat,N: nat,B: nat] :
( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(375,plain,
( ( ! [A: int,N: nat,B: int] :
( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B @ ( suc @ N ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(376,plain,
( ( ! [A: real,N: nat,B: real] :
( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ ( power_power_real @ B @ ( suc @ N ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(377,plain,
( ( ! [A: nat,N: nat,B: nat] :
( ( ( power_power_nat @ A @ ( suc @ N ) )
= ( power_power_nat @ B @ ( suc @ N ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( A = B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(378,plain,
( ( ! [A: int,N: nat,B: int] :
( ( ( power_power_int @ A @ ( suc @ N ) )
= ( power_power_int @ B @ ( suc @ N ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( A = B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(379,plain,
( ( ! [A: real,N: nat,B: real] :
( ( ( power_power_real @ A @ ( suc @ N ) )
= ( power_power_real @ B @ ( suc @ N ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( A = B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(380,plain,
( ( ! [A: real,N: nat,B: real] :
( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_real @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(381,plain,
( ( ! [A: real,B: real,N: nat] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(382,plain,
( ( ! [A: real,N: nat] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(383,plain,
( ( ! [N: nat,P: nat > $o] :
( ( ? [I3: nat] :
( ( ord_less_nat @ I3 @ ( suc @ N ) )
& ( P @ I3 ) ) )
= ( ( P @ zero_zero_nat )
| ? [I3: nat] :
( ( ord_less_nat @ I3 @ N )
& ( P @ ( suc @ I3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(384,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( ? [M5: nat] :
( N
= ( suc @ M5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(385,plain,
( ( ! [N: nat,P: nat > $o] :
( ( ! [I3: nat] :
( ( ord_less_nat @ I3 @ ( suc @ N ) )
=> ( P @ I3 ) ) )
= ( ( P @ zero_zero_nat )
& ! [I3: nat] :
( ( ord_less_nat @ I3 @ N )
=> ( P @ ( suc @ I3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(386,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ? [M4: nat] :
( N
= ( suc @ M4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(387,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
= ( ( M = zero_zero_nat )
| ? [J3: nat] :
( ( M
= ( suc @ J3 ) )
& ( ord_less_nat @ J3 @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(388,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
=> ? [M4: nat] :
( N
= ( suc @ M4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(389,plain,
( ( ! [P: nat > $o,Nat: nat] :
( ( P @ zero_zero_nat )
=> ( ! [Nat3: nat] :
( ( P @ Nat3 )
=> ( P @ ( suc @ Nat3 ) ) )
=> ( P @ Nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(390,plain,
( ( ! [Y: nat] :
( ( Y != zero_zero_nat )
=> ~ ! [Nat3: nat] :
( Y
!= ( suc @ Nat3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(391,plain,
( ( ! [M: nat] :
( zero_zero_nat
!= ( suc @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(392,plain,
( ( ! [M: nat] :
( zero_zero_nat
!= ( suc @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(393,plain,
( ( ! [M: nat] :
( ( suc @ M )
!= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(394,plain,
( ( ! [P: nat > $o,K2: nat] :
( ( P @ K2 )
=> ( ! [N2: nat] :
( ( P @ ( suc @ N2 ) )
=> ( P @ N2 ) )
=> ( P @ zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(395,plain,
( ( ! [P: nat > nat > $o,M: nat,N: nat] :
( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
=> ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
=> ( ! [X3: nat,Y3: nat] :
( ( P @ X3 @ Y3 )
=> ( P @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
=> ( P @ M @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(396,plain,
( ( ! [P: nat > $o,N: nat] :
( ( P @ zero_zero_nat )
=> ( ! [N2: nat] :
( ( P @ N2 )
=> ( P @ ( suc @ N2 ) ) )
=> ( P @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(397,plain,
( ( ! [Nat: nat,X2: nat] :
( ( Nat
= ( suc @ X2 ) )
=> ( Nat != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(398,plain,
( ( ! [Nat2: nat] :
( zero_zero_nat
!= ( suc @ Nat2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(399,plain,
( ( ! [Nat2: nat] :
( ( suc @ Nat2 )
!= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(400,plain,
( ( ! [X2: nat] :
( zero_zero_nat
!= ( suc @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(401,plain,
( ( ! [N: nat,K2: nat] :
( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
=> ( ord_less_nat @ K2 @ ( power_power_nat @ N @ K2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(402,plain,
( ( ! [P: nat > $o] :
( ~ ( P @ zero_zero_nat )
=> ( ? [X_1: nat] : ( P @ X_1 )
=> ? [N2: nat] :
( ~ ( P @ N2 )
& ( P @ ( suc @ N2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(403,plain,
( ( ! [X: real] :
? [Z2: int] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(404,plain,
( ( ! [A: real,B: real,N: nat] :
( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N )
= ( divide_divide_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(405,plain,
( ( ! [F: nat > nat,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_eq_nat @ N @ N3 )
=> ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(406,plain,
( ( ! [F: nat > int,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_eq_nat @ N @ N3 )
=> ( ord_less_eq_int @ ( F @ N ) @ ( F @ N3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(407,plain,
( ( ! [F: nat > real,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_eq_nat @ N @ N3 )
=> ( ord_less_eq_real @ ( F @ N ) @ ( F @ N3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(408,plain,
( ( ! [F: nat > nat,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
=> ( ( ord_less_eq_nat @ N @ N3 )
=> ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(409,plain,
( ( ! [F: nat > int,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
=> ( ( ord_less_eq_nat @ N @ N3 )
=> ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(410,plain,
( ( ! [F: nat > real,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_eq_real @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
=> ( ( ord_less_eq_nat @ N @ N3 )
=> ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(411,plain,
( ( ! [X: int,B: int,W: nat] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
= ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(412,plain,
( ( ! [B: int,W: nat,X: int] :
( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X ) )
= ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(413,plain,
( ( ! [W: int,Z: int] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
= ( ord_less_eq_int @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(414,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(415,plain,
( ( ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(416,plain,
( ( ! [A: nat] :
( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(417,plain,
( ( ! [A: int] :
( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(418,plain,
( ( ! [A: real] :
( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(419,plain,
( ( ! [N: nat] :
( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
= ( suc @ zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(420,plain,
( ( ! [X: nat,M: nat] :
( ( ( power_power_nat @ X @ M )
= ( suc @ zero_zero_nat ) )
= ( ( M = zero_zero_nat )
| ( X
= ( suc @ zero_zero_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(421,plain,
( ( nthRoo1352626670d_root @ p @ pm )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(422,plain,
( ( p
= ( suc @ pm ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(423,plain,
( ( ord_less_eq_int @ na @ ( power_power_int @ ya @ p ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(424,plain,
( ( ord_less_nat @ zero_zero_nat @ pm )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(425,plain,
( ( pm != zero_zero_nat )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(426,plain,
( ( ord_less_int @ na @ ( power_power_int @ ya @ p ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(427,plain,
( ( ! [X: real] :
? [Z2: int] : ( ord_less_real @ X @ ( ring_1_of_int_real @ Z2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(428,plain,
( ( ! [X: real] :
? [Z2: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z2 ) @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(429,plain,
( ( ny
= ( divide_divide_real @ ( ring_1_of_int_real @ na ) @ ( power_power_real @ ( ring_1_of_int_real @ ya ) @ pm ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(430,plain,
( ( ! [A: real,N: nat] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(431,plain,
( ( ! [A: real,N: nat] :
( ( ord_less_real @ zero_zero_real @ A )
=> ? [R: real] :
( ( ord_less_real @ zero_zero_real @ R )
& ( ( power_power_real @ R @ ( suc @ N ) )
= A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(432,plain,
( ( ! [A: real,N: nat] :
( ( ( power_power_real @ A @ N )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( ord_less_nat @ zero_zero_nat @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(433,plain,
( ( ord_less_real @ zero_zero_real @ ny )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(434,plain,
( ( ! [N: nat] :
( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(435,plain,
( ( ! [N: nat] :
( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
= zero_zero_int ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(436,plain,
( ( ! [N: nat] :
( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
= zero_zero_real ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(437,plain,
( ( ! [F: nat > nat,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_nat @ N @ N3 )
=> ( ord_less_nat @ ( F @ N ) @ ( F @ N3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(438,plain,
( ( ! [F: nat > int,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_nat @ N @ N3 )
=> ( ord_less_int @ ( F @ N ) @ ( F @ N3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(439,plain,
( ( ! [F: nat > real,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_nat @ N @ N3 )
=> ( ord_less_real @ ( F @ N ) @ ( F @ N3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(440,plain,
( ( ! [F: nat > nat,N: nat,M: nat] :
( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
= ( ord_less_nat @ N @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(441,plain,
( ( ! [F: nat > int,N: nat,M: nat] :
( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
= ( ord_less_nat @ N @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(442,plain,
( ( ! [F: nat > real,N: nat,M: nat] :
( ! [N2: nat] : ( ord_less_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_real @ ( F @ N ) @ ( F @ M ) )
= ( ord_less_nat @ N @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(443,plain,
( ( ! [X: nat,Y: nat] :
( ( ( suc @ X )
= ( suc @ Y ) )
=> ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(444,plain,
( ( ! [N: nat] :
( N
!= ( suc @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(445,plain,
( ( ! [Z: int] :
( ( ord_less_int @ zero_zero_int @ Z )
=> ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(446,plain,
( ( ! [I: nat,K2: nat] :
( ( ord_less_nat @ I @ K2 )
=> ( ( K2
!= ( suc @ I ) )
=> ~ ! [J2: nat] :
( ( ord_less_nat @ I @ J2 )
=> ( K2
!= ( suc @ J2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(447,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ ( suc @ M ) @ N )
=> ( ord_less_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(448,plain,
( ( ! [I: nat,K2: nat] :
( ( ord_less_nat @ ( suc @ I ) @ K2 )
=> ~ ! [J2: nat] :
( ( ord_less_nat @ I @ J2 )
=> ( K2
!= ( suc @ J2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(449,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ( ( suc @ M )
!= N )
=> ( ord_less_nat @ ( suc @ M ) @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(450,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
=> ( ~ ( ord_less_nat @ M @ N )
=> ( M = N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(451,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_nat @ M @ ( suc @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(452,plain,
( ( ! [N: nat,P: nat > $o] :
( ( ? [I3: nat] :
( ( ord_less_nat @ I3 @ ( suc @ N ) )
& ( P @ I3 ) ) )
= ( ( P @ N )
| ? [I3: nat] :
( ( ord_less_nat @ I3 @ N )
& ( P @ I3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(453,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
= ( ( ord_less_nat @ M @ N )
| ( M = N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(454,plain,
( ( ! [M: nat,N: nat] :
( ( ~ ( ord_less_nat @ M @ N ) )
= ( ord_less_nat @ N @ ( suc @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(455,plain,
( ( ! [N: nat,P: nat > $o] :
( ( ! [I3: nat] :
( ( ord_less_nat @ I3 @ ( suc @ N ) )
=> ( P @ I3 ) ) )
= ( ( P @ N )
& ! [I3: nat] :
( ( ord_less_nat @ I3 @ N )
=> ( P @ I3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(456,plain,
( ( ! [N: nat,M: nat] :
( ( ord_less_nat @ ( suc @ N ) @ M )
= ( ? [M2: nat] :
( ( M
= ( suc @ M2 ) )
& ( ord_less_nat @ N @ M2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(457,plain,
( ( ! [N: nat,M: nat] :
( ~ ( ord_less_nat @ N @ M )
=> ( ( ord_less_nat @ N @ ( suc @ M ) )
=> ( M = N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(458,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
=> ( ord_less_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(459,plain,
( ( ! [I: nat,J: nat,K2: nat] :
( ( ord_less_nat @ I @ J )
=> ( ( ord_less_nat @ J @ K2 )
=> ( ord_less_nat @ ( suc @ I ) @ K2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(460,plain,
( ( ! [I: nat,J: nat,P: nat > nat > $o] :
( ( ord_less_nat @ I @ J )
=> ( ! [I2: nat] : ( P @ I2 @ ( suc @ I2 ) )
=> ( ! [I2: nat,J2: nat,K: nat] :
( ( ord_less_nat @ I2 @ J2 )
=> ( ( ord_less_nat @ J2 @ K )
=> ( ( P @ I2 @ J2 )
=> ( ( P @ J2 @ K )
=> ( P @ I2 @ K ) ) ) ) )
=> ( P @ I @ J ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(461,plain,
( ( ! [I: nat,J: nat,P: nat > $o] :
( ( ord_less_nat @ I @ J )
=> ( ! [I2: nat] :
( ( J
= ( suc @ I2 ) )
=> ( P @ I2 ) )
=> ( ! [I2: nat] :
( ( ord_less_nat @ I2 @ J )
=> ( ( P @ ( suc @ I2 ) )
=> ( P @ I2 ) ) )
=> ( P @ I ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(462,plain,
( ( ! [N: nat,M: nat] :
( ~ ( ord_less_nat @ N @ M )
=> ( ( ord_less_nat @ N @ ( suc @ M ) )
= ( N = M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(463,plain,
( ( ! [Z: int] :
( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
= ( ord_less_int @ zero_zero_int @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(464,plain,
( ( ! [Z: int] :
( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
= ( ord_less_int @ Z @ zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(465,plain,
( ( ! [Z: int] :
( ( ( ring_1_of_int_real @ Z )
= zero_zero_real )
= ( Z = zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(466,plain,
( ( ! [Z: int] :
( ( zero_zero_real
= ( ring_1_of_int_real @ Z ) )
= ( Z = zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(467,plain,
( ( ( ring_1_of_int_real @ zero_zero_int )
= zero_zero_real )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(468,plain,
( ( ord_less_eq_int @ zero_zero_int @ na )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(469,plain,
( ( ord_less_eq_int @ zero_zero_int @ ya )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(470,plain,
( ( ~ ( ( ord_less_int @ ya @ zero_zero_int )
| ( ord_less_int @ na @ zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(471,plain,
( ( ~ ( ( ord_less_int @ ya @ zero_zero_int )
| ( ord_less_int @ na @ zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(472,plain,
( ( ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(473,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(474,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
= ( ord_less_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(475,plain,
( ( ( ord_less_int @ zero_zero_int @ ya )
| ( ya = zero_zero_int ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(476,plain,
( ( ya != zero_zero_int )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(477,plain,
( ( ! [Nat: nat,Nat2: nat] :
( ( ( suc @ Nat )
= ( suc @ Nat2 ) )
= ( Nat = Nat2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(478,plain,
( ( ! [X2: nat,Y2: nat] :
( ( ( suc @ X2 )
= ( suc @ Y2 ) )
= ( X2 = Y2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(479,plain,
( ( ! [W: int,Z: int] :
( ( ( ring_1_of_int_real @ W )
= ( ring_1_of_int_real @ Z ) )
= ( W = Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(480,plain,
( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ ya ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(481,plain,
( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ na ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(482,plain,
( ( ! [W: int,Z: int] :
( ( ord_less_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
= ( ord_less_int @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(483,plain,
( ( ! [X: int,B: int,W: nat] :
( ( ( ring_1_of_int_real @ X )
= ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
= ( X
= ( power_power_int @ B @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(484,plain,
( ( ! [B: int,W: nat,X: int] :
( ( ( power_power_real @ ( ring_1_of_int_real @ B ) @ W )
= ( ring_1_of_int_real @ X ) )
= ( ( power_power_int @ B @ W )
= X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(485,plain,
( ( ! [Z: int,N: nat] :
( ( ring_1_of_int_real @ ( power_power_int @ Z @ N ) )
= ( power_power_real @ ( ring_1_of_int_real @ Z ) @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(486,plain,
( ( ! [X: int,B: int,W: nat] :
( ( ord_less_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
= ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(487,plain,
( ( ! [B: int,W: nat,X: int] :
( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X ) )
= ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(488,plain,
( ( na != zero_zero_int )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(489,plain,
( ( ~ ( ord_less_real @ ( ring_1_of_int_real @ na ) @ ( power_power_real @ ( ring_1_of_int_real @ ya ) @ ( suc @ pm ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[322]) ).
thf(490,plain,
( ( na != zero_zero_int )
= $true ),
inference(copy,[status(thm)],[488]) ).
thf(491,plain,
( ( ! [B: int,W: nat,X: int] :
( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X ) )
= ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[487]) ).
thf(492,plain,
( ( ! [X: int,B: int,W: nat] :
( ( ord_less_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
= ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[486]) ).
thf(493,plain,
( ( ! [Z: int,N: nat] :
( ( ring_1_of_int_real @ ( power_power_int @ Z @ N ) )
= ( power_power_real @ ( ring_1_of_int_real @ Z ) @ N ) ) )
= $true ),
inference(copy,[status(thm)],[485]) ).
thf(494,plain,
( ( ! [B: int,W: nat,X: int] :
( ( ( power_power_real @ ( ring_1_of_int_real @ B ) @ W )
= ( ring_1_of_int_real @ X ) )
= ( ( power_power_int @ B @ W )
= X ) ) )
= $true ),
inference(copy,[status(thm)],[484]) ).
thf(495,plain,
( ( ! [X: int,B: int,W: nat] :
( ( ( ring_1_of_int_real @ X )
= ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
= ( X
= ( power_power_int @ B @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[483]) ).
thf(496,plain,
( ( ! [W: int,Z: int] :
( ( ord_less_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
= ( ord_less_int @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[482]) ).
thf(497,plain,
( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ na ) )
= $true ),
inference(copy,[status(thm)],[481]) ).
thf(498,plain,
( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ ya ) )
= $true ),
inference(copy,[status(thm)],[480]) ).
thf(499,plain,
( ( ! [W: int,Z: int] :
( ( ( ring_1_of_int_real @ W )
= ( ring_1_of_int_real @ Z ) )
= ( W = Z ) ) )
= $true ),
inference(copy,[status(thm)],[479]) ).
thf(500,plain,
( ( ! [X2: nat,Y2: nat] :
( ( ( suc @ X2 )
= ( suc @ Y2 ) )
= ( X2 = Y2 ) ) )
= $true ),
inference(copy,[status(thm)],[478]) ).
thf(501,plain,
( ( ! [Nat: nat,Nat2: nat] :
( ( ( suc @ Nat )
= ( suc @ Nat2 ) )
= ( Nat = Nat2 ) ) )
= $true ),
inference(copy,[status(thm)],[477]) ).
thf(502,plain,
( ( ya != zero_zero_int )
= $true ),
inference(copy,[status(thm)],[476]) ).
thf(503,plain,
( ( ( ord_less_int @ zero_zero_int @ ya )
| ( ya = zero_zero_int ) )
= $true ),
inference(copy,[status(thm)],[475]) ).
thf(504,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
= ( ord_less_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[474]) ).
thf(505,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[473]) ).
thf(506,plain,
( ( ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) )
= $true ),
inference(copy,[status(thm)],[472]) ).
thf(507,plain,
( ( ~ ( ( ord_less_int @ ya @ zero_zero_int )
| ( ord_less_int @ na @ zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[471]) ).
thf(508,plain,
( ( ~ ( ( ord_less_int @ ya @ zero_zero_int )
| ( ord_less_int @ na @ zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[470]) ).
thf(509,plain,
( ( ord_less_eq_int @ zero_zero_int @ ya )
= $true ),
inference(copy,[status(thm)],[469]) ).
thf(510,plain,
( ( ord_less_eq_int @ zero_zero_int @ na )
= $true ),
inference(copy,[status(thm)],[468]) ).
thf(511,plain,
( ( ( ring_1_of_int_real @ zero_zero_int )
= zero_zero_real )
= $true ),
inference(copy,[status(thm)],[467]) ).
thf(512,plain,
( ( ! [Z: int] :
( ( zero_zero_real
= ( ring_1_of_int_real @ Z ) )
= ( Z = zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[466]) ).
thf(513,plain,
( ( ! [Z: int] :
( ( ( ring_1_of_int_real @ Z )
= zero_zero_real )
= ( Z = zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[465]) ).
thf(514,plain,
( ( ! [Z: int] :
( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
= ( ord_less_int @ Z @ zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[464]) ).
thf(515,plain,
( ( ! [Z: int] :
( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
= ( ord_less_int @ zero_zero_int @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[463]) ).
thf(516,plain,
( ( ! [N: nat,M: nat] :
( ~ ( ord_less_nat @ N @ M )
=> ( ( ord_less_nat @ N @ ( suc @ M ) )
= ( N = M ) ) ) )
= $true ),
inference(copy,[status(thm)],[462]) ).
thf(517,plain,
( ( ! [I: nat,J: nat,P: nat > $o] :
( ( ord_less_nat @ I @ J )
=> ( ! [I2: nat] :
( ( J
= ( suc @ I2 ) )
=> ( P @ I2 ) )
=> ( ! [I2: nat] :
( ( ord_less_nat @ I2 @ J )
=> ( ( P @ ( suc @ I2 ) )
=> ( P @ I2 ) ) )
=> ( P @ I ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[461]) ).
thf(518,plain,
( ( ! [I: nat,J: nat,P: nat > nat > $o] :
( ( ord_less_nat @ I @ J )
=> ( ! [I2: nat] : ( P @ I2 @ ( suc @ I2 ) )
=> ( ! [I2: nat,J2: nat,K: nat] :
( ( ord_less_nat @ I2 @ J2 )
=> ( ( ord_less_nat @ J2 @ K )
=> ( ( P @ I2 @ J2 )
=> ( ( P @ J2 @ K )
=> ( P @ I2 @ K ) ) ) ) )
=> ( P @ I @ J ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[460]) ).
thf(519,plain,
( ( ! [I: nat,J: nat,K2: nat] :
( ( ord_less_nat @ I @ J )
=> ( ( ord_less_nat @ J @ K2 )
=> ( ord_less_nat @ ( suc @ I ) @ K2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[459]) ).
thf(520,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
=> ( ord_less_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[458]) ).
thf(521,plain,
( ( ! [N: nat,M: nat] :
( ~ ( ord_less_nat @ N @ M )
=> ( ( ord_less_nat @ N @ ( suc @ M ) )
=> ( M = N ) ) ) )
= $true ),
inference(copy,[status(thm)],[457]) ).
thf(522,plain,
( ( ! [N: nat,M: nat] :
( ( ord_less_nat @ ( suc @ N ) @ M )
= ( ? [M2: nat] :
( ( M
= ( suc @ M2 ) )
& ( ord_less_nat @ N @ M2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[456]) ).
thf(523,plain,
( ( ! [N: nat,P: nat > $o] :
( ( ! [I3: nat] :
( ( ord_less_nat @ I3 @ ( suc @ N ) )
=> ( P @ I3 ) ) )
= ( ( P @ N )
& ! [I3: nat] :
( ( ord_less_nat @ I3 @ N )
=> ( P @ I3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[455]) ).
thf(524,plain,
( ( ! [M: nat,N: nat] :
( ( ~ ( ord_less_nat @ M @ N ) )
= ( ord_less_nat @ N @ ( suc @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[454]) ).
thf(525,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
= ( ( ord_less_nat @ M @ N )
| ( M = N ) ) ) )
= $true ),
inference(copy,[status(thm)],[453]) ).
thf(526,plain,
( ( ! [N: nat,P: nat > $o] :
( ( ? [I3: nat] :
( ( ord_less_nat @ I3 @ ( suc @ N ) )
& ( P @ I3 ) ) )
= ( ( P @ N )
| ? [I3: nat] :
( ( ord_less_nat @ I3 @ N )
& ( P @ I3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[452]) ).
thf(527,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_nat @ M @ ( suc @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[451]) ).
thf(528,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
=> ( ~ ( ord_less_nat @ M @ N )
=> ( M = N ) ) ) )
= $true ),
inference(copy,[status(thm)],[450]) ).
thf(529,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ( ( suc @ M )
!= N )
=> ( ord_less_nat @ ( suc @ M ) @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[449]) ).
thf(530,plain,
( ( ! [I: nat,K2: nat] :
( ( ord_less_nat @ ( suc @ I ) @ K2 )
=> ~ ! [J2: nat] :
( ( ord_less_nat @ I @ J2 )
=> ( K2
!= ( suc @ J2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[448]) ).
thf(531,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ ( suc @ M ) @ N )
=> ( ord_less_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[447]) ).
thf(532,plain,
( ( ! [I: nat,K2: nat] :
( ( ord_less_nat @ I @ K2 )
=> ( ( K2
!= ( suc @ I ) )
=> ~ ! [J2: nat] :
( ( ord_less_nat @ I @ J2 )
=> ( K2
!= ( suc @ J2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[446]) ).
thf(533,plain,
( ( ! [Z: int] :
( ( ord_less_int @ zero_zero_int @ Z )
=> ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[445]) ).
thf(534,plain,
( ( ! [N: nat] :
( N
!= ( suc @ N ) ) )
= $true ),
inference(copy,[status(thm)],[444]) ).
thf(535,plain,
( ( ! [X: nat,Y: nat] :
( ( ( suc @ X )
= ( suc @ Y ) )
=> ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[443]) ).
thf(536,plain,
( ( ! [F: nat > real,N: nat,M: nat] :
( ! [N2: nat] : ( ord_less_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_real @ ( F @ N ) @ ( F @ M ) )
= ( ord_less_nat @ N @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[442]) ).
thf(537,plain,
( ( ! [F: nat > int,N: nat,M: nat] :
( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
= ( ord_less_nat @ N @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[441]) ).
thf(538,plain,
( ( ! [F: nat > nat,N: nat,M: nat] :
( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
= ( ord_less_nat @ N @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(539,plain,
( ( ! [F: nat > real,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_nat @ N @ N3 )
=> ( ord_less_real @ ( F @ N ) @ ( F @ N3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[439]) ).
thf(540,plain,
( ( ! [F: nat > int,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_nat @ N @ N3 )
=> ( ord_less_int @ ( F @ N ) @ ( F @ N3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[438]) ).
thf(541,plain,
( ( ! [F: nat > nat,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_nat @ N @ N3 )
=> ( ord_less_nat @ ( F @ N ) @ ( F @ N3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(542,plain,
( ( ! [N: nat] :
( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
= zero_zero_real ) )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(543,plain,
( ( ! [N: nat] :
( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
= zero_zero_int ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(544,plain,
( ( ! [N: nat] :
( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(545,plain,
( ( ord_less_real @ zero_zero_real @ ny )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(546,plain,
( ( ! [A: real,N: nat] :
( ( ( power_power_real @ A @ N )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( ord_less_nat @ zero_zero_nat @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(547,plain,
( ( ! [A: real,N: nat] :
( ( ord_less_real @ zero_zero_real @ A )
=> ? [R: real] :
( ( ord_less_real @ zero_zero_real @ R )
& ( ( power_power_real @ R @ ( suc @ N ) )
= A ) ) ) )
= $true ),
inference(copy,[status(thm)],[431]) ).
thf(548,plain,
( ( ! [A: real,N: nat] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(549,plain,
( ( ny
= ( divide_divide_real @ ( ring_1_of_int_real @ na ) @ ( power_power_real @ ( ring_1_of_int_real @ ya ) @ pm ) ) )
= $true ),
inference(copy,[status(thm)],[429]) ).
thf(550,plain,
( ( ! [X: real] :
? [Z2: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z2 ) @ X ) )
= $true ),
inference(copy,[status(thm)],[428]) ).
thf(551,plain,
( ( ! [X: real] :
? [Z2: int] : ( ord_less_real @ X @ ( ring_1_of_int_real @ Z2 ) ) )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(552,plain,
( ( ord_less_int @ na @ ( power_power_int @ ya @ p ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(553,plain,
( ( pm != zero_zero_nat )
= $true ),
inference(copy,[status(thm)],[425]) ).
thf(554,plain,
( ( ord_less_nat @ zero_zero_nat @ pm )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(555,plain,
( ( ord_less_eq_int @ na @ ( power_power_int @ ya @ p ) )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(556,plain,
( ( p
= ( suc @ pm ) )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(557,plain,
( ( nthRoo1352626670d_root @ p @ pm )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(558,plain,
( ( ! [X: nat,M: nat] :
( ( ( power_power_nat @ X @ M )
= ( suc @ zero_zero_nat ) )
= ( ( M = zero_zero_nat )
| ( X
= ( suc @ zero_zero_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(559,plain,
( ( ! [N: nat] :
( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
= ( suc @ zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(560,plain,
( ( ! [A: real] :
( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(561,plain,
( ( ! [A: int] :
( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(562,plain,
( ( ! [A: nat] :
( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(563,plain,
( ( ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(564,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(565,plain,
( ( ! [W: int,Z: int] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
= ( ord_less_eq_int @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(566,plain,
( ( ! [B: int,W: nat,X: int] :
( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X ) )
= ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(567,plain,
( ( ! [X: int,B: int,W: nat] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
= ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(568,plain,
( ( ! [F: nat > real,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_eq_real @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
=> ( ( ord_less_eq_nat @ N @ N3 )
=> ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(569,plain,
( ( ! [F: nat > int,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
=> ( ( ord_less_eq_nat @ N @ N3 )
=> ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(570,plain,
( ( ! [F: nat > nat,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
=> ( ( ord_less_eq_nat @ N @ N3 )
=> ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(571,plain,
( ( ! [F: nat > real,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_eq_nat @ N @ N3 )
=> ( ord_less_eq_real @ ( F @ N ) @ ( F @ N3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(572,plain,
( ( ! [F: nat > int,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_eq_nat @ N @ N3 )
=> ( ord_less_eq_int @ ( F @ N ) @ ( F @ N3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(573,plain,
( ( ! [F: nat > nat,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_eq_nat @ N @ N3 )
=> ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(574,plain,
( ( ! [A: real,B: real,N: nat] :
( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N )
= ( divide_divide_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(575,plain,
( ( ! [X: real] :
? [Z2: int] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z2 ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(576,plain,
( ( ! [P: nat > $o] :
( ~ ( P @ zero_zero_nat )
=> ( ? [X_1: nat] : ( P @ X_1 )
=> ? [N2: nat] :
( ~ ( P @ N2 )
& ( P @ ( suc @ N2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(577,plain,
( ( ! [N: nat,K2: nat] :
( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
=> ( ord_less_nat @ K2 @ ( power_power_nat @ N @ K2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(578,plain,
( ( ! [X2: nat] :
( zero_zero_nat
!= ( suc @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(579,plain,
( ( ! [Nat2: nat] :
( ( suc @ Nat2 )
!= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(580,plain,
( ( ! [Nat2: nat] :
( zero_zero_nat
!= ( suc @ Nat2 ) ) )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(581,plain,
( ( ! [Nat: nat,X2: nat] :
( ( Nat
= ( suc @ X2 ) )
=> ( Nat != zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(582,plain,
( ( ! [P: nat > $o,N: nat] :
( ( P @ zero_zero_nat )
=> ( ! [N2: nat] :
( ( P @ N2 )
=> ( P @ ( suc @ N2 ) ) )
=> ( P @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(583,plain,
( ( ! [P: nat > nat > $o,M: nat,N: nat] :
( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
=> ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
=> ( ! [X3: nat,Y3: nat] :
( ( P @ X3 @ Y3 )
=> ( P @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
=> ( P @ M @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[395]) ).
thf(584,plain,
( ( ! [P: nat > $o,K2: nat] :
( ( P @ K2 )
=> ( ! [N2: nat] :
( ( P @ ( suc @ N2 ) )
=> ( P @ N2 ) )
=> ( P @ zero_zero_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[394]) ).
thf(585,plain,
( ( ! [M: nat] :
( ( suc @ M )
!= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(586,plain,
( ( ! [M: nat] :
( zero_zero_nat
!= ( suc @ M ) ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(587,plain,
( ( ! [M: nat] :
( zero_zero_nat
!= ( suc @ M ) ) )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(588,plain,
( ( ! [Y: nat] :
( ( Y != zero_zero_nat )
=> ~ ! [Nat3: nat] :
( Y
!= ( suc @ Nat3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(589,plain,
( ( ! [P: nat > $o,Nat: nat] :
( ( P @ zero_zero_nat )
=> ( ! [Nat3: nat] :
( ( P @ Nat3 )
=> ( P @ ( suc @ Nat3 ) ) )
=> ( P @ Nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(590,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
=> ? [M4: nat] :
( N
= ( suc @ M4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[388]) ).
thf(591,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
= ( ( M = zero_zero_nat )
| ? [J3: nat] :
( ( M
= ( suc @ J3 ) )
& ( ord_less_nat @ J3 @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[387]) ).
thf(592,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ? [M4: nat] :
( N
= ( suc @ M4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(593,plain,
( ( ! [N: nat,P: nat > $o] :
( ( ! [I3: nat] :
( ( ord_less_nat @ I3 @ ( suc @ N ) )
=> ( P @ I3 ) ) )
= ( ( P @ zero_zero_nat )
& ! [I3: nat] :
( ( ord_less_nat @ I3 @ N )
=> ( P @ ( suc @ I3 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[385]) ).
thf(594,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( ? [M5: nat] :
( N
= ( suc @ M5 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(595,plain,
( ( ! [N: nat,P: nat > $o] :
( ( ? [I3: nat] :
( ( ord_less_nat @ I3 @ ( suc @ N ) )
& ( P @ I3 ) ) )
= ( ( P @ zero_zero_nat )
| ? [I3: nat] :
( ( ord_less_nat @ I3 @ N )
& ( P @ ( suc @ I3 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(596,plain,
( ( ! [A: real,N: nat] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(597,plain,
( ( ! [A: real,B: real,N: nat] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(598,plain,
( ( ! [A: real,N: nat,B: real] :
( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_real @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[380]) ).
thf(599,plain,
( ( ! [A: real,N: nat,B: real] :
( ( ( power_power_real @ A @ ( suc @ N ) )
= ( power_power_real @ B @ ( suc @ N ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( A = B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(600,plain,
( ( ! [A: int,N: nat,B: int] :
( ( ( power_power_int @ A @ ( suc @ N ) )
= ( power_power_int @ B @ ( suc @ N ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( A = B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[378]) ).
thf(601,plain,
( ( ! [A: nat,N: nat,B: nat] :
( ( ( power_power_nat @ A @ ( suc @ N ) )
= ( power_power_nat @ B @ ( suc @ N ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( A = B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(602,plain,
( ( ! [A: real,N: nat,B: real] :
( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ ( power_power_real @ B @ ( suc @ N ) ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(603,plain,
( ( ! [A: int,N: nat,B: int] :
( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B @ ( suc @ N ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(604,plain,
( ( ! [A: nat,N: nat,B: nat] :
( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(605,plain,
( ( ! [N: nat,A: real] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ? [R: real] :
( ( ord_less_real @ zero_zero_real @ R )
& ( ( power_power_real @ R @ N )
= A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(606,plain,
( ( ! [N: nat,A: real] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( ord_less_real @ zero_zero_real @ A )
=> ? [X3: real] :
( ( ord_less_real @ zero_zero_real @ X3 )
& ( ( power_power_real @ X3 @ N )
= A )
& ! [Y4: real] :
( ( ( ord_less_real @ zero_zero_real @ Y4 )
& ( ( power_power_real @ Y4 @ N )
= A ) )
=> ( Y4 = X3 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(607,plain,
( ( ! [A: real,N: nat] :
( ( A != zero_zero_real )
=> ( ( power_power_real @ A @ N )
!= zero_zero_real ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(608,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( power_power_real @ zero_zero_real @ N )
= zero_zero_real ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(609,plain,
( ( ! [N: nat,M: nat] :
( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
= ( ord_less_eq_nat @ N @ M ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(610,plain,
( ( ! [M: nat,N: nat,R2: nat > nat > $o] :
( ( ord_less_eq_nat @ M @ N )
=> ( ! [X3: nat] : ( R2 @ X3 @ X3 )
=> ( ! [X3: nat,Y3: nat,Z2: nat] :
( ( R2 @ X3 @ Y3 )
=> ( ( R2 @ Y3 @ Z2 )
=> ( R2 @ X3 @ Z2 ) ) )
=> ( ! [N2: nat] : ( R2 @ N2 @ ( suc @ N2 ) )
=> ( R2 @ M @ N ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(611,plain,
( ( ! [M: nat,N: nat,P: nat > $o] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( P @ M )
=> ( ! [N2: nat] :
( ( ord_less_eq_nat @ M @ N2 )
=> ( ( P @ N2 )
=> ( P @ ( suc @ N2 ) ) ) )
=> ( P @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(612,plain,
( ( ! [P: nat > $o,N: nat] :
( ! [N2: nat] :
( ! [M3: nat] :
( ( ord_less_eq_nat @ ( suc @ M3 ) @ N2 )
=> ( P @ M3 ) )
=> ( P @ N2 ) )
=> ( P @ N ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(613,plain,
( ( ! [M: nat,N: nat] :
( ( ~ ( ord_less_eq_nat @ M @ N ) )
= ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(614,plain,
( ( ! [N: nat] :
~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(615,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ ( suc @ N ) )
= ( ( ord_less_eq_nat @ M @ N )
| ( M
= ( suc @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(616,plain,
( ( ! [N: nat,M6: nat] :
( ( ord_less_eq_nat @ ( suc @ N ) @ M6 )
=> ? [M4: nat] :
( M6
= ( suc @ M4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(617,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(618,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ ( suc @ N ) )
=> ( ~ ( ord_less_eq_nat @ M @ N )
=> ( M
= ( suc @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(619,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ ( suc @ M ) @ N )
=> ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(620,plain,
( ( ! [P2: nat,Pm: nat] :
( ( P2
= ( suc @ Pm ) )
=> ( nthRoo1352626670d_root @ P2 @ Pm ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(621,plain,
( ( nthRoo1352626670d_root
= ( ^ [P3: nat,Pm2: nat] :
( P3
= ( suc @ Pm2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[357]) ).
thf(622,plain,
( ( ! [P2: nat,Pm: nat] :
( ( nthRoo1352626670d_root @ P2 @ Pm )
=> ( P2
= ( suc @ Pm ) ) ) )
= $true ),
inference(copy,[status(thm)],[356]) ).
thf(623,plain,
( ( ! [I: nat,N: nat] :
( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
=> ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[355]) ).
thf(624,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) )
= $true ),
inference(copy,[status(thm)],[354]) ).
thf(625,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ ( suc @ M ) @ N )
= ( ord_less_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[353]) ).
thf(626,plain,
( ( ! [I: nat,J: nat,P: nat > $o] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( P @ I )
=> ( ! [N2: nat] :
( ( ord_less_eq_nat @ I @ N2 )
=> ( ( ord_less_nat @ N2 @ J )
=> ( ( P @ N2 )
=> ( P @ ( suc @ N2 ) ) ) ) )
=> ( P @ J ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[352]) ).
thf(627,plain,
( ( ! [I: nat,J: nat,P: nat > $o] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( P @ J )
=> ( ! [N2: nat] :
( ( ord_less_eq_nat @ I @ N2 )
=> ( ( ord_less_nat @ N2 @ J )
=> ( ( P @ ( suc @ N2 ) )
=> ( P @ N2 ) ) ) )
=> ( P @ I ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[351]) ).
thf(628,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ ( suc @ M ) @ N )
=> ( ord_less_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[350]) ).
thf(629,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( ord_less_nat @ N @ ( suc @ M ) )
= ( N = M ) ) ) )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(630,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
= ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[348]) ).
thf(631,plain,
( ( ord_less_nat
= ( ^ [N4: nat] : ( ord_less_eq_nat @ ( suc @ N4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[347]) ).
thf(632,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ord_less_nat @ M @ ( suc @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[346]) ).
thf(633,plain,
( ( ! [X4: real] :
? [X_12: real] : ( ord_less_real @ X4 @ X_12 ) )
= $true ),
inference(copy,[status(thm)],[345]) ).
thf(634,plain,
( ( ! [X4: real] :
? [Y3: real] : ( ord_less_real @ Y3 @ X4 ) )
= $true ),
inference(copy,[status(thm)],[344]) ).
thf(635,plain,
( ( ! [P: nat > $o,N: nat] :
( ( P @ N )
=> ( ~ ( P @ zero_zero_nat )
=> ? [K: nat] :
( ( ord_less_nat @ K @ N )
& ! [I4: nat] :
( ( ord_less_eq_nat @ I4 @ K )
=> ~ ( P @ I4 ) )
& ( P @ ( suc @ K ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[343]) ).
thf(636,plain,
( ( ! [X: real,Y: real] :
( ( ord_less_real @ X @ zero_zero_real )
=> ( ( ord_less_real @ Y @ zero_zero_real )
=> ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[342]) ).
thf(637,plain,
( ( ! [X: real,Y: real] :
( ( ord_less_real @ X @ zero_zero_real )
=> ( ( ord_less_real @ zero_zero_real @ Y )
=> ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) )
= $true ),
inference(copy,[status(thm)],[341]) ).
thf(638,plain,
( ( ! [X: real,Y: real] :
( ( ord_less_real @ zero_zero_real @ X )
=> ( ( ord_less_real @ Y @ zero_zero_real )
=> ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) )
= $true ),
inference(copy,[status(thm)],[340]) ).
thf(639,plain,
( ( ! [X: real,Y: real] :
( ( ord_less_real @ zero_zero_real @ X )
=> ( ( ord_less_real @ zero_zero_real @ Y )
=> ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[339]) ).
thf(640,plain,
( ( ! [A: real,B: real] :
( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
= ( ( ( ord_less_real @ zero_zero_real @ A )
& ( ord_less_real @ B @ zero_zero_real ) )
| ( ( ord_less_real @ A @ zero_zero_real )
& ( ord_less_real @ zero_zero_real @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[338]) ).
thf(641,plain,
( ( ! [A: real,C: real,B: real] :
( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
= ( ( ( ord_less_real @ zero_zero_real @ C )
=> ( ord_less_real @ A @ B ) )
& ( ( ord_less_real @ C @ zero_zero_real )
=> ( ord_less_real @ B @ A ) )
& ( C != zero_zero_real ) ) ) )
= $true ),
inference(copy,[status(thm)],[337]) ).
thf(642,plain,
( ( ! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
= ( ( ( ord_less_real @ zero_zero_real @ A )
& ( ord_less_real @ zero_zero_real @ B ) )
| ( ( ord_less_real @ A @ zero_zero_real )
& ( ord_less_real @ B @ zero_zero_real ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[336]) ).
thf(643,plain,
( ( ! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ zero_zero_real @ C )
=> ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[335]) ).
thf(644,plain,
( ( ! [B: real,A: real,C: real] :
( ( ord_less_real @ B @ A )
=> ( ( ord_less_real @ C @ zero_zero_real )
=> ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[334]) ).
thf(645,plain,
( ( ! [Y: real,X: real,W: real,Z: real] :
( ( ord_less_eq_real @ zero_zero_real @ Y )
=> ( ( ord_less_eq_real @ X @ Y )
=> ( ( ord_less_real @ zero_zero_real @ W )
=> ( ( ord_less_eq_real @ W @ Z )
=> ( ord_less_eq_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[333]) ).
thf(646,plain,
( ( ! [X: real,Y: real,W: real,Z: real] :
( ( ord_less_eq_real @ zero_zero_real @ X )
=> ( ( ord_less_real @ X @ Y )
=> ( ( ord_less_real @ zero_zero_real @ W )
=> ( ( ord_less_eq_real @ W @ Z )
=> ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[332]) ).
thf(647,plain,
( ( ! [X: real,Y: real,W: real,Z: real] :
( ( ord_less_real @ zero_zero_real @ X )
=> ( ( ord_less_eq_real @ X @ Y )
=> ( ( ord_less_real @ zero_zero_real @ W )
=> ( ( ord_less_real @ W @ Z )
=> ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[331]) ).
thf(648,plain,
( ( ! [A: real,C: real,B: real] :
( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
= ( ( ( ord_less_real @ zero_zero_real @ C )
=> ( ord_less_eq_real @ A @ B ) )
& ( ( ord_less_real @ C @ zero_zero_real )
=> ( ord_less_eq_real @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[330]) ).
thf(649,plain,
( ( ! [X: real,Y: real] :
( ( ord_less_eq_real @ zero_zero_real @ X )
=> ( ( ord_less_real @ Y @ zero_zero_real )
=> ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) )
= $true ),
inference(copy,[status(thm)],[329]) ).
thf(650,plain,
( ( ! [X: real,Y: real] :
( ( ord_less_eq_real @ zero_zero_real @ X )
=> ( ( ord_less_real @ zero_zero_real @ Y )
=> ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[328]) ).
thf(651,plain,
( ( ! [X: real,Y: real] :
( ( ord_less_eq_real @ X @ zero_zero_real )
=> ( ( ord_less_real @ Y @ zero_zero_real )
=> ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[327]) ).
thf(652,plain,
( ( ! [X: real,Y: real] :
( ( ord_less_eq_real @ X @ zero_zero_real )
=> ( ( ord_less_real @ zero_zero_real @ Y )
=> ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) )
= $true ),
inference(copy,[status(thm)],[326]) ).
thf(653,plain,
( ( ! [M: nat] :
( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
= M ) )
= $true ),
inference(copy,[status(thm)],[325]) ).
thf(654,plain,
( ( ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ ( divide_divide_nat @ ( suc @ M ) @ N ) ) )
= $true ),
inference(copy,[status(thm)],[324]) ).
thf(655,plain,
( ( ! [X: real,Y: real] :
( ( X != Y )
=> ( ~ ( ord_less_real @ X @ Y )
=> ( ord_less_real @ Y @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[323]) ).
thf(656,plain,
( ( ~ ( ord_less_real @ ( ring_1_of_int_real @ na ) @ ( power_power_real @ ( ring_1_of_int_real @ ya ) @ ( suc @ pm ) ) ) )
= $true ),
inference(copy,[status(thm)],[489]) ).
thf(657,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( SX0
!= ( suc @ SX1 ) )
| ( nthRoo1352626670d_root @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[620]) ).
thf(658,plain,
( ( ! [SX0: real,SX1: real,SX2: real] :
( ~ ( ord_less_real @ SX0 @ SX1 )
| ~ ( ord_less_real @ zero_zero_real @ SX2 )
| ( ord_less_real @ ( divide_divide_real @ SX0 @ SX2 ) @ ( divide_divide_real @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[643]) ).
thf(659,plain,
( ( ! [SX0: real,SX1: real] :
( ~ ( ord_less_eq_real @ SX0 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SX1 )
| ( ord_less_eq_real @ ( divide_divide_real @ SX0 @ SX1 ) @ zero_zero_real ) ) )
= $true ),
inference(unfold_def,[status(thm)],[652]) ).
thf(660,plain,
( ( ! [SX0: nat] :
( ( ord_less_nat @ zero_zero_nat @ SX0 )
= ( ~ ! [SX1: nat] :
( SX0
!= ( suc @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[594]) ).
thf(661,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ ( suc @ SX0 ) @ SX1 )
| ( ord_less_nat @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[531]) ).
thf(662,plain,
( ( ! [SX0: nat,SX1: nat > $o] :
( ( ~ ! [SX2: nat] :
~ ~ ( ~ ( ord_less_nat @ SX2 @ ( suc @ SX0 ) )
| ~ ( SX1 @ SX2 ) ) )
= ( ( SX1 @ zero_zero_nat )
| ~ ! [SX2: nat] :
~ ~ ( ~ ( ord_less_nat @ SX2 @ SX0 )
| ~ ( SX1 @ ( suc @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[595]) ).
thf(663,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_nat @ SX0 @ ( suc @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[527]) ).
thf(664,plain,
( ( ! [SX0: real,SX1: nat,SX2: real] :
( ~ ( ord_less_real @ ( power_power_real @ SX0 @ SX1 ) @ ( power_power_real @ SX2 @ SX1 ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ SX2 )
| ( ord_less_real @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[598]) ).
thf(665,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ( ( power_power_nat @ SX0 @ ( suc @ SX1 ) )
!= ( power_power_nat @ SX2 @ ( suc @ SX1 ) ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SX0 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SX2 )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[601]) ).
thf(666,plain,
( ( ! [SX0: real,SX1: real,SX2: real] :
( ( ord_less_eq_real @ ( divide_divide_real @ SX0 @ SX1 ) @ ( divide_divide_real @ SX2 @ SX1 ) )
= ( ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SX1 )
| ( ord_less_eq_real @ SX0 @ SX2 ) )
| ~ ( ~ ( ord_less_real @ SX1 @ zero_zero_real )
| ( ord_less_eq_real @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[648]) ).
thf(667,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat > $o] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( SX2 @ SX0 )
| ~ ! [SX3: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX3 )
| ~ ( SX2 @ SX3 )
| ( SX2 @ ( suc @ SX3 ) ) )
| ( SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[611]) ).
thf(668,plain,
( ( ! [SX0: nat > $o,SX1: nat] :
( ~ ! [SX2: nat] :
( ~ ! [SX3: nat] :
( ~ ( ord_less_eq_nat @ ( suc @ SX3 ) @ SX2 )
| ( SX0 @ SX3 ) )
| ( SX0 @ SX2 ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[612]) ).
thf(669,plain,
( ( ! [SX0: real,SX1: real,SX2: real,SX3: real] :
( ~ ( ord_less_eq_real @ zero_zero_real @ SX0 )
| ~ ( ord_less_real @ SX0 @ SX1 )
| ~ ( ord_less_real @ zero_zero_real @ SX2 )
| ~ ( ord_less_eq_real @ SX2 @ SX3 )
| ( ord_less_real @ ( divide_divide_real @ SX0 @ SX3 ) @ ( divide_divide_real @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[646]) ).
thf(670,plain,
( ( ! [SX0: nat > int,SX1: nat,SX2: nat] :
( ~ ! [SX3: nat] : ( ord_less_eq_int @ ( SX0 @ SX3 ) @ ( SX0 @ ( suc @ SX3 ) ) )
| ~ ( ord_less_eq_nat @ SX1 @ SX2 )
| ( ord_less_eq_int @ ( SX0 @ SX1 ) @ ( SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[572]) ).
thf(671,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ ( suc @ SX1 ) )
| ~ ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( SX0
= ( suc @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[618]) ).
thf(672,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ord_less_nat @ SX0 @ ( suc @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[632]) ).
thf(673,plain,
( ( ! [SX0: real] :
~ ! [SX1: real] :
~ ( ord_less_real @ SX0 @ SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[633]) ).
thf(674,plain,
( ( ! [SX0: nat > real,SX1: nat,SX2: nat] :
( ~ ! [SX3: nat] : ( ord_less_eq_real @ ( SX0 @ SX3 ) @ ( SX0 @ ( suc @ SX3 ) ) )
| ~ ( ord_less_eq_nat @ SX1 @ SX2 )
| ( ord_less_eq_real @ ( SX0 @ SX1 ) @ ( SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[571]) ).
thf(675,plain,
( ( ! [SX0: real,SX1: nat] :
( ~ ( ( SX0 != zero_zero_real ) )
| ( ( power_power_real @ SX0 @ SX1 )
!= zero_zero_real ) ) )
= $true ),
inference(unfold_def,[status(thm)],[607]) ).
thf(676,plain,
( ( ! [SX0: real,SX1: nat] :
( ( ( power_power_real @ SX0 @ SX1 )
= zero_zero_real )
= ( ~ ( ( SX0 != zero_zero_real )
| ~ ( ord_less_nat @ zero_zero_nat @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[546]) ).
thf(677,plain,
( ( ! [SX0: nat,SX1: real] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ~ ( ord_less_real @ zero_zero_real @ SX1 )
| ~ ! [SX2: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SX2 )
| ( ( power_power_real @ SX2 @ SX0 )
!= SX1 ) )
| ~ ! [SX3: real] :
( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SX3 )
| ( ( power_power_real @ SX3 @ SX0 )
!= SX1 ) )
| ( SX3 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[606]) ).
thf(678,plain,
( ( ! [SX0: real,SX1: nat,SX2: real] :
( ~ ( ord_less_eq_real @ ( power_power_real @ SX0 @ ( suc @ SX1 ) ) @ ( power_power_real @ SX2 @ ( suc @ SX1 ) ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ SX2 )
| ( ord_less_eq_real @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[602]) ).
thf(679,plain,
( ( ! [SX0: nat > nat,SX1: nat,SX2: nat] :
( ~ ! [SX3: nat] : ( ord_less_nat @ ( SX0 @ SX3 ) @ ( SX0 @ ( suc @ SX3 ) ) )
| ~ ( ord_less_nat @ SX1 @ SX2 )
| ( ord_less_nat @ ( SX0 @ SX1 ) @ ( SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[541]) ).
thf(680,plain,
( ( ! [SX0: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ( ( power_power_real @ zero_zero_real @ SX0 )
= zero_zero_real ) ) )
= $true ),
inference(unfold_def,[status(thm)],[608]) ).
thf(681,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ ( suc @ SX0 ) @ ( suc @ SX1 ) )
| ( ord_less_nat @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[520]) ).
thf(682,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ ( suc @ SX1 ) )
| ~ ~ ( ord_less_nat @ SX0 @ SX1 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[528]) ).
thf(683,plain,
( ( ! [SX0: nat > int,SX1: nat,SX2: nat] :
( ~ ! [SX3: nat] : ( ord_less_int @ ( SX0 @ SX3 ) @ ( SX0 @ ( suc @ SX3 ) ) )
| ( ( ord_less_int @ ( SX0 @ SX1 ) @ ( SX0 @ SX2 ) )
= ( ord_less_nat @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[537]) ).
thf(684,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ~ ( ( SX1
!= ( suc @ SX0 ) ) )
| ~ ! [SX2: nat] :
( ~ ( ord_less_nat @ SX0 @ SX2 )
| ( SX1
!= ( suc @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[532]) ).
thf(685,plain,
( ( ! [SX0: nat > $o,SX1: nat] :
( ~ ( SX0 @ zero_zero_nat )
| ~ ! [SX2: nat] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( suc @ SX2 ) ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[589]) ).
thf(686,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_int @ zero_zero_int @ SX0 )
| ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[533]) ).
thf(687,plain,
( ( ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ SX0 @ zero_zero_real )
| ~ ( ord_less_real @ SX1 @ zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[636]) ).
thf(688,plain,
( ( ! [SX0: nat > nat,SX1: nat,SX2: nat] :
( ~ ! [SX3: nat] : ( ord_less_nat @ ( SX0 @ SX3 ) @ ( SX0 @ ( suc @ SX3 ) ) )
| ( ( ord_less_nat @ ( SX0 @ SX1 ) @ ( SX0 @ SX2 ) )
= ( ord_less_nat @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[538]) ).
thf(689,plain,
( ( ! [SX0: real,SX1: nat] :
( ~ ( ord_less_real @ zero_zero_real @ SX0 )
| ~ ! [SX2: real] :
~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SX2 )
| ( ( power_power_real @ SX2 @ ( suc @ SX1 ) )
!= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[547]) ).
thf(690,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_nat @ ( suc @ SX0 ) @ ( suc @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[505]) ).
thf(691,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ ( suc @ SX0 ) @ SX1 )
| ~ ! [SX2: nat] :
( ~ ( ord_less_nat @ SX0 @ SX2 )
| ( SX1
!= ( suc @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[530]) ).
thf(692,plain,
( ( ! [SX0: real,SX1: nat,SX2: real] :
( ( ( power_power_real @ SX0 @ ( suc @ SX1 ) )
!= ( power_power_real @ SX2 @ ( suc @ SX1 ) ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ SX0 )
| ~ ( ord_less_eq_real @ zero_zero_real @ SX2 )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[599]) ).
thf(693,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat > $o] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ~ ! [SX3: nat] :
( ( SX1
!= ( suc @ SX3 ) )
| ( SX2 @ SX3 ) )
| ~ ! [SX3: nat] :
( ~ ( ord_less_nat @ SX3 @ SX1 )
| ~ ( SX2 @ ( suc @ SX3 ) )
| ( SX2 @ SX3 ) )
| ( SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[517]) ).
thf(694,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat > nat > $o] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ~ ! [SX3: nat] : ( SX2 @ SX3 @ ( suc @ SX3 ) )
| ~ ! [SX3: nat,SX4: nat,SX5: nat] :
( ~ ( ord_less_nat @ SX3 @ SX4 )
| ~ ( ord_less_nat @ SX4 @ SX5 )
| ~ ( SX2 @ SX3 @ SX4 )
| ~ ( SX2 @ SX4 @ SX5 )
| ( SX2 @ SX3 @ SX5 ) )
| ( SX2 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[518]) ).
thf(695,plain,
( ( ! [SX0: nat] :
( ~ ( ( SX0 != zero_zero_nat ) )
| ~ ! [SX1: nat] :
( SX0
!= ( suc @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[590]) ).
thf(696,plain,
( ( ! [SX0: nat > nat,SX1: nat,SX2: nat] :
( ~ ! [SX3: nat] : ( ord_less_eq_nat @ ( SX0 @ SX3 ) @ ( SX0 @ ( suc @ SX3 ) ) )
| ~ ( ord_less_eq_nat @ SX1 @ SX2 )
| ( ord_less_eq_nat @ ( SX0 @ SX1 ) @ ( SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[573]) ).
thf(697,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat > $o] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( SX2 @ SX0 )
| ~ ! [SX3: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX3 )
| ~ ( ord_less_nat @ SX3 @ SX1 )
| ~ ( SX2 @ SX3 )
| ( SX2 @ ( suc @ SX3 ) ) )
| ( SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[626]) ).
thf(698,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ ( suc @ zero_zero_nat ) @ SX0 )
| ( ord_less_nat @ SX1 @ ( power_power_nat @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[577]) ).
thf(699,plain,
( ( ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ SX0 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SX1 )
| ( ord_less_real @ ( divide_divide_real @ SX0 @ SX1 ) @ zero_zero_real ) ) )
= $true ),
inference(unfold_def,[status(thm)],[637]) ).
thf(700,plain,
( ( ! [SX0: nat > nat > $o,SX1: nat,SX2: nat] :
( ~ ! [SX3: nat] : ( SX0 @ SX3 @ zero_zero_nat )
| ~ ! [SX3: nat] : ( SX0 @ zero_zero_nat @ ( suc @ SX3 ) )
| ~ ! [SX3: nat,SX4: nat] :
( ~ ( SX0 @ SX3 @ SX4 )
| ( SX0 @ ( suc @ SX3 ) @ ( suc @ SX4 ) ) )
| ( SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[583]) ).
thf(701,plain,
( ( ! [SX0: nat > int,SX1: nat,SX2: nat] :
( ~ ! [SX3: nat] : ( ord_less_int @ ( SX0 @ SX3 ) @ ( SX0 @ ( suc @ SX3 ) ) )
| ~ ( ord_less_nat @ SX1 @ SX2 )
| ( ord_less_int @ ( SX0 @ SX1 ) @ ( SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[540]) ).
thf(702,plain,
( ( ! [SX0: nat,SX1: nat > $o] :
( ( ! [SX2: nat] :
( ~ ( ord_less_nat @ SX2 @ ( suc @ SX0 ) )
| ( SX1 @ SX2 ) ) )
= ( ~ ( ~ ( SX1 @ zero_zero_nat )
| ~ ! [SX2: nat] :
( ~ ( ord_less_nat @ SX2 @ SX0 )
| ( SX1 @ ( suc @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[593]) ).
thf(703,plain,
( ( ! [SX0: nat > real,SX1: nat,SX2: nat] :
( ~ ! [SX3: nat] : ( ord_less_real @ ( SX0 @ SX3 ) @ ( SX0 @ ( suc @ SX3 ) ) )
| ~ ( ord_less_nat @ SX1 @ SX2 )
| ( ord_less_real @ ( SX0 @ SX1 ) @ ( SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[539]) ).
thf(704,plain,
( ( ! [SX0: int,SX1: nat,SX2: int] :
( ( ( power_power_int @ SX0 @ ( suc @ SX1 ) )
!= ( power_power_int @ SX2 @ ( suc @ SX1 ) ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ SX0 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SX2 )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[600]) ).
thf(705,plain,
( ( na != zero_zero_int )
= $true ),
inference(unfold_def,[status(thm)],[490]) ).
thf(706,plain,
( ( ! [SX0: nat] :
( zero_zero_nat
!= ( suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[587]) ).
thf(707,plain,
( ( ! [SX0: nat > int,SX1: nat,SX2: nat] :
( ~ ! [SX3: nat] : ( ord_less_eq_int @ ( SX0 @ ( suc @ SX3 ) ) @ ( SX0 @ SX3 ) )
| ~ ( ord_less_eq_nat @ SX1 @ SX2 )
| ( ord_less_eq_int @ ( SX0 @ SX2 ) @ ( SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[569]) ).
thf(708,plain,
( ( ! [SX0: real,SX1: real] :
( ~ ( ord_less_eq_real @ zero_zero_real @ SX0 )
| ~ ( ord_less_real @ zero_zero_real @ SX1 )
| ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[650]) ).
thf(709,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ~ ( ord_less_nat @ SX1 @ SX2 )
| ( ord_less_nat @ ( suc @ SX0 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[519]) ).
thf(710,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ ( suc @ SX0 ) @ SX1 )
| ( ord_less_nat @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[628]) ).
thf(711,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( SX0
!= ( suc @ SX1 ) )
| ( SX0 != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[581]) ).
thf(712,plain,
( ( ! [SX0: nat] :
( ( suc @ SX0 )
!= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[579]) ).
thf(713,plain,
( ( ! [SX0: real,SX1: nat] :
( ~ ( ord_less_real @ zero_zero_real @ SX0 )
| ( ord_less_real @ zero_zero_real @ ( power_power_real @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[548]) ).
thf(714,plain,
( ( ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ zero_zero_real @ SX0 )
| ~ ( ord_less_real @ zero_zero_real @ SX1 )
| ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[639]) ).
thf(715,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ ( power_power_nat @ SX0 @ ( suc @ SX1 ) ) @ ( power_power_nat @ SX2 @ ( suc @ SX1 ) ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SX2 )
| ( ord_less_eq_nat @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[604]) ).
thf(716,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_eq_nat @ ( suc @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[624]) ).
thf(717,plain,
( ( ! [SX0: int,SX1: nat,SX2: int] :
( ~ ( ord_less_eq_int @ ( power_power_int @ SX0 @ ( suc @ SX1 ) ) @ ( power_power_int @ SX2 @ ( suc @ SX1 ) ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ SX2 )
| ( ord_less_eq_int @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[603]) ).
thf(718,plain,
( ( ! [SX0: real,SX1: real,SX2: nat] :
( ~ ( ord_less_eq_real @ SX0 @ SX1 )
| ~ ( ord_less_eq_real @ zero_zero_real @ SX0 )
| ( ord_less_eq_real @ ( power_power_real @ SX0 @ SX2 ) @ ( power_power_real @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[597]) ).
thf(719,plain,
( ( ! [SX0: real,SX1: real,SX2: real] :
( ( ord_less_real @ ( divide_divide_real @ SX0 @ SX1 ) @ ( divide_divide_real @ SX2 @ SX1 ) )
= ( ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SX1 )
| ( ord_less_real @ SX0 @ SX2 ) )
| ~ ( ~ ( ord_less_real @ SX1 @ zero_zero_real )
| ( ord_less_real @ SX2 @ SX0 ) ) )
| ~ ( ( SX1 != zero_zero_real ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[641]) ).
thf(720,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ( ord_less_nat @ SX0 @ ( suc @ SX1 ) )
= ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[516]) ).
thf(721,plain,
( ( ! [SX0: nat] :
( zero_zero_nat
!= ( suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[586]) ).
thf(722,plain,
( ( ! [SX0: nat > real,SX1: nat,SX2: nat] :
( ~ ! [SX3: nat] : ( ord_less_real @ ( SX0 @ SX3 ) @ ( SX0 @ ( suc @ SX3 ) ) )
| ( ( ord_less_real @ ( SX0 @ SX1 ) @ ( SX0 @ SX2 ) )
= ( ord_less_nat @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[536]) ).
thf(723,plain,
( ( ! [SX0: nat > $o,SX1: nat] :
( ~ ( SX0 @ SX1 )
| ~ ! [SX2: nat] :
( ~ ( SX0 @ ( suc @ SX2 ) )
| ( SX0 @ SX2 ) )
| ( SX0 @ zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[584]) ).
thf(724,plain,
( ( ! [SX0: real] :
~ ! [SX1: int] :
~ ( ord_less_eq_real @ SX0 @ ( ring_1_of_int_real @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[575]) ).
thf(725,plain,
( ( ! [SX0: nat > $o,SX1: nat] :
( ~ ( SX0 @ zero_zero_nat )
| ~ ! [SX2: nat] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( suc @ SX2 ) ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[582]) ).
thf(726,plain,
( ( ! [SX0: nat,SX1: nat > $o] :
( ( ~ ! [SX2: nat] :
~ ~ ( ~ ( ord_less_nat @ SX2 @ ( suc @ SX0 ) )
| ~ ( SX1 @ SX2 ) ) )
= ( ( SX1 @ SX0 )
| ~ ! [SX2: nat] :
~ ~ ( ~ ( ord_less_nat @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[526]) ).
thf(727,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ ( suc @ SX0 ) @ SX1 )
| ~ ! [SX2: nat] :
( SX1
!= ( suc @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[616]) ).
thf(728,plain,
( ( ! [SX0: real,SX1: real] :
( ~ ( ( SX0 != SX1 ) )
| ~ ~ ( ord_less_real @ SX0 @ SX1 )
| ( ord_less_real @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[655]) ).
thf(729,plain,
( ( ! [SX0: nat > $o] :
( ~ ~ ( SX0 @ zero_zero_nat )
| ~ ~ ! [SX1: nat] :
~ ( SX0 @ SX1 )
| ~ ! [SX1: nat] :
~ ~ ( ~ ~ ( SX0 @ SX1 )
| ~ ( SX0 @ ( suc @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[576]) ).
thf(730,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( ord_less_nat @ SX1 @ ( suc @ SX0 ) )
= ( SX1 = SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[629]) ).
thf(731,plain,
( ( ! [SX0: real,SX1: real] :
( ~ ( ord_less_real @ zero_zero_real @ SX0 )
| ~ ( ord_less_real @ SX1 @ zero_zero_real )
| ( ord_less_real @ ( divide_divide_real @ SX0 @ SX1 ) @ zero_zero_real ) ) )
= $true ),
inference(unfold_def,[status(thm)],[638]) ).
thf(732,plain,
( ( ! [SX0: real,SX1: real,SX2: real] :
( ~ ( ord_less_real @ SX0 @ SX1 )
| ~ ( ord_less_real @ SX2 @ zero_zero_real )
| ( ord_less_real @ ( divide_divide_real @ SX1 @ SX2 ) @ ( divide_divide_real @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[644]) ).
thf(733,plain,
( ( pm != zero_zero_nat )
= $true ),
inference(unfold_def,[status(thm)],[553]) ).
thf(734,plain,
( ( ya != zero_zero_int )
= $true ),
inference(unfold_def,[status(thm)],[502]) ).
thf(735,plain,
( ( ! [SX0: nat,SX1: nat > $o] :
( ( ! [SX2: nat] :
( ~ ( ord_less_nat @ SX2 @ ( suc @ SX0 ) )
| ( SX1 @ SX2 ) ) )
= ( ~ ( ~ ( SX1 @ SX0 )
| ~ ! [SX2: nat] :
( ~ ( ord_less_nat @ SX2 @ SX0 )
| ( SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[523]) ).
thf(736,plain,
( ( ! [SX0: nat > real,SX1: nat,SX2: nat] :
( ~ ! [SX3: nat] : ( ord_less_eq_real @ ( SX0 @ ( suc @ SX3 ) ) @ ( SX0 @ SX3 ) )
| ~ ( ord_less_eq_nat @ SX1 @ SX2 )
| ( ord_less_eq_real @ ( SX0 @ SX2 ) @ ( SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[568]) ).
thf(737,plain,
( ( ! [SX0: nat > nat,SX1: nat,SX2: nat] :
( ~ ! [SX3: nat] : ( ord_less_eq_nat @ ( SX0 @ ( suc @ SX3 ) ) @ ( SX0 @ SX3 ) )
| ~ ( ord_less_eq_nat @ SX1 @ SX2 )
| ( ord_less_eq_nat @ ( SX0 @ SX2 ) @ ( SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[570]) ).
thf(738,plain,
( ( ! [SX0: real,SX1: real,SX2: real,SX3: real] :
( ~ ( ord_less_real @ zero_zero_real @ SX0 )
| ~ ( ord_less_eq_real @ SX0 @ SX1 )
| ~ ( ord_less_real @ zero_zero_real @ SX2 )
| ~ ( ord_less_real @ SX2 @ SX3 )
| ( ord_less_real @ ( divide_divide_real @ SX0 @ SX3 ) @ ( divide_divide_real @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[647]) ).
thf(739,plain,
( ( ! [SX0: real,SX1: real] :
( ~ ( ord_less_eq_real @ zero_zero_real @ SX0 )
| ~ ( ord_less_real @ SX1 @ zero_zero_real )
| ( ord_less_eq_real @ ( divide_divide_real @ SX0 @ SX1 ) @ zero_zero_real ) ) )
= $true ),
inference(unfold_def,[status(thm)],[649]) ).
thf(740,plain,
( ( ! [SX0: nat > $o,SX1: nat] :
( ~ ( SX0 @ SX1 )
| ~ ~ ( SX0 @ zero_zero_nat )
| ~ ! [SX2: nat] :
~ ~ ( ~ ~ ( ~ ( ord_less_nat @ SX2 @ SX1 )
| ~ ! [SX3: nat] :
( ~ ( ord_less_eq_nat @ SX3 @ SX2 )
| ~ ( SX0 @ SX3 ) ) )
| ~ ( SX0 @ ( suc @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[635]) ).
thf(741,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( ord_less_nat @ ( suc @ SX0 ) @ SX1 )
= ( ~ ! [SX2: nat] :
~ ~ ( ( SX1
!= ( suc @ SX2 ) )
| ~ ( ord_less_nat @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[522]) ).
thf(742,plain,
( ( ! [SX0: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ~ ! [SX1: nat] :
( SX0
!= ( suc @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[592]) ).
thf(743,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( ( suc @ SX0 )
!= ( suc @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[535]) ).
thf(744,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ~ ( ( ( suc @ SX0 )
!= SX1 ) )
| ( ord_less_nat @ ( suc @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[529]) ).
thf(745,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat > nat > $o] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ! [SX3: nat] : ( SX2 @ SX3 @ SX3 )
| ~ ! [SX3: nat,SX4: nat,SX5: nat] :
( ~ ( SX2 @ SX3 @ SX4 )
| ~ ( SX2 @ SX4 @ SX5 )
| ( SX2 @ SX3 @ SX5 ) )
| ~ ! [SX3: nat] : ( SX2 @ SX3 @ ( suc @ SX3 ) )
| ( SX2 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[610]) ).
thf(746,plain,
( ( ! [SX0: real,SX1: real] :
( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SX0 @ SX1 ) )
= ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SX0 )
| ~ ( ord_less_real @ zero_zero_real @ SX1 ) )
| ~ ( ~ ( ord_less_real @ SX0 @ zero_zero_real )
| ~ ( ord_less_real @ SX1 @ zero_zero_real ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[642]) ).
thf(747,plain,
( ( ! [SX0: nat] :
( SX0
!= ( suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[534]) ).
thf(748,plain,
( ( ! [SX0: nat] :
( zero_zero_nat
!= ( suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[578]) ).
thf(749,plain,
( ( ! [SX0: real] :
~ ! [SX1: int] :
~ ( ord_less_real @ SX0 @ ( ring_1_of_int_real @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[551]) ).
thf(750,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ SX0 )
| ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[623]) ).
thf(751,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( ord_less_nat @ SX0 @ ( suc @ SX1 ) )
= ( ( SX0 = zero_zero_nat )
| ~ ! [SX2: nat] :
~ ~ ( ( SX0
!= ( suc @ SX2 ) )
| ~ ( ord_less_nat @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[591]) ).
thf(752,plain,
( ( ! [SX0: nat,SX1: real] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ~ ( ord_less_real @ zero_zero_real @ SX1 )
| ~ ! [SX2: real] :
~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SX2 )
| ( ( power_power_real @ SX2 @ SX0 )
!= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[605]) ).
thf(753,plain,
( ( ! [SX0: real,SX1: real] :
( ~ ( ord_less_eq_real @ SX0 @ zero_zero_real )
| ~ ( ord_less_real @ SX1 @ zero_zero_real )
| ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[651]) ).
thf(754,plain,
( ( ! [SX0: real,SX1: nat] :
( ~ ( ord_less_eq_real @ zero_zero_real @ SX0 )
| ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[596]) ).
thf(755,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ord_less_eq_nat @ SX0 @ ( suc @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[617]) ).
thf(756,plain,
( ( ! [SX0: nat] :
( zero_zero_nat
!= ( suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[580]) ).
thf(757,plain,
( ( ! [SX0: real,SX1: real,SX2: real,SX3: real] :
( ~ ( ord_less_eq_real @ zero_zero_real @ SX0 )
| ~ ( ord_less_eq_real @ SX1 @ SX0 )
| ~ ( ord_less_real @ zero_zero_real @ SX2 )
| ~ ( ord_less_eq_real @ SX2 @ SX3 )
| ( ord_less_eq_real @ ( divide_divide_real @ SX1 @ SX3 ) @ ( divide_divide_real @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[645]) ).
thf(758,plain,
( ( ! [SX0: real] :
~ ! [SX1: int] :
~ ( ord_less_real @ ( ring_1_of_int_real @ SX1 ) @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[550]) ).
thf(759,plain,
( ( ! [SX0: real,SX1: real] :
( ( ord_less_real @ ( divide_divide_real @ SX0 @ SX1 ) @ zero_zero_real )
= ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SX0 )
| ~ ( ord_less_real @ SX1 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SX0 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[640]) ).
thf(760,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat > $o] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( SX2 @ SX1 )
| ~ ! [SX3: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX3 )
| ~ ( ord_less_nat @ SX3 @ SX1 )
| ~ ( SX2 @ ( suc @ SX3 ) )
| ( SX2 @ SX3 ) )
| ( SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[627]) ).
thf(761,plain,
( ( ! [SX0: real] :
~ ! [SX1: real] :
~ ( ord_less_real @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[634]) ).
thf(762,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ ( suc @ SX0 ) @ SX1 )
| ( ord_less_eq_nat @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[619]) ).
thf(763,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ~ ( ord_less_nat @ SX0 @ SX1 )
| ~ ( ord_less_nat @ SX0 @ ( suc @ SX1 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[521]) ).
thf(764,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( nthRoo1352626670d_root @ SX0 @ SX1 )
| ( SX0
= ( suc @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[622]) ).
thf(765,plain,
( ( ! [SX0: nat] :
( ( suc @ SX0 )
!= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[585]) ).
thf(766,plain,
( ( ! [SX0: nat] :
( ~ ( ( SX0 != zero_zero_nat ) )
| ~ ! [SX1: nat] :
( SX0
!= ( suc @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[588]) ).
thf(767,plain,
! [SV1: int] :
( ( ! [SY370: nat,SY371: int] :
( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ SV1 ) @ SY370 ) @ ( ring_1_of_int_real @ SY371 ) )
= ( ord_less_int @ ( power_power_int @ SV1 @ SY370 ) @ SY371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(768,plain,
! [SV2: int] :
( ( ! [SY372: int,SY373: nat] :
( ( ord_less_real @ ( ring_1_of_int_real @ SV2 ) @ ( power_power_real @ ( ring_1_of_int_real @ SY372 ) @ SY373 ) )
= ( ord_less_int @ SV2 @ ( power_power_int @ SY372 @ SY373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(769,plain,
! [SV3: int] :
( ( ! [SY374: nat] :
( ( ring_1_of_int_real @ ( power_power_int @ SV3 @ SY374 ) )
= ( power_power_real @ ( ring_1_of_int_real @ SV3 ) @ SY374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(770,plain,
! [SV4: int] :
( ( ! [SY375: nat,SY376: int] :
( ( ( power_power_real @ ( ring_1_of_int_real @ SV4 ) @ SY375 )
= ( ring_1_of_int_real @ SY376 ) )
= ( ( power_power_int @ SV4 @ SY375 )
= SY376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(771,plain,
! [SV5: int] :
( ( ! [SY377: int,SY378: nat] :
( ( ( ring_1_of_int_real @ SV5 )
= ( power_power_real @ ( ring_1_of_int_real @ SY377 ) @ SY378 ) )
= ( SV5
= ( power_power_int @ SY377 @ SY378 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(772,plain,
! [SV6: int] :
( ( ! [SY379: int] :
( ( ord_less_real @ ( ring_1_of_int_real @ SV6 ) @ ( ring_1_of_int_real @ SY379 ) )
= ( ord_less_int @ SV6 @ SY379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(773,plain,
! [SV7: int] :
( ( ! [SY380: int] :
( ( ( ring_1_of_int_real @ SV7 )
= ( ring_1_of_int_real @ SY380 ) )
= ( SV7 = SY380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(774,plain,
! [SV8: nat] :
( ( ! [SY381: nat] :
( ( ( suc @ SV8 )
= ( suc @ SY381 ) )
= ( SV8 = SY381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(775,plain,
! [SV9: nat] :
( ( ! [SY382: nat] :
( ( ( suc @ SV9 )
= ( suc @ SY382 ) )
= ( SV9 = SY382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(776,plain,
( ( ( ord_less_int @ zero_zero_int @ ya )
= $true )
| ( ( ya = zero_zero_int )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[503]) ).
thf(777,plain,
! [SV10: nat] :
( ( ! [SY383: nat] :
( ( ord_less_nat @ ( suc @ SV10 ) @ ( suc @ SY383 ) )
= ( ord_less_nat @ SV10 @ SY383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(778,plain,
! [SV11: nat] :
( ( ord_less_nat @ SV11 @ ( suc @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(779,plain,
( ( ( ord_less_int @ ya @ zero_zero_int )
| ( ord_less_int @ na @ zero_zero_int ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(780,plain,
( ( ( ord_less_int @ ya @ zero_zero_int )
| ( ord_less_int @ na @ zero_zero_int ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(781,plain,
! [SV12: int] :
( ( ( zero_zero_real
= ( ring_1_of_int_real @ SV12 ) )
= ( SV12 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(782,plain,
! [SV13: int] :
( ( ( ( ring_1_of_int_real @ SV13 )
= zero_zero_real )
= ( SV13 = zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(783,plain,
! [SV14: int] :
( ( ( ord_less_real @ ( ring_1_of_int_real @ SV14 ) @ zero_zero_real )
= ( ord_less_int @ SV14 @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(784,plain,
! [SV15: int] :
( ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ SV15 ) )
= ( ord_less_int @ zero_zero_int @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(785,plain,
! [SV16: nat] :
( ( ! [SY384: nat] :
( ( ~ ( ord_less_nat @ SV16 @ SY384 ) )
= ( ord_less_nat @ SY384 @ ( suc @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(786,plain,
! [SV17: nat] :
( ( ! [SY385: nat] :
( ( ord_less_nat @ SV17 @ ( suc @ SY385 ) )
= ( ( ord_less_nat @ SV17 @ SY385 )
| ( SV17 = SY385 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(787,plain,
! [SV18: nat] :
( ( ( power_power_real @ zero_zero_real @ ( suc @ SV18 ) )
= zero_zero_real )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(788,plain,
! [SV19: nat] :
( ( ( power_power_int @ zero_zero_int @ ( suc @ SV19 ) )
= zero_zero_int )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(789,plain,
! [SV20: nat] :
( ( ( power_power_nat @ zero_zero_nat @ ( suc @ SV20 ) )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(790,plain,
! [SV21: nat] :
( ( ! [SY386: nat] :
( ( ( power_power_nat @ SV21 @ SY386 )
= ( suc @ zero_zero_nat ) )
= ( ( SY386 = zero_zero_nat )
| ( SV21
= ( suc @ zero_zero_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(791,plain,
! [SV22: nat] :
( ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ SV22 )
= ( suc @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(792,plain,
! [SV23: real] :
( ( ( power_power_real @ SV23 @ ( suc @ zero_zero_nat ) )
= SV23 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(793,plain,
! [SV24: int] :
( ( ( power_power_int @ SV24 @ ( suc @ zero_zero_nat ) )
= SV24 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(794,plain,
! [SV25: nat] :
( ( ( power_power_nat @ SV25 @ ( suc @ zero_zero_nat ) )
= SV25 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(795,plain,
! [SV26: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( suc @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(796,plain,
! [SV27: nat] :
( ( ( ord_less_nat @ SV27 @ ( suc @ zero_zero_nat ) )
= ( SV27 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(797,plain,
! [SV28: int] :
( ( ! [SY387: int] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV28 ) @ ( ring_1_of_int_real @ SY387 ) )
= ( ord_less_eq_int @ SV28 @ SY387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(798,plain,
! [SV29: int] :
( ( ! [SY388: nat,SY389: int] :
( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ SV29 ) @ SY388 ) @ ( ring_1_of_int_real @ SY389 ) )
= ( ord_less_eq_int @ ( power_power_int @ SV29 @ SY388 ) @ SY389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(799,plain,
! [SV30: int] :
( ( ! [SY390: int,SY391: nat] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV30 ) @ ( power_power_real @ ( ring_1_of_int_real @ SY390 ) @ SY391 ) )
= ( ord_less_eq_int @ SV30 @ ( power_power_int @ SY390 @ SY391 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(800,plain,
! [SV31: real] :
( ( ! [SY392: real,SY393: nat] :
( ( power_power_real @ ( divide_divide_real @ SV31 @ SY392 ) @ SY393 )
= ( divide_divide_real @ ( power_power_real @ SV31 @ SY393 ) @ ( power_power_real @ SY392 @ SY393 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(801,plain,
! [SV32: nat] :
( ( ! [SY394: nat] :
( ( ord_less_eq_nat @ ( suc @ SV32 ) @ ( suc @ SY394 ) )
= ( ord_less_eq_nat @ SV32 @ SY394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(802,plain,
! [SV33: nat] :
( ( ! [SY395: nat] :
( ( ~ ( ord_less_eq_nat @ SV33 @ SY395 ) )
= ( ord_less_eq_nat @ ( suc @ SY395 ) @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(803,plain,
! [SV34: nat] :
( ( ~ ( ord_less_eq_nat @ ( suc @ SV34 ) @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(804,plain,
! [SV35: nat] :
( ( ! [SY396: nat] :
( ( ord_less_eq_nat @ SV35 @ ( suc @ SY396 ) )
= ( ( ord_less_eq_nat @ SV35 @ SY396 )
| ( SV35
= ( suc @ SY396 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(805,plain,
( ( ! [SV36: nat] :
( ( nthRoo1352626670d_root @ SV36 )
= ( ^ [SY397: nat] :
( SV36
= ( suc @ SY397 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[621]) ).
thf(806,plain,
( ( nthRoo1352626670d_root
= ( ^ [P3: nat,Pm2: nat] :
( P3
= ( suc @ Pm2 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[621]) ).
thf(807,plain,
! [SV37: nat] :
( ( ! [SY398: nat] :
( ( ord_less_eq_nat @ ( suc @ SV37 ) @ SY398 )
= ( ord_less_nat @ SV37 @ SY398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(808,plain,
! [SV38: nat] :
( ( ! [SY399: nat] :
( ( ord_less_nat @ SV38 @ ( suc @ SY399 ) )
= ( ord_less_eq_nat @ SV38 @ SY399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(809,plain,
( ( ! [SV39: nat] :
( ( ord_less_nat @ SV39 )
= ( ord_less_eq_nat @ ( suc @ SV39 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[631]) ).
thf(810,plain,
( ( ord_less_nat
= ( ^ [N4: nat] : ( ord_less_eq_nat @ ( suc @ N4 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[631]) ).
thf(811,plain,
! [SV40: nat] :
( ( ( divide_divide_nat @ SV40 @ ( suc @ zero_zero_nat ) )
= SV40 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(812,plain,
! [SV41: nat] :
( ( ! [SY400: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ SV41 @ SY400 ) @ ( divide_divide_nat @ ( suc @ SV41 ) @ SY400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(813,plain,
( ( ord_less_real @ ( ring_1_of_int_real @ na ) @ ( power_power_real @ ( ring_1_of_int_real @ ya ) @ ( suc @ pm ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(814,plain,
! [SV42: nat] :
( ( ! [SY401: nat] :
( ( SV42
!= ( suc @ SY401 ) )
| ( nthRoo1352626670d_root @ SV42 @ SY401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(815,plain,
! [SV43: real] :
( ( ! [SY402: real,SY403: real] :
( ~ ( ord_less_real @ SV43 @ SY402 )
| ~ ( ord_less_real @ zero_zero_real @ SY403 )
| ( ord_less_real @ ( divide_divide_real @ SV43 @ SY403 ) @ ( divide_divide_real @ SY402 @ SY403 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(816,plain,
! [SV44: real] :
( ( ! [SY404: real] :
( ~ ( ord_less_eq_real @ SV44 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SY404 )
| ( ord_less_eq_real @ ( divide_divide_real @ SV44 @ SY404 ) @ zero_zero_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(817,plain,
! [SV45: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV45 )
= ( ~ ! [SY405: nat] :
( SV45
!= ( suc @ SY405 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(818,plain,
! [SV46: nat] :
( ( ! [SY406: nat] :
( ~ ( ord_less_nat @ ( suc @ SV46 ) @ SY406 )
| ( ord_less_nat @ SV46 @ SY406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(819,plain,
! [SV47: nat] :
( ( ! [SY407: nat > $o] :
( ( ~ ! [SY408: nat] :
~ ~ ( ~ ( ord_less_nat @ SY408 @ ( suc @ SV47 ) )
| ~ ( SY407 @ SY408 ) ) )
= ( ( SY407 @ zero_zero_nat )
| ~ ! [SY409: nat] :
~ ~ ( ~ ( ord_less_nat @ SY409 @ SV47 )
| ~ ( SY407 @ ( suc @ SY409 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(820,plain,
! [SV48: nat] :
( ( ! [SY410: nat] :
( ~ ( ord_less_nat @ SV48 @ SY410 )
| ( ord_less_nat @ SV48 @ ( suc @ SY410 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(821,plain,
! [SV49: real] :
( ( ! [SY411: nat,SY412: real] :
( ~ ( ord_less_real @ ( power_power_real @ SV49 @ SY411 ) @ ( power_power_real @ SY412 @ SY411 ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ SY412 )
| ( ord_less_real @ SV49 @ SY412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(822,plain,
! [SV50: nat] :
( ( ! [SY413: nat,SY414: nat] :
( ( ( power_power_nat @ SV50 @ ( suc @ SY413 ) )
!= ( power_power_nat @ SY414 @ ( suc @ SY413 ) ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV50 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY414 )
| ( SV50 = SY414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(823,plain,
! [SV51: real] :
( ( ! [SY415: real,SY416: real] :
( ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SY415 ) @ ( divide_divide_real @ SY416 @ SY415 ) )
= ( ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SY415 )
| ( ord_less_eq_real @ SV51 @ SY416 ) )
| ~ ( ~ ( ord_less_real @ SY415 @ zero_zero_real )
| ( ord_less_eq_real @ SY416 @ SV51 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(824,plain,
! [SV52: nat] :
( ( ! [SY417: nat,SY418: nat > $o] :
( ~ ( ord_less_eq_nat @ SV52 @ SY417 )
| ~ ( SY418 @ SV52 )
| ~ ! [SY419: nat] :
( ~ ( ord_less_eq_nat @ SV52 @ SY419 )
| ~ ( SY418 @ SY419 )
| ( SY418 @ ( suc @ SY419 ) ) )
| ( SY418 @ SY417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(825,plain,
! [SV53: nat > $o] :
( ( ! [SY420: nat] :
( ~ ! [SY421: nat] :
( ~ ! [SY422: nat] :
( ~ ( ord_less_eq_nat @ ( suc @ SY422 ) @ SY421 )
| ( SV53 @ SY422 ) )
| ( SV53 @ SY421 ) )
| ( SV53 @ SY420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(826,plain,
! [SV54: real] :
( ( ! [SY423: real,SY424: real,SY425: real] :
( ~ ( ord_less_eq_real @ zero_zero_real @ SV54 )
| ~ ( ord_less_real @ SV54 @ SY423 )
| ~ ( ord_less_real @ zero_zero_real @ SY424 )
| ~ ( ord_less_eq_real @ SY424 @ SY425 )
| ( ord_less_real @ ( divide_divide_real @ SV54 @ SY425 ) @ ( divide_divide_real @ SY423 @ SY424 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(827,plain,
! [SV55: nat > int] :
( ( ! [SY426: nat,SY427: nat] :
( ~ ! [SY428: nat] : ( ord_less_eq_int @ ( SV55 @ SY428 ) @ ( SV55 @ ( suc @ SY428 ) ) )
| ~ ( ord_less_eq_nat @ SY426 @ SY427 )
| ( ord_less_eq_int @ ( SV55 @ SY426 ) @ ( SV55 @ SY427 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(828,plain,
! [SV56: nat] :
( ( ! [SY429: nat] :
( ~ ( ord_less_eq_nat @ SV56 @ ( suc @ SY429 ) )
| ~ ~ ( ord_less_eq_nat @ SV56 @ SY429 )
| ( SV56
= ( suc @ SY429 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(829,plain,
! [SV57: nat] :
( ( ! [SY430: nat] :
( ~ ( ord_less_eq_nat @ SV57 @ SY430 )
| ( ord_less_nat @ SV57 @ ( suc @ SY430 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(830,plain,
! [SV58: real] :
( ( ~ ! [SY431: real] :
~ ( ord_less_real @ SV58 @ SY431 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(831,plain,
! [SV59: nat > real] :
( ( ! [SY432: nat,SY433: nat] :
( ~ ! [SY434: nat] : ( ord_less_eq_real @ ( SV59 @ SY434 ) @ ( SV59 @ ( suc @ SY434 ) ) )
| ~ ( ord_less_eq_nat @ SY432 @ SY433 )
| ( ord_less_eq_real @ ( SV59 @ SY432 ) @ ( SV59 @ SY433 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(832,plain,
! [SV60: real] :
( ( ! [SY435: nat] :
( ~ ( ( SV60 != zero_zero_real ) )
| ( ( power_power_real @ SV60 @ SY435 )
!= zero_zero_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(833,plain,
! [SV61: real] :
( ( ! [SY436: nat] :
( ( ( power_power_real @ SV61 @ SY436 )
= zero_zero_real )
= ( ~ ( ( SV61 != zero_zero_real )
| ~ ( ord_less_nat @ zero_zero_nat @ SY436 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(834,plain,
! [SV62: nat] :
( ( ! [SY437: real] :
( ~ ( ord_less_nat @ zero_zero_nat @ SV62 )
| ~ ( ord_less_real @ zero_zero_real @ SY437 )
| ~ ! [SY438: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY438 )
| ( ( power_power_real @ SY438 @ SV62 )
!= SY437 ) )
| ~ ! [SY439: real] :
( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY439 )
| ( ( power_power_real @ SY439 @ SV62 )
!= SY437 ) )
| ( SY439 = SY438 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(835,plain,
! [SV63: real] :
( ( ! [SY440: nat,SY441: real] :
( ~ ( ord_less_eq_real @ ( power_power_real @ SV63 @ ( suc @ SY440 ) ) @ ( power_power_real @ SY441 @ ( suc @ SY440 ) ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ SY441 )
| ( ord_less_eq_real @ SV63 @ SY441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(836,plain,
! [SV64: nat > nat] :
( ( ! [SY442: nat,SY443: nat] :
( ~ ! [SY444: nat] : ( ord_less_nat @ ( SV64 @ SY444 ) @ ( SV64 @ ( suc @ SY444 ) ) )
| ~ ( ord_less_nat @ SY442 @ SY443 )
| ( ord_less_nat @ ( SV64 @ SY442 ) @ ( SV64 @ SY443 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(837,plain,
! [SV65: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ SV65 )
| ( ( power_power_real @ zero_zero_real @ SV65 )
= zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(838,plain,
! [SV66: nat] :
( ( ! [SY445: nat] :
( ~ ( ord_less_nat @ ( suc @ SV66 ) @ ( suc @ SY445 ) )
| ( ord_less_nat @ SV66 @ SY445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(839,plain,
! [SV67: nat] :
( ( ! [SY446: nat] :
( ~ ( ord_less_nat @ SV67 @ ( suc @ SY446 ) )
| ~ ~ ( ord_less_nat @ SV67 @ SY446 )
| ( SV67 = SY446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(840,plain,
! [SV68: nat > int] :
( ( ! [SY447: nat,SY448: nat] :
( ~ ! [SY449: nat] : ( ord_less_int @ ( SV68 @ SY449 ) @ ( SV68 @ ( suc @ SY449 ) ) )
| ( ( ord_less_int @ ( SV68 @ SY447 ) @ ( SV68 @ SY448 ) )
= ( ord_less_nat @ SY447 @ SY448 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(841,plain,
! [SV69: nat] :
( ( ! [SY450: nat] :
( ~ ( ord_less_nat @ SV69 @ SY450 )
| ~ ( ( SY450
!= ( suc @ SV69 ) ) )
| ~ ! [SY451: nat] :
( ~ ( ord_less_nat @ SV69 @ SY451 )
| ( SY450
!= ( suc @ SY451 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(842,plain,
! [SV70: nat > $o] :
( ( ! [SY452: nat] :
( ~ ( SV70 @ zero_zero_nat )
| ~ ! [SY453: nat] :
( ~ ( SV70 @ SY453 )
| ( SV70 @ ( suc @ SY453 ) ) )
| ( SV70 @ SY452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(843,plain,
! [SV71: int] :
( ( ~ ( ord_less_int @ zero_zero_int @ SV71 )
| ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(844,plain,
! [SV72: real] :
( ( ! [SY454: real] :
( ~ ( ord_less_real @ SV72 @ zero_zero_real )
| ~ ( ord_less_real @ SY454 @ zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV72 @ SY454 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(845,plain,
! [SV73: nat > nat] :
( ( ! [SY455: nat,SY456: nat] :
( ~ ! [SY457: nat] : ( ord_less_nat @ ( SV73 @ SY457 ) @ ( SV73 @ ( suc @ SY457 ) ) )
| ( ( ord_less_nat @ ( SV73 @ SY455 ) @ ( SV73 @ SY456 ) )
= ( ord_less_nat @ SY455 @ SY456 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(846,plain,
! [SV74: real] :
( ( ! [SY458: nat] :
( ~ ( ord_less_real @ zero_zero_real @ SV74 )
| ~ ! [SY459: real] :
~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY459 )
| ( ( power_power_real @ SY459 @ ( suc @ SY458 ) )
!= SV74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(847,plain,
! [SV75: nat] :
( ( ! [SY460: nat] :
( ~ ( ord_less_nat @ SV75 @ SY460 )
| ( ord_less_nat @ ( suc @ SV75 ) @ ( suc @ SY460 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(848,plain,
! [SV76: nat] :
( ( ! [SY461: nat] :
( ~ ( ord_less_nat @ ( suc @ SV76 ) @ SY461 )
| ~ ! [SY462: nat] :
( ~ ( ord_less_nat @ SV76 @ SY462 )
| ( SY461
!= ( suc @ SY462 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(849,plain,
! [SV77: real] :
( ( ! [SY463: nat,SY464: real] :
( ( ( power_power_real @ SV77 @ ( suc @ SY463 ) )
!= ( power_power_real @ SY464 @ ( suc @ SY463 ) ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ SV77 )
| ~ ( ord_less_eq_real @ zero_zero_real @ SY464 )
| ( SV77 = SY464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(850,plain,
! [SV78: nat] :
( ( ! [SY465: nat,SY466: nat > $o] :
( ~ ( ord_less_nat @ SV78 @ SY465 )
| ~ ! [SX3: nat] :
( ( SY465
!= ( suc @ SX3 ) )
| ( SY466 @ SX3 ) )
| ~ ! [SX3: nat] :
( ~ ( ord_less_nat @ SX3 @ SY465 )
| ~ ( SY466 @ ( suc @ SX3 ) )
| ( SY466 @ SX3 ) )
| ( SY466 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(851,plain,
! [SV79: nat] :
( ( ! [SY469: nat,SY470: nat > nat > $o] :
( ~ ( ord_less_nat @ SV79 @ SY469 )
| ~ ! [SX3: nat] : ( SY470 @ SX3 @ ( suc @ SX3 ) )
| ~ ! [SX3: nat,SX4: nat,SX5: nat] :
( ~ ( ord_less_nat @ SX3 @ SX4 )
| ~ ( ord_less_nat @ SX4 @ SX5 )
| ~ ( SY470 @ SX3 @ SX4 )
| ~ ( SY470 @ SX4 @ SX5 )
| ( SY470 @ SX3 @ SX5 ) )
| ( SY470 @ SV79 @ SY469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(852,plain,
! [SV80: nat] :
( ( ~ ( ( SV80 != zero_zero_nat ) )
| ~ ! [SY475: nat] :
( SV80
!= ( suc @ SY475 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(853,plain,
! [SV81: nat > nat] :
( ( ! [SY476: nat,SY477: nat] :
( ~ ! [SY478: nat] : ( ord_less_eq_nat @ ( SV81 @ SY478 ) @ ( SV81 @ ( suc @ SY478 ) ) )
| ~ ( ord_less_eq_nat @ SY476 @ SY477 )
| ( ord_less_eq_nat @ ( SV81 @ SY476 ) @ ( SV81 @ SY477 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(854,plain,
! [SV82: nat] :
( ( ! [SY479: nat,SY480: nat > $o] :
( ~ ( ord_less_eq_nat @ SV82 @ SY479 )
| ~ ( SY480 @ SV82 )
| ~ ! [SY481: nat] :
( ~ ( ord_less_eq_nat @ SV82 @ SY481 )
| ~ ( ord_less_nat @ SY481 @ SY479 )
| ~ ( SY480 @ SY481 )
| ( SY480 @ ( suc @ SY481 ) ) )
| ( SY480 @ SY479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(855,plain,
! [SV83: nat] :
( ( ! [SY482: nat] :
( ~ ( ord_less_nat @ ( suc @ zero_zero_nat ) @ SV83 )
| ( ord_less_nat @ SY482 @ ( power_power_nat @ SV83 @ SY482 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(856,plain,
! [SV84: real] :
( ( ! [SY483: real] :
( ~ ( ord_less_real @ SV84 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SY483 )
| ( ord_less_real @ ( divide_divide_real @ SV84 @ SY483 ) @ zero_zero_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(857,plain,
! [SV85: nat > nat > $o] :
( ( ! [SY484: nat,SY485: nat] :
( ~ ! [SY486: nat] : ( SV85 @ SY486 @ zero_zero_nat )
| ~ ! [SY487: nat] : ( SV85 @ zero_zero_nat @ ( suc @ SY487 ) )
| ~ ! [SY488: nat,SY489: nat] :
( ~ ( SV85 @ SY488 @ SY489 )
| ( SV85 @ ( suc @ SY488 ) @ ( suc @ SY489 ) ) )
| ( SV85 @ SY484 @ SY485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(858,plain,
! [SV86: nat > int] :
( ( ! [SY490: nat,SY491: nat] :
( ~ ! [SY492: nat] : ( ord_less_int @ ( SV86 @ SY492 ) @ ( SV86 @ ( suc @ SY492 ) ) )
| ~ ( ord_less_nat @ SY490 @ SY491 )
| ( ord_less_int @ ( SV86 @ SY490 ) @ ( SV86 @ SY491 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(859,plain,
! [SV87: nat] :
( ( ! [SY493: nat > $o] :
( ( ! [SY494: nat] :
( ~ ( ord_less_nat @ SY494 @ ( suc @ SV87 ) )
| ( SY493 @ SY494 ) ) )
= ( ~ ( ~ ( SY493 @ zero_zero_nat )
| ~ ! [SY495: nat] :
( ~ ( ord_less_nat @ SY495 @ SV87 )
| ( SY493 @ ( suc @ SY495 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(860,plain,
! [SV88: nat > real] :
( ( ! [SY496: nat,SY497: nat] :
( ~ ! [SY498: nat] : ( ord_less_real @ ( SV88 @ SY498 ) @ ( SV88 @ ( suc @ SY498 ) ) )
| ~ ( ord_less_nat @ SY496 @ SY497 )
| ( ord_less_real @ ( SV88 @ SY496 ) @ ( SV88 @ SY497 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(861,plain,
! [SV89: int] :
( ( ! [SY499: nat,SY500: int] :
( ( ( power_power_int @ SV89 @ ( suc @ SY499 ) )
!= ( power_power_int @ SY500 @ ( suc @ SY499 ) ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV89 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SY500 )
| ( SV89 = SY500 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(862,plain,
( ( na = zero_zero_int )
= $false ),
inference(extcnf_not_pos,[status(thm)],[705]) ).
thf(863,plain,
! [SV90: nat] :
( ( zero_zero_nat
!= ( suc @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(864,plain,
! [SV91: nat > int] :
( ( ! [SY501: nat,SY502: nat] :
( ~ ! [SY503: nat] : ( ord_less_eq_int @ ( SV91 @ ( suc @ SY503 ) ) @ ( SV91 @ SY503 ) )
| ~ ( ord_less_eq_nat @ SY501 @ SY502 )
| ( ord_less_eq_int @ ( SV91 @ SY502 ) @ ( SV91 @ SY501 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(865,plain,
! [SV92: real] :
( ( ! [SY504: real] :
( ~ ( ord_less_eq_real @ zero_zero_real @ SV92 )
| ~ ( ord_less_real @ zero_zero_real @ SY504 )
| ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ SV92 @ SY504 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(866,plain,
! [SV93: nat] :
( ( ! [SY505: nat,SY506: nat] :
( ~ ( ord_less_nat @ SV93 @ SY505 )
| ~ ( ord_less_nat @ SY505 @ SY506 )
| ( ord_less_nat @ ( suc @ SV93 ) @ SY506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(867,plain,
! [SV94: nat] :
( ( ! [SY507: nat] :
( ~ ( ord_less_eq_nat @ ( suc @ SV94 ) @ SY507 )
| ( ord_less_nat @ SV94 @ SY507 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(868,plain,
! [SV95: nat] :
( ( ! [SY508: nat] :
( ( SV95
!= ( suc @ SY508 ) )
| ( SV95 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(869,plain,
! [SV96: nat] :
( ( ( suc @ SV96 )
!= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(870,plain,
! [SV97: real] :
( ( ! [SY509: nat] :
( ~ ( ord_less_real @ zero_zero_real @ SV97 )
| ( ord_less_real @ zero_zero_real @ ( power_power_real @ SV97 @ SY509 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(871,plain,
! [SV98: real] :
( ( ! [SY510: real] :
( ~ ( ord_less_real @ zero_zero_real @ SV98 )
| ~ ( ord_less_real @ zero_zero_real @ SY510 )
| ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV98 @ SY510 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(872,plain,
! [SV99: nat] :
( ( ! [SY511: nat,SY512: nat] :
( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV99 @ ( suc @ SY511 ) ) @ ( power_power_nat @ SY512 @ ( suc @ SY511 ) ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY512 )
| ( ord_less_eq_nat @ SV99 @ SY512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(873,plain,
! [SV100: nat] :
( ( ! [SY513: nat] :
( ~ ( ord_less_nat @ SV100 @ SY513 )
| ( ord_less_eq_nat @ ( suc @ SV100 ) @ SY513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(874,plain,
! [SV101: int] :
( ( ! [SY514: nat,SY515: int] :
( ~ ( ord_less_eq_int @ ( power_power_int @ SV101 @ ( suc @ SY514 ) ) @ ( power_power_int @ SY515 @ ( suc @ SY514 ) ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ SY515 )
| ( ord_less_eq_int @ SV101 @ SY515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(875,plain,
! [SV102: real] :
( ( ! [SY516: real,SY517: nat] :
( ~ ( ord_less_eq_real @ SV102 @ SY516 )
| ~ ( ord_less_eq_real @ zero_zero_real @ SV102 )
| ( ord_less_eq_real @ ( power_power_real @ SV102 @ SY517 ) @ ( power_power_real @ SY516 @ SY517 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(876,plain,
! [SV103: real] :
( ( ! [SY518: real,SY519: real] :
( ( ord_less_real @ ( divide_divide_real @ SV103 @ SY518 ) @ ( divide_divide_real @ SY519 @ SY518 ) )
= ( ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SY518 )
| ( ord_less_real @ SV103 @ SY519 ) )
| ~ ( ~ ( ord_less_real @ SY518 @ zero_zero_real )
| ( ord_less_real @ SY519 @ SV103 ) ) )
| ~ ( ( SY518 != zero_zero_real ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(877,plain,
! [SV104: nat] :
( ( ! [SY520: nat] :
( ~ ~ ( ord_less_nat @ SV104 @ SY520 )
| ( ( ord_less_nat @ SV104 @ ( suc @ SY520 ) )
= ( SV104 = SY520 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(878,plain,
! [SV105: nat] :
( ( zero_zero_nat
!= ( suc @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(879,plain,
! [SV106: nat > real] :
( ( ! [SY521: nat,SY522: nat] :
( ~ ! [SY523: nat] : ( ord_less_real @ ( SV106 @ SY523 ) @ ( SV106 @ ( suc @ SY523 ) ) )
| ( ( ord_less_real @ ( SV106 @ SY521 ) @ ( SV106 @ SY522 ) )
= ( ord_less_nat @ SY521 @ SY522 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(880,plain,
! [SV107: nat > $o] :
( ( ! [SY524: nat] :
( ~ ( SV107 @ SY524 )
| ~ ! [SY525: nat] :
( ~ ( SV107 @ ( suc @ SY525 ) )
| ( SV107 @ SY525 ) )
| ( SV107 @ zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(881,plain,
! [SV108: real] :
( ( ~ ! [SY526: int] :
~ ( ord_less_eq_real @ SV108 @ ( ring_1_of_int_real @ SY526 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(882,plain,
! [SV109: nat > $o] :
( ( ! [SY527: nat] :
( ~ ( SV109 @ zero_zero_nat )
| ~ ! [SY528: nat] :
( ~ ( SV109 @ SY528 )
| ( SV109 @ ( suc @ SY528 ) ) )
| ( SV109 @ SY527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(883,plain,
! [SV110: nat] :
( ( ! [SY529: nat > $o] :
( ( ~ ! [SY530: nat] :
~ ~ ( ~ ( ord_less_nat @ SY530 @ ( suc @ SV110 ) )
| ~ ( SY529 @ SY530 ) ) )
= ( ( SY529 @ SV110 )
| ~ ! [SY531: nat] :
~ ~ ( ~ ( ord_less_nat @ SY531 @ SV110 )
| ~ ( SY529 @ SY531 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(884,plain,
! [SV111: nat] :
( ( ! [SY532: nat] :
( ~ ( ord_less_eq_nat @ ( suc @ SV111 ) @ SY532 )
| ~ ! [SX2: nat] :
( SY532
!= ( suc @ SX2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(885,plain,
! [SV112: real] :
( ( ! [SY534: real] :
( ~ ( ( SV112 != SY534 ) )
| ~ ~ ( ord_less_real @ SV112 @ SY534 )
| ( ord_less_real @ SY534 @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(886,plain,
! [SV113: nat > $o] :
( ( ~ ~ ( SV113 @ zero_zero_nat )
| ~ ~ ! [SY535: nat] :
~ ( SV113 @ SY535 )
| ~ ! [SY536: nat] :
~ ~ ( ~ ~ ( SV113 @ SY536 )
| ~ ( SV113 @ ( suc @ SY536 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(887,plain,
! [SV114: nat] :
( ( ! [SY537: nat] :
( ~ ( ord_less_eq_nat @ SV114 @ SY537 )
| ( ( ord_less_nat @ SY537 @ ( suc @ SV114 ) )
= ( SY537 = SV114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(888,plain,
! [SV115: real] :
( ( ! [SY538: real] :
( ~ ( ord_less_real @ zero_zero_real @ SV115 )
| ~ ( ord_less_real @ SY538 @ zero_zero_real )
| ( ord_less_real @ ( divide_divide_real @ SV115 @ SY538 ) @ zero_zero_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(889,plain,
! [SV116: real] :
( ( ! [SY539: real,SY540: real] :
( ~ ( ord_less_real @ SV116 @ SY539 )
| ~ ( ord_less_real @ SY540 @ zero_zero_real )
| ( ord_less_real @ ( divide_divide_real @ SY539 @ SY540 ) @ ( divide_divide_real @ SV116 @ SY540 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(890,plain,
( ( pm = zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[733]) ).
thf(891,plain,
( ( ya = zero_zero_int )
= $false ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(892,plain,
! [SV117: nat] :
( ( ! [SY541: nat > $o] :
( ( ! [SY542: nat] :
( ~ ( ord_less_nat @ SY542 @ ( suc @ SV117 ) )
| ( SY541 @ SY542 ) ) )
= ( ~ ( ~ ( SY541 @ SV117 )
| ~ ! [SY543: nat] :
( ~ ( ord_less_nat @ SY543 @ SV117 )
| ( SY541 @ SY543 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(893,plain,
! [SV118: nat > real] :
( ( ! [SY544: nat,SY545: nat] :
( ~ ! [SY546: nat] : ( ord_less_eq_real @ ( SV118 @ ( suc @ SY546 ) ) @ ( SV118 @ SY546 ) )
| ~ ( ord_less_eq_nat @ SY544 @ SY545 )
| ( ord_less_eq_real @ ( SV118 @ SY545 ) @ ( SV118 @ SY544 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(894,plain,
! [SV119: nat > nat] :
( ( ! [SY547: nat,SY548: nat] :
( ~ ! [SY549: nat] : ( ord_less_eq_nat @ ( SV119 @ ( suc @ SY549 ) ) @ ( SV119 @ SY549 ) )
| ~ ( ord_less_eq_nat @ SY547 @ SY548 )
| ( ord_less_eq_nat @ ( SV119 @ SY548 ) @ ( SV119 @ SY547 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(895,plain,
! [SV120: real] :
( ( ! [SY550: real,SY551: real,SY552: real] :
( ~ ( ord_less_real @ zero_zero_real @ SV120 )
| ~ ( ord_less_eq_real @ SV120 @ SY550 )
| ~ ( ord_less_real @ zero_zero_real @ SY551 )
| ~ ( ord_less_real @ SY551 @ SY552 )
| ( ord_less_real @ ( divide_divide_real @ SV120 @ SY552 ) @ ( divide_divide_real @ SY550 @ SY551 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(896,plain,
! [SV121: real] :
( ( ! [SY553: real] :
( ~ ( ord_less_eq_real @ zero_zero_real @ SV121 )
| ~ ( ord_less_real @ SY553 @ zero_zero_real )
| ( ord_less_eq_real @ ( divide_divide_real @ SV121 @ SY553 ) @ zero_zero_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(897,plain,
! [SV122: nat > $o] :
( ( ! [SY554: nat] :
( ~ ( SV122 @ SY554 )
| ~ ~ ( SV122 @ zero_zero_nat )
| ~ ! [SY555: nat] :
~ ~ ( ~ ~ ( ~ ( ord_less_nat @ SY555 @ SY554 )
| ~ ! [SY556: nat] :
( ~ ( ord_less_eq_nat @ SY556 @ SY555 )
| ~ ( SV122 @ SY556 ) ) )
| ~ ( SV122 @ ( suc @ SY555 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(898,plain,
! [SV123: nat] :
( ( ! [SY557: nat] :
( ( ord_less_nat @ ( suc @ SV123 ) @ SY557 )
= ( ~ ! [SY558: nat] :
~ ~ ( ( SY557
!= ( suc @ SY558 ) )
| ~ ( ord_less_nat @ SV123 @ SY558 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(899,plain,
! [SV124: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ SV124 )
| ~ ! [SY559: nat] :
( SV124
!= ( suc @ SY559 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(900,plain,
! [SV125: nat] :
( ( ! [SY560: nat] :
( ( ( suc @ SV125 )
!= ( suc @ SY560 ) )
| ( SV125 = SY560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(901,plain,
! [SV126: nat] :
( ( ! [SY561: nat] :
( ~ ( ord_less_nat @ SV126 @ SY561 )
| ~ ( ( ( suc @ SV126 )
!= SY561 ) )
| ( ord_less_nat @ ( suc @ SV126 ) @ SY561 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(902,plain,
! [SV127: nat] :
( ( ! [SY562: nat,SY563: nat > nat > $o] :
( ~ ( ord_less_eq_nat @ SV127 @ SY562 )
| ~ ! [SX3: nat] : ( SY563 @ SX3 @ SX3 )
| ~ ! [SX3: nat,SX4: nat,SX5: nat] :
( ~ ( SY563 @ SX3 @ SX4 )
| ~ ( SY563 @ SX4 @ SX5 )
| ( SY563 @ SX3 @ SX5 ) )
| ~ ! [SX3: nat] : ( SY563 @ SX3 @ ( suc @ SX3 ) )
| ( SY563 @ SV127 @ SY562 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(903,plain,
! [SV128: real] :
( ( ! [SY569: real] :
( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SY569 ) )
= ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SY569 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SY569 @ zero_zero_real ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(904,plain,
! [SV129: nat] :
( ( SV129
!= ( suc @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(905,plain,
! [SV130: nat] :
( ( zero_zero_nat
!= ( suc @ SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(906,plain,
! [SV131: real] :
( ( ~ ! [SY570: int] :
~ ( ord_less_real @ SV131 @ ( ring_1_of_int_real @ SY570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(907,plain,
! [SV132: nat] :
( ( ! [SY571: nat] :
( ~ ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ SV132 )
| ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ SV132 @ SY571 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(908,plain,
! [SV133: nat] :
( ( ! [SY572: nat] :
( ( ord_less_nat @ SV133 @ ( suc @ SY572 ) )
= ( ( SV133 = zero_zero_nat )
| ~ ! [SY573: nat] :
~ ~ ( ( SV133
!= ( suc @ SY573 ) )
| ~ ( ord_less_nat @ SY573 @ SY572 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(909,plain,
! [SV134: nat] :
( ( ! [SY574: real] :
( ~ ( ord_less_nat @ zero_zero_nat @ SV134 )
| ~ ( ord_less_real @ zero_zero_real @ SY574 )
| ~ ! [SY575: real] :
~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY575 )
| ( ( power_power_real @ SY575 @ SV134 )
!= SY574 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(910,plain,
! [SV135: real] :
( ( ! [SY576: real] :
( ~ ( ord_less_eq_real @ SV135 @ zero_zero_real )
| ~ ( ord_less_real @ SY576 @ zero_zero_real )
| ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ SV135 @ SY576 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(911,plain,
! [SV136: real] :
( ( ! [SY577: nat] :
( ~ ( ord_less_eq_real @ zero_zero_real @ SV136 )
| ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ SV136 @ SY577 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(912,plain,
! [SV137: nat] :
( ( ! [SY578: nat] :
( ~ ( ord_less_eq_nat @ SV137 @ SY578 )
| ( ord_less_eq_nat @ SV137 @ ( suc @ SY578 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(913,plain,
! [SV138: nat] :
( ( zero_zero_nat
!= ( suc @ SV138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(914,plain,
! [SV139: real] :
( ( ! [SY579: real,SY580: real,SY581: real] :
( ~ ( ord_less_eq_real @ zero_zero_real @ SV139 )
| ~ ( ord_less_eq_real @ SY579 @ SV139 )
| ~ ( ord_less_real @ zero_zero_real @ SY580 )
| ~ ( ord_less_eq_real @ SY580 @ SY581 )
| ( ord_less_eq_real @ ( divide_divide_real @ SY579 @ SY581 ) @ ( divide_divide_real @ SV139 @ SY580 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(915,plain,
! [SV140: real] :
( ( ~ ! [SY582: int] :
~ ( ord_less_real @ ( ring_1_of_int_real @ SY582 ) @ SV140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(916,plain,
! [SV141: real] :
( ( ! [SY583: real] :
( ( ord_less_real @ ( divide_divide_real @ SV141 @ SY583 ) @ zero_zero_real )
= ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SY583 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SY583 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(917,plain,
! [SV142: nat] :
( ( ! [SY584: nat,SY585: nat > $o] :
( ~ ( ord_less_eq_nat @ SV142 @ SY584 )
| ~ ( SY585 @ SY584 )
| ~ ! [SY586: nat] :
( ~ ( ord_less_eq_nat @ SV142 @ SY586 )
| ~ ( ord_less_nat @ SY586 @ SY584 )
| ~ ( SY585 @ ( suc @ SY586 ) )
| ( SY585 @ SY586 ) )
| ( SY585 @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(918,plain,
! [SV143: real] :
( ( ~ ! [SY587: real] :
~ ( ord_less_real @ SY587 @ SV143 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(919,plain,
! [SV144: nat] :
( ( ! [SY588: nat] :
( ~ ( ord_less_eq_nat @ ( suc @ SV144 ) @ SY588 )
| ( ord_less_eq_nat @ SV144 @ SY588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(920,plain,
! [SV145: nat] :
( ( ! [SY589: nat] :
( ~ ~ ( ord_less_nat @ SV145 @ SY589 )
| ~ ( ord_less_nat @ SV145 @ ( suc @ SY589 ) )
| ( SY589 = SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(921,plain,
! [SV146: nat] :
( ( ! [SY590: nat] :
( ~ ( nthRoo1352626670d_root @ SV146 @ SY590 )
| ( SV146
= ( suc @ SY590 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(922,plain,
! [SV147: nat] :
( ( ( suc @ SV147 )
!= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(923,plain,
! [SV148: nat] :
( ( ~ ( ( SV148 != zero_zero_nat ) )
| ~ ! [SY591: nat] :
( SV148
!= ( suc @ SY591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(924,plain,
! [SV149: nat,SV1: int] :
( ( ! [SY592: int] :
( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ SV1 ) @ SV149 ) @ ( ring_1_of_int_real @ SY592 ) )
= ( ord_less_int @ ( power_power_int @ SV1 @ SV149 ) @ SY592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(925,plain,
! [SV150: int,SV2: int] :
( ( ! [SY593: nat] :
( ( ord_less_real @ ( ring_1_of_int_real @ SV2 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV150 ) @ SY593 ) )
= ( ord_less_int @ SV2 @ ( power_power_int @ SV150 @ SY593 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(926,plain,
! [SV151: nat,SV3: int] :
( ( ( ring_1_of_int_real @ ( power_power_int @ SV3 @ SV151 ) )
= ( power_power_real @ ( ring_1_of_int_real @ SV3 ) @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(927,plain,
! [SV152: nat,SV4: int] :
( ( ! [SY594: int] :
( ( ( power_power_real @ ( ring_1_of_int_real @ SV4 ) @ SV152 )
= ( ring_1_of_int_real @ SY594 ) )
= ( ( power_power_int @ SV4 @ SV152 )
= SY594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(928,plain,
! [SV153: int,SV5: int] :
( ( ! [SY595: nat] :
( ( ( ring_1_of_int_real @ SV5 )
= ( power_power_real @ ( ring_1_of_int_real @ SV153 ) @ SY595 ) )
= ( SV5
= ( power_power_int @ SV153 @ SY595 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(929,plain,
! [SV154: int,SV6: int] :
( ( ( ord_less_real @ ( ring_1_of_int_real @ SV6 ) @ ( ring_1_of_int_real @ SV154 ) )
= ( ord_less_int @ SV6 @ SV154 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(930,plain,
! [SV155: int,SV7: int] :
( ( ( ( ring_1_of_int_real @ SV7 )
= ( ring_1_of_int_real @ SV155 ) )
= ( SV7 = SV155 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(931,plain,
! [SV156: nat,SV8: nat] :
( ( ( ( suc @ SV8 )
= ( suc @ SV156 ) )
= ( SV8 = SV156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(932,plain,
! [SV157: nat,SV9: nat] :
( ( ( ( suc @ SV9 )
= ( suc @ SV157 ) )
= ( SV9 = SV157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(933,plain,
! [SV158: nat,SV10: nat] :
( ( ( ord_less_nat @ ( suc @ SV10 ) @ ( suc @ SV158 ) )
= ( ord_less_nat @ SV10 @ SV158 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(934,plain,
( ( ord_less_int @ ya @ zero_zero_int )
= $false ),
inference(extcnf_or_neg,[status(thm)],[779]) ).
thf(935,plain,
( ( ord_less_int @ na @ zero_zero_int )
= $false ),
inference(extcnf_or_neg,[status(thm)],[779]) ).
thf(936,plain,
( ( ord_less_int @ ya @ zero_zero_int )
= $false ),
inference(extcnf_or_neg,[status(thm)],[780]) ).
thf(937,plain,
( ( ord_less_int @ na @ zero_zero_int )
= $false ),
inference(extcnf_or_neg,[status(thm)],[780]) ).
thf(938,plain,
! [SV12: int] :
( ( ~ ( ( zero_zero_real
= ( ring_1_of_int_real @ SV12 ) )
| ( SV12 = zero_zero_int ) )
| ~ ( ( zero_zero_real
!= ( ring_1_of_int_real @ SV12 ) )
| ( SV12 != zero_zero_int ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[781]) ).
thf(939,plain,
! [SV12: int] :
( ( ( zero_zero_real
= ( ring_1_of_int_real @ SV12 ) )
= ( SV12 = zero_zero_int ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[781]) ).
thf(940,plain,
! [SV13: int] :
( ( ~ ( ( ( ring_1_of_int_real @ SV13 )
= zero_zero_real )
| ( SV13 = zero_zero_int ) )
| ~ ( ( ( ring_1_of_int_real @ SV13 )
!= zero_zero_real )
| ( SV13 != zero_zero_int ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[782]) ).
thf(941,plain,
! [SV13: int] :
( ( ( ( ring_1_of_int_real @ SV13 )
= zero_zero_real )
= ( SV13 = zero_zero_int ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[782]) ).
thf(942,plain,
! [SV14: int] :
( ( ~ ( ( ord_less_real @ ( ring_1_of_int_real @ SV14 ) @ zero_zero_real )
| ( ord_less_int @ SV14 @ zero_zero_int ) )
| ~ ( ~ ( ord_less_real @ ( ring_1_of_int_real @ SV14 ) @ zero_zero_real )
| ~ ( ord_less_int @ SV14 @ zero_zero_int ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[783]) ).
thf(943,plain,
! [SV14: int] :
( ( ( ord_less_real @ ( ring_1_of_int_real @ SV14 ) @ zero_zero_real )
= ( ord_less_int @ SV14 @ zero_zero_int ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[783]) ).
thf(944,plain,
! [SV15: int] :
( ( ~ ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ SV15 ) )
| ( ord_less_int @ zero_zero_int @ SV15 ) )
| ~ ( ~ ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ SV15 ) )
| ~ ( ord_less_int @ zero_zero_int @ SV15 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[784]) ).
thf(945,plain,
! [SV15: int] :
( ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ SV15 ) )
= ( ord_less_int @ zero_zero_int @ SV15 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[784]) ).
thf(946,plain,
! [SV159: nat,SV16: nat] :
( ( ( ~ ( ord_less_nat @ SV16 @ SV159 ) )
= ( ord_less_nat @ SV159 @ ( suc @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(947,plain,
! [SV160: nat,SV17: nat] :
( ( ( ord_less_nat @ SV17 @ ( suc @ SV160 ) )
= ( ( ord_less_nat @ SV17 @ SV160 )
| ( SV17 = SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(948,plain,
! [SV161: nat,SV21: nat] :
( ( ( ( power_power_nat @ SV21 @ SV161 )
= ( suc @ zero_zero_nat ) )
= ( ( SV161 = zero_zero_nat )
| ( SV21
= ( suc @ zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(949,plain,
! [SV27: nat] :
( ( ~ ( ( ord_less_nat @ SV27 @ ( suc @ zero_zero_nat ) )
| ( SV27 = zero_zero_nat ) )
| ~ ( ~ ( ord_less_nat @ SV27 @ ( suc @ zero_zero_nat ) )
| ( SV27 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[796]) ).
thf(950,plain,
! [SV27: nat] :
( ( ( ord_less_nat @ SV27 @ ( suc @ zero_zero_nat ) )
= ( SV27 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[796]) ).
thf(951,plain,
! [SV162: int,SV28: int] :
( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV28 ) @ ( ring_1_of_int_real @ SV162 ) )
= ( ord_less_eq_int @ SV28 @ SV162 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(952,plain,
! [SV163: nat,SV29: int] :
( ( ! [SY596: int] :
( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ SV29 ) @ SV163 ) @ ( ring_1_of_int_real @ SY596 ) )
= ( ord_less_eq_int @ ( power_power_int @ SV29 @ SV163 ) @ SY596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(953,plain,
! [SV164: int,SV30: int] :
( ( ! [SY597: nat] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV30 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV164 ) @ SY597 ) )
= ( ord_less_eq_int @ SV30 @ ( power_power_int @ SV164 @ SY597 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(954,plain,
! [SV165: real,SV31: real] :
( ( ! [SY598: nat] :
( ( power_power_real @ ( divide_divide_real @ SV31 @ SV165 ) @ SY598 )
= ( divide_divide_real @ ( power_power_real @ SV31 @ SY598 ) @ ( power_power_real @ SV165 @ SY598 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(955,plain,
! [SV166: nat,SV32: nat] :
( ( ( ord_less_eq_nat @ ( suc @ SV32 ) @ ( suc @ SV166 ) )
= ( ord_less_eq_nat @ SV32 @ SV166 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(956,plain,
! [SV167: nat,SV33: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV33 @ SV167 ) )
= ( ord_less_eq_nat @ ( suc @ SV167 ) @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(957,plain,
! [SV34: nat] :
( ( ord_less_eq_nat @ ( suc @ SV34 ) @ SV34 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[803]) ).
thf(958,plain,
! [SV168: nat,SV35: nat] :
( ( ( ord_less_eq_nat @ SV35 @ ( suc @ SV168 ) )
= ( ( ord_less_eq_nat @ SV35 @ SV168 )
| ( SV35
= ( suc @ SV168 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(959,plain,
! [SV169: nat] :
( ( ( nthRoo1352626670d_root @ SV169 )
= ( ^ [SY599: nat] :
( SV169
= ( suc @ SY599 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(960,plain,
! [SV170: nat,SV37: nat] :
( ( ( ord_less_eq_nat @ ( suc @ SV37 ) @ SV170 )
= ( ord_less_nat @ SV37 @ SV170 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(961,plain,
! [SV171: nat,SV38: nat] :
( ( ( ord_less_nat @ SV38 @ ( suc @ SV171 ) )
= ( ord_less_eq_nat @ SV38 @ SV171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(962,plain,
! [SV172: nat] :
( ( ( ord_less_nat @ SV172 )
= ( ord_less_eq_nat @ ( suc @ SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(963,plain,
! [SV173: nat,SV41: nat] :
( ( ord_less_eq_nat @ ( divide_divide_nat @ SV41 @ SV173 ) @ ( divide_divide_nat @ ( suc @ SV41 ) @ SV173 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(964,plain,
! [SV174: nat,SV42: nat] :
( ( ( SV42
!= ( suc @ SV174 ) )
| ( nthRoo1352626670d_root @ SV42 @ SV174 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(965,plain,
! [SV175: real,SV43: real] :
( ( ! [SY600: real] :
( ~ ( ord_less_real @ SV43 @ SV175 )
| ~ ( ord_less_real @ zero_zero_real @ SY600 )
| ( ord_less_real @ ( divide_divide_real @ SV43 @ SY600 ) @ ( divide_divide_real @ SV175 @ SY600 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(966,plain,
! [SV176: real,SV44: real] :
( ( ~ ( ord_less_eq_real @ SV44 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV176 )
| ( ord_less_eq_real @ ( divide_divide_real @ SV44 @ SV176 ) @ zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(967,plain,
! [SV45: nat] :
( ( ~ ( ( ord_less_nat @ zero_zero_nat @ SV45 )
| ~ ! [SY405: nat] :
( SV45
!= ( suc @ SY405 ) ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV45 )
| ~ ~ ! [SY405: nat] :
( SV45
!= ( suc @ SY405 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[817]) ).
thf(968,plain,
! [SV45: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV45 )
= ( ~ ! [SY405: nat] :
( SV45
!= ( suc @ SY405 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[817]) ).
thf(969,plain,
! [SV177: nat,SV46: nat] :
( ( ~ ( ord_less_nat @ ( suc @ SV46 ) @ SV177 )
| ( ord_less_nat @ SV46 @ SV177 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(970,plain,
! [SV178: nat > $o,SV47: nat] :
( ( ( ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) ) )
= ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(971,plain,
! [SV179: nat,SV48: nat] :
( ( ~ ( ord_less_nat @ SV48 @ SV179 )
| ( ord_less_nat @ SV48 @ ( suc @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(972,plain,
! [SV180: nat,SV49: real] :
( ( ! [SY603: real] :
( ~ ( ord_less_real @ ( power_power_real @ SV49 @ SV180 ) @ ( power_power_real @ SY603 @ SV180 ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ SY603 )
| ( ord_less_real @ SV49 @ SY603 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(973,plain,
! [SV181: nat,SV50: nat] :
( ( ! [SY604: nat] :
( ( ( power_power_nat @ SV50 @ ( suc @ SV181 ) )
!= ( power_power_nat @ SY604 @ ( suc @ SV181 ) ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV50 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY604 )
| ( SV50 = SY604 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(974,plain,
! [SV182: real,SV51: real] :
( ( ! [SY605: real] :
( ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SY605 @ SV182 ) )
= ( ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SY605 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SY605 @ SV51 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(975,plain,
! [SV183: nat,SV52: nat] :
( ( ! [SY606: nat > $o] :
( ~ ( ord_less_eq_nat @ SV52 @ SV183 )
| ~ ( SY606 @ SV52 )
| ~ ! [SY419: nat] :
( ~ ( ord_less_eq_nat @ SV52 @ SY419 )
| ~ ( SY606 @ SY419 )
| ( SY606 @ ( suc @ SY419 ) ) )
| ( SY606 @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(976,plain,
! [SV184: nat,SV53: nat > $o] :
( ( ~ ! [SY421: nat] :
( ~ ! [SY422: nat] :
( ~ ( ord_less_eq_nat @ ( suc @ SY422 ) @ SY421 )
| ( SV53 @ SY422 ) )
| ( SV53 @ SY421 ) )
| ( SV53 @ SV184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(977,plain,
! [SV185: real,SV54: real] :
( ( ! [SY610: real,SY611: real] :
( ~ ( ord_less_eq_real @ zero_zero_real @ SV54 )
| ~ ( ord_less_real @ SV54 @ SV185 )
| ~ ( ord_less_real @ zero_zero_real @ SY610 )
| ~ ( ord_less_eq_real @ SY610 @ SY611 )
| ( ord_less_real @ ( divide_divide_real @ SV54 @ SY611 ) @ ( divide_divide_real @ SV185 @ SY610 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(978,plain,
! [SV186: nat,SV55: nat > int] :
( ( ! [SY612: nat] :
( ~ ! [SY428: nat] : ( ord_less_eq_int @ ( SV55 @ SY428 ) @ ( SV55 @ ( suc @ SY428 ) ) )
| ~ ( ord_less_eq_nat @ SV186 @ SY612 )
| ( ord_less_eq_int @ ( SV55 @ SV186 ) @ ( SV55 @ SY612 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(979,plain,
! [SV187: nat,SV56: nat] :
( ( ~ ( ord_less_eq_nat @ SV56 @ ( suc @ SV187 ) )
| ~ ~ ( ord_less_eq_nat @ SV56 @ SV187 )
| ( SV56
= ( suc @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(980,plain,
! [SV188: nat,SV57: nat] :
( ( ~ ( ord_less_eq_nat @ SV57 @ SV188 )
| ( ord_less_nat @ SV57 @ ( suc @ SV188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(981,plain,
! [SV58: real] :
( ( ! [SY431: real] :
~ ( ord_less_real @ SV58 @ SY431 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[830]) ).
thf(982,plain,
! [SV189: nat,SV59: nat > real] :
( ( ! [SY614: nat] :
( ~ ! [SY434: nat] : ( ord_less_eq_real @ ( SV59 @ SY434 ) @ ( SV59 @ ( suc @ SY434 ) ) )
| ~ ( ord_less_eq_nat @ SV189 @ SY614 )
| ( ord_less_eq_real @ ( SV59 @ SV189 ) @ ( SV59 @ SY614 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(983,plain,
! [SV190: nat,SV60: real] :
( ( ~ ( ( SV60 != zero_zero_real ) )
| ( ( power_power_real @ SV60 @ SV190 )
!= zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(984,plain,
! [SV191: nat,SV61: real] :
( ( ( ( power_power_real @ SV61 @ SV191 )
= zero_zero_real )
= ( ~ ( ( SV61 != zero_zero_real )
| ~ ( ord_less_nat @ zero_zero_nat @ SV191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(985,plain,
! [SV192: real,SV62: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ SV62 )
| ~ ( ord_less_real @ zero_zero_real @ SV192 )
| ~ ! [SY616: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY616 )
| ( ( power_power_real @ SY616 @ SV62 )
!= SV192 ) )
| ~ ! [SY617: real] :
( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY617 )
| ( ( power_power_real @ SY617 @ SV62 )
!= SV192 ) )
| ( SY617 = SY616 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(986,plain,
! [SV193: nat,SV63: real] :
( ( ! [SY618: real] :
( ~ ( ord_less_eq_real @ ( power_power_real @ SV63 @ ( suc @ SV193 ) ) @ ( power_power_real @ SY618 @ ( suc @ SV193 ) ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ SY618 )
| ( ord_less_eq_real @ SV63 @ SY618 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(987,plain,
! [SV194: nat,SV64: nat > nat] :
( ( ! [SY619: nat] :
( ~ ! [SY444: nat] : ( ord_less_nat @ ( SV64 @ SY444 ) @ ( SV64 @ ( suc @ SY444 ) ) )
| ~ ( ord_less_nat @ SV194 @ SY619 )
| ( ord_less_nat @ ( SV64 @ SV194 ) @ ( SV64 @ SY619 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(988,plain,
! [SV65: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV65 ) )
= $true )
| ( ( ( power_power_real @ zero_zero_real @ SV65 )
= zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[837]) ).
thf(989,plain,
! [SV195: nat,SV66: nat] :
( ( ~ ( ord_less_nat @ ( suc @ SV66 ) @ ( suc @ SV195 ) )
| ( ord_less_nat @ SV66 @ SV195 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(990,plain,
! [SV196: nat,SV67: nat] :
( ( ~ ( ord_less_nat @ SV67 @ ( suc @ SV196 ) )
| ~ ~ ( ord_less_nat @ SV67 @ SV196 )
| ( SV67 = SV196 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(991,plain,
! [SV197: nat,SV68: nat > int] :
( ( ! [SY621: nat] :
( ~ ! [SY449: nat] : ( ord_less_int @ ( SV68 @ SY449 ) @ ( SV68 @ ( suc @ SY449 ) ) )
| ( ( ord_less_int @ ( SV68 @ SV197 ) @ ( SV68 @ SY621 ) )
= ( ord_less_nat @ SV197 @ SY621 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(992,plain,
! [SV198: nat,SV69: nat] :
( ( ~ ( ord_less_nat @ SV69 @ SV198 )
| ~ ( ( SV198
!= ( suc @ SV69 ) ) )
| ~ ! [SY623: nat] :
( ~ ( ord_less_nat @ SV69 @ SY623 )
| ( SV198
!= ( suc @ SY623 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(993,plain,
! [SV199: nat,SV70: nat > $o] :
( ( ~ ( SV70 @ zero_zero_nat )
| ~ ! [SY453: nat] :
( ~ ( SV70 @ SY453 )
| ( SV70 @ ( suc @ SY453 ) ) )
| ( SV70 @ SV199 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(994,plain,
! [SV71: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV71 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[843]) ).
thf(995,plain,
! [SV200: real,SV72: real] :
( ( ~ ( ord_less_real @ SV72 @ zero_zero_real )
| ~ ( ord_less_real @ SV200 @ zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV72 @ SV200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(996,plain,
! [SV201: nat,SV73: nat > nat] :
( ( ! [SY625: nat] :
( ~ ! [SY457: nat] : ( ord_less_nat @ ( SV73 @ SY457 ) @ ( SV73 @ ( suc @ SY457 ) ) )
| ( ( ord_less_nat @ ( SV73 @ SV201 ) @ ( SV73 @ SY625 ) )
= ( ord_less_nat @ SV201 @ SY625 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(997,plain,
! [SV202: nat,SV74: real] :
( ( ~ ( ord_less_real @ zero_zero_real @ SV74 )
| ~ ! [SY627: real] :
~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY627 )
| ( ( power_power_real @ SY627 @ ( suc @ SV202 ) )
!= SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(998,plain,
! [SV203: nat,SV75: nat] :
( ( ~ ( ord_less_nat @ SV75 @ SV203 )
| ( ord_less_nat @ ( suc @ SV75 ) @ ( suc @ SV203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(999,plain,
! [SV204: nat,SV76: nat] :
( ( ~ ( ord_less_nat @ ( suc @ SV76 ) @ SV204 )
| ~ ! [SY628: nat] :
( ~ ( ord_less_nat @ SV76 @ SY628 )
| ( SV204
!= ( suc @ SY628 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(1000,plain,
! [SV205: nat,SV77: real] :
( ( ! [SY629: real] :
( ( ( power_power_real @ SV77 @ ( suc @ SV205 ) )
!= ( power_power_real @ SY629 @ ( suc @ SV205 ) ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ SV77 )
| ~ ( ord_less_eq_real @ zero_zero_real @ SY629 )
| ( SV77 = SY629 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(1001,plain,
! [SV206: nat,SV78: nat] :
( ( ! [SY630: nat > $o] :
( ~ ( ord_less_nat @ SV78 @ SV206 )
| ~ ! [SY631: nat] :
( ( SV206
!= ( suc @ SY631 ) )
| ( SY630 @ SY631 ) )
| ~ ! [SY632: nat] :
( ~ ( ord_less_nat @ SY632 @ SV206 )
| ~ ( SY630 @ ( suc @ SY632 ) )
| ( SY630 @ SY632 ) )
| ( SY630 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(1002,plain,
! [SV207: nat,SV79: nat] :
( ( ! [SY633: nat > nat > $o] :
( ~ ( ord_less_nat @ SV79 @ SV207 )
| ~ ! [SX3: nat] : ( SY633 @ SX3 @ ( suc @ SX3 ) )
| ~ ! [SX3: nat,SX4: nat,SX5: nat] :
( ~ ( ord_less_nat @ SX3 @ SX4 )
| ~ ( ord_less_nat @ SX4 @ SX5 )
| ~ ( SY633 @ SX3 @ SX4 )
| ~ ( SY633 @ SX4 @ SX5 )
| ( SY633 @ SX3 @ SX5 ) )
| ( SY633 @ SV79 @ SV207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(1003,plain,
! [SV80: nat] :
( ( ( ~ ( ( SV80 != zero_zero_nat ) ) )
= $true )
| ( ( ~ ! [SY475: nat] :
( SV80
!= ( suc @ SY475 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[852]) ).
thf(1004,plain,
! [SV208: nat,SV81: nat > nat] :
( ( ! [SY638: nat] :
( ~ ! [SY478: nat] : ( ord_less_eq_nat @ ( SV81 @ SY478 ) @ ( SV81 @ ( suc @ SY478 ) ) )
| ~ ( ord_less_eq_nat @ SV208 @ SY638 )
| ( ord_less_eq_nat @ ( SV81 @ SV208 ) @ ( SV81 @ SY638 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(1005,plain,
! [SV209: nat,SV82: nat] :
( ( ! [SY640: nat > $o] :
( ~ ( ord_less_eq_nat @ SV82 @ SV209 )
| ~ ( SY640 @ SV82 )
| ~ ! [SY641: nat] :
( ~ ( ord_less_eq_nat @ SV82 @ SY641 )
| ~ ( ord_less_nat @ SY641 @ SV209 )
| ~ ( SY640 @ SY641 )
| ( SY640 @ ( suc @ SY641 ) ) )
| ( SY640 @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(1006,plain,
! [SV210: nat,SV83: nat] :
( ( ~ ( ord_less_nat @ ( suc @ zero_zero_nat ) @ SV83 )
| ( ord_less_nat @ SV210 @ ( power_power_nat @ SV83 @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(1007,plain,
! [SV211: real,SV84: real] :
( ( ~ ( ord_less_real @ SV84 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV211 )
| ( ord_less_real @ ( divide_divide_real @ SV84 @ SV211 ) @ zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(1008,plain,
! [SV212: nat,SV85: nat > nat > $o] :
( ( ! [SY642: nat] :
( ~ ! [SY486: nat] : ( SV85 @ SY486 @ zero_zero_nat )
| ~ ! [SY487: nat] : ( SV85 @ zero_zero_nat @ ( suc @ SY487 ) )
| ~ ! [SY488: nat,SY489: nat] :
( ~ ( SV85 @ SY488 @ SY489 )
| ( SV85 @ ( suc @ SY488 ) @ ( suc @ SY489 ) ) )
| ( SV85 @ SV212 @ SY642 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1009,plain,
! [SV213: nat,SV86: nat > int] :
( ( ! [SY647: nat] :
( ~ ! [SY492: nat] : ( ord_less_int @ ( SV86 @ SY492 ) @ ( SV86 @ ( suc @ SY492 ) ) )
| ~ ( ord_less_nat @ SV213 @ SY647 )
| ( ord_less_int @ ( SV86 @ SV213 ) @ ( SV86 @ SY647 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(1010,plain,
! [SV214: nat > $o,SV87: nat] :
( ( ( ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) ) )
= ( ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1011,plain,
! [SV215: nat,SV88: nat > real] :
( ( ! [SY651: nat] :
( ~ ! [SY498: nat] : ( ord_less_real @ ( SV88 @ SY498 ) @ ( SV88 @ ( suc @ SY498 ) ) )
| ~ ( ord_less_nat @ SV215 @ SY651 )
| ( ord_less_real @ ( SV88 @ SV215 ) @ ( SV88 @ SY651 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(1012,plain,
! [SV216: nat,SV89: int] :
( ( ! [SY653: int] :
( ( ( power_power_int @ SV89 @ ( suc @ SV216 ) )
!= ( power_power_int @ SY653 @ ( suc @ SV216 ) ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV89 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SY653 )
| ( SV89 = SY653 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1013,plain,
! [SV90: nat] :
( ( zero_zero_nat
= ( suc @ SV90 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[863]) ).
thf(1014,plain,
! [SV217: nat,SV91: nat > int] :
( ( ! [SY654: nat] :
( ~ ! [SY503: nat] : ( ord_less_eq_int @ ( SV91 @ ( suc @ SY503 ) ) @ ( SV91 @ SY503 ) )
| ~ ( ord_less_eq_nat @ SV217 @ SY654 )
| ( ord_less_eq_int @ ( SV91 @ SY654 ) @ ( SV91 @ SV217 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(1015,plain,
! [SV218: real,SV92: real] :
( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV92 )
| ~ ( ord_less_real @ zero_zero_real @ SV218 )
| ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ SV92 @ SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(1016,plain,
! [SV219: nat,SV93: nat] :
( ( ! [SY656: nat] :
( ~ ( ord_less_nat @ SV93 @ SV219 )
| ~ ( ord_less_nat @ SV219 @ SY656 )
| ( ord_less_nat @ ( suc @ SV93 ) @ SY656 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(1017,plain,
! [SV220: nat,SV94: nat] :
( ( ~ ( ord_less_eq_nat @ ( suc @ SV94 ) @ SV220 )
| ( ord_less_nat @ SV94 @ SV220 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(1018,plain,
! [SV221: nat,SV95: nat] :
( ( ( SV95
!= ( suc @ SV221 ) )
| ( SV95 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(1019,plain,
! [SV96: nat] :
( ( ( suc @ SV96 )
= zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[869]) ).
thf(1020,plain,
! [SV222: nat,SV97: real] :
( ( ~ ( ord_less_real @ zero_zero_real @ SV97 )
| ( ord_less_real @ zero_zero_real @ ( power_power_real @ SV97 @ SV222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(1021,plain,
! [SV223: real,SV98: real] :
( ( ~ ( ord_less_real @ zero_zero_real @ SV98 )
| ~ ( ord_less_real @ zero_zero_real @ SV223 )
| ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV98 @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(1022,plain,
! [SV224: nat,SV99: nat] :
( ( ! [SY657: nat] :
( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV99 @ ( suc @ SV224 ) ) @ ( power_power_nat @ SY657 @ ( suc @ SV224 ) ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY657 )
| ( ord_less_eq_nat @ SV99 @ SY657 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(1023,plain,
! [SV225: nat,SV100: nat] :
( ( ~ ( ord_less_nat @ SV100 @ SV225 )
| ( ord_less_eq_nat @ ( suc @ SV100 ) @ SV225 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(1024,plain,
! [SV226: nat,SV101: int] :
( ( ! [SY658: int] :
( ~ ( ord_less_eq_int @ ( power_power_int @ SV101 @ ( suc @ SV226 ) ) @ ( power_power_int @ SY658 @ ( suc @ SV226 ) ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ SY658 )
| ( ord_less_eq_int @ SV101 @ SY658 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(1025,plain,
! [SV227: real,SV102: real] :
( ( ! [SY659: nat] :
( ~ ( ord_less_eq_real @ SV102 @ SV227 )
| ~ ( ord_less_eq_real @ zero_zero_real @ SV102 )
| ( ord_less_eq_real @ ( power_power_real @ SV102 @ SY659 ) @ ( power_power_real @ SV227 @ SY659 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(1026,plain,
! [SV228: real,SV103: real] :
( ( ! [SY660: real] :
( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SY660 @ SV228 ) )
= ( ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SY660 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SY660 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(1027,plain,
! [SV229: nat,SV104: nat] :
( ( ~ ~ ( ord_less_nat @ SV104 @ SV229 )
| ( ( ord_less_nat @ SV104 @ ( suc @ SV229 ) )
= ( SV104 = SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[877]) ).
thf(1028,plain,
! [SV105: nat] :
( ( zero_zero_nat
= ( suc @ SV105 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(1029,plain,
! [SV230: nat,SV106: nat > real] :
( ( ! [SY661: nat] :
( ~ ! [SY523: nat] : ( ord_less_real @ ( SV106 @ SY523 ) @ ( SV106 @ ( suc @ SY523 ) ) )
| ( ( ord_less_real @ ( SV106 @ SV230 ) @ ( SV106 @ SY661 ) )
= ( ord_less_nat @ SV230 @ SY661 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(1030,plain,
! [SV231: nat,SV107: nat > $o] :
( ( ~ ( SV107 @ SV231 )
| ~ ! [SY525: nat] :
( ~ ( SV107 @ ( suc @ SY525 ) )
| ( SV107 @ SY525 ) )
| ( SV107 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(1031,plain,
! [SV108: real] :
( ( ! [SY526: int] :
~ ( ord_less_eq_real @ SV108 @ ( ring_1_of_int_real @ SY526 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[881]) ).
thf(1032,plain,
! [SV232: nat,SV109: nat > $o] :
( ( ~ ( SV109 @ zero_zero_nat )
| ~ ! [SY528: nat] :
( ~ ( SV109 @ SY528 )
| ( SV109 @ ( suc @ SY528 ) ) )
| ( SV109 @ SV232 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(1033,plain,
! [SV233: nat > $o,SV110: nat] :
( ( ( ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) ) )
= ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(1034,plain,
! [SV234: nat,SV111: nat] :
( ( ~ ( ord_less_eq_nat @ ( suc @ SV111 ) @ SV234 )
| ~ ! [SY667: nat] :
( SV234
!= ( suc @ SY667 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(1035,plain,
! [SV235: real,SV112: real] :
( ( ~ ( ( SV112 != SV235 ) )
| ~ ~ ( ord_less_real @ SV112 @ SV235 )
| ( ord_less_real @ SV235 @ SV112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(1036,plain,
! [SV113: nat > $o] :
( ( ( ~ ~ ( SV113 @ zero_zero_nat ) )
= $true )
| ( ( ~ ~ ! [SY535: nat] :
~ ( SV113 @ SY535 )
| ~ ! [SY536: nat] :
~ ~ ( ~ ~ ( SV113 @ SY536 )
| ~ ( SV113 @ ( suc @ SY536 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[886]) ).
thf(1037,plain,
! [SV236: nat,SV114: nat] :
( ( ~ ( ord_less_eq_nat @ SV114 @ SV236 )
| ( ( ord_less_nat @ SV236 @ ( suc @ SV114 ) )
= ( SV236 = SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(1038,plain,
! [SV237: real,SV115: real] :
( ( ~ ( ord_less_real @ zero_zero_real @ SV115 )
| ~ ( ord_less_real @ SV237 @ zero_zero_real )
| ( ord_less_real @ ( divide_divide_real @ SV115 @ SV237 ) @ zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(1039,plain,
! [SV238: real,SV116: real] :
( ( ! [SY668: real] :
( ~ ( ord_less_real @ SV116 @ SV238 )
| ~ ( ord_less_real @ SY668 @ zero_zero_real )
| ( ord_less_real @ ( divide_divide_real @ SV238 @ SY668 ) @ ( divide_divide_real @ SV116 @ SY668 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1040,plain,
! [SV239: nat > $o,SV117: nat] :
( ( ( ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) ) )
= ( ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(1041,plain,
! [SV240: nat,SV118: nat > real] :
( ( ! [SY671: nat] :
( ~ ! [SY546: nat] : ( ord_less_eq_real @ ( SV118 @ ( suc @ SY546 ) ) @ ( SV118 @ SY546 ) )
| ~ ( ord_less_eq_nat @ SV240 @ SY671 )
| ( ord_less_eq_real @ ( SV118 @ SY671 ) @ ( SV118 @ SV240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1042,plain,
! [SV241: nat,SV119: nat > nat] :
( ( ! [SY673: nat] :
( ~ ! [SY549: nat] : ( ord_less_eq_nat @ ( SV119 @ ( suc @ SY549 ) ) @ ( SV119 @ SY549 ) )
| ~ ( ord_less_eq_nat @ SV241 @ SY673 )
| ( ord_less_eq_nat @ ( SV119 @ SY673 ) @ ( SV119 @ SV241 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1043,plain,
! [SV242: real,SV120: real] :
( ( ! [SY675: real,SY676: real] :
( ~ ( ord_less_real @ zero_zero_real @ SV120 )
| ~ ( ord_less_eq_real @ SV120 @ SV242 )
| ~ ( ord_less_real @ zero_zero_real @ SY675 )
| ~ ( ord_less_real @ SY675 @ SY676 )
| ( ord_less_real @ ( divide_divide_real @ SV120 @ SY676 ) @ ( divide_divide_real @ SV242 @ SY675 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(1044,plain,
! [SV243: real,SV121: real] :
( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV121 )
| ~ ( ord_less_real @ SV243 @ zero_zero_real )
| ( ord_less_eq_real @ ( divide_divide_real @ SV121 @ SV243 ) @ zero_zero_real ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1045,plain,
! [SV244: nat,SV122: nat > $o] :
( ( ~ ( SV122 @ SV244 )
| ~ ~ ( SV122 @ zero_zero_nat )
| ~ ! [SY677: nat] :
~ ~ ( ~ ~ ( ~ ( ord_less_nat @ SY677 @ SV244 )
| ~ ! [SY556: nat] :
( ~ ( ord_less_eq_nat @ SY556 @ SY677 )
| ~ ( SV122 @ SY556 ) ) )
| ~ ( SV122 @ ( suc @ SY677 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1046,plain,
! [SV245: nat,SV123: nat] :
( ( ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
= ( ~ ! [SY679: nat] :
~ ~ ( ( SV245
!= ( suc @ SY679 ) )
| ~ ( ord_less_nat @ SV123 @ SY679 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1047,plain,
! [SV124: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV124 ) )
= $true )
| ( ( ~ ! [SY559: nat] :
( SV124
!= ( suc @ SY559 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[899]) ).
thf(1048,plain,
! [SV246: nat,SV125: nat] :
( ( ( ( suc @ SV125 )
!= ( suc @ SV246 ) )
| ( SV125 = SV246 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(1049,plain,
! [SV247: nat,SV126: nat] :
( ( ~ ( ord_less_nat @ SV126 @ SV247 )
| ~ ( ( ( suc @ SV126 )
!= SV247 ) )
| ( ord_less_nat @ ( suc @ SV126 ) @ SV247 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(1050,plain,
! [SV248: nat,SV127: nat] :
( ( ! [SY680: nat > nat > $o] :
( ~ ( ord_less_eq_nat @ SV127 @ SV248 )
| ~ ! [SX3: nat] : ( SY680 @ SX3 @ SX3 )
| ~ ! [SX3: nat,SX4: nat,SX5: nat] :
( ~ ( SY680 @ SX3 @ SX4 )
| ~ ( SY680 @ SX4 @ SX5 )
| ( SY680 @ SX3 @ SX5 ) )
| ~ ! [SX3: nat] : ( SY680 @ SX3 @ ( suc @ SX3 ) )
| ( SY680 @ SV127 @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(1051,plain,
! [SV249: real,SV128: real] :
( ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
= ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1052,plain,
! [SV129: nat] :
( ( SV129
= ( suc @ SV129 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[904]) ).
thf(1053,plain,
! [SV130: nat] :
( ( zero_zero_nat
= ( suc @ SV130 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[905]) ).
thf(1054,plain,
! [SV131: real] :
( ( ! [SY570: int] :
~ ( ord_less_real @ SV131 @ ( ring_1_of_int_real @ SY570 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[906]) ).
thf(1055,plain,
! [SV250: nat,SV132: nat] :
( ( ~ ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ SV132 )
| ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ SV132 @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(1056,plain,
! [SV251: nat,SV133: nat] :
( ( ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
= ( ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(1057,plain,
! [SV252: real,SV134: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ SV134 )
| ~ ( ord_less_real @ zero_zero_real @ SV252 )
| ~ ! [SY687: real] :
~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY687 )
| ( ( power_power_real @ SY687 @ SV134 )
!= SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1058,plain,
! [SV253: real,SV135: real] :
( ( ~ ( ord_less_eq_real @ SV135 @ zero_zero_real )
| ~ ( ord_less_real @ SV253 @ zero_zero_real )
| ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ SV135 @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1059,plain,
! [SV254: nat,SV136: real] :
( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV136 )
| ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ SV136 @ SV254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1060,plain,
! [SV255: nat,SV137: nat] :
( ( ~ ( ord_less_eq_nat @ SV137 @ SV255 )
| ( ord_less_eq_nat @ SV137 @ ( suc @ SV255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[912]) ).
thf(1061,plain,
! [SV138: nat] :
( ( zero_zero_nat
= ( suc @ SV138 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[913]) ).
thf(1062,plain,
! [SV256: real,SV139: real] :
( ( ! [SY688: real,SY689: real] :
( ~ ( ord_less_eq_real @ zero_zero_real @ SV139 )
| ~ ( ord_less_eq_real @ SV256 @ SV139 )
| ~ ( ord_less_real @ zero_zero_real @ SY688 )
| ~ ( ord_less_eq_real @ SY688 @ SY689 )
| ( ord_less_eq_real @ ( divide_divide_real @ SV256 @ SY689 ) @ ( divide_divide_real @ SV139 @ SY688 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1063,plain,
! [SV140: real] :
( ( ! [SY582: int] :
~ ( ord_less_real @ ( ring_1_of_int_real @ SY582 ) @ SV140 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[915]) ).
thf(1064,plain,
! [SV257: real,SV141: real] :
( ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
= ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1065,plain,
! [SV258: nat,SV142: nat] :
( ( ! [SY690: nat > $o] :
( ~ ( ord_less_eq_nat @ SV142 @ SV258 )
| ~ ( SY690 @ SV258 )
| ~ ! [SY691: nat] :
( ~ ( ord_less_eq_nat @ SV142 @ SY691 )
| ~ ( ord_less_nat @ SY691 @ SV258 )
| ~ ( SY690 @ ( suc @ SY691 ) )
| ( SY690 @ SY691 ) )
| ( SY690 @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1066,plain,
! [SV143: real] :
( ( ! [SY587: real] :
~ ( ord_less_real @ SY587 @ SV143 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(1067,plain,
! [SV259: nat,SV144: nat] :
( ( ~ ( ord_less_eq_nat @ ( suc @ SV144 ) @ SV259 )
| ( ord_less_eq_nat @ SV144 @ SV259 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1068,plain,
! [SV260: nat,SV145: nat] :
( ( ~ ~ ( ord_less_nat @ SV145 @ SV260 )
| ~ ( ord_less_nat @ SV145 @ ( suc @ SV260 ) )
| ( SV260 = SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1069,plain,
! [SV261: nat,SV146: nat] :
( ( ~ ( nthRoo1352626670d_root @ SV146 @ SV261 )
| ( SV146
= ( suc @ SV261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1070,plain,
! [SV147: nat] :
( ( ( suc @ SV147 )
= zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[922]) ).
thf(1071,plain,
! [SV148: nat] :
( ( ( ~ ( ( SV148 != zero_zero_nat ) ) )
= $true )
| ( ( ~ ! [SY591: nat] :
( SV148
!= ( suc @ SY591 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[923]) ).
thf(1072,plain,
! [SV262: int,SV149: nat,SV1: int] :
( ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ SV1 ) @ SV149 ) @ ( ring_1_of_int_real @ SV262 ) )
= ( ord_less_int @ ( power_power_int @ SV1 @ SV149 ) @ SV262 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1073,plain,
! [SV263: nat,SV150: int,SV2: int] :
( ( ( ord_less_real @ ( ring_1_of_int_real @ SV2 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV150 ) @ SV263 ) )
= ( ord_less_int @ SV2 @ ( power_power_int @ SV150 @ SV263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1074,plain,
! [SV264: int,SV152: nat,SV4: int] :
( ( ( ( power_power_real @ ( ring_1_of_int_real @ SV4 ) @ SV152 )
= ( ring_1_of_int_real @ SV264 ) )
= ( ( power_power_int @ SV4 @ SV152 )
= SV264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1075,plain,
! [SV265: nat,SV153: int,SV5: int] :
( ( ( ( ring_1_of_int_real @ SV5 )
= ( power_power_real @ ( ring_1_of_int_real @ SV153 ) @ SV265 ) )
= ( SV5
= ( power_power_int @ SV153 @ SV265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1076,plain,
! [SV154: int,SV6: int] :
( ( ~ ( ( ord_less_real @ ( ring_1_of_int_real @ SV6 ) @ ( ring_1_of_int_real @ SV154 ) )
| ( ord_less_int @ SV6 @ SV154 ) )
| ~ ( ~ ( ord_less_real @ ( ring_1_of_int_real @ SV6 ) @ ( ring_1_of_int_real @ SV154 ) )
| ~ ( ord_less_int @ SV6 @ SV154 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[929]) ).
thf(1077,plain,
! [SV154: int,SV6: int] :
( ( ( ord_less_real @ ( ring_1_of_int_real @ SV6 ) @ ( ring_1_of_int_real @ SV154 ) )
= ( ord_less_int @ SV6 @ SV154 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[929]) ).
thf(1078,plain,
! [SV155: int,SV7: int] :
( ( ~ ( ( ( ring_1_of_int_real @ SV7 )
= ( ring_1_of_int_real @ SV155 ) )
| ( SV7 = SV155 ) )
| ~ ( ( ( ring_1_of_int_real @ SV7 )
!= ( ring_1_of_int_real @ SV155 ) )
| ( SV7 != SV155 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[930]) ).
thf(1079,plain,
! [SV155: int,SV7: int] :
( ( ( ( ring_1_of_int_real @ SV7 )
= ( ring_1_of_int_real @ SV155 ) )
= ( SV7 = SV155 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[930]) ).
thf(1080,plain,
! [SV156: nat,SV8: nat] :
( ( ~ ( ( ( suc @ SV8 )
= ( suc @ SV156 ) )
| ( SV8 = SV156 ) )
| ~ ( ( ( suc @ SV8 )
!= ( suc @ SV156 ) )
| ( SV8 != SV156 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[931]) ).
thf(1081,plain,
! [SV156: nat,SV8: nat] :
( ( ( ( suc @ SV8 )
= ( suc @ SV156 ) )
= ( SV8 = SV156 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[931]) ).
thf(1082,plain,
! [SV157: nat,SV9: nat] :
( ( ~ ( ( ( suc @ SV9 )
= ( suc @ SV157 ) )
| ( SV9 = SV157 ) )
| ~ ( ( ( suc @ SV9 )
!= ( suc @ SV157 ) )
| ( SV9 != SV157 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[932]) ).
thf(1083,plain,
! [SV157: nat,SV9: nat] :
( ( ( ( suc @ SV9 )
= ( suc @ SV157 ) )
= ( SV9 = SV157 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[932]) ).
thf(1084,plain,
! [SV158: nat,SV10: nat] :
( ( ~ ( ( ord_less_nat @ ( suc @ SV10 ) @ ( suc @ SV158 ) )
| ( ord_less_nat @ SV10 @ SV158 ) )
| ~ ( ~ ( ord_less_nat @ ( suc @ SV10 ) @ ( suc @ SV158 ) )
| ~ ( ord_less_nat @ SV10 @ SV158 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[933]) ).
thf(1085,plain,
! [SV158: nat,SV10: nat] :
( ( ( ord_less_nat @ ( suc @ SV10 ) @ ( suc @ SV158 ) )
= ( ord_less_nat @ SV10 @ SV158 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[933]) ).
thf(1086,plain,
! [SV12: int] :
( ( ( ~ ( ( zero_zero_real
= ( ring_1_of_int_real @ SV12 ) )
| ( SV12 = zero_zero_int ) ) )
= $true )
| ( ( ~ ( ( zero_zero_real
!= ( ring_1_of_int_real @ SV12 ) )
| ( SV12 != zero_zero_int ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[938]) ).
thf(1087,plain,
! [SV13: int] :
( ( ( ~ ( ( ( ring_1_of_int_real @ SV13 )
= zero_zero_real )
| ( SV13 = zero_zero_int ) ) )
= $true )
| ( ( ~ ( ( ( ring_1_of_int_real @ SV13 )
!= zero_zero_real )
| ( SV13 != zero_zero_int ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[940]) ).
thf(1088,plain,
! [SV14: int] :
( ( ( ~ ( ( ord_less_real @ ( ring_1_of_int_real @ SV14 ) @ zero_zero_real )
| ( ord_less_int @ SV14 @ zero_zero_int ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( ring_1_of_int_real @ SV14 ) @ zero_zero_real )
| ~ ( ord_less_int @ SV14 @ zero_zero_int ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[942]) ).
thf(1089,plain,
! [SV15: int] :
( ( ( ~ ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ SV15 ) )
| ( ord_less_int @ zero_zero_int @ SV15 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ SV15 ) )
| ~ ( ord_less_int @ zero_zero_int @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[944]) ).
thf(1090,plain,
! [SV159: nat,SV16: nat] :
( ( ~ ( ~ ( ord_less_nat @ SV16 @ SV159 )
| ( ord_less_nat @ SV159 @ ( suc @ SV16 ) ) )
| ~ ( ~ ~ ( ord_less_nat @ SV16 @ SV159 )
| ~ ( ord_less_nat @ SV159 @ ( suc @ SV16 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[946]) ).
thf(1091,plain,
! [SV159: nat,SV16: nat] :
( ( ( ~ ( ord_less_nat @ SV16 @ SV159 ) )
= ( ord_less_nat @ SV159 @ ( suc @ SV16 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[946]) ).
thf(1092,plain,
! [SV160: nat,SV17: nat] :
( ( ~ ( ( ord_less_nat @ SV17 @ ( suc @ SV160 ) )
| ( ord_less_nat @ SV17 @ SV160 )
| ( SV17 = SV160 ) )
| ~ ( ~ ( ord_less_nat @ SV17 @ ( suc @ SV160 ) )
| ~ ( ( ord_less_nat @ SV17 @ SV160 )
| ( SV17 = SV160 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[947]) ).
thf(1093,plain,
! [SV160: nat,SV17: nat] :
( ( ( ord_less_nat @ SV17 @ ( suc @ SV160 ) )
= ( ( ord_less_nat @ SV17 @ SV160 )
| ( SV17 = SV160 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[947]) ).
thf(1094,plain,
! [SV161: nat,SV21: nat] :
( ( ~ ( ( ( power_power_nat @ SV21 @ SV161 )
= ( suc @ zero_zero_nat ) )
| ( SV161 = zero_zero_nat )
| ( SV21
= ( suc @ zero_zero_nat ) ) )
| ~ ( ( ( power_power_nat @ SV21 @ SV161 )
!= ( suc @ zero_zero_nat ) )
| ~ ( ( SV161 = zero_zero_nat )
| ( SV21
= ( suc @ zero_zero_nat ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[948]) ).
thf(1095,plain,
! [SV161: nat,SV21: nat] :
( ( ( ( power_power_nat @ SV21 @ SV161 )
= ( suc @ zero_zero_nat ) )
= ( ( SV161 = zero_zero_nat )
| ( SV21
= ( suc @ zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[948]) ).
thf(1096,plain,
! [SV27: nat] :
( ( ( ~ ( ( ord_less_nat @ SV27 @ ( suc @ zero_zero_nat ) )
| ( SV27 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV27 @ ( suc @ zero_zero_nat ) )
| ( SV27 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[949]) ).
thf(1097,plain,
! [SV162: int,SV28: int] :
( ( ~ ( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV28 ) @ ( ring_1_of_int_real @ SV162 ) )
| ( ord_less_eq_int @ SV28 @ SV162 ) )
| ~ ( ~ ( ord_less_eq_real @ ( ring_1_of_int_real @ SV28 ) @ ( ring_1_of_int_real @ SV162 ) )
| ~ ( ord_less_eq_int @ SV28 @ SV162 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[951]) ).
thf(1098,plain,
! [SV162: int,SV28: int] :
( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV28 ) @ ( ring_1_of_int_real @ SV162 ) )
= ( ord_less_eq_int @ SV28 @ SV162 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[951]) ).
thf(1099,plain,
! [SV266: int,SV163: nat,SV29: int] :
( ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ SV29 ) @ SV163 ) @ ( ring_1_of_int_real @ SV266 ) )
= ( ord_less_eq_int @ ( power_power_int @ SV29 @ SV163 ) @ SV266 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1100,plain,
! [SV267: nat,SV164: int,SV30: int] :
( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV30 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV164 ) @ SV267 ) )
= ( ord_less_eq_int @ SV30 @ ( power_power_int @ SV164 @ SV267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1101,plain,
! [SV268: nat,SV165: real,SV31: real] :
( ( ( power_power_real @ ( divide_divide_real @ SV31 @ SV165 ) @ SV268 )
= ( divide_divide_real @ ( power_power_real @ SV31 @ SV268 ) @ ( power_power_real @ SV165 @ SV268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1102,plain,
! [SV166: nat,SV32: nat] :
( ( ~ ( ( ord_less_eq_nat @ ( suc @ SV32 ) @ ( suc @ SV166 ) )
| ( ord_less_eq_nat @ SV32 @ SV166 ) )
| ~ ( ~ ( ord_less_eq_nat @ ( suc @ SV32 ) @ ( suc @ SV166 ) )
| ~ ( ord_less_eq_nat @ SV32 @ SV166 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[955]) ).
thf(1103,plain,
! [SV166: nat,SV32: nat] :
( ( ( ord_less_eq_nat @ ( suc @ SV32 ) @ ( suc @ SV166 ) )
= ( ord_less_eq_nat @ SV32 @ SV166 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[955]) ).
thf(1104,plain,
! [SV167: nat,SV33: nat] :
( ( ~ ( ~ ( ord_less_eq_nat @ SV33 @ SV167 )
| ( ord_less_eq_nat @ ( suc @ SV167 ) @ SV33 ) )
| ~ ( ~ ~ ( ord_less_eq_nat @ SV33 @ SV167 )
| ~ ( ord_less_eq_nat @ ( suc @ SV167 ) @ SV33 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[956]) ).
thf(1105,plain,
! [SV167: nat,SV33: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV33 @ SV167 ) )
= ( ord_less_eq_nat @ ( suc @ SV167 ) @ SV33 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[956]) ).
thf(1106,plain,
! [SV168: nat,SV35: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV35 @ ( suc @ SV168 ) )
| ( ord_less_eq_nat @ SV35 @ SV168 )
| ( SV35
= ( suc @ SV168 ) ) )
| ~ ( ~ ( ord_less_eq_nat @ SV35 @ ( suc @ SV168 ) )
| ~ ( ( ord_less_eq_nat @ SV35 @ SV168 )
| ( SV35
= ( suc @ SV168 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[958]) ).
thf(1107,plain,
! [SV168: nat,SV35: nat] :
( ( ( ord_less_eq_nat @ SV35 @ ( suc @ SV168 ) )
= ( ( ord_less_eq_nat @ SV35 @ SV168 )
| ( SV35
= ( suc @ SV168 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[958]) ).
thf(1108,plain,
! [SV169: nat] :
( ( ! [SV269: nat] :
( ( nthRoo1352626670d_root @ SV169 @ SV269 )
= ( SV169
= ( suc @ SV269 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[959]) ).
thf(1109,plain,
! [SV169: nat] :
( ( ( nthRoo1352626670d_root @ SV169 )
= ( ^ [SY599: nat] :
( SV169
= ( suc @ SY599 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[959]) ).
thf(1110,plain,
! [SV170: nat,SV37: nat] :
( ( ~ ( ( ord_less_eq_nat @ ( suc @ SV37 ) @ SV170 )
| ( ord_less_nat @ SV37 @ SV170 ) )
| ~ ( ~ ( ord_less_eq_nat @ ( suc @ SV37 ) @ SV170 )
| ~ ( ord_less_nat @ SV37 @ SV170 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[960]) ).
thf(1111,plain,
! [SV170: nat,SV37: nat] :
( ( ( ord_less_eq_nat @ ( suc @ SV37 ) @ SV170 )
= ( ord_less_nat @ SV37 @ SV170 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[960]) ).
thf(1112,plain,
! [SV171: nat,SV38: nat] :
( ( ~ ( ( ord_less_nat @ SV38 @ ( suc @ SV171 ) )
| ( ord_less_eq_nat @ SV38 @ SV171 ) )
| ~ ( ~ ( ord_less_nat @ SV38 @ ( suc @ SV171 ) )
| ~ ( ord_less_eq_nat @ SV38 @ SV171 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[961]) ).
thf(1113,plain,
! [SV171: nat,SV38: nat] :
( ( ( ord_less_nat @ SV38 @ ( suc @ SV171 ) )
= ( ord_less_eq_nat @ SV38 @ SV171 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[961]) ).
thf(1114,plain,
! [SV172: nat] :
( ( ! [SV270: nat] :
( ( ord_less_nat @ SV172 @ SV270 )
= ( ord_less_eq_nat @ ( suc @ SV172 ) @ SV270 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[962]) ).
thf(1115,plain,
! [SV172: nat] :
( ( ( ord_less_nat @ SV172 )
= ( ord_less_eq_nat @ ( suc @ SV172 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[962]) ).
thf(1116,plain,
! [SV174: nat,SV42: nat] :
( ( ( SV42
!= ( suc @ SV174 ) )
= $true )
| ( ( nthRoo1352626670d_root @ SV42 @ SV174 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[964]) ).
thf(1117,plain,
! [SV271: real,SV175: real,SV43: real] :
( ( ~ ( ord_less_real @ SV43 @ SV175 )
| ~ ( ord_less_real @ zero_zero_real @ SV271 )
| ( ord_less_real @ ( divide_divide_real @ SV43 @ SV271 ) @ ( divide_divide_real @ SV175 @ SV271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1118,plain,
! [SV176: real,SV44: real] :
( ( ( ~ ( ord_less_eq_real @ SV44 @ zero_zero_real ) )
= $true )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV176 )
| ( ord_less_eq_real @ ( divide_divide_real @ SV44 @ SV176 ) @ zero_zero_real ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[966]) ).
thf(1119,plain,
! [SV45: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ SV45 )
| ~ ! [SY405: nat] :
( SV45
!= ( suc @ SY405 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV45 )
| ~ ~ ! [SY405: nat] :
( SV45
!= ( suc @ SY405 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[967]) ).
thf(1120,plain,
! [SV177: nat,SV46: nat] :
( ( ( ~ ( ord_less_nat @ ( suc @ SV46 ) @ SV177 ) )
= $true )
| ( ( ord_less_nat @ SV46 @ SV177 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[969]) ).
thf(1121,plain,
! [SV178: nat > $o,SV47: nat] :
( ( ~ ( ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) )
| ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) )
| ~ ( ~ ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) )
| ~ ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[970]) ).
thf(1122,plain,
! [SV178: nat > $o,SV47: nat] :
( ( ( ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) ) )
= ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[970]) ).
thf(1123,plain,
! [SV179: nat,SV48: nat] :
( ( ( ~ ( ord_less_nat @ SV48 @ SV179 ) )
= $true )
| ( ( ord_less_nat @ SV48 @ ( suc @ SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[971]) ).
thf(1124,plain,
! [SV272: real,SV180: nat,SV49: real] :
( ( ~ ( ord_less_real @ ( power_power_real @ SV49 @ SV180 ) @ ( power_power_real @ SV272 @ SV180 ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ SV272 )
| ( ord_less_real @ SV49 @ SV272 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1125,plain,
! [SV273: nat,SV181: nat,SV50: nat] :
( ( ( ( power_power_nat @ SV50 @ ( suc @ SV181 ) )
!= ( power_power_nat @ SV273 @ ( suc @ SV181 ) ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV50 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV273 )
| ( SV50 = SV273 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1126,plain,
! [SV274: real,SV182: real,SV51: real] :
( ( ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
= ( ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1127,plain,
! [SV275: nat > $o,SV183: nat,SV52: nat] :
( ( ~ ( ord_less_eq_nat @ SV52 @ SV183 )
| ~ ( SV275 @ SV52 )
| ~ ! [SY692: nat] :
( ~ ( ord_less_eq_nat @ SV52 @ SY692 )
| ~ ( SV275 @ SY692 )
| ( SV275 @ ( suc @ SY692 ) ) )
| ( SV275 @ SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1128,plain,
! [SV184: nat,SV53: nat > $o] :
( ( ( ~ ! [SY421: nat] :
( ~ ! [SY422: nat] :
( ~ ( ord_less_eq_nat @ ( suc @ SY422 ) @ SY421 )
| ( SV53 @ SY422 ) )
| ( SV53 @ SY421 ) ) )
= $true )
| ( ( SV53 @ SV184 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[976]) ).
thf(1129,plain,
! [SV276: real,SV185: real,SV54: real] :
( ( ! [SY693: real] :
( ~ ( ord_less_eq_real @ zero_zero_real @ SV54 )
| ~ ( ord_less_real @ SV54 @ SV185 )
| ~ ( ord_less_real @ zero_zero_real @ SV276 )
| ~ ( ord_less_eq_real @ SV276 @ SY693 )
| ( ord_less_real @ ( divide_divide_real @ SV54 @ SY693 ) @ ( divide_divide_real @ SV185 @ SV276 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1130,plain,
! [SV277: nat,SV186: nat,SV55: nat > int] :
( ( ~ ! [SY428: nat] : ( ord_less_eq_int @ ( SV55 @ SY428 ) @ ( SV55 @ ( suc @ SY428 ) ) )
| ~ ( ord_less_eq_nat @ SV186 @ SV277 )
| ( ord_less_eq_int @ ( SV55 @ SV186 ) @ ( SV55 @ SV277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1131,plain,
! [SV187: nat,SV56: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV56 @ ( suc @ SV187 ) ) )
= $true )
| ( ( ~ ~ ( ord_less_eq_nat @ SV56 @ SV187 )
| ( SV56
= ( suc @ SV187 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[979]) ).
thf(1132,plain,
! [SV188: nat,SV57: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV57 @ SV188 ) )
= $true )
| ( ( ord_less_nat @ SV57 @ ( suc @ SV188 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[980]) ).
thf(1133,plain,
! [SV58: real] :
( ( ~ ( ord_less_real @ SV58 @ ( sK1_SY431 @ SV58 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[981]) ).
thf(1134,plain,
! [SV278: nat,SV189: nat,SV59: nat > real] :
( ( ~ ! [SY434: nat] : ( ord_less_eq_real @ ( SV59 @ SY434 ) @ ( SV59 @ ( suc @ SY434 ) ) )
| ~ ( ord_less_eq_nat @ SV189 @ SV278 )
| ( ord_less_eq_real @ ( SV59 @ SV189 ) @ ( SV59 @ SV278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1135,plain,
! [SV190: nat,SV60: real] :
( ( ( ~ ( ( SV60 != zero_zero_real ) ) )
= $true )
| ( ( ( power_power_real @ SV60 @ SV190 )
!= zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[983]) ).
thf(1136,plain,
! [SV191: nat,SV61: real] :
( ( ~ ( ( ( power_power_real @ SV61 @ SV191 )
= zero_zero_real )
| ~ ( ( SV61 != zero_zero_real )
| ~ ( ord_less_nat @ zero_zero_nat @ SV191 ) ) )
| ~ ( ( ( power_power_real @ SV61 @ SV191 )
!= zero_zero_real )
| ~ ~ ( ( SV61 != zero_zero_real )
| ~ ( ord_less_nat @ zero_zero_nat @ SV191 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[984]) ).
thf(1137,plain,
! [SV191: nat,SV61: real] :
( ( ( ( power_power_real @ SV61 @ SV191 )
= zero_zero_real )
= ( ~ ( ( SV61 != zero_zero_real )
| ~ ( ord_less_nat @ zero_zero_nat @ SV191 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[984]) ).
thf(1138,plain,
! [SV192: real,SV62: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV62 ) )
= $true )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV192 )
| ~ ! [SY616: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY616 )
| ( ( power_power_real @ SY616 @ SV62 )
!= SV192 ) )
| ~ ! [SY617: real] :
( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY617 )
| ( ( power_power_real @ SY617 @ SV62 )
!= SV192 ) )
| ( SY617 = SY616 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[985]) ).
thf(1139,plain,
! [SV279: real,SV193: nat,SV63: real] :
( ( ~ ( ord_less_eq_real @ ( power_power_real @ SV63 @ ( suc @ SV193 ) ) @ ( power_power_real @ SV279 @ ( suc @ SV193 ) ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ SV279 )
| ( ord_less_eq_real @ SV63 @ SV279 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1140,plain,
! [SV280: nat,SV194: nat,SV64: nat > nat] :
( ( ~ ! [SY444: nat] : ( ord_less_nat @ ( SV64 @ SY444 ) @ ( SV64 @ ( suc @ SY444 ) ) )
| ~ ( ord_less_nat @ SV194 @ SV280 )
| ( ord_less_nat @ ( SV64 @ SV194 ) @ ( SV64 @ SV280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1141,plain,
! [SV65: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV65 )
= $false )
| ( ( ( power_power_real @ zero_zero_real @ SV65 )
= zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[988]) ).
thf(1142,plain,
! [SV195: nat,SV66: nat] :
( ( ( ~ ( ord_less_nat @ ( suc @ SV66 ) @ ( suc @ SV195 ) ) )
= $true )
| ( ( ord_less_nat @ SV66 @ SV195 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[989]) ).
thf(1143,plain,
! [SV196: nat,SV67: nat] :
( ( ( ~ ( ord_less_nat @ SV67 @ ( suc @ SV196 ) ) )
= $true )
| ( ( ~ ~ ( ord_less_nat @ SV67 @ SV196 )
| ( SV67 = SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[990]) ).
thf(1144,plain,
! [SV281: nat,SV197: nat,SV68: nat > int] :
( ( ~ ! [SY449: nat] : ( ord_less_int @ ( SV68 @ SY449 ) @ ( SV68 @ ( suc @ SY449 ) ) )
| ( ( ord_less_int @ ( SV68 @ SV197 ) @ ( SV68 @ SV281 ) )
= ( ord_less_nat @ SV197 @ SV281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1145,plain,
! [SV198: nat,SV69: nat] :
( ( ( ~ ( ord_less_nat @ SV69 @ SV198 ) )
= $true )
| ( ( ~ ( ( SV198
!= ( suc @ SV69 ) ) )
| ~ ! [SY623: nat] :
( ~ ( ord_less_nat @ SV69 @ SY623 )
| ( SV198
!= ( suc @ SY623 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[992]) ).
thf(1146,plain,
! [SV199: nat,SV70: nat > $o] :
( ( ( ~ ( SV70 @ zero_zero_nat ) )
= $true )
| ( ( ~ ! [SY453: nat] :
( ~ ( SV70 @ SY453 )
| ( SV70 @ ( suc @ SY453 ) ) )
| ( SV70 @ SV199 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[993]) ).
thf(1147,plain,
! [SV71: int] :
( ( ( ord_less_int @ zero_zero_int @ SV71 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[994]) ).
thf(1148,plain,
! [SV200: real,SV72: real] :
( ( ( ~ ( ord_less_real @ SV72 @ zero_zero_real ) )
= $true )
| ( ( ~ ( ord_less_real @ SV200 @ zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV72 @ SV200 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[995]) ).
thf(1149,plain,
! [SV282: nat,SV201: nat,SV73: nat > nat] :
( ( ~ ! [SY457: nat] : ( ord_less_nat @ ( SV73 @ SY457 ) @ ( SV73 @ ( suc @ SY457 ) ) )
| ( ( ord_less_nat @ ( SV73 @ SV201 ) @ ( SV73 @ SV282 ) )
= ( ord_less_nat @ SV201 @ SV282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1150,plain,
! [SV202: nat,SV74: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV74 ) )
= $true )
| ( ( ~ ! [SY627: real] :
~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY627 )
| ( ( power_power_real @ SY627 @ ( suc @ SV202 ) )
!= SV74 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[997]) ).
thf(1151,plain,
! [SV203: nat,SV75: nat] :
( ( ( ~ ( ord_less_nat @ SV75 @ SV203 ) )
= $true )
| ( ( ord_less_nat @ ( suc @ SV75 ) @ ( suc @ SV203 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[998]) ).
thf(1152,plain,
! [SV204: nat,SV76: nat] :
( ( ( ~ ( ord_less_nat @ ( suc @ SV76 ) @ SV204 ) )
= $true )
| ( ( ~ ! [SY628: nat] :
( ~ ( ord_less_nat @ SV76 @ SY628 )
| ( SV204
!= ( suc @ SY628 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[999]) ).
thf(1153,plain,
! [SV283: real,SV205: nat,SV77: real] :
( ( ( ( power_power_real @ SV77 @ ( suc @ SV205 ) )
!= ( power_power_real @ SV283 @ ( suc @ SV205 ) ) )
| ~ ( ord_less_eq_real @ zero_zero_real @ SV77 )
| ~ ( ord_less_eq_real @ zero_zero_real @ SV283 )
| ( SV77 = SV283 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1154,plain,
! [SV284: nat > $o,SV206: nat,SV78: nat] :
( ( ~ ( ord_less_nat @ SV78 @ SV206 )
| ~ ! [SY699: nat] :
( ( SV206
!= ( suc @ SY699 ) )
| ( SV284 @ SY699 ) )
| ~ ! [SY700: nat] :
( ~ ( ord_less_nat @ SY700 @ SV206 )
| ~ ( SV284 @ ( suc @ SY700 ) )
| ( SV284 @ SY700 ) )
| ( SV284 @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1155,plain,
! [SV285: nat > nat > $o,SV207: nat,SV79: nat] :
( ( ~ ( ord_less_nat @ SV79 @ SV207 )
| ~ ! [SY701: nat] : ( SV285 @ SY701 @ ( suc @ SY701 ) )
| ~ ! [SY702: nat,SY703: nat,SY704: nat] :
( ~ ( ord_less_nat @ SY702 @ SY703 )
| ~ ( ord_less_nat @ SY703 @ SY704 )
| ~ ( SV285 @ SY702 @ SY703 )
| ~ ( SV285 @ SY703 @ SY704 )
| ( SV285 @ SY702 @ SY704 ) )
| ( SV285 @ SV79 @ SV207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1156,plain,
! [SV80: nat] :
( ( ( SV80 != zero_zero_nat )
= $false )
| ( ( ~ ! [SY475: nat] :
( SV80
!= ( suc @ SY475 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1003]) ).
thf(1157,plain,
! [SV286: nat,SV208: nat,SV81: nat > nat] :
( ( ~ ! [SY478: nat] : ( ord_less_eq_nat @ ( SV81 @ SY478 ) @ ( SV81 @ ( suc @ SY478 ) ) )
| ~ ( ord_less_eq_nat @ SV208 @ SV286 )
| ( ord_less_eq_nat @ ( SV81 @ SV208 ) @ ( SV81 @ SV286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1158,plain,
! [SV287: nat > $o,SV209: nat,SV82: nat] :
( ( ~ ( ord_less_eq_nat @ SV82 @ SV209 )
| ~ ( SV287 @ SV82 )
| ~ ! [SY706: nat] :
( ~ ( ord_less_eq_nat @ SV82 @ SY706 )
| ~ ( ord_less_nat @ SY706 @ SV209 )
| ~ ( SV287 @ SY706 )
| ( SV287 @ ( suc @ SY706 ) ) )
| ( SV287 @ SV209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1159,plain,
! [SV210: nat,SV83: nat] :
( ( ( ~ ( ord_less_nat @ ( suc @ zero_zero_nat ) @ SV83 ) )
= $true )
| ( ( ord_less_nat @ SV210 @ ( power_power_nat @ SV83 @ SV210 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1006]) ).
thf(1160,plain,
! [SV211: real,SV84: real] :
( ( ( ~ ( ord_less_real @ SV84 @ zero_zero_real ) )
= $true )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV211 )
| ( ord_less_real @ ( divide_divide_real @ SV84 @ SV211 ) @ zero_zero_real ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1007]) ).
thf(1161,plain,
! [SV288: nat,SV212: nat,SV85: nat > nat > $o] :
( ( ~ ! [SY486: nat] : ( SV85 @ SY486 @ zero_zero_nat )
| ~ ! [SY487: nat] : ( SV85 @ zero_zero_nat @ ( suc @ SY487 ) )
| ~ ! [SY488: nat,SY489: nat] :
( ~ ( SV85 @ SY488 @ SY489 )
| ( SV85 @ ( suc @ SY488 ) @ ( suc @ SY489 ) ) )
| ( SV85 @ SV212 @ SV288 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1162,plain,
! [SV289: nat,SV213: nat,SV86: nat > int] :
( ( ~ ! [SY492: nat] : ( ord_less_int @ ( SV86 @ SY492 ) @ ( SV86 @ ( suc @ SY492 ) ) )
| ~ ( ord_less_nat @ SV213 @ SV289 )
| ( ord_less_int @ ( SV86 @ SV213 ) @ ( SV86 @ SV289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1163,plain,
! [SV214: nat > $o,SV87: nat] :
( ( ~ ( ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) )
| ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) )
| ~ ( ~ ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) )
| ~ ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1010]) ).
thf(1164,plain,
! [SV214: nat > $o,SV87: nat] :
( ( ( ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) ) )
= ( ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1010]) ).
thf(1165,plain,
! [SV290: nat,SV215: nat,SV88: nat > real] :
( ( ~ ! [SY498: nat] : ( ord_less_real @ ( SV88 @ SY498 ) @ ( SV88 @ ( suc @ SY498 ) ) )
| ~ ( ord_less_nat @ SV215 @ SV290 )
| ( ord_less_real @ ( SV88 @ SV215 ) @ ( SV88 @ SV290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1166,plain,
! [SV291: int,SV216: nat,SV89: int] :
( ( ( ( power_power_int @ SV89 @ ( suc @ SV216 ) )
!= ( power_power_int @ SV291 @ ( suc @ SV216 ) ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV89 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV291 )
| ( SV89 = SV291 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1167,plain,
! [SV292: nat,SV217: nat,SV91: nat > int] :
( ( ~ ! [SY503: nat] : ( ord_less_eq_int @ ( SV91 @ ( suc @ SY503 ) ) @ ( SV91 @ SY503 ) )
| ~ ( ord_less_eq_nat @ SV217 @ SV292 )
| ( ord_less_eq_int @ ( SV91 @ SV292 ) @ ( SV91 @ SV217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1168,plain,
! [SV218: real,SV92: real] :
( ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV92 ) )
= $true )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV218 )
| ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ SV92 @ SV218 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1015]) ).
thf(1169,plain,
! [SV293: nat,SV219: nat,SV93: nat] :
( ( ~ ( ord_less_nat @ SV93 @ SV219 )
| ~ ( ord_less_nat @ SV219 @ SV293 )
| ( ord_less_nat @ ( suc @ SV93 ) @ SV293 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1170,plain,
! [SV220: nat,SV94: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( suc @ SV94 ) @ SV220 ) )
= $true )
| ( ( ord_less_nat @ SV94 @ SV220 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1017]) ).
thf(1171,plain,
! [SV221: nat,SV95: nat] :
( ( ( SV95
!= ( suc @ SV221 ) )
= $true )
| ( ( SV95 != zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1018]) ).
thf(1172,plain,
! [SV222: nat,SV97: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV97 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ SV97 @ SV222 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1020]) ).
thf(1173,plain,
! [SV223: real,SV98: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV98 ) )
= $true )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV223 )
| ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV98 @ SV223 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1021]) ).
thf(1174,plain,
! [SV294: nat,SV224: nat,SV99: nat] :
( ( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV99 @ ( suc @ SV224 ) ) @ ( power_power_nat @ SV294 @ ( suc @ SV224 ) ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV294 )
| ( ord_less_eq_nat @ SV99 @ SV294 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1175,plain,
! [SV225: nat,SV100: nat] :
( ( ( ~ ( ord_less_nat @ SV100 @ SV225 ) )
= $true )
| ( ( ord_less_eq_nat @ ( suc @ SV100 ) @ SV225 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1023]) ).
thf(1176,plain,
! [SV295: int,SV226: nat,SV101: int] :
( ( ~ ( ord_less_eq_int @ ( power_power_int @ SV101 @ ( suc @ SV226 ) ) @ ( power_power_int @ SV295 @ ( suc @ SV226 ) ) )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV295 )
| ( ord_less_eq_int @ SV101 @ SV295 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1177,plain,
! [SV296: nat,SV227: real,SV102: real] :
( ( ~ ( ord_less_eq_real @ SV102 @ SV227 )
| ~ ( ord_less_eq_real @ zero_zero_real @ SV102 )
| ( ord_less_eq_real @ ( power_power_real @ SV102 @ SV296 ) @ ( power_power_real @ SV227 @ SV296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1178,plain,
! [SV297: real,SV228: real,SV103: real] :
( ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
= ( ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1179,plain,
! [SV229: nat,SV104: nat] :
( ( ( ~ ~ ( ord_less_nat @ SV104 @ SV229 ) )
= $true )
| ( ( ( ord_less_nat @ SV104 @ ( suc @ SV229 ) )
= ( SV104 = SV229 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1027]) ).
thf(1180,plain,
! [SV298: nat,SV230: nat,SV106: nat > real] :
( ( ~ ! [SY523: nat] : ( ord_less_real @ ( SV106 @ SY523 ) @ ( SV106 @ ( suc @ SY523 ) ) )
| ( ( ord_less_real @ ( SV106 @ SV230 ) @ ( SV106 @ SV298 ) )
= ( ord_less_nat @ SV230 @ SV298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1181,plain,
! [SV231: nat,SV107: nat > $o] :
( ( ( ~ ( SV107 @ SV231 ) )
= $true )
| ( ( ~ ! [SY525: nat] :
( ~ ( SV107 @ ( suc @ SY525 ) )
| ( SV107 @ SY525 ) )
| ( SV107 @ zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1030]) ).
thf(1182,plain,
! [SV108: real] :
( ( ~ ( ord_less_eq_real @ SV108 @ ( ring_1_of_int_real @ ( sK2_SY526 @ SV108 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1031]) ).
thf(1183,plain,
! [SV232: nat,SV109: nat > $o] :
( ( ( ~ ( SV109 @ zero_zero_nat ) )
= $true )
| ( ( ~ ! [SY528: nat] :
( ~ ( SV109 @ SY528 )
| ( SV109 @ ( suc @ SY528 ) ) )
| ( SV109 @ SV232 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1032]) ).
thf(1184,plain,
! [SV233: nat > $o,SV110: nat] :
( ( ~ ( ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) )
| ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) )
| ~ ( ~ ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) )
| ~ ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1033]) ).
thf(1185,plain,
! [SV233: nat > $o,SV110: nat] :
( ( ( ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) ) )
= ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1033]) ).
thf(1186,plain,
! [SV234: nat,SV111: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( suc @ SV111 ) @ SV234 ) )
= $true )
| ( ( ~ ! [SY667: nat] :
( SV234
!= ( suc @ SY667 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1034]) ).
thf(1187,plain,
! [SV235: real,SV112: real] :
( ( ( ~ ( ( SV112 != SV235 ) ) )
= $true )
| ( ( ~ ~ ( ord_less_real @ SV112 @ SV235 )
| ( ord_less_real @ SV235 @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1035]) ).
thf(1188,plain,
! [SV113: nat > $o] :
( ( ( ~ ( SV113 @ zero_zero_nat ) )
= $false )
| ( ( ~ ~ ! [SY535: nat] :
~ ( SV113 @ SY535 )
| ~ ! [SY536: nat] :
~ ~ ( ~ ~ ( SV113 @ SY536 )
| ~ ( SV113 @ ( suc @ SY536 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1036]) ).
thf(1189,plain,
! [SV236: nat,SV114: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV114 @ SV236 ) )
= $true )
| ( ( ( ord_less_nat @ SV236 @ ( suc @ SV114 ) )
= ( SV236 = SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1037]) ).
thf(1190,plain,
! [SV237: real,SV115: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV115 ) )
= $true )
| ( ( ~ ( ord_less_real @ SV237 @ zero_zero_real )
| ( ord_less_real @ ( divide_divide_real @ SV115 @ SV237 ) @ zero_zero_real ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1038]) ).
thf(1191,plain,
! [SV299: real,SV238: real,SV116: real] :
( ( ~ ( ord_less_real @ SV116 @ SV238 )
| ~ ( ord_less_real @ SV299 @ zero_zero_real )
| ( ord_less_real @ ( divide_divide_real @ SV238 @ SV299 ) @ ( divide_divide_real @ SV116 @ SV299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1192,plain,
! [SV239: nat > $o,SV117: nat] :
( ( ~ ( ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) )
| ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) )
| ~ ( ~ ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) )
| ~ ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1040]) ).
thf(1193,plain,
! [SV239: nat > $o,SV117: nat] :
( ( ( ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) ) )
= ( ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1040]) ).
thf(1194,plain,
! [SV300: nat,SV240: nat,SV118: nat > real] :
( ( ~ ! [SY546: nat] : ( ord_less_eq_real @ ( SV118 @ ( suc @ SY546 ) ) @ ( SV118 @ SY546 ) )
| ~ ( ord_less_eq_nat @ SV240 @ SV300 )
| ( ord_less_eq_real @ ( SV118 @ SV300 ) @ ( SV118 @ SV240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1195,plain,
! [SV301: nat,SV241: nat,SV119: nat > nat] :
( ( ~ ! [SY549: nat] : ( ord_less_eq_nat @ ( SV119 @ ( suc @ SY549 ) ) @ ( SV119 @ SY549 ) )
| ~ ( ord_less_eq_nat @ SV241 @ SV301 )
| ( ord_less_eq_nat @ ( SV119 @ SV301 ) @ ( SV119 @ SV241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1196,plain,
! [SV302: real,SV242: real,SV120: real] :
( ( ! [SY717: real] :
( ~ ( ord_less_real @ zero_zero_real @ SV120 )
| ~ ( ord_less_eq_real @ SV120 @ SV242 )
| ~ ( ord_less_real @ zero_zero_real @ SV302 )
| ~ ( ord_less_real @ SV302 @ SY717 )
| ( ord_less_real @ ( divide_divide_real @ SV120 @ SY717 ) @ ( divide_divide_real @ SV242 @ SV302 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1197,plain,
! [SV243: real,SV121: real] :
( ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV121 ) )
= $true )
| ( ( ~ ( ord_less_real @ SV243 @ zero_zero_real )
| ( ord_less_eq_real @ ( divide_divide_real @ SV121 @ SV243 ) @ zero_zero_real ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1044]) ).
thf(1198,plain,
! [SV244: nat,SV122: nat > $o] :
( ( ( ~ ( SV122 @ SV244 ) )
= $true )
| ( ( ~ ~ ( SV122 @ zero_zero_nat )
| ~ ! [SY677: nat] :
~ ~ ( ~ ~ ( ~ ( ord_less_nat @ SY677 @ SV244 )
| ~ ! [SY556: nat] :
( ~ ( ord_less_eq_nat @ SY556 @ SY677 )
| ~ ( SV122 @ SY556 ) ) )
| ~ ( SV122 @ ( suc @ SY677 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1045]) ).
thf(1199,plain,
! [SV245: nat,SV123: nat] :
( ( ~ ( ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
| ~ ! [SY679: nat] :
~ ~ ( ( SV245
!= ( suc @ SY679 ) )
| ~ ( ord_less_nat @ SV123 @ SY679 ) ) )
| ~ ( ~ ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
| ~ ~ ! [SY679: nat] :
~ ~ ( ( SV245
!= ( suc @ SY679 ) )
| ~ ( ord_less_nat @ SV123 @ SY679 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1046]) ).
thf(1200,plain,
! [SV245: nat,SV123: nat] :
( ( ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
= ( ~ ! [SY679: nat] :
~ ~ ( ( SV245
!= ( suc @ SY679 ) )
| ~ ( ord_less_nat @ SV123 @ SY679 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1046]) ).
thf(1201,plain,
! [SV124: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV124 )
= $false )
| ( ( ~ ! [SY559: nat] :
( SV124
!= ( suc @ SY559 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1047]) ).
thf(1202,plain,
! [SV246: nat,SV125: nat] :
( ( ( ( suc @ SV125 )
!= ( suc @ SV246 ) )
= $true )
| ( ( SV125 = SV246 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1048]) ).
thf(1203,plain,
! [SV247: nat,SV126: nat] :
( ( ( ~ ( ord_less_nat @ SV126 @ SV247 ) )
= $true )
| ( ( ~ ( ( ( suc @ SV126 )
!= SV247 ) )
| ( ord_less_nat @ ( suc @ SV126 ) @ SV247 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1049]) ).
thf(1204,plain,
! [SV303: nat > nat > $o,SV248: nat,SV127: nat] :
( ( ~ ( ord_less_eq_nat @ SV127 @ SV248 )
| ~ ! [SY718: nat] : ( SV303 @ SY718 @ SY718 )
| ~ ! [SY719: nat,SY720: nat,SY721: nat] :
( ~ ( SV303 @ SY719 @ SY720 )
| ~ ( SV303 @ SY720 @ SY721 )
| ( SV303 @ SY719 @ SY721 ) )
| ~ ! [SY722: nat] : ( SV303 @ SY722 @ ( suc @ SY722 ) )
| ( SV303 @ SV127 @ SV248 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1205,plain,
! [SV249: real,SV128: real] :
( ( ~ ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
| ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) )
| ~ ( ~ ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1051]) ).
thf(1206,plain,
! [SV249: real,SV128: real] :
( ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
= ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1051]) ).
thf(1207,plain,
! [SV131: real] :
( ( ~ ( ord_less_real @ SV131 @ ( ring_1_of_int_real @ ( sK3_SY570 @ SV131 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1054]) ).
thf(1208,plain,
! [SV250: nat,SV132: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ SV132 ) )
= $true )
| ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ SV132 @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1055]) ).
thf(1209,plain,
! [SV251: nat,SV133: nat] :
( ( ~ ( ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
| ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) )
| ~ ( ~ ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
| ~ ( ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1056]) ).
thf(1210,plain,
! [SV251: nat,SV133: nat] :
( ( ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
= ( ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1056]) ).
thf(1211,plain,
! [SV252: real,SV134: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV134 ) )
= $true )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV252 )
| ~ ! [SY687: real] :
~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY687 )
| ( ( power_power_real @ SY687 @ SV134 )
!= SV252 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1057]) ).
thf(1212,plain,
! [SV253: real,SV135: real] :
( ( ( ~ ( ord_less_eq_real @ SV135 @ zero_zero_real ) )
= $true )
| ( ( ~ ( ord_less_real @ SV253 @ zero_zero_real )
| ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ SV135 @ SV253 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1058]) ).
thf(1213,plain,
! [SV254: nat,SV136: real] :
( ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV136 ) )
= $true )
| ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ SV136 @ SV254 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1059]) ).
thf(1214,plain,
! [SV255: nat,SV137: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV137 @ SV255 ) )
= $true )
| ( ( ord_less_eq_nat @ SV137 @ ( suc @ SV255 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1060]) ).
thf(1215,plain,
! [SV304: real,SV256: real,SV139: real] :
( ( ! [SY723: real] :
( ~ ( ord_less_eq_real @ zero_zero_real @ SV139 )
| ~ ( ord_less_eq_real @ SV256 @ SV139 )
| ~ ( ord_less_real @ zero_zero_real @ SV304 )
| ~ ( ord_less_eq_real @ SV304 @ SY723 )
| ( ord_less_eq_real @ ( divide_divide_real @ SV256 @ SY723 ) @ ( divide_divide_real @ SV139 @ SV304 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1216,plain,
! [SV140: real] :
( ( ~ ( ord_less_real @ ( ring_1_of_int_real @ ( sK4_SY582 @ SV140 ) ) @ SV140 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1063]) ).
thf(1217,plain,
! [SV257: real,SV141: real] :
( ( ~ ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
| ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) )
| ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1064]) ).
thf(1218,plain,
! [SV257: real,SV141: real] :
( ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
= ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1064]) ).
thf(1219,plain,
! [SV305: nat > $o,SV258: nat,SV142: nat] :
( ( ~ ( ord_less_eq_nat @ SV142 @ SV258 )
| ~ ( SV305 @ SV258 )
| ~ ! [SY724: nat] :
( ~ ( ord_less_eq_nat @ SV142 @ SY724 )
| ~ ( ord_less_nat @ SY724 @ SV258 )
| ~ ( SV305 @ ( suc @ SY724 ) )
| ( SV305 @ SY724 ) )
| ( SV305 @ SV142 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1220,plain,
! [SV143: real] :
( ( ~ ( ord_less_real @ ( sK5_SY587 @ SV143 ) @ SV143 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1066]) ).
thf(1221,plain,
! [SV259: nat,SV144: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( suc @ SV144 ) @ SV259 ) )
= $true )
| ( ( ord_less_eq_nat @ SV144 @ SV259 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1067]) ).
thf(1222,plain,
! [SV260: nat,SV145: nat] :
( ( ( ~ ~ ( ord_less_nat @ SV145 @ SV260 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV145 @ ( suc @ SV260 ) )
| ( SV260 = SV145 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1068]) ).
thf(1223,plain,
! [SV261: nat,SV146: nat] :
( ( ( ~ ( nthRoo1352626670d_root @ SV146 @ SV261 ) )
= $true )
| ( ( SV146
= ( suc @ SV261 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1069]) ).
thf(1224,plain,
! [SV148: nat] :
( ( ( SV148 != zero_zero_nat )
= $false )
| ( ( ~ ! [SY591: nat] :
( SV148
!= ( suc @ SY591 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1071]) ).
thf(1225,plain,
! [SV262: int,SV149: nat,SV1: int] :
( ( ~ ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ SV1 ) @ SV149 ) @ ( ring_1_of_int_real @ SV262 ) )
| ( ord_less_int @ ( power_power_int @ SV1 @ SV149 ) @ SV262 ) )
| ~ ( ~ ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ SV1 ) @ SV149 ) @ ( ring_1_of_int_real @ SV262 ) )
| ~ ( ord_less_int @ ( power_power_int @ SV1 @ SV149 ) @ SV262 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1072]) ).
thf(1226,plain,
! [SV262: int,SV149: nat,SV1: int] :
( ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ SV1 ) @ SV149 ) @ ( ring_1_of_int_real @ SV262 ) )
= ( ord_less_int @ ( power_power_int @ SV1 @ SV149 ) @ SV262 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1072]) ).
thf(1227,plain,
! [SV263: nat,SV150: int,SV2: int] :
( ( ~ ( ( ord_less_real @ ( ring_1_of_int_real @ SV2 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV150 ) @ SV263 ) )
| ( ord_less_int @ SV2 @ ( power_power_int @ SV150 @ SV263 ) ) )
| ~ ( ~ ( ord_less_real @ ( ring_1_of_int_real @ SV2 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV150 ) @ SV263 ) )
| ~ ( ord_less_int @ SV2 @ ( power_power_int @ SV150 @ SV263 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1073]) ).
thf(1228,plain,
! [SV263: nat,SV150: int,SV2: int] :
( ( ( ord_less_real @ ( ring_1_of_int_real @ SV2 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV150 ) @ SV263 ) )
= ( ord_less_int @ SV2 @ ( power_power_int @ SV150 @ SV263 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1073]) ).
thf(1229,plain,
! [SV264: int,SV152: nat,SV4: int] :
( ( ~ ( ( ( power_power_real @ ( ring_1_of_int_real @ SV4 ) @ SV152 )
= ( ring_1_of_int_real @ SV264 ) )
| ( ( power_power_int @ SV4 @ SV152 )
= SV264 ) )
| ~ ( ( ( power_power_real @ ( ring_1_of_int_real @ SV4 ) @ SV152 )
!= ( ring_1_of_int_real @ SV264 ) )
| ( ( power_power_int @ SV4 @ SV152 )
!= SV264 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1074]) ).
thf(1230,plain,
! [SV264: int,SV152: nat,SV4: int] :
( ( ( ( power_power_real @ ( ring_1_of_int_real @ SV4 ) @ SV152 )
= ( ring_1_of_int_real @ SV264 ) )
= ( ( power_power_int @ SV4 @ SV152 )
= SV264 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1074]) ).
thf(1231,plain,
! [SV265: nat,SV153: int,SV5: int] :
( ( ~ ( ( ( ring_1_of_int_real @ SV5 )
= ( power_power_real @ ( ring_1_of_int_real @ SV153 ) @ SV265 ) )
| ( SV5
= ( power_power_int @ SV153 @ SV265 ) ) )
| ~ ( ( ( ring_1_of_int_real @ SV5 )
!= ( power_power_real @ ( ring_1_of_int_real @ SV153 ) @ SV265 ) )
| ( SV5
!= ( power_power_int @ SV153 @ SV265 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1075]) ).
thf(1232,plain,
! [SV265: nat,SV153: int,SV5: int] :
( ( ( ( ring_1_of_int_real @ SV5 )
= ( power_power_real @ ( ring_1_of_int_real @ SV153 ) @ SV265 ) )
= ( SV5
= ( power_power_int @ SV153 @ SV265 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1075]) ).
thf(1233,plain,
! [SV154: int,SV6: int] :
( ( ( ~ ( ( ord_less_real @ ( ring_1_of_int_real @ SV6 ) @ ( ring_1_of_int_real @ SV154 ) )
| ( ord_less_int @ SV6 @ SV154 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( ring_1_of_int_real @ SV6 ) @ ( ring_1_of_int_real @ SV154 ) )
| ~ ( ord_less_int @ SV6 @ SV154 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1076]) ).
thf(1234,plain,
! [SV155: int,SV7: int] :
( ( ( ~ ( ( ( ring_1_of_int_real @ SV7 )
= ( ring_1_of_int_real @ SV155 ) )
| ( SV7 = SV155 ) ) )
= $true )
| ( ( ~ ( ( ( ring_1_of_int_real @ SV7 )
!= ( ring_1_of_int_real @ SV155 ) )
| ( SV7 != SV155 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1078]) ).
thf(1235,plain,
! [SV156: nat,SV8: nat] :
( ( ( ~ ( ( ( suc @ SV8 )
= ( suc @ SV156 ) )
| ( SV8 = SV156 ) ) )
= $true )
| ( ( ~ ( ( ( suc @ SV8 )
!= ( suc @ SV156 ) )
| ( SV8 != SV156 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1080]) ).
thf(1236,plain,
! [SV157: nat,SV9: nat] :
( ( ( ~ ( ( ( suc @ SV9 )
= ( suc @ SV157 ) )
| ( SV9 = SV157 ) ) )
= $true )
| ( ( ~ ( ( ( suc @ SV9 )
!= ( suc @ SV157 ) )
| ( SV9 != SV157 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1082]) ).
thf(1237,plain,
! [SV158: nat,SV10: nat] :
( ( ( ~ ( ( ord_less_nat @ ( suc @ SV10 ) @ ( suc @ SV158 ) )
| ( ord_less_nat @ SV10 @ SV158 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( suc @ SV10 ) @ ( suc @ SV158 ) )
| ~ ( ord_less_nat @ SV10 @ SV158 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1084]) ).
thf(1238,plain,
! [SV12: int] :
( ( ( ( zero_zero_real
= ( ring_1_of_int_real @ SV12 ) )
| ( SV12 = zero_zero_int ) )
= $false )
| ( ( ~ ( ( zero_zero_real
!= ( ring_1_of_int_real @ SV12 ) )
| ( SV12 != zero_zero_int ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1086]) ).
thf(1239,plain,
! [SV13: int] :
( ( ( ( ( ring_1_of_int_real @ SV13 )
= zero_zero_real )
| ( SV13 = zero_zero_int ) )
= $false )
| ( ( ~ ( ( ( ring_1_of_int_real @ SV13 )
!= zero_zero_real )
| ( SV13 != zero_zero_int ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1087]) ).
thf(1240,plain,
! [SV14: int] :
( ( ( ( ord_less_real @ ( ring_1_of_int_real @ SV14 ) @ zero_zero_real )
| ( ord_less_int @ SV14 @ zero_zero_int ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( ring_1_of_int_real @ SV14 ) @ zero_zero_real )
| ~ ( ord_less_int @ SV14 @ zero_zero_int ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1088]) ).
thf(1241,plain,
! [SV15: int] :
( ( ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ SV15 ) )
| ( ord_less_int @ zero_zero_int @ SV15 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ SV15 ) )
| ~ ( ord_less_int @ zero_zero_int @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1242,plain,
! [SV159: nat,SV16: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV16 @ SV159 )
| ( ord_less_nat @ SV159 @ ( suc @ SV16 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ SV16 @ SV159 )
| ~ ( ord_less_nat @ SV159 @ ( suc @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1090]) ).
thf(1243,plain,
! [SV160: nat,SV17: nat] :
( ( ( ~ ( ( ord_less_nat @ SV17 @ ( suc @ SV160 ) )
| ( ord_less_nat @ SV17 @ SV160 )
| ( SV17 = SV160 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV17 @ ( suc @ SV160 ) )
| ~ ( ( ord_less_nat @ SV17 @ SV160 )
| ( SV17 = SV160 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1092]) ).
thf(1244,plain,
! [SV161: nat,SV21: nat] :
( ( ( ~ ( ( ( power_power_nat @ SV21 @ SV161 )
= ( suc @ zero_zero_nat ) )
| ( SV161 = zero_zero_nat )
| ( SV21
= ( suc @ zero_zero_nat ) ) ) )
= $true )
| ( ( ~ ( ( ( power_power_nat @ SV21 @ SV161 )
!= ( suc @ zero_zero_nat ) )
| ~ ( ( SV161 = zero_zero_nat )
| ( SV21
= ( suc @ zero_zero_nat ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1094]) ).
thf(1245,plain,
! [SV27: nat] :
( ( ( ( ord_less_nat @ SV27 @ ( suc @ zero_zero_nat ) )
| ( SV27 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV27 @ ( suc @ zero_zero_nat ) )
| ( SV27 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1096]) ).
thf(1246,plain,
! [SV162: int,SV28: int] :
( ( ( ~ ( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV28 ) @ ( ring_1_of_int_real @ SV162 ) )
| ( ord_less_eq_int @ SV28 @ SV162 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( ring_1_of_int_real @ SV28 ) @ ( ring_1_of_int_real @ SV162 ) )
| ~ ( ord_less_eq_int @ SV28 @ SV162 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1097]) ).
thf(1247,plain,
! [SV266: int,SV163: nat,SV29: int] :
( ( ~ ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ SV29 ) @ SV163 ) @ ( ring_1_of_int_real @ SV266 ) )
| ( ord_less_eq_int @ ( power_power_int @ SV29 @ SV163 ) @ SV266 ) )
| ~ ( ~ ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ SV29 ) @ SV163 ) @ ( ring_1_of_int_real @ SV266 ) )
| ~ ( ord_less_eq_int @ ( power_power_int @ SV29 @ SV163 ) @ SV266 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1099]) ).
thf(1248,plain,
! [SV266: int,SV163: nat,SV29: int] :
( ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ SV29 ) @ SV163 ) @ ( ring_1_of_int_real @ SV266 ) )
= ( ord_less_eq_int @ ( power_power_int @ SV29 @ SV163 ) @ SV266 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1099]) ).
thf(1249,plain,
! [SV267: nat,SV164: int,SV30: int] :
( ( ~ ( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV30 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV164 ) @ SV267 ) )
| ( ord_less_eq_int @ SV30 @ ( power_power_int @ SV164 @ SV267 ) ) )
| ~ ( ~ ( ord_less_eq_real @ ( ring_1_of_int_real @ SV30 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV164 ) @ SV267 ) )
| ~ ( ord_less_eq_int @ SV30 @ ( power_power_int @ SV164 @ SV267 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1100]) ).
thf(1250,plain,
! [SV267: nat,SV164: int,SV30: int] :
( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV30 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV164 ) @ SV267 ) )
= ( ord_less_eq_int @ SV30 @ ( power_power_int @ SV164 @ SV267 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1100]) ).
thf(1251,plain,
! [SV166: nat,SV32: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ ( suc @ SV32 ) @ ( suc @ SV166 ) )
| ( ord_less_eq_nat @ SV32 @ SV166 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( suc @ SV32 ) @ ( suc @ SV166 ) )
| ~ ( ord_less_eq_nat @ SV32 @ SV166 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1102]) ).
thf(1252,plain,
! [SV167: nat,SV33: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV33 @ SV167 )
| ( ord_less_eq_nat @ ( suc @ SV167 ) @ SV33 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_eq_nat @ SV33 @ SV167 )
| ~ ( ord_less_eq_nat @ ( suc @ SV167 ) @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1104]) ).
thf(1253,plain,
! [SV168: nat,SV35: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV35 @ ( suc @ SV168 ) )
| ( ord_less_eq_nat @ SV35 @ SV168 )
| ( SV35
= ( suc @ SV168 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV35 @ ( suc @ SV168 ) )
| ~ ( ( ord_less_eq_nat @ SV35 @ SV168 )
| ( SV35
= ( suc @ SV168 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1106]) ).
thf(1254,plain,
! [SV306: nat,SV169: nat] :
( ( ( nthRoo1352626670d_root @ SV169 @ SV306 )
= ( SV169
= ( suc @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1255,plain,
! [SV170: nat,SV37: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ ( suc @ SV37 ) @ SV170 )
| ( ord_less_nat @ SV37 @ SV170 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( suc @ SV37 ) @ SV170 )
| ~ ( ord_less_nat @ SV37 @ SV170 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1110]) ).
thf(1256,plain,
! [SV171: nat,SV38: nat] :
( ( ( ~ ( ( ord_less_nat @ SV38 @ ( suc @ SV171 ) )
| ( ord_less_eq_nat @ SV38 @ SV171 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV38 @ ( suc @ SV171 ) )
| ~ ( ord_less_eq_nat @ SV38 @ SV171 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1112]) ).
thf(1257,plain,
! [SV307: nat,SV172: nat] :
( ( ( ord_less_nat @ SV172 @ SV307 )
= ( ord_less_eq_nat @ ( suc @ SV172 ) @ SV307 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1258,plain,
! [SV174: nat,SV42: nat] :
( ( ( SV42
= ( suc @ SV174 ) )
= $false )
| ( ( nthRoo1352626670d_root @ SV42 @ SV174 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1116]) ).
thf(1259,plain,
! [SV271: real,SV175: real,SV43: real] :
( ( ( ~ ( ord_less_real @ SV43 @ SV175 ) )
= $true )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV271 )
| ( ord_less_real @ ( divide_divide_real @ SV43 @ SV271 ) @ ( divide_divide_real @ SV175 @ SV271 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1117]) ).
thf(1260,plain,
! [SV176: real,SV44: real] :
( ( ( ord_less_eq_real @ SV44 @ zero_zero_real )
= $false )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV176 )
| ( ord_less_eq_real @ ( divide_divide_real @ SV44 @ SV176 ) @ zero_zero_real ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1118]) ).
thf(1261,plain,
! [SV45: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ SV45 )
| ~ ! [SY405: nat] :
( SV45
!= ( suc @ SY405 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV45 )
| ~ ~ ! [SY405: nat] :
( SV45
!= ( suc @ SY405 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1119]) ).
thf(1262,plain,
! [SV177: nat,SV46: nat] :
( ( ( ord_less_nat @ ( suc @ SV46 ) @ SV177 )
= $false )
| ( ( ord_less_nat @ SV46 @ SV177 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1120]) ).
thf(1263,plain,
! [SV178: nat > $o,SV47: nat] :
( ( ( ~ ( ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) )
| ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) )
| ~ ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1121]) ).
thf(1264,plain,
! [SV179: nat,SV48: nat] :
( ( ( ord_less_nat @ SV48 @ SV179 )
= $false )
| ( ( ord_less_nat @ SV48 @ ( suc @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1123]) ).
thf(1265,plain,
! [SV272: real,SV180: nat,SV49: real] :
( ( ( ~ ( ord_less_real @ ( power_power_real @ SV49 @ SV180 ) @ ( power_power_real @ SV272 @ SV180 ) ) )
= $true )
| ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV272 )
| ( ord_less_real @ SV49 @ SV272 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1124]) ).
thf(1266,plain,
! [SV273: nat,SV181: nat,SV50: nat] :
( ( ( ( power_power_nat @ SV50 @ ( suc @ SV181 ) )
!= ( power_power_nat @ SV273 @ ( suc @ SV181 ) ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV50 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV273 )
| ( SV50 = SV273 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1125]) ).
thf(1267,plain,
! [SV274: real,SV182: real,SV51: real] :
( ( ~ ( ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) )
| ~ ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
| ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1126]) ).
thf(1268,plain,
! [SV274: real,SV182: real,SV51: real] :
( ( ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
= ( ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1126]) ).
thf(1269,plain,
! [SV275: nat > $o,SV183: nat,SV52: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV52 @ SV183 ) )
= $true )
| ( ( ~ ( SV275 @ SV52 )
| ~ ! [SY692: nat] :
( ~ ( ord_less_eq_nat @ SV52 @ SY692 )
| ~ ( SV275 @ SY692 )
| ( SV275 @ ( suc @ SY692 ) ) )
| ( SV275 @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1127]) ).
thf(1270,plain,
! [SV184: nat,SV53: nat > $o] :
( ( ( ! [SY421: nat] :
( ~ ! [SY422: nat] :
( ~ ( ord_less_eq_nat @ ( suc @ SY422 ) @ SY421 )
| ( SV53 @ SY422 ) )
| ( SV53 @ SY421 ) ) )
= $false )
| ( ( SV53 @ SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1128]) ).
thf(1271,plain,
! [SV308: real,SV276: real,SV185: real,SV54: real] :
( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV54 )
| ~ ( ord_less_real @ SV54 @ SV185 )
| ~ ( ord_less_real @ zero_zero_real @ SV276 )
| ~ ( ord_less_eq_real @ SV276 @ SV308 )
| ( ord_less_real @ ( divide_divide_real @ SV54 @ SV308 ) @ ( divide_divide_real @ SV185 @ SV276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1272,plain,
! [SV277: nat,SV186: nat,SV55: nat > int] :
( ( ( ~ ! [SY428: nat] : ( ord_less_eq_int @ ( SV55 @ SY428 ) @ ( SV55 @ ( suc @ SY428 ) ) ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV186 @ SV277 )
| ( ord_less_eq_int @ ( SV55 @ SV186 ) @ ( SV55 @ SV277 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1130]) ).
thf(1273,plain,
! [SV187: nat,SV56: nat] :
( ( ( ord_less_eq_nat @ SV56 @ ( suc @ SV187 ) )
= $false )
| ( ( ~ ~ ( ord_less_eq_nat @ SV56 @ SV187 )
| ( SV56
= ( suc @ SV187 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1131]) ).
thf(1274,plain,
! [SV188: nat,SV57: nat] :
( ( ( ord_less_eq_nat @ SV57 @ SV188 )
= $false )
| ( ( ord_less_nat @ SV57 @ ( suc @ SV188 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1132]) ).
thf(1275,plain,
! [SV58: real] :
( ( ord_less_real @ SV58 @ ( sK1_SY431 @ SV58 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1133]) ).
thf(1276,plain,
! [SV278: nat,SV189: nat,SV59: nat > real] :
( ( ( ~ ! [SY434: nat] : ( ord_less_eq_real @ ( SV59 @ SY434 ) @ ( SV59 @ ( suc @ SY434 ) ) ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV189 @ SV278 )
| ( ord_less_eq_real @ ( SV59 @ SV189 ) @ ( SV59 @ SV278 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1134]) ).
thf(1277,plain,
! [SV190: nat,SV60: real] :
( ( ( SV60 != zero_zero_real )
= $false )
| ( ( ( power_power_real @ SV60 @ SV190 )
!= zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1135]) ).
thf(1278,plain,
! [SV191: nat,SV61: real] :
( ( ( ~ ( ( ( power_power_real @ SV61 @ SV191 )
= zero_zero_real )
| ~ ( ( SV61 != zero_zero_real )
| ~ ( ord_less_nat @ zero_zero_nat @ SV191 ) ) ) )
= $true )
| ( ( ~ ( ( ( power_power_real @ SV61 @ SV191 )
!= zero_zero_real )
| ~ ~ ( ( SV61 != zero_zero_real )
| ~ ( ord_less_nat @ zero_zero_nat @ SV191 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1136]) ).
thf(1279,plain,
! [SV192: real,SV62: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV192 )
| ~ ! [SY616: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY616 )
| ( ( power_power_real @ SY616 @ SV62 )
!= SV192 ) )
| ~ ! [SY617: real] :
( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY617 )
| ( ( power_power_real @ SY617 @ SV62 )
!= SV192 ) )
| ( SY617 = SY616 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1138]) ).
thf(1280,plain,
! [SV279: real,SV193: nat,SV63: real] :
( ( ( ~ ( ord_less_eq_real @ ( power_power_real @ SV63 @ ( suc @ SV193 ) ) @ ( power_power_real @ SV279 @ ( suc @ SV193 ) ) ) )
= $true )
| ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV279 )
| ( ord_less_eq_real @ SV63 @ SV279 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1139]) ).
thf(1281,plain,
! [SV280: nat,SV194: nat,SV64: nat > nat] :
( ( ( ~ ! [SY444: nat] : ( ord_less_nat @ ( SV64 @ SY444 ) @ ( SV64 @ ( suc @ SY444 ) ) ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV194 @ SV280 )
| ( ord_less_nat @ ( SV64 @ SV194 ) @ ( SV64 @ SV280 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1140]) ).
thf(1282,plain,
! [SV195: nat,SV66: nat] :
( ( ( ord_less_nat @ ( suc @ SV66 ) @ ( suc @ SV195 ) )
= $false )
| ( ( ord_less_nat @ SV66 @ SV195 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1142]) ).
thf(1283,plain,
! [SV196: nat,SV67: nat] :
( ( ( ord_less_nat @ SV67 @ ( suc @ SV196 ) )
= $false )
| ( ( ~ ~ ( ord_less_nat @ SV67 @ SV196 )
| ( SV67 = SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1143]) ).
thf(1284,plain,
! [SV281: nat,SV197: nat,SV68: nat > int] :
( ( ( ~ ! [SY449: nat] : ( ord_less_int @ ( SV68 @ SY449 ) @ ( SV68 @ ( suc @ SY449 ) ) ) )
= $true )
| ( ( ( ord_less_int @ ( SV68 @ SV197 ) @ ( SV68 @ SV281 ) )
= ( ord_less_nat @ SV197 @ SV281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1144]) ).
thf(1285,plain,
! [SV198: nat,SV69: nat] :
( ( ( ord_less_nat @ SV69 @ SV198 )
= $false )
| ( ( ~ ( ( SV198
!= ( suc @ SV69 ) ) )
| ~ ! [SY623: nat] :
( ~ ( ord_less_nat @ SV69 @ SY623 )
| ( SV198
!= ( suc @ SY623 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1286,plain,
! [SV199: nat,SV70: nat > $o] :
( ( ( SV70 @ zero_zero_nat )
= $false )
| ( ( ~ ! [SY453: nat] :
( ~ ( SV70 @ SY453 )
| ( SV70 @ ( suc @ SY453 ) ) )
| ( SV70 @ SV199 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1146]) ).
thf(1287,plain,
! [SV200: real,SV72: real] :
( ( ( ord_less_real @ SV72 @ zero_zero_real )
= $false )
| ( ( ~ ( ord_less_real @ SV200 @ zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV72 @ SV200 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1288,plain,
! [SV282: nat,SV201: nat,SV73: nat > nat] :
( ( ( ~ ! [SY457: nat] : ( ord_less_nat @ ( SV73 @ SY457 ) @ ( SV73 @ ( suc @ SY457 ) ) ) )
= $true )
| ( ( ( ord_less_nat @ ( SV73 @ SV201 ) @ ( SV73 @ SV282 ) )
= ( ord_less_nat @ SV201 @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1149]) ).
thf(1289,plain,
! [SV202: nat,SV74: real] :
( ( ( ord_less_real @ zero_zero_real @ SV74 )
= $false )
| ( ( ~ ! [SY627: real] :
~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY627 )
| ( ( power_power_real @ SY627 @ ( suc @ SV202 ) )
!= SV74 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1150]) ).
thf(1290,plain,
! [SV203: nat,SV75: nat] :
( ( ( ord_less_nat @ SV75 @ SV203 )
= $false )
| ( ( ord_less_nat @ ( suc @ SV75 ) @ ( suc @ SV203 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1151]) ).
thf(1291,plain,
! [SV204: nat,SV76: nat] :
( ( ( ord_less_nat @ ( suc @ SV76 ) @ SV204 )
= $false )
| ( ( ~ ! [SY628: nat] :
( ~ ( ord_less_nat @ SV76 @ SY628 )
| ( SV204
!= ( suc @ SY628 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1152]) ).
thf(1292,plain,
! [SV283: real,SV205: nat,SV77: real] :
( ( ( ( power_power_real @ SV77 @ ( suc @ SV205 ) )
!= ( power_power_real @ SV283 @ ( suc @ SV205 ) ) )
= $true )
| ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV77 )
| ~ ( ord_less_eq_real @ zero_zero_real @ SV283 )
| ( SV77 = SV283 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1153]) ).
thf(1293,plain,
! [SV284: nat > $o,SV206: nat,SV78: nat] :
( ( ( ~ ( ord_less_nat @ SV78 @ SV206 ) )
= $true )
| ( ( ~ ! [SY699: nat] :
( ( SV206
!= ( suc @ SY699 ) )
| ( SV284 @ SY699 ) )
| ~ ! [SY700: nat] :
( ~ ( ord_less_nat @ SY700 @ SV206 )
| ~ ( SV284 @ ( suc @ SY700 ) )
| ( SV284 @ SY700 ) )
| ( SV284 @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1154]) ).
thf(1294,plain,
! [SV285: nat > nat > $o,SV207: nat,SV79: nat] :
( ( ( ~ ( ord_less_nat @ SV79 @ SV207 ) )
= $true )
| ( ( ~ ! [SY701: nat] : ( SV285 @ SY701 @ ( suc @ SY701 ) )
| ~ ! [SY702: nat,SY703: nat,SY704: nat] :
( ~ ( ord_less_nat @ SY702 @ SY703 )
| ~ ( ord_less_nat @ SY703 @ SY704 )
| ~ ( SV285 @ SY702 @ SY703 )
| ~ ( SV285 @ SY703 @ SY704 )
| ( SV285 @ SY702 @ SY704 ) )
| ( SV285 @ SV79 @ SV207 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1155]) ).
thf(1295,plain,
! [SV80: nat] :
( ( ( SV80 = zero_zero_nat )
= $true )
| ( ( ~ ! [SY475: nat] :
( SV80
!= ( suc @ SY475 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1156]) ).
thf(1296,plain,
! [SV286: nat,SV208: nat,SV81: nat > nat] :
( ( ( ~ ! [SY478: nat] : ( ord_less_eq_nat @ ( SV81 @ SY478 ) @ ( SV81 @ ( suc @ SY478 ) ) ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV208 @ SV286 )
| ( ord_less_eq_nat @ ( SV81 @ SV208 ) @ ( SV81 @ SV286 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1157]) ).
thf(1297,plain,
! [SV287: nat > $o,SV209: nat,SV82: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV82 @ SV209 ) )
= $true )
| ( ( ~ ( SV287 @ SV82 )
| ~ ! [SY706: nat] :
( ~ ( ord_less_eq_nat @ SV82 @ SY706 )
| ~ ( ord_less_nat @ SY706 @ SV209 )
| ~ ( SV287 @ SY706 )
| ( SV287 @ ( suc @ SY706 ) ) )
| ( SV287 @ SV209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1158]) ).
thf(1298,plain,
! [SV210: nat,SV83: nat] :
( ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ SV83 )
= $false )
| ( ( ord_less_nat @ SV210 @ ( power_power_nat @ SV83 @ SV210 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1159]) ).
thf(1299,plain,
! [SV211: real,SV84: real] :
( ( ( ord_less_real @ SV84 @ zero_zero_real )
= $false )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV211 )
| ( ord_less_real @ ( divide_divide_real @ SV84 @ SV211 ) @ zero_zero_real ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1160]) ).
thf(1300,plain,
! [SV288: nat,SV212: nat,SV85: nat > nat > $o] :
( ( ( ~ ! [SY486: nat] : ( SV85 @ SY486 @ zero_zero_nat ) )
= $true )
| ( ( ~ ! [SY487: nat] : ( SV85 @ zero_zero_nat @ ( suc @ SY487 ) )
| ~ ! [SY488: nat,SY489: nat] :
( ~ ( SV85 @ SY488 @ SY489 )
| ( SV85 @ ( suc @ SY488 ) @ ( suc @ SY489 ) ) )
| ( SV85 @ SV212 @ SV288 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1161]) ).
thf(1301,plain,
! [SV289: nat,SV213: nat,SV86: nat > int] :
( ( ( ~ ! [SY492: nat] : ( ord_less_int @ ( SV86 @ SY492 ) @ ( SV86 @ ( suc @ SY492 ) ) ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV213 @ SV289 )
| ( ord_less_int @ ( SV86 @ SV213 ) @ ( SV86 @ SV289 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1162]) ).
thf(1302,plain,
! [SV214: nat > $o,SV87: nat] :
( ( ( ~ ( ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) )
| ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) )
| ~ ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1163]) ).
thf(1303,plain,
! [SV290: nat,SV215: nat,SV88: nat > real] :
( ( ( ~ ! [SY498: nat] : ( ord_less_real @ ( SV88 @ SY498 ) @ ( SV88 @ ( suc @ SY498 ) ) ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV215 @ SV290 )
| ( ord_less_real @ ( SV88 @ SV215 ) @ ( SV88 @ SV290 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1165]) ).
thf(1304,plain,
! [SV291: int,SV216: nat,SV89: int] :
( ( ( ( power_power_int @ SV89 @ ( suc @ SV216 ) )
!= ( power_power_int @ SV291 @ ( suc @ SV216 ) ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV89 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV291 )
| ( SV89 = SV291 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1166]) ).
thf(1305,plain,
! [SV292: nat,SV217: nat,SV91: nat > int] :
( ( ( ~ ! [SY503: nat] : ( ord_less_eq_int @ ( SV91 @ ( suc @ SY503 ) ) @ ( SV91 @ SY503 ) ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV217 @ SV292 )
| ( ord_less_eq_int @ ( SV91 @ SV292 ) @ ( SV91 @ SV217 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1167]) ).
thf(1306,plain,
! [SV218: real,SV92: real] :
( ( ( ord_less_eq_real @ zero_zero_real @ SV92 )
= $false )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV218 )
| ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ SV92 @ SV218 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1168]) ).
thf(1307,plain,
! [SV293: nat,SV219: nat,SV93: nat] :
( ( ( ~ ( ord_less_nat @ SV93 @ SV219 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV219 @ SV293 )
| ( ord_less_nat @ ( suc @ SV93 ) @ SV293 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1169]) ).
thf(1308,plain,
! [SV220: nat,SV94: nat] :
( ( ( ord_less_eq_nat @ ( suc @ SV94 ) @ SV220 )
= $false )
| ( ( ord_less_nat @ SV94 @ SV220 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1170]) ).
thf(1309,plain,
! [SV221: nat,SV95: nat] :
( ( ( SV95
= ( suc @ SV221 ) )
= $false )
| ( ( SV95 != zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1171]) ).
thf(1310,plain,
! [SV222: nat,SV97: real] :
( ( ( ord_less_real @ zero_zero_real @ SV97 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ SV97 @ SV222 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1172]) ).
thf(1311,plain,
! [SV223: real,SV98: real] :
( ( ( ord_less_real @ zero_zero_real @ SV98 )
= $false )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV223 )
| ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV98 @ SV223 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1173]) ).
thf(1312,plain,
! [SV294: nat,SV224: nat,SV99: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV99 @ ( suc @ SV224 ) ) @ ( power_power_nat @ SV294 @ ( suc @ SV224 ) ) ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV294 )
| ( ord_less_eq_nat @ SV99 @ SV294 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1174]) ).
thf(1313,plain,
! [SV225: nat,SV100: nat] :
( ( ( ord_less_nat @ SV100 @ SV225 )
= $false )
| ( ( ord_less_eq_nat @ ( suc @ SV100 ) @ SV225 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1314,plain,
! [SV295: int,SV226: nat,SV101: int] :
( ( ( ~ ( ord_less_eq_int @ ( power_power_int @ SV101 @ ( suc @ SV226 ) ) @ ( power_power_int @ SV295 @ ( suc @ SV226 ) ) ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV295 )
| ( ord_less_eq_int @ SV101 @ SV295 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1176]) ).
thf(1315,plain,
! [SV296: nat,SV227: real,SV102: real] :
( ( ( ~ ( ord_less_eq_real @ SV102 @ SV227 ) )
= $true )
| ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV102 )
| ( ord_less_eq_real @ ( power_power_real @ SV102 @ SV296 ) @ ( power_power_real @ SV227 @ SV296 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1177]) ).
thf(1316,plain,
! [SV297: real,SV228: real,SV103: real] :
( ( ~ ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) )
| ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1178]) ).
thf(1317,plain,
! [SV297: real,SV228: real,SV103: real] :
( ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
= ( ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1178]) ).
thf(1318,plain,
! [SV229: nat,SV104: nat] :
( ( ( ~ ( ord_less_nat @ SV104 @ SV229 ) )
= $false )
| ( ( ( ord_less_nat @ SV104 @ ( suc @ SV229 ) )
= ( SV104 = SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1179]) ).
thf(1319,plain,
! [SV298: nat,SV230: nat,SV106: nat > real] :
( ( ( ~ ! [SY523: nat] : ( ord_less_real @ ( SV106 @ SY523 ) @ ( SV106 @ ( suc @ SY523 ) ) ) )
= $true )
| ( ( ( ord_less_real @ ( SV106 @ SV230 ) @ ( SV106 @ SV298 ) )
= ( ord_less_nat @ SV230 @ SV298 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1180]) ).
thf(1320,plain,
! [SV231: nat,SV107: nat > $o] :
( ( ( SV107 @ SV231 )
= $false )
| ( ( ~ ! [SY525: nat] :
( ~ ( SV107 @ ( suc @ SY525 ) )
| ( SV107 @ SY525 ) )
| ( SV107 @ zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1181]) ).
thf(1321,plain,
! [SV108: real] :
( ( ord_less_eq_real @ SV108 @ ( ring_1_of_int_real @ ( sK2_SY526 @ SV108 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1182]) ).
thf(1322,plain,
! [SV232: nat,SV109: nat > $o] :
( ( ( SV109 @ zero_zero_nat )
= $false )
| ( ( ~ ! [SY528: nat] :
( ~ ( SV109 @ SY528 )
| ( SV109 @ ( suc @ SY528 ) ) )
| ( SV109 @ SV232 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1183]) ).
thf(1323,plain,
! [SV233: nat > $o,SV110: nat] :
( ( ( ~ ( ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) )
| ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) )
| ~ ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1184]) ).
thf(1324,plain,
! [SV234: nat,SV111: nat] :
( ( ( ord_less_eq_nat @ ( suc @ SV111 ) @ SV234 )
= $false )
| ( ( ~ ! [SY667: nat] :
( SV234
!= ( suc @ SY667 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1186]) ).
thf(1325,plain,
! [SV235: real,SV112: real] :
( ( ( SV112 != SV235 )
= $false )
| ( ( ~ ~ ( ord_less_real @ SV112 @ SV235 )
| ( ord_less_real @ SV235 @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1187]) ).
thf(1326,plain,
! [SV113: nat > $o] :
( ( ( SV113 @ zero_zero_nat )
= $true )
| ( ( ~ ~ ! [SY535: nat] :
~ ( SV113 @ SY535 )
| ~ ! [SY536: nat] :
~ ~ ( ~ ~ ( SV113 @ SY536 )
| ~ ( SV113 @ ( suc @ SY536 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1188]) ).
thf(1327,plain,
! [SV236: nat,SV114: nat] :
( ( ( ord_less_eq_nat @ SV114 @ SV236 )
= $false )
| ( ( ( ord_less_nat @ SV236 @ ( suc @ SV114 ) )
= ( SV236 = SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1189]) ).
thf(1328,plain,
! [SV237: real,SV115: real] :
( ( ( ord_less_real @ zero_zero_real @ SV115 )
= $false )
| ( ( ~ ( ord_less_real @ SV237 @ zero_zero_real )
| ( ord_less_real @ ( divide_divide_real @ SV115 @ SV237 ) @ zero_zero_real ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1190]) ).
thf(1329,plain,
! [SV299: real,SV238: real,SV116: real] :
( ( ( ~ ( ord_less_real @ SV116 @ SV238 ) )
= $true )
| ( ( ~ ( ord_less_real @ SV299 @ zero_zero_real )
| ( ord_less_real @ ( divide_divide_real @ SV238 @ SV299 ) @ ( divide_divide_real @ SV116 @ SV299 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1191]) ).
thf(1330,plain,
! [SV239: nat > $o,SV117: nat] :
( ( ( ~ ( ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) )
| ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) )
| ~ ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1192]) ).
thf(1331,plain,
! [SV300: nat,SV240: nat,SV118: nat > real] :
( ( ( ~ ! [SY546: nat] : ( ord_less_eq_real @ ( SV118 @ ( suc @ SY546 ) ) @ ( SV118 @ SY546 ) ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV240 @ SV300 )
| ( ord_less_eq_real @ ( SV118 @ SV300 ) @ ( SV118 @ SV240 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1194]) ).
thf(1332,plain,
! [SV301: nat,SV241: nat,SV119: nat > nat] :
( ( ( ~ ! [SY549: nat] : ( ord_less_eq_nat @ ( SV119 @ ( suc @ SY549 ) ) @ ( SV119 @ SY549 ) ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV241 @ SV301 )
| ( ord_less_eq_nat @ ( SV119 @ SV301 ) @ ( SV119 @ SV241 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1195]) ).
thf(1333,plain,
! [SV309: real,SV302: real,SV242: real,SV120: real] :
( ( ~ ( ord_less_real @ zero_zero_real @ SV120 )
| ~ ( ord_less_eq_real @ SV120 @ SV242 )
| ~ ( ord_less_real @ zero_zero_real @ SV302 )
| ~ ( ord_less_real @ SV302 @ SV309 )
| ( ord_less_real @ ( divide_divide_real @ SV120 @ SV309 ) @ ( divide_divide_real @ SV242 @ SV302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1334,plain,
! [SV243: real,SV121: real] :
( ( ( ord_less_eq_real @ zero_zero_real @ SV121 )
= $false )
| ( ( ~ ( ord_less_real @ SV243 @ zero_zero_real )
| ( ord_less_eq_real @ ( divide_divide_real @ SV121 @ SV243 ) @ zero_zero_real ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1197]) ).
thf(1335,plain,
! [SV244: nat,SV122: nat > $o] :
( ( ( SV122 @ SV244 )
= $false )
| ( ( ~ ~ ( SV122 @ zero_zero_nat )
| ~ ! [SY677: nat] :
~ ~ ( ~ ~ ( ~ ( ord_less_nat @ SY677 @ SV244 )
| ~ ! [SY556: nat] :
( ~ ( ord_less_eq_nat @ SY556 @ SY677 )
| ~ ( SV122 @ SY556 ) ) )
| ~ ( SV122 @ ( suc @ SY677 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1198]) ).
thf(1336,plain,
! [SV245: nat,SV123: nat] :
( ( ( ~ ( ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
| ~ ! [SY679: nat] :
~ ~ ( ( SV245
!= ( suc @ SY679 ) )
| ~ ( ord_less_nat @ SV123 @ SY679 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
| ~ ~ ! [SY679: nat] :
~ ~ ( ( SV245
!= ( suc @ SY679 ) )
| ~ ( ord_less_nat @ SV123 @ SY679 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1199]) ).
thf(1337,plain,
! [SV124: nat] :
( ( ( ! [SY559: nat] :
( SV124
!= ( suc @ SY559 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1338,plain,
! [SV246: nat,SV125: nat] :
( ( ( ( suc @ SV125 )
= ( suc @ SV246 ) )
= $false )
| ( ( SV125 = SV246 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1339,plain,
! [SV247: nat,SV126: nat] :
( ( ( ord_less_nat @ SV126 @ SV247 )
= $false )
| ( ( ~ ( ( ( suc @ SV126 )
!= SV247 ) )
| ( ord_less_nat @ ( suc @ SV126 ) @ SV247 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1203]) ).
thf(1340,plain,
! [SV303: nat > nat > $o,SV248: nat,SV127: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV127 @ SV248 ) )
= $true )
| ( ( ~ ! [SY718: nat] : ( SV303 @ SY718 @ SY718 )
| ~ ! [SY719: nat,SY720: nat,SY721: nat] :
( ~ ( SV303 @ SY719 @ SY720 )
| ~ ( SV303 @ SY720 @ SY721 )
| ( SV303 @ SY719 @ SY721 ) )
| ~ ! [SY722: nat] : ( SV303 @ SY722 @ ( suc @ SY722 ) )
| ( SV303 @ SV127 @ SV248 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1204]) ).
thf(1341,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
| ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1205]) ).
thf(1342,plain,
! [SV131: real] :
( ( ord_less_real @ SV131 @ ( ring_1_of_int_real @ ( sK3_SY570 @ SV131 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1207]) ).
thf(1343,plain,
! [SV250: nat,SV132: nat] :
( ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ SV132 )
= $false )
| ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ SV132 @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1208]) ).
thf(1344,plain,
! [SV251: nat,SV133: nat] :
( ( ( ~ ( ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
| ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
| ~ ( ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1209]) ).
thf(1345,plain,
! [SV252: real,SV134: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV134 )
= $false )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV252 )
| ~ ! [SY687: real] :
~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY687 )
| ( ( power_power_real @ SY687 @ SV134 )
!= SV252 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1211]) ).
thf(1346,plain,
! [SV253: real,SV135: real] :
( ( ( ord_less_eq_real @ SV135 @ zero_zero_real )
= $false )
| ( ( ~ ( ord_less_real @ SV253 @ zero_zero_real )
| ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ SV135 @ SV253 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1212]) ).
thf(1347,plain,
! [SV254: nat,SV136: real] :
( ( ( ord_less_eq_real @ zero_zero_real @ SV136 )
= $false )
| ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ SV136 @ SV254 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1213]) ).
thf(1348,plain,
! [SV255: nat,SV137: nat] :
( ( ( ord_less_eq_nat @ SV137 @ SV255 )
= $false )
| ( ( ord_less_eq_nat @ SV137 @ ( suc @ SV255 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1214]) ).
thf(1349,plain,
! [SV310: real,SV304: real,SV256: real,SV139: real] :
( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV139 )
| ~ ( ord_less_eq_real @ SV256 @ SV139 )
| ~ ( ord_less_real @ zero_zero_real @ SV304 )
| ~ ( ord_less_eq_real @ SV304 @ SV310 )
| ( ord_less_eq_real @ ( divide_divide_real @ SV256 @ SV310 ) @ ( divide_divide_real @ SV139 @ SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1350,plain,
! [SV140: real] :
( ( ord_less_real @ ( ring_1_of_int_real @ ( sK4_SY582 @ SV140 ) ) @ SV140 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1216]) ).
thf(1351,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
| ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1217]) ).
thf(1352,plain,
! [SV305: nat > $o,SV258: nat,SV142: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV142 @ SV258 ) )
= $true )
| ( ( ~ ( SV305 @ SV258 )
| ~ ! [SY724: nat] :
( ~ ( ord_less_eq_nat @ SV142 @ SY724 )
| ~ ( ord_less_nat @ SY724 @ SV258 )
| ~ ( SV305 @ ( suc @ SY724 ) )
| ( SV305 @ SY724 ) )
| ( SV305 @ SV142 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1219]) ).
thf(1353,plain,
! [SV143: real] :
( ( ord_less_real @ ( sK5_SY587 @ SV143 ) @ SV143 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1220]) ).
thf(1354,plain,
! [SV259: nat,SV144: nat] :
( ( ( ord_less_eq_nat @ ( suc @ SV144 ) @ SV259 )
= $false )
| ( ( ord_less_eq_nat @ SV144 @ SV259 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1221]) ).
thf(1355,plain,
! [SV260: nat,SV145: nat] :
( ( ( ~ ( ord_less_nat @ SV145 @ SV260 ) )
= $false )
| ( ( ~ ( ord_less_nat @ SV145 @ ( suc @ SV260 ) )
| ( SV260 = SV145 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1222]) ).
thf(1356,plain,
! [SV261: nat,SV146: nat] :
( ( ( nthRoo1352626670d_root @ SV146 @ SV261 )
= $false )
| ( ( SV146
= ( suc @ SV261 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1223]) ).
thf(1357,plain,
! [SV148: nat] :
( ( ( SV148 = zero_zero_nat )
= $true )
| ( ( ~ ! [SY591: nat] :
( SV148
!= ( suc @ SY591 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1224]) ).
thf(1358,plain,
! [SV262: int,SV149: nat,SV1: int] :
( ( ( ~ ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ SV1 ) @ SV149 ) @ ( ring_1_of_int_real @ SV262 ) )
| ( ord_less_int @ ( power_power_int @ SV1 @ SV149 ) @ SV262 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ SV1 ) @ SV149 ) @ ( ring_1_of_int_real @ SV262 ) )
| ~ ( ord_less_int @ ( power_power_int @ SV1 @ SV149 ) @ SV262 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1225]) ).
thf(1359,plain,
! [SV263: nat,SV150: int,SV2: int] :
( ( ( ~ ( ( ord_less_real @ ( ring_1_of_int_real @ SV2 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV150 ) @ SV263 ) )
| ( ord_less_int @ SV2 @ ( power_power_int @ SV150 @ SV263 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( ring_1_of_int_real @ SV2 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV150 ) @ SV263 ) )
| ~ ( ord_less_int @ SV2 @ ( power_power_int @ SV150 @ SV263 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1227]) ).
thf(1360,plain,
! [SV264: int,SV152: nat,SV4: int] :
( ( ( ~ ( ( ( power_power_real @ ( ring_1_of_int_real @ SV4 ) @ SV152 )
= ( ring_1_of_int_real @ SV264 ) )
| ( ( power_power_int @ SV4 @ SV152 )
= SV264 ) ) )
= $true )
| ( ( ~ ( ( ( power_power_real @ ( ring_1_of_int_real @ SV4 ) @ SV152 )
!= ( ring_1_of_int_real @ SV264 ) )
| ( ( power_power_int @ SV4 @ SV152 )
!= SV264 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1229]) ).
thf(1361,plain,
! [SV265: nat,SV153: int,SV5: int] :
( ( ( ~ ( ( ( ring_1_of_int_real @ SV5 )
= ( power_power_real @ ( ring_1_of_int_real @ SV153 ) @ SV265 ) )
| ( SV5
= ( power_power_int @ SV153 @ SV265 ) ) ) )
= $true )
| ( ( ~ ( ( ( ring_1_of_int_real @ SV5 )
!= ( power_power_real @ ( ring_1_of_int_real @ SV153 ) @ SV265 ) )
| ( SV5
!= ( power_power_int @ SV153 @ SV265 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1231]) ).
thf(1362,plain,
! [SV154: int,SV6: int] :
( ( ( ( ord_less_real @ ( ring_1_of_int_real @ SV6 ) @ ( ring_1_of_int_real @ SV154 ) )
| ( ord_less_int @ SV6 @ SV154 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( ring_1_of_int_real @ SV6 ) @ ( ring_1_of_int_real @ SV154 ) )
| ~ ( ord_less_int @ SV6 @ SV154 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1233]) ).
thf(1363,plain,
! [SV155: int,SV7: int] :
( ( ( ( ( ring_1_of_int_real @ SV7 )
= ( ring_1_of_int_real @ SV155 ) )
| ( SV7 = SV155 ) )
= $false )
| ( ( ~ ( ( ( ring_1_of_int_real @ SV7 )
!= ( ring_1_of_int_real @ SV155 ) )
| ( SV7 != SV155 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1234]) ).
thf(1364,plain,
! [SV156: nat,SV8: nat] :
( ( ( ( ( suc @ SV8 )
= ( suc @ SV156 ) )
| ( SV8 = SV156 ) )
= $false )
| ( ( ~ ( ( ( suc @ SV8 )
!= ( suc @ SV156 ) )
| ( SV8 != SV156 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1235]) ).
thf(1365,plain,
! [SV157: nat,SV9: nat] :
( ( ( ( ( suc @ SV9 )
= ( suc @ SV157 ) )
| ( SV9 = SV157 ) )
= $false )
| ( ( ~ ( ( ( suc @ SV9 )
!= ( suc @ SV157 ) )
| ( SV9 != SV157 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1236]) ).
thf(1366,plain,
! [SV158: nat,SV10: nat] :
( ( ( ( ord_less_nat @ ( suc @ SV10 ) @ ( suc @ SV158 ) )
| ( ord_less_nat @ SV10 @ SV158 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( suc @ SV10 ) @ ( suc @ SV158 ) )
| ~ ( ord_less_nat @ SV10 @ SV158 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1367,plain,
! [SV12: int] :
( ( ( zero_zero_real
= ( ring_1_of_int_real @ SV12 ) )
= $false )
| ( ( ~ ( ( zero_zero_real
!= ( ring_1_of_int_real @ SV12 ) )
| ( SV12 != zero_zero_int ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1238]) ).
thf(1368,plain,
! [SV12: int] :
( ( ( SV12 = zero_zero_int )
= $false )
| ( ( ~ ( ( zero_zero_real
!= ( ring_1_of_int_real @ SV12 ) )
| ( SV12 != zero_zero_int ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1238]) ).
thf(1369,plain,
! [SV13: int] :
( ( ( ( ring_1_of_int_real @ SV13 )
= zero_zero_real )
= $false )
| ( ( ~ ( ( ( ring_1_of_int_real @ SV13 )
!= zero_zero_real )
| ( SV13 != zero_zero_int ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1239]) ).
thf(1370,plain,
! [SV13: int] :
( ( ( SV13 = zero_zero_int )
= $false )
| ( ( ~ ( ( ( ring_1_of_int_real @ SV13 )
!= zero_zero_real )
| ( SV13 != zero_zero_int ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1239]) ).
thf(1371,plain,
! [SV14: int] :
( ( ( ord_less_real @ ( ring_1_of_int_real @ SV14 ) @ zero_zero_real )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( ring_1_of_int_real @ SV14 ) @ zero_zero_real )
| ~ ( ord_less_int @ SV14 @ zero_zero_int ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1240]) ).
thf(1372,plain,
! [SV14: int] :
( ( ( ord_less_int @ SV14 @ zero_zero_int )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( ring_1_of_int_real @ SV14 ) @ zero_zero_real )
| ~ ( ord_less_int @ SV14 @ zero_zero_int ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1240]) ).
thf(1373,plain,
! [SV15: int] :
( ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ SV15 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ SV15 ) )
| ~ ( ord_less_int @ zero_zero_int @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1241]) ).
thf(1374,plain,
! [SV15: int] :
( ( ( ord_less_int @ zero_zero_int @ SV15 )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ SV15 ) )
| ~ ( ord_less_int @ zero_zero_int @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1241]) ).
thf(1375,plain,
! [SV159: nat,SV16: nat] :
( ( ( ~ ( ord_less_nat @ SV16 @ SV159 )
| ( ord_less_nat @ SV159 @ ( suc @ SV16 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ SV16 @ SV159 )
| ~ ( ord_less_nat @ SV159 @ ( suc @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1242]) ).
thf(1376,plain,
! [SV160: nat,SV17: nat] :
( ( ( ( ord_less_nat @ SV17 @ ( suc @ SV160 ) )
| ( ord_less_nat @ SV17 @ SV160 )
| ( SV17 = SV160 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV17 @ ( suc @ SV160 ) )
| ~ ( ( ord_less_nat @ SV17 @ SV160 )
| ( SV17 = SV160 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1243]) ).
thf(1377,plain,
! [SV161: nat,SV21: nat] :
( ( ( ( ( power_power_nat @ SV21 @ SV161 )
= ( suc @ zero_zero_nat ) )
| ( SV161 = zero_zero_nat )
| ( SV21
= ( suc @ zero_zero_nat ) ) )
= $false )
| ( ( ~ ( ( ( power_power_nat @ SV21 @ SV161 )
!= ( suc @ zero_zero_nat ) )
| ~ ( ( SV161 = zero_zero_nat )
| ( SV21
= ( suc @ zero_zero_nat ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1244]) ).
thf(1378,plain,
! [SV27: nat] :
( ( ( ord_less_nat @ SV27 @ ( suc @ zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV27 @ ( suc @ zero_zero_nat ) )
| ( SV27 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1245]) ).
thf(1379,plain,
! [SV27: nat] :
( ( ( SV27 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV27 @ ( suc @ zero_zero_nat ) )
| ( SV27 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1245]) ).
thf(1380,plain,
! [SV162: int,SV28: int] :
( ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV28 ) @ ( ring_1_of_int_real @ SV162 ) )
| ( ord_less_eq_int @ SV28 @ SV162 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( ring_1_of_int_real @ SV28 ) @ ( ring_1_of_int_real @ SV162 ) )
| ~ ( ord_less_eq_int @ SV28 @ SV162 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1246]) ).
thf(1381,plain,
! [SV266: int,SV163: nat,SV29: int] :
( ( ( ~ ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ SV29 ) @ SV163 ) @ ( ring_1_of_int_real @ SV266 ) )
| ( ord_less_eq_int @ ( power_power_int @ SV29 @ SV163 ) @ SV266 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ SV29 ) @ SV163 ) @ ( ring_1_of_int_real @ SV266 ) )
| ~ ( ord_less_eq_int @ ( power_power_int @ SV29 @ SV163 ) @ SV266 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1247]) ).
thf(1382,plain,
! [SV267: nat,SV164: int,SV30: int] :
( ( ( ~ ( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV30 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV164 ) @ SV267 ) )
| ( ord_less_eq_int @ SV30 @ ( power_power_int @ SV164 @ SV267 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( ring_1_of_int_real @ SV30 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV164 ) @ SV267 ) )
| ~ ( ord_less_eq_int @ SV30 @ ( power_power_int @ SV164 @ SV267 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1249]) ).
thf(1383,plain,
! [SV166: nat,SV32: nat] :
( ( ( ( ord_less_eq_nat @ ( suc @ SV32 ) @ ( suc @ SV166 ) )
| ( ord_less_eq_nat @ SV32 @ SV166 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( suc @ SV32 ) @ ( suc @ SV166 ) )
| ~ ( ord_less_eq_nat @ SV32 @ SV166 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1251]) ).
thf(1384,plain,
! [SV167: nat,SV33: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV33 @ SV167 )
| ( ord_less_eq_nat @ ( suc @ SV167 ) @ SV33 ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_eq_nat @ SV33 @ SV167 )
| ~ ( ord_less_eq_nat @ ( suc @ SV167 ) @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1252]) ).
thf(1385,plain,
! [SV168: nat,SV35: nat] :
( ( ( ( ord_less_eq_nat @ SV35 @ ( suc @ SV168 ) )
| ( ord_less_eq_nat @ SV35 @ SV168 )
| ( SV35
= ( suc @ SV168 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV35 @ ( suc @ SV168 ) )
| ~ ( ( ord_less_eq_nat @ SV35 @ SV168 )
| ( SV35
= ( suc @ SV168 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1253]) ).
thf(1386,plain,
! [SV306: nat,SV169: nat] :
( ( ~ ( ( nthRoo1352626670d_root @ SV169 @ SV306 )
| ( SV169
= ( suc @ SV306 ) ) )
| ~ ( ~ ( nthRoo1352626670d_root @ SV169 @ SV306 )
| ( SV169
!= ( suc @ SV306 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1254]) ).
thf(1387,plain,
! [SV306: nat,SV169: nat] :
( ( ( nthRoo1352626670d_root @ SV169 @ SV306 )
= ( SV169
= ( suc @ SV306 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1254]) ).
thf(1388,plain,
! [SV170: nat,SV37: nat] :
( ( ( ( ord_less_eq_nat @ ( suc @ SV37 ) @ SV170 )
| ( ord_less_nat @ SV37 @ SV170 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( suc @ SV37 ) @ SV170 )
| ~ ( ord_less_nat @ SV37 @ SV170 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1255]) ).
thf(1389,plain,
! [SV171: nat,SV38: nat] :
( ( ( ( ord_less_nat @ SV38 @ ( suc @ SV171 ) )
| ( ord_less_eq_nat @ SV38 @ SV171 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV38 @ ( suc @ SV171 ) )
| ~ ( ord_less_eq_nat @ SV38 @ SV171 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1256]) ).
thf(1390,plain,
! [SV307: nat,SV172: nat] :
( ( ~ ( ( ord_less_nat @ SV172 @ SV307 )
| ( ord_less_eq_nat @ ( suc @ SV172 ) @ SV307 ) )
| ~ ( ~ ( ord_less_nat @ SV172 @ SV307 )
| ~ ( ord_less_eq_nat @ ( suc @ SV172 ) @ SV307 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1257]) ).
thf(1391,plain,
! [SV307: nat,SV172: nat] :
( ( ( ord_less_nat @ SV172 @ SV307 )
= ( ord_less_eq_nat @ ( suc @ SV172 ) @ SV307 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1257]) ).
thf(1392,plain,
! [SV271: real,SV175: real,SV43: real] :
( ( ( ord_less_real @ SV43 @ SV175 )
= $false )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV271 )
| ( ord_less_real @ ( divide_divide_real @ SV43 @ SV271 ) @ ( divide_divide_real @ SV175 @ SV271 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1259]) ).
thf(1393,plain,
! [SV44: real,SV176: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV176 ) )
= $true )
| ( ( ord_less_eq_real @ ( divide_divide_real @ SV44 @ SV176 ) @ zero_zero_real )
= $true )
| ( ( ord_less_eq_real @ SV44 @ zero_zero_real )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1260]) ).
thf(1394,plain,
! [SV45: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV45 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV45 )
| ~ ~ ! [SY405: nat] :
( SV45
!= ( suc @ SY405 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1261]) ).
thf(1395,plain,
! [SV45: nat] :
( ( ( ~ ! [SY405: nat] :
( SV45
!= ( suc @ SY405 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV45 )
| ~ ~ ! [SY405: nat] :
( SV45
!= ( suc @ SY405 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1261]) ).
thf(1396,plain,
! [SV178: nat > $o,SV47: nat] :
( ( ( ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) )
| ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) )
| ~ ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1263]) ).
thf(1397,plain,
! [SV272: real,SV180: nat,SV49: real] :
( ( ( ord_less_real @ ( power_power_real @ SV49 @ SV180 ) @ ( power_power_real @ SV272 @ SV180 ) )
= $false )
| ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV272 )
| ( ord_less_real @ SV49 @ SV272 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1265]) ).
thf(1398,plain,
! [SV273: nat,SV181: nat,SV50: nat] :
( ( ( ( power_power_nat @ SV50 @ ( suc @ SV181 ) )
= ( power_power_nat @ SV273 @ ( suc @ SV181 ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV50 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV273 )
| ( SV50 = SV273 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1266]) ).
thf(1399,plain,
! [SV274: real,SV182: real,SV51: real] :
( ( ( ~ ( ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
| ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1267]) ).
thf(1400,plain,
! [SV275: nat > $o,SV183: nat,SV52: nat] :
( ( ( ord_less_eq_nat @ SV52 @ SV183 )
= $false )
| ( ( ~ ( SV275 @ SV52 )
| ~ ! [SY692: nat] :
( ~ ( ord_less_eq_nat @ SV52 @ SY692 )
| ~ ( SV275 @ SY692 )
| ( SV275 @ ( suc @ SY692 ) ) )
| ( SV275 @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1401,plain,
! [SV53: nat > $o,SV184: nat] :
( ( ( ~ ! [SY725: nat] :
( ~ ( ord_less_eq_nat @ ( suc @ SY725 ) @ ( sK6_SY421 @ SV184 @ SV53 ) )
| ( SV53 @ SY725 ) )
| ( SV53 @ ( sK6_SY421 @ SV184 @ SV53 ) ) )
= $false )
| ( ( SV53 @ SV184 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1270]) ).
thf(1402,plain,
! [SV308: real,SV276: real,SV185: real,SV54: real] :
( ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV54 ) )
= $true )
| ( ( ~ ( ord_less_real @ SV54 @ SV185 )
| ~ ( ord_less_real @ zero_zero_real @ SV276 )
| ~ ( ord_less_eq_real @ SV276 @ SV308 )
| ( ord_less_real @ ( divide_divide_real @ SV54 @ SV308 ) @ ( divide_divide_real @ SV185 @ SV276 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1271]) ).
thf(1403,plain,
! [SV277: nat,SV186: nat,SV55: nat > int] :
( ( ( ! [SY428: nat] : ( ord_less_eq_int @ ( SV55 @ SY428 ) @ ( SV55 @ ( suc @ SY428 ) ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV186 @ SV277 )
| ( ord_less_eq_int @ ( SV55 @ SV186 ) @ ( SV55 @ SV277 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1272]) ).
thf(1404,plain,
! [SV187: nat,SV56: nat] :
( ( ( ~ ~ ( ord_less_eq_nat @ SV56 @ SV187 ) )
= $true )
| ( ( SV56
= ( suc @ SV187 ) )
= $true )
| ( ( ord_less_eq_nat @ SV56 @ ( suc @ SV187 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1273]) ).
thf(1405,plain,
! [SV278: nat,SV189: nat,SV59: nat > real] :
( ( ( ! [SY434: nat] : ( ord_less_eq_real @ ( SV59 @ SY434 ) @ ( SV59 @ ( suc @ SY434 ) ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV189 @ SV278 )
| ( ord_less_eq_real @ ( SV59 @ SV189 ) @ ( SV59 @ SV278 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1276]) ).
thf(1406,plain,
! [SV190: nat,SV60: real] :
( ( ( SV60 = zero_zero_real )
= $true )
| ( ( ( power_power_real @ SV60 @ SV190 )
!= zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1277]) ).
thf(1407,plain,
! [SV191: nat,SV61: real] :
( ( ( ( ( power_power_real @ SV61 @ SV191 )
= zero_zero_real )
| ~ ( ( SV61 != zero_zero_real )
| ~ ( ord_less_nat @ zero_zero_nat @ SV191 ) ) )
= $false )
| ( ( ~ ( ( ( power_power_real @ SV61 @ SV191 )
!= zero_zero_real )
| ~ ~ ( ( SV61 != zero_zero_real )
| ~ ( ord_less_nat @ zero_zero_nat @ SV191 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1408,plain,
! [SV62: nat,SV192: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV192 ) )
= $true )
| ( ( ~ ! [SY616: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY616 )
| ( ( power_power_real @ SY616 @ SV62 )
!= SV192 ) )
| ~ ! [SY617: real] :
( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY617 )
| ( ( power_power_real @ SY617 @ SV62 )
!= SV192 ) )
| ( SY617 = SY616 ) ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1279]) ).
thf(1409,plain,
! [SV279: real,SV193: nat,SV63: real] :
( ( ( ord_less_eq_real @ ( power_power_real @ SV63 @ ( suc @ SV193 ) ) @ ( power_power_real @ SV279 @ ( suc @ SV193 ) ) )
= $false )
| ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV279 )
| ( ord_less_eq_real @ SV63 @ SV279 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1410,plain,
! [SV280: nat,SV194: nat,SV64: nat > nat] :
( ( ( ! [SY444: nat] : ( ord_less_nat @ ( SV64 @ SY444 ) @ ( SV64 @ ( suc @ SY444 ) ) ) )
= $false )
| ( ( ~ ( ord_less_nat @ SV194 @ SV280 )
| ( ord_less_nat @ ( SV64 @ SV194 ) @ ( SV64 @ SV280 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1411,plain,
! [SV196: nat,SV67: nat] :
( ( ( ~ ~ ( ord_less_nat @ SV67 @ SV196 ) )
= $true )
| ( ( SV67 = SV196 )
= $true )
| ( ( ord_less_nat @ SV67 @ ( suc @ SV196 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1283]) ).
thf(1412,plain,
! [SV281: nat,SV197: nat,SV68: nat > int] :
( ( ( ! [SY449: nat] : ( ord_less_int @ ( SV68 @ SY449 ) @ ( SV68 @ ( suc @ SY449 ) ) ) )
= $false )
| ( ( ( ord_less_int @ ( SV68 @ SV197 ) @ ( SV68 @ SV281 ) )
= ( ord_less_nat @ SV197 @ SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1284]) ).
thf(1413,plain,
! [SV69: nat,SV198: nat] :
( ( ( ~ ( ( SV198
!= ( suc @ SV69 ) ) ) )
= $true )
| ( ( ~ ! [SY623: nat] :
( ~ ( ord_less_nat @ SV69 @ SY623 )
| ( SV198
!= ( suc @ SY623 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV69 @ SV198 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1285]) ).
thf(1414,plain,
! [SV199: nat,SV70: nat > $o] :
( ( ( ~ ! [SY453: nat] :
( ~ ( SV70 @ SY453 )
| ( SV70 @ ( suc @ SY453 ) ) ) )
= $true )
| ( ( SV70 @ SV199 )
= $true )
| ( ( SV70 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1286]) ).
thf(1415,plain,
! [SV72: real,SV200: real] :
( ( ( ~ ( ord_less_real @ SV200 @ zero_zero_real ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV72 @ SV200 ) )
= $true )
| ( ( ord_less_real @ SV72 @ zero_zero_real )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1287]) ).
thf(1416,plain,
! [SV282: nat,SV201: nat,SV73: nat > nat] :
( ( ( ! [SY457: nat] : ( ord_less_nat @ ( SV73 @ SY457 ) @ ( SV73 @ ( suc @ SY457 ) ) ) )
= $false )
| ( ( ( ord_less_nat @ ( SV73 @ SV201 ) @ ( SV73 @ SV282 ) )
= ( ord_less_nat @ SV201 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1288]) ).
thf(1417,plain,
! [SV74: real,SV202: nat] :
( ( ( ! [SY627: real] :
~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY627 )
| ( ( power_power_real @ SY627 @ ( suc @ SV202 ) )
!= SV74 ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1289]) ).
thf(1418,plain,
! [SV204: nat,SV76: nat] :
( ( ( ! [SY628: nat] :
( ~ ( ord_less_nat @ SV76 @ SY628 )
| ( SV204
!= ( suc @ SY628 ) ) ) )
= $false )
| ( ( ord_less_nat @ ( suc @ SV76 ) @ SV204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1291]) ).
thf(1419,plain,
! [SV283: real,SV205: nat,SV77: real] :
( ( ( ( power_power_real @ SV77 @ ( suc @ SV205 ) )
= ( power_power_real @ SV283 @ ( suc @ SV205 ) ) )
= $false )
| ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV77 )
| ~ ( ord_less_eq_real @ zero_zero_real @ SV283 )
| ( SV77 = SV283 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1292]) ).
thf(1420,plain,
! [SV284: nat > $o,SV206: nat,SV78: nat] :
( ( ( ord_less_nat @ SV78 @ SV206 )
= $false )
| ( ( ~ ! [SY699: nat] :
( ( SV206
!= ( suc @ SY699 ) )
| ( SV284 @ SY699 ) )
| ~ ! [SY700: nat] :
( ~ ( ord_less_nat @ SY700 @ SV206 )
| ~ ( SV284 @ ( suc @ SY700 ) )
| ( SV284 @ SY700 ) )
| ( SV284 @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1293]) ).
thf(1421,plain,
! [SV285: nat > nat > $o,SV207: nat,SV79: nat] :
( ( ( ord_less_nat @ SV79 @ SV207 )
= $false )
| ( ( ~ ! [SY701: nat] : ( SV285 @ SY701 @ ( suc @ SY701 ) )
| ~ ! [SY702: nat,SY703: nat,SY704: nat] :
( ~ ( ord_less_nat @ SY702 @ SY703 )
| ~ ( ord_less_nat @ SY703 @ SY704 )
| ~ ( SV285 @ SY702 @ SY703 )
| ~ ( SV285 @ SY703 @ SY704 )
| ( SV285 @ SY702 @ SY704 ) )
| ( SV285 @ SV79 @ SV207 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1294]) ).
thf(1422,plain,
! [SV80: nat] :
( ( ( ! [SY475: nat] :
( SV80
!= ( suc @ SY475 ) ) )
= $false )
| ( ( SV80 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1423,plain,
! [SV286: nat,SV208: nat,SV81: nat > nat] :
( ( ( ! [SY478: nat] : ( ord_less_eq_nat @ ( SV81 @ SY478 ) @ ( SV81 @ ( suc @ SY478 ) ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV208 @ SV286 )
| ( ord_less_eq_nat @ ( SV81 @ SV208 ) @ ( SV81 @ SV286 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1296]) ).
thf(1424,plain,
! [SV287: nat > $o,SV209: nat,SV82: nat] :
( ( ( ord_less_eq_nat @ SV82 @ SV209 )
= $false )
| ( ( ~ ( SV287 @ SV82 )
| ~ ! [SY706: nat] :
( ~ ( ord_less_eq_nat @ SV82 @ SY706 )
| ~ ( ord_less_nat @ SY706 @ SV209 )
| ~ ( SV287 @ SY706 )
| ( SV287 @ ( suc @ SY706 ) ) )
| ( SV287 @ SV209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1297]) ).
thf(1425,plain,
! [SV84: real,SV211: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV211 ) )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV84 @ SV211 ) @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV84 @ zero_zero_real )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1299]) ).
thf(1426,plain,
! [SV288: nat,SV212: nat,SV85: nat > nat > $o] :
( ( ( ! [SY486: nat] : ( SV85 @ SY486 @ zero_zero_nat ) )
= $false )
| ( ( ~ ! [SY487: nat] : ( SV85 @ zero_zero_nat @ ( suc @ SY487 ) )
| ~ ! [SY488: nat,SY489: nat] :
( ~ ( SV85 @ SY488 @ SY489 )
| ( SV85 @ ( suc @ SY488 ) @ ( suc @ SY489 ) ) )
| ( SV85 @ SV212 @ SV288 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1300]) ).
thf(1427,plain,
! [SV289: nat,SV213: nat,SV86: nat > int] :
( ( ( ! [SY492: nat] : ( ord_less_int @ ( SV86 @ SY492 ) @ ( SV86 @ ( suc @ SY492 ) ) ) )
= $false )
| ( ( ~ ( ord_less_nat @ SV213 @ SV289 )
| ( ord_less_int @ ( SV86 @ SV213 ) @ ( SV86 @ SV289 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1301]) ).
thf(1428,plain,
! [SV214: nat > $o,SV87: nat] :
( ( ( ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) )
| ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) )
| ~ ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1302]) ).
thf(1429,plain,
! [SV290: nat,SV215: nat,SV88: nat > real] :
( ( ( ! [SY498: nat] : ( ord_less_real @ ( SV88 @ SY498 ) @ ( SV88 @ ( suc @ SY498 ) ) ) )
= $false )
| ( ( ~ ( ord_less_nat @ SV215 @ SV290 )
| ( ord_less_real @ ( SV88 @ SV215 ) @ ( SV88 @ SV290 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1303]) ).
thf(1430,plain,
! [SV291: int,SV216: nat,SV89: int] :
( ( ( ( power_power_int @ SV89 @ ( suc @ SV216 ) )
= ( power_power_int @ SV291 @ ( suc @ SV216 ) ) )
= $false )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV89 )
| ~ ( ord_less_eq_int @ zero_zero_int @ SV291 )
| ( SV89 = SV291 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1304]) ).
thf(1431,plain,
! [SV292: nat,SV217: nat,SV91: nat > int] :
( ( ( ! [SY503: nat] : ( ord_less_eq_int @ ( SV91 @ ( suc @ SY503 ) ) @ ( SV91 @ SY503 ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV217 @ SV292 )
| ( ord_less_eq_int @ ( SV91 @ SV292 ) @ ( SV91 @ SV217 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1305]) ).
thf(1432,plain,
! [SV92: real,SV218: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV218 ) )
= $true )
| ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ SV92 @ SV218 ) )
= $true )
| ( ( ord_less_eq_real @ zero_zero_real @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1306]) ).
thf(1433,plain,
! [SV293: nat,SV219: nat,SV93: nat] :
( ( ( ord_less_nat @ SV93 @ SV219 )
= $false )
| ( ( ~ ( ord_less_nat @ SV219 @ SV293 )
| ( ord_less_nat @ ( suc @ SV93 ) @ SV293 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1307]) ).
thf(1434,plain,
! [SV221: nat,SV95: nat] :
( ( ( SV95 = zero_zero_nat )
= $false )
| ( ( SV95
= ( suc @ SV221 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1309]) ).
thf(1435,plain,
! [SV98: real,SV223: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV223 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV98 @ SV223 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1311]) ).
thf(1436,plain,
! [SV294: nat,SV224: nat,SV99: nat] :
( ( ( ord_less_eq_nat @ ( power_power_nat @ SV99 @ ( suc @ SV224 ) ) @ ( power_power_nat @ SV294 @ ( suc @ SV224 ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV294 )
| ( ord_less_eq_nat @ SV99 @ SV294 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1312]) ).
thf(1437,plain,
! [SV295: int,SV226: nat,SV101: int] :
( ( ( ord_less_eq_int @ ( power_power_int @ SV101 @ ( suc @ SV226 ) ) @ ( power_power_int @ SV295 @ ( suc @ SV226 ) ) )
= $false )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV295 )
| ( ord_less_eq_int @ SV101 @ SV295 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1314]) ).
thf(1438,plain,
! [SV296: nat,SV227: real,SV102: real] :
( ( ( ord_less_eq_real @ SV102 @ SV227 )
= $false )
| ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV102 )
| ( ord_less_eq_real @ ( power_power_real @ SV102 @ SV296 ) @ ( power_power_real @ SV227 @ SV296 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1315]) ).
thf(1439,plain,
! [SV297: real,SV228: real,SV103: real] :
( ( ( ~ ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1316]) ).
thf(1440,plain,
! [SV229: nat,SV104: nat] :
( ( ( ord_less_nat @ SV104 @ SV229 )
= $true )
| ( ( ( ord_less_nat @ SV104 @ ( suc @ SV229 ) )
= ( SV104 = SV229 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1318]) ).
thf(1441,plain,
! [SV298: nat,SV230: nat,SV106: nat > real] :
( ( ( ! [SY523: nat] : ( ord_less_real @ ( SV106 @ SY523 ) @ ( SV106 @ ( suc @ SY523 ) ) ) )
= $false )
| ( ( ( ord_less_real @ ( SV106 @ SV230 ) @ ( SV106 @ SV298 ) )
= ( ord_less_nat @ SV230 @ SV298 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1319]) ).
thf(1442,plain,
! [SV231: nat,SV107: nat > $o] :
( ( ( ~ ! [SY525: nat] :
( ~ ( SV107 @ ( suc @ SY525 ) )
| ( SV107 @ SY525 ) ) )
= $true )
| ( ( SV107 @ zero_zero_nat )
= $true )
| ( ( SV107 @ SV231 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1320]) ).
thf(1443,plain,
! [SV232: nat,SV109: nat > $o] :
( ( ( ~ ! [SY528: nat] :
( ~ ( SV109 @ SY528 )
| ( SV109 @ ( suc @ SY528 ) ) ) )
= $true )
| ( ( SV109 @ SV232 )
= $true )
| ( ( SV109 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1322]) ).
thf(1444,plain,
! [SV233: nat > $o,SV110: nat] :
( ( ( ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) )
| ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) )
| ~ ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1323]) ).
thf(1445,plain,
! [SV111: nat,SV234: nat] :
( ( ( ! [SY667: nat] :
( SV234
!= ( suc @ SY667 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( suc @ SV111 ) @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1324]) ).
thf(1446,plain,
! [SV235: real,SV112: real] :
( ( ( SV112 = SV235 )
= $true )
| ( ( ~ ~ ( ord_less_real @ SV112 @ SV235 )
| ( ord_less_real @ SV235 @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1325]) ).
thf(1447,plain,
! [SV113: nat > $o] :
( ( ( ~ ~ ! [SY535: nat] :
~ ( SV113 @ SY535 ) )
= $true )
| ( ( ~ ! [SY536: nat] :
~ ~ ( ~ ~ ( SV113 @ SY536 )
| ~ ( SV113 @ ( suc @ SY536 ) ) ) )
= $true )
| ( ( SV113 @ zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1326]) ).
thf(1448,plain,
! [SV114: nat,SV236: nat] :
( ( ( ~ ( ( ord_less_nat @ SV236 @ ( suc @ SV114 ) )
| ( SV236 = SV114 ) )
| ~ ( ~ ( ord_less_nat @ SV236 @ ( suc @ SV114 ) )
| ( SV236 != SV114 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV114 @ SV236 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1327]) ).
thf(1449,plain,
! [SV114: nat,SV236: nat] :
( ( ( ( ord_less_nat @ SV236 @ ( suc @ SV114 ) )
= ( SV236 = SV114 ) )
= $true )
| ( ( ord_less_eq_nat @ SV114 @ SV236 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1327]) ).
thf(1450,plain,
! [SV115: real,SV237: real] :
( ( ( ~ ( ord_less_real @ SV237 @ zero_zero_real ) )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV115 @ SV237 ) @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV115 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1328]) ).
thf(1451,plain,
! [SV299: real,SV238: real,SV116: real] :
( ( ( ord_less_real @ SV116 @ SV238 )
= $false )
| ( ( ~ ( ord_less_real @ SV299 @ zero_zero_real )
| ( ord_less_real @ ( divide_divide_real @ SV238 @ SV299 ) @ ( divide_divide_real @ SV116 @ SV299 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1329]) ).
thf(1452,plain,
! [SV239: nat > $o,SV117: nat] :
( ( ( ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) )
| ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) )
| ~ ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1330]) ).
thf(1453,plain,
! [SV300: nat,SV240: nat,SV118: nat > real] :
( ( ( ! [SY546: nat] : ( ord_less_eq_real @ ( SV118 @ ( suc @ SY546 ) ) @ ( SV118 @ SY546 ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV240 @ SV300 )
| ( ord_less_eq_real @ ( SV118 @ SV300 ) @ ( SV118 @ SV240 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1331]) ).
thf(1454,plain,
! [SV301: nat,SV241: nat,SV119: nat > nat] :
( ( ( ! [SY549: nat] : ( ord_less_eq_nat @ ( SV119 @ ( suc @ SY549 ) ) @ ( SV119 @ SY549 ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV241 @ SV301 )
| ( ord_less_eq_nat @ ( SV119 @ SV301 ) @ ( SV119 @ SV241 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1332]) ).
thf(1455,plain,
! [SV309: real,SV302: real,SV242: real,SV120: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV120 ) )
= $true )
| ( ( ~ ( ord_less_eq_real @ SV120 @ SV242 )
| ~ ( ord_less_real @ zero_zero_real @ SV302 )
| ~ ( ord_less_real @ SV302 @ SV309 )
| ( ord_less_real @ ( divide_divide_real @ SV120 @ SV309 ) @ ( divide_divide_real @ SV242 @ SV302 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1333]) ).
thf(1456,plain,
! [SV121: real,SV243: real] :
( ( ( ~ ( ord_less_real @ SV243 @ zero_zero_real ) )
= $true )
| ( ( ord_less_eq_real @ ( divide_divide_real @ SV121 @ SV243 ) @ zero_zero_real )
= $true )
| ( ( ord_less_eq_real @ zero_zero_real @ SV121 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1334]) ).
thf(1457,plain,
! [SV244: nat,SV122: nat > $o] :
( ( ( ~ ~ ( SV122 @ zero_zero_nat ) )
= $true )
| ( ( ~ ! [SY677: nat] :
~ ~ ( ~ ~ ( ~ ( ord_less_nat @ SY677 @ SV244 )
| ~ ! [SY556: nat] :
( ~ ( ord_less_eq_nat @ SY556 @ SY677 )
| ~ ( SV122 @ SY556 ) ) )
| ~ ( SV122 @ ( suc @ SY677 ) ) ) )
= $true )
| ( ( SV122 @ SV244 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1335]) ).
thf(1458,plain,
! [SV245: nat,SV123: nat] :
( ( ( ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
| ~ ! [SY679: nat] :
~ ~ ( ( SV245
!= ( suc @ SY679 ) )
| ~ ( ord_less_nat @ SV123 @ SY679 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
| ~ ~ ! [SY679: nat] :
~ ~ ( ( SV245
!= ( suc @ SY679 ) )
| ~ ( ord_less_nat @ SV123 @ SY679 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1336]) ).
thf(1459,plain,
! [SV124: nat] :
( ( ( SV124
!= ( suc @ ( sK7_SY559 @ SV124 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV124 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1337]) ).
thf(1460,plain,
! [SV247: nat,SV126: nat] :
( ( ( ~ ( ( ( suc @ SV126 )
!= SV247 ) ) )
= $true )
| ( ( ord_less_nat @ ( suc @ SV126 ) @ SV247 )
= $true )
| ( ( ord_less_nat @ SV126 @ SV247 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1339]) ).
thf(1461,plain,
! [SV303: nat > nat > $o,SV248: nat,SV127: nat] :
( ( ( ord_less_eq_nat @ SV127 @ SV248 )
= $false )
| ( ( ~ ! [SY718: nat] : ( SV303 @ SY718 @ SY718 )
| ~ ! [SY719: nat,SY720: nat,SY721: nat] :
( ~ ( SV303 @ SY719 @ SY720 )
| ~ ( SV303 @ SY720 @ SY721 )
| ( SV303 @ SY719 @ SY721 ) )
| ~ ! [SY722: nat] : ( SV303 @ SY722 @ ( suc @ SY722 ) )
| ( SV303 @ SV127 @ SV248 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1340]) ).
thf(1462,plain,
! [SV249: real,SV128: real] :
( ( ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
| ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1341]) ).
thf(1463,plain,
! [SV251: nat,SV133: nat] :
( ( ( ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
| ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
| ~ ( ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1344]) ).
thf(1464,plain,
! [SV134: nat,SV252: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV252 ) )
= $true )
| ( ( ~ ! [SY687: real] :
~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY687 )
| ( ( power_power_real @ SY687 @ SV134 )
!= SV252 ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1345]) ).
thf(1465,plain,
! [SV135: real,SV253: real] :
( ( ( ~ ( ord_less_real @ SV253 @ zero_zero_real ) )
= $true )
| ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ SV135 @ SV253 ) )
= $true )
| ( ( ord_less_eq_real @ SV135 @ zero_zero_real )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1346]) ).
thf(1466,plain,
! [SV310: real,SV304: real,SV256: real,SV139: real] :
( ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV139 ) )
= $true )
| ( ( ~ ( ord_less_eq_real @ SV256 @ SV139 )
| ~ ( ord_less_real @ zero_zero_real @ SV304 )
| ~ ( ord_less_eq_real @ SV304 @ SV310 )
| ( ord_less_eq_real @ ( divide_divide_real @ SV256 @ SV310 ) @ ( divide_divide_real @ SV139 @ SV304 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1349]) ).
thf(1467,plain,
! [SV257: real,SV141: real] :
( ( ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
| ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1351]) ).
thf(1468,plain,
! [SV305: nat > $o,SV258: nat,SV142: nat] :
( ( ( ord_less_eq_nat @ SV142 @ SV258 )
= $false )
| ( ( ~ ( SV305 @ SV258 )
| ~ ! [SY724: nat] :
( ~ ( ord_less_eq_nat @ SV142 @ SY724 )
| ~ ( ord_less_nat @ SY724 @ SV258 )
| ~ ( SV305 @ ( suc @ SY724 ) )
| ( SV305 @ SY724 ) )
| ( SV305 @ SV142 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1352]) ).
thf(1469,plain,
! [SV260: nat,SV145: nat] :
( ( ( ord_less_nat @ SV145 @ SV260 )
= $true )
| ( ( ~ ( ord_less_nat @ SV145 @ ( suc @ SV260 ) )
| ( SV260 = SV145 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1355]) ).
thf(1470,plain,
! [SV148: nat] :
( ( ( ! [SY591: nat] :
( SV148
!= ( suc @ SY591 ) ) )
= $false )
| ( ( SV148 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1357]) ).
thf(1471,plain,
! [SV262: int,SV149: nat,SV1: int] :
( ( ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ SV1 ) @ SV149 ) @ ( ring_1_of_int_real @ SV262 ) )
| ( ord_less_int @ ( power_power_int @ SV1 @ SV149 ) @ SV262 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ SV1 ) @ SV149 ) @ ( ring_1_of_int_real @ SV262 ) )
| ~ ( ord_less_int @ ( power_power_int @ SV1 @ SV149 ) @ SV262 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1358]) ).
thf(1472,plain,
! [SV263: nat,SV150: int,SV2: int] :
( ( ( ( ord_less_real @ ( ring_1_of_int_real @ SV2 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV150 ) @ SV263 ) )
| ( ord_less_int @ SV2 @ ( power_power_int @ SV150 @ SV263 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( ring_1_of_int_real @ SV2 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV150 ) @ SV263 ) )
| ~ ( ord_less_int @ SV2 @ ( power_power_int @ SV150 @ SV263 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1359]) ).
thf(1473,plain,
! [SV264: int,SV152: nat,SV4: int] :
( ( ( ( ( power_power_real @ ( ring_1_of_int_real @ SV4 ) @ SV152 )
= ( ring_1_of_int_real @ SV264 ) )
| ( ( power_power_int @ SV4 @ SV152 )
= SV264 ) )
= $false )
| ( ( ~ ( ( ( power_power_real @ ( ring_1_of_int_real @ SV4 ) @ SV152 )
!= ( ring_1_of_int_real @ SV264 ) )
| ( ( power_power_int @ SV4 @ SV152 )
!= SV264 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1360]) ).
thf(1474,plain,
! [SV265: nat,SV153: int,SV5: int] :
( ( ( ( ( ring_1_of_int_real @ SV5 )
= ( power_power_real @ ( ring_1_of_int_real @ SV153 ) @ SV265 ) )
| ( SV5
= ( power_power_int @ SV153 @ SV265 ) ) )
= $false )
| ( ( ~ ( ( ( ring_1_of_int_real @ SV5 )
!= ( power_power_real @ ( ring_1_of_int_real @ SV153 ) @ SV265 ) )
| ( SV5
!= ( power_power_int @ SV153 @ SV265 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1361]) ).
thf(1475,plain,
! [SV154: int,SV6: int] :
( ( ( ord_less_real @ ( ring_1_of_int_real @ SV6 ) @ ( ring_1_of_int_real @ SV154 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( ring_1_of_int_real @ SV6 ) @ ( ring_1_of_int_real @ SV154 ) )
| ~ ( ord_less_int @ SV6 @ SV154 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1362]) ).
thf(1476,plain,
! [SV154: int,SV6: int] :
( ( ( ord_less_int @ SV6 @ SV154 )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( ring_1_of_int_real @ SV6 ) @ ( ring_1_of_int_real @ SV154 ) )
| ~ ( ord_less_int @ SV6 @ SV154 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1362]) ).
thf(1477,plain,
! [SV155: int,SV7: int] :
( ( ( ( ring_1_of_int_real @ SV7 )
= ( ring_1_of_int_real @ SV155 ) )
= $false )
| ( ( ~ ( ( ( ring_1_of_int_real @ SV7 )
!= ( ring_1_of_int_real @ SV155 ) )
| ( SV7 != SV155 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1363]) ).
thf(1478,plain,
! [SV155: int,SV7: int] :
( ( ( SV7 = SV155 )
= $false )
| ( ( ~ ( ( ( ring_1_of_int_real @ SV7 )
!= ( ring_1_of_int_real @ SV155 ) )
| ( SV7 != SV155 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1363]) ).
thf(1479,plain,
! [SV156: nat,SV8: nat] :
( ( ( ( suc @ SV8 )
= ( suc @ SV156 ) )
= $false )
| ( ( ~ ( ( ( suc @ SV8 )
!= ( suc @ SV156 ) )
| ( SV8 != SV156 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1364]) ).
thf(1480,plain,
! [SV156: nat,SV8: nat] :
( ( ( SV8 = SV156 )
= $false )
| ( ( ~ ( ( ( suc @ SV8 )
!= ( suc @ SV156 ) )
| ( SV8 != SV156 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1364]) ).
thf(1481,plain,
! [SV157: nat,SV9: nat] :
( ( ( ( suc @ SV9 )
= ( suc @ SV157 ) )
= $false )
| ( ( ~ ( ( ( suc @ SV9 )
!= ( suc @ SV157 ) )
| ( SV9 != SV157 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1365]) ).
thf(1482,plain,
! [SV157: nat,SV9: nat] :
( ( ( SV9 = SV157 )
= $false )
| ( ( ~ ( ( ( suc @ SV9 )
!= ( suc @ SV157 ) )
| ( SV9 != SV157 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1365]) ).
thf(1483,plain,
! [SV158: nat,SV10: nat] :
( ( ( ord_less_nat @ ( suc @ SV10 ) @ ( suc @ SV158 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( suc @ SV10 ) @ ( suc @ SV158 ) )
| ~ ( ord_less_nat @ SV10 @ SV158 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1366]) ).
thf(1484,plain,
! [SV158: nat,SV10: nat] :
( ( ( ord_less_nat @ SV10 @ SV158 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( suc @ SV10 ) @ ( suc @ SV158 ) )
| ~ ( ord_less_nat @ SV10 @ SV158 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1366]) ).
thf(1485,plain,
! [SV12: int] :
( ( ( ( zero_zero_real
!= ( ring_1_of_int_real @ SV12 ) )
| ( SV12 != zero_zero_int ) )
= $false )
| ( ( zero_zero_real
= ( ring_1_of_int_real @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1367]) ).
thf(1486,plain,
! [SV12: int] :
( ( ( ( zero_zero_real
!= ( ring_1_of_int_real @ SV12 ) )
| ( SV12 != zero_zero_int ) )
= $false )
| ( ( SV12 = zero_zero_int )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1368]) ).
thf(1487,plain,
! [SV13: int] :
( ( ( ( ( ring_1_of_int_real @ SV13 )
!= zero_zero_real )
| ( SV13 != zero_zero_int ) )
= $false )
| ( ( ( ring_1_of_int_real @ SV13 )
= zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1369]) ).
thf(1488,plain,
! [SV13: int] :
( ( ( ( ( ring_1_of_int_real @ SV13 )
!= zero_zero_real )
| ( SV13 != zero_zero_int ) )
= $false )
| ( ( SV13 = zero_zero_int )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1370]) ).
thf(1489,plain,
! [SV14: int] :
( ( ( ~ ( ord_less_real @ ( ring_1_of_int_real @ SV14 ) @ zero_zero_real )
| ~ ( ord_less_int @ SV14 @ zero_zero_int ) )
= $false )
| ( ( ord_less_real @ ( ring_1_of_int_real @ SV14 ) @ zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1371]) ).
thf(1490,plain,
! [SV14: int] :
( ( ( ~ ( ord_less_real @ ( ring_1_of_int_real @ SV14 ) @ zero_zero_real )
| ~ ( ord_less_int @ SV14 @ zero_zero_int ) )
= $false )
| ( ( ord_less_int @ SV14 @ zero_zero_int )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1372]) ).
thf(1491,plain,
! [SV15: int] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ SV15 ) )
| ~ ( ord_less_int @ zero_zero_int @ SV15 ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1492,plain,
! [SV15: int] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ SV15 ) )
| ~ ( ord_less_int @ zero_zero_int @ SV15 ) )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1374]) ).
thf(1493,plain,
! [SV159: nat,SV16: nat] :
( ( ( ~ ( ord_less_nat @ SV16 @ SV159 ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ SV16 @ SV159 )
| ~ ( ord_less_nat @ SV159 @ ( suc @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1375]) ).
thf(1494,plain,
! [SV16: nat,SV159: nat] :
( ( ( ord_less_nat @ SV159 @ ( suc @ SV16 ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ SV16 @ SV159 )
| ~ ( ord_less_nat @ SV159 @ ( suc @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1375]) ).
thf(1495,plain,
! [SV160: nat,SV17: nat] :
( ( ( ord_less_nat @ SV17 @ ( suc @ SV160 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV17 @ ( suc @ SV160 ) )
| ~ ( ( ord_less_nat @ SV17 @ SV160 )
| ( SV17 = SV160 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1376]) ).
thf(1496,plain,
! [SV160: nat,SV17: nat] :
( ( ( ( ord_less_nat @ SV17 @ SV160 )
| ( SV17 = SV160 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV17 @ ( suc @ SV160 ) )
| ~ ( ( ord_less_nat @ SV17 @ SV160 )
| ( SV17 = SV160 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1376]) ).
thf(1497,plain,
! [SV161: nat,SV21: nat] :
( ( ( ( power_power_nat @ SV21 @ SV161 )
= ( suc @ zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( power_power_nat @ SV21 @ SV161 )
!= ( suc @ zero_zero_nat ) )
| ~ ( ( SV161 = zero_zero_nat )
| ( SV21
= ( suc @ zero_zero_nat ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1377]) ).
thf(1498,plain,
! [SV21: nat,SV161: nat] :
( ( ( ( SV161 = zero_zero_nat )
| ( SV21
= ( suc @ zero_zero_nat ) ) )
= $false )
| ( ( ~ ( ( ( power_power_nat @ SV21 @ SV161 )
!= ( suc @ zero_zero_nat ) )
| ~ ( ( SV161 = zero_zero_nat )
| ( SV21
= ( suc @ zero_zero_nat ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1377]) ).
thf(1499,plain,
! [SV27: nat] :
( ( ( ~ ( ord_less_nat @ SV27 @ ( suc @ zero_zero_nat ) )
| ( SV27 != zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ SV27 @ ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1378]) ).
thf(1500,plain,
! [SV27: nat] :
( ( ( ~ ( ord_less_nat @ SV27 @ ( suc @ zero_zero_nat ) )
| ( SV27 != zero_zero_nat ) )
= $false )
| ( ( SV27 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1379]) ).
thf(1501,plain,
! [SV162: int,SV28: int] :
( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV28 ) @ ( ring_1_of_int_real @ SV162 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( ring_1_of_int_real @ SV28 ) @ ( ring_1_of_int_real @ SV162 ) )
| ~ ( ord_less_eq_int @ SV28 @ SV162 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1380]) ).
thf(1502,plain,
! [SV162: int,SV28: int] :
( ( ( ord_less_eq_int @ SV28 @ SV162 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( ring_1_of_int_real @ SV28 ) @ ( ring_1_of_int_real @ SV162 ) )
| ~ ( ord_less_eq_int @ SV28 @ SV162 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1380]) ).
thf(1503,plain,
! [SV266: int,SV163: nat,SV29: int] :
( ( ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ SV29 ) @ SV163 ) @ ( ring_1_of_int_real @ SV266 ) )
| ( ord_less_eq_int @ ( power_power_int @ SV29 @ SV163 ) @ SV266 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ SV29 ) @ SV163 ) @ ( ring_1_of_int_real @ SV266 ) )
| ~ ( ord_less_eq_int @ ( power_power_int @ SV29 @ SV163 ) @ SV266 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1381]) ).
thf(1504,plain,
! [SV267: nat,SV164: int,SV30: int] :
( ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV30 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV164 ) @ SV267 ) )
| ( ord_less_eq_int @ SV30 @ ( power_power_int @ SV164 @ SV267 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( ring_1_of_int_real @ SV30 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV164 ) @ SV267 ) )
| ~ ( ord_less_eq_int @ SV30 @ ( power_power_int @ SV164 @ SV267 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1382]) ).
thf(1505,plain,
! [SV166: nat,SV32: nat] :
( ( ( ord_less_eq_nat @ ( suc @ SV32 ) @ ( suc @ SV166 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( suc @ SV32 ) @ ( suc @ SV166 ) )
| ~ ( ord_less_eq_nat @ SV32 @ SV166 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1383]) ).
thf(1506,plain,
! [SV166: nat,SV32: nat] :
( ( ( ord_less_eq_nat @ SV32 @ SV166 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( suc @ SV32 ) @ ( suc @ SV166 ) )
| ~ ( ord_less_eq_nat @ SV32 @ SV166 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1383]) ).
thf(1507,plain,
! [SV167: nat,SV33: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV33 @ SV167 ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_eq_nat @ SV33 @ SV167 )
| ~ ( ord_less_eq_nat @ ( suc @ SV167 ) @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1384]) ).
thf(1508,plain,
! [SV33: nat,SV167: nat] :
( ( ( ord_less_eq_nat @ ( suc @ SV167 ) @ SV33 )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_eq_nat @ SV33 @ SV167 )
| ~ ( ord_less_eq_nat @ ( suc @ SV167 ) @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1384]) ).
thf(1509,plain,
! [SV168: nat,SV35: nat] :
( ( ( ord_less_eq_nat @ SV35 @ ( suc @ SV168 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV35 @ ( suc @ SV168 ) )
| ~ ( ( ord_less_eq_nat @ SV35 @ SV168 )
| ( SV35
= ( suc @ SV168 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1385]) ).
thf(1510,plain,
! [SV168: nat,SV35: nat] :
( ( ( ( ord_less_eq_nat @ SV35 @ SV168 )
| ( SV35
= ( suc @ SV168 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV35 @ ( suc @ SV168 ) )
| ~ ( ( ord_less_eq_nat @ SV35 @ SV168 )
| ( SV35
= ( suc @ SV168 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1385]) ).
thf(1511,plain,
! [SV306: nat,SV169: nat] :
( ( ( ~ ( ( nthRoo1352626670d_root @ SV169 @ SV306 )
| ( SV169
= ( suc @ SV306 ) ) ) )
= $true )
| ( ( ~ ( ~ ( nthRoo1352626670d_root @ SV169 @ SV306 )
| ( SV169
!= ( suc @ SV306 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1386]) ).
thf(1512,plain,
! [SV170: nat,SV37: nat] :
( ( ( ord_less_eq_nat @ ( suc @ SV37 ) @ SV170 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( suc @ SV37 ) @ SV170 )
| ~ ( ord_less_nat @ SV37 @ SV170 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1388]) ).
thf(1513,plain,
! [SV170: nat,SV37: nat] :
( ( ( ord_less_nat @ SV37 @ SV170 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( suc @ SV37 ) @ SV170 )
| ~ ( ord_less_nat @ SV37 @ SV170 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1388]) ).
thf(1514,plain,
! [SV171: nat,SV38: nat] :
( ( ( ord_less_nat @ SV38 @ ( suc @ SV171 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV38 @ ( suc @ SV171 ) )
| ~ ( ord_less_eq_nat @ SV38 @ SV171 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1389]) ).
thf(1515,plain,
! [SV171: nat,SV38: nat] :
( ( ( ord_less_eq_nat @ SV38 @ SV171 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV38 @ ( suc @ SV171 ) )
| ~ ( ord_less_eq_nat @ SV38 @ SV171 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1389]) ).
thf(1516,plain,
! [SV307: nat,SV172: nat] :
( ( ( ~ ( ( ord_less_nat @ SV172 @ SV307 )
| ( ord_less_eq_nat @ ( suc @ SV172 ) @ SV307 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV172 @ SV307 )
| ~ ( ord_less_eq_nat @ ( suc @ SV172 ) @ SV307 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1390]) ).
thf(1517,plain,
! [SV175: real,SV43: real,SV271: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV271 ) )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV43 @ SV271 ) @ ( divide_divide_real @ SV175 @ SV271 ) )
= $true )
| ( ( ord_less_real @ SV43 @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1392]) ).
thf(1518,plain,
! [SV44: real,SV176: real] :
( ( ( ord_less_real @ zero_zero_real @ SV176 )
= $false )
| ( ( ord_less_eq_real @ ( divide_divide_real @ SV44 @ SV176 ) @ zero_zero_real )
= $true )
| ( ( ord_less_eq_real @ SV44 @ zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1393]) ).
thf(1519,plain,
! [SV45: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV45 )
| ~ ~ ! [SY405: nat] :
( SV45
!= ( suc @ SY405 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1394]) ).
thf(1520,plain,
! [SV45: nat] :
( ( ( ! [SY405: nat] :
( SV45
!= ( suc @ SY405 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV45 )
| ~ ~ ! [SY405: nat] :
( SV45
!= ( suc @ SY405 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1395]) ).
thf(1521,plain,
! [SV178: nat > $o,SV47: nat] :
( ( ( ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) )
| ~ ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1396]) ).
thf(1522,plain,
! [SV47: nat,SV178: nat > $o] :
( ( ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) )
| ~ ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1396]) ).
thf(1523,plain,
! [SV180: nat,SV49: real,SV272: real] :
( ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV272 ) )
= $true )
| ( ( ord_less_real @ SV49 @ SV272 )
= $true )
| ( ( ord_less_real @ ( power_power_real @ SV49 @ SV180 ) @ ( power_power_real @ SV272 @ SV180 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1397]) ).
thf(1524,plain,
! [SV181: nat,SV273: nat,SV50: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV50 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV273 )
| ( SV50 = SV273 ) )
= $true )
| ( ( ( power_power_nat @ SV50 @ ( suc @ SV181 ) )
= ( power_power_nat @ SV273 @ ( suc @ SV181 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1398]) ).
thf(1525,plain,
! [SV274: real,SV182: real,SV51: real] :
( ( ( ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
| ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1399]) ).
thf(1526,plain,
! [SV183: nat,SV52: nat,SV275: nat > $o] :
( ( ( ~ ( SV275 @ SV52 ) )
= $true )
| ( ( ~ ! [SY692: nat] :
( ~ ( ord_less_eq_nat @ SV52 @ SY692 )
| ~ ( SV275 @ SY692 )
| ( SV275 @ ( suc @ SY692 ) ) )
| ( SV275 @ SV183 ) )
= $true )
| ( ( ord_less_eq_nat @ SV52 @ SV183 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1400]) ).
thf(1527,plain,
! [SV53: nat > $o,SV184: nat] :
( ( ( ~ ! [SY725: nat] :
( ~ ( ord_less_eq_nat @ ( suc @ SY725 ) @ ( sK6_SY421 @ SV184 @ SV53 ) )
| ( SV53 @ SY725 ) ) )
= $false )
| ( ( SV53 @ SV184 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1401]) ).
thf(1528,plain,
! [SV184: nat,SV53: nat > $o] :
( ( ( SV53 @ ( sK6_SY421 @ SV184 @ SV53 ) )
= $false )
| ( ( SV53 @ SV184 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1401]) ).
thf(1529,plain,
! [SV308: real,SV276: real,SV185: real,SV54: real] :
( ( ( ord_less_eq_real @ zero_zero_real @ SV54 )
= $false )
| ( ( ~ ( ord_less_real @ SV54 @ SV185 )
| ~ ( ord_less_real @ zero_zero_real @ SV276 )
| ~ ( ord_less_eq_real @ SV276 @ SV308 )
| ( ord_less_real @ ( divide_divide_real @ SV54 @ SV308 ) @ ( divide_divide_real @ SV185 @ SV276 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1402]) ).
thf(1530,plain,
! [SV186: nat,SV277: nat,SV55: nat > int] :
( ( ( ord_less_eq_int @ ( SV55 @ ( sK8_SY428 @ SV277 @ SV186 @ SV55 ) ) @ ( SV55 @ ( suc @ ( sK8_SY428 @ SV277 @ SV186 @ SV55 ) ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV186 @ SV277 )
| ( ord_less_eq_int @ ( SV55 @ SV186 ) @ ( SV55 @ SV277 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1403]) ).
thf(1531,plain,
! [SV187: nat,SV56: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV56 @ SV187 ) )
= $false )
| ( ( SV56
= ( suc @ SV187 ) )
= $true )
| ( ( ord_less_eq_nat @ SV56 @ ( suc @ SV187 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1404]) ).
thf(1532,plain,
! [SV189: nat,SV278: nat,SV59: nat > real] :
( ( ( ord_less_eq_real @ ( SV59 @ ( sK9_SY434 @ SV278 @ SV189 @ SV59 ) ) @ ( SV59 @ ( suc @ ( sK9_SY434 @ SV278 @ SV189 @ SV59 ) ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV189 @ SV278 )
| ( ord_less_eq_real @ ( SV59 @ SV189 ) @ ( SV59 @ SV278 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1405]) ).
thf(1533,plain,
! [SV190: nat,SV60: real] :
( ( ( ( power_power_real @ SV60 @ SV190 )
= zero_zero_real )
= $false )
| ( ( SV60 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1406]) ).
thf(1534,plain,
! [SV191: nat,SV61: real] :
( ( ( ( power_power_real @ SV61 @ SV191 )
= zero_zero_real )
= $false )
| ( ( ~ ( ( ( power_power_real @ SV61 @ SV191 )
!= zero_zero_real )
| ~ ~ ( ( SV61 != zero_zero_real )
| ~ ( ord_less_nat @ zero_zero_nat @ SV191 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1407]) ).
thf(1535,plain,
! [SV191: nat,SV61: real] :
( ( ( ~ ( ( SV61 != zero_zero_real )
| ~ ( ord_less_nat @ zero_zero_nat @ SV191 ) ) )
= $false )
| ( ( ~ ( ( ( power_power_real @ SV61 @ SV191 )
!= zero_zero_real )
| ~ ~ ( ( SV61 != zero_zero_real )
| ~ ( ord_less_nat @ zero_zero_nat @ SV191 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1407]) ).
thf(1536,plain,
! [SV62: nat,SV192: real] :
( ( ( ord_less_real @ zero_zero_real @ SV192 )
= $false )
| ( ( ~ ! [SY616: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY616 )
| ( ( power_power_real @ SY616 @ SV62 )
!= SV192 ) )
| ~ ! [SY617: real] :
( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY617 )
| ( ( power_power_real @ SY617 @ SV62 )
!= SV192 ) )
| ( SY617 = SY616 ) ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1408]) ).
thf(1537,plain,
! [SV193: nat,SV63: real,SV279: real] :
( ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV279 ) )
= $true )
| ( ( ord_less_eq_real @ SV63 @ SV279 )
= $true )
| ( ( ord_less_eq_real @ ( power_power_real @ SV63 @ ( suc @ SV193 ) ) @ ( power_power_real @ SV279 @ ( suc @ SV193 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1409]) ).
thf(1538,plain,
! [SV194: nat,SV280: nat,SV64: nat > nat] :
( ( ( ord_less_nat @ ( SV64 @ ( sK10_SY444 @ SV280 @ SV194 @ SV64 ) ) @ ( SV64 @ ( suc @ ( sK10_SY444 @ SV280 @ SV194 @ SV64 ) ) ) )
= $false )
| ( ( ~ ( ord_less_nat @ SV194 @ SV280 )
| ( ord_less_nat @ ( SV64 @ SV194 ) @ ( SV64 @ SV280 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1410]) ).
thf(1539,plain,
! [SV196: nat,SV67: nat] :
( ( ( ~ ( ord_less_nat @ SV67 @ SV196 ) )
= $false )
| ( ( SV67 = SV196 )
= $true )
| ( ( ord_less_nat @ SV67 @ ( suc @ SV196 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1411]) ).
thf(1540,plain,
! [SV197: nat,SV281: nat,SV68: nat > int] :
( ( ( ord_less_int @ ( SV68 @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) @ ( SV68 @ ( suc @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) ) )
= $false )
| ( ( ( ord_less_int @ ( SV68 @ SV197 ) @ ( SV68 @ SV281 ) )
= ( ord_less_nat @ SV197 @ SV281 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1412]) ).
thf(1541,plain,
! [SV69: nat,SV198: nat] :
( ( ( SV198
!= ( suc @ SV69 ) )
= $false )
| ( ( ~ ! [SY623: nat] :
( ~ ( ord_less_nat @ SV69 @ SY623 )
| ( SV198
!= ( suc @ SY623 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV69 @ SV198 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1413]) ).
thf(1542,plain,
! [SV199: nat,SV70: nat > $o] :
( ( ( ! [SY453: nat] :
( ~ ( SV70 @ SY453 )
| ( SV70 @ ( suc @ SY453 ) ) ) )
= $false )
| ( ( SV70 @ SV199 )
= $true )
| ( ( SV70 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1543,plain,
! [SV72: real,SV200: real] :
( ( ( ord_less_real @ SV200 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV72 @ SV200 ) )
= $true )
| ( ( ord_less_real @ SV72 @ zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1415]) ).
thf(1544,plain,
! [SV201: nat,SV282: nat,SV73: nat > nat] :
( ( ( ord_less_nat @ ( SV73 @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) @ ( SV73 @ ( suc @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) ) )
= $false )
| ( ( ( ord_less_nat @ ( SV73 @ SV201 ) @ ( SV73 @ SV282 ) )
= ( ord_less_nat @ SV201 @ SV282 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1416]) ).
thf(1545,plain,
! [SV202: nat,SV74: real] :
( ( ( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ ( sK13_SY627 @ SV74 @ SV202 ) )
| ( ( power_power_real @ ( sK13_SY627 @ SV74 @ SV202 ) @ ( suc @ SV202 ) )
!= SV74 ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV74 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1417]) ).
thf(1546,plain,
! [SV204: nat,SV76: nat] :
( ( ( ~ ( ord_less_nat @ SV76 @ ( sK14_SY628 @ SV204 @ SV76 ) )
| ( SV204
!= ( suc @ ( sK14_SY628 @ SV204 @ SV76 ) ) ) )
= $false )
| ( ( ord_less_nat @ ( suc @ SV76 ) @ SV204 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1418]) ).
thf(1547,plain,
! [SV205: nat,SV283: real,SV77: real] :
( ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV77 ) )
= $true )
| ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV283 )
| ( SV77 = SV283 ) )
= $true )
| ( ( ( power_power_real @ SV77 @ ( suc @ SV205 ) )
= ( power_power_real @ SV283 @ ( suc @ SV205 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1419]) ).
thf(1548,plain,
! [SV78: nat,SV284: nat > $o,SV206: nat] :
( ( ( ~ ! [SY699: nat] :
( ( SV206
!= ( suc @ SY699 ) )
| ( SV284 @ SY699 ) ) )
= $true )
| ( ( ~ ! [SY700: nat] :
( ~ ( ord_less_nat @ SY700 @ SV206 )
| ~ ( SV284 @ ( suc @ SY700 ) )
| ( SV284 @ SY700 ) )
| ( SV284 @ SV78 ) )
= $true )
| ( ( ord_less_nat @ SV78 @ SV206 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1420]) ).
thf(1549,plain,
! [SV207: nat,SV79: nat,SV285: nat > nat > $o] :
( ( ( ~ ! [SY701: nat] : ( SV285 @ SY701 @ ( suc @ SY701 ) ) )
= $true )
| ( ( ~ ! [SY702: nat,SY703: nat,SY704: nat] :
( ~ ( ord_less_nat @ SY702 @ SY703 )
| ~ ( ord_less_nat @ SY703 @ SY704 )
| ~ ( SV285 @ SY702 @ SY703 )
| ~ ( SV285 @ SY703 @ SY704 )
| ( SV285 @ SY702 @ SY704 ) )
| ( SV285 @ SV79 @ SV207 ) )
= $true )
| ( ( ord_less_nat @ SV79 @ SV207 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1421]) ).
thf(1550,plain,
! [SV80: nat] :
( ( ( SV80
!= ( suc @ ( sK15_SY475 @ SV80 ) ) )
= $false )
| ( ( SV80 = zero_zero_nat )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1422]) ).
thf(1551,plain,
! [SV208: nat,SV286: nat,SV81: nat > nat] :
( ( ( ord_less_eq_nat @ ( SV81 @ ( sK16_SY478 @ SV286 @ SV208 @ SV81 ) ) @ ( SV81 @ ( suc @ ( sK16_SY478 @ SV286 @ SV208 @ SV81 ) ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV208 @ SV286 )
| ( ord_less_eq_nat @ ( SV81 @ SV208 ) @ ( SV81 @ SV286 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1423]) ).
thf(1552,plain,
! [SV209: nat,SV82: nat,SV287: nat > $o] :
( ( ( ~ ( SV287 @ SV82 ) )
= $true )
| ( ( ~ ! [SY706: nat] :
( ~ ( ord_less_eq_nat @ SV82 @ SY706 )
| ~ ( ord_less_nat @ SY706 @ SV209 )
| ~ ( SV287 @ SY706 )
| ( SV287 @ ( suc @ SY706 ) ) )
| ( SV287 @ SV209 ) )
= $true )
| ( ( ord_less_eq_nat @ SV82 @ SV209 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1424]) ).
thf(1553,plain,
! [SV84: real,SV211: real] :
( ( ( ord_less_real @ zero_zero_real @ SV211 )
= $false )
| ( ( ord_less_real @ ( divide_divide_real @ SV84 @ SV211 ) @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV84 @ zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1425]) ).
thf(1554,plain,
! [SV212: nat,SV288: nat,SV85: nat > nat > $o] :
( ( ( SV85 @ ( sK17_SY486 @ SV288 @ SV212 @ SV85 ) @ zero_zero_nat )
= $false )
| ( ( ~ ! [SY487: nat] : ( SV85 @ zero_zero_nat @ ( suc @ SY487 ) )
| ~ ! [SY488: nat,SY489: nat] :
( ~ ( SV85 @ SY488 @ SY489 )
| ( SV85 @ ( suc @ SY488 ) @ ( suc @ SY489 ) ) )
| ( SV85 @ SV212 @ SV288 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1426]) ).
thf(1555,plain,
! [SV213: nat,SV289: nat,SV86: nat > int] :
( ( ( ord_less_int @ ( SV86 @ ( sK18_SY492 @ SV289 @ SV213 @ SV86 ) ) @ ( SV86 @ ( suc @ ( sK18_SY492 @ SV289 @ SV213 @ SV86 ) ) ) )
= $false )
| ( ( ~ ( ord_less_nat @ SV213 @ SV289 )
| ( ord_less_int @ ( SV86 @ SV213 ) @ ( SV86 @ SV289 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1427]) ).
thf(1556,plain,
! [SV214: nat > $o,SV87: nat] :
( ( ( ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) )
| ~ ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1428]) ).
thf(1557,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) )
| ~ ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1428]) ).
thf(1558,plain,
! [SV215: nat,SV290: nat,SV88: nat > real] :
( ( ( ord_less_real @ ( SV88 @ ( sK19_SY498 @ SV290 @ SV215 @ SV88 ) ) @ ( SV88 @ ( suc @ ( sK19_SY498 @ SV290 @ SV215 @ SV88 ) ) ) )
= $false )
| ( ( ~ ( ord_less_nat @ SV215 @ SV290 )
| ( ord_less_real @ ( SV88 @ SV215 ) @ ( SV88 @ SV290 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1429]) ).
thf(1559,plain,
! [SV216: nat,SV291: int,SV89: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV89 ) )
= $true )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV291 )
| ( SV89 = SV291 ) )
= $true )
| ( ( ( power_power_int @ SV89 @ ( suc @ SV216 ) )
= ( power_power_int @ SV291 @ ( suc @ SV216 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1430]) ).
thf(1560,plain,
! [SV217: nat,SV292: nat,SV91: nat > int] :
( ( ( ord_less_eq_int @ ( SV91 @ ( suc @ ( sK20_SY503 @ SV292 @ SV217 @ SV91 ) ) ) @ ( SV91 @ ( sK20_SY503 @ SV292 @ SV217 @ SV91 ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV217 @ SV292 )
| ( ord_less_eq_int @ ( SV91 @ SV292 ) @ ( SV91 @ SV217 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1431]) ).
thf(1561,plain,
! [SV92: real,SV218: real] :
( ( ( ord_less_real @ zero_zero_real @ SV218 )
= $false )
| ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ SV92 @ SV218 ) )
= $true )
| ( ( ord_less_eq_real @ zero_zero_real @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1432]) ).
thf(1562,plain,
! [SV93: nat,SV293: nat,SV219: nat] :
( ( ( ~ ( ord_less_nat @ SV219 @ SV293 ) )
= $true )
| ( ( ord_less_nat @ ( suc @ SV93 ) @ SV293 )
= $true )
| ( ( ord_less_nat @ SV93 @ SV219 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1433]) ).
thf(1563,plain,
! [SV98: real,SV223: real] :
( ( ( ord_less_real @ zero_zero_real @ SV223 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV98 @ SV223 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1435]) ).
thf(1564,plain,
! [SV224: nat,SV99: nat,SV294: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV294 ) )
= $true )
| ( ( ord_less_eq_nat @ SV99 @ SV294 )
= $true )
| ( ( ord_less_eq_nat @ ( power_power_nat @ SV99 @ ( suc @ SV224 ) ) @ ( power_power_nat @ SV294 @ ( suc @ SV224 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1436]) ).
thf(1565,plain,
! [SV226: nat,SV101: int,SV295: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV295 ) )
= $true )
| ( ( ord_less_eq_int @ SV101 @ SV295 )
= $true )
| ( ( ord_less_eq_int @ ( power_power_int @ SV101 @ ( suc @ SV226 ) ) @ ( power_power_int @ SV295 @ ( suc @ SV226 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1437]) ).
thf(1566,plain,
! [SV227: real,SV296: nat,SV102: real] :
( ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV102 ) )
= $true )
| ( ( ord_less_eq_real @ ( power_power_real @ SV102 @ SV296 ) @ ( power_power_real @ SV227 @ SV296 ) )
= $true )
| ( ( ord_less_eq_real @ SV102 @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1438]) ).
thf(1567,plain,
! [SV297: real,SV228: real,SV103: real] :
( ( ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1439]) ).
thf(1568,plain,
! [SV229: nat,SV104: nat] :
( ( ( ~ ( ( ord_less_nat @ SV104 @ ( suc @ SV229 ) )
| ( SV104 = SV229 ) )
| ~ ( ~ ( ord_less_nat @ SV104 @ ( suc @ SV229 ) )
| ( SV104 != SV229 ) ) )
= $true )
| ( ( ord_less_nat @ SV104 @ SV229 )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1440]) ).
thf(1569,plain,
! [SV229: nat,SV104: nat] :
( ( ( ( ord_less_nat @ SV104 @ ( suc @ SV229 ) )
= ( SV104 = SV229 ) )
= $true )
| ( ( ord_less_nat @ SV104 @ SV229 )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1440]) ).
thf(1570,plain,
! [SV230: nat,SV298: nat,SV106: nat > real] :
( ( ( ord_less_real @ ( SV106 @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) @ ( SV106 @ ( suc @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) ) )
= $false )
| ( ( ( ord_less_real @ ( SV106 @ SV230 ) @ ( SV106 @ SV298 ) )
= ( ord_less_nat @ SV230 @ SV298 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1441]) ).
thf(1571,plain,
! [SV231: nat,SV107: nat > $o] :
( ( ( ! [SY525: nat] :
( ~ ( SV107 @ ( suc @ SY525 ) )
| ( SV107 @ SY525 ) ) )
= $false )
| ( ( SV107 @ zero_zero_nat )
= $true )
| ( ( SV107 @ SV231 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1442]) ).
thf(1572,plain,
! [SV232: nat,SV109: nat > $o] :
( ( ( ! [SY528: nat] :
( ~ ( SV109 @ SY528 )
| ( SV109 @ ( suc @ SY528 ) ) ) )
= $false )
| ( ( SV109 @ SV232 )
= $true )
| ( ( SV109 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1443]) ).
thf(1573,plain,
! [SV233: nat > $o,SV110: nat] :
( ( ( ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) )
| ~ ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1444]) ).
thf(1574,plain,
! [SV110: nat,SV233: nat > $o] :
( ( ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) )
| ~ ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1444]) ).
thf(1575,plain,
! [SV111: nat,SV234: nat] :
( ( ( SV234
!= ( suc @ ( sK22_SY667 @ SV111 @ SV234 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( suc @ SV111 ) @ SV234 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1445]) ).
thf(1576,plain,
! [SV235: real,SV112: real] :
( ( ( ~ ~ ( ord_less_real @ SV112 @ SV235 ) )
= $true )
| ( ( ord_less_real @ SV235 @ SV112 )
= $true )
| ( ( SV112 = SV235 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1446]) ).
thf(1577,plain,
! [SV113: nat > $o] :
( ( ( ~ ! [SY535: nat] :
~ ( SV113 @ SY535 ) )
= $false )
| ( ( ~ ! [SY536: nat] :
~ ~ ( ~ ~ ( SV113 @ SY536 )
| ~ ( SV113 @ ( suc @ SY536 ) ) ) )
= $true )
| ( ( SV113 @ zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1447]) ).
thf(1578,plain,
! [SV114: nat,SV236: nat] :
( ( ( ~ ( ( ord_less_nat @ SV236 @ ( suc @ SV114 ) )
| ( SV236 = SV114 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV236 @ ( suc @ SV114 ) )
| ( SV236 != SV114 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV114 @ SV236 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1448]) ).
thf(1579,plain,
! [SV115: real,SV237: real] :
( ( ( ord_less_real @ SV237 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ ( divide_divide_real @ SV115 @ SV237 ) @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1450]) ).
thf(1580,plain,
! [SV116: real,SV238: real,SV299: real] :
( ( ( ~ ( ord_less_real @ SV299 @ zero_zero_real ) )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV238 @ SV299 ) @ ( divide_divide_real @ SV116 @ SV299 ) )
= $true )
| ( ( ord_less_real @ SV116 @ SV238 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1451]) ).
thf(1581,plain,
! [SV239: nat > $o,SV117: nat] :
( ( ( ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) )
| ~ ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1452]) ).
thf(1582,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) )
| ~ ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1452]) ).
thf(1583,plain,
! [SV240: nat,SV300: nat,SV118: nat > real] :
( ( ( ord_less_eq_real @ ( SV118 @ ( suc @ ( sK23_SY546 @ SV300 @ SV240 @ SV118 ) ) ) @ ( SV118 @ ( sK23_SY546 @ SV300 @ SV240 @ SV118 ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV240 @ SV300 )
| ( ord_less_eq_real @ ( SV118 @ SV300 ) @ ( SV118 @ SV240 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1453]) ).
thf(1584,plain,
! [SV241: nat,SV301: nat,SV119: nat > nat] :
( ( ( ord_less_eq_nat @ ( SV119 @ ( suc @ ( sK24_SY549 @ SV301 @ SV241 @ SV119 ) ) ) @ ( SV119 @ ( sK24_SY549 @ SV301 @ SV241 @ SV119 ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV241 @ SV301 )
| ( ord_less_eq_nat @ ( SV119 @ SV301 ) @ ( SV119 @ SV241 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1454]) ).
thf(1585,plain,
! [SV309: real,SV302: real,SV242: real,SV120: real] :
( ( ( ord_less_real @ zero_zero_real @ SV120 )
= $false )
| ( ( ~ ( ord_less_eq_real @ SV120 @ SV242 )
| ~ ( ord_less_real @ zero_zero_real @ SV302 )
| ~ ( ord_less_real @ SV302 @ SV309 )
| ( ord_less_real @ ( divide_divide_real @ SV120 @ SV309 ) @ ( divide_divide_real @ SV242 @ SV302 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1455]) ).
thf(1586,plain,
! [SV121: real,SV243: real] :
( ( ( ord_less_real @ SV243 @ zero_zero_real )
= $false )
| ( ( ord_less_eq_real @ ( divide_divide_real @ SV121 @ SV243 ) @ zero_zero_real )
= $true )
| ( ( ord_less_eq_real @ zero_zero_real @ SV121 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1456]) ).
thf(1587,plain,
! [SV244: nat,SV122: nat > $o] :
( ( ( ~ ( SV122 @ zero_zero_nat ) )
= $false )
| ( ( ~ ! [SY677: nat] :
~ ~ ( ~ ~ ( ~ ( ord_less_nat @ SY677 @ SV244 )
| ~ ! [SY556: nat] :
( ~ ( ord_less_eq_nat @ SY556 @ SY677 )
| ~ ( SV122 @ SY556 ) ) )
| ~ ( SV122 @ ( suc @ SY677 ) ) ) )
= $true )
| ( ( SV122 @ SV244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1457]) ).
thf(1588,plain,
! [SV245: nat,SV123: nat] :
( ( ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
| ~ ~ ! [SY679: nat] :
~ ~ ( ( SV245
!= ( suc @ SY679 ) )
| ~ ( ord_less_nat @ SV123 @ SY679 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1458]) ).
thf(1589,plain,
! [SV123: nat,SV245: nat] :
( ( ( ~ ! [SY679: nat] :
~ ~ ( ( SV245
!= ( suc @ SY679 ) )
| ~ ( ord_less_nat @ SV123 @ SY679 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
| ~ ~ ! [SY679: nat] :
~ ~ ( ( SV245
!= ( suc @ SY679 ) )
| ~ ( ord_less_nat @ SV123 @ SY679 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1458]) ).
thf(1590,plain,
! [SV124: nat] :
( ( ( SV124
= ( suc @ ( sK7_SY559 @ SV124 ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1459]) ).
thf(1591,plain,
! [SV247: nat,SV126: nat] :
( ( ( ( suc @ SV126 )
!= SV247 )
= $false )
| ( ( ord_less_nat @ ( suc @ SV126 ) @ SV247 )
= $true )
| ( ( ord_less_nat @ SV126 @ SV247 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1460]) ).
thf(1592,plain,
! [SV248: nat,SV127: nat,SV303: nat > nat > $o] :
( ( ( ~ ! [SY718: nat] : ( SV303 @ SY718 @ SY718 ) )
= $true )
| ( ( ~ ! [SY719: nat,SY720: nat,SY721: nat] :
( ~ ( SV303 @ SY719 @ SY720 )
| ~ ( SV303 @ SY720 @ SY721 )
| ( SV303 @ SY719 @ SY721 ) )
| ~ ! [SY722: nat] : ( SV303 @ SY722 @ ( suc @ SY722 ) )
| ( SV303 @ SV127 @ SV248 ) )
= $true )
| ( ( ord_less_eq_nat @ SV127 @ SV248 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1461]) ).
thf(1593,plain,
! [SV249: real,SV128: real] :
( ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1462]) ).
thf(1594,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1462]) ).
thf(1595,plain,
! [SV251: nat,SV133: nat] :
( ( ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
| ~ ( ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1463]) ).
thf(1596,plain,
! [SV251: nat,SV133: nat] :
( ( ( ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
| ~ ( ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1463]) ).
thf(1597,plain,
! [SV134: nat,SV252: real] :
( ( ( ord_less_real @ zero_zero_real @ SV252 )
= $false )
| ( ( ~ ! [SY687: real] :
~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY687 )
| ( ( power_power_real @ SY687 @ SV134 )
!= SV252 ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1464]) ).
thf(1598,plain,
! [SV135: real,SV253: real] :
( ( ( ord_less_real @ SV253 @ zero_zero_real )
= $false )
| ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ SV135 @ SV253 ) )
= $true )
| ( ( ord_less_eq_real @ SV135 @ zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1465]) ).
thf(1599,plain,
! [SV310: real,SV304: real,SV256: real,SV139: real] :
( ( ( ord_less_eq_real @ zero_zero_real @ SV139 )
= $false )
| ( ( ~ ( ord_less_eq_real @ SV256 @ SV139 )
| ~ ( ord_less_real @ zero_zero_real @ SV304 )
| ~ ( ord_less_eq_real @ SV304 @ SV310 )
| ( ord_less_eq_real @ ( divide_divide_real @ SV256 @ SV310 ) @ ( divide_divide_real @ SV139 @ SV304 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1466]) ).
thf(1600,plain,
! [SV257: real,SV141: real] :
( ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1467]) ).
thf(1601,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1467]) ).
thf(1602,plain,
! [SV142: nat,SV258: nat,SV305: nat > $o] :
( ( ( ~ ( SV305 @ SV258 ) )
= $true )
| ( ( ~ ! [SY724: nat] :
( ~ ( ord_less_eq_nat @ SV142 @ SY724 )
| ~ ( ord_less_nat @ SY724 @ SV258 )
| ~ ( SV305 @ ( suc @ SY724 ) )
| ( SV305 @ SY724 ) )
| ( SV305 @ SV142 ) )
= $true )
| ( ( ord_less_eq_nat @ SV142 @ SV258 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1468]) ).
thf(1603,plain,
! [SV260: nat,SV145: nat] :
( ( ( ~ ( ord_less_nat @ SV145 @ ( suc @ SV260 ) ) )
= $true )
| ( ( SV260 = SV145 )
= $true )
| ( ( ord_less_nat @ SV145 @ SV260 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1469]) ).
thf(1604,plain,
! [SV148: nat] :
( ( ( SV148
!= ( suc @ ( sK25_SY591 @ SV148 ) ) )
= $false )
| ( ( SV148 = zero_zero_nat )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1470]) ).
thf(1605,plain,
! [SV262: int,SV149: nat,SV1: int] :
( ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ SV1 ) @ SV149 ) @ ( ring_1_of_int_real @ SV262 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ SV1 ) @ SV149 ) @ ( ring_1_of_int_real @ SV262 ) )
| ~ ( ord_less_int @ ( power_power_int @ SV1 @ SV149 ) @ SV262 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1471]) ).
thf(1606,plain,
! [SV262: int,SV149: nat,SV1: int] :
( ( ( ord_less_int @ ( power_power_int @ SV1 @ SV149 ) @ SV262 )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ SV1 ) @ SV149 ) @ ( ring_1_of_int_real @ SV262 ) )
| ~ ( ord_less_int @ ( power_power_int @ SV1 @ SV149 ) @ SV262 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1471]) ).
thf(1607,plain,
! [SV263: nat,SV150: int,SV2: int] :
( ( ( ord_less_real @ ( ring_1_of_int_real @ SV2 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV150 ) @ SV263 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( ring_1_of_int_real @ SV2 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV150 ) @ SV263 ) )
| ~ ( ord_less_int @ SV2 @ ( power_power_int @ SV150 @ SV263 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1608,plain,
! [SV263: nat,SV150: int,SV2: int] :
( ( ( ord_less_int @ SV2 @ ( power_power_int @ SV150 @ SV263 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( ring_1_of_int_real @ SV2 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV150 ) @ SV263 ) )
| ~ ( ord_less_int @ SV2 @ ( power_power_int @ SV150 @ SV263 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1609,plain,
! [SV264: int,SV152: nat,SV4: int] :
( ( ( ( power_power_real @ ( ring_1_of_int_real @ SV4 ) @ SV152 )
= ( ring_1_of_int_real @ SV264 ) )
= $false )
| ( ( ~ ( ( ( power_power_real @ ( ring_1_of_int_real @ SV4 ) @ SV152 )
!= ( ring_1_of_int_real @ SV264 ) )
| ( ( power_power_int @ SV4 @ SV152 )
!= SV264 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1473]) ).
thf(1610,plain,
! [SV264: int,SV152: nat,SV4: int] :
( ( ( ( power_power_int @ SV4 @ SV152 )
= SV264 )
= $false )
| ( ( ~ ( ( ( power_power_real @ ( ring_1_of_int_real @ SV4 ) @ SV152 )
!= ( ring_1_of_int_real @ SV264 ) )
| ( ( power_power_int @ SV4 @ SV152 )
!= SV264 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1473]) ).
thf(1611,plain,
! [SV265: nat,SV153: int,SV5: int] :
( ( ( ( ring_1_of_int_real @ SV5 )
= ( power_power_real @ ( ring_1_of_int_real @ SV153 ) @ SV265 ) )
= $false )
| ( ( ~ ( ( ( ring_1_of_int_real @ SV5 )
!= ( power_power_real @ ( ring_1_of_int_real @ SV153 ) @ SV265 ) )
| ( SV5
!= ( power_power_int @ SV153 @ SV265 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1474]) ).
thf(1612,plain,
! [SV265: nat,SV153: int,SV5: int] :
( ( ( SV5
= ( power_power_int @ SV153 @ SV265 ) )
= $false )
| ( ( ~ ( ( ( ring_1_of_int_real @ SV5 )
!= ( power_power_real @ ( ring_1_of_int_real @ SV153 ) @ SV265 ) )
| ( SV5
!= ( power_power_int @ SV153 @ SV265 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1474]) ).
thf(1613,plain,
! [SV154: int,SV6: int] :
( ( ( ~ ( ord_less_real @ ( ring_1_of_int_real @ SV6 ) @ ( ring_1_of_int_real @ SV154 ) )
| ~ ( ord_less_int @ SV6 @ SV154 ) )
= $false )
| ( ( ord_less_real @ ( ring_1_of_int_real @ SV6 ) @ ( ring_1_of_int_real @ SV154 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1475]) ).
thf(1614,plain,
! [SV154: int,SV6: int] :
( ( ( ~ ( ord_less_real @ ( ring_1_of_int_real @ SV6 ) @ ( ring_1_of_int_real @ SV154 ) )
| ~ ( ord_less_int @ SV6 @ SV154 ) )
= $false )
| ( ( ord_less_int @ SV6 @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1476]) ).
thf(1615,plain,
! [SV155: int,SV7: int] :
( ( ( ( ( ring_1_of_int_real @ SV7 )
!= ( ring_1_of_int_real @ SV155 ) )
| ( SV7 != SV155 ) )
= $false )
| ( ( ( ring_1_of_int_real @ SV7 )
= ( ring_1_of_int_real @ SV155 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1477]) ).
thf(1616,plain,
! [SV155: int,SV7: int] :
( ( ( ( ( ring_1_of_int_real @ SV7 )
!= ( ring_1_of_int_real @ SV155 ) )
| ( SV7 != SV155 ) )
= $false )
| ( ( SV7 = SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1478]) ).
thf(1617,plain,
! [SV156: nat,SV8: nat] :
( ( ( ( ( suc @ SV8 )
!= ( suc @ SV156 ) )
| ( SV8 != SV156 ) )
= $false )
| ( ( ( suc @ SV8 )
= ( suc @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1479]) ).
thf(1618,plain,
! [SV156: nat,SV8: nat] :
( ( ( ( ( suc @ SV8 )
!= ( suc @ SV156 ) )
| ( SV8 != SV156 ) )
= $false )
| ( ( SV8 = SV156 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1480]) ).
thf(1619,plain,
! [SV157: nat,SV9: nat] :
( ( ( ( ( suc @ SV9 )
!= ( suc @ SV157 ) )
| ( SV9 != SV157 ) )
= $false )
| ( ( ( suc @ SV9 )
= ( suc @ SV157 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1481]) ).
thf(1620,plain,
! [SV157: nat,SV9: nat] :
( ( ( ( ( suc @ SV9 )
!= ( suc @ SV157 ) )
| ( SV9 != SV157 ) )
= $false )
| ( ( SV9 = SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1482]) ).
thf(1621,plain,
! [SV158: nat,SV10: nat] :
( ( ( ~ ( ord_less_nat @ ( suc @ SV10 ) @ ( suc @ SV158 ) )
| ~ ( ord_less_nat @ SV10 @ SV158 ) )
= $false )
| ( ( ord_less_nat @ ( suc @ SV10 ) @ ( suc @ SV158 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1483]) ).
thf(1622,plain,
! [SV158: nat,SV10: nat] :
( ( ( ~ ( ord_less_nat @ ( suc @ SV10 ) @ ( suc @ SV158 ) )
| ~ ( ord_less_nat @ SV10 @ SV158 ) )
= $false )
| ( ( ord_less_nat @ SV10 @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1484]) ).
thf(1623,plain,
! [SV12: int] :
( ( ( zero_zero_real
!= ( ring_1_of_int_real @ SV12 ) )
= $false )
| ( ( zero_zero_real
= ( ring_1_of_int_real @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1485]) ).
thf(1624,plain,
! [SV12: int] :
( ( ( SV12 != zero_zero_int )
= $false )
| ( ( zero_zero_real
= ( ring_1_of_int_real @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1485]) ).
thf(1625,plain,
! [SV12: int] :
( ( ( zero_zero_real
!= ( ring_1_of_int_real @ SV12 ) )
= $false )
| ( ( SV12 = zero_zero_int )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1486]) ).
thf(1626,plain,
! [SV12: int] :
( ( ( SV12 != zero_zero_int )
= $false )
| ( ( SV12 = zero_zero_int )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1486]) ).
thf(1627,plain,
! [SV13: int] :
( ( ( ( ring_1_of_int_real @ SV13 )
!= zero_zero_real )
= $false )
| ( ( ( ring_1_of_int_real @ SV13 )
= zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1487]) ).
thf(1628,plain,
! [SV13: int] :
( ( ( SV13 != zero_zero_int )
= $false )
| ( ( ( ring_1_of_int_real @ SV13 )
= zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1487]) ).
thf(1629,plain,
! [SV13: int] :
( ( ( ( ring_1_of_int_real @ SV13 )
!= zero_zero_real )
= $false )
| ( ( SV13 = zero_zero_int )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1488]) ).
thf(1630,plain,
! [SV13: int] :
( ( ( SV13 != zero_zero_int )
= $false )
| ( ( SV13 = zero_zero_int )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1488]) ).
thf(1631,plain,
! [SV14: int] :
( ( ( ~ ( ord_less_real @ ( ring_1_of_int_real @ SV14 ) @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ ( ring_1_of_int_real @ SV14 ) @ zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1489]) ).
thf(1632,plain,
! [SV14: int] :
( ( ( ~ ( ord_less_int @ SV14 @ zero_zero_int ) )
= $false )
| ( ( ord_less_real @ ( ring_1_of_int_real @ SV14 ) @ zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1489]) ).
thf(1633,plain,
! [SV14: int] :
( ( ( ~ ( ord_less_real @ ( ring_1_of_int_real @ SV14 ) @ zero_zero_real ) )
= $false )
| ( ( ord_less_int @ SV14 @ zero_zero_int )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1490]) ).
thf(1634,plain,
! [SV14: int] :
( ( ( ~ ( ord_less_int @ SV14 @ zero_zero_int ) )
= $false )
| ( ( ord_less_int @ SV14 @ zero_zero_int )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1490]) ).
thf(1635,plain,
! [SV15: int] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ SV15 ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1491]) ).
thf(1636,plain,
! [SV15: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV15 ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1491]) ).
thf(1637,plain,
! [SV15: int] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ SV15 ) ) )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1492]) ).
thf(1638,plain,
! [SV15: int] :
( ( ( ~ ( ord_less_int @ zero_zero_int @ SV15 ) )
= $false )
| ( ( ord_less_int @ zero_zero_int @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1492]) ).
thf(1639,plain,
! [SV159: nat,SV16: nat] :
( ( ( ord_less_nat @ SV16 @ SV159 )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ SV16 @ SV159 )
| ~ ( ord_less_nat @ SV159 @ ( suc @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1493]) ).
thf(1640,plain,
! [SV159: nat,SV16: nat] :
( ( ( ~ ~ ( ord_less_nat @ SV16 @ SV159 )
| ~ ( ord_less_nat @ SV159 @ ( suc @ SV16 ) ) )
= $false )
| ( ( ord_less_nat @ SV159 @ ( suc @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1494]) ).
thf(1641,plain,
! [SV160: nat,SV17: nat] :
( ( ( ~ ( ord_less_nat @ SV17 @ ( suc @ SV160 ) )
| ~ ( ( ord_less_nat @ SV17 @ SV160 )
| ( SV17 = SV160 ) ) )
= $false )
| ( ( ord_less_nat @ SV17 @ ( suc @ SV160 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1495]) ).
thf(1642,plain,
! [SV160: nat,SV17: nat] :
( ( ( ord_less_nat @ SV17 @ SV160 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV17 @ ( suc @ SV160 ) )
| ~ ( ( ord_less_nat @ SV17 @ SV160 )
| ( SV17 = SV160 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1496]) ).
thf(1643,plain,
! [SV160: nat,SV17: nat] :
( ( ( SV17 = SV160 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV17 @ ( suc @ SV160 ) )
| ~ ( ( ord_less_nat @ SV17 @ SV160 )
| ( SV17 = SV160 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1496]) ).
thf(1644,plain,
! [SV161: nat,SV21: nat] :
( ( ( ( ( power_power_nat @ SV21 @ SV161 )
!= ( suc @ zero_zero_nat ) )
| ~ ( ( SV161 = zero_zero_nat )
| ( SV21
= ( suc @ zero_zero_nat ) ) ) )
= $false )
| ( ( ( power_power_nat @ SV21 @ SV161 )
= ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1497]) ).
thf(1645,plain,
! [SV21: nat,SV161: nat] :
( ( ( SV161 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( power_power_nat @ SV21 @ SV161 )
!= ( suc @ zero_zero_nat ) )
| ~ ( ( SV161 = zero_zero_nat )
| ( SV21
= ( suc @ zero_zero_nat ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1498]) ).
thf(1646,plain,
! [SV161: nat,SV21: nat] :
( ( ( SV21
= ( suc @ zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( power_power_nat @ SV21 @ SV161 )
!= ( suc @ zero_zero_nat ) )
| ~ ( ( SV161 = zero_zero_nat )
| ( SV21
= ( suc @ zero_zero_nat ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1498]) ).
thf(1647,plain,
! [SV27: nat] :
( ( ( ~ ( ord_less_nat @ SV27 @ ( suc @ zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ SV27 @ ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1499]) ).
thf(1648,plain,
! [SV27: nat] :
( ( ( SV27 != zero_zero_nat )
= $false )
| ( ( ord_less_nat @ SV27 @ ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1499]) ).
thf(1649,plain,
! [SV27: nat] :
( ( ( ~ ( ord_less_nat @ SV27 @ ( suc @ zero_zero_nat ) ) )
= $false )
| ( ( SV27 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1500]) ).
thf(1650,plain,
! [SV27: nat] :
( ( ( SV27 != zero_zero_nat )
= $false )
| ( ( SV27 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1500]) ).
thf(1651,plain,
! [SV162: int,SV28: int] :
( ( ( ~ ( ord_less_eq_real @ ( ring_1_of_int_real @ SV28 ) @ ( ring_1_of_int_real @ SV162 ) )
| ~ ( ord_less_eq_int @ SV28 @ SV162 ) )
= $false )
| ( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV28 ) @ ( ring_1_of_int_real @ SV162 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1501]) ).
thf(1652,plain,
! [SV162: int,SV28: int] :
( ( ( ~ ( ord_less_eq_real @ ( ring_1_of_int_real @ SV28 ) @ ( ring_1_of_int_real @ SV162 ) )
| ~ ( ord_less_eq_int @ SV28 @ SV162 ) )
= $false )
| ( ( ord_less_eq_int @ SV28 @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1502]) ).
thf(1653,plain,
! [SV266: int,SV163: nat,SV29: int] :
( ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ SV29 ) @ SV163 ) @ ( ring_1_of_int_real @ SV266 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ SV29 ) @ SV163 ) @ ( ring_1_of_int_real @ SV266 ) )
| ~ ( ord_less_eq_int @ ( power_power_int @ SV29 @ SV163 ) @ SV266 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1503]) ).
thf(1654,plain,
! [SV266: int,SV163: nat,SV29: int] :
( ( ( ord_less_eq_int @ ( power_power_int @ SV29 @ SV163 ) @ SV266 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ SV29 ) @ SV163 ) @ ( ring_1_of_int_real @ SV266 ) )
| ~ ( ord_less_eq_int @ ( power_power_int @ SV29 @ SV163 ) @ SV266 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1503]) ).
thf(1655,plain,
! [SV267: nat,SV164: int,SV30: int] :
( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV30 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV164 ) @ SV267 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( ring_1_of_int_real @ SV30 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV164 ) @ SV267 ) )
| ~ ( ord_less_eq_int @ SV30 @ ( power_power_int @ SV164 @ SV267 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1504]) ).
thf(1656,plain,
! [SV267: nat,SV164: int,SV30: int] :
( ( ( ord_less_eq_int @ SV30 @ ( power_power_int @ SV164 @ SV267 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( ring_1_of_int_real @ SV30 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV164 ) @ SV267 ) )
| ~ ( ord_less_eq_int @ SV30 @ ( power_power_int @ SV164 @ SV267 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1504]) ).
thf(1657,plain,
! [SV166: nat,SV32: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( suc @ SV32 ) @ ( suc @ SV166 ) )
| ~ ( ord_less_eq_nat @ SV32 @ SV166 ) )
= $false )
| ( ( ord_less_eq_nat @ ( suc @ SV32 ) @ ( suc @ SV166 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1505]) ).
thf(1658,plain,
! [SV166: nat,SV32: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( suc @ SV32 ) @ ( suc @ SV166 ) )
| ~ ( ord_less_eq_nat @ SV32 @ SV166 ) )
= $false )
| ( ( ord_less_eq_nat @ SV32 @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1506]) ).
thf(1659,plain,
! [SV167: nat,SV33: nat] :
( ( ( ord_less_eq_nat @ SV33 @ SV167 )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_eq_nat @ SV33 @ SV167 )
| ~ ( ord_less_eq_nat @ ( suc @ SV167 ) @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1507]) ).
thf(1660,plain,
! [SV167: nat,SV33: nat] :
( ( ( ~ ~ ( ord_less_eq_nat @ SV33 @ SV167 )
| ~ ( ord_less_eq_nat @ ( suc @ SV167 ) @ SV33 ) )
= $false )
| ( ( ord_less_eq_nat @ ( suc @ SV167 ) @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1508]) ).
thf(1661,plain,
! [SV168: nat,SV35: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV35 @ ( suc @ SV168 ) )
| ~ ( ( ord_less_eq_nat @ SV35 @ SV168 )
| ( SV35
= ( suc @ SV168 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV35 @ ( suc @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1509]) ).
thf(1662,plain,
! [SV168: nat,SV35: nat] :
( ( ( ord_less_eq_nat @ SV35 @ SV168 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV35 @ ( suc @ SV168 ) )
| ~ ( ( ord_less_eq_nat @ SV35 @ SV168 )
| ( SV35
= ( suc @ SV168 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1510]) ).
thf(1663,plain,
! [SV168: nat,SV35: nat] :
( ( ( SV35
= ( suc @ SV168 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV35 @ ( suc @ SV168 ) )
| ~ ( ( ord_less_eq_nat @ SV35 @ SV168 )
| ( SV35
= ( suc @ SV168 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1510]) ).
thf(1664,plain,
! [SV306: nat,SV169: nat] :
( ( ( ( nthRoo1352626670d_root @ SV169 @ SV306 )
| ( SV169
= ( suc @ SV306 ) ) )
= $false )
| ( ( ~ ( ~ ( nthRoo1352626670d_root @ SV169 @ SV306 )
| ( SV169
!= ( suc @ SV306 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1511]) ).
thf(1665,plain,
! [SV170: nat,SV37: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( suc @ SV37 ) @ SV170 )
| ~ ( ord_less_nat @ SV37 @ SV170 ) )
= $false )
| ( ( ord_less_eq_nat @ ( suc @ SV37 ) @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1512]) ).
thf(1666,plain,
! [SV170: nat,SV37: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( suc @ SV37 ) @ SV170 )
| ~ ( ord_less_nat @ SV37 @ SV170 ) )
= $false )
| ( ( ord_less_nat @ SV37 @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1513]) ).
thf(1667,plain,
! [SV171: nat,SV38: nat] :
( ( ( ~ ( ord_less_nat @ SV38 @ ( suc @ SV171 ) )
| ~ ( ord_less_eq_nat @ SV38 @ SV171 ) )
= $false )
| ( ( ord_less_nat @ SV38 @ ( suc @ SV171 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1514]) ).
thf(1668,plain,
! [SV171: nat,SV38: nat] :
( ( ( ~ ( ord_less_nat @ SV38 @ ( suc @ SV171 ) )
| ~ ( ord_less_eq_nat @ SV38 @ SV171 ) )
= $false )
| ( ( ord_less_eq_nat @ SV38 @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1515]) ).
thf(1669,plain,
! [SV307: nat,SV172: nat] :
( ( ( ( ord_less_nat @ SV172 @ SV307 )
| ( ord_less_eq_nat @ ( suc @ SV172 ) @ SV307 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV172 @ SV307 )
| ~ ( ord_less_eq_nat @ ( suc @ SV172 ) @ SV307 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1516]) ).
thf(1670,plain,
! [SV175: real,SV43: real,SV271: real] :
( ( ( ord_less_real @ zero_zero_real @ SV271 )
= $false )
| ( ( ord_less_real @ ( divide_divide_real @ SV43 @ SV271 ) @ ( divide_divide_real @ SV175 @ SV271 ) )
= $true )
| ( ( ord_less_real @ SV43 @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1517]) ).
thf(1671,plain,
! [SV45: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV45 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1519]) ).
thf(1672,plain,
! [SV45: nat] :
( ( ( ~ ~ ! [SY405: nat] :
( SV45
!= ( suc @ SY405 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1519]) ).
thf(1673,plain,
! [SV311: nat,SV45: nat] :
( ( ( SV45
!= ( suc @ SV311 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV45 )
| ~ ~ ! [SY405: nat] :
( SV45
!= ( suc @ SY405 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(1674,plain,
! [SV178: nat > $o,SV47: nat] :
( ( ( ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) )
| ~ ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1521]) ).
thf(1675,plain,
! [SV47: nat,SV178: nat > $o] :
( ( ( SV178 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) )
| ~ ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1522]) ).
thf(1676,plain,
! [SV178: nat > $o,SV47: nat] :
( ( ( ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) )
| ~ ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1522]) ).
thf(1677,plain,
! [SV180: nat,SV49: real,SV272: real] :
( ( ( ord_less_eq_real @ zero_zero_real @ SV272 )
= $false )
| ( ( ord_less_real @ SV49 @ SV272 )
= $true )
| ( ( ord_less_real @ ( power_power_real @ SV49 @ SV180 ) @ ( power_power_real @ SV272 @ SV180 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1523]) ).
thf(1678,plain,
! [SV181: nat,SV273: nat,SV50: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV50 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV273 )
| ( SV50 = SV273 ) )
= $true )
| ( ( ( power_power_nat @ SV50 @ ( suc @ SV181 ) )
= ( power_power_nat @ SV273 @ ( suc @ SV181 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1524]) ).
thf(1679,plain,
! [SV274: real,SV182: real,SV51: real] :
( ( ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
| ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1525]) ).
thf(1680,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
| ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1525]) ).
thf(1681,plain,
! [SV183: nat,SV52: nat,SV275: nat > $o] :
( ( ( SV275 @ SV52 )
= $false )
| ( ( ~ ! [SY692: nat] :
( ~ ( ord_less_eq_nat @ SV52 @ SY692 )
| ~ ( SV275 @ SY692 )
| ( SV275 @ ( suc @ SY692 ) ) )
| ( SV275 @ SV183 ) )
= $true )
| ( ( ord_less_eq_nat @ SV52 @ SV183 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1526]) ).
thf(1682,plain,
! [SV53: nat > $o,SV184: nat] :
( ( ( ! [SY725: nat] :
( ~ ( ord_less_eq_nat @ ( suc @ SY725 ) @ ( sK6_SY421 @ SV184 @ SV53 ) )
| ( SV53 @ SY725 ) ) )
= $true )
| ( ( SV53 @ SV184 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1527]) ).
thf(1683,plain,
! [SV308: real,SV276: real,SV185: real,SV54: real] :
( ( ( ~ ( ord_less_real @ SV54 @ SV185 ) )
= $true )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV276 )
| ~ ( ord_less_eq_real @ SV276 @ SV308 )
| ( ord_less_real @ ( divide_divide_real @ SV54 @ SV308 ) @ ( divide_divide_real @ SV185 @ SV276 ) ) )
= $true )
| ( ( ord_less_eq_real @ zero_zero_real @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1529]) ).
thf(1684,plain,
! [SV55: nat > int,SV277: nat,SV186: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV186 @ SV277 ) )
= $true )
| ( ( ord_less_eq_int @ ( SV55 @ SV186 ) @ ( SV55 @ SV277 ) )
= $true )
| ( ( ord_less_eq_int @ ( SV55 @ ( sK8_SY428 @ SV277 @ SV186 @ SV55 ) ) @ ( SV55 @ ( suc @ ( sK8_SY428 @ SV277 @ SV186 @ SV55 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1530]) ).
thf(1685,plain,
! [SV187: nat,SV56: nat] :
( ( ( ord_less_eq_nat @ SV56 @ SV187 )
= $true )
| ( ( SV56
= ( suc @ SV187 ) )
= $true )
| ( ( ord_less_eq_nat @ SV56 @ ( suc @ SV187 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1531]) ).
thf(1686,plain,
! [SV59: nat > real,SV278: nat,SV189: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV189 @ SV278 ) )
= $true )
| ( ( ord_less_eq_real @ ( SV59 @ SV189 ) @ ( SV59 @ SV278 ) )
= $true )
| ( ( ord_less_eq_real @ ( SV59 @ ( sK9_SY434 @ SV278 @ SV189 @ SV59 ) ) @ ( SV59 @ ( suc @ ( sK9_SY434 @ SV278 @ SV189 @ SV59 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1532]) ).
thf(1687,plain,
! [SV191: nat,SV61: real] :
( ( ( ( ( power_power_real @ SV61 @ SV191 )
!= zero_zero_real )
| ~ ~ ( ( SV61 != zero_zero_real )
| ~ ( ord_less_nat @ zero_zero_nat @ SV191 ) ) )
= $false )
| ( ( ( power_power_real @ SV61 @ SV191 )
= zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1534]) ).
thf(1688,plain,
! [SV191: nat,SV61: real] :
( ( ( ( SV61 != zero_zero_real )
| ~ ( ord_less_nat @ zero_zero_nat @ SV191 ) )
= $true )
| ( ( ~ ( ( ( power_power_real @ SV61 @ SV191 )
!= zero_zero_real )
| ~ ~ ( ( SV61 != zero_zero_real )
| ~ ( ord_less_nat @ zero_zero_nat @ SV191 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1535]) ).
thf(1689,plain,
! [SV192: real,SV62: nat] :
( ( ( ! [SY616: real] :
~ ~ ( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY616 )
| ( ( power_power_real @ SY616 @ SV62 )
!= SV192 ) )
| ~ ! [SY617: real] :
( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY617 )
| ( ( power_power_real @ SY617 @ SV62 )
!= SV192 ) )
| ( SY617 = SY616 ) ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV192 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1536]) ).
thf(1690,plain,
! [SV193: nat,SV63: real,SV279: real] :
( ( ( ord_less_eq_real @ zero_zero_real @ SV279 )
= $false )
| ( ( ord_less_eq_real @ SV63 @ SV279 )
= $true )
| ( ( ord_less_eq_real @ ( power_power_real @ SV63 @ ( suc @ SV193 ) ) @ ( power_power_real @ SV279 @ ( suc @ SV193 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1537]) ).
thf(1691,plain,
! [SV64: nat > nat,SV280: nat,SV194: nat] :
( ( ( ~ ( ord_less_nat @ SV194 @ SV280 ) )
= $true )
| ( ( ord_less_nat @ ( SV64 @ SV194 ) @ ( SV64 @ SV280 ) )
= $true )
| ( ( ord_less_nat @ ( SV64 @ ( sK10_SY444 @ SV280 @ SV194 @ SV64 ) ) @ ( SV64 @ ( suc @ ( sK10_SY444 @ SV280 @ SV194 @ SV64 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1538]) ).
thf(1692,plain,
! [SV196: nat,SV67: nat] :
( ( ( ord_less_nat @ SV67 @ SV196 )
= $true )
| ( ( SV67 = SV196 )
= $true )
| ( ( ord_less_nat @ SV67 @ ( suc @ SV196 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1539]) ).
thf(1693,plain,
! [SV281: nat,SV197: nat,SV68: nat > int] :
( ( ( ~ ( ( ord_less_int @ ( SV68 @ SV197 ) @ ( SV68 @ SV281 ) )
| ( ord_less_nat @ SV197 @ SV281 ) )
| ~ ( ~ ( ord_less_int @ ( SV68 @ SV197 ) @ ( SV68 @ SV281 ) )
| ~ ( ord_less_nat @ SV197 @ SV281 ) ) )
= $true )
| ( ( ord_less_int @ ( SV68 @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) @ ( SV68 @ ( suc @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1540]) ).
thf(1694,plain,
! [SV281: nat,SV197: nat,SV68: nat > int] :
( ( ( ( ord_less_int @ ( SV68 @ SV197 ) @ ( SV68 @ SV281 ) )
= ( ord_less_nat @ SV197 @ SV281 ) )
= $true )
| ( ( ord_less_int @ ( SV68 @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) @ ( SV68 @ ( suc @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1540]) ).
thf(1695,plain,
! [SV69: nat,SV198: nat] :
( ( ( SV198
= ( suc @ SV69 ) )
= $true )
| ( ( ~ ! [SY623: nat] :
( ~ ( ord_less_nat @ SV69 @ SY623 )
| ( SV198
!= ( suc @ SY623 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV69 @ SV198 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1541]) ).
thf(1696,plain,
! [SV199: nat,SV70: nat > $o] :
( ( ( ~ ( SV70 @ ( sK26_SY453 @ SV199 @ SV70 ) )
| ( SV70 @ ( suc @ ( sK26_SY453 @ SV199 @ SV70 ) ) ) )
= $false )
| ( ( SV70 @ SV199 )
= $true )
| ( ( SV70 @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1542]) ).
thf(1697,plain,
! [SV282: nat,SV201: nat,SV73: nat > nat] :
( ( ( ~ ( ( ord_less_nat @ ( SV73 @ SV201 ) @ ( SV73 @ SV282 ) )
| ( ord_less_nat @ SV201 @ SV282 ) )
| ~ ( ~ ( ord_less_nat @ ( SV73 @ SV201 ) @ ( SV73 @ SV282 ) )
| ~ ( ord_less_nat @ SV201 @ SV282 ) ) )
= $true )
| ( ( ord_less_nat @ ( SV73 @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) @ ( SV73 @ ( suc @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1544]) ).
thf(1698,plain,
! [SV282: nat,SV201: nat,SV73: nat > nat] :
( ( ( ( ord_less_nat @ ( SV73 @ SV201 ) @ ( SV73 @ SV282 ) )
= ( ord_less_nat @ SV201 @ SV282 ) )
= $true )
| ( ( ord_less_nat @ ( SV73 @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) @ ( SV73 @ ( suc @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1544]) ).
thf(1699,plain,
! [SV202: nat,SV74: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ ( sK13_SY627 @ SV74 @ SV202 ) )
| ( ( power_power_real @ ( sK13_SY627 @ SV74 @ SV202 ) @ ( suc @ SV202 ) )
!= SV74 ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1545]) ).
thf(1700,plain,
! [SV204: nat,SV76: nat] :
( ( ( ~ ( ord_less_nat @ SV76 @ ( sK14_SY628 @ SV204 @ SV76 ) ) )
= $false )
| ( ( ord_less_nat @ ( suc @ SV76 ) @ SV204 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1546]) ).
thf(1701,plain,
! [SV76: nat,SV204: nat] :
( ( ( SV204
!= ( suc @ ( sK14_SY628 @ SV204 @ SV76 ) ) )
= $false )
| ( ( ord_less_nat @ ( suc @ SV76 ) @ SV204 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1546]) ).
thf(1702,plain,
! [SV205: nat,SV283: real,SV77: real] :
( ( ( ord_less_eq_real @ zero_zero_real @ SV77 )
= $false )
| ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV283 )
| ( SV77 = SV283 ) )
= $true )
| ( ( ( power_power_real @ SV77 @ ( suc @ SV205 ) )
= ( power_power_real @ SV283 @ ( suc @ SV205 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1547]) ).
thf(1703,plain,
! [SV78: nat,SV284: nat > $o,SV206: nat] :
( ( ( ! [SY699: nat] :
( ( SV206
!= ( suc @ SY699 ) )
| ( SV284 @ SY699 ) ) )
= $false )
| ( ( ~ ! [SY700: nat] :
( ~ ( ord_less_nat @ SY700 @ SV206 )
| ~ ( SV284 @ ( suc @ SY700 ) )
| ( SV284 @ SY700 ) )
| ( SV284 @ SV78 ) )
= $true )
| ( ( ord_less_nat @ SV78 @ SV206 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1548]) ).
thf(1704,plain,
! [SV207: nat,SV79: nat,SV285: nat > nat > $o] :
( ( ( ! [SY701: nat] : ( SV285 @ SY701 @ ( suc @ SY701 ) ) )
= $false )
| ( ( ~ ! [SY702: nat,SY703: nat,SY704: nat] :
( ~ ( ord_less_nat @ SY702 @ SY703 )
| ~ ( ord_less_nat @ SY703 @ SY704 )
| ~ ( SV285 @ SY702 @ SY703 )
| ~ ( SV285 @ SY703 @ SY704 )
| ( SV285 @ SY702 @ SY704 ) )
| ( SV285 @ SV79 @ SV207 ) )
= $true )
| ( ( ord_less_nat @ SV79 @ SV207 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1549]) ).
thf(1705,plain,
! [SV80: nat] :
( ( ( SV80
= ( suc @ ( sK15_SY475 @ SV80 ) ) )
= $true )
| ( ( SV80 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1550]) ).
thf(1706,plain,
! [SV81: nat > nat,SV286: nat,SV208: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV208 @ SV286 ) )
= $true )
| ( ( ord_less_eq_nat @ ( SV81 @ SV208 ) @ ( SV81 @ SV286 ) )
= $true )
| ( ( ord_less_eq_nat @ ( SV81 @ ( sK16_SY478 @ SV286 @ SV208 @ SV81 ) ) @ ( SV81 @ ( suc @ ( sK16_SY478 @ SV286 @ SV208 @ SV81 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1551]) ).
thf(1707,plain,
! [SV209: nat,SV82: nat,SV287: nat > $o] :
( ( ( SV287 @ SV82 )
= $false )
| ( ( ~ ! [SY706: nat] :
( ~ ( ord_less_eq_nat @ SV82 @ SY706 )
| ~ ( ord_less_nat @ SY706 @ SV209 )
| ~ ( SV287 @ SY706 )
| ( SV287 @ ( suc @ SY706 ) ) )
| ( SV287 @ SV209 ) )
= $true )
| ( ( ord_less_eq_nat @ SV82 @ SV209 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1552]) ).
thf(1708,plain,
! [SV288: nat,SV212: nat,SV85: nat > nat > $o] :
( ( ( ~ ! [SY487: nat] : ( SV85 @ zero_zero_nat @ ( suc @ SY487 ) ) )
= $true )
| ( ( ~ ! [SY488: nat,SY489: nat] :
( ~ ( SV85 @ SY488 @ SY489 )
| ( SV85 @ ( suc @ SY488 ) @ ( suc @ SY489 ) ) )
| ( SV85 @ SV212 @ SV288 ) )
= $true )
| ( ( SV85 @ ( sK17_SY486 @ SV288 @ SV212 @ SV85 ) @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1554]) ).
thf(1709,plain,
! [SV86: nat > int,SV289: nat,SV213: nat] :
( ( ( ~ ( ord_less_nat @ SV213 @ SV289 ) )
= $true )
| ( ( ord_less_int @ ( SV86 @ SV213 ) @ ( SV86 @ SV289 ) )
= $true )
| ( ( ord_less_int @ ( SV86 @ ( sK18_SY492 @ SV289 @ SV213 @ SV86 ) ) @ ( SV86 @ ( suc @ ( sK18_SY492 @ SV289 @ SV213 @ SV86 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1555]) ).
thf(1710,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK27_SY649 @ SV214 @ SV87 ) @ ( suc @ SV87 ) )
| ( SV214 @ ( sK27_SY649 @ SV214 @ SV87 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) )
| ~ ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1556]) ).
thf(1711,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) )
| ~ ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1557]) ).
thf(1712,plain,
! [SV88: nat > real,SV290: nat,SV215: nat] :
( ( ( ~ ( ord_less_nat @ SV215 @ SV290 ) )
= $true )
| ( ( ord_less_real @ ( SV88 @ SV215 ) @ ( SV88 @ SV290 ) )
= $true )
| ( ( ord_less_real @ ( SV88 @ ( sK19_SY498 @ SV290 @ SV215 @ SV88 ) ) @ ( SV88 @ ( suc @ ( sK19_SY498 @ SV290 @ SV215 @ SV88 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1558]) ).
thf(1713,plain,
! [SV216: nat,SV291: int,SV89: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV89 )
= $false )
| ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV291 )
| ( SV89 = SV291 ) )
= $true )
| ( ( ( power_power_int @ SV89 @ ( suc @ SV216 ) )
= ( power_power_int @ SV291 @ ( suc @ SV216 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1559]) ).
thf(1714,plain,
! [SV91: nat > int,SV292: nat,SV217: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV217 @ SV292 ) )
= $true )
| ( ( ord_less_eq_int @ ( SV91 @ SV292 ) @ ( SV91 @ SV217 ) )
= $true )
| ( ( ord_less_eq_int @ ( SV91 @ ( suc @ ( sK20_SY503 @ SV292 @ SV217 @ SV91 ) ) ) @ ( SV91 @ ( sK20_SY503 @ SV292 @ SV217 @ SV91 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1560]) ).
thf(1715,plain,
! [SV93: nat,SV293: nat,SV219: nat] :
( ( ( ord_less_nat @ SV219 @ SV293 )
= $false )
| ( ( ord_less_nat @ ( suc @ SV93 ) @ SV293 )
= $true )
| ( ( ord_less_nat @ SV93 @ SV219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1562]) ).
thf(1716,plain,
! [SV224: nat,SV99: nat,SV294: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV294 )
= $false )
| ( ( ord_less_eq_nat @ SV99 @ SV294 )
= $true )
| ( ( ord_less_eq_nat @ ( power_power_nat @ SV99 @ ( suc @ SV224 ) ) @ ( power_power_nat @ SV294 @ ( suc @ SV224 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1564]) ).
thf(1717,plain,
! [SV226: nat,SV101: int,SV295: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV295 )
= $false )
| ( ( ord_less_eq_int @ SV101 @ SV295 )
= $true )
| ( ( ord_less_eq_int @ ( power_power_int @ SV101 @ ( suc @ SV226 ) ) @ ( power_power_int @ SV295 @ ( suc @ SV226 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1565]) ).
thf(1718,plain,
! [SV227: real,SV296: nat,SV102: real] :
( ( ( ord_less_eq_real @ zero_zero_real @ SV102 )
= $false )
| ( ( ord_less_eq_real @ ( power_power_real @ SV102 @ SV296 ) @ ( power_power_real @ SV227 @ SV296 ) )
= $true )
| ( ( ord_less_eq_real @ SV102 @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1566]) ).
thf(1719,plain,
! [SV297: real,SV228: real,SV103: real] :
( ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1567]) ).
thf(1720,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1567]) ).
thf(1721,plain,
! [SV229: nat,SV104: nat] :
( ( ( ~ ( ( ord_less_nat @ SV104 @ ( suc @ SV229 ) )
| ( SV104 = SV229 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV104 @ ( suc @ SV229 ) )
| ( SV104 != SV229 ) ) )
= $true )
| ( ( ord_less_nat @ SV104 @ SV229 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1568]) ).
thf(1722,plain,
! [SV298: nat,SV230: nat,SV106: nat > real] :
( ( ( ~ ( ( ord_less_real @ ( SV106 @ SV230 ) @ ( SV106 @ SV298 ) )
| ( ord_less_nat @ SV230 @ SV298 ) )
| ~ ( ~ ( ord_less_real @ ( SV106 @ SV230 ) @ ( SV106 @ SV298 ) )
| ~ ( ord_less_nat @ SV230 @ SV298 ) ) )
= $true )
| ( ( ord_less_real @ ( SV106 @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) @ ( SV106 @ ( suc @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1570]) ).
thf(1723,plain,
! [SV298: nat,SV230: nat,SV106: nat > real] :
( ( ( ( ord_less_real @ ( SV106 @ SV230 ) @ ( SV106 @ SV298 ) )
= ( ord_less_nat @ SV230 @ SV298 ) )
= $true )
| ( ( ord_less_real @ ( SV106 @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) @ ( SV106 @ ( suc @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1570]) ).
thf(1724,plain,
! [SV231: nat,SV107: nat > $o] :
( ( ( ~ ( SV107 @ ( suc @ ( sK28_SY525 @ SV231 @ SV107 ) ) )
| ( SV107 @ ( sK28_SY525 @ SV231 @ SV107 ) ) )
= $false )
| ( ( SV107 @ zero_zero_nat )
= $true )
| ( ( SV107 @ SV231 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1571]) ).
thf(1725,plain,
! [SV232: nat,SV109: nat > $o] :
( ( ( ~ ( SV109 @ ( sK29_SY528 @ SV232 @ SV109 ) )
| ( SV109 @ ( suc @ ( sK29_SY528 @ SV232 @ SV109 ) ) ) )
= $false )
| ( ( SV109 @ SV232 )
= $true )
| ( ( SV109 @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1572]) ).
thf(1726,plain,
! [SV233: nat > $o,SV110: nat] :
( ( ( ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) )
| ~ ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1573]) ).
thf(1727,plain,
! [SV110: nat,SV233: nat > $o] :
( ( ( SV233 @ SV110 )
= $false )
| ( ( ~ ( ~ ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) )
| ~ ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1574]) ).
thf(1728,plain,
! [SV233: nat > $o,SV110: nat] :
( ( ( ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) )
| ~ ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1574]) ).
thf(1729,plain,
! [SV111: nat,SV234: nat] :
( ( ( SV234
= ( suc @ ( sK22_SY667 @ SV111 @ SV234 ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( suc @ SV111 ) @ SV234 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1575]) ).
thf(1730,plain,
! [SV235: real,SV112: real] :
( ( ( ~ ( ord_less_real @ SV112 @ SV235 ) )
= $false )
| ( ( ord_less_real @ SV235 @ SV112 )
= $true )
| ( ( SV112 = SV235 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1576]) ).
thf(1731,plain,
! [SV113: nat > $o] :
( ( ( ! [SY535: nat] :
~ ( SV113 @ SY535 ) )
= $true )
| ( ( ~ ! [SY536: nat] :
~ ~ ( ~ ~ ( SV113 @ SY536 )
| ~ ( SV113 @ ( suc @ SY536 ) ) ) )
= $true )
| ( ( SV113 @ zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1577]) ).
thf(1732,plain,
! [SV114: nat,SV236: nat] :
( ( ( ( ord_less_nat @ SV236 @ ( suc @ SV114 ) )
| ( SV236 = SV114 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV236 @ ( suc @ SV114 ) )
| ( SV236 != SV114 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV114 @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1578]) ).
thf(1733,plain,
! [SV116: real,SV238: real,SV299: real] :
( ( ( ord_less_real @ SV299 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ ( divide_divide_real @ SV238 @ SV299 ) @ ( divide_divide_real @ SV116 @ SV299 ) )
= $true )
| ( ( ord_less_real @ SV116 @ SV238 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1580]) ).
thf(1734,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK30_SY669 @ SV239 @ SV117 ) @ ( suc @ SV117 ) )
| ( SV239 @ ( sK30_SY669 @ SV239 @ SV117 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) )
| ~ ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1581]) ).
thf(1735,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) )
| ~ ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1582]) ).
thf(1736,plain,
! [SV118: nat > real,SV300: nat,SV240: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV240 @ SV300 ) )
= $true )
| ( ( ord_less_eq_real @ ( SV118 @ SV300 ) @ ( SV118 @ SV240 ) )
= $true )
| ( ( ord_less_eq_real @ ( SV118 @ ( suc @ ( sK23_SY546 @ SV300 @ SV240 @ SV118 ) ) ) @ ( SV118 @ ( sK23_SY546 @ SV300 @ SV240 @ SV118 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1583]) ).
thf(1737,plain,
! [SV119: nat > nat,SV301: nat,SV241: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV241 @ SV301 ) )
= $true )
| ( ( ord_less_eq_nat @ ( SV119 @ SV301 ) @ ( SV119 @ SV241 ) )
= $true )
| ( ( ord_less_eq_nat @ ( SV119 @ ( suc @ ( sK24_SY549 @ SV301 @ SV241 @ SV119 ) ) ) @ ( SV119 @ ( sK24_SY549 @ SV301 @ SV241 @ SV119 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1584]) ).
thf(1738,plain,
! [SV309: real,SV302: real,SV242: real,SV120: real] :
( ( ( ~ ( ord_less_eq_real @ SV120 @ SV242 ) )
= $true )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV302 )
| ~ ( ord_less_real @ SV302 @ SV309 )
| ( ord_less_real @ ( divide_divide_real @ SV120 @ SV309 ) @ ( divide_divide_real @ SV242 @ SV302 ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1585]) ).
thf(1739,plain,
! [SV244: nat,SV122: nat > $o] :
( ( ( SV122 @ zero_zero_nat )
= $true )
| ( ( ~ ! [SY677: nat] :
~ ~ ( ~ ~ ( ~ ( ord_less_nat @ SY677 @ SV244 )
| ~ ! [SY556: nat] :
( ~ ( ord_less_eq_nat @ SY556 @ SY677 )
| ~ ( SV122 @ SY556 ) ) )
| ~ ( SV122 @ ( suc @ SY677 ) ) ) )
= $true )
| ( ( SV122 @ SV244 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1587]) ).
thf(1740,plain,
! [SV245: nat,SV123: nat] :
( ( ( ~ ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
| ~ ~ ! [SY679: nat] :
~ ~ ( ( SV245
!= ( suc @ SY679 ) )
| ~ ( ord_less_nat @ SV123 @ SY679 ) ) )
= $false )
| ( ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1588]) ).
thf(1741,plain,
! [SV123: nat,SV245: nat] :
( ( ( ! [SY679: nat] :
~ ~ ( ( SV245
!= ( suc @ SY679 ) )
| ~ ( ord_less_nat @ SV123 @ SY679 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
| ~ ~ ! [SY679: nat] :
~ ~ ( ( SV245
!= ( suc @ SY679 ) )
| ~ ( ord_less_nat @ SV123 @ SY679 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1589]) ).
thf(1742,plain,
! [SV247: nat,SV126: nat] :
( ( ( ( suc @ SV126 )
= SV247 )
= $true )
| ( ( ord_less_nat @ ( suc @ SV126 ) @ SV247 )
= $true )
| ( ( ord_less_nat @ SV126 @ SV247 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1591]) ).
thf(1743,plain,
! [SV248: nat,SV127: nat,SV303: nat > nat > $o] :
( ( ( ! [SY718: nat] : ( SV303 @ SY718 @ SY718 ) )
= $false )
| ( ( ~ ! [SY719: nat,SY720: nat,SY721: nat] :
( ~ ( SV303 @ SY719 @ SY720 )
| ~ ( SV303 @ SY720 @ SY721 )
| ( SV303 @ SY719 @ SY721 ) )
| ~ ! [SY722: nat] : ( SV303 @ SY722 @ ( suc @ SY722 ) )
| ( SV303 @ SV127 @ SV248 ) )
= $true )
| ( ( ord_less_eq_nat @ SV127 @ SV248 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1592]) ).
thf(1744,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1593]) ).
thf(1745,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1594]) ).
thf(1746,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1594]) ).
thf(1747,plain,
! [SV251: nat,SV133: nat] :
( ( ( ~ ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
| ~ ( ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1595]) ).
thf(1748,plain,
! [SV251: nat,SV133: nat] :
( ( ( SV133 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
| ~ ( ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1596]) ).
thf(1749,plain,
! [SV251: nat,SV133: nat] :
( ( ( ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
| ~ ( ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1596]) ).
thf(1750,plain,
! [SV252: real,SV134: nat] :
( ( ( ! [SY687: real] :
~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY687 )
| ( ( power_power_real @ SY687 @ SV134 )
!= SV252 ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV252 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1597]) ).
thf(1751,plain,
! [SV310: real,SV304: real,SV139: real,SV256: real] :
( ( ( ~ ( ord_less_eq_real @ SV256 @ SV139 ) )
= $true )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV304 )
| ~ ( ord_less_eq_real @ SV304 @ SV310 )
| ( ord_less_eq_real @ ( divide_divide_real @ SV256 @ SV310 ) @ ( divide_divide_real @ SV139 @ SV304 ) ) )
= $true )
| ( ( ord_less_eq_real @ zero_zero_real @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1599]) ).
thf(1752,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) ) )
= $false )
| ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1600]) ).
thf(1753,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1601]) ).
thf(1754,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1601]) ).
thf(1755,plain,
! [SV142: nat,SV258: nat,SV305: nat > $o] :
( ( ( SV305 @ SV258 )
= $false )
| ( ( ~ ! [SY724: nat] :
( ~ ( ord_less_eq_nat @ SV142 @ SY724 )
| ~ ( ord_less_nat @ SY724 @ SV258 )
| ~ ( SV305 @ ( suc @ SY724 ) )
| ( SV305 @ SY724 ) )
| ( SV305 @ SV142 ) )
= $true )
| ( ( ord_less_eq_nat @ SV142 @ SV258 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1602]) ).
thf(1756,plain,
! [SV260: nat,SV145: nat] :
( ( ( ord_less_nat @ SV145 @ ( suc @ SV260 ) )
= $false )
| ( ( SV260 = SV145 )
= $true )
| ( ( ord_less_nat @ SV145 @ SV260 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1603]) ).
thf(1757,plain,
! [SV148: nat] :
( ( ( SV148
= ( suc @ ( sK25_SY591 @ SV148 ) ) )
= $true )
| ( ( SV148 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1604]) ).
thf(1758,plain,
! [SV262: int,SV149: nat,SV1: int] :
( ( ( ~ ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ SV1 ) @ SV149 ) @ ( ring_1_of_int_real @ SV262 ) )
| ~ ( ord_less_int @ ( power_power_int @ SV1 @ SV149 ) @ SV262 ) )
= $false )
| ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ SV1 ) @ SV149 ) @ ( ring_1_of_int_real @ SV262 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1605]) ).
thf(1759,plain,
! [SV262: int,SV149: nat,SV1: int] :
( ( ( ~ ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ SV1 ) @ SV149 ) @ ( ring_1_of_int_real @ SV262 ) )
| ~ ( ord_less_int @ ( power_power_int @ SV1 @ SV149 ) @ SV262 ) )
= $false )
| ( ( ord_less_int @ ( power_power_int @ SV1 @ SV149 ) @ SV262 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1606]) ).
thf(1760,plain,
! [SV263: nat,SV150: int,SV2: int] :
( ( ( ~ ( ord_less_real @ ( ring_1_of_int_real @ SV2 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV150 ) @ SV263 ) )
| ~ ( ord_less_int @ SV2 @ ( power_power_int @ SV150 @ SV263 ) ) )
= $false )
| ( ( ord_less_real @ ( ring_1_of_int_real @ SV2 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV150 ) @ SV263 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1607]) ).
thf(1761,plain,
! [SV263: nat,SV150: int,SV2: int] :
( ( ( ~ ( ord_less_real @ ( ring_1_of_int_real @ SV2 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV150 ) @ SV263 ) )
| ~ ( ord_less_int @ SV2 @ ( power_power_int @ SV150 @ SV263 ) ) )
= $false )
| ( ( ord_less_int @ SV2 @ ( power_power_int @ SV150 @ SV263 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1608]) ).
thf(1762,plain,
! [SV264: int,SV152: nat,SV4: int] :
( ( ( ( ( power_power_real @ ( ring_1_of_int_real @ SV4 ) @ SV152 )
!= ( ring_1_of_int_real @ SV264 ) )
| ( ( power_power_int @ SV4 @ SV152 )
!= SV264 ) )
= $false )
| ( ( ( power_power_real @ ( ring_1_of_int_real @ SV4 ) @ SV152 )
= ( ring_1_of_int_real @ SV264 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1609]) ).
thf(1763,plain,
! [SV264: int,SV152: nat,SV4: int] :
( ( ( ( ( power_power_real @ ( ring_1_of_int_real @ SV4 ) @ SV152 )
!= ( ring_1_of_int_real @ SV264 ) )
| ( ( power_power_int @ SV4 @ SV152 )
!= SV264 ) )
= $false )
| ( ( ( power_power_int @ SV4 @ SV152 )
= SV264 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1610]) ).
thf(1764,plain,
! [SV265: nat,SV153: int,SV5: int] :
( ( ( ( ( ring_1_of_int_real @ SV5 )
!= ( power_power_real @ ( ring_1_of_int_real @ SV153 ) @ SV265 ) )
| ( SV5
!= ( power_power_int @ SV153 @ SV265 ) ) )
= $false )
| ( ( ( ring_1_of_int_real @ SV5 )
= ( power_power_real @ ( ring_1_of_int_real @ SV153 ) @ SV265 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1611]) ).
thf(1765,plain,
! [SV265: nat,SV153: int,SV5: int] :
( ( ( ( ( ring_1_of_int_real @ SV5 )
!= ( power_power_real @ ( ring_1_of_int_real @ SV153 ) @ SV265 ) )
| ( SV5
!= ( power_power_int @ SV153 @ SV265 ) ) )
= $false )
| ( ( SV5
= ( power_power_int @ SV153 @ SV265 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1612]) ).
thf(1766,plain,
! [SV154: int,SV6: int] :
( ( ( ~ ( ord_less_real @ ( ring_1_of_int_real @ SV6 ) @ ( ring_1_of_int_real @ SV154 ) ) )
= $false )
| ( ( ord_less_real @ ( ring_1_of_int_real @ SV6 ) @ ( ring_1_of_int_real @ SV154 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1613]) ).
thf(1767,plain,
! [SV154: int,SV6: int] :
( ( ( ~ ( ord_less_int @ SV6 @ SV154 ) )
= $false )
| ( ( ord_less_real @ ( ring_1_of_int_real @ SV6 ) @ ( ring_1_of_int_real @ SV154 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1613]) ).
thf(1768,plain,
! [SV154: int,SV6: int] :
( ( ( ~ ( ord_less_real @ ( ring_1_of_int_real @ SV6 ) @ ( ring_1_of_int_real @ SV154 ) ) )
= $false )
| ( ( ord_less_int @ SV6 @ SV154 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1614]) ).
thf(1769,plain,
! [SV154: int,SV6: int] :
( ( ( ~ ( ord_less_int @ SV6 @ SV154 ) )
= $false )
| ( ( ord_less_int @ SV6 @ SV154 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1614]) ).
thf(1770,plain,
! [SV155: int,SV7: int] :
( ( ( ( ring_1_of_int_real @ SV7 )
!= ( ring_1_of_int_real @ SV155 ) )
= $false )
| ( ( ( ring_1_of_int_real @ SV7 )
= ( ring_1_of_int_real @ SV155 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1615]) ).
thf(1771,plain,
! [SV155: int,SV7: int] :
( ( ( SV7 != SV155 )
= $false )
| ( ( ( ring_1_of_int_real @ SV7 )
= ( ring_1_of_int_real @ SV155 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1615]) ).
thf(1772,plain,
! [SV155: int,SV7: int] :
( ( ( ( ring_1_of_int_real @ SV7 )
!= ( ring_1_of_int_real @ SV155 ) )
= $false )
| ( ( SV7 = SV155 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1616]) ).
thf(1773,plain,
! [SV155: int,SV7: int] :
( ( ( SV7 != SV155 )
= $false )
| ( ( SV7 = SV155 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1616]) ).
thf(1774,plain,
! [SV156: nat,SV8: nat] :
( ( ( ( suc @ SV8 )
!= ( suc @ SV156 ) )
= $false )
| ( ( ( suc @ SV8 )
= ( suc @ SV156 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1617]) ).
thf(1775,plain,
! [SV156: nat,SV8: nat] :
( ( ( SV8 != SV156 )
= $false )
| ( ( ( suc @ SV8 )
= ( suc @ SV156 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1617]) ).
thf(1776,plain,
! [SV156: nat,SV8: nat] :
( ( ( ( suc @ SV8 )
!= ( suc @ SV156 ) )
= $false )
| ( ( SV8 = SV156 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1618]) ).
thf(1777,plain,
! [SV156: nat,SV8: nat] :
( ( ( SV8 != SV156 )
= $false )
| ( ( SV8 = SV156 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1618]) ).
thf(1778,plain,
! [SV157: nat,SV9: nat] :
( ( ( ( suc @ SV9 )
!= ( suc @ SV157 ) )
= $false )
| ( ( ( suc @ SV9 )
= ( suc @ SV157 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1619]) ).
thf(1779,plain,
! [SV157: nat,SV9: nat] :
( ( ( SV9 != SV157 )
= $false )
| ( ( ( suc @ SV9 )
= ( suc @ SV157 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1619]) ).
thf(1780,plain,
! [SV157: nat,SV9: nat] :
( ( ( ( suc @ SV9 )
!= ( suc @ SV157 ) )
= $false )
| ( ( SV9 = SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1620]) ).
thf(1781,plain,
! [SV157: nat,SV9: nat] :
( ( ( SV9 != SV157 )
= $false )
| ( ( SV9 = SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1620]) ).
thf(1782,plain,
! [SV158: nat,SV10: nat] :
( ( ( ~ ( ord_less_nat @ ( suc @ SV10 ) @ ( suc @ SV158 ) ) )
= $false )
| ( ( ord_less_nat @ ( suc @ SV10 ) @ ( suc @ SV158 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1621]) ).
thf(1783,plain,
! [SV158: nat,SV10: nat] :
( ( ( ~ ( ord_less_nat @ SV10 @ SV158 ) )
= $false )
| ( ( ord_less_nat @ ( suc @ SV10 ) @ ( suc @ SV158 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1621]) ).
thf(1784,plain,
! [SV158: nat,SV10: nat] :
( ( ( ~ ( ord_less_nat @ ( suc @ SV10 ) @ ( suc @ SV158 ) ) )
= $false )
| ( ( ord_less_nat @ SV10 @ SV158 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1622]) ).
thf(1785,plain,
! [SV158: nat,SV10: nat] :
( ( ( ~ ( ord_less_nat @ SV10 @ SV158 ) )
= $false )
| ( ( ord_less_nat @ SV10 @ SV158 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1622]) ).
thf(1786,plain,
! [SV12: int] :
( ( ( zero_zero_real
= ( ring_1_of_int_real @ SV12 ) )
= $true )
| ( ( zero_zero_real
= ( ring_1_of_int_real @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1623]) ).
thf(1787,plain,
! [SV12: int] :
( ( ( SV12 = zero_zero_int )
= $true )
| ( ( zero_zero_real
= ( ring_1_of_int_real @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1624]) ).
thf(1788,plain,
! [SV12: int] :
( ( ( zero_zero_real
= ( ring_1_of_int_real @ SV12 ) )
= $true )
| ( ( SV12 = zero_zero_int )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1625]) ).
thf(1789,plain,
! [SV12: int] :
( ( ( SV12 = zero_zero_int )
= $true )
| ( ( SV12 = zero_zero_int )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1626]) ).
thf(1790,plain,
! [SV13: int] :
( ( ( ( ring_1_of_int_real @ SV13 )
= zero_zero_real )
= $true )
| ( ( ( ring_1_of_int_real @ SV13 )
= zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1627]) ).
thf(1791,plain,
! [SV13: int] :
( ( ( SV13 = zero_zero_int )
= $true )
| ( ( ( ring_1_of_int_real @ SV13 )
= zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1628]) ).
thf(1792,plain,
! [SV13: int] :
( ( ( ( ring_1_of_int_real @ SV13 )
= zero_zero_real )
= $true )
| ( ( SV13 = zero_zero_int )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1629]) ).
thf(1793,plain,
! [SV13: int] :
( ( ( SV13 = zero_zero_int )
= $true )
| ( ( SV13 = zero_zero_int )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1630]) ).
thf(1794,plain,
! [SV14: int] :
( ( ( ord_less_real @ ( ring_1_of_int_real @ SV14 ) @ zero_zero_real )
= $true )
| ( ( ord_less_real @ ( ring_1_of_int_real @ SV14 ) @ zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1631]) ).
thf(1795,plain,
! [SV14: int] :
( ( ( ord_less_int @ SV14 @ zero_zero_int )
= $true )
| ( ( ord_less_real @ ( ring_1_of_int_real @ SV14 ) @ zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1632]) ).
thf(1796,plain,
! [SV14: int] :
( ( ( ord_less_real @ ( ring_1_of_int_real @ SV14 ) @ zero_zero_real )
= $true )
| ( ( ord_less_int @ SV14 @ zero_zero_int )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1633]) ).
thf(1797,plain,
! [SV14: int] :
( ( ( ord_less_int @ SV14 @ zero_zero_int )
= $true )
| ( ( ord_less_int @ SV14 @ zero_zero_int )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1634]) ).
thf(1798,plain,
! [SV15: int] :
( ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ SV15 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1635]) ).
thf(1799,plain,
! [SV15: int] :
( ( ( ord_less_int @ zero_zero_int @ SV15 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1636]) ).
thf(1800,plain,
! [SV15: int] :
( ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ SV15 ) )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1637]) ).
thf(1801,plain,
! [SV15: int] :
( ( ( ord_less_int @ zero_zero_int @ SV15 )
= $true )
| ( ( ord_less_int @ zero_zero_int @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1638]) ).
thf(1802,plain,
! [SV159: nat,SV16: nat] :
( ( ( ~ ~ ( ord_less_nat @ SV16 @ SV159 )
| ~ ( ord_less_nat @ SV159 @ ( suc @ SV16 ) ) )
= $false )
| ( ( ord_less_nat @ SV16 @ SV159 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1639]) ).
thf(1803,plain,
! [SV159: nat,SV16: nat] :
( ( ( ~ ~ ( ord_less_nat @ SV16 @ SV159 ) )
= $false )
| ( ( ord_less_nat @ SV159 @ ( suc @ SV16 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1640]) ).
thf(1804,plain,
! [SV16: nat,SV159: nat] :
( ( ( ~ ( ord_less_nat @ SV159 @ ( suc @ SV16 ) ) )
= $false )
| ( ( ord_less_nat @ SV159 @ ( suc @ SV16 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1640]) ).
thf(1805,plain,
! [SV160: nat,SV17: nat] :
( ( ( ~ ( ord_less_nat @ SV17 @ ( suc @ SV160 ) ) )
= $false )
| ( ( ord_less_nat @ SV17 @ ( suc @ SV160 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1641]) ).
thf(1806,plain,
! [SV160: nat,SV17: nat] :
( ( ( ~ ( ( ord_less_nat @ SV17 @ SV160 )
| ( SV17 = SV160 ) ) )
= $false )
| ( ( ord_less_nat @ SV17 @ ( suc @ SV160 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1641]) ).
thf(1807,plain,
! [SV160: nat,SV17: nat] :
( ( ( ~ ( ord_less_nat @ SV17 @ ( suc @ SV160 ) )
| ~ ( ( ord_less_nat @ SV17 @ SV160 )
| ( SV17 = SV160 ) ) )
= $false )
| ( ( ord_less_nat @ SV17 @ SV160 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1642]) ).
thf(1808,plain,
! [SV160: nat,SV17: nat] :
( ( ( ~ ( ord_less_nat @ SV17 @ ( suc @ SV160 ) )
| ~ ( ( ord_less_nat @ SV17 @ SV160 )
| ( SV17 = SV160 ) ) )
= $false )
| ( ( SV17 = SV160 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1643]) ).
thf(1809,plain,
! [SV161: nat,SV21: nat] :
( ( ( ( power_power_nat @ SV21 @ SV161 )
!= ( suc @ zero_zero_nat ) )
= $false )
| ( ( ( power_power_nat @ SV21 @ SV161 )
= ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1644]) ).
thf(1810,plain,
! [SV21: nat,SV161: nat] :
( ( ( ~ ( ( SV161 = zero_zero_nat )
| ( SV21
= ( suc @ zero_zero_nat ) ) ) )
= $false )
| ( ( ( power_power_nat @ SV21 @ SV161 )
= ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1644]) ).
thf(1811,plain,
! [SV161: nat,SV21: nat] :
( ( ( ( ( power_power_nat @ SV21 @ SV161 )
!= ( suc @ zero_zero_nat ) )
| ~ ( ( SV161 = zero_zero_nat )
| ( SV21
= ( suc @ zero_zero_nat ) ) ) )
= $false )
| ( ( SV161 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1645]) ).
thf(1812,plain,
! [SV161: nat,SV21: nat] :
( ( ( ( ( power_power_nat @ SV21 @ SV161 )
!= ( suc @ zero_zero_nat ) )
| ~ ( ( SV161 = zero_zero_nat )
| ( SV21
= ( suc @ zero_zero_nat ) ) ) )
= $false )
| ( ( SV21
= ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1646]) ).
thf(1813,plain,
! [SV27: nat] :
( ( ( ord_less_nat @ SV27 @ ( suc @ zero_zero_nat ) )
= $true )
| ( ( ord_less_nat @ SV27 @ ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1647]) ).
thf(1814,plain,
! [SV27: nat] :
( ( ( SV27 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV27 @ ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1648]) ).
thf(1815,plain,
! [SV27: nat] :
( ( ( ord_less_nat @ SV27 @ ( suc @ zero_zero_nat ) )
= $true )
| ( ( SV27 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1649]) ).
thf(1816,plain,
! [SV27: nat] :
( ( ( SV27 = zero_zero_nat )
= $true )
| ( ( SV27 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1650]) ).
thf(1817,plain,
! [SV162: int,SV28: int] :
( ( ( ~ ( ord_less_eq_real @ ( ring_1_of_int_real @ SV28 ) @ ( ring_1_of_int_real @ SV162 ) ) )
= $false )
| ( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV28 ) @ ( ring_1_of_int_real @ SV162 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1651]) ).
thf(1818,plain,
! [SV162: int,SV28: int] :
( ( ( ~ ( ord_less_eq_int @ SV28 @ SV162 ) )
= $false )
| ( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV28 ) @ ( ring_1_of_int_real @ SV162 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1651]) ).
thf(1819,plain,
! [SV162: int,SV28: int] :
( ( ( ~ ( ord_less_eq_real @ ( ring_1_of_int_real @ SV28 ) @ ( ring_1_of_int_real @ SV162 ) ) )
= $false )
| ( ( ord_less_eq_int @ SV28 @ SV162 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1652]) ).
thf(1820,plain,
! [SV162: int,SV28: int] :
( ( ( ~ ( ord_less_eq_int @ SV28 @ SV162 ) )
= $false )
| ( ( ord_less_eq_int @ SV28 @ SV162 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1652]) ).
thf(1821,plain,
! [SV266: int,SV163: nat,SV29: int] :
( ( ( ~ ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ SV29 ) @ SV163 ) @ ( ring_1_of_int_real @ SV266 ) )
| ~ ( ord_less_eq_int @ ( power_power_int @ SV29 @ SV163 ) @ SV266 ) )
= $false )
| ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ SV29 ) @ SV163 ) @ ( ring_1_of_int_real @ SV266 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1653]) ).
thf(1822,plain,
! [SV266: int,SV163: nat,SV29: int] :
( ( ( ~ ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ SV29 ) @ SV163 ) @ ( ring_1_of_int_real @ SV266 ) )
| ~ ( ord_less_eq_int @ ( power_power_int @ SV29 @ SV163 ) @ SV266 ) )
= $false )
| ( ( ord_less_eq_int @ ( power_power_int @ SV29 @ SV163 ) @ SV266 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1654]) ).
thf(1823,plain,
! [SV267: nat,SV164: int,SV30: int] :
( ( ( ~ ( ord_less_eq_real @ ( ring_1_of_int_real @ SV30 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV164 ) @ SV267 ) )
| ~ ( ord_less_eq_int @ SV30 @ ( power_power_int @ SV164 @ SV267 ) ) )
= $false )
| ( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV30 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV164 ) @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1655]) ).
thf(1824,plain,
! [SV267: nat,SV164: int,SV30: int] :
( ( ( ~ ( ord_less_eq_real @ ( ring_1_of_int_real @ SV30 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV164 ) @ SV267 ) )
| ~ ( ord_less_eq_int @ SV30 @ ( power_power_int @ SV164 @ SV267 ) ) )
= $false )
| ( ( ord_less_eq_int @ SV30 @ ( power_power_int @ SV164 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1656]) ).
thf(1825,plain,
! [SV166: nat,SV32: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( suc @ SV32 ) @ ( suc @ SV166 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( suc @ SV32 ) @ ( suc @ SV166 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1657]) ).
thf(1826,plain,
! [SV166: nat,SV32: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV32 @ SV166 ) )
= $false )
| ( ( ord_less_eq_nat @ ( suc @ SV32 ) @ ( suc @ SV166 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1657]) ).
thf(1827,plain,
! [SV166: nat,SV32: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( suc @ SV32 ) @ ( suc @ SV166 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV32 @ SV166 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1658]) ).
thf(1828,plain,
! [SV166: nat,SV32: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV32 @ SV166 ) )
= $false )
| ( ( ord_less_eq_nat @ SV32 @ SV166 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1658]) ).
thf(1829,plain,
! [SV167: nat,SV33: nat] :
( ( ( ~ ~ ( ord_less_eq_nat @ SV33 @ SV167 )
| ~ ( ord_less_eq_nat @ ( suc @ SV167 ) @ SV33 ) )
= $false )
| ( ( ord_less_eq_nat @ SV33 @ SV167 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1659]) ).
thf(1830,plain,
! [SV167: nat,SV33: nat] :
( ( ( ~ ~ ( ord_less_eq_nat @ SV33 @ SV167 ) )
= $false )
| ( ( ord_less_eq_nat @ ( suc @ SV167 ) @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1660]) ).
thf(1831,plain,
! [SV33: nat,SV167: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( suc @ SV167 ) @ SV33 ) )
= $false )
| ( ( ord_less_eq_nat @ ( suc @ SV167 ) @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1660]) ).
thf(1832,plain,
! [SV168: nat,SV35: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV35 @ ( suc @ SV168 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV35 @ ( suc @ SV168 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1661]) ).
thf(1833,plain,
! [SV168: nat,SV35: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV35 @ SV168 )
| ( SV35
= ( suc @ SV168 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV35 @ ( suc @ SV168 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1661]) ).
thf(1834,plain,
! [SV168: nat,SV35: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV35 @ ( suc @ SV168 ) )
| ~ ( ( ord_less_eq_nat @ SV35 @ SV168 )
| ( SV35
= ( suc @ SV168 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV35 @ SV168 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1662]) ).
thf(1835,plain,
! [SV168: nat,SV35: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV35 @ ( suc @ SV168 ) )
| ~ ( ( ord_less_eq_nat @ SV35 @ SV168 )
| ( SV35
= ( suc @ SV168 ) ) ) )
= $false )
| ( ( SV35
= ( suc @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1663]) ).
thf(1836,plain,
! [SV306: nat,SV169: nat] :
( ( ( nthRoo1352626670d_root @ SV169 @ SV306 )
= $false )
| ( ( ~ ( ~ ( nthRoo1352626670d_root @ SV169 @ SV306 )
| ( SV169
!= ( suc @ SV306 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1664]) ).
thf(1837,plain,
! [SV306: nat,SV169: nat] :
( ( ( SV169
= ( suc @ SV306 ) )
= $false )
| ( ( ~ ( ~ ( nthRoo1352626670d_root @ SV169 @ SV306 )
| ( SV169
!= ( suc @ SV306 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1664]) ).
thf(1838,plain,
! [SV170: nat,SV37: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( suc @ SV37 ) @ SV170 ) )
= $false )
| ( ( ord_less_eq_nat @ ( suc @ SV37 ) @ SV170 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1665]) ).
thf(1839,plain,
! [SV170: nat,SV37: nat] :
( ( ( ~ ( ord_less_nat @ SV37 @ SV170 ) )
= $false )
| ( ( ord_less_eq_nat @ ( suc @ SV37 ) @ SV170 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1665]) ).
thf(1840,plain,
! [SV170: nat,SV37: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( suc @ SV37 ) @ SV170 ) )
= $false )
| ( ( ord_less_nat @ SV37 @ SV170 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1666]) ).
thf(1841,plain,
! [SV170: nat,SV37: nat] :
( ( ( ~ ( ord_less_nat @ SV37 @ SV170 ) )
= $false )
| ( ( ord_less_nat @ SV37 @ SV170 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1666]) ).
thf(1842,plain,
! [SV171: nat,SV38: nat] :
( ( ( ~ ( ord_less_nat @ SV38 @ ( suc @ SV171 ) ) )
= $false )
| ( ( ord_less_nat @ SV38 @ ( suc @ SV171 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1667]) ).
thf(1843,plain,
! [SV171: nat,SV38: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV38 @ SV171 ) )
= $false )
| ( ( ord_less_nat @ SV38 @ ( suc @ SV171 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1667]) ).
thf(1844,plain,
! [SV171: nat,SV38: nat] :
( ( ( ~ ( ord_less_nat @ SV38 @ ( suc @ SV171 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV38 @ SV171 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1668]) ).
thf(1845,plain,
! [SV171: nat,SV38: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV38 @ SV171 ) )
= $false )
| ( ( ord_less_eq_nat @ SV38 @ SV171 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1668]) ).
thf(1846,plain,
! [SV307: nat,SV172: nat] :
( ( ( ord_less_nat @ SV172 @ SV307 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV172 @ SV307 )
| ~ ( ord_less_eq_nat @ ( suc @ SV172 ) @ SV307 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1669]) ).
thf(1847,plain,
! [SV307: nat,SV172: nat] :
( ( ( ord_less_eq_nat @ ( suc @ SV172 ) @ SV307 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV172 @ SV307 )
| ~ ( ord_less_eq_nat @ ( suc @ SV172 ) @ SV307 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1669]) ).
thf(1848,plain,
! [SV45: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV45 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1671]) ).
thf(1849,plain,
! [SV45: nat] :
( ( ( ~ ! [SY405: nat] :
( SV45
!= ( suc @ SY405 ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1672]) ).
thf(1850,plain,
! [SV311: nat,SV45: nat] :
( ( ( SV45
= ( suc @ SV311 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV45 )
| ~ ~ ! [SY405: nat] :
( SV45
!= ( suc @ SY405 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1673]) ).
thf(1851,plain,
! [SV178: nat > $o,SV47: nat,SV312: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ SV312 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SV312 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) )
| ~ ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(1852,plain,
! [SV178: nat > $o,SV47: nat] :
( ( ( ~ ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) )
| ~ ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) )
= $false )
| ( ( SV178 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1675]) ).
thf(1853,plain,
! [SV178: nat > $o,SV47: nat] :
( ( ( ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) )
| ~ ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1676]) ).
thf(1854,plain,
! [SV181: nat,SV50: nat,SV273: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV273 ) )
= $true )
| ( ( SV50 = SV273 )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV50 )
= $false )
| ( ( ( power_power_nat @ SV50 @ ( suc @ SV181 ) )
= ( power_power_nat @ SV273 @ ( suc @ SV181 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1678]) ).
thf(1855,plain,
! [SV274: real,SV182: real,SV51: real] :
( ( ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
| ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) )
= $false )
| ( ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1679]) ).
thf(1856,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
| ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1680]) ).
thf(1857,plain,
! [SV183: nat,SV275: nat > $o,SV52: nat] :
( ( ( ~ ! [SY692: nat] :
( ~ ( ord_less_eq_nat @ SV52 @ SY692 )
| ~ ( SV275 @ SY692 )
| ( SV275 @ ( suc @ SY692 ) ) ) )
= $true )
| ( ( SV275 @ SV183 )
= $true )
| ( ( SV275 @ SV52 )
= $false )
| ( ( ord_less_eq_nat @ SV52 @ SV183 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1681]) ).
thf(1858,plain,
! [SV53: nat > $o,SV184: nat,SV313: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( suc @ SV313 ) @ ( sK6_SY421 @ SV184 @ SV53 ) )
| ( SV53 @ SV313 ) )
= $true )
| ( ( SV53 @ SV184 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(1859,plain,
! [SV308: real,SV276: real,SV185: real,SV54: real] :
( ( ( ord_less_real @ SV54 @ SV185 )
= $false )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV276 )
| ~ ( ord_less_eq_real @ SV276 @ SV308 )
| ( ord_less_real @ ( divide_divide_real @ SV54 @ SV308 ) @ ( divide_divide_real @ SV185 @ SV276 ) ) )
= $true )
| ( ( ord_less_eq_real @ zero_zero_real @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1683]) ).
thf(1860,plain,
! [SV55: nat > int,SV277: nat,SV186: nat] :
( ( ( ord_less_eq_nat @ SV186 @ SV277 )
= $false )
| ( ( ord_less_eq_int @ ( SV55 @ SV186 ) @ ( SV55 @ SV277 ) )
= $true )
| ( ( ord_less_eq_int @ ( SV55 @ ( sK8_SY428 @ SV277 @ SV186 @ SV55 ) ) @ ( SV55 @ ( suc @ ( sK8_SY428 @ SV277 @ SV186 @ SV55 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1684]) ).
thf(1861,plain,
! [SV59: nat > real,SV278: nat,SV189: nat] :
( ( ( ord_less_eq_nat @ SV189 @ SV278 )
= $false )
| ( ( ord_less_eq_real @ ( SV59 @ SV189 ) @ ( SV59 @ SV278 ) )
= $true )
| ( ( ord_less_eq_real @ ( SV59 @ ( sK9_SY434 @ SV278 @ SV189 @ SV59 ) ) @ ( SV59 @ ( suc @ ( sK9_SY434 @ SV278 @ SV189 @ SV59 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1686]) ).
thf(1862,plain,
! [SV191: nat,SV61: real] :
( ( ( ( power_power_real @ SV61 @ SV191 )
!= zero_zero_real )
= $false )
| ( ( ( power_power_real @ SV61 @ SV191 )
= zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1687]) ).
thf(1863,plain,
! [SV191: nat,SV61: real] :
( ( ( ~ ~ ( ( SV61 != zero_zero_real )
| ~ ( ord_less_nat @ zero_zero_nat @ SV191 ) ) )
= $false )
| ( ( ( power_power_real @ SV61 @ SV191 )
= zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1687]) ).
thf(1864,plain,
! [SV191: nat,SV61: real] :
( ( ( SV61 != zero_zero_real )
= $true )
| ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV191 ) )
= $true )
| ( ( ~ ( ( ( power_power_real @ SV61 @ SV191 )
!= zero_zero_real )
| ~ ~ ( ( SV61 != zero_zero_real )
| ~ ( ord_less_nat @ zero_zero_nat @ SV191 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1688]) ).
thf(1865,plain,
! [SV62: nat,SV192: real] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ ( sK31_SY616 @ SV192 @ SV62 ) )
| ( ( power_power_real @ ( sK31_SY616 @ SV192 @ SV62 ) @ SV62 )
!= SV192 ) )
| ~ ! [SY726: real] :
( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY726 )
| ( ( power_power_real @ SY726 @ SV62 )
!= SV192 ) )
| ( SY726
= ( sK31_SY616 @ SV192 @ SV62 ) ) ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV192 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1689]) ).
thf(1866,plain,
! [SV64: nat > nat,SV280: nat,SV194: nat] :
( ( ( ord_less_nat @ SV194 @ SV280 )
= $false )
| ( ( ord_less_nat @ ( SV64 @ SV194 ) @ ( SV64 @ SV280 ) )
= $true )
| ( ( ord_less_nat @ ( SV64 @ ( sK10_SY444 @ SV280 @ SV194 @ SV64 ) ) @ ( SV64 @ ( suc @ ( sK10_SY444 @ SV280 @ SV194 @ SV64 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1691]) ).
thf(1867,plain,
! [SV281: nat,SV197: nat,SV68: nat > int] :
( ( ( ~ ( ( ord_less_int @ ( SV68 @ SV197 ) @ ( SV68 @ SV281 ) )
| ( ord_less_nat @ SV197 @ SV281 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_int @ ( SV68 @ SV197 ) @ ( SV68 @ SV281 ) )
| ~ ( ord_less_nat @ SV197 @ SV281 ) ) )
= $true )
| ( ( ord_less_int @ ( SV68 @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) @ ( SV68 @ ( suc @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1693]) ).
thf(1868,plain,
! [SV198: nat,SV69: nat] :
( ( ( ! [SY623: nat] :
( ~ ( ord_less_nat @ SV69 @ SY623 )
| ( SV198
!= ( suc @ SY623 ) ) ) )
= $false )
| ( ( SV198
= ( suc @ SV69 ) )
= $true )
| ( ( ord_less_nat @ SV69 @ SV198 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1695]) ).
thf(1869,plain,
! [SV199: nat,SV70: nat > $o] :
( ( ( ~ ( SV70 @ ( sK26_SY453 @ SV199 @ SV70 ) ) )
= $false )
| ( ( SV70 @ SV199 )
= $true )
| ( ( SV70 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1696]) ).
thf(1870,plain,
! [SV199: nat,SV70: nat > $o] :
( ( ( SV70 @ ( suc @ ( sK26_SY453 @ SV199 @ SV70 ) ) )
= $false )
| ( ( SV70 @ SV199 )
= $true )
| ( ( SV70 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1696]) ).
thf(1871,plain,
! [SV282: nat,SV201: nat,SV73: nat > nat] :
( ( ( ~ ( ( ord_less_nat @ ( SV73 @ SV201 ) @ ( SV73 @ SV282 ) )
| ( ord_less_nat @ SV201 @ SV282 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( SV73 @ SV201 ) @ ( SV73 @ SV282 ) )
| ~ ( ord_less_nat @ SV201 @ SV282 ) ) )
= $true )
| ( ( ord_less_nat @ ( SV73 @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) @ ( SV73 @ ( suc @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1697]) ).
thf(1872,plain,
! [SV202: nat,SV74: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ ( sK13_SY627 @ SV74 @ SV202 ) )
| ( ( power_power_real @ ( sK13_SY627 @ SV74 @ SV202 ) @ ( suc @ SV202 ) )
!= SV74 ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1699]) ).
thf(1873,plain,
! [SV204: nat,SV76: nat] :
( ( ( ord_less_nat @ SV76 @ ( sK14_SY628 @ SV204 @ SV76 ) )
= $true )
| ( ( ord_less_nat @ ( suc @ SV76 ) @ SV204 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1700]) ).
thf(1874,plain,
! [SV76: nat,SV204: nat] :
( ( ( SV204
= ( suc @ ( sK14_SY628 @ SV204 @ SV76 ) ) )
= $true )
| ( ( ord_less_nat @ ( suc @ SV76 ) @ SV204 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1701]) ).
thf(1875,plain,
! [SV205: nat,SV77: real,SV283: real] :
( ( ( ~ ( ord_less_eq_real @ zero_zero_real @ SV283 ) )
= $true )
| ( ( SV77 = SV283 )
= $true )
| ( ( ord_less_eq_real @ zero_zero_real @ SV77 )
= $false )
| ( ( ( power_power_real @ SV77 @ ( suc @ SV205 ) )
= ( power_power_real @ SV283 @ ( suc @ SV205 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1702]) ).
thf(1876,plain,
! [SV284: nat > $o,SV78: nat,SV206: nat] :
( ( ( ( SV206
!= ( suc @ ( sK32_SY699 @ SV78 @ SV284 @ SV206 ) ) )
| ( SV284 @ ( sK32_SY699 @ SV78 @ SV284 @ SV206 ) ) )
= $false )
| ( ( ~ ! [SY700: nat] :
( ~ ( ord_less_nat @ SY700 @ SV206 )
| ~ ( SV284 @ ( suc @ SY700 ) )
| ( SV284 @ SY700 ) )
| ( SV284 @ SV78 ) )
= $true )
| ( ( ord_less_nat @ SV78 @ SV206 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1703]) ).
thf(1877,plain,
! [SV79: nat,SV207: nat,SV285: nat > nat > $o] :
( ( ( SV285 @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) @ ( suc @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) ) )
= $false )
| ( ( ~ ! [SY702: nat,SY703: nat,SY704: nat] :
( ~ ( ord_less_nat @ SY702 @ SY703 )
| ~ ( ord_less_nat @ SY703 @ SY704 )
| ~ ( SV285 @ SY702 @ SY703 )
| ~ ( SV285 @ SY703 @ SY704 )
| ( SV285 @ SY702 @ SY704 ) )
| ( SV285 @ SV79 @ SV207 ) )
= $true )
| ( ( ord_less_nat @ SV79 @ SV207 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1704]) ).
thf(1878,plain,
! [SV81: nat > nat,SV286: nat,SV208: nat] :
( ( ( ord_less_eq_nat @ SV208 @ SV286 )
= $false )
| ( ( ord_less_eq_nat @ ( SV81 @ SV208 ) @ ( SV81 @ SV286 ) )
= $true )
| ( ( ord_less_eq_nat @ ( SV81 @ ( sK16_SY478 @ SV286 @ SV208 @ SV81 ) ) @ ( SV81 @ ( suc @ ( sK16_SY478 @ SV286 @ SV208 @ SV81 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1706]) ).
thf(1879,plain,
! [SV287: nat > $o,SV209: nat,SV82: nat] :
( ( ( ~ ! [SY706: nat] :
( ~ ( ord_less_eq_nat @ SV82 @ SY706 )
| ~ ( ord_less_nat @ SY706 @ SV209 )
| ~ ( SV287 @ SY706 )
| ( SV287 @ ( suc @ SY706 ) ) ) )
= $true )
| ( ( SV287 @ SV209 )
= $true )
| ( ( SV287 @ SV82 )
= $false )
| ( ( ord_less_eq_nat @ SV82 @ SV209 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1707]) ).
thf(1880,plain,
! [SV288: nat,SV212: nat,SV85: nat > nat > $o] :
( ( ( ! [SY487: nat] : ( SV85 @ zero_zero_nat @ ( suc @ SY487 ) ) )
= $false )
| ( ( ~ ! [SY488: nat,SY489: nat] :
( ~ ( SV85 @ SY488 @ SY489 )
| ( SV85 @ ( suc @ SY488 ) @ ( suc @ SY489 ) ) )
| ( SV85 @ SV212 @ SV288 ) )
= $true )
| ( ( SV85 @ ( sK17_SY486 @ SV288 @ SV212 @ SV85 ) @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1708]) ).
thf(1881,plain,
! [SV86: nat > int,SV289: nat,SV213: nat] :
( ( ( ord_less_nat @ SV213 @ SV289 )
= $false )
| ( ( ord_less_int @ ( SV86 @ SV213 ) @ ( SV86 @ SV289 ) )
= $true )
| ( ( ord_less_int @ ( SV86 @ ( sK18_SY492 @ SV289 @ SV213 @ SV86 ) ) @ ( SV86 @ ( suc @ ( sK18_SY492 @ SV289 @ SV213 @ SV86 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1709]) ).
thf(1882,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK27_SY649 @ SV214 @ SV87 ) @ ( suc @ SV87 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) )
| ~ ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1710]) ).
thf(1883,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( SV214 @ ( sK27_SY649 @ SV214 @ SV87 ) )
= $false )
| ( ( ~ ( ~ ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) )
| ~ ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1710]) ).
thf(1884,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( ~ ( SV214 @ zero_zero_nat ) )
= $true )
| ( ( ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) )
| ~ ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1711]) ).
thf(1885,plain,
! [SV88: nat > real,SV290: nat,SV215: nat] :
( ( ( ord_less_nat @ SV215 @ SV290 )
= $false )
| ( ( ord_less_real @ ( SV88 @ SV215 ) @ ( SV88 @ SV290 ) )
= $true )
| ( ( ord_less_real @ ( SV88 @ ( sK19_SY498 @ SV290 @ SV215 @ SV88 ) ) @ ( SV88 @ ( suc @ ( sK19_SY498 @ SV290 @ SV215 @ SV88 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1712]) ).
thf(1886,plain,
! [SV216: nat,SV89: int,SV291: int] :
( ( ( ~ ( ord_less_eq_int @ zero_zero_int @ SV291 ) )
= $true )
| ( ( SV89 = SV291 )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV89 )
= $false )
| ( ( ( power_power_int @ SV89 @ ( suc @ SV216 ) )
= ( power_power_int @ SV291 @ ( suc @ SV216 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1713]) ).
thf(1887,plain,
! [SV91: nat > int,SV292: nat,SV217: nat] :
( ( ( ord_less_eq_nat @ SV217 @ SV292 )
= $false )
| ( ( ord_less_eq_int @ ( SV91 @ SV292 ) @ ( SV91 @ SV217 ) )
= $true )
| ( ( ord_less_eq_int @ ( SV91 @ ( suc @ ( sK20_SY503 @ SV292 @ SV217 @ SV91 ) ) ) @ ( SV91 @ ( sK20_SY503 @ SV292 @ SV217 @ SV91 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1714]) ).
thf(1888,plain,
! [SV297: real,SV228: real,SV103: real] :
( ( ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) )
= $false )
| ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1719]) ).
thf(1889,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1720]) ).
thf(1890,plain,
! [SV229: nat,SV104: nat] :
( ( ( ( ord_less_nat @ SV104 @ ( suc @ SV229 ) )
| ( SV104 = SV229 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV104 @ ( suc @ SV229 ) )
| ( SV104 != SV229 ) ) )
= $true )
| ( ( ord_less_nat @ SV104 @ SV229 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1721]) ).
thf(1891,plain,
! [SV298: nat,SV230: nat,SV106: nat > real] :
( ( ( ~ ( ( ord_less_real @ ( SV106 @ SV230 ) @ ( SV106 @ SV298 ) )
| ( ord_less_nat @ SV230 @ SV298 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( SV106 @ SV230 ) @ ( SV106 @ SV298 ) )
| ~ ( ord_less_nat @ SV230 @ SV298 ) ) )
= $true )
| ( ( ord_less_real @ ( SV106 @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) @ ( SV106 @ ( suc @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1722]) ).
thf(1892,plain,
! [SV231: nat,SV107: nat > $o] :
( ( ( ~ ( SV107 @ ( suc @ ( sK28_SY525 @ SV231 @ SV107 ) ) ) )
= $false )
| ( ( SV107 @ zero_zero_nat )
= $true )
| ( ( SV107 @ SV231 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1724]) ).
thf(1893,plain,
! [SV231: nat,SV107: nat > $o] :
( ( ( SV107 @ ( sK28_SY525 @ SV231 @ SV107 ) )
= $false )
| ( ( SV107 @ zero_zero_nat )
= $true )
| ( ( SV107 @ SV231 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1724]) ).
thf(1894,plain,
! [SV232: nat,SV109: nat > $o] :
( ( ( ~ ( SV109 @ ( sK29_SY528 @ SV232 @ SV109 ) ) )
= $false )
| ( ( SV109 @ SV232 )
= $true )
| ( ( SV109 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1725]) ).
thf(1895,plain,
! [SV232: nat,SV109: nat > $o] :
( ( ( SV109 @ ( suc @ ( sK29_SY528 @ SV232 @ SV109 ) ) )
= $false )
| ( ( SV109 @ SV232 )
= $true )
| ( ( SV109 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1725]) ).
thf(1896,plain,
! [SV233: nat > $o,SV110: nat,SV314: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ SV314 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SV314 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) )
| ~ ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1726]) ).
thf(1897,plain,
! [SV233: nat > $o,SV110: nat] :
( ( ( ~ ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) )
| ~ ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) )
= $false )
| ( ( SV233 @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1727]) ).
thf(1898,plain,
! [SV233: nat > $o,SV110: nat] :
( ( ( ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) )
| ~ ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1728]) ).
thf(1899,plain,
! [SV235: real,SV112: real] :
( ( ( ord_less_real @ SV112 @ SV235 )
= $true )
| ( ( ord_less_real @ SV235 @ SV112 )
= $true )
| ( ( SV112 = SV235 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1730]) ).
thf(1900,plain,
! [SV315: nat,SV113: nat > $o] :
( ( ( ~ ( SV113 @ SV315 ) )
= $true )
| ( ( ~ ! [SY536: nat] :
~ ~ ( ~ ~ ( SV113 @ SY536 )
| ~ ( SV113 @ ( suc @ SY536 ) ) ) )
= $true )
| ( ( SV113 @ zero_zero_nat )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1731]) ).
thf(1901,plain,
! [SV114: nat,SV236: nat] :
( ( ( ord_less_nat @ SV236 @ ( suc @ SV114 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV236 @ ( suc @ SV114 ) )
| ( SV236 != SV114 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV114 @ SV236 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1732]) ).
thf(1902,plain,
! [SV114: nat,SV236: nat] :
( ( ( SV236 = SV114 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV236 @ ( suc @ SV114 ) )
| ( SV236 != SV114 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV114 @ SV236 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1732]) ).
thf(1903,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK30_SY669 @ SV239 @ SV117 ) @ ( suc @ SV117 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) )
| ~ ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1734]) ).
thf(1904,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( SV239 @ ( sK30_SY669 @ SV239 @ SV117 ) )
= $false )
| ( ( ~ ( ~ ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) )
| ~ ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1734]) ).
thf(1905,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( ~ ( SV239 @ SV117 ) )
= $true )
| ( ( ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) )
| ~ ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1735]) ).
thf(1906,plain,
! [SV118: nat > real,SV300: nat,SV240: nat] :
( ( ( ord_less_eq_nat @ SV240 @ SV300 )
= $false )
| ( ( ord_less_eq_real @ ( SV118 @ SV300 ) @ ( SV118 @ SV240 ) )
= $true )
| ( ( ord_less_eq_real @ ( SV118 @ ( suc @ ( sK23_SY546 @ SV300 @ SV240 @ SV118 ) ) ) @ ( SV118 @ ( sK23_SY546 @ SV300 @ SV240 @ SV118 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1736]) ).
thf(1907,plain,
! [SV119: nat > nat,SV301: nat,SV241: nat] :
( ( ( ord_less_eq_nat @ SV241 @ SV301 )
= $false )
| ( ( ord_less_eq_nat @ ( SV119 @ SV301 ) @ ( SV119 @ SV241 ) )
= $true )
| ( ( ord_less_eq_nat @ ( SV119 @ ( suc @ ( sK24_SY549 @ SV301 @ SV241 @ SV119 ) ) ) @ ( SV119 @ ( sK24_SY549 @ SV301 @ SV241 @ SV119 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1737]) ).
thf(1908,plain,
! [SV309: real,SV302: real,SV242: real,SV120: real] :
( ( ( ord_less_eq_real @ SV120 @ SV242 )
= $false )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV302 )
| ~ ( ord_less_real @ SV302 @ SV309 )
| ( ord_less_real @ ( divide_divide_real @ SV120 @ SV309 ) @ ( divide_divide_real @ SV242 @ SV302 ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1738]) ).
thf(1909,plain,
! [SV122: nat > $o,SV244: nat] :
( ( ( ! [SY677: nat] :
~ ~ ( ~ ~ ( ~ ( ord_less_nat @ SY677 @ SV244 )
| ~ ! [SY556: nat] :
( ~ ( ord_less_eq_nat @ SY556 @ SY677 )
| ~ ( SV122 @ SY556 ) ) )
| ~ ( SV122 @ ( suc @ SY677 ) ) ) )
= $false )
| ( ( SV122 @ zero_zero_nat )
= $true )
| ( ( SV122 @ SV244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1739]) ).
thf(1910,plain,
! [SV245: nat,SV123: nat] :
( ( ( ~ ( ord_less_nat @ ( suc @ SV123 ) @ SV245 ) )
= $false )
| ( ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1740]) ).
thf(1911,plain,
! [SV123: nat,SV245: nat] :
( ( ( ~ ~ ! [SY679: nat] :
~ ~ ( ( SV245
!= ( suc @ SY679 ) )
| ~ ( ord_less_nat @ SV123 @ SY679 ) ) )
= $false )
| ( ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1740]) ).
thf(1912,plain,
! [SV123: nat,SV316: nat,SV245: nat] :
( ( ( ~ ~ ( ( SV245
!= ( suc @ SV316 ) )
| ~ ( ord_less_nat @ SV123 @ SV316 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
| ~ ~ ! [SY679: nat] :
~ ~ ( ( SV245
!= ( suc @ SY679 ) )
| ~ ( ord_less_nat @ SV123 @ SY679 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(1913,plain,
! [SV127: nat,SV248: nat,SV303: nat > nat > $o] :
( ( ( SV303 @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) )
= $false )
| ( ( ~ ! [SY719: nat,SY720: nat,SY721: nat] :
( ~ ( SV303 @ SY719 @ SY720 )
| ~ ( SV303 @ SY720 @ SY721 )
| ( SV303 @ SY719 @ SY721 ) )
| ~ ! [SY722: nat] : ( SV303 @ SY722 @ ( suc @ SY722 ) )
| ( SV303 @ SV127 @ SV248 ) )
= $true )
| ( ( ord_less_eq_nat @ SV127 @ SV248 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1743]) ).
thf(1914,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1744]) ).
thf(1915,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1744]) ).
thf(1916,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1745]) ).
thf(1917,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1746]) ).
thf(1918,plain,
! [SV251: nat,SV133: nat] :
( ( ( ~ ( ord_less_nat @ SV133 @ ( suc @ SV251 ) ) )
= $false )
| ( ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1747]) ).
thf(1919,plain,
! [SV251: nat,SV133: nat] :
( ( ( ~ ( ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1747]) ).
thf(1920,plain,
! [SV251: nat,SV133: nat] :
( ( ( ~ ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
| ~ ( ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) ) )
= $false )
| ( ( SV133 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1748]) ).
thf(1921,plain,
! [SV251: nat,SV133: nat] :
( ( ( ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
| ~ ( ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1749]) ).
thf(1922,plain,
! [SV134: nat,SV252: real] :
( ( ( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ ( sK35_SY687 @ SV252 @ SV134 ) )
| ( ( power_power_real @ ( sK35_SY687 @ SV252 @ SV134 ) @ SV134 )
!= SV252 ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV252 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV134 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1750]) ).
thf(1923,plain,
! [SV310: real,SV304: real,SV139: real,SV256: real] :
( ( ( ord_less_eq_real @ SV256 @ SV139 )
= $false )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV304 )
| ~ ( ord_less_eq_real @ SV304 @ SV310 )
| ( ord_less_eq_real @ ( divide_divide_real @ SV256 @ SV310 ) @ ( divide_divide_real @ SV139 @ SV304 ) ) )
= $true )
| ( ( ord_less_eq_real @ zero_zero_real @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1751]) ).
thf(1924,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1752]) ).
thf(1925,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) ) )
= $false )
| ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1752]) ).
thf(1926,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1753]) ).
thf(1927,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1754]) ).
thf(1928,plain,
! [SV305: nat > $o,SV258: nat,SV142: nat] :
( ( ( ~ ! [SY724: nat] :
( ~ ( ord_less_eq_nat @ SV142 @ SY724 )
| ~ ( ord_less_nat @ SY724 @ SV258 )
| ~ ( SV305 @ ( suc @ SY724 ) )
| ( SV305 @ SY724 ) ) )
= $true )
| ( ( SV305 @ SV142 )
= $true )
| ( ( SV305 @ SV258 )
= $false )
| ( ( ord_less_eq_nat @ SV142 @ SV258 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1755]) ).
thf(1929,plain,
! [SV262: int,SV149: nat,SV1: int] :
( ( ( ~ ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ SV1 ) @ SV149 ) @ ( ring_1_of_int_real @ SV262 ) ) )
= $false )
| ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ SV1 ) @ SV149 ) @ ( ring_1_of_int_real @ SV262 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1758]) ).
thf(1930,plain,
! [SV262: int,SV149: nat,SV1: int] :
( ( ( ~ ( ord_less_int @ ( power_power_int @ SV1 @ SV149 ) @ SV262 ) )
= $false )
| ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ SV1 ) @ SV149 ) @ ( ring_1_of_int_real @ SV262 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1758]) ).
thf(1931,plain,
! [SV262: int,SV149: nat,SV1: int] :
( ( ( ~ ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ SV1 ) @ SV149 ) @ ( ring_1_of_int_real @ SV262 ) ) )
= $false )
| ( ( ord_less_int @ ( power_power_int @ SV1 @ SV149 ) @ SV262 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1759]) ).
thf(1932,plain,
! [SV262: int,SV149: nat,SV1: int] :
( ( ( ~ ( ord_less_int @ ( power_power_int @ SV1 @ SV149 ) @ SV262 ) )
= $false )
| ( ( ord_less_int @ ( power_power_int @ SV1 @ SV149 ) @ SV262 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1759]) ).
thf(1933,plain,
! [SV263: nat,SV150: int,SV2: int] :
( ( ( ~ ( ord_less_real @ ( ring_1_of_int_real @ SV2 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV150 ) @ SV263 ) ) )
= $false )
| ( ( ord_less_real @ ( ring_1_of_int_real @ SV2 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV150 ) @ SV263 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1760]) ).
thf(1934,plain,
! [SV263: nat,SV150: int,SV2: int] :
( ( ( ~ ( ord_less_int @ SV2 @ ( power_power_int @ SV150 @ SV263 ) ) )
= $false )
| ( ( ord_less_real @ ( ring_1_of_int_real @ SV2 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV150 ) @ SV263 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1760]) ).
thf(1935,plain,
! [SV263: nat,SV150: int,SV2: int] :
( ( ( ~ ( ord_less_real @ ( ring_1_of_int_real @ SV2 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV150 ) @ SV263 ) ) )
= $false )
| ( ( ord_less_int @ SV2 @ ( power_power_int @ SV150 @ SV263 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1761]) ).
thf(1936,plain,
! [SV263: nat,SV150: int,SV2: int] :
( ( ( ~ ( ord_less_int @ SV2 @ ( power_power_int @ SV150 @ SV263 ) ) )
= $false )
| ( ( ord_less_int @ SV2 @ ( power_power_int @ SV150 @ SV263 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1761]) ).
thf(1937,plain,
! [SV264: int,SV152: nat,SV4: int] :
( ( ( ( power_power_real @ ( ring_1_of_int_real @ SV4 ) @ SV152 )
!= ( ring_1_of_int_real @ SV264 ) )
= $false )
| ( ( ( power_power_real @ ( ring_1_of_int_real @ SV4 ) @ SV152 )
= ( ring_1_of_int_real @ SV264 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1762]) ).
thf(1938,plain,
! [SV264: int,SV152: nat,SV4: int] :
( ( ( ( power_power_int @ SV4 @ SV152 )
!= SV264 )
= $false )
| ( ( ( power_power_real @ ( ring_1_of_int_real @ SV4 ) @ SV152 )
= ( ring_1_of_int_real @ SV264 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1762]) ).
thf(1939,plain,
! [SV264: int,SV152: nat,SV4: int] :
( ( ( ( power_power_real @ ( ring_1_of_int_real @ SV4 ) @ SV152 )
!= ( ring_1_of_int_real @ SV264 ) )
= $false )
| ( ( ( power_power_int @ SV4 @ SV152 )
= SV264 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1763]) ).
thf(1940,plain,
! [SV264: int,SV152: nat,SV4: int] :
( ( ( ( power_power_int @ SV4 @ SV152 )
!= SV264 )
= $false )
| ( ( ( power_power_int @ SV4 @ SV152 )
= SV264 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1763]) ).
thf(1941,plain,
! [SV265: nat,SV153: int,SV5: int] :
( ( ( ( ring_1_of_int_real @ SV5 )
!= ( power_power_real @ ( ring_1_of_int_real @ SV153 ) @ SV265 ) )
= $false )
| ( ( ( ring_1_of_int_real @ SV5 )
= ( power_power_real @ ( ring_1_of_int_real @ SV153 ) @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1764]) ).
thf(1942,plain,
! [SV265: nat,SV153: int,SV5: int] :
( ( ( SV5
!= ( power_power_int @ SV153 @ SV265 ) )
= $false )
| ( ( ( ring_1_of_int_real @ SV5 )
= ( power_power_real @ ( ring_1_of_int_real @ SV153 ) @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1764]) ).
thf(1943,plain,
! [SV265: nat,SV153: int,SV5: int] :
( ( ( ( ring_1_of_int_real @ SV5 )
!= ( power_power_real @ ( ring_1_of_int_real @ SV153 ) @ SV265 ) )
= $false )
| ( ( SV5
= ( power_power_int @ SV153 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1765]) ).
thf(1944,plain,
! [SV265: nat,SV153: int,SV5: int] :
( ( ( SV5
!= ( power_power_int @ SV153 @ SV265 ) )
= $false )
| ( ( SV5
= ( power_power_int @ SV153 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1765]) ).
thf(1945,plain,
! [SV154: int,SV6: int] :
( ( ( ord_less_real @ ( ring_1_of_int_real @ SV6 ) @ ( ring_1_of_int_real @ SV154 ) )
= $true )
| ( ( ord_less_real @ ( ring_1_of_int_real @ SV6 ) @ ( ring_1_of_int_real @ SV154 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1766]) ).
thf(1946,plain,
! [SV154: int,SV6: int] :
( ( ( ord_less_int @ SV6 @ SV154 )
= $true )
| ( ( ord_less_real @ ( ring_1_of_int_real @ SV6 ) @ ( ring_1_of_int_real @ SV154 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1767]) ).
thf(1947,plain,
! [SV154: int,SV6: int] :
( ( ( ord_less_real @ ( ring_1_of_int_real @ SV6 ) @ ( ring_1_of_int_real @ SV154 ) )
= $true )
| ( ( ord_less_int @ SV6 @ SV154 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1768]) ).
thf(1948,plain,
! [SV154: int,SV6: int] :
( ( ( ord_less_int @ SV6 @ SV154 )
= $true )
| ( ( ord_less_int @ SV6 @ SV154 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1769]) ).
thf(1949,plain,
! [SV155: int,SV7: int] :
( ( ( ( ring_1_of_int_real @ SV7 )
= ( ring_1_of_int_real @ SV155 ) )
= $true )
| ( ( ( ring_1_of_int_real @ SV7 )
= ( ring_1_of_int_real @ SV155 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1770]) ).
thf(1950,plain,
! [SV155: int,SV7: int] :
( ( ( SV7 = SV155 )
= $true )
| ( ( ( ring_1_of_int_real @ SV7 )
= ( ring_1_of_int_real @ SV155 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1771]) ).
thf(1951,plain,
! [SV155: int,SV7: int] :
( ( ( ( ring_1_of_int_real @ SV7 )
= ( ring_1_of_int_real @ SV155 ) )
= $true )
| ( ( SV7 = SV155 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1772]) ).
thf(1952,plain,
! [SV155: int,SV7: int] :
( ( ( SV7 = SV155 )
= $true )
| ( ( SV7 = SV155 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1773]) ).
thf(1953,plain,
! [SV156: nat,SV8: nat] :
( ( ( ( suc @ SV8 )
= ( suc @ SV156 ) )
= $true )
| ( ( ( suc @ SV8 )
= ( suc @ SV156 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1774]) ).
thf(1954,plain,
! [SV156: nat,SV8: nat] :
( ( ( SV8 = SV156 )
= $true )
| ( ( ( suc @ SV8 )
= ( suc @ SV156 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1775]) ).
thf(1955,plain,
! [SV156: nat,SV8: nat] :
( ( ( ( suc @ SV8 )
= ( suc @ SV156 ) )
= $true )
| ( ( SV8 = SV156 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1776]) ).
thf(1956,plain,
! [SV156: nat,SV8: nat] :
( ( ( SV8 = SV156 )
= $true )
| ( ( SV8 = SV156 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1777]) ).
thf(1957,plain,
! [SV157: nat,SV9: nat] :
( ( ( ( suc @ SV9 )
= ( suc @ SV157 ) )
= $true )
| ( ( ( suc @ SV9 )
= ( suc @ SV157 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1778]) ).
thf(1958,plain,
! [SV157: nat,SV9: nat] :
( ( ( SV9 = SV157 )
= $true )
| ( ( ( suc @ SV9 )
= ( suc @ SV157 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1779]) ).
thf(1959,plain,
! [SV157: nat,SV9: nat] :
( ( ( ( suc @ SV9 )
= ( suc @ SV157 ) )
= $true )
| ( ( SV9 = SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1780]) ).
thf(1960,plain,
! [SV157: nat,SV9: nat] :
( ( ( SV9 = SV157 )
= $true )
| ( ( SV9 = SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1781]) ).
thf(1961,plain,
! [SV158: nat,SV10: nat] :
( ( ( ord_less_nat @ ( suc @ SV10 ) @ ( suc @ SV158 ) )
= $true )
| ( ( ord_less_nat @ ( suc @ SV10 ) @ ( suc @ SV158 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1782]) ).
thf(1962,plain,
! [SV158: nat,SV10: nat] :
( ( ( ord_less_nat @ SV10 @ SV158 )
= $true )
| ( ( ord_less_nat @ ( suc @ SV10 ) @ ( suc @ SV158 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1783]) ).
thf(1963,plain,
! [SV158: nat,SV10: nat] :
( ( ( ord_less_nat @ ( suc @ SV10 ) @ ( suc @ SV158 ) )
= $true )
| ( ( ord_less_nat @ SV10 @ SV158 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1784]) ).
thf(1964,plain,
! [SV158: nat,SV10: nat] :
( ( ( ord_less_nat @ SV10 @ SV158 )
= $true )
| ( ( ord_less_nat @ SV10 @ SV158 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1785]) ).
thf(1965,plain,
! [SV159: nat,SV16: nat] :
( ( ( ~ ~ ( ord_less_nat @ SV16 @ SV159 ) )
= $false )
| ( ( ord_less_nat @ SV16 @ SV159 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1802]) ).
thf(1966,plain,
! [SV16: nat,SV159: nat] :
( ( ( ~ ( ord_less_nat @ SV159 @ ( suc @ SV16 ) ) )
= $false )
| ( ( ord_less_nat @ SV16 @ SV159 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1802]) ).
thf(1967,plain,
! [SV159: nat,SV16: nat] :
( ( ( ~ ( ord_less_nat @ SV16 @ SV159 ) )
= $true )
| ( ( ord_less_nat @ SV159 @ ( suc @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1803]) ).
thf(1968,plain,
! [SV16: nat,SV159: nat] :
( ( ( ord_less_nat @ SV159 @ ( suc @ SV16 ) )
= $true )
| ( ( ord_less_nat @ SV159 @ ( suc @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1804]) ).
thf(1969,plain,
! [SV160: nat,SV17: nat] :
( ( ( ord_less_nat @ SV17 @ ( suc @ SV160 ) )
= $true )
| ( ( ord_less_nat @ SV17 @ ( suc @ SV160 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1805]) ).
thf(1970,plain,
! [SV160: nat,SV17: nat] :
( ( ( ( ord_less_nat @ SV17 @ SV160 )
| ( SV17 = SV160 ) )
= $true )
| ( ( ord_less_nat @ SV17 @ ( suc @ SV160 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1806]) ).
thf(1971,plain,
! [SV160: nat,SV17: nat] :
( ( ( ~ ( ord_less_nat @ SV17 @ ( suc @ SV160 ) ) )
= $false )
| ( ( ord_less_nat @ SV17 @ SV160 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1807]) ).
thf(1972,plain,
! [SV160: nat,SV17: nat] :
( ( ( ~ ( ( ord_less_nat @ SV17 @ SV160 )
| ( SV17 = SV160 ) ) )
= $false )
| ( ( ord_less_nat @ SV17 @ SV160 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1807]) ).
thf(1973,plain,
! [SV160: nat,SV17: nat] :
( ( ( ~ ( ord_less_nat @ SV17 @ ( suc @ SV160 ) ) )
= $false )
| ( ( SV17 = SV160 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1808]) ).
thf(1974,plain,
! [SV160: nat,SV17: nat] :
( ( ( ~ ( ( ord_less_nat @ SV17 @ SV160 )
| ( SV17 = SV160 ) ) )
= $false )
| ( ( SV17 = SV160 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1808]) ).
thf(1975,plain,
! [SV161: nat,SV21: nat] :
( ( ( ( power_power_nat @ SV21 @ SV161 )
= ( suc @ zero_zero_nat ) )
= $true )
| ( ( ( power_power_nat @ SV21 @ SV161 )
= ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1809]) ).
thf(1976,plain,
! [SV21: nat,SV161: nat] :
( ( ( ( SV161 = zero_zero_nat )
| ( SV21
= ( suc @ zero_zero_nat ) ) )
= $true )
| ( ( ( power_power_nat @ SV21 @ SV161 )
= ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1810]) ).
thf(1977,plain,
! [SV161: nat,SV21: nat] :
( ( ( ( power_power_nat @ SV21 @ SV161 )
!= ( suc @ zero_zero_nat ) )
= $false )
| ( ( SV161 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1811]) ).
thf(1978,plain,
! [SV21: nat,SV161: nat] :
( ( ( ~ ( ( SV161 = zero_zero_nat )
| ( SV21
= ( suc @ zero_zero_nat ) ) ) )
= $false )
| ( ( SV161 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1811]) ).
thf(1979,plain,
! [SV161: nat,SV21: nat] :
( ( ( ( power_power_nat @ SV21 @ SV161 )
!= ( suc @ zero_zero_nat ) )
= $false )
| ( ( SV21
= ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1812]) ).
thf(1980,plain,
! [SV21: nat,SV161: nat] :
( ( ( ~ ( ( SV161 = zero_zero_nat )
| ( SV21
= ( suc @ zero_zero_nat ) ) ) )
= $false )
| ( ( SV21
= ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1812]) ).
thf(1981,plain,
! [SV162: int,SV28: int] :
( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV28 ) @ ( ring_1_of_int_real @ SV162 ) )
= $true )
| ( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV28 ) @ ( ring_1_of_int_real @ SV162 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1817]) ).
thf(1982,plain,
! [SV162: int,SV28: int] :
( ( ( ord_less_eq_int @ SV28 @ SV162 )
= $true )
| ( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV28 ) @ ( ring_1_of_int_real @ SV162 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1818]) ).
thf(1983,plain,
! [SV162: int,SV28: int] :
( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV28 ) @ ( ring_1_of_int_real @ SV162 ) )
= $true )
| ( ( ord_less_eq_int @ SV28 @ SV162 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1819]) ).
thf(1984,plain,
! [SV162: int,SV28: int] :
( ( ( ord_less_eq_int @ SV28 @ SV162 )
= $true )
| ( ( ord_less_eq_int @ SV28 @ SV162 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1820]) ).
thf(1985,plain,
! [SV266: int,SV163: nat,SV29: int] :
( ( ( ~ ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ SV29 ) @ SV163 ) @ ( ring_1_of_int_real @ SV266 ) ) )
= $false )
| ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ SV29 ) @ SV163 ) @ ( ring_1_of_int_real @ SV266 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1821]) ).
thf(1986,plain,
! [SV266: int,SV163: nat,SV29: int] :
( ( ( ~ ( ord_less_eq_int @ ( power_power_int @ SV29 @ SV163 ) @ SV266 ) )
= $false )
| ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ SV29 ) @ SV163 ) @ ( ring_1_of_int_real @ SV266 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1821]) ).
thf(1987,plain,
! [SV266: int,SV163: nat,SV29: int] :
( ( ( ~ ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ SV29 ) @ SV163 ) @ ( ring_1_of_int_real @ SV266 ) ) )
= $false )
| ( ( ord_less_eq_int @ ( power_power_int @ SV29 @ SV163 ) @ SV266 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1822]) ).
thf(1988,plain,
! [SV266: int,SV163: nat,SV29: int] :
( ( ( ~ ( ord_less_eq_int @ ( power_power_int @ SV29 @ SV163 ) @ SV266 ) )
= $false )
| ( ( ord_less_eq_int @ ( power_power_int @ SV29 @ SV163 ) @ SV266 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1822]) ).
thf(1989,plain,
! [SV267: nat,SV164: int,SV30: int] :
( ( ( ~ ( ord_less_eq_real @ ( ring_1_of_int_real @ SV30 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV164 ) @ SV267 ) ) )
= $false )
| ( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV30 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV164 ) @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1823]) ).
thf(1990,plain,
! [SV267: nat,SV164: int,SV30: int] :
( ( ( ~ ( ord_less_eq_int @ SV30 @ ( power_power_int @ SV164 @ SV267 ) ) )
= $false )
| ( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV30 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV164 ) @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1823]) ).
thf(1991,plain,
! [SV267: nat,SV164: int,SV30: int] :
( ( ( ~ ( ord_less_eq_real @ ( ring_1_of_int_real @ SV30 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV164 ) @ SV267 ) ) )
= $false )
| ( ( ord_less_eq_int @ SV30 @ ( power_power_int @ SV164 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1824]) ).
thf(1992,plain,
! [SV267: nat,SV164: int,SV30: int] :
( ( ( ~ ( ord_less_eq_int @ SV30 @ ( power_power_int @ SV164 @ SV267 ) ) )
= $false )
| ( ( ord_less_eq_int @ SV30 @ ( power_power_int @ SV164 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1824]) ).
thf(1993,plain,
! [SV166: nat,SV32: nat] :
( ( ( ord_less_eq_nat @ ( suc @ SV32 ) @ ( suc @ SV166 ) )
= $true )
| ( ( ord_less_eq_nat @ ( suc @ SV32 ) @ ( suc @ SV166 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1825]) ).
thf(1994,plain,
! [SV166: nat,SV32: nat] :
( ( ( ord_less_eq_nat @ SV32 @ SV166 )
= $true )
| ( ( ord_less_eq_nat @ ( suc @ SV32 ) @ ( suc @ SV166 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1826]) ).
thf(1995,plain,
! [SV166: nat,SV32: nat] :
( ( ( ord_less_eq_nat @ ( suc @ SV32 ) @ ( suc @ SV166 ) )
= $true )
| ( ( ord_less_eq_nat @ SV32 @ SV166 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1827]) ).
thf(1996,plain,
! [SV166: nat,SV32: nat] :
( ( ( ord_less_eq_nat @ SV32 @ SV166 )
= $true )
| ( ( ord_less_eq_nat @ SV32 @ SV166 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1828]) ).
thf(1997,plain,
! [SV167: nat,SV33: nat] :
( ( ( ~ ~ ( ord_less_eq_nat @ SV33 @ SV167 ) )
= $false )
| ( ( ord_less_eq_nat @ SV33 @ SV167 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1829]) ).
thf(1998,plain,
! [SV33: nat,SV167: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( suc @ SV167 ) @ SV33 ) )
= $false )
| ( ( ord_less_eq_nat @ SV33 @ SV167 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1829]) ).
thf(1999,plain,
! [SV167: nat,SV33: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV33 @ SV167 ) )
= $true )
| ( ( ord_less_eq_nat @ ( suc @ SV167 ) @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1830]) ).
thf(2000,plain,
! [SV33: nat,SV167: nat] :
( ( ( ord_less_eq_nat @ ( suc @ SV167 ) @ SV33 )
= $true )
| ( ( ord_less_eq_nat @ ( suc @ SV167 ) @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1831]) ).
thf(2001,plain,
! [SV168: nat,SV35: nat] :
( ( ( ord_less_eq_nat @ SV35 @ ( suc @ SV168 ) )
= $true )
| ( ( ord_less_eq_nat @ SV35 @ ( suc @ SV168 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1832]) ).
thf(2002,plain,
! [SV168: nat,SV35: nat] :
( ( ( ( ord_less_eq_nat @ SV35 @ SV168 )
| ( SV35
= ( suc @ SV168 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV35 @ ( suc @ SV168 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1833]) ).
thf(2003,plain,
! [SV168: nat,SV35: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV35 @ ( suc @ SV168 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV35 @ SV168 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1834]) ).
thf(2004,plain,
! [SV168: nat,SV35: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV35 @ SV168 )
| ( SV35
= ( suc @ SV168 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV35 @ SV168 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1834]) ).
thf(2005,plain,
! [SV168: nat,SV35: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV35 @ ( suc @ SV168 ) ) )
= $false )
| ( ( SV35
= ( suc @ SV168 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1835]) ).
thf(2006,plain,
! [SV168: nat,SV35: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV35 @ SV168 )
| ( SV35
= ( suc @ SV168 ) ) ) )
= $false )
| ( ( SV35
= ( suc @ SV168 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1835]) ).
thf(2007,plain,
! [SV306: nat,SV169: nat] :
( ( ( ~ ( nthRoo1352626670d_root @ SV169 @ SV306 )
| ( SV169
!= ( suc @ SV306 ) ) )
= $false )
| ( ( nthRoo1352626670d_root @ SV169 @ SV306 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1836]) ).
thf(2008,plain,
! [SV306: nat,SV169: nat] :
( ( ( ~ ( nthRoo1352626670d_root @ SV169 @ SV306 )
| ( SV169
!= ( suc @ SV306 ) ) )
= $false )
| ( ( SV169
= ( suc @ SV306 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1837]) ).
thf(2009,plain,
! [SV170: nat,SV37: nat] :
( ( ( ord_less_eq_nat @ ( suc @ SV37 ) @ SV170 )
= $true )
| ( ( ord_less_eq_nat @ ( suc @ SV37 ) @ SV170 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1838]) ).
thf(2010,plain,
! [SV170: nat,SV37: nat] :
( ( ( ord_less_nat @ SV37 @ SV170 )
= $true )
| ( ( ord_less_eq_nat @ ( suc @ SV37 ) @ SV170 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1839]) ).
thf(2011,plain,
! [SV170: nat,SV37: nat] :
( ( ( ord_less_eq_nat @ ( suc @ SV37 ) @ SV170 )
= $true )
| ( ( ord_less_nat @ SV37 @ SV170 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1840]) ).
thf(2012,plain,
! [SV170: nat,SV37: nat] :
( ( ( ord_less_nat @ SV37 @ SV170 )
= $true )
| ( ( ord_less_nat @ SV37 @ SV170 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1841]) ).
thf(2013,plain,
! [SV171: nat,SV38: nat] :
( ( ( ord_less_nat @ SV38 @ ( suc @ SV171 ) )
= $true )
| ( ( ord_less_nat @ SV38 @ ( suc @ SV171 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1842]) ).
thf(2014,plain,
! [SV171: nat,SV38: nat] :
( ( ( ord_less_eq_nat @ SV38 @ SV171 )
= $true )
| ( ( ord_less_nat @ SV38 @ ( suc @ SV171 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1843]) ).
thf(2015,plain,
! [SV171: nat,SV38: nat] :
( ( ( ord_less_nat @ SV38 @ ( suc @ SV171 ) )
= $true )
| ( ( ord_less_eq_nat @ SV38 @ SV171 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1844]) ).
thf(2016,plain,
! [SV171: nat,SV38: nat] :
( ( ( ord_less_eq_nat @ SV38 @ SV171 )
= $true )
| ( ( ord_less_eq_nat @ SV38 @ SV171 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1845]) ).
thf(2017,plain,
! [SV307: nat,SV172: nat] :
( ( ( ~ ( ord_less_nat @ SV172 @ SV307 )
| ~ ( ord_less_eq_nat @ ( suc @ SV172 ) @ SV307 ) )
= $false )
| ( ( ord_less_nat @ SV172 @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1846]) ).
thf(2018,plain,
! [SV307: nat,SV172: nat] :
( ( ( ~ ( ord_less_nat @ SV172 @ SV307 )
| ~ ( ord_less_eq_nat @ ( suc @ SV172 ) @ SV307 ) )
= $false )
| ( ( ord_less_eq_nat @ ( suc @ SV172 ) @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1847]) ).
thf(2019,plain,
! [SV45: nat] :
( ( ( ! [SY405: nat] :
( SV45
!= ( suc @ SY405 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1849]) ).
thf(2020,plain,
! [SV311: nat,SV45: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV45 )
| ~ ~ ! [SY405: nat] :
( SV45
!= ( suc @ SY405 ) ) )
= $false )
| ( ( SV45
= ( suc @ SV311 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1850]) ).
thf(2021,plain,
! [SV178: nat > $o,SV47: nat,SV312: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV312 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SV312 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) )
| ~ ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1851]) ).
thf(2022,plain,
! [SV178: nat > $o,SV47: nat] :
( ( ( ~ ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) ) )
= $false )
| ( ( SV178 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1852]) ).
thf(2023,plain,
! [SV47: nat,SV178: nat > $o] :
( ( ( ~ ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) )
= $false )
| ( ( SV178 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1852]) ).
thf(2024,plain,
! [SV178: nat > $o,SV47: nat,SV317: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ SV317 @ SV47 )
| ~ ( SV178 @ ( suc @ SV317 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) )
| ~ ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1853]) ).
thf(2025,plain,
! [SV181: nat,SV50: nat,SV273: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV273 )
= $false )
| ( ( SV50 = SV273 )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV50 )
= $false )
| ( ( ( power_power_nat @ SV50 @ ( suc @ SV181 ) )
= ( power_power_nat @ SV273 @ ( suc @ SV181 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1854]) ).
thf(2026,plain,
! [SV274: real,SV182: real,SV51: real] :
( ( ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) ) )
= $false )
| ( ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1855]) ).
thf(2027,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) )
= $false )
| ( ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1855]) ).
thf(2028,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
| ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1856]) ).
thf(2029,plain,
! [SV183: nat,SV275: nat > $o,SV52: nat] :
( ( ( ! [SY692: nat] :
( ~ ( ord_less_eq_nat @ SV52 @ SY692 )
| ~ ( SV275 @ SY692 )
| ( SV275 @ ( suc @ SY692 ) ) ) )
= $false )
| ( ( SV275 @ SV183 )
= $true )
| ( ( SV275 @ SV52 )
= $false )
| ( ( ord_less_eq_nat @ SV52 @ SV183 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1857]) ).
thf(2030,plain,
! [SV53: nat > $o,SV184: nat,SV313: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( suc @ SV313 ) @ ( sK6_SY421 @ SV184 @ SV53 ) ) )
= $true )
| ( ( SV53 @ SV313 )
= $true )
| ( ( SV53 @ SV184 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1858]) ).
thf(2031,plain,
! [SV185: real,SV54: real,SV308: real,SV276: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV276 ) )
= $true )
| ( ( ~ ( ord_less_eq_real @ SV276 @ SV308 )
| ( ord_less_real @ ( divide_divide_real @ SV54 @ SV308 ) @ ( divide_divide_real @ SV185 @ SV276 ) ) )
= $true )
| ( ( ord_less_real @ SV54 @ SV185 )
= $false )
| ( ( ord_less_eq_real @ zero_zero_real @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1859]) ).
thf(2032,plain,
! [SV191: nat,SV61: real] :
( ( ( ( power_power_real @ SV61 @ SV191 )
= zero_zero_real )
= $true )
| ( ( ( power_power_real @ SV61 @ SV191 )
= zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1862]) ).
thf(2033,plain,
! [SV191: nat,SV61: real] :
( ( ( ~ ( ( SV61 != zero_zero_real )
| ~ ( ord_less_nat @ zero_zero_nat @ SV191 ) ) )
= $true )
| ( ( ( power_power_real @ SV61 @ SV191 )
= zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1863]) ).
thf(2034,plain,
! [SV191: nat,SV61: real] :
( ( ( SV61 = zero_zero_real )
= $false )
| ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV191 ) )
= $true )
| ( ( ~ ( ( ( power_power_real @ SV61 @ SV191 )
!= zero_zero_real )
| ~ ~ ( ( SV61 != zero_zero_real )
| ~ ( ord_less_nat @ zero_zero_nat @ SV191 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1864]) ).
thf(2035,plain,
! [SV62: nat,SV192: real] :
( ( ( ~ ( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ ( sK31_SY616 @ SV192 @ SV62 ) )
| ( ( power_power_real @ ( sK31_SY616 @ SV192 @ SV62 ) @ SV62 )
!= SV192 ) )
| ~ ! [SY726: real] :
( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY726 )
| ( ( power_power_real @ SY726 @ SV62 )
!= SV192 ) )
| ( SY726
= ( sK31_SY616 @ SV192 @ SV62 ) ) ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV192 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1865]) ).
thf(2036,plain,
! [SV281: nat,SV197: nat,SV68: nat > int] :
( ( ( ( ord_less_int @ ( SV68 @ SV197 ) @ ( SV68 @ SV281 ) )
| ( ord_less_nat @ SV197 @ SV281 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_int @ ( SV68 @ SV197 ) @ ( SV68 @ SV281 ) )
| ~ ( ord_less_nat @ SV197 @ SV281 ) ) )
= $true )
| ( ( ord_less_int @ ( SV68 @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) @ ( SV68 @ ( suc @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1867]) ).
thf(2037,plain,
! [SV198: nat,SV69: nat] :
( ( ( ~ ( ord_less_nat @ SV69 @ ( sK36_SY623 @ SV198 @ SV69 ) )
| ( SV198
!= ( suc @ ( sK36_SY623 @ SV198 @ SV69 ) ) ) )
= $false )
| ( ( SV198
= ( suc @ SV69 ) )
= $true )
| ( ( ord_less_nat @ SV69 @ SV198 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1868]) ).
thf(2038,plain,
! [SV199: nat,SV70: nat > $o] :
( ( ( SV70 @ ( sK26_SY453 @ SV199 @ SV70 ) )
= $true )
| ( ( SV70 @ SV199 )
= $true )
| ( ( SV70 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1869]) ).
thf(2039,plain,
! [SV282: nat,SV201: nat,SV73: nat > nat] :
( ( ( ( ord_less_nat @ ( SV73 @ SV201 ) @ ( SV73 @ SV282 ) )
| ( ord_less_nat @ SV201 @ SV282 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( SV73 @ SV201 ) @ ( SV73 @ SV282 ) )
| ~ ( ord_less_nat @ SV201 @ SV282 ) ) )
= $true )
| ( ( ord_less_nat @ ( SV73 @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) @ ( SV73 @ ( suc @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1871]) ).
thf(2040,plain,
! [SV202: nat,SV74: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ ( sK13_SY627 @ SV74 @ SV202 ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1872]) ).
thf(2041,plain,
! [SV202: nat,SV74: real] :
( ( ( ( power_power_real @ ( sK13_SY627 @ SV74 @ SV202 ) @ ( suc @ SV202 ) )
!= SV74 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1872]) ).
thf(2042,plain,
! [SV205: nat,SV77: real,SV283: real] :
( ( ( ord_less_eq_real @ zero_zero_real @ SV283 )
= $false )
| ( ( SV77 = SV283 )
= $true )
| ( ( ord_less_eq_real @ zero_zero_real @ SV77 )
= $false )
| ( ( ( power_power_real @ SV77 @ ( suc @ SV205 ) )
= ( power_power_real @ SV283 @ ( suc @ SV205 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1875]) ).
thf(2043,plain,
! [SV284: nat > $o,SV78: nat,SV206: nat] :
( ( ( SV206
!= ( suc @ ( sK32_SY699 @ SV78 @ SV284 @ SV206 ) ) )
= $false )
| ( ( ~ ! [SY700: nat] :
( ~ ( ord_less_nat @ SY700 @ SV206 )
| ~ ( SV284 @ ( suc @ SY700 ) )
| ( SV284 @ SY700 ) )
| ( SV284 @ SV78 ) )
= $true )
| ( ( ord_less_nat @ SV78 @ SV206 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1876]) ).
thf(2044,plain,
! [SV206: nat,SV78: nat,SV284: nat > $o] :
( ( ( SV284 @ ( sK32_SY699 @ SV78 @ SV284 @ SV206 ) )
= $false )
| ( ( ~ ! [SY700: nat] :
( ~ ( ord_less_nat @ SY700 @ SV206 )
| ~ ( SV284 @ ( suc @ SY700 ) )
| ( SV284 @ SY700 ) )
| ( SV284 @ SV78 ) )
= $true )
| ( ( ord_less_nat @ SV78 @ SV206 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1876]) ).
thf(2045,plain,
! [SV207: nat,SV79: nat,SV285: nat > nat > $o] :
( ( ( ~ ! [SY702: nat,SY703: nat,SY704: nat] :
( ~ ( ord_less_nat @ SY702 @ SY703 )
| ~ ( ord_less_nat @ SY703 @ SY704 )
| ~ ( SV285 @ SY702 @ SY703 )
| ~ ( SV285 @ SY703 @ SY704 )
| ( SV285 @ SY702 @ SY704 ) ) )
= $true )
| ( ( SV285 @ SV79 @ SV207 )
= $true )
| ( ( SV285 @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) @ ( suc @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) ) )
= $false )
| ( ( ord_less_nat @ SV79 @ SV207 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1877]) ).
thf(2046,plain,
! [SV287: nat > $o,SV209: nat,SV82: nat] :
( ( ( ! [SY706: nat] :
( ~ ( ord_less_eq_nat @ SV82 @ SY706 )
| ~ ( ord_less_nat @ SY706 @ SV209 )
| ~ ( SV287 @ SY706 )
| ( SV287 @ ( suc @ SY706 ) ) ) )
= $false )
| ( ( SV287 @ SV209 )
= $true )
| ( ( SV287 @ SV82 )
= $false )
| ( ( ord_less_eq_nat @ SV82 @ SV209 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1879]) ).
thf(2047,plain,
! [SV212: nat,SV288: nat,SV85: nat > nat > $o] :
( ( ( SV85 @ zero_zero_nat @ ( suc @ ( sK37_SY487 @ SV288 @ SV212 @ SV85 ) ) )
= $false )
| ( ( ~ ! [SY488: nat,SY489: nat] :
( ~ ( SV85 @ SY488 @ SY489 )
| ( SV85 @ ( suc @ SY488 ) @ ( suc @ SY489 ) ) )
| ( SV85 @ SV212 @ SV288 ) )
= $true )
| ( ( SV85 @ ( sK17_SY486 @ SV288 @ SV212 @ SV85 ) @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1880]) ).
thf(2048,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( ord_less_nat @ ( sK27_SY649 @ SV214 @ SV87 ) @ ( suc @ SV87 ) )
= $true )
| ( ( ~ ( ~ ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) )
| ~ ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1882]) ).
thf(2049,plain,
! [SV214: nat > $o,SV87: nat] :
( ( ( ~ ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) )
| ~ ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) )
= $false )
| ( ( SV214 @ ( sK27_SY649 @ SV214 @ SV87 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1883]) ).
thf(2050,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) )
| ~ ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1884]) ).
thf(2051,plain,
! [SV216: nat,SV89: int,SV291: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ SV291 )
= $false )
| ( ( SV89 = SV291 )
= $true )
| ( ( ord_less_eq_int @ zero_zero_int @ SV89 )
= $false )
| ( ( ( power_power_int @ SV89 @ ( suc @ SV216 ) )
= ( power_power_int @ SV291 @ ( suc @ SV216 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1886]) ).
thf(2052,plain,
! [SV297: real,SV228: real,SV103: real] :
( ( ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) ) )
= $false )
| ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1888]) ).
thf(2053,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) )
= $false )
| ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1888]) ).
thf(2054,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) ) )
= $true )
| ( ( ~ ( ( SV228 != zero_zero_real ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1889]) ).
thf(2055,plain,
! [SV229: nat,SV104: nat] :
( ( ( ord_less_nat @ SV104 @ ( suc @ SV229 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV104 @ ( suc @ SV229 ) )
| ( SV104 != SV229 ) ) )
= $true )
| ( ( ord_less_nat @ SV104 @ SV229 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1890]) ).
thf(2056,plain,
! [SV229: nat,SV104: nat] :
( ( ( SV104 = SV229 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV104 @ ( suc @ SV229 ) )
| ( SV104 != SV229 ) ) )
= $true )
| ( ( ord_less_nat @ SV104 @ SV229 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1890]) ).
thf(2057,plain,
! [SV298: nat,SV230: nat,SV106: nat > real] :
( ( ( ( ord_less_real @ ( SV106 @ SV230 ) @ ( SV106 @ SV298 ) )
| ( ord_less_nat @ SV230 @ SV298 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( SV106 @ SV230 ) @ ( SV106 @ SV298 ) )
| ~ ( ord_less_nat @ SV230 @ SV298 ) ) )
= $true )
| ( ( ord_less_real @ ( SV106 @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) @ ( SV106 @ ( suc @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1891]) ).
thf(2058,plain,
! [SV231: nat,SV107: nat > $o] :
( ( ( SV107 @ ( suc @ ( sK28_SY525 @ SV231 @ SV107 ) ) )
= $true )
| ( ( SV107 @ zero_zero_nat )
= $true )
| ( ( SV107 @ SV231 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1892]) ).
thf(2059,plain,
! [SV232: nat,SV109: nat > $o] :
( ( ( SV109 @ ( sK29_SY528 @ SV232 @ SV109 ) )
= $true )
| ( ( SV109 @ SV232 )
= $true )
| ( ( SV109 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1894]) ).
thf(2060,plain,
! [SV233: nat > $o,SV110: nat,SV314: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV314 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SV314 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) )
| ~ ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1896]) ).
thf(2061,plain,
! [SV233: nat > $o,SV110: nat] :
( ( ( ~ ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) ) )
= $false )
| ( ( SV233 @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1897]) ).
thf(2062,plain,
! [SV110: nat,SV233: nat > $o] :
( ( ( ~ ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) )
= $false )
| ( ( SV233 @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1897]) ).
thf(2063,plain,
! [SV233: nat > $o,SV110: nat,SV318: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ SV318 @ SV110 )
| ~ ( SV233 @ SV318 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) )
| ~ ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(2064,plain,
! [SV315: nat,SV113: nat > $o] :
( ( ( SV113 @ SV315 )
= $false )
| ( ( ~ ! [SY536: nat] :
~ ~ ( ~ ~ ( SV113 @ SY536 )
| ~ ( SV113 @ ( suc @ SY536 ) ) ) )
= $true )
| ( ( SV113 @ zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1900]) ).
thf(2065,plain,
! [SV114: nat,SV236: nat] :
( ( ( ~ ( ord_less_nat @ SV236 @ ( suc @ SV114 ) )
| ( SV236 != SV114 ) )
= $false )
| ( ( ord_less_nat @ SV236 @ ( suc @ SV114 ) )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1901]) ).
thf(2066,plain,
! [SV114: nat,SV236: nat] :
( ( ( ~ ( ord_less_nat @ SV236 @ ( suc @ SV114 ) )
| ( SV236 != SV114 ) )
= $false )
| ( ( SV236 = SV114 )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1902]) ).
thf(2067,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( ord_less_nat @ ( sK30_SY669 @ SV239 @ SV117 ) @ ( suc @ SV117 ) )
= $true )
| ( ( ~ ( ~ ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) )
| ~ ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1903]) ).
thf(2068,plain,
! [SV239: nat > $o,SV117: nat] :
( ( ( ~ ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) )
| ~ ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) )
= $false )
| ( ( SV239 @ ( sK30_SY669 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1904]) ).
thf(2069,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( SV239 @ SV117 )
= $false )
| ( ( ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) )
| ~ ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1905]) ).
thf(2070,plain,
! [SV242: real,SV120: real,SV309: real,SV302: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV302 ) )
= $true )
| ( ( ~ ( ord_less_real @ SV302 @ SV309 )
| ( ord_less_real @ ( divide_divide_real @ SV120 @ SV309 ) @ ( divide_divide_real @ SV242 @ SV302 ) ) )
= $true )
| ( ( ord_less_eq_real @ SV120 @ SV242 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1908]) ).
thf(2071,plain,
! [SV244: nat,SV122: nat > $o] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ord_less_nat @ ( sK38_SY677 @ SV122 @ SV244 ) @ SV244 )
| ~ ! [SY727: nat] :
( ~ ( ord_less_eq_nat @ SY727 @ ( sK38_SY677 @ SV122 @ SV244 ) )
| ~ ( SV122 @ SY727 ) ) )
| ~ ( SV122 @ ( suc @ ( sK38_SY677 @ SV122 @ SV244 ) ) ) ) )
= $false )
| ( ( SV122 @ zero_zero_nat )
= $true )
| ( ( SV122 @ SV244 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1909]) ).
thf(2072,plain,
! [SV245: nat,SV123: nat] :
( ( ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
= $true )
| ( ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1910]) ).
thf(2073,plain,
! [SV123: nat,SV245: nat] :
( ( ( ~ ! [SY679: nat] :
~ ~ ( ( SV245
!= ( suc @ SY679 ) )
| ~ ( ord_less_nat @ SV123 @ SY679 ) ) )
= $true )
| ( ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1911]) ).
thf(2074,plain,
! [SV123: nat,SV316: nat,SV245: nat] :
( ( ( ~ ( ( SV245
!= ( suc @ SV316 ) )
| ~ ( ord_less_nat @ SV123 @ SV316 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
| ~ ~ ! [SY679: nat] :
~ ~ ( ( SV245
!= ( suc @ SY679 ) )
| ~ ( ord_less_nat @ SV123 @ SY679 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1912]) ).
thf(2075,plain,
! [SV248: nat,SV127: nat,SV303: nat > nat > $o] :
( ( ( ~ ! [SY719: nat,SY720: nat,SY721: nat] :
( ~ ( SV303 @ SY719 @ SY720 )
| ~ ( SV303 @ SY720 @ SY721 )
| ( SV303 @ SY719 @ SY721 ) ) )
= $true )
| ( ( ~ ! [SY722: nat] : ( SV303 @ SY722 @ ( suc @ SY722 ) )
| ( SV303 @ SV127 @ SV248 ) )
= $true )
| ( ( SV303 @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV248 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1913]) ).
thf(2076,plain,
! [SV249: real,SV128: real] :
( ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1914]) ).
thf(2077,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1915]) ).
thf(2078,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV128 ) )
= $true )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1916]) ).
thf(2079,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ord_less_real @ SV128 @ zero_zero_real ) )
= $true )
| ( ( ~ ( ord_less_real @ SV249 @ zero_zero_real ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1917]) ).
thf(2080,plain,
! [SV251: nat,SV133: nat] :
( ( ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
= $true )
| ( ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1918]) ).
thf(2081,plain,
! [SV251: nat,SV133: nat] :
( ( ( ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) )
= $true )
| ( ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1919]) ).
thf(2082,plain,
! [SV251: nat,SV133: nat] :
( ( ( ~ ( ord_less_nat @ SV133 @ ( suc @ SV251 ) ) )
= $false )
| ( ( SV133 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1920]) ).
thf(2083,plain,
! [SV251: nat,SV133: nat] :
( ( ( ~ ( ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) ) )
= $false )
| ( ( SV133 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1920]) ).
thf(2084,plain,
! [SV251: nat,SV319: nat,SV133: nat] :
( ( ( ~ ~ ( ( SV133
!= ( suc @ SV319 ) )
| ~ ( ord_less_nat @ SV319 @ SV251 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
| ~ ( ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2085,plain,
! [SV134: nat,SV252: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ ( sK35_SY687 @ SV252 @ SV134 ) )
| ( ( power_power_real @ ( sK35_SY687 @ SV252 @ SV134 ) @ SV134 )
!= SV252 ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV252 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1922]) ).
thf(2086,plain,
! [SV139: real,SV256: real,SV310: real,SV304: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV304 ) )
= $true )
| ( ( ~ ( ord_less_eq_real @ SV304 @ SV310 )
| ( ord_less_eq_real @ ( divide_divide_real @ SV256 @ SV310 ) @ ( divide_divide_real @ SV139 @ SV304 ) ) )
= $true )
| ( ( ord_less_eq_real @ SV256 @ SV139 )
= $false )
| ( ( ord_less_eq_real @ zero_zero_real @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1923]) ).
thf(2087,plain,
! [SV257: real,SV141: real] :
( ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1924]) ).
thf(2088,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1925]) ).
thf(2089,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV141 ) )
= $true )
| ( ( ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1926]) ).
thf(2090,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ord_less_real @ SV141 @ zero_zero_real ) )
= $true )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV257 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1927]) ).
thf(2091,plain,
! [SV305: nat > $o,SV258: nat,SV142: nat] :
( ( ( ! [SY724: nat] :
( ~ ( ord_less_eq_nat @ SV142 @ SY724 )
| ~ ( ord_less_nat @ SY724 @ SV258 )
| ~ ( SV305 @ ( suc @ SY724 ) )
| ( SV305 @ SY724 ) ) )
= $false )
| ( ( SV305 @ SV142 )
= $true )
| ( ( SV305 @ SV258 )
= $false )
| ( ( ord_less_eq_nat @ SV142 @ SV258 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1928]) ).
thf(2092,plain,
! [SV262: int,SV149: nat,SV1: int] :
( ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ SV1 ) @ SV149 ) @ ( ring_1_of_int_real @ SV262 ) )
= $true )
| ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ SV1 ) @ SV149 ) @ ( ring_1_of_int_real @ SV262 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1929]) ).
thf(2093,plain,
! [SV262: int,SV149: nat,SV1: int] :
( ( ( ord_less_int @ ( power_power_int @ SV1 @ SV149 ) @ SV262 )
= $true )
| ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ SV1 ) @ SV149 ) @ ( ring_1_of_int_real @ SV262 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1930]) ).
thf(2094,plain,
! [SV262: int,SV149: nat,SV1: int] :
( ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ SV1 ) @ SV149 ) @ ( ring_1_of_int_real @ SV262 ) )
= $true )
| ( ( ord_less_int @ ( power_power_int @ SV1 @ SV149 ) @ SV262 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1931]) ).
thf(2095,plain,
! [SV262: int,SV149: nat,SV1: int] :
( ( ( ord_less_int @ ( power_power_int @ SV1 @ SV149 ) @ SV262 )
= $true )
| ( ( ord_less_int @ ( power_power_int @ SV1 @ SV149 ) @ SV262 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1932]) ).
thf(2096,plain,
! [SV263: nat,SV150: int,SV2: int] :
( ( ( ord_less_real @ ( ring_1_of_int_real @ SV2 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV150 ) @ SV263 ) )
= $true )
| ( ( ord_less_real @ ( ring_1_of_int_real @ SV2 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV150 ) @ SV263 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1933]) ).
thf(2097,plain,
! [SV263: nat,SV150: int,SV2: int] :
( ( ( ord_less_int @ SV2 @ ( power_power_int @ SV150 @ SV263 ) )
= $true )
| ( ( ord_less_real @ ( ring_1_of_int_real @ SV2 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV150 ) @ SV263 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1934]) ).
thf(2098,plain,
! [SV263: nat,SV150: int,SV2: int] :
( ( ( ord_less_real @ ( ring_1_of_int_real @ SV2 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV150 ) @ SV263 ) )
= $true )
| ( ( ord_less_int @ SV2 @ ( power_power_int @ SV150 @ SV263 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1935]) ).
thf(2099,plain,
! [SV263: nat,SV150: int,SV2: int] :
( ( ( ord_less_int @ SV2 @ ( power_power_int @ SV150 @ SV263 ) )
= $true )
| ( ( ord_less_int @ SV2 @ ( power_power_int @ SV150 @ SV263 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1936]) ).
thf(2100,plain,
! [SV264: int,SV152: nat,SV4: int] :
( ( ( ( power_power_real @ ( ring_1_of_int_real @ SV4 ) @ SV152 )
= ( ring_1_of_int_real @ SV264 ) )
= $true )
| ( ( ( power_power_real @ ( ring_1_of_int_real @ SV4 ) @ SV152 )
= ( ring_1_of_int_real @ SV264 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1937]) ).
thf(2101,plain,
! [SV264: int,SV152: nat,SV4: int] :
( ( ( ( power_power_int @ SV4 @ SV152 )
= SV264 )
= $true )
| ( ( ( power_power_real @ ( ring_1_of_int_real @ SV4 ) @ SV152 )
= ( ring_1_of_int_real @ SV264 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1938]) ).
thf(2102,plain,
! [SV264: int,SV152: nat,SV4: int] :
( ( ( ( power_power_real @ ( ring_1_of_int_real @ SV4 ) @ SV152 )
= ( ring_1_of_int_real @ SV264 ) )
= $true )
| ( ( ( power_power_int @ SV4 @ SV152 )
= SV264 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1939]) ).
thf(2103,plain,
! [SV264: int,SV152: nat,SV4: int] :
( ( ( ( power_power_int @ SV4 @ SV152 )
= SV264 )
= $true )
| ( ( ( power_power_int @ SV4 @ SV152 )
= SV264 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1940]) ).
thf(2104,plain,
! [SV265: nat,SV153: int,SV5: int] :
( ( ( ( ring_1_of_int_real @ SV5 )
= ( power_power_real @ ( ring_1_of_int_real @ SV153 ) @ SV265 ) )
= $true )
| ( ( ( ring_1_of_int_real @ SV5 )
= ( power_power_real @ ( ring_1_of_int_real @ SV153 ) @ SV265 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1941]) ).
thf(2105,plain,
! [SV265: nat,SV153: int,SV5: int] :
( ( ( SV5
= ( power_power_int @ SV153 @ SV265 ) )
= $true )
| ( ( ( ring_1_of_int_real @ SV5 )
= ( power_power_real @ ( ring_1_of_int_real @ SV153 ) @ SV265 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1942]) ).
thf(2106,plain,
! [SV265: nat,SV153: int,SV5: int] :
( ( ( ( ring_1_of_int_real @ SV5 )
= ( power_power_real @ ( ring_1_of_int_real @ SV153 ) @ SV265 ) )
= $true )
| ( ( SV5
= ( power_power_int @ SV153 @ SV265 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1943]) ).
thf(2107,plain,
! [SV265: nat,SV153: int,SV5: int] :
( ( ( SV5
= ( power_power_int @ SV153 @ SV265 ) )
= $true )
| ( ( SV5
= ( power_power_int @ SV153 @ SV265 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1944]) ).
thf(2108,plain,
! [SV159: nat,SV16: nat] :
( ( ( ~ ( ord_less_nat @ SV16 @ SV159 ) )
= $true )
| ( ( ord_less_nat @ SV16 @ SV159 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1965]) ).
thf(2109,plain,
! [SV16: nat,SV159: nat] :
( ( ( ord_less_nat @ SV159 @ ( suc @ SV16 ) )
= $true )
| ( ( ord_less_nat @ SV16 @ SV159 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1966]) ).
thf(2110,plain,
! [SV159: nat,SV16: nat] :
( ( ( ord_less_nat @ SV16 @ SV159 )
= $false )
| ( ( ord_less_nat @ SV159 @ ( suc @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1967]) ).
thf(2111,plain,
! [SV160: nat,SV17: nat] :
( ( ( ord_less_nat @ SV17 @ SV160 )
= $true )
| ( ( SV17 = SV160 )
= $true )
| ( ( ord_less_nat @ SV17 @ ( suc @ SV160 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1970]) ).
thf(2112,plain,
! [SV160: nat,SV17: nat] :
( ( ( ord_less_nat @ SV17 @ ( suc @ SV160 ) )
= $true )
| ( ( ord_less_nat @ SV17 @ SV160 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1971]) ).
thf(2113,plain,
! [SV160: nat,SV17: nat] :
( ( ( ( ord_less_nat @ SV17 @ SV160 )
| ( SV17 = SV160 ) )
= $true )
| ( ( ord_less_nat @ SV17 @ SV160 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1972]) ).
thf(2114,plain,
! [SV160: nat,SV17: nat] :
( ( ( ord_less_nat @ SV17 @ ( suc @ SV160 ) )
= $true )
| ( ( SV17 = SV160 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1973]) ).
thf(2115,plain,
! [SV160: nat,SV17: nat] :
( ( ( ( ord_less_nat @ SV17 @ SV160 )
| ( SV17 = SV160 ) )
= $true )
| ( ( SV17 = SV160 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1974]) ).
thf(2116,plain,
! [SV21: nat,SV161: nat] :
( ( ( SV161 = zero_zero_nat )
= $true )
| ( ( SV21
= ( suc @ zero_zero_nat ) )
= $true )
| ( ( ( power_power_nat @ SV21 @ SV161 )
= ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1976]) ).
thf(2117,plain,
! [SV161: nat,SV21: nat] :
( ( ( ( power_power_nat @ SV21 @ SV161 )
= ( suc @ zero_zero_nat ) )
= $true )
| ( ( SV161 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1977]) ).
thf(2118,plain,
! [SV21: nat,SV161: nat] :
( ( ( ( SV161 = zero_zero_nat )
| ( SV21
= ( suc @ zero_zero_nat ) ) )
= $true )
| ( ( SV161 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1978]) ).
thf(2119,plain,
! [SV161: nat,SV21: nat] :
( ( ( ( power_power_nat @ SV21 @ SV161 )
= ( suc @ zero_zero_nat ) )
= $true )
| ( ( SV21
= ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1979]) ).
thf(2120,plain,
! [SV21: nat,SV161: nat] :
( ( ( ( SV161 = zero_zero_nat )
| ( SV21
= ( suc @ zero_zero_nat ) ) )
= $true )
| ( ( SV21
= ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1980]) ).
thf(2121,plain,
! [SV266: int,SV163: nat,SV29: int] :
( ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ SV29 ) @ SV163 ) @ ( ring_1_of_int_real @ SV266 ) )
= $true )
| ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ SV29 ) @ SV163 ) @ ( ring_1_of_int_real @ SV266 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1985]) ).
thf(2122,plain,
! [SV266: int,SV163: nat,SV29: int] :
( ( ( ord_less_eq_int @ ( power_power_int @ SV29 @ SV163 ) @ SV266 )
= $true )
| ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ SV29 ) @ SV163 ) @ ( ring_1_of_int_real @ SV266 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1986]) ).
thf(2123,plain,
! [SV266: int,SV163: nat,SV29: int] :
( ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ SV29 ) @ SV163 ) @ ( ring_1_of_int_real @ SV266 ) )
= $true )
| ( ( ord_less_eq_int @ ( power_power_int @ SV29 @ SV163 ) @ SV266 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1987]) ).
thf(2124,plain,
! [SV266: int,SV163: nat,SV29: int] :
( ( ( ord_less_eq_int @ ( power_power_int @ SV29 @ SV163 ) @ SV266 )
= $true )
| ( ( ord_less_eq_int @ ( power_power_int @ SV29 @ SV163 ) @ SV266 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1988]) ).
thf(2125,plain,
! [SV267: nat,SV164: int,SV30: int] :
( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV30 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV164 ) @ SV267 ) )
= $true )
| ( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV30 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV164 ) @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1989]) ).
thf(2126,plain,
! [SV267: nat,SV164: int,SV30: int] :
( ( ( ord_less_eq_int @ SV30 @ ( power_power_int @ SV164 @ SV267 ) )
= $true )
| ( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV30 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV164 ) @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1990]) ).
thf(2127,plain,
! [SV267: nat,SV164: int,SV30: int] :
( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ SV30 ) @ ( power_power_real @ ( ring_1_of_int_real @ SV164 ) @ SV267 ) )
= $true )
| ( ( ord_less_eq_int @ SV30 @ ( power_power_int @ SV164 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1991]) ).
thf(2128,plain,
! [SV267: nat,SV164: int,SV30: int] :
( ( ( ord_less_eq_int @ SV30 @ ( power_power_int @ SV164 @ SV267 ) )
= $true )
| ( ( ord_less_eq_int @ SV30 @ ( power_power_int @ SV164 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1992]) ).
thf(2129,plain,
! [SV167: nat,SV33: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV33 @ SV167 ) )
= $true )
| ( ( ord_less_eq_nat @ SV33 @ SV167 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1997]) ).
thf(2130,plain,
! [SV33: nat,SV167: nat] :
( ( ( ord_less_eq_nat @ ( suc @ SV167 ) @ SV33 )
= $true )
| ( ( ord_less_eq_nat @ SV33 @ SV167 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1998]) ).
thf(2131,plain,
! [SV167: nat,SV33: nat] :
( ( ( ord_less_eq_nat @ SV33 @ SV167 )
= $false )
| ( ( ord_less_eq_nat @ ( suc @ SV167 ) @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1999]) ).
thf(2132,plain,
! [SV168: nat,SV35: nat] :
( ( ( ord_less_eq_nat @ SV35 @ SV168 )
= $true )
| ( ( SV35
= ( suc @ SV168 ) )
= $true )
| ( ( ord_less_eq_nat @ SV35 @ ( suc @ SV168 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2002]) ).
thf(2133,plain,
! [SV168: nat,SV35: nat] :
( ( ( ord_less_eq_nat @ SV35 @ ( suc @ SV168 ) )
= $true )
| ( ( ord_less_eq_nat @ SV35 @ SV168 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2003]) ).
thf(2134,plain,
! [SV168: nat,SV35: nat] :
( ( ( ( ord_less_eq_nat @ SV35 @ SV168 )
| ( SV35
= ( suc @ SV168 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV35 @ SV168 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2004]) ).
thf(2135,plain,
! [SV168: nat,SV35: nat] :
( ( ( ord_less_eq_nat @ SV35 @ ( suc @ SV168 ) )
= $true )
| ( ( SV35
= ( suc @ SV168 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2005]) ).
thf(2136,plain,
! [SV168: nat,SV35: nat] :
( ( ( ( ord_less_eq_nat @ SV35 @ SV168 )
| ( SV35
= ( suc @ SV168 ) ) )
= $true )
| ( ( SV35
= ( suc @ SV168 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2006]) ).
thf(2137,plain,
! [SV306: nat,SV169: nat] :
( ( ( ~ ( nthRoo1352626670d_root @ SV169 @ SV306 ) )
= $false )
| ( ( nthRoo1352626670d_root @ SV169 @ SV306 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2007]) ).
thf(2138,plain,
! [SV306: nat,SV169: nat] :
( ( ( SV169
!= ( suc @ SV306 ) )
= $false )
| ( ( nthRoo1352626670d_root @ SV169 @ SV306 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2007]) ).
thf(2139,plain,
! [SV306: nat,SV169: nat] :
( ( ( ~ ( nthRoo1352626670d_root @ SV169 @ SV306 ) )
= $false )
| ( ( SV169
= ( suc @ SV306 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2008]) ).
thf(2140,plain,
! [SV306: nat,SV169: nat] :
( ( ( SV169
!= ( suc @ SV306 ) )
= $false )
| ( ( SV169
= ( suc @ SV306 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2008]) ).
thf(2141,plain,
! [SV307: nat,SV172: nat] :
( ( ( ~ ( ord_less_nat @ SV172 @ SV307 ) )
= $false )
| ( ( ord_less_nat @ SV172 @ SV307 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2017]) ).
thf(2142,plain,
! [SV307: nat,SV172: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( suc @ SV172 ) @ SV307 ) )
= $false )
| ( ( ord_less_nat @ SV172 @ SV307 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2017]) ).
thf(2143,plain,
! [SV307: nat,SV172: nat] :
( ( ( ~ ( ord_less_nat @ SV172 @ SV307 ) )
= $false )
| ( ( ord_less_eq_nat @ ( suc @ SV172 ) @ SV307 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2018]) ).
thf(2144,plain,
! [SV307: nat,SV172: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( suc @ SV172 ) @ SV307 ) )
= $false )
| ( ( ord_less_eq_nat @ ( suc @ SV172 ) @ SV307 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2018]) ).
thf(2145,plain,
! [SV45: nat] :
( ( ( SV45
!= ( suc @ ( sK39_SY405 @ SV45 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV45 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2019]) ).
thf(2146,plain,
! [SV311: nat,SV45: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV45 ) )
= $false )
| ( ( SV45
= ( suc @ SV311 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2020]) ).
thf(2147,plain,
! [SV311: nat,SV45: nat] :
( ( ( ~ ~ ! [SY405: nat] :
( SV45
!= ( suc @ SY405 ) ) )
= $false )
| ( ( SV45
= ( suc @ SV311 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2020]) ).
thf(2148,plain,
! [SV178: nat > $o,SV47: nat,SV312: nat] :
( ( ( ~ ( ord_less_nat @ SV312 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SV312 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) )
| ~ ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2021]) ).
thf(2149,plain,
! [SV178: nat > $o,SV47: nat] :
( ( ( ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) ) )
= $true )
| ( ( SV178 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2022]) ).
thf(2150,plain,
! [SV47: nat,SV178: nat > $o] :
( ( ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) )
= $true )
| ( ( SV178 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2023]) ).
thf(2151,plain,
! [SV178: nat > $o,SV47: nat,SV317: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV317 @ SV47 )
| ~ ( SV178 @ ( suc @ SV317 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) )
| ~ ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2024]) ).
thf(2152,plain,
! [SV274: real,SV182: real,SV51: real] :
( ( ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
= $true )
| ( ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2026]) ).
thf(2153,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) )
= $true )
| ( ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2027]) ).
thf(2154,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
| ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2028]) ).
thf(2155,plain,
! [SV275: nat > $o,SV183: nat,SV52: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV52 @ ( sK40_SY692 @ SV183 @ SV275 @ SV52 ) )
| ~ ( SV275 @ ( sK40_SY692 @ SV183 @ SV275 @ SV52 ) )
| ( SV275 @ ( suc @ ( sK40_SY692 @ SV183 @ SV275 @ SV52 ) ) ) )
= $false )
| ( ( SV275 @ SV183 )
= $true )
| ( ( SV275 @ SV52 )
= $false )
| ( ( ord_less_eq_nat @ SV52 @ SV183 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2029]) ).
thf(2156,plain,
! [SV53: nat > $o,SV184: nat,SV313: nat] :
( ( ( ord_less_eq_nat @ ( suc @ SV313 ) @ ( sK6_SY421 @ SV184 @ SV53 ) )
= $false )
| ( ( SV53 @ SV313 )
= $true )
| ( ( SV53 @ SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2030]) ).
thf(2157,plain,
! [SV185: real,SV54: real,SV308: real,SV276: real] :
( ( ( ord_less_real @ zero_zero_real @ SV276 )
= $false )
| ( ( ~ ( ord_less_eq_real @ SV276 @ SV308 )
| ( ord_less_real @ ( divide_divide_real @ SV54 @ SV308 ) @ ( divide_divide_real @ SV185 @ SV276 ) ) )
= $true )
| ( ( ord_less_real @ SV54 @ SV185 )
= $false )
| ( ( ord_less_eq_real @ zero_zero_real @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2031]) ).
thf(2158,plain,
! [SV191: nat,SV61: real] :
( ( ( ( SV61 != zero_zero_real )
| ~ ( ord_less_nat @ zero_zero_nat @ SV191 ) )
= $false )
| ( ( ( power_power_real @ SV61 @ SV191 )
= zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2033]) ).
thf(2159,plain,
! [SV61: real,SV191: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV191 )
= $false )
| ( ( SV61 = zero_zero_real )
= $false )
| ( ( ~ ( ( ( power_power_real @ SV61 @ SV191 )
!= zero_zero_real )
| ~ ~ ( ( SV61 != zero_zero_real )
| ~ ( ord_less_nat @ zero_zero_nat @ SV191 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2034]) ).
thf(2160,plain,
! [SV62: nat,SV192: real] :
( ( ( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ ( sK31_SY616 @ SV192 @ SV62 ) )
| ( ( power_power_real @ ( sK31_SY616 @ SV192 @ SV62 ) @ SV62 )
!= SV192 ) )
| ~ ! [SY726: real] :
( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY726 )
| ( ( power_power_real @ SY726 @ SV62 )
!= SV192 ) )
| ( SY726
= ( sK31_SY616 @ SV192 @ SV62 ) ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV192 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2035]) ).
thf(2161,plain,
! [SV281: nat,SV197: nat,SV68: nat > int] :
( ( ( ord_less_int @ ( SV68 @ SV197 ) @ ( SV68 @ SV281 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_int @ ( SV68 @ SV197 ) @ ( SV68 @ SV281 ) )
| ~ ( ord_less_nat @ SV197 @ SV281 ) ) )
= $true )
| ( ( ord_less_int @ ( SV68 @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) @ ( SV68 @ ( suc @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2036]) ).
thf(2162,plain,
! [SV68: nat > int,SV281: nat,SV197: nat] :
( ( ( ord_less_nat @ SV197 @ SV281 )
= $false )
| ( ( ~ ( ~ ( ord_less_int @ ( SV68 @ SV197 ) @ ( SV68 @ SV281 ) )
| ~ ( ord_less_nat @ SV197 @ SV281 ) ) )
= $true )
| ( ( ord_less_int @ ( SV68 @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) @ ( SV68 @ ( suc @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2036]) ).
thf(2163,plain,
! [SV198: nat,SV69: nat] :
( ( ( ~ ( ord_less_nat @ SV69 @ ( sK36_SY623 @ SV198 @ SV69 ) ) )
= $false )
| ( ( SV198
= ( suc @ SV69 ) )
= $true )
| ( ( ord_less_nat @ SV69 @ SV198 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2037]) ).
thf(2164,plain,
! [SV69: nat,SV198: nat] :
( ( ( SV198
!= ( suc @ ( sK36_SY623 @ SV198 @ SV69 ) ) )
= $false )
| ( ( SV198
= ( suc @ SV69 ) )
= $true )
| ( ( ord_less_nat @ SV69 @ SV198 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2037]) ).
thf(2165,plain,
! [SV282: nat,SV201: nat,SV73: nat > nat] :
( ( ( ord_less_nat @ ( SV73 @ SV201 ) @ ( SV73 @ SV282 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( SV73 @ SV201 ) @ ( SV73 @ SV282 ) )
| ~ ( ord_less_nat @ SV201 @ SV282 ) ) )
= $true )
| ( ( ord_less_nat @ ( SV73 @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) @ ( SV73 @ ( suc @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2039]) ).
thf(2166,plain,
! [SV73: nat > nat,SV282: nat,SV201: nat] :
( ( ( ord_less_nat @ SV201 @ SV282 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( SV73 @ SV201 ) @ ( SV73 @ SV282 ) )
| ~ ( ord_less_nat @ SV201 @ SV282 ) ) )
= $true )
| ( ( ord_less_nat @ ( SV73 @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) @ ( SV73 @ ( suc @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2039]) ).
thf(2167,plain,
! [SV202: nat,SV74: real] :
( ( ( ord_less_real @ zero_zero_real @ ( sK13_SY627 @ SV74 @ SV202 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2040]) ).
thf(2168,plain,
! [SV202: nat,SV74: real] :
( ( ( ( power_power_real @ ( sK13_SY627 @ SV74 @ SV202 ) @ ( suc @ SV202 ) )
= SV74 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2041]) ).
thf(2169,plain,
! [SV284: nat > $o,SV78: nat,SV206: nat] :
( ( ( SV206
= ( suc @ ( sK32_SY699 @ SV78 @ SV284 @ SV206 ) ) )
= $true )
| ( ( ~ ! [SY700: nat] :
( ~ ( ord_less_nat @ SY700 @ SV206 )
| ~ ( SV284 @ ( suc @ SY700 ) )
| ( SV284 @ SY700 ) )
| ( SV284 @ SV78 ) )
= $true )
| ( ( ord_less_nat @ SV78 @ SV206 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2043]) ).
thf(2170,plain,
! [SV78: nat,SV284: nat > $o,SV206: nat] :
( ( ( ~ ! [SY700: nat] :
( ~ ( ord_less_nat @ SY700 @ SV206 )
| ~ ( SV284 @ ( suc @ SY700 ) )
| ( SV284 @ SY700 ) ) )
= $true )
| ( ( SV284 @ SV78 )
= $true )
| ( ( SV284 @ ( sK32_SY699 @ SV78 @ SV284 @ SV206 ) )
= $false )
| ( ( ord_less_nat @ SV78 @ SV206 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2044]) ).
thf(2171,plain,
! [SV207: nat,SV79: nat,SV285: nat > nat > $o] :
( ( ( ! [SY702: nat,SY703: nat,SY704: nat] :
( ~ ( ord_less_nat @ SY702 @ SY703 )
| ~ ( ord_less_nat @ SY703 @ SY704 )
| ~ ( SV285 @ SY702 @ SY703 )
| ~ ( SV285 @ SY703 @ SY704 )
| ( SV285 @ SY702 @ SY704 ) ) )
= $false )
| ( ( SV285 @ SV79 @ SV207 )
= $true )
| ( ( SV285 @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) @ ( suc @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) ) )
= $false )
| ( ( ord_less_nat @ SV79 @ SV207 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2045]) ).
thf(2172,plain,
! [SV209: nat,SV287: nat > $o,SV82: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV82 @ ( sK41_SY706 @ SV287 @ SV209 @ SV82 ) )
| ~ ( ord_less_nat @ ( sK41_SY706 @ SV287 @ SV209 @ SV82 ) @ SV209 )
| ~ ( SV287 @ ( sK41_SY706 @ SV287 @ SV209 @ SV82 ) )
| ( SV287 @ ( suc @ ( sK41_SY706 @ SV287 @ SV209 @ SV82 ) ) ) )
= $false )
| ( ( SV287 @ SV209 )
= $true )
| ( ( SV287 @ SV82 )
= $false )
| ( ( ord_less_eq_nat @ SV82 @ SV209 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2046]) ).
thf(2173,plain,
! [SV288: nat,SV212: nat,SV85: nat > nat > $o] :
( ( ( ~ ! [SY488: nat,SY489: nat] :
( ~ ( SV85 @ SY488 @ SY489 )
| ( SV85 @ ( suc @ SY488 ) @ ( suc @ SY489 ) ) ) )
= $true )
| ( ( SV85 @ SV212 @ SV288 )
= $true )
| ( ( SV85 @ zero_zero_nat @ ( suc @ ( sK37_SY487 @ SV288 @ SV212 @ SV85 ) ) )
= $false )
| ( ( SV85 @ ( sK17_SY486 @ SV288 @ SV212 @ SV85 ) @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2047]) ).
thf(2174,plain,
! [SV214: nat > $o,SV87: nat] :
( ( ( ~ ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) )
| ~ ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK27_SY649 @ SV214 @ SV87 ) @ ( suc @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2048]) ).
thf(2175,plain,
! [SV214: nat > $o,SV87: nat] :
( ( ( ~ ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) ) )
= $false )
| ( ( SV214 @ ( sK27_SY649 @ SV214 @ SV87 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2049]) ).
thf(2176,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( ~ ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) )
= $false )
| ( ( SV214 @ ( sK27_SY649 @ SV214 @ SV87 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2049]) ).
thf(2177,plain,
! [SV214: nat > $o,SV87: nat] :
( ( ( ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) )
= $false )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) )
| ~ ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2050]) ).
thf(2178,plain,
! [SV297: real,SV228: real,SV103: real] :
( ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2052]) ).
thf(2179,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2053]) ).
thf(2180,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) ) )
= $false )
| ( ( ~ ( ( SV228 != zero_zero_real ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2054]) ).
thf(2181,plain,
! [SV229: nat,SV104: nat] :
( ( ( ~ ( ord_less_nat @ SV104 @ ( suc @ SV229 ) )
| ( SV104 != SV229 ) )
= $false )
| ( ( ord_less_nat @ SV104 @ ( suc @ SV229 ) )
= $false )
| ( ( ord_less_nat @ SV104 @ SV229 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2055]) ).
thf(2182,plain,
! [SV229: nat,SV104: nat] :
( ( ( ~ ( ord_less_nat @ SV104 @ ( suc @ SV229 ) )
| ( SV104 != SV229 ) )
= $false )
| ( ( SV104 = SV229 )
= $false )
| ( ( ord_less_nat @ SV104 @ SV229 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2056]) ).
thf(2183,plain,
! [SV298: nat,SV230: nat,SV106: nat > real] :
( ( ( ord_less_real @ ( SV106 @ SV230 ) @ ( SV106 @ SV298 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( SV106 @ SV230 ) @ ( SV106 @ SV298 ) )
| ~ ( ord_less_nat @ SV230 @ SV298 ) ) )
= $true )
| ( ( ord_less_real @ ( SV106 @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) @ ( SV106 @ ( suc @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2057]) ).
thf(2184,plain,
! [SV106: nat > real,SV298: nat,SV230: nat] :
( ( ( ord_less_nat @ SV230 @ SV298 )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( SV106 @ SV230 ) @ ( SV106 @ SV298 ) )
| ~ ( ord_less_nat @ SV230 @ SV298 ) ) )
= $true )
| ( ( ord_less_real @ ( SV106 @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) @ ( SV106 @ ( suc @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2057]) ).
thf(2185,plain,
! [SV233: nat > $o,SV110: nat,SV314: nat] :
( ( ( ~ ( ord_less_nat @ SV314 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SV314 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) )
| ~ ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2060]) ).
thf(2186,plain,
! [SV233: nat > $o,SV110: nat] :
( ( ( ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) ) )
= $true )
| ( ( SV233 @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2061]) ).
thf(2187,plain,
! [SV110: nat,SV233: nat > $o] :
( ( ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) )
= $true )
| ( ( SV233 @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2062]) ).
thf(2188,plain,
! [SV233: nat > $o,SV110: nat,SV318: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV318 @ SV110 )
| ~ ( SV233 @ SV318 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) )
| ~ ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2063]) ).
thf(2189,plain,
! [SV315: nat,SV113: nat > $o] :
( ( ( ! [SY536: nat] :
~ ~ ( ~ ~ ( SV113 @ SY536 )
| ~ ( SV113 @ ( suc @ SY536 ) ) ) )
= $false )
| ( ( SV113 @ SV315 )
= $false )
| ( ( SV113 @ zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2064]) ).
thf(2190,plain,
! [SV114: nat,SV236: nat] :
( ( ( ~ ( ord_less_nat @ SV236 @ ( suc @ SV114 ) ) )
= $false )
| ( ( ord_less_nat @ SV236 @ ( suc @ SV114 ) )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV236 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2065]) ).
thf(2191,plain,
! [SV114: nat,SV236: nat] :
( ( ( SV236 != SV114 )
= $false )
| ( ( ord_less_nat @ SV236 @ ( suc @ SV114 ) )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV236 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2065]) ).
thf(2192,plain,
! [SV114: nat,SV236: nat] :
( ( ( ~ ( ord_less_nat @ SV236 @ ( suc @ SV114 ) ) )
= $false )
| ( ( SV236 = SV114 )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV236 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2066]) ).
thf(2193,plain,
! [SV114: nat,SV236: nat] :
( ( ( SV236 != SV114 )
= $false )
| ( ( SV236 = SV114 )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV236 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2066]) ).
thf(2194,plain,
! [SV239: nat > $o,SV117: nat] :
( ( ( ~ ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) )
| ~ ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK30_SY669 @ SV239 @ SV117 ) @ ( suc @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2067]) ).
thf(2195,plain,
! [SV239: nat > $o,SV117: nat] :
( ( ( ~ ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) ) )
= $false )
| ( ( SV239 @ ( sK30_SY669 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2068]) ).
thf(2196,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( ~ ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) )
= $false )
| ( ( SV239 @ ( sK30_SY669 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2068]) ).
thf(2197,plain,
! [SV239: nat > $o,SV117: nat] :
( ( ( ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) )
= $false )
| ( ( SV239 @ SV117 )
= $false )
| ( ( ~ ( ~ ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) )
| ~ ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2069]) ).
thf(2198,plain,
! [SV242: real,SV120: real,SV309: real,SV302: real] :
( ( ( ord_less_real @ zero_zero_real @ SV302 )
= $false )
| ( ( ~ ( ord_less_real @ SV302 @ SV309 )
| ( ord_less_real @ ( divide_divide_real @ SV120 @ SV309 ) @ ( divide_divide_real @ SV242 @ SV302 ) ) )
= $true )
| ( ( ord_less_eq_real @ SV120 @ SV242 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2070]) ).
thf(2199,plain,
! [SV244: nat,SV122: nat > $o] :
( ( ( ~ ( ~ ~ ( ~ ( ord_less_nat @ ( sK38_SY677 @ SV122 @ SV244 ) @ SV244 )
| ~ ! [SY727: nat] :
( ~ ( ord_less_eq_nat @ SY727 @ ( sK38_SY677 @ SV122 @ SV244 ) )
| ~ ( SV122 @ SY727 ) ) )
| ~ ( SV122 @ ( suc @ ( sK38_SY677 @ SV122 @ SV244 ) ) ) ) )
= $true )
| ( ( SV122 @ zero_zero_nat )
= $true )
| ( ( SV122 @ SV244 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2071]) ).
thf(2200,plain,
! [SV123: nat,SV245: nat] :
( ( ( ! [SY679: nat] :
~ ~ ( ( SV245
!= ( suc @ SY679 ) )
| ~ ( ord_less_nat @ SV123 @ SY679 ) ) )
= $false )
| ( ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2073]) ).
thf(2201,plain,
! [SV123: nat,SV316: nat,SV245: nat] :
( ( ( ( SV245
!= ( suc @ SV316 ) )
| ~ ( ord_less_nat @ SV123 @ SV316 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
| ~ ~ ! [SY679: nat] :
~ ~ ( ( SV245
!= ( suc @ SY679 ) )
| ~ ( ord_less_nat @ SV123 @ SY679 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2074]) ).
thf(2202,plain,
! [SV248: nat,SV127: nat,SV303: nat > nat > $o] :
( ( ( ! [SY719: nat,SY720: nat,SY721: nat] :
( ~ ( SV303 @ SY719 @ SY720 )
| ~ ( SV303 @ SY720 @ SY721 )
| ( SV303 @ SY719 @ SY721 ) ) )
= $false )
| ( ( ~ ! [SY722: nat] : ( SV303 @ SY722 @ ( suc @ SY722 ) )
| ( SV303 @ SV127 @ SV248 ) )
= $true )
| ( ( SV303 @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV248 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2075]) ).
thf(2203,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2077]) ).
thf(2204,plain,
! [SV249: real,SV128: real] :
( ( ( ord_less_real @ zero_zero_real @ SV128 )
= $false )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2078]) ).
thf(2205,plain,
! [SV249: real,SV128: real] :
( ( ( ord_less_real @ SV128 @ zero_zero_real )
= $false )
| ( ( ~ ( ord_less_real @ SV249 @ zero_zero_real ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2079]) ).
thf(2206,plain,
! [SV251: nat,SV133: nat] :
( ( ( SV133 = zero_zero_nat )
= $true )
| ( ( ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) )
= $true )
| ( ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2081]) ).
thf(2207,plain,
! [SV251: nat,SV133: nat] :
( ( ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
= $true )
| ( ( SV133 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2082]) ).
thf(2208,plain,
! [SV251: nat,SV133: nat] :
( ( ( ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) )
= $true )
| ( ( SV133 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2083]) ).
thf(2209,plain,
! [SV251: nat,SV319: nat,SV133: nat] :
( ( ( ~ ( ( SV133
!= ( suc @ SV319 ) )
| ~ ( ord_less_nat @ SV319 @ SV251 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
| ~ ( ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2084]) ).
thf(2210,plain,
! [SV134: nat,SV252: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ ( sK35_SY687 @ SV252 @ SV134 ) )
| ( ( power_power_real @ ( sK35_SY687 @ SV252 @ SV134 ) @ SV134 )
!= SV252 ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV252 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2085]) ).
thf(2211,plain,
! [SV139: real,SV256: real,SV310: real,SV304: real] :
( ( ( ord_less_real @ zero_zero_real @ SV304 )
= $false )
| ( ( ~ ( ord_less_eq_real @ SV304 @ SV310 )
| ( ord_less_eq_real @ ( divide_divide_real @ SV256 @ SV310 ) @ ( divide_divide_real @ SV139 @ SV304 ) ) )
= $true )
| ( ( ord_less_eq_real @ SV256 @ SV139 )
= $false )
| ( ( ord_less_eq_real @ zero_zero_real @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2086]) ).
thf(2212,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2088]) ).
thf(2213,plain,
! [SV257: real,SV141: real] :
( ( ( ord_less_real @ zero_zero_real @ SV141 )
= $false )
| ( ( ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2089]) ).
thf(2214,plain,
! [SV257: real,SV141: real] :
( ( ( ord_less_real @ SV141 @ zero_zero_real )
= $false )
| ( ( ~ ( ord_less_real @ zero_zero_real @ SV257 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2090]) ).
thf(2215,plain,
! [SV258: nat,SV305: nat > $o,SV142: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV142 @ ( sK42_SY724 @ SV305 @ SV258 @ SV142 ) )
| ~ ( ord_less_nat @ ( sK42_SY724 @ SV305 @ SV258 @ SV142 ) @ SV258 )
| ~ ( SV305 @ ( suc @ ( sK42_SY724 @ SV305 @ SV258 @ SV142 ) ) )
| ( SV305 @ ( sK42_SY724 @ SV305 @ SV258 @ SV142 ) ) )
= $false )
| ( ( SV305 @ SV142 )
= $true )
| ( ( SV305 @ SV258 )
= $false )
| ( ( ord_less_eq_nat @ SV142 @ SV258 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2091]) ).
thf(2216,plain,
! [SV159: nat,SV16: nat] :
( ( ( ord_less_nat @ SV16 @ SV159 )
= $false )
| ( ( ord_less_nat @ SV16 @ SV159 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2108]) ).
thf(2217,plain,
! [SV160: nat,SV17: nat] :
( ( ( ord_less_nat @ SV17 @ SV160 )
= $true )
| ( ( SV17 = SV160 )
= $true )
| ( ( ord_less_nat @ SV17 @ SV160 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2113]) ).
thf(2218,plain,
! [SV160: nat,SV17: nat] :
( ( ( ord_less_nat @ SV17 @ SV160 )
= $true )
| ( ( SV17 = SV160 )
= $true )
| ( ( SV17 = SV160 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2115]) ).
thf(2219,plain,
! [SV21: nat,SV161: nat] :
( ( ( SV161 = zero_zero_nat )
= $true )
| ( ( SV21
= ( suc @ zero_zero_nat ) )
= $true )
| ( ( SV161 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2118]) ).
thf(2220,plain,
! [SV21: nat,SV161: nat] :
( ( ( SV161 = zero_zero_nat )
= $true )
| ( ( SV21
= ( suc @ zero_zero_nat ) )
= $true )
| ( ( SV21
= ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2120]) ).
thf(2221,plain,
! [SV167: nat,SV33: nat] :
( ( ( ord_less_eq_nat @ SV33 @ SV167 )
= $false )
| ( ( ord_less_eq_nat @ SV33 @ SV167 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2129]) ).
thf(2222,plain,
! [SV168: nat,SV35: nat] :
( ( ( ord_less_eq_nat @ SV35 @ SV168 )
= $true )
| ( ( SV35
= ( suc @ SV168 ) )
= $true )
| ( ( ord_less_eq_nat @ SV35 @ SV168 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2134]) ).
thf(2223,plain,
! [SV168: nat,SV35: nat] :
( ( ( ord_less_eq_nat @ SV35 @ SV168 )
= $true )
| ( ( SV35
= ( suc @ SV168 ) )
= $true )
| ( ( SV35
= ( suc @ SV168 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2136]) ).
thf(2224,plain,
! [SV306: nat,SV169: nat] :
( ( ( nthRoo1352626670d_root @ SV169 @ SV306 )
= $true )
| ( ( nthRoo1352626670d_root @ SV169 @ SV306 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2137]) ).
thf(2225,plain,
! [SV306: nat,SV169: nat] :
( ( ( SV169
= ( suc @ SV306 ) )
= $true )
| ( ( nthRoo1352626670d_root @ SV169 @ SV306 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2138]) ).
thf(2226,plain,
! [SV306: nat,SV169: nat] :
( ( ( nthRoo1352626670d_root @ SV169 @ SV306 )
= $true )
| ( ( SV169
= ( suc @ SV306 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2139]) ).
thf(2227,plain,
! [SV306: nat,SV169: nat] :
( ( ( SV169
= ( suc @ SV306 ) )
= $true )
| ( ( SV169
= ( suc @ SV306 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2140]) ).
thf(2228,plain,
! [SV307: nat,SV172: nat] :
( ( ( ord_less_nat @ SV172 @ SV307 )
= $true )
| ( ( ord_less_nat @ SV172 @ SV307 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2141]) ).
thf(2229,plain,
! [SV307: nat,SV172: nat] :
( ( ( ord_less_eq_nat @ ( suc @ SV172 ) @ SV307 )
= $true )
| ( ( ord_less_nat @ SV172 @ SV307 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2142]) ).
thf(2230,plain,
! [SV307: nat,SV172: nat] :
( ( ( ord_less_nat @ SV172 @ SV307 )
= $true )
| ( ( ord_less_eq_nat @ ( suc @ SV172 ) @ SV307 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2143]) ).
thf(2231,plain,
! [SV307: nat,SV172: nat] :
( ( ( ord_less_eq_nat @ ( suc @ SV172 ) @ SV307 )
= $true )
| ( ( ord_less_eq_nat @ ( suc @ SV172 ) @ SV307 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2144]) ).
thf(2232,plain,
! [SV45: nat] :
( ( ( SV45
= ( suc @ ( sK39_SY405 @ SV45 ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2145]) ).
thf(2233,plain,
! [SV311: nat,SV45: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV45 )
= $true )
| ( ( SV45
= ( suc @ SV311 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2146]) ).
thf(2234,plain,
! [SV311: nat,SV45: nat] :
( ( ( ~ ! [SY405: nat] :
( SV45
!= ( suc @ SY405 ) ) )
= $true )
| ( ( SV45
= ( suc @ SV311 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2147]) ).
thf(2235,plain,
! [SV178: nat > $o,SV47: nat,SV312: nat] :
( ( ( ~ ( ord_less_nat @ SV312 @ ( suc @ SV47 ) ) )
= $true )
| ( ( ~ ( SV178 @ SV312 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) )
| ~ ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2148]) ).
thf(2236,plain,
! [SV178: nat > $o,SV47: nat] :
( ( ( ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) ) )
= $false )
| ( ( SV178 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2149]) ).
thf(2237,plain,
! [SV47: nat,SV178: nat > $o] :
( ( ( SV178 @ zero_zero_nat )
= $true )
| ( ( ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) )
= $true )
| ( ( SV178 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2150]) ).
thf(2238,plain,
! [SV178: nat > $o,SV47: nat,SV317: nat] :
( ( ( ~ ( ord_less_nat @ SV317 @ SV47 )
| ~ ( SV178 @ ( suc @ SV317 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) )
| ~ ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2151]) ).
thf(2239,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) )
= $false )
| ( ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2153]) ).
thf(2240,plain,
! [SV51: real,SV274: real,SV182: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV182 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
| ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2154]) ).
thf(2241,plain,
! [SV182: real,SV274: real,SV51: real] :
( ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
| ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2154]) ).
thf(2242,plain,
! [SV275: nat > $o,SV183: nat,SV52: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV52 @ ( sK40_SY692 @ SV183 @ SV275 @ SV52 ) ) )
= $false )
| ( ( SV275 @ SV183 )
= $true )
| ( ( SV275 @ SV52 )
= $false )
| ( ( ord_less_eq_nat @ SV52 @ SV183 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2155]) ).
thf(2243,plain,
! [SV52: nat,SV183: nat,SV275: nat > $o] :
( ( ( ~ ( SV275 @ ( sK40_SY692 @ SV183 @ SV275 @ SV52 ) )
| ( SV275 @ ( suc @ ( sK40_SY692 @ SV183 @ SV275 @ SV52 ) ) ) )
= $false )
| ( ( SV275 @ SV183 )
= $true )
| ( ( SV275 @ SV52 )
= $false )
| ( ( ord_less_eq_nat @ SV52 @ SV183 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2155]) ).
thf(2244,plain,
! [SV185: real,SV54: real,SV308: real,SV276: real] :
( ( ( ~ ( ord_less_eq_real @ SV276 @ SV308 ) )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV54 @ SV308 ) @ ( divide_divide_real @ SV185 @ SV276 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV276 )
= $false )
| ( ( ord_less_real @ SV54 @ SV185 )
= $false )
| ( ( ord_less_eq_real @ zero_zero_real @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2157]) ).
thf(2245,plain,
! [SV191: nat,SV61: real] :
( ( ( SV61 != zero_zero_real )
= $false )
| ( ( ( power_power_real @ SV61 @ SV191 )
= zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2158]) ).
thf(2246,plain,
! [SV61: real,SV191: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV191 ) )
= $false )
| ( ( ( power_power_real @ SV61 @ SV191 )
= zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2158]) ).
thf(2247,plain,
! [SV191: nat,SV61: real] :
( ( ( ( ( power_power_real @ SV61 @ SV191 )
!= zero_zero_real )
| ~ ~ ( ( SV61 != zero_zero_real )
| ~ ( ord_less_nat @ zero_zero_nat @ SV191 ) ) )
= $false )
| ( ( SV61 = zero_zero_real )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2159]) ).
thf(2248,plain,
! [SV62: nat,SV192: real] :
( ( ( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ ( sK31_SY616 @ SV192 @ SV62 ) )
| ( ( power_power_real @ ( sK31_SY616 @ SV192 @ SV62 ) @ SV62 )
!= SV192 ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV192 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2160]) ).
thf(2249,plain,
! [SV192: real,SV62: nat] :
( ( ( ~ ! [SY726: real] :
( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY726 )
| ( ( power_power_real @ SY726 @ SV62 )
!= SV192 ) )
| ( SY726
= ( sK31_SY616 @ SV192 @ SV62 ) ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV192 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2160]) ).
thf(2250,plain,
! [SV281: nat,SV197: nat,SV68: nat > int] :
( ( ( ~ ( ord_less_int @ ( SV68 @ SV197 ) @ ( SV68 @ SV281 ) )
| ~ ( ord_less_nat @ SV197 @ SV281 ) )
= $false )
| ( ( ord_less_int @ ( SV68 @ SV197 ) @ ( SV68 @ SV281 ) )
= $false )
| ( ( ord_less_int @ ( SV68 @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) @ ( SV68 @ ( suc @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2161]) ).
thf(2251,plain,
! [SV281: nat,SV197: nat,SV68: nat > int] :
( ( ( ~ ( ord_less_int @ ( SV68 @ SV197 ) @ ( SV68 @ SV281 ) )
| ~ ( ord_less_nat @ SV197 @ SV281 ) )
= $false )
| ( ( ord_less_nat @ SV197 @ SV281 )
= $false )
| ( ( ord_less_int @ ( SV68 @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) @ ( SV68 @ ( suc @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2162]) ).
thf(2252,plain,
! [SV198: nat,SV69: nat] :
( ( ( ord_less_nat @ SV69 @ ( sK36_SY623 @ SV198 @ SV69 ) )
= $true )
| ( ( SV198
= ( suc @ SV69 ) )
= $true )
| ( ( ord_less_nat @ SV69 @ SV198 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2163]) ).
thf(2253,plain,
! [SV69: nat,SV198: nat] :
( ( ( SV198
= ( suc @ ( sK36_SY623 @ SV198 @ SV69 ) ) )
= $true )
| ( ( SV198
= ( suc @ SV69 ) )
= $true )
| ( ( ord_less_nat @ SV69 @ SV198 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2164]) ).
thf(2254,plain,
! [SV282: nat,SV201: nat,SV73: nat > nat] :
( ( ( ~ ( ord_less_nat @ ( SV73 @ SV201 ) @ ( SV73 @ SV282 ) )
| ~ ( ord_less_nat @ SV201 @ SV282 ) )
= $false )
| ( ( ord_less_nat @ ( SV73 @ SV201 ) @ ( SV73 @ SV282 ) )
= $false )
| ( ( ord_less_nat @ ( SV73 @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) @ ( SV73 @ ( suc @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2165]) ).
thf(2255,plain,
! [SV282: nat,SV201: nat,SV73: nat > nat] :
( ( ( ~ ( ord_less_nat @ ( SV73 @ SV201 ) @ ( SV73 @ SV282 ) )
| ~ ( ord_less_nat @ SV201 @ SV282 ) )
= $false )
| ( ( ord_less_nat @ SV201 @ SV282 )
= $false )
| ( ( ord_less_nat @ ( SV73 @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) @ ( SV73 @ ( suc @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2166]) ).
thf(2256,plain,
! [SV78: nat,SV284: nat > $o,SV206: nat] :
( ( ( ~ ! [SY700: nat] :
( ~ ( ord_less_nat @ SY700 @ SV206 )
| ~ ( SV284 @ ( suc @ SY700 ) )
| ( SV284 @ SY700 ) ) )
= $true )
| ( ( SV284 @ SV78 )
= $true )
| ( ( SV206
= ( suc @ ( sK32_SY699 @ SV78 @ SV284 @ SV206 ) ) )
= $true )
| ( ( ord_less_nat @ SV78 @ SV206 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2169]) ).
thf(2257,plain,
! [SV78: nat,SV284: nat > $o,SV206: nat] :
( ( ( ! [SY700: nat] :
( ~ ( ord_less_nat @ SY700 @ SV206 )
| ~ ( SV284 @ ( suc @ SY700 ) )
| ( SV284 @ SY700 ) ) )
= $false )
| ( ( SV284 @ SV78 )
= $true )
| ( ( SV284 @ ( sK32_SY699 @ SV78 @ SV284 @ SV206 ) )
= $false )
| ( ( ord_less_nat @ SV78 @ SV206 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2170]) ).
thf(2258,plain,
! [SV285: nat > nat > $o,SV79: nat,SV207: nat] :
( ( ( ! [SY728: nat,SY729: nat] :
( ~ ( ord_less_nat @ ( sK43_SY702 @ SV207 @ SV79 @ SV285 ) @ SY728 )
| ~ ( ord_less_nat @ SY728 @ SY729 )
| ~ ( SV285 @ ( sK43_SY702 @ SV207 @ SV79 @ SV285 ) @ SY728 )
| ~ ( SV285 @ SY728 @ SY729 )
| ( SV285 @ ( sK43_SY702 @ SV207 @ SV79 @ SV285 ) @ SY729 ) ) )
= $false )
| ( ( SV285 @ SV79 @ SV207 )
= $true )
| ( ( SV285 @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) @ ( suc @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) ) )
= $false )
| ( ( ord_less_nat @ SV79 @ SV207 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2171]) ).
thf(2259,plain,
! [SV209: nat,SV287: nat > $o,SV82: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV82 @ ( sK41_SY706 @ SV287 @ SV209 @ SV82 ) ) )
= $false )
| ( ( SV287 @ SV209 )
= $true )
| ( ( SV287 @ SV82 )
= $false )
| ( ( ord_less_eq_nat @ SV82 @ SV209 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2172]) ).
thf(2260,plain,
! [SV82: nat,SV209: nat,SV287: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK41_SY706 @ SV287 @ SV209 @ SV82 ) @ SV209 )
| ~ ( SV287 @ ( sK41_SY706 @ SV287 @ SV209 @ SV82 ) )
| ( SV287 @ ( suc @ ( sK41_SY706 @ SV287 @ SV209 @ SV82 ) ) ) )
= $false )
| ( ( SV287 @ SV209 )
= $true )
| ( ( SV287 @ SV82 )
= $false )
| ( ( ord_less_eq_nat @ SV82 @ SV209 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2172]) ).
thf(2261,plain,
! [SV288: nat,SV212: nat,SV85: nat > nat > $o] :
( ( ( ! [SY488: nat,SY489: nat] :
( ~ ( SV85 @ SY488 @ SY489 )
| ( SV85 @ ( suc @ SY488 ) @ ( suc @ SY489 ) ) ) )
= $false )
| ( ( SV85 @ SV212 @ SV288 )
= $true )
| ( ( SV85 @ zero_zero_nat @ ( suc @ ( sK37_SY487 @ SV288 @ SV212 @ SV85 ) ) )
= $false )
| ( ( SV85 @ ( sK17_SY486 @ SV288 @ SV212 @ SV85 ) @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2173]) ).
thf(2262,plain,
! [SV214: nat > $o,SV87: nat] :
( ( ( ~ ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) ) )
= $false )
| ( ( ord_less_nat @ ( sK27_SY649 @ SV214 @ SV87 ) @ ( suc @ SV87 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2174]) ).
thf(2263,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( ~ ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK27_SY649 @ SV214 @ SV87 ) @ ( suc @ SV87 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2174]) ).
thf(2264,plain,
! [SV214: nat > $o,SV87: nat] :
( ( ( ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) ) )
= $true )
| ( ( SV214 @ ( sK27_SY649 @ SV214 @ SV87 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2175]) ).
thf(2265,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) )
= $true )
| ( ( SV214 @ ( sK27_SY649 @ SV214 @ SV87 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2176]) ).
thf(2266,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK44_SY650 @ SV214 @ SV87 ) @ SV87 )
| ( SV214 @ ( suc @ ( sK44_SY650 @ SV214 @ SV87 ) ) ) )
= $false )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) )
| ~ ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2177]) ).
thf(2267,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) )
= $false )
| ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2179]) ).
thf(2268,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
= $true )
| ( ( ~ ( ( SV228 != zero_zero_real ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2180]) ).
thf(2269,plain,
! [SV229: nat,SV104: nat] :
( ( ( ~ ( ord_less_nat @ SV104 @ ( suc @ SV229 ) ) )
= $false )
| ( ( ord_less_nat @ SV104 @ ( suc @ SV229 ) )
= $false )
| ( ( ord_less_nat @ SV104 @ SV229 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2181]) ).
thf(2270,plain,
! [SV229: nat,SV104: nat] :
( ( ( SV104 != SV229 )
= $false )
| ( ( ord_less_nat @ SV104 @ ( suc @ SV229 ) )
= $false )
| ( ( ord_less_nat @ SV104 @ SV229 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2181]) ).
thf(2271,plain,
! [SV229: nat,SV104: nat] :
( ( ( ~ ( ord_less_nat @ SV104 @ ( suc @ SV229 ) ) )
= $false )
| ( ( SV104 = SV229 )
= $false )
| ( ( ord_less_nat @ SV104 @ SV229 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2182]) ).
thf(2272,plain,
! [SV229: nat,SV104: nat] :
( ( ( SV104 != SV229 )
= $false )
| ( ( SV104 = SV229 )
= $false )
| ( ( ord_less_nat @ SV104 @ SV229 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2182]) ).
thf(2273,plain,
! [SV298: nat,SV230: nat,SV106: nat > real] :
( ( ( ~ ( ord_less_real @ ( SV106 @ SV230 ) @ ( SV106 @ SV298 ) )
| ~ ( ord_less_nat @ SV230 @ SV298 ) )
= $false )
| ( ( ord_less_real @ ( SV106 @ SV230 ) @ ( SV106 @ SV298 ) )
= $false )
| ( ( ord_less_real @ ( SV106 @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) @ ( SV106 @ ( suc @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2183]) ).
thf(2274,plain,
! [SV298: nat,SV230: nat,SV106: nat > real] :
( ( ( ~ ( ord_less_real @ ( SV106 @ SV230 ) @ ( SV106 @ SV298 ) )
| ~ ( ord_less_nat @ SV230 @ SV298 ) )
= $false )
| ( ( ord_less_nat @ SV230 @ SV298 )
= $false )
| ( ( ord_less_real @ ( SV106 @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) @ ( SV106 @ ( suc @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2184]) ).
thf(2275,plain,
! [SV233: nat > $o,SV110: nat,SV314: nat] :
( ( ( ~ ( ord_less_nat @ SV314 @ ( suc @ SV110 ) ) )
= $true )
| ( ( ~ ( SV233 @ SV314 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) )
| ~ ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2185]) ).
thf(2276,plain,
! [SV233: nat > $o,SV110: nat] :
( ( ( ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) ) )
= $false )
| ( ( SV233 @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2186]) ).
thf(2277,plain,
! [SV110: nat,SV233: nat > $o] :
( ( ( SV233 @ SV110 )
= $true )
| ( ( ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) )
= $true )
| ( ( SV233 @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2187]) ).
thf(2278,plain,
! [SV233: nat > $o,SV110: nat,SV318: nat] :
( ( ( ~ ( ord_less_nat @ SV318 @ SV110 )
| ~ ( SV233 @ SV318 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) )
| ~ ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2188]) ).
thf(2279,plain,
! [SV315: nat,SV113: nat > $o] :
( ( ( ~ ~ ( ~ ~ ( SV113 @ ( sK45_SY536 @ SV315 @ SV113 ) )
| ~ ( SV113 @ ( suc @ ( sK45_SY536 @ SV315 @ SV113 ) ) ) ) )
= $false )
| ( ( SV113 @ SV315 )
= $false )
| ( ( SV113 @ zero_zero_nat )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2189]) ).
thf(2280,plain,
! [SV114: nat,SV236: nat] :
( ( ( ord_less_nat @ SV236 @ ( suc @ SV114 ) )
= $true )
| ( ( ord_less_nat @ SV236 @ ( suc @ SV114 ) )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV236 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2190]) ).
thf(2281,plain,
! [SV114: nat,SV236: nat] :
( ( ( SV236 = SV114 )
= $true )
| ( ( ord_less_nat @ SV236 @ ( suc @ SV114 ) )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV236 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2191]) ).
thf(2282,plain,
! [SV114: nat,SV236: nat] :
( ( ( ord_less_nat @ SV236 @ ( suc @ SV114 ) )
= $true )
| ( ( SV236 = SV114 )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV236 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2192]) ).
thf(2283,plain,
! [SV114: nat,SV236: nat] :
( ( ( SV236 = SV114 )
= $true )
| ( ( SV236 = SV114 )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV236 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2193]) ).
thf(2284,plain,
! [SV239: nat > $o,SV117: nat] :
( ( ( ~ ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) ) )
= $false )
| ( ( ord_less_nat @ ( sK30_SY669 @ SV239 @ SV117 ) @ ( suc @ SV117 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2194]) ).
thf(2285,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( ~ ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK30_SY669 @ SV239 @ SV117 ) @ ( suc @ SV117 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2194]) ).
thf(2286,plain,
! [SV239: nat > $o,SV117: nat] :
( ( ( ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) ) )
= $true )
| ( ( SV239 @ ( sK30_SY669 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2195]) ).
thf(2287,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) )
= $true )
| ( ( SV239 @ ( sK30_SY669 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2196]) ).
thf(2288,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK46_SY670 @ SV239 @ SV117 ) @ SV117 )
| ( SV239 @ ( sK46_SY670 @ SV239 @ SV117 ) ) )
= $false )
| ( ( SV239 @ SV117 )
= $false )
| ( ( ~ ( ~ ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) )
| ~ ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2197]) ).
thf(2289,plain,
! [SV242: real,SV120: real,SV309: real,SV302: real] :
( ( ( ~ ( ord_less_real @ SV302 @ SV309 ) )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV120 @ SV309 ) @ ( divide_divide_real @ SV242 @ SV302 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV302 )
= $false )
| ( ( ord_less_eq_real @ SV120 @ SV242 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2198]) ).
thf(2290,plain,
! [SV244: nat,SV122: nat > $o] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ ( sK38_SY677 @ SV122 @ SV244 ) @ SV244 )
| ~ ! [SY727: nat] :
( ~ ( ord_less_eq_nat @ SY727 @ ( sK38_SY677 @ SV122 @ SV244 ) )
| ~ ( SV122 @ SY727 ) ) )
| ~ ( SV122 @ ( suc @ ( sK38_SY677 @ SV122 @ SV244 ) ) ) )
= $false )
| ( ( SV122 @ zero_zero_nat )
= $true )
| ( ( SV122 @ SV244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2199]) ).
thf(2291,plain,
! [SV123: nat,SV245: nat] :
( ( ( ~ ~ ( ( SV245
!= ( suc @ ( sK47_SY679 @ SV123 @ SV245 ) ) )
| ~ ( ord_less_nat @ SV123 @ ( sK47_SY679 @ SV123 @ SV245 ) ) ) )
= $false )
| ( ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2200]) ).
thf(2292,plain,
! [SV123: nat,SV316: nat,SV245: nat] :
( ( ( SV245
!= ( suc @ SV316 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV123 @ SV316 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
| ~ ~ ! [SY679: nat] :
~ ~ ( ( SV245
!= ( suc @ SY679 ) )
| ~ ( ord_less_nat @ SV123 @ SY679 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2201]) ).
thf(2293,plain,
! [SV127: nat,SV248: nat,SV303: nat > nat > $o] :
( ( ( ! [SY730: nat,SY731: nat] :
( ~ ( SV303 @ ( sK48_SY719 @ SV248 @ SV127 @ SV303 ) @ SY730 )
| ~ ( SV303 @ SY730 @ SY731 )
| ( SV303 @ ( sK48_SY719 @ SV248 @ SV127 @ SV303 ) @ SY731 ) ) )
= $false )
| ( ( ~ ! [SY722: nat] : ( SV303 @ SY722 @ ( suc @ SY722 ) )
| ( SV303 @ SV127 @ SV248 ) )
= $true )
| ( ( SV303 @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV248 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2202]) ).
thf(2294,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2203]) ).
thf(2295,plain,
! [SV128: real,SV249: real] :
( ( ( ord_less_real @ zero_zero_real @ SV249 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2204]) ).
thf(2296,plain,
! [SV128: real,SV249: real] :
( ( ( ord_less_real @ SV249 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV128 @ zero_zero_real )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2205]) ).
thf(2297,plain,
! [SV251: nat,SV133: nat] :
( ( ( ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) )
= $false )
| ( ( SV133 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2206]) ).
thf(2298,plain,
! [SV251: nat,SV133: nat] :
( ( ( SV133 = zero_zero_nat )
= $true )
| ( ( ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) )
= $true )
| ( ( SV133 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2208]) ).
thf(2299,plain,
! [SV251: nat,SV319: nat,SV133: nat] :
( ( ( ( SV133
!= ( suc @ SV319 ) )
| ~ ( ord_less_nat @ SV319 @ SV251 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
| ~ ( ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2209]) ).
thf(2300,plain,
! [SV134: nat,SV252: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ ( sK35_SY687 @ SV252 @ SV134 ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV252 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2210]) ).
thf(2301,plain,
! [SV134: nat,SV252: real] :
( ( ( ( power_power_real @ ( sK35_SY687 @ SV252 @ SV134 ) @ SV134 )
!= SV252 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV252 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2210]) ).
thf(2302,plain,
! [SV139: real,SV256: real,SV310: real,SV304: real] :
( ( ( ~ ( ord_less_eq_real @ SV304 @ SV310 ) )
= $true )
| ( ( ord_less_eq_real @ ( divide_divide_real @ SV256 @ SV310 ) @ ( divide_divide_real @ SV139 @ SV304 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV304 )
= $false )
| ( ( ord_less_eq_real @ SV256 @ SV139 )
= $false )
| ( ( ord_less_eq_real @ zero_zero_real @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2211]) ).
thf(2303,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2212]) ).
thf(2304,plain,
! [SV141: real,SV257: real] :
( ( ( ord_less_real @ SV257 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2213]) ).
thf(2305,plain,
! [SV141: real,SV257: real] :
( ( ( ord_less_real @ zero_zero_real @ SV257 )
= $false )
| ( ( ord_less_real @ SV141 @ zero_zero_real )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2214]) ).
thf(2306,plain,
! [SV258: nat,SV305: nat > $o,SV142: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV142 @ ( sK42_SY724 @ SV305 @ SV258 @ SV142 ) ) )
= $false )
| ( ( SV305 @ SV142 )
= $true )
| ( ( SV305 @ SV258 )
= $false )
| ( ( ord_less_eq_nat @ SV142 @ SV258 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2215]) ).
thf(2307,plain,
! [SV142: nat,SV258: nat,SV305: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK42_SY724 @ SV305 @ SV258 @ SV142 ) @ SV258 )
| ~ ( SV305 @ ( suc @ ( sK42_SY724 @ SV305 @ SV258 @ SV142 ) ) )
| ( SV305 @ ( sK42_SY724 @ SV305 @ SV258 @ SV142 ) ) )
= $false )
| ( ( SV305 @ SV142 )
= $true )
| ( ( SV305 @ SV258 )
= $false )
| ( ( ord_less_eq_nat @ SV142 @ SV258 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2215]) ).
thf(2308,plain,
! [SV311: nat,SV45: nat] :
( ( ( ! [SY405: nat] :
( SV45
!= ( suc @ SY405 ) ) )
= $false )
| ( ( SV45
= ( suc @ SV311 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2234]) ).
thf(2309,plain,
! [SV178: nat > $o,SV47: nat,SV312: nat] :
( ( ( ord_less_nat @ SV312 @ ( suc @ SV47 ) )
= $false )
| ( ( ~ ( SV178 @ SV312 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) )
| ~ ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2235]) ).
thf(2310,plain,
! [SV47: nat,SV178: nat > $o] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ ( sK49_SY601 @ SV178 @ SV47 ) @ ( suc @ SV47 ) )
| ~ ( SV178 @ ( sK49_SY601 @ SV178 @ SV47 ) ) ) )
= $false )
| ( ( SV178 @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2236]) ).
thf(2311,plain,
! [SV178: nat > $o,SV47: nat] :
( ( ( ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) )
= $false )
| ( ( SV178 @ zero_zero_nat )
= $true )
| ( ( SV178 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2237]) ).
thf(2312,plain,
! [SV178: nat > $o,SV47: nat,SV317: nat] :
( ( ( ~ ( ord_less_nat @ SV317 @ SV47 ) )
= $true )
| ( ( ~ ( SV178 @ ( suc @ SV317 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) )
| ~ ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2238]) ).
thf(2313,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) ) )
= $false )
| ( ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2239]) ).
thf(2314,plain,
! [SV51: real,SV274: real,SV182: real] :
( ( ( ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) )
= $false )
| ( ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2239]) ).
thf(2315,plain,
! [SV51: real,SV274: real,SV182: real] :
( ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
| ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2240]) ).
thf(2316,plain,
! [SV51: real,SV274: real,SV182: real] :
( ( ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) )
= $false )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
| ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2241]) ).
thf(2317,plain,
! [SV275: nat > $o,SV183: nat,SV52: nat] :
( ( ( ord_less_eq_nat @ SV52 @ ( sK40_SY692 @ SV183 @ SV275 @ SV52 ) )
= $true )
| ( ( SV275 @ SV183 )
= $true )
| ( ( SV275 @ SV52 )
= $false )
| ( ( ord_less_eq_nat @ SV52 @ SV183 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2242]) ).
thf(2318,plain,
! [SV52: nat,SV183: nat,SV275: nat > $o] :
( ( ( ~ ( SV275 @ ( sK40_SY692 @ SV183 @ SV275 @ SV52 ) ) )
= $false )
| ( ( SV275 @ SV183 )
= $true )
| ( ( SV275 @ SV52 )
= $false )
| ( ( ord_less_eq_nat @ SV52 @ SV183 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2243]) ).
thf(2319,plain,
! [SV52: nat,SV183: nat,SV275: nat > $o] :
( ( ( SV275 @ ( suc @ ( sK40_SY692 @ SV183 @ SV275 @ SV52 ) ) )
= $false )
| ( ( SV275 @ SV183 )
= $true )
| ( ( SV275 @ SV52 )
= $false )
| ( ( ord_less_eq_nat @ SV52 @ SV183 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2243]) ).
thf(2320,plain,
! [SV185: real,SV54: real,SV308: real,SV276: real] :
( ( ( ord_less_eq_real @ SV276 @ SV308 )
= $false )
| ( ( ord_less_real @ ( divide_divide_real @ SV54 @ SV308 ) @ ( divide_divide_real @ SV185 @ SV276 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV276 )
= $false )
| ( ( ord_less_real @ SV54 @ SV185 )
= $false )
| ( ( ord_less_eq_real @ zero_zero_real @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2244]) ).
thf(2321,plain,
! [SV191: nat,SV61: real] :
( ( ( SV61 = zero_zero_real )
= $true )
| ( ( ( power_power_real @ SV61 @ SV191 )
= zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2245]) ).
thf(2322,plain,
! [SV61: real,SV191: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV191 )
= $true )
| ( ( ( power_power_real @ SV61 @ SV191 )
= zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2246]) ).
thf(2323,plain,
! [SV191: nat,SV61: real] :
( ( ( ( power_power_real @ SV61 @ SV191 )
!= zero_zero_real )
= $false )
| ( ( SV61 = zero_zero_real )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV191 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2247]) ).
thf(2324,plain,
! [SV191: nat,SV61: real] :
( ( ( ~ ~ ( ( SV61 != zero_zero_real )
| ~ ( ord_less_nat @ zero_zero_nat @ SV191 ) ) )
= $false )
| ( ( SV61 = zero_zero_real )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV191 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2247]) ).
thf(2325,plain,
! [SV62: nat,SV192: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ ( sK31_SY616 @ SV192 @ SV62 ) )
| ( ( power_power_real @ ( sK31_SY616 @ SV192 @ SV62 ) @ SV62 )
!= SV192 ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV192 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2248]) ).
thf(2326,plain,
! [SV192: real,SV62: nat] :
( ( ( ! [SY726: real] :
( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SY726 )
| ( ( power_power_real @ SY726 @ SV62 )
!= SV192 ) )
| ( SY726
= ( sK31_SY616 @ SV192 @ SV62 ) ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV192 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2249]) ).
thf(2327,plain,
! [SV281: nat,SV197: nat,SV68: nat > int] :
( ( ( ~ ( ord_less_int @ ( SV68 @ SV197 ) @ ( SV68 @ SV281 ) ) )
= $false )
| ( ( ord_less_int @ ( SV68 @ SV197 ) @ ( SV68 @ SV281 ) )
= $false )
| ( ( ord_less_int @ ( SV68 @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) @ ( SV68 @ ( suc @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2250]) ).
thf(2328,plain,
! [SV68: nat > int,SV281: nat,SV197: nat] :
( ( ( ~ ( ord_less_nat @ SV197 @ SV281 ) )
= $false )
| ( ( ord_less_int @ ( SV68 @ SV197 ) @ ( SV68 @ SV281 ) )
= $false )
| ( ( ord_less_int @ ( SV68 @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) @ ( SV68 @ ( suc @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2250]) ).
thf(2329,plain,
! [SV281: nat,SV197: nat,SV68: nat > int] :
( ( ( ~ ( ord_less_int @ ( SV68 @ SV197 ) @ ( SV68 @ SV281 ) ) )
= $false )
| ( ( ord_less_nat @ SV197 @ SV281 )
= $false )
| ( ( ord_less_int @ ( SV68 @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) @ ( SV68 @ ( suc @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2251]) ).
thf(2330,plain,
! [SV68: nat > int,SV281: nat,SV197: nat] :
( ( ( ~ ( ord_less_nat @ SV197 @ SV281 ) )
= $false )
| ( ( ord_less_nat @ SV197 @ SV281 )
= $false )
| ( ( ord_less_int @ ( SV68 @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) @ ( SV68 @ ( suc @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2251]) ).
thf(2331,plain,
! [SV282: nat,SV201: nat,SV73: nat > nat] :
( ( ( ~ ( ord_less_nat @ ( SV73 @ SV201 ) @ ( SV73 @ SV282 ) ) )
= $false )
| ( ( ord_less_nat @ ( SV73 @ SV201 ) @ ( SV73 @ SV282 ) )
= $false )
| ( ( ord_less_nat @ ( SV73 @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) @ ( SV73 @ ( suc @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2254]) ).
thf(2332,plain,
! [SV73: nat > nat,SV282: nat,SV201: nat] :
( ( ( ~ ( ord_less_nat @ SV201 @ SV282 ) )
= $false )
| ( ( ord_less_nat @ ( SV73 @ SV201 ) @ ( SV73 @ SV282 ) )
= $false )
| ( ( ord_less_nat @ ( SV73 @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) @ ( SV73 @ ( suc @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2254]) ).
thf(2333,plain,
! [SV282: nat,SV201: nat,SV73: nat > nat] :
( ( ( ~ ( ord_less_nat @ ( SV73 @ SV201 ) @ ( SV73 @ SV282 ) ) )
= $false )
| ( ( ord_less_nat @ SV201 @ SV282 )
= $false )
| ( ( ord_less_nat @ ( SV73 @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) @ ( SV73 @ ( suc @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2255]) ).
thf(2334,plain,
! [SV73: nat > nat,SV282: nat,SV201: nat] :
( ( ( ~ ( ord_less_nat @ SV201 @ SV282 ) )
= $false )
| ( ( ord_less_nat @ SV201 @ SV282 )
= $false )
| ( ( ord_less_nat @ ( SV73 @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) @ ( SV73 @ ( suc @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2255]) ).
thf(2335,plain,
! [SV78: nat,SV284: nat > $o,SV206: nat] :
( ( ( ! [SY700: nat] :
( ~ ( ord_less_nat @ SY700 @ SV206 )
| ~ ( SV284 @ ( suc @ SY700 ) )
| ( SV284 @ SY700 ) ) )
= $false )
| ( ( SV284 @ SV78 )
= $true )
| ( ( SV206
= ( suc @ ( sK32_SY699 @ SV78 @ SV284 @ SV206 ) ) )
= $true )
| ( ( ord_less_nat @ SV78 @ SV206 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2256]) ).
thf(2336,plain,
! [SV206: nat,SV284: nat > $o,SV78: nat] :
( ( ( ~ ( ord_less_nat @ ( sK50_SY700 @ SV78 @ SV284 @ SV206 ) @ SV206 )
| ~ ( SV284 @ ( suc @ ( sK50_SY700 @ SV78 @ SV284 @ SV206 ) ) )
| ( SV284 @ ( sK50_SY700 @ SV78 @ SV284 @ SV206 ) ) )
= $false )
| ( ( SV284 @ SV78 )
= $true )
| ( ( SV284 @ ( sK32_SY699 @ SV78 @ SV284 @ SV206 ) )
= $false )
| ( ( ord_less_nat @ SV78 @ SV206 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2257]) ).
thf(2337,plain,
! [SV285: nat > nat > $o,SV79: nat,SV207: nat] :
( ( ( ! [SY732: nat] :
( ~ ( ord_less_nat @ ( sK43_SY702 @ SV207 @ SV79 @ SV285 ) @ ( sK51_SY728 @ SV285 @ SV79 @ SV207 ) )
| ~ ( ord_less_nat @ ( sK51_SY728 @ SV285 @ SV79 @ SV207 ) @ SY732 )
| ~ ( SV285 @ ( sK43_SY702 @ SV207 @ SV79 @ SV285 ) @ ( sK51_SY728 @ SV285 @ SV79 @ SV207 ) )
| ~ ( SV285 @ ( sK51_SY728 @ SV285 @ SV79 @ SV207 ) @ SY732 )
| ( SV285 @ ( sK43_SY702 @ SV207 @ SV79 @ SV285 ) @ SY732 ) ) )
= $false )
| ( ( SV285 @ SV79 @ SV207 )
= $true )
| ( ( SV285 @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) @ ( suc @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) ) )
= $false )
| ( ( ord_less_nat @ SV79 @ SV207 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2258]) ).
thf(2338,plain,
! [SV209: nat,SV287: nat > $o,SV82: nat] :
( ( ( ord_less_eq_nat @ SV82 @ ( sK41_SY706 @ SV287 @ SV209 @ SV82 ) )
= $true )
| ( ( SV287 @ SV209 )
= $true )
| ( ( SV287 @ SV82 )
= $false )
| ( ( ord_less_eq_nat @ SV82 @ SV209 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2259]) ).
thf(2339,plain,
! [SV82: nat,SV209: nat,SV287: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK41_SY706 @ SV287 @ SV209 @ SV82 ) @ SV209 ) )
= $false )
| ( ( SV287 @ SV209 )
= $true )
| ( ( SV287 @ SV82 )
= $false )
| ( ( ord_less_eq_nat @ SV82 @ SV209 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2260]) ).
thf(2340,plain,
! [SV82: nat,SV209: nat,SV287: nat > $o] :
( ( ( ~ ( SV287 @ ( sK41_SY706 @ SV287 @ SV209 @ SV82 ) )
| ( SV287 @ ( suc @ ( sK41_SY706 @ SV287 @ SV209 @ SV82 ) ) ) )
= $false )
| ( ( SV287 @ SV209 )
= $true )
| ( ( SV287 @ SV82 )
= $false )
| ( ( ord_less_eq_nat @ SV82 @ SV209 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2260]) ).
thf(2341,plain,
! [SV212: nat,SV288: nat,SV85: nat > nat > $o] :
( ( ( ! [SY733: nat] :
( ~ ( SV85 @ ( sK52_SY488 @ SV288 @ SV212 @ SV85 ) @ SY733 )
| ( SV85 @ ( suc @ ( sK52_SY488 @ SV288 @ SV212 @ SV85 ) ) @ ( suc @ SY733 ) ) ) )
= $false )
| ( ( SV85 @ SV212 @ SV288 )
= $true )
| ( ( SV85 @ zero_zero_nat @ ( suc @ ( sK37_SY487 @ SV288 @ SV212 @ SV85 ) ) )
= $false )
| ( ( SV85 @ ( sK17_SY486 @ SV288 @ SV212 @ SV85 ) @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2261]) ).
thf(2342,plain,
! [SV214: nat > $o,SV87: nat] :
( ( ( ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) ) )
= $true )
| ( ( ord_less_nat @ ( sK27_SY649 @ SV214 @ SV87 ) @ ( suc @ SV87 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2262]) ).
thf(2343,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK27_SY649 @ SV214 @ SV87 ) @ ( suc @ SV87 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2263]) ).
thf(2344,plain,
! [SV214: nat > $o,SV87: nat,SV320: nat] :
( ( ( ~ ( ord_less_nat @ SV320 @ ( suc @ SV87 ) )
| ( SV214 @ SV320 ) )
= $true )
| ( ( SV214 @ ( sK27_SY649 @ SV214 @ SV87 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2264]) ).
thf(2345,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) )
= $false )
| ( ( SV214 @ ( sK27_SY649 @ SV214 @ SV87 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2265]) ).
thf(2346,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK44_SY650 @ SV214 @ SV87 ) @ SV87 ) )
= $false )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) )
| ~ ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2266]) ).
thf(2347,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( SV214 @ ( suc @ ( sK44_SY650 @ SV214 @ SV87 ) ) )
= $false )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) )
| ~ ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2266]) ).
thf(2348,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) ) )
= $false )
| ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2267]) ).
thf(2349,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ( SV228 != zero_zero_real ) ) )
= $false )
| ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2267]) ).
thf(2350,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
= $true )
| ( ( ~ ( ( SV228 != zero_zero_real ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2268]) ).
thf(2351,plain,
! [SV229: nat,SV104: nat] :
( ( ( ord_less_nat @ SV104 @ ( suc @ SV229 ) )
= $true )
| ( ( ord_less_nat @ SV104 @ ( suc @ SV229 ) )
= $false )
| ( ( ord_less_nat @ SV104 @ SV229 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2269]) ).
thf(2352,plain,
! [SV229: nat,SV104: nat] :
( ( ( SV104 = SV229 )
= $true )
| ( ( ord_less_nat @ SV104 @ ( suc @ SV229 ) )
= $false )
| ( ( ord_less_nat @ SV104 @ SV229 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2270]) ).
thf(2353,plain,
! [SV229: nat,SV104: nat] :
( ( ( ord_less_nat @ SV104 @ ( suc @ SV229 ) )
= $true )
| ( ( SV104 = SV229 )
= $false )
| ( ( ord_less_nat @ SV104 @ SV229 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2271]) ).
thf(2354,plain,
! [SV229: nat,SV104: nat] :
( ( ( SV104 = SV229 )
= $true )
| ( ( SV104 = SV229 )
= $false )
| ( ( ord_less_nat @ SV104 @ SV229 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2272]) ).
thf(2355,plain,
! [SV298: nat,SV230: nat,SV106: nat > real] :
( ( ( ~ ( ord_less_real @ ( SV106 @ SV230 ) @ ( SV106 @ SV298 ) ) )
= $false )
| ( ( ord_less_real @ ( SV106 @ SV230 ) @ ( SV106 @ SV298 ) )
= $false )
| ( ( ord_less_real @ ( SV106 @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) @ ( SV106 @ ( suc @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2273]) ).
thf(2356,plain,
! [SV106: nat > real,SV298: nat,SV230: nat] :
( ( ( ~ ( ord_less_nat @ SV230 @ SV298 ) )
= $false )
| ( ( ord_less_real @ ( SV106 @ SV230 ) @ ( SV106 @ SV298 ) )
= $false )
| ( ( ord_less_real @ ( SV106 @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) @ ( SV106 @ ( suc @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2273]) ).
thf(2357,plain,
! [SV298: nat,SV230: nat,SV106: nat > real] :
( ( ( ~ ( ord_less_real @ ( SV106 @ SV230 ) @ ( SV106 @ SV298 ) ) )
= $false )
| ( ( ord_less_nat @ SV230 @ SV298 )
= $false )
| ( ( ord_less_real @ ( SV106 @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) @ ( SV106 @ ( suc @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2274]) ).
thf(2358,plain,
! [SV106: nat > real,SV298: nat,SV230: nat] :
( ( ( ~ ( ord_less_nat @ SV230 @ SV298 ) )
= $false )
| ( ( ord_less_nat @ SV230 @ SV298 )
= $false )
| ( ( ord_less_real @ ( SV106 @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) @ ( SV106 @ ( suc @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2274]) ).
thf(2359,plain,
! [SV233: nat > $o,SV110: nat,SV314: nat] :
( ( ( ord_less_nat @ SV314 @ ( suc @ SV110 ) )
= $false )
| ( ( ~ ( SV233 @ SV314 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) )
| ~ ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2275]) ).
thf(2360,plain,
! [SV110: nat,SV233: nat > $o] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ ( sK53_SY665 @ SV233 @ SV110 ) @ ( suc @ SV110 ) )
| ~ ( SV233 @ ( sK53_SY665 @ SV233 @ SV110 ) ) ) )
= $false )
| ( ( SV233 @ SV110 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2276]) ).
thf(2361,plain,
! [SV233: nat > $o,SV110: nat] :
( ( ( ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) )
= $false )
| ( ( SV233 @ SV110 )
= $true )
| ( ( SV233 @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2277]) ).
thf(2362,plain,
! [SV233: nat > $o,SV110: nat,SV318: nat] :
( ( ( ~ ( ord_less_nat @ SV318 @ SV110 ) )
= $true )
| ( ( ~ ( SV233 @ SV318 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) )
| ~ ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2278]) ).
thf(2363,plain,
! [SV315: nat,SV113: nat > $o] :
( ( ( ~ ( ~ ~ ( SV113 @ ( sK45_SY536 @ SV315 @ SV113 ) )
| ~ ( SV113 @ ( suc @ ( sK45_SY536 @ SV315 @ SV113 ) ) ) ) )
= $true )
| ( ( SV113 @ SV315 )
= $false )
| ( ( SV113 @ zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2279]) ).
thf(2364,plain,
! [SV239: nat > $o,SV117: nat] :
( ( ( ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) ) )
= $true )
| ( ( ord_less_nat @ ( sK30_SY669 @ SV239 @ SV117 ) @ ( suc @ SV117 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2284]) ).
thf(2365,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK30_SY669 @ SV239 @ SV117 ) @ ( suc @ SV117 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2285]) ).
thf(2366,plain,
! [SV239: nat > $o,SV117: nat,SV321: nat] :
( ( ( ~ ( ord_less_nat @ SV321 @ ( suc @ SV117 ) )
| ( SV239 @ SV321 ) )
= $true )
| ( ( SV239 @ ( sK30_SY669 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2286]) ).
thf(2367,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) )
= $false )
| ( ( SV239 @ ( sK30_SY669 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2287]) ).
thf(2368,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK46_SY670 @ SV239 @ SV117 ) @ SV117 ) )
= $false )
| ( ( SV239 @ SV117 )
= $false )
| ( ( ~ ( ~ ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) )
| ~ ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2288]) ).
thf(2369,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( SV239 @ ( sK46_SY670 @ SV239 @ SV117 ) )
= $false )
| ( ( SV239 @ SV117 )
= $false )
| ( ( ~ ( ~ ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) )
| ~ ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2288]) ).
thf(2370,plain,
! [SV242: real,SV120: real,SV309: real,SV302: real] :
( ( ( ord_less_real @ SV302 @ SV309 )
= $false )
| ( ( ord_less_real @ ( divide_divide_real @ SV120 @ SV309 ) @ ( divide_divide_real @ SV242 @ SV302 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV302 )
= $false )
| ( ( ord_less_eq_real @ SV120 @ SV242 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2289]) ).
thf(2371,plain,
! [SV244: nat,SV122: nat > $o] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ ( sK38_SY677 @ SV122 @ SV244 ) @ SV244 )
| ~ ! [SY727: nat] :
( ~ ( ord_less_eq_nat @ SY727 @ ( sK38_SY677 @ SV122 @ SV244 ) )
| ~ ( SV122 @ SY727 ) ) ) )
= $false )
| ( ( SV122 @ zero_zero_nat )
= $true )
| ( ( SV122 @ SV244 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2290]) ).
thf(2372,plain,
! [SV244: nat,SV122: nat > $o] :
( ( ( ~ ( SV122 @ ( suc @ ( sK38_SY677 @ SV122 @ SV244 ) ) ) )
= $false )
| ( ( SV122 @ zero_zero_nat )
= $true )
| ( ( SV122 @ SV244 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2290]) ).
thf(2373,plain,
! [SV123: nat,SV245: nat] :
( ( ( ~ ( ( SV245
!= ( suc @ ( sK47_SY679 @ SV123 @ SV245 ) ) )
| ~ ( ord_less_nat @ SV123 @ ( sK47_SY679 @ SV123 @ SV245 ) ) ) )
= $true )
| ( ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2291]) ).
thf(2374,plain,
! [SV123: nat,SV316: nat,SV245: nat] :
( ( ( SV245
= ( suc @ SV316 ) )
= $false )
| ( ( ~ ( ord_less_nat @ SV123 @ SV316 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
| ~ ~ ! [SY679: nat] :
~ ~ ( ( SV245
!= ( suc @ SY679 ) )
| ~ ( ord_less_nat @ SV123 @ SY679 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2292]) ).
thf(2375,plain,
! [SV127: nat,SV248: nat,SV303: nat > nat > $o] :
( ( ( ! [SY734: nat] :
( ~ ( SV303 @ ( sK48_SY719 @ SV248 @ SV127 @ SV303 ) @ ( sK54_SY730 @ SV127 @ SV248 @ SV303 ) )
| ~ ( SV303 @ ( sK54_SY730 @ SV127 @ SV248 @ SV303 ) @ SY734 )
| ( SV303 @ ( sK48_SY719 @ SV248 @ SV127 @ SV303 ) @ SY734 ) ) )
= $false )
| ( ( ~ ! [SY722: nat] : ( SV303 @ SY722 @ ( suc @ SY722 ) )
| ( SV303 @ SV127 @ SV248 ) )
= $true )
| ( ( SV303 @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV248 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2293]) ).
thf(2376,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV128 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2294]) ).
thf(2377,plain,
! [SV128: real,SV249: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2294]) ).
thf(2378,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2295]) ).
thf(2379,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) ) )
= $false )
| ( ( ord_less_real @ SV128 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV249 @ zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2296]) ).
thf(2380,plain,
! [SV251: nat,SV133: nat] :
( ( ( ~ ~ ( ( SV133
!= ( suc @ ( sK55_SY686 @ SV251 @ SV133 ) ) )
| ~ ( ord_less_nat @ ( sK55_SY686 @ SV251 @ SV133 ) @ SV251 ) ) )
= $false )
| ( ( SV133 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2297]) ).
thf(2381,plain,
! [SV251: nat,SV133: nat] :
( ( ( ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) )
= $false )
| ( ( SV133 = zero_zero_nat )
= $true )
| ( ( SV133 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2298]) ).
thf(2382,plain,
! [SV251: nat,SV319: nat,SV133: nat] :
( ( ( SV133
!= ( suc @ SV319 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV319 @ SV251 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
| ~ ( ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2299]) ).
thf(2383,plain,
! [SV134: nat,SV252: real] :
( ( ( ord_less_real @ zero_zero_real @ ( sK35_SY687 @ SV252 @ SV134 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV252 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2300]) ).
thf(2384,plain,
! [SV134: nat,SV252: real] :
( ( ( ( power_power_real @ ( sK35_SY687 @ SV252 @ SV134 ) @ SV134 )
= SV252 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV252 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2301]) ).
thf(2385,plain,
! [SV139: real,SV256: real,SV310: real,SV304: real] :
( ( ( ord_less_eq_real @ SV304 @ SV310 )
= $false )
| ( ( ord_less_eq_real @ ( divide_divide_real @ SV256 @ SV310 ) @ ( divide_divide_real @ SV139 @ SV304 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV304 )
= $false )
| ( ( ord_less_eq_real @ SV256 @ SV139 )
= $false )
| ( ( ord_less_eq_real @ zero_zero_real @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2302]) ).
thf(2386,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV141 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2303]) ).
thf(2387,plain,
! [SV141: real,SV257: real] :
( ( ( ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2303]) ).
thf(2388,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2304]) ).
thf(2389,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
| ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) ) )
= $false )
| ( ( ord_less_real @ SV141 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV257 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2305]) ).
thf(2390,plain,
! [SV258: nat,SV305: nat > $o,SV142: nat] :
( ( ( ord_less_eq_nat @ SV142 @ ( sK42_SY724 @ SV305 @ SV258 @ SV142 ) )
= $true )
| ( ( SV305 @ SV142 )
= $true )
| ( ( SV305 @ SV258 )
= $false )
| ( ( ord_less_eq_nat @ SV142 @ SV258 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2306]) ).
thf(2391,plain,
! [SV142: nat,SV258: nat,SV305: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK42_SY724 @ SV305 @ SV258 @ SV142 ) @ SV258 ) )
= $false )
| ( ( SV305 @ SV142 )
= $true )
| ( ( SV305 @ SV258 )
= $false )
| ( ( ord_less_eq_nat @ SV142 @ SV258 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2307]) ).
thf(2392,plain,
! [SV142: nat,SV258: nat,SV305: nat > $o] :
( ( ( ~ ( SV305 @ ( suc @ ( sK42_SY724 @ SV305 @ SV258 @ SV142 ) ) )
| ( SV305 @ ( sK42_SY724 @ SV305 @ SV258 @ SV142 ) ) )
= $false )
| ( ( SV305 @ SV142 )
= $true )
| ( ( SV305 @ SV258 )
= $false )
| ( ( ord_less_eq_nat @ SV142 @ SV258 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2307]) ).
thf(2393,plain,
! [SV311: nat,SV45: nat] :
( ( ( SV45
!= ( suc @ ( sK56_SY405 @ SV311 @ SV45 ) ) )
= $false )
| ( ( SV45
= ( suc @ SV311 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2308]) ).
thf(2394,plain,
! [SV47: nat,SV312: nat,SV178: nat > $o] :
( ( ( SV178 @ SV312 )
= $false )
| ( ( ord_less_nat @ SV312 @ ( suc @ SV47 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) )
| ~ ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2309]) ).
thf(2395,plain,
! [SV47: nat,SV178: nat > $o] :
( ( ( ~ ( ~ ( ord_less_nat @ ( sK49_SY601 @ SV178 @ SV47 ) @ ( suc @ SV47 ) )
| ~ ( SV178 @ ( sK49_SY601 @ SV178 @ SV47 ) ) ) )
= $true )
| ( ( SV178 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2310]) ).
thf(2396,plain,
! [SV47: nat,SV178: nat > $o] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ ( sK57_SY602 @ SV178 @ SV47 ) @ SV47 )
| ~ ( SV178 @ ( suc @ ( sK57_SY602 @ SV178 @ SV47 ) ) ) ) )
= $false )
| ( ( SV178 @ zero_zero_nat )
= $true )
| ( ( SV178 @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2311]) ).
thf(2397,plain,
! [SV178: nat > $o,SV47: nat,SV317: nat] :
( ( ( ord_less_nat @ SV317 @ SV47 )
= $false )
| ( ( ~ ( SV178 @ ( suc @ SV317 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) )
| ~ ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2312]) ).
thf(2398,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
= $true )
| ( ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2313]) ).
thf(2399,plain,
! [SV51: real,SV274: real,SV182: real] :
( ( ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) )
= $true )
| ( ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2314]) ).
thf(2400,plain,
! [SV51: real,SV274: real,SV182: real] :
( ( ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
| ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2315]) ).
thf(2401,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ord_less_real @ SV182 @ zero_zero_real ) )
= $false )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
| ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2316]) ).
thf(2402,plain,
! [SV182: real,SV51: real,SV274: real] :
( ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
| ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2316]) ).
thf(2403,plain,
! [SV52: nat,SV183: nat,SV275: nat > $o] :
( ( ( SV275 @ ( sK40_SY692 @ SV183 @ SV275 @ SV52 ) )
= $true )
| ( ( SV275 @ SV183 )
= $true )
| ( ( SV275 @ SV52 )
= $false )
| ( ( ord_less_eq_nat @ SV52 @ SV183 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2318]) ).
thf(2404,plain,
! [SV191: nat,SV61: real] :
( ( ( ( power_power_real @ SV61 @ SV191 )
= zero_zero_real )
= $true )
| ( ( SV61 = zero_zero_real )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2323]) ).
thf(2405,plain,
! [SV191: nat,SV61: real] :
( ( ( ~ ( ( SV61 != zero_zero_real )
| ~ ( ord_less_nat @ zero_zero_nat @ SV191 ) ) )
= $true )
| ( ( SV61 = zero_zero_real )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2324]) ).
thf(2406,plain,
! [SV62: nat,SV192: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ ( sK31_SY616 @ SV192 @ SV62 ) )
| ( ( power_power_real @ ( sK31_SY616 @ SV192 @ SV62 ) @ SV62 )
!= SV192 ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV192 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2325]) ).
thf(2407,plain,
! [SV192: real,SV62: nat,SV322: real] :
( ( ( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SV322 )
| ( ( power_power_real @ SV322 @ SV62 )
!= SV192 ) )
| ( SV322
= ( sK31_SY616 @ SV192 @ SV62 ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV192 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2326]) ).
thf(2408,plain,
! [SV281: nat,SV197: nat,SV68: nat > int] :
( ( ( ord_less_int @ ( SV68 @ SV197 ) @ ( SV68 @ SV281 ) )
= $true )
| ( ( ord_less_int @ ( SV68 @ SV197 ) @ ( SV68 @ SV281 ) )
= $false )
| ( ( ord_less_int @ ( SV68 @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) @ ( SV68 @ ( suc @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2327]) ).
thf(2409,plain,
! [SV68: nat > int,SV281: nat,SV197: nat] :
( ( ( ord_less_nat @ SV197 @ SV281 )
= $true )
| ( ( ord_less_int @ ( SV68 @ SV197 ) @ ( SV68 @ SV281 ) )
= $false )
| ( ( ord_less_int @ ( SV68 @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) @ ( SV68 @ ( suc @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2328]) ).
thf(2410,plain,
! [SV281: nat,SV197: nat,SV68: nat > int] :
( ( ( ord_less_int @ ( SV68 @ SV197 ) @ ( SV68 @ SV281 ) )
= $true )
| ( ( ord_less_nat @ SV197 @ SV281 )
= $false )
| ( ( ord_less_int @ ( SV68 @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) @ ( SV68 @ ( suc @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2329]) ).
thf(2411,plain,
! [SV68: nat > int,SV281: nat,SV197: nat] :
( ( ( ord_less_nat @ SV197 @ SV281 )
= $true )
| ( ( ord_less_nat @ SV197 @ SV281 )
= $false )
| ( ( ord_less_int @ ( SV68 @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) @ ( SV68 @ ( suc @ ( sK11_SY449 @ SV281 @ SV197 @ SV68 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2330]) ).
thf(2412,plain,
! [SV282: nat,SV201: nat,SV73: nat > nat] :
( ( ( ord_less_nat @ ( SV73 @ SV201 ) @ ( SV73 @ SV282 ) )
= $true )
| ( ( ord_less_nat @ ( SV73 @ SV201 ) @ ( SV73 @ SV282 ) )
= $false )
| ( ( ord_less_nat @ ( SV73 @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) @ ( SV73 @ ( suc @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2331]) ).
thf(2413,plain,
! [SV73: nat > nat,SV282: nat,SV201: nat] :
( ( ( ord_less_nat @ SV201 @ SV282 )
= $true )
| ( ( ord_less_nat @ ( SV73 @ SV201 ) @ ( SV73 @ SV282 ) )
= $false )
| ( ( ord_less_nat @ ( SV73 @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) @ ( SV73 @ ( suc @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2332]) ).
thf(2414,plain,
! [SV282: nat,SV201: nat,SV73: nat > nat] :
( ( ( ord_less_nat @ ( SV73 @ SV201 ) @ ( SV73 @ SV282 ) )
= $true )
| ( ( ord_less_nat @ SV201 @ SV282 )
= $false )
| ( ( ord_less_nat @ ( SV73 @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) @ ( SV73 @ ( suc @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2333]) ).
thf(2415,plain,
! [SV73: nat > nat,SV282: nat,SV201: nat] :
( ( ( ord_less_nat @ SV201 @ SV282 )
= $true )
| ( ( ord_less_nat @ SV201 @ SV282 )
= $false )
| ( ( ord_less_nat @ ( SV73 @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) @ ( SV73 @ ( suc @ ( sK12_SY457 @ SV282 @ SV201 @ SV73 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2334]) ).
thf(2416,plain,
! [SV206: nat,SV284: nat > $o,SV78: nat] :
( ( ( ~ ( ord_less_nat @ ( sK58_SY700 @ SV78 @ SV284 @ SV206 ) @ SV206 )
| ~ ( SV284 @ ( suc @ ( sK58_SY700 @ SV78 @ SV284 @ SV206 ) ) )
| ( SV284 @ ( sK58_SY700 @ SV78 @ SV284 @ SV206 ) ) )
= $false )
| ( ( SV284 @ SV78 )
= $true )
| ( ( SV206
= ( suc @ ( sK32_SY699 @ SV78 @ SV284 @ SV206 ) ) )
= $true )
| ( ( ord_less_nat @ SV78 @ SV206 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2335]) ).
thf(2417,plain,
! [SV206: nat,SV284: nat > $o,SV78: nat] :
( ( ( ~ ( ord_less_nat @ ( sK50_SY700 @ SV78 @ SV284 @ SV206 ) @ SV206 ) )
= $false )
| ( ( SV284 @ SV78 )
= $true )
| ( ( SV284 @ ( sK32_SY699 @ SV78 @ SV284 @ SV206 ) )
= $false )
| ( ( ord_less_nat @ SV78 @ SV206 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2336]) ).
thf(2418,plain,
! [SV206: nat,SV78: nat,SV284: nat > $o] :
( ( ( ~ ( SV284 @ ( suc @ ( sK50_SY700 @ SV78 @ SV284 @ SV206 ) ) )
| ( SV284 @ ( sK50_SY700 @ SV78 @ SV284 @ SV206 ) ) )
= $false )
| ( ( SV284 @ SV78 )
= $true )
| ( ( SV284 @ ( sK32_SY699 @ SV78 @ SV284 @ SV206 ) )
= $false )
| ( ( ord_less_nat @ SV78 @ SV206 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2336]) ).
thf(2419,plain,
! [SV285: nat > nat > $o,SV79: nat,SV207: nat] :
( ( ( ~ ( ord_less_nat @ ( sK43_SY702 @ SV207 @ SV79 @ SV285 ) @ ( sK51_SY728 @ SV285 @ SV79 @ SV207 ) )
| ~ ( ord_less_nat @ ( sK51_SY728 @ SV285 @ SV79 @ SV207 ) @ ( sK59_SY732 @ SV285 @ SV79 @ SV207 ) )
| ~ ( SV285 @ ( sK43_SY702 @ SV207 @ SV79 @ SV285 ) @ ( sK51_SY728 @ SV285 @ SV79 @ SV207 ) )
| ~ ( SV285 @ ( sK51_SY728 @ SV285 @ SV79 @ SV207 ) @ ( sK59_SY732 @ SV285 @ SV79 @ SV207 ) )
| ( SV285 @ ( sK43_SY702 @ SV207 @ SV79 @ SV285 ) @ ( sK59_SY732 @ SV285 @ SV79 @ SV207 ) ) )
= $false )
| ( ( SV285 @ SV79 @ SV207 )
= $true )
| ( ( SV285 @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) @ ( suc @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) ) )
= $false )
| ( ( ord_less_nat @ SV79 @ SV207 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2337]) ).
thf(2420,plain,
! [SV82: nat,SV209: nat,SV287: nat > $o] :
( ( ( ord_less_nat @ ( sK41_SY706 @ SV287 @ SV209 @ SV82 ) @ SV209 )
= $true )
| ( ( SV287 @ SV209 )
= $true )
| ( ( SV287 @ SV82 )
= $false )
| ( ( ord_less_eq_nat @ SV82 @ SV209 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2339]) ).
thf(2421,plain,
! [SV82: nat,SV209: nat,SV287: nat > $o] :
( ( ( ~ ( SV287 @ ( sK41_SY706 @ SV287 @ SV209 @ SV82 ) ) )
= $false )
| ( ( SV287 @ SV209 )
= $true )
| ( ( SV287 @ SV82 )
= $false )
| ( ( ord_less_eq_nat @ SV82 @ SV209 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2340]) ).
thf(2422,plain,
! [SV82: nat,SV209: nat,SV287: nat > $o] :
( ( ( SV287 @ ( suc @ ( sK41_SY706 @ SV287 @ SV209 @ SV82 ) ) )
= $false )
| ( ( SV287 @ SV209 )
= $true )
| ( ( SV287 @ SV82 )
= $false )
| ( ( ord_less_eq_nat @ SV82 @ SV209 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2340]) ).
thf(2423,plain,
! [SV212: nat,SV288: nat,SV85: nat > nat > $o] :
( ( ( ~ ( SV85 @ ( sK52_SY488 @ SV288 @ SV212 @ SV85 ) @ ( sK60_SY733 @ SV212 @ SV288 @ SV85 ) )
| ( SV85 @ ( suc @ ( sK52_SY488 @ SV288 @ SV212 @ SV85 ) ) @ ( suc @ ( sK60_SY733 @ SV212 @ SV288 @ SV85 ) ) ) )
= $false )
| ( ( SV85 @ SV212 @ SV288 )
= $true )
| ( ( SV85 @ zero_zero_nat @ ( suc @ ( sK37_SY487 @ SV288 @ SV212 @ SV85 ) ) )
= $false )
| ( ( SV85 @ ( sK17_SY486 @ SV288 @ SV212 @ SV85 ) @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2341]) ).
thf(2424,plain,
! [SV214: nat > $o,SV87: nat,SV323: nat] :
( ( ( ~ ( ord_less_nat @ SV323 @ ( suc @ SV87 ) )
| ( SV214 @ SV323 ) )
= $true )
| ( ( ord_less_nat @ ( sK27_SY649 @ SV214 @ SV87 ) @ ( suc @ SV87 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2342]) ).
thf(2425,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK27_SY649 @ SV214 @ SV87 ) @ ( suc @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2343]) ).
thf(2426,plain,
! [SV214: nat > $o,SV87: nat,SV320: nat] :
( ( ( ~ ( ord_less_nat @ SV320 @ ( suc @ SV87 ) ) )
= $true )
| ( ( SV214 @ SV320 )
= $true )
| ( ( SV214 @ ( sK27_SY649 @ SV214 @ SV87 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2344]) ).
thf(2427,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( ~ ( SV214 @ zero_zero_nat ) )
= $false )
| ( ( SV214 @ ( sK27_SY649 @ SV214 @ SV87 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2345]) ).
thf(2428,plain,
! [SV214: nat > $o,SV87: nat] :
( ( ( ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) )
= $false )
| ( ( SV214 @ ( sK27_SY649 @ SV214 @ SV87 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2345]) ).
thf(2429,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( ord_less_nat @ ( sK44_SY650 @ SV214 @ SV87 ) @ SV87 )
= $true )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) )
| ~ ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2346]) ).
thf(2430,plain,
! [SV214: nat > $o,SV87: nat] :
( ( ( ~ ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) )
| ~ ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) )
= $false )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( SV214 @ ( suc @ ( sK44_SY650 @ SV214 @ SV87 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2347]) ).
thf(2431,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) ) )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2348]) ).
thf(2432,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( SV228 != zero_zero_real )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2349]) ).
thf(2433,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
= $true )
| ( ( ~ ( ( SV228 != zero_zero_real ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2350]) ).
thf(2434,plain,
! [SV298: nat,SV230: nat,SV106: nat > real] :
( ( ( ord_less_real @ ( SV106 @ SV230 ) @ ( SV106 @ SV298 ) )
= $true )
| ( ( ord_less_real @ ( SV106 @ SV230 ) @ ( SV106 @ SV298 ) )
= $false )
| ( ( ord_less_real @ ( SV106 @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) @ ( SV106 @ ( suc @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2355]) ).
thf(2435,plain,
! [SV106: nat > real,SV298: nat,SV230: nat] :
( ( ( ord_less_nat @ SV230 @ SV298 )
= $true )
| ( ( ord_less_real @ ( SV106 @ SV230 ) @ ( SV106 @ SV298 ) )
= $false )
| ( ( ord_less_real @ ( SV106 @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) @ ( SV106 @ ( suc @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2356]) ).
thf(2436,plain,
! [SV298: nat,SV230: nat,SV106: nat > real] :
( ( ( ord_less_real @ ( SV106 @ SV230 ) @ ( SV106 @ SV298 ) )
= $true )
| ( ( ord_less_nat @ SV230 @ SV298 )
= $false )
| ( ( ord_less_real @ ( SV106 @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) @ ( SV106 @ ( suc @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2357]) ).
thf(2437,plain,
! [SV106: nat > real,SV298: nat,SV230: nat] :
( ( ( ord_less_nat @ SV230 @ SV298 )
= $true )
| ( ( ord_less_nat @ SV230 @ SV298 )
= $false )
| ( ( ord_less_real @ ( SV106 @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) @ ( SV106 @ ( suc @ ( sK21_SY523 @ SV298 @ SV230 @ SV106 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2358]) ).
thf(2438,plain,
! [SV110: nat,SV314: nat,SV233: nat > $o] :
( ( ( SV233 @ SV314 )
= $false )
| ( ( ord_less_nat @ SV314 @ ( suc @ SV110 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) )
| ~ ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2359]) ).
thf(2439,plain,
! [SV110: nat,SV233: nat > $o] :
( ( ( ~ ( ~ ( ord_less_nat @ ( sK53_SY665 @ SV233 @ SV110 ) @ ( suc @ SV110 ) )
| ~ ( SV233 @ ( sK53_SY665 @ SV233 @ SV110 ) ) ) )
= $true )
| ( ( SV233 @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2360]) ).
thf(2440,plain,
! [SV110: nat,SV233: nat > $o] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ ( sK61_SY666 @ SV233 @ SV110 ) @ SV110 )
| ~ ( SV233 @ ( sK61_SY666 @ SV233 @ SV110 ) ) ) )
= $false )
| ( ( SV233 @ SV110 )
= $true )
| ( ( SV233 @ SV110 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2361]) ).
thf(2441,plain,
! [SV233: nat > $o,SV110: nat,SV318: nat] :
( ( ( ord_less_nat @ SV318 @ SV110 )
= $false )
| ( ( ~ ( SV233 @ SV318 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) )
| ~ ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2362]) ).
thf(2442,plain,
! [SV315: nat,SV113: nat > $o] :
( ( ( ~ ~ ( SV113 @ ( sK45_SY536 @ SV315 @ SV113 ) )
| ~ ( SV113 @ ( suc @ ( sK45_SY536 @ SV315 @ SV113 ) ) ) )
= $false )
| ( ( SV113 @ SV315 )
= $false )
| ( ( SV113 @ zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2363]) ).
thf(2443,plain,
! [SV239: nat > $o,SV117: nat,SV324: nat] :
( ( ( ~ ( ord_less_nat @ SV324 @ ( suc @ SV117 ) )
| ( SV239 @ SV324 ) )
= $true )
| ( ( ord_less_nat @ ( sK30_SY669 @ SV239 @ SV117 ) @ ( suc @ SV117 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2364]) ).
thf(2444,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) )
= $false )
| ( ( ord_less_nat @ ( sK30_SY669 @ SV239 @ SV117 ) @ ( suc @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2365]) ).
thf(2445,plain,
! [SV239: nat > $o,SV117: nat,SV321: nat] :
( ( ( ~ ( ord_less_nat @ SV321 @ ( suc @ SV117 ) ) )
= $true )
| ( ( SV239 @ SV321 )
= $true )
| ( ( SV239 @ ( sK30_SY669 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2366]) ).
thf(2446,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( ~ ( SV239 @ SV117 ) )
= $false )
| ( ( SV239 @ ( sK30_SY669 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2367]) ).
thf(2447,plain,
! [SV239: nat > $o,SV117: nat] :
( ( ( ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) )
= $false )
| ( ( SV239 @ ( sK30_SY669 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2367]) ).
thf(2448,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( ord_less_nat @ ( sK46_SY670 @ SV239 @ SV117 ) @ SV117 )
= $true )
| ( ( SV239 @ SV117 )
= $false )
| ( ( ~ ( ~ ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) )
| ~ ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2368]) ).
thf(2449,plain,
! [SV239: nat > $o,SV117: nat] :
( ( ( ~ ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) )
| ~ ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) )
= $false )
| ( ( SV239 @ SV117 )
= $false )
| ( ( SV239 @ ( sK46_SY670 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2369]) ).
thf(2450,plain,
! [SV244: nat,SV122: nat > $o] :
( ( ( ~ ( ~ ( ord_less_nat @ ( sK38_SY677 @ SV122 @ SV244 ) @ SV244 )
| ~ ! [SY727: nat] :
( ~ ( ord_less_eq_nat @ SY727 @ ( sK38_SY677 @ SV122 @ SV244 ) )
| ~ ( SV122 @ SY727 ) ) ) )
= $true )
| ( ( SV122 @ zero_zero_nat )
= $true )
| ( ( SV122 @ SV244 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2371]) ).
thf(2451,plain,
! [SV244: nat,SV122: nat > $o] :
( ( ( SV122 @ ( suc @ ( sK38_SY677 @ SV122 @ SV244 ) ) )
= $true )
| ( ( SV122 @ zero_zero_nat )
= $true )
| ( ( SV122 @ SV244 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2372]) ).
thf(2452,plain,
! [SV123: nat,SV245: nat] :
( ( ( ( SV245
!= ( suc @ ( sK47_SY679 @ SV123 @ SV245 ) ) )
| ~ ( ord_less_nat @ SV123 @ ( sK47_SY679 @ SV123 @ SV245 ) ) )
= $false )
| ( ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2373]) ).
thf(2453,plain,
! [SV245: nat,SV316: nat,SV123: nat] :
( ( ( ord_less_nat @ SV123 @ SV316 )
= $false )
| ( ( SV245
= ( suc @ SV316 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
| ~ ~ ! [SY679: nat] :
~ ~ ( ( SV245
!= ( suc @ SY679 ) )
| ~ ( ord_less_nat @ SV123 @ SY679 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2374]) ).
thf(2454,plain,
! [SV127: nat,SV248: nat,SV303: nat > nat > $o] :
( ( ( ~ ( SV303 @ ( sK48_SY719 @ SV248 @ SV127 @ SV303 ) @ ( sK54_SY730 @ SV127 @ SV248 @ SV303 ) )
| ~ ( SV303 @ ( sK54_SY730 @ SV127 @ SV248 @ SV303 ) @ ( sK62_SY734 @ SV127 @ SV248 @ SV303 ) )
| ( SV303 @ ( sK48_SY719 @ SV248 @ SV127 @ SV303 ) @ ( sK62_SY734 @ SV127 @ SV248 @ SV303 ) ) )
= $false )
| ( ( ~ ! [SY722: nat] : ( SV303 @ SY722 @ ( suc @ SY722 ) )
| ( SV303 @ SV127 @ SV248 ) )
= $true )
| ( ( SV303 @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV248 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2375]) ).
thf(2455,plain,
! [SV249: real,SV128: real] :
( ( ( ord_less_real @ zero_zero_real @ SV128 )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2376]) ).
thf(2456,plain,
! [SV128: real,SV249: real] :
( ( ( ord_less_real @ zero_zero_real @ SV249 )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2377]) ).
thf(2457,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2378]) ).
thf(2458,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2378]) ).
thf(2459,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) ) )
= $false )
| ( ( ord_less_real @ SV128 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV249 @ zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2379]) ).
thf(2460,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) ) )
= $false )
| ( ( ord_less_real @ SV128 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV249 @ zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2379]) ).
thf(2461,plain,
! [SV251: nat,SV133: nat] :
( ( ( ~ ( ( SV133
!= ( suc @ ( sK55_SY686 @ SV251 @ SV133 ) ) )
| ~ ( ord_less_nat @ ( sK55_SY686 @ SV251 @ SV133 ) @ SV251 ) ) )
= $true )
| ( ( SV133 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2380]) ).
thf(2462,plain,
! [SV251: nat,SV133: nat] :
( ( ( ~ ~ ( ( SV133
!= ( suc @ ( sK63_SY686 @ SV251 @ SV133 ) ) )
| ~ ( ord_less_nat @ ( sK63_SY686 @ SV251 @ SV133 ) @ SV251 ) ) )
= $false )
| ( ( SV133 = zero_zero_nat )
= $true )
| ( ( SV133 = zero_zero_nat )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2381]) ).
thf(2463,plain,
! [SV251: nat,SV319: nat,SV133: nat] :
( ( ( SV133
= ( suc @ SV319 ) )
= $false )
| ( ( ~ ( ord_less_nat @ SV319 @ SV251 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
| ~ ( ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2382]) ).
thf(2464,plain,
! [SV257: real,SV141: real] :
( ( ( ord_less_real @ zero_zero_real @ SV141 )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2386]) ).
thf(2465,plain,
! [SV141: real,SV257: real] :
( ( ( ord_less_real @ SV257 @ zero_zero_real )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2387]) ).
thf(2466,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2388]) ).
thf(2467,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2388]) ).
thf(2468,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ SV141 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV257 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2389]) ).
thf(2469,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) ) )
= $false )
| ( ( ord_less_real @ SV141 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV257 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2389]) ).
thf(2470,plain,
! [SV142: nat,SV258: nat,SV305: nat > $o] :
( ( ( ord_less_nat @ ( sK42_SY724 @ SV305 @ SV258 @ SV142 ) @ SV258 )
= $true )
| ( ( SV305 @ SV142 )
= $true )
| ( ( SV305 @ SV258 )
= $false )
| ( ( ord_less_eq_nat @ SV142 @ SV258 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2391]) ).
thf(2471,plain,
! [SV142: nat,SV258: nat,SV305: nat > $o] :
( ( ( ~ ( SV305 @ ( suc @ ( sK42_SY724 @ SV305 @ SV258 @ SV142 ) ) ) )
= $false )
| ( ( SV305 @ SV142 )
= $true )
| ( ( SV305 @ SV258 )
= $false )
| ( ( ord_less_eq_nat @ SV142 @ SV258 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2392]) ).
thf(2472,plain,
! [SV142: nat,SV258: nat,SV305: nat > $o] :
( ( ( SV305 @ ( sK42_SY724 @ SV305 @ SV258 @ SV142 ) )
= $false )
| ( ( SV305 @ SV142 )
= $true )
| ( ( SV305 @ SV258 )
= $false )
| ( ( ord_less_eq_nat @ SV142 @ SV258 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2392]) ).
thf(2473,plain,
! [SV311: nat,SV45: nat] :
( ( ( SV45
= ( suc @ ( sK56_SY405 @ SV311 @ SV45 ) ) )
= $true )
| ( ( SV45
= ( suc @ SV311 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2393]) ).
thf(2474,plain,
! [SV312: nat,SV178: nat > $o,SV47: nat] :
( ( ( ~ ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) )
| ~ ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ SV312 @ ( suc @ SV47 ) )
= $false )
| ( ( SV178 @ SV312 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2394]) ).
thf(2475,plain,
! [SV47: nat,SV178: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK49_SY601 @ SV178 @ SV47 ) @ ( suc @ SV47 ) )
| ~ ( SV178 @ ( sK49_SY601 @ SV178 @ SV47 ) ) )
= $false )
| ( ( SV178 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2395]) ).
thf(2476,plain,
! [SV47: nat,SV178: nat > $o] :
( ( ( ~ ( ~ ( ord_less_nat @ ( sK57_SY602 @ SV178 @ SV47 ) @ SV47 )
| ~ ( SV178 @ ( suc @ ( sK57_SY602 @ SV178 @ SV47 ) ) ) ) )
= $true )
| ( ( SV178 @ zero_zero_nat )
= $true )
| ( ( SV178 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2396]) ).
thf(2477,plain,
! [SV47: nat,SV317: nat,SV178: nat > $o] :
( ( ( SV178 @ ( suc @ SV317 ) )
= $false )
| ( ( ord_less_nat @ SV317 @ SV47 )
= $false )
| ( ( ~ ( ~ ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) )
| ~ ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2397]) ).
thf(2478,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV182 ) )
= $true )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $true )
| ( ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2398]) ).
thf(2479,plain,
! [SV51: real,SV274: real,SV182: real] :
( ( ( ~ ( ord_less_real @ SV182 @ zero_zero_real ) )
= $true )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $true )
| ( ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2399]) ).
thf(2480,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ord_less_real @ SV182 @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
| ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2400]) ).
thf(2481,plain,
! [SV182: real,SV51: real,SV274: real] :
( ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
| ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2400]) ).
thf(2482,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
| ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2401]) ).
thf(2483,plain,
! [SV274: real,SV182: real,SV51: real] :
( ( ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
| ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) )
= $false )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2402]) ).
thf(2484,plain,
! [SV191: nat,SV61: real] :
( ( ( ( SV61 != zero_zero_real )
| ~ ( ord_less_nat @ zero_zero_nat @ SV191 ) )
= $false )
| ( ( SV61 = zero_zero_real )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2405]) ).
thf(2485,plain,
! [SV62: nat,SV192: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ ( sK31_SY616 @ SV192 @ SV62 ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV192 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2406]) ).
thf(2486,plain,
! [SV62: nat,SV192: real] :
( ( ( ( power_power_real @ ( sK31_SY616 @ SV192 @ SV62 ) @ SV62 )
!= SV192 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV192 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2406]) ).
thf(2487,plain,
! [SV192: real,SV62: nat,SV322: real] :
( ( ( ~ ~ ( ~ ( ord_less_real @ zero_zero_real @ SV322 )
| ( ( power_power_real @ SV322 @ SV62 )
!= SV192 ) ) )
= $true )
| ( ( SV322
= ( sK31_SY616 @ SV192 @ SV62 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV192 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2407]) ).
thf(2488,plain,
! [SV206: nat,SV284: nat > $o,SV78: nat] :
( ( ( ~ ( ord_less_nat @ ( sK58_SY700 @ SV78 @ SV284 @ SV206 ) @ SV206 ) )
= $false )
| ( ( SV284 @ SV78 )
= $true )
| ( ( SV206
= ( suc @ ( sK32_SY699 @ SV78 @ SV284 @ SV206 ) ) )
= $true )
| ( ( ord_less_nat @ SV78 @ SV206 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2416]) ).
thf(2489,plain,
! [SV206: nat,SV78: nat,SV284: nat > $o] :
( ( ( ~ ( SV284 @ ( suc @ ( sK58_SY700 @ SV78 @ SV284 @ SV206 ) ) )
| ( SV284 @ ( sK58_SY700 @ SV78 @ SV284 @ SV206 ) ) )
= $false )
| ( ( SV284 @ SV78 )
= $true )
| ( ( SV206
= ( suc @ ( sK32_SY699 @ SV78 @ SV284 @ SV206 ) ) )
= $true )
| ( ( ord_less_nat @ SV78 @ SV206 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2416]) ).
thf(2490,plain,
! [SV206: nat,SV284: nat > $o,SV78: nat] :
( ( ( ord_less_nat @ ( sK50_SY700 @ SV78 @ SV284 @ SV206 ) @ SV206 )
= $true )
| ( ( SV284 @ SV78 )
= $true )
| ( ( SV284 @ ( sK32_SY699 @ SV78 @ SV284 @ SV206 ) )
= $false )
| ( ( ord_less_nat @ SV78 @ SV206 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2417]) ).
thf(2491,plain,
! [SV206: nat,SV78: nat,SV284: nat > $o] :
( ( ( ~ ( SV284 @ ( suc @ ( sK50_SY700 @ SV78 @ SV284 @ SV206 ) ) ) )
= $false )
| ( ( SV284 @ SV78 )
= $true )
| ( ( SV284 @ ( sK32_SY699 @ SV78 @ SV284 @ SV206 ) )
= $false )
| ( ( ord_less_nat @ SV78 @ SV206 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2418]) ).
thf(2492,plain,
! [SV206: nat,SV78: nat,SV284: nat > $o] :
( ( ( SV284 @ ( sK50_SY700 @ SV78 @ SV284 @ SV206 ) )
= $false )
| ( ( SV284 @ SV78 )
= $true )
| ( ( SV284 @ ( sK32_SY699 @ SV78 @ SV284 @ SV206 ) )
= $false )
| ( ( ord_less_nat @ SV78 @ SV206 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2418]) ).
thf(2493,plain,
! [SV285: nat > nat > $o,SV79: nat,SV207: nat] :
( ( ( ~ ( ord_less_nat @ ( sK43_SY702 @ SV207 @ SV79 @ SV285 ) @ ( sK51_SY728 @ SV285 @ SV79 @ SV207 ) ) )
= $false )
| ( ( SV285 @ SV79 @ SV207 )
= $true )
| ( ( SV285 @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) @ ( suc @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) ) )
= $false )
| ( ( ord_less_nat @ SV79 @ SV207 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2419]) ).
thf(2494,plain,
! [SV207: nat,SV79: nat,SV285: nat > nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK51_SY728 @ SV285 @ SV79 @ SV207 ) @ ( sK59_SY732 @ SV285 @ SV79 @ SV207 ) )
| ~ ( SV285 @ ( sK43_SY702 @ SV207 @ SV79 @ SV285 ) @ ( sK51_SY728 @ SV285 @ SV79 @ SV207 ) )
| ~ ( SV285 @ ( sK51_SY728 @ SV285 @ SV79 @ SV207 ) @ ( sK59_SY732 @ SV285 @ SV79 @ SV207 ) )
| ( SV285 @ ( sK43_SY702 @ SV207 @ SV79 @ SV285 ) @ ( sK59_SY732 @ SV285 @ SV79 @ SV207 ) ) )
= $false )
| ( ( SV285 @ SV79 @ SV207 )
= $true )
| ( ( SV285 @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) @ ( suc @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) ) )
= $false )
| ( ( ord_less_nat @ SV79 @ SV207 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2419]) ).
thf(2495,plain,
! [SV82: nat,SV209: nat,SV287: nat > $o] :
( ( ( SV287 @ ( sK41_SY706 @ SV287 @ SV209 @ SV82 ) )
= $true )
| ( ( SV287 @ SV209 )
= $true )
| ( ( SV287 @ SV82 )
= $false )
| ( ( ord_less_eq_nat @ SV82 @ SV209 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2421]) ).
thf(2496,plain,
! [SV212: nat,SV288: nat,SV85: nat > nat > $o] :
( ( ( ~ ( SV85 @ ( sK52_SY488 @ SV288 @ SV212 @ SV85 ) @ ( sK60_SY733 @ SV212 @ SV288 @ SV85 ) ) )
= $false )
| ( ( SV85 @ SV212 @ SV288 )
= $true )
| ( ( SV85 @ zero_zero_nat @ ( suc @ ( sK37_SY487 @ SV288 @ SV212 @ SV85 ) ) )
= $false )
| ( ( SV85 @ ( sK17_SY486 @ SV288 @ SV212 @ SV85 ) @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2423]) ).
thf(2497,plain,
! [SV212: nat,SV288: nat,SV85: nat > nat > $o] :
( ( ( SV85 @ ( suc @ ( sK52_SY488 @ SV288 @ SV212 @ SV85 ) ) @ ( suc @ ( sK60_SY733 @ SV212 @ SV288 @ SV85 ) ) )
= $false )
| ( ( SV85 @ SV212 @ SV288 )
= $true )
| ( ( SV85 @ zero_zero_nat @ ( suc @ ( sK37_SY487 @ SV288 @ SV212 @ SV85 ) ) )
= $false )
| ( ( SV85 @ ( sK17_SY486 @ SV288 @ SV212 @ SV85 ) @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2423]) ).
thf(2498,plain,
! [SV214: nat > $o,SV87: nat,SV323: nat] :
( ( ( ~ ( ord_less_nat @ SV323 @ ( suc @ SV87 ) ) )
= $true )
| ( ( SV214 @ SV323 )
= $true )
| ( ( ord_less_nat @ ( sK27_SY649 @ SV214 @ SV87 ) @ ( suc @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2424]) ).
thf(2499,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( ~ ( SV214 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ ( sK27_SY649 @ SV214 @ SV87 ) @ ( suc @ SV87 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2425]) ).
thf(2500,plain,
! [SV214: nat > $o,SV87: nat] :
( ( ( ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK27_SY649 @ SV214 @ SV87 ) @ ( suc @ SV87 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2425]) ).
thf(2501,plain,
! [SV214: nat > $o,SV87: nat,SV320: nat] :
( ( ( ord_less_nat @ SV320 @ ( suc @ SV87 ) )
= $false )
| ( ( SV214 @ SV320 )
= $true )
| ( ( SV214 @ ( sK27_SY649 @ SV214 @ SV87 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2426]) ).
thf(2502,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( SV214 @ zero_zero_nat )
= $true )
| ( ( SV214 @ ( sK27_SY649 @ SV214 @ SV87 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2427]) ).
thf(2503,plain,
! [SV214: nat > $o,SV87: nat] :
( ( ( ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) )
= $true )
| ( ( SV214 @ ( sK27_SY649 @ SV214 @ SV87 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2428]) ).
thf(2504,plain,
! [SV214: nat > $o,SV87: nat] :
( ( ( ~ ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) )
| ~ ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) )
= $false )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK44_SY650 @ SV214 @ SV87 ) @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2429]) ).
thf(2505,plain,
! [SV214: nat > $o,SV87: nat] :
( ( ( ~ ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) ) )
= $false )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( SV214 @ ( suc @ ( sK44_SY650 @ SV214 @ SV87 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2430]) ).
thf(2506,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( ~ ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) )
= $false )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( SV214 @ ( suc @ ( sK44_SY650 @ SV214 @ SV87 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2430]) ).
thf(2507,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
= $false )
| ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2431]) ).
thf(2508,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( SV228 = zero_zero_real )
= $false )
| ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2432]) ).
thf(2509,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV228 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
= $true )
| ( ( ~ ( ( SV228 != zero_zero_real ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2433]) ).
thf(2510,plain,
! [SV228: real,SV297: real,SV103: real] :
( ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
= $true )
| ( ( ~ ( ( SV228 != zero_zero_real ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2433]) ).
thf(2511,plain,
! [SV314: nat,SV233: nat > $o,SV110: nat] :
( ( ( ~ ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) )
| ~ ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV314 @ ( suc @ SV110 ) )
= $false )
| ( ( SV233 @ SV314 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2438]) ).
thf(2512,plain,
! [SV110: nat,SV233: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK53_SY665 @ SV233 @ SV110 ) @ ( suc @ SV110 ) )
| ~ ( SV233 @ ( sK53_SY665 @ SV233 @ SV110 ) ) )
= $false )
| ( ( SV233 @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2439]) ).
thf(2513,plain,
! [SV110: nat,SV233: nat > $o] :
( ( ( ~ ( ~ ( ord_less_nat @ ( sK61_SY666 @ SV233 @ SV110 ) @ SV110 )
| ~ ( SV233 @ ( sK61_SY666 @ SV233 @ SV110 ) ) ) )
= $true )
| ( ( SV233 @ SV110 )
= $true )
| ( ( SV233 @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2440]) ).
thf(2514,plain,
! [SV110: nat,SV318: nat,SV233: nat > $o] :
( ( ( SV233 @ SV318 )
= $false )
| ( ( ord_less_nat @ SV318 @ SV110 )
= $false )
| ( ( ~ ( ~ ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) )
| ~ ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2441]) ).
thf(2515,plain,
! [SV315: nat,SV113: nat > $o] :
( ( ( ~ ~ ( SV113 @ ( sK45_SY536 @ SV315 @ SV113 ) ) )
= $false )
| ( ( SV113 @ SV315 )
= $false )
| ( ( SV113 @ zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2442]) ).
thf(2516,plain,
! [SV315: nat,SV113: nat > $o] :
( ( ( ~ ( SV113 @ ( suc @ ( sK45_SY536 @ SV315 @ SV113 ) ) ) )
= $false )
| ( ( SV113 @ SV315 )
= $false )
| ( ( SV113 @ zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2442]) ).
thf(2517,plain,
! [SV239: nat > $o,SV117: nat,SV324: nat] :
( ( ( ~ ( ord_less_nat @ SV324 @ ( suc @ SV117 ) ) )
= $true )
| ( ( SV239 @ SV324 )
= $true )
| ( ( ord_less_nat @ ( sK30_SY669 @ SV239 @ SV117 ) @ ( suc @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2443]) ).
thf(2518,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( ~ ( SV239 @ SV117 ) )
= $false )
| ( ( ord_less_nat @ ( sK30_SY669 @ SV239 @ SV117 ) @ ( suc @ SV117 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2444]) ).
thf(2519,plain,
! [SV239: nat > $o,SV117: nat] :
( ( ( ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) )
= $false )
| ( ( ord_less_nat @ ( sK30_SY669 @ SV239 @ SV117 ) @ ( suc @ SV117 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2444]) ).
thf(2520,plain,
! [SV239: nat > $o,SV117: nat,SV321: nat] :
( ( ( ord_less_nat @ SV321 @ ( suc @ SV117 ) )
= $false )
| ( ( SV239 @ SV321 )
= $true )
| ( ( SV239 @ ( sK30_SY669 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2445]) ).
thf(2521,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( SV239 @ SV117 )
= $true )
| ( ( SV239 @ ( sK30_SY669 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2446]) ).
thf(2522,plain,
! [SV239: nat > $o,SV117: nat] :
( ( ( ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) )
= $true )
| ( ( SV239 @ ( sK30_SY669 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2447]) ).
thf(2523,plain,
! [SV239: nat > $o,SV117: nat] :
( ( ( ~ ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) )
| ~ ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) )
= $false )
| ( ( SV239 @ SV117 )
= $false )
| ( ( ord_less_nat @ ( sK46_SY670 @ SV239 @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2448]) ).
thf(2524,plain,
! [SV239: nat > $o,SV117: nat] :
( ( ( ~ ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) ) )
= $false )
| ( ( SV239 @ SV117 )
= $false )
| ( ( SV239 @ ( sK46_SY670 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2449]) ).
thf(2525,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( ~ ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) )
= $false )
| ( ( SV239 @ SV117 )
= $false )
| ( ( SV239 @ ( sK46_SY670 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2449]) ).
thf(2526,plain,
! [SV244: nat,SV122: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK38_SY677 @ SV122 @ SV244 ) @ SV244 )
| ~ ! [SY727: nat] :
( ~ ( ord_less_eq_nat @ SY727 @ ( sK38_SY677 @ SV122 @ SV244 ) )
| ~ ( SV122 @ SY727 ) ) )
= $false )
| ( ( SV122 @ zero_zero_nat )
= $true )
| ( ( SV122 @ SV244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2450]) ).
thf(2527,plain,
! [SV123: nat,SV245: nat] :
( ( ( SV245
!= ( suc @ ( sK47_SY679 @ SV123 @ SV245 ) ) )
= $false )
| ( ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2452]) ).
thf(2528,plain,
! [SV245: nat,SV123: nat] :
( ( ( ~ ( ord_less_nat @ SV123 @ ( sK47_SY679 @ SV123 @ SV245 ) ) )
= $false )
| ( ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2452]) ).
thf(2529,plain,
! [SV316: nat,SV245: nat,SV123: nat] :
( ( ( ~ ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
| ~ ~ ! [SY679: nat] :
~ ~ ( ( SV245
!= ( suc @ SY679 ) )
| ~ ( ord_less_nat @ SV123 @ SY679 ) ) )
= $false )
| ( ( SV245
= ( suc @ SV316 ) )
= $false )
| ( ( ord_less_nat @ SV123 @ SV316 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2453]) ).
thf(2530,plain,
! [SV127: nat,SV248: nat,SV303: nat > nat > $o] :
( ( ( ~ ( SV303 @ ( sK48_SY719 @ SV248 @ SV127 @ SV303 ) @ ( sK54_SY730 @ SV127 @ SV248 @ SV303 ) ) )
= $false )
| ( ( ~ ! [SY722: nat] : ( SV303 @ SY722 @ ( suc @ SY722 ) )
| ( SV303 @ SV127 @ SV248 ) )
= $true )
| ( ( SV303 @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV248 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2454]) ).
thf(2531,plain,
! [SV248: nat,SV127: nat,SV303: nat > nat > $o] :
( ( ( ~ ( SV303 @ ( sK54_SY730 @ SV127 @ SV248 @ SV303 ) @ ( sK62_SY734 @ SV127 @ SV248 @ SV303 ) )
| ( SV303 @ ( sK48_SY719 @ SV248 @ SV127 @ SV303 ) @ ( sK62_SY734 @ SV127 @ SV248 @ SV303 ) ) )
= $false )
| ( ( ~ ! [SY722: nat] : ( SV303 @ SY722 @ ( suc @ SY722 ) )
| ( SV303 @ SV127 @ SV248 ) )
= $true )
| ( ( SV303 @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV248 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2454]) ).
thf(2532,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2455]) ).
thf(2533,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2456]) ).
thf(2534,plain,
! [SV249: real,SV128: real] :
( ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2457]) ).
thf(2535,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2458]) ).
thf(2536,plain,
! [SV249: real,SV128: real] :
( ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
= $true )
| ( ( ord_less_real @ SV128 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV249 @ zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2459]) ).
thf(2537,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
| ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ SV128 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV249 @ zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2460]) ).
thf(2538,plain,
! [SV251: nat,SV133: nat] :
( ( ( ( SV133
!= ( suc @ ( sK55_SY686 @ SV251 @ SV133 ) ) )
| ~ ( ord_less_nat @ ( sK55_SY686 @ SV251 @ SV133 ) @ SV251 ) )
= $false )
| ( ( SV133 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2461]) ).
thf(2539,plain,
! [SV251: nat,SV133: nat] :
( ( ( ~ ( ( SV133
!= ( suc @ ( sK63_SY686 @ SV251 @ SV133 ) ) )
| ~ ( ord_less_nat @ ( sK63_SY686 @ SV251 @ SV133 ) @ SV251 ) ) )
= $true )
| ( ( SV133 = zero_zero_nat )
= $true )
| ( ( SV133 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2462]) ).
thf(2540,plain,
! [SV133: nat,SV251: nat,SV319: nat] :
( ( ( ord_less_nat @ SV319 @ SV251 )
= $false )
| ( ( SV133
= ( suc @ SV319 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
| ~ ( ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2463]) ).
thf(2541,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2464]) ).
thf(2542,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2465]) ).
thf(2543,plain,
! [SV257: real,SV141: real] :
( ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2466]) ).
thf(2544,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2467]) ).
thf(2545,plain,
! [SV257: real,SV141: real] :
( ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV141 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV257 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2468]) ).
thf(2546,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
| ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) )
= $true )
| ( ( ord_less_real @ SV141 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV257 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2469]) ).
thf(2547,plain,
! [SV142: nat,SV258: nat,SV305: nat > $o] :
( ( ( SV305 @ ( suc @ ( sK42_SY724 @ SV305 @ SV258 @ SV142 ) ) )
= $true )
| ( ( SV305 @ SV142 )
= $true )
| ( ( SV305 @ SV258 )
= $false )
| ( ( ord_less_eq_nat @ SV142 @ SV258 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2471]) ).
thf(2548,plain,
! [SV312: nat,SV178: nat > $o,SV47: nat] :
( ( ( ~ ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) ) )
= $false )
| ( ( ord_less_nat @ SV312 @ ( suc @ SV47 ) )
= $false )
| ( ( SV178 @ SV312 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2474]) ).
thf(2549,plain,
! [SV312: nat,SV47: nat,SV178: nat > $o] :
( ( ( ~ ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ SV312 @ ( suc @ SV47 ) )
= $false )
| ( ( SV178 @ SV312 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2474]) ).
thf(2550,plain,
! [SV47: nat,SV178: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK49_SY601 @ SV178 @ SV47 ) @ ( suc @ SV47 ) ) )
= $false )
| ( ( SV178 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2475]) ).
thf(2551,plain,
! [SV47: nat,SV178: nat > $o] :
( ( ( ~ ( SV178 @ ( sK49_SY601 @ SV178 @ SV47 ) ) )
= $false )
| ( ( SV178 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2475]) ).
thf(2552,plain,
! [SV47: nat,SV178: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK57_SY602 @ SV178 @ SV47 ) @ SV47 )
| ~ ( SV178 @ ( suc @ ( sK57_SY602 @ SV178 @ SV47 ) ) ) )
= $false )
| ( ( SV178 @ zero_zero_nat )
= $true )
| ( ( SV178 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2476]) ).
thf(2553,plain,
! [SV317: nat,SV178: nat > $o,SV47: nat] :
( ( ( ~ ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) )
| ~ ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ SV317 @ SV47 )
= $false )
| ( ( SV178 @ ( suc @ SV317 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2477]) ).
thf(2554,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ord_less_real @ zero_zero_real @ SV182 )
= $false )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $true )
| ( ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2478]) ).
thf(2555,plain,
! [SV51: real,SV274: real,SV182: real] :
( ( ( ord_less_real @ SV182 @ zero_zero_real )
= $false )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $true )
| ( ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2479]) ).
thf(2556,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
| ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2480]) ).
thf(2557,plain,
! [SV274: real,SV182: real,SV51: real] :
( ( ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
| ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2481]) ).
thf(2558,plain,
! [SV274: real,SV182: real,SV51: real] :
( ( ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
| ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) )
= $false )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2482]) ).
thf(2559,plain,
! [SV274: real,SV182: real,SV51: real] :
( ( ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) ) )
= $false )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2483]) ).
thf(2560,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) )
= $false )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2483]) ).
thf(2561,plain,
! [SV191: nat,SV61: real] :
( ( ( SV61 != zero_zero_real )
= $false )
| ( ( SV61 = zero_zero_real )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV191 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2484]) ).
thf(2562,plain,
! [SV61: real,SV191: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV191 ) )
= $false )
| ( ( SV61 = zero_zero_real )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV191 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2484]) ).
thf(2563,plain,
! [SV62: nat,SV192: real] :
( ( ( ord_less_real @ zero_zero_real @ ( sK31_SY616 @ SV192 @ SV62 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV192 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2485]) ).
thf(2564,plain,
! [SV62: nat,SV192: real] :
( ( ( ( power_power_real @ ( sK31_SY616 @ SV192 @ SV62 ) @ SV62 )
= SV192 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV192 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2486]) ).
thf(2565,plain,
! [SV192: real,SV62: nat,SV322: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV322 )
| ( ( power_power_real @ SV322 @ SV62 )
!= SV192 ) ) )
= $false )
| ( ( SV322
= ( sK31_SY616 @ SV192 @ SV62 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV192 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2487]) ).
thf(2566,plain,
! [SV206: nat,SV284: nat > $o,SV78: nat] :
( ( ( ord_less_nat @ ( sK58_SY700 @ SV78 @ SV284 @ SV206 ) @ SV206 )
= $true )
| ( ( SV284 @ SV78 )
= $true )
| ( ( SV206
= ( suc @ ( sK32_SY699 @ SV78 @ SV284 @ SV206 ) ) )
= $true )
| ( ( ord_less_nat @ SV78 @ SV206 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2488]) ).
thf(2567,plain,
! [SV206: nat,SV78: nat,SV284: nat > $o] :
( ( ( ~ ( SV284 @ ( suc @ ( sK58_SY700 @ SV78 @ SV284 @ SV206 ) ) ) )
= $false )
| ( ( SV284 @ SV78 )
= $true )
| ( ( SV206
= ( suc @ ( sK32_SY699 @ SV78 @ SV284 @ SV206 ) ) )
= $true )
| ( ( ord_less_nat @ SV78 @ SV206 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2489]) ).
thf(2568,plain,
! [SV206: nat,SV78: nat,SV284: nat > $o] :
( ( ( SV284 @ ( sK58_SY700 @ SV78 @ SV284 @ SV206 ) )
= $false )
| ( ( SV284 @ SV78 )
= $true )
| ( ( SV206
= ( suc @ ( sK32_SY699 @ SV78 @ SV284 @ SV206 ) ) )
= $true )
| ( ( ord_less_nat @ SV78 @ SV206 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2489]) ).
thf(2569,plain,
! [SV206: nat,SV78: nat,SV284: nat > $o] :
( ( ( SV284 @ ( suc @ ( sK50_SY700 @ SV78 @ SV284 @ SV206 ) ) )
= $true )
| ( ( SV284 @ SV78 )
= $true )
| ( ( SV284 @ ( sK32_SY699 @ SV78 @ SV284 @ SV206 ) )
= $false )
| ( ( ord_less_nat @ SV78 @ SV206 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2491]) ).
thf(2570,plain,
! [SV285: nat > nat > $o,SV79: nat,SV207: nat] :
( ( ( ord_less_nat @ ( sK43_SY702 @ SV207 @ SV79 @ SV285 ) @ ( sK51_SY728 @ SV285 @ SV79 @ SV207 ) )
= $true )
| ( ( SV285 @ SV79 @ SV207 )
= $true )
| ( ( SV285 @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) @ ( suc @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) ) )
= $false )
| ( ( ord_less_nat @ SV79 @ SV207 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2493]) ).
thf(2571,plain,
! [SV207: nat,SV79: nat,SV285: nat > nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK51_SY728 @ SV285 @ SV79 @ SV207 ) @ ( sK59_SY732 @ SV285 @ SV79 @ SV207 ) ) )
= $false )
| ( ( SV285 @ SV79 @ SV207 )
= $true )
| ( ( SV285 @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) @ ( suc @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) ) )
= $false )
| ( ( ord_less_nat @ SV79 @ SV207 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2494]) ).
thf(2572,plain,
! [SV79: nat,SV207: nat,SV285: nat > nat > $o] :
( ( ( ~ ( SV285 @ ( sK43_SY702 @ SV207 @ SV79 @ SV285 ) @ ( sK51_SY728 @ SV285 @ SV79 @ SV207 ) )
| ~ ( SV285 @ ( sK51_SY728 @ SV285 @ SV79 @ SV207 ) @ ( sK59_SY732 @ SV285 @ SV79 @ SV207 ) )
| ( SV285 @ ( sK43_SY702 @ SV207 @ SV79 @ SV285 ) @ ( sK59_SY732 @ SV285 @ SV79 @ SV207 ) ) )
= $false )
| ( ( SV285 @ SV79 @ SV207 )
= $true )
| ( ( SV285 @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) @ ( suc @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) ) )
= $false )
| ( ( ord_less_nat @ SV79 @ SV207 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2494]) ).
thf(2573,plain,
! [SV212: nat,SV288: nat,SV85: nat > nat > $o] :
( ( ( SV85 @ ( sK52_SY488 @ SV288 @ SV212 @ SV85 ) @ ( sK60_SY733 @ SV212 @ SV288 @ SV85 ) )
= $true )
| ( ( SV85 @ SV212 @ SV288 )
= $true )
| ( ( SV85 @ zero_zero_nat @ ( suc @ ( sK37_SY487 @ SV288 @ SV212 @ SV85 ) ) )
= $false )
| ( ( SV85 @ ( sK17_SY486 @ SV288 @ SV212 @ SV85 ) @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2496]) ).
thf(2574,plain,
! [SV214: nat > $o,SV87: nat,SV323: nat] :
( ( ( ord_less_nat @ SV323 @ ( suc @ SV87 ) )
= $false )
| ( ( SV214 @ SV323 )
= $true )
| ( ( ord_less_nat @ ( sK27_SY649 @ SV214 @ SV87 ) @ ( suc @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2498]) ).
thf(2575,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( SV214 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ ( sK27_SY649 @ SV214 @ SV87 ) @ ( suc @ SV87 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2499]) ).
thf(2576,plain,
! [SV214: nat > $o,SV87: nat] :
( ( ( ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK27_SY649 @ SV214 @ SV87 ) @ ( suc @ SV87 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2500]) ).
thf(2577,plain,
! [SV214: nat > $o,SV87: nat,SV325: nat] :
( ( ( ~ ( ord_less_nat @ SV325 @ SV87 )
| ( SV214 @ ( suc @ SV325 ) ) )
= $true )
| ( ( SV214 @ ( sK27_SY649 @ SV214 @ SV87 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2503]) ).
thf(2578,plain,
! [SV214: nat > $o,SV87: nat] :
( ( ( ~ ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) ) )
= $false )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK44_SY650 @ SV214 @ SV87 ) @ SV87 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2504]) ).
thf(2579,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( ~ ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) )
= $false )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK44_SY650 @ SV214 @ SV87 ) @ SV87 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2504]) ).
thf(2580,plain,
! [SV214: nat > $o,SV87: nat] :
( ( ( ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) ) )
= $true )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( SV214 @ ( suc @ ( sK44_SY650 @ SV214 @ SV87 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2505]) ).
thf(2581,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) )
= $true )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( SV214 @ ( suc @ ( sK44_SY650 @ SV214 @ SV87 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2506]) ).
thf(2582,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) ) )
= $false )
| ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2507]) ).
thf(2583,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
= $false )
| ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2507]) ).
thf(2584,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
= $true )
| ( ( ~ ( ( SV228 != zero_zero_real ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2509]) ).
thf(2585,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( ~ ( ( SV228 != zero_zero_real ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2510]) ).
thf(2586,plain,
! [SV314: nat,SV233: nat > $o,SV110: nat] :
( ( ( ~ ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) ) )
= $false )
| ( ( ord_less_nat @ SV314 @ ( suc @ SV110 ) )
= $false )
| ( ( SV233 @ SV314 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2511]) ).
thf(2587,plain,
! [SV314: nat,SV110: nat,SV233: nat > $o] :
( ( ( ~ ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV314 @ ( suc @ SV110 ) )
= $false )
| ( ( SV233 @ SV314 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2511]) ).
thf(2588,plain,
! [SV110: nat,SV233: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK53_SY665 @ SV233 @ SV110 ) @ ( suc @ SV110 ) ) )
= $false )
| ( ( SV233 @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2512]) ).
thf(2589,plain,
! [SV110: nat,SV233: nat > $o] :
( ( ( ~ ( SV233 @ ( sK53_SY665 @ SV233 @ SV110 ) ) )
= $false )
| ( ( SV233 @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2512]) ).
thf(2590,plain,
! [SV110: nat,SV233: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK61_SY666 @ SV233 @ SV110 ) @ SV110 )
| ~ ( SV233 @ ( sK61_SY666 @ SV233 @ SV110 ) ) )
= $false )
| ( ( SV233 @ SV110 )
= $true )
| ( ( SV233 @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2513]) ).
thf(2591,plain,
! [SV318: nat,SV233: nat > $o,SV110: nat] :
( ( ( ~ ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) )
| ~ ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV318 @ SV110 )
= $false )
| ( ( SV233 @ SV318 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2514]) ).
thf(2592,plain,
! [SV315: nat,SV113: nat > $o] :
( ( ( ~ ( SV113 @ ( sK45_SY536 @ SV315 @ SV113 ) ) )
= $true )
| ( ( SV113 @ SV315 )
= $false )
| ( ( SV113 @ zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2515]) ).
thf(2593,plain,
! [SV315: nat,SV113: nat > $o] :
( ( ( SV113 @ ( suc @ ( sK45_SY536 @ SV315 @ SV113 ) ) )
= $true )
| ( ( SV113 @ SV315 )
= $false )
| ( ( SV113 @ zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2516]) ).
thf(2594,plain,
! [SV239: nat > $o,SV117: nat,SV324: nat] :
( ( ( ord_less_nat @ SV324 @ ( suc @ SV117 ) )
= $false )
| ( ( SV239 @ SV324 )
= $true )
| ( ( ord_less_nat @ ( sK30_SY669 @ SV239 @ SV117 ) @ ( suc @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2517]) ).
thf(2595,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( SV239 @ SV117 )
= $true )
| ( ( ord_less_nat @ ( sK30_SY669 @ SV239 @ SV117 ) @ ( suc @ SV117 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2518]) ).
thf(2596,plain,
! [SV239: nat > $o,SV117: nat] :
( ( ( ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) )
= $true )
| ( ( ord_less_nat @ ( sK30_SY669 @ SV239 @ SV117 ) @ ( suc @ SV117 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2519]) ).
thf(2597,plain,
! [SV239: nat > $o,SV117: nat,SV326: nat] :
( ( ( ~ ( ord_less_nat @ SV326 @ SV117 )
| ( SV239 @ SV326 ) )
= $true )
| ( ( SV239 @ ( sK30_SY669 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2522]) ).
thf(2598,plain,
! [SV239: nat > $o,SV117: nat] :
( ( ( ~ ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) ) )
= $false )
| ( ( SV239 @ SV117 )
= $false )
| ( ( ord_less_nat @ ( sK46_SY670 @ SV239 @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2523]) ).
thf(2599,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( ~ ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) )
= $false )
| ( ( SV239 @ SV117 )
= $false )
| ( ( ord_less_nat @ ( sK46_SY670 @ SV239 @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2523]) ).
thf(2600,plain,
! [SV239: nat > $o,SV117: nat] :
( ( ( ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) ) )
= $true )
| ( ( SV239 @ SV117 )
= $false )
| ( ( SV239 @ ( sK46_SY670 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2524]) ).
thf(2601,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) )
= $true )
| ( ( SV239 @ SV117 )
= $false )
| ( ( SV239 @ ( sK46_SY670 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2525]) ).
thf(2602,plain,
! [SV244: nat,SV122: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK38_SY677 @ SV122 @ SV244 ) @ SV244 ) )
= $false )
| ( ( SV122 @ zero_zero_nat )
= $true )
| ( ( SV122 @ SV244 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2526]) ).
thf(2603,plain,
! [SV244: nat,SV122: nat > $o] :
( ( ( ~ ! [SY727: nat] :
( ~ ( ord_less_eq_nat @ SY727 @ ( sK38_SY677 @ SV122 @ SV244 ) )
| ~ ( SV122 @ SY727 ) ) )
= $false )
| ( ( SV122 @ zero_zero_nat )
= $true )
| ( ( SV122 @ SV244 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2526]) ).
thf(2604,plain,
! [SV123: nat,SV245: nat] :
( ( ( SV245
= ( suc @ ( sK47_SY679 @ SV123 @ SV245 ) ) )
= $true )
| ( ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2527]) ).
thf(2605,plain,
! [SV245: nat,SV123: nat] :
( ( ( ord_less_nat @ SV123 @ ( sK47_SY679 @ SV123 @ SV245 ) )
= $true )
| ( ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2528]) ).
thf(2606,plain,
! [SV316: nat,SV245: nat,SV123: nat] :
( ( ( ~ ( ord_less_nat @ ( suc @ SV123 ) @ SV245 ) )
= $false )
| ( ( SV245
= ( suc @ SV316 ) )
= $false )
| ( ( ord_less_nat @ SV123 @ SV316 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2529]) ).
thf(2607,plain,
! [SV316: nat,SV123: nat,SV245: nat] :
( ( ( ~ ~ ! [SY679: nat] :
~ ~ ( ( SV245
!= ( suc @ SY679 ) )
| ~ ( ord_less_nat @ SV123 @ SY679 ) ) )
= $false )
| ( ( SV245
= ( suc @ SV316 ) )
= $false )
| ( ( ord_less_nat @ SV123 @ SV316 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2529]) ).
thf(2608,plain,
! [SV127: nat,SV248: nat,SV303: nat > nat > $o] :
( ( ( SV303 @ ( sK48_SY719 @ SV248 @ SV127 @ SV303 ) @ ( sK54_SY730 @ SV127 @ SV248 @ SV303 ) )
= $true )
| ( ( ~ ! [SY722: nat] : ( SV303 @ SY722 @ ( suc @ SY722 ) )
| ( SV303 @ SV127 @ SV248 ) )
= $true )
| ( ( SV303 @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV248 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2530]) ).
thf(2609,plain,
! [SV248: nat,SV127: nat,SV303: nat > nat > $o] :
( ( ( ~ ( SV303 @ ( sK54_SY730 @ SV127 @ SV248 @ SV303 ) @ ( sK62_SY734 @ SV127 @ SV248 @ SV303 ) ) )
= $false )
| ( ( ~ ! [SY722: nat] : ( SV303 @ SY722 @ ( suc @ SY722 ) )
| ( SV303 @ SV127 @ SV248 ) )
= $true )
| ( ( SV303 @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV248 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2531]) ).
thf(2610,plain,
! [SV127: nat,SV248: nat,SV303: nat > nat > $o] :
( ( ( SV303 @ ( sK48_SY719 @ SV248 @ SV127 @ SV303 ) @ ( sK62_SY734 @ SV127 @ SV248 @ SV303 ) )
= $false )
| ( ( ~ ! [SY722: nat] : ( SV303 @ SY722 @ ( suc @ SY722 ) )
| ( SV303 @ SV127 @ SV248 ) )
= $true )
| ( ( SV303 @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV248 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2531]) ).
thf(2611,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ord_less_real @ SV128 @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2532]) ).
thf(2612,plain,
! [SV128: real,SV249: real] :
( ( ( ~ ( ord_less_real @ SV249 @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2532]) ).
thf(2613,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ord_less_real @ SV128 @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2533]) ).
thf(2614,plain,
! [SV128: real,SV249: real] :
( ( ( ~ ( ord_less_real @ SV249 @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2533]) ).
thf(2615,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2535]) ).
thf(2616,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ SV128 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV249 @ zero_zero_real )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2537]) ).
thf(2617,plain,
! [SV251: nat,SV133: nat] :
( ( ( SV133
!= ( suc @ ( sK55_SY686 @ SV251 @ SV133 ) ) )
= $false )
| ( ( SV133 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2538]) ).
thf(2618,plain,
! [SV133: nat,SV251: nat] :
( ( ( ~ ( ord_less_nat @ ( sK55_SY686 @ SV251 @ SV133 ) @ SV251 ) )
= $false )
| ( ( SV133 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2538]) ).
thf(2619,plain,
! [SV251: nat,SV133: nat] :
( ( ( ( SV133
!= ( suc @ ( sK63_SY686 @ SV251 @ SV133 ) ) )
| ~ ( ord_less_nat @ ( sK63_SY686 @ SV251 @ SV133 ) @ SV251 ) )
= $false )
| ( ( SV133 = zero_zero_nat )
= $true )
| ( ( SV133 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2539]) ).
thf(2620,plain,
! [SV319: nat,SV251: nat,SV133: nat] :
( ( ( ~ ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
| ~ ( ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) ) )
= $false )
| ( ( SV133
= ( suc @ SV319 ) )
= $false )
| ( ( ord_less_nat @ SV319 @ SV251 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2540]) ).
thf(2621,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ord_less_real @ SV141 @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2541]) ).
thf(2622,plain,
! [SV141: real,SV257: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV257 ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2541]) ).
thf(2623,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ord_less_real @ SV141 @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2542]) ).
thf(2624,plain,
! [SV141: real,SV257: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV257 ) )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2542]) ).
thf(2625,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2544]) ).
thf(2626,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) )
= $true )
| ( ( ord_less_real @ SV141 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV257 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2546]) ).
thf(2627,plain,
! [SV312: nat,SV178: nat > $o,SV47: nat] :
( ( ( ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) ) )
= $true )
| ( ( ord_less_nat @ SV312 @ ( suc @ SV47 ) )
= $false )
| ( ( SV178 @ SV312 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2548]) ).
thf(2628,plain,
! [SV312: nat,SV47: nat,SV178: nat > $o] :
( ( ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV312 @ ( suc @ SV47 ) )
= $false )
| ( ( SV178 @ SV312 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2549]) ).
thf(2629,plain,
! [SV47: nat,SV178: nat > $o] :
( ( ( ord_less_nat @ ( sK49_SY601 @ SV178 @ SV47 ) @ ( suc @ SV47 ) )
= $true )
| ( ( SV178 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2550]) ).
thf(2630,plain,
! [SV47: nat,SV178: nat > $o] :
( ( ( SV178 @ ( sK49_SY601 @ SV178 @ SV47 ) )
= $true )
| ( ( SV178 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2551]) ).
thf(2631,plain,
! [SV47: nat,SV178: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK57_SY602 @ SV178 @ SV47 ) @ SV47 ) )
= $false )
| ( ( SV178 @ zero_zero_nat )
= $true )
| ( ( SV178 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2552]) ).
thf(2632,plain,
! [SV47: nat,SV178: nat > $o] :
( ( ( ~ ( SV178 @ ( suc @ ( sK57_SY602 @ SV178 @ SV47 ) ) ) )
= $false )
| ( ( SV178 @ zero_zero_nat )
= $true )
| ( ( SV178 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2552]) ).
thf(2633,plain,
! [SV317: nat,SV178: nat > $o,SV47: nat] :
( ( ( ~ ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) ) )
= $false )
| ( ( ord_less_nat @ SV317 @ SV47 )
= $false )
| ( ( SV178 @ ( suc @ SV317 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2553]) ).
thf(2634,plain,
! [SV317: nat,SV47: nat,SV178: nat > $o] :
( ( ( ~ ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ SV317 @ SV47 )
= $false )
| ( ( SV178 @ ( suc @ SV317 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2553]) ).
thf(2635,plain,
! [SV274: real,SV182: real,SV51: real] :
( ( ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
| ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2556]) ).
thf(2636,plain,
! [SV274: real,SV182: real,SV51: real] :
( ( ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2557]) ).
thf(2637,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2557]) ).
thf(2638,plain,
! [SV274: real,SV182: real,SV51: real] :
( ( ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) ) )
= $false )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2558]) ).
thf(2639,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) )
= $false )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2558]) ).
thf(2640,plain,
! [SV274: real,SV182: real,SV51: real] :
( ( ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
= $true )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2559]) ).
thf(2641,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) )
= $true )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2560]) ).
thf(2642,plain,
! [SV191: nat,SV61: real] :
( ( ( SV61 = zero_zero_real )
= $true )
| ( ( SV61 = zero_zero_real )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2561]) ).
thf(2643,plain,
! [SV61: real,SV191: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV191 )
= $true )
| ( ( SV61 = zero_zero_real )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2562]) ).
thf(2644,plain,
! [SV192: real,SV62: nat,SV322: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV322 )
| ( ( power_power_real @ SV322 @ SV62 )
!= SV192 ) )
= $true )
| ( ( SV322
= ( sK31_SY616 @ SV192 @ SV62 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV192 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2565]) ).
thf(2645,plain,
! [SV206: nat,SV78: nat,SV284: nat > $o] :
( ( ( SV284 @ ( suc @ ( sK58_SY700 @ SV78 @ SV284 @ SV206 ) ) )
= $true )
| ( ( SV284 @ SV78 )
= $true )
| ( ( SV206
= ( suc @ ( sK32_SY699 @ SV78 @ SV284 @ SV206 ) ) )
= $true )
| ( ( ord_less_nat @ SV78 @ SV206 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2567]) ).
thf(2646,plain,
! [SV207: nat,SV79: nat,SV285: nat > nat > $o] :
( ( ( ord_less_nat @ ( sK51_SY728 @ SV285 @ SV79 @ SV207 ) @ ( sK59_SY732 @ SV285 @ SV79 @ SV207 ) )
= $true )
| ( ( SV285 @ SV79 @ SV207 )
= $true )
| ( ( SV285 @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) @ ( suc @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) ) )
= $false )
| ( ( ord_less_nat @ SV79 @ SV207 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2571]) ).
thf(2647,plain,
! [SV79: nat,SV207: nat,SV285: nat > nat > $o] :
( ( ( ~ ( SV285 @ ( sK43_SY702 @ SV207 @ SV79 @ SV285 ) @ ( sK51_SY728 @ SV285 @ SV79 @ SV207 ) ) )
= $false )
| ( ( SV285 @ SV79 @ SV207 )
= $true )
| ( ( SV285 @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) @ ( suc @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) ) )
= $false )
| ( ( ord_less_nat @ SV79 @ SV207 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2572]) ).
thf(2648,plain,
! [SV207: nat,SV79: nat,SV285: nat > nat > $o] :
( ( ( ~ ( SV285 @ ( sK51_SY728 @ SV285 @ SV79 @ SV207 ) @ ( sK59_SY732 @ SV285 @ SV79 @ SV207 ) )
| ( SV285 @ ( sK43_SY702 @ SV207 @ SV79 @ SV285 ) @ ( sK59_SY732 @ SV285 @ SV79 @ SV207 ) ) )
= $false )
| ( ( SV285 @ SV79 @ SV207 )
= $true )
| ( ( SV285 @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) @ ( suc @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) ) )
= $false )
| ( ( ord_less_nat @ SV79 @ SV207 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2572]) ).
thf(2649,plain,
! [SV214: nat > $o,SV87: nat,SV327: nat] :
( ( ( ~ ( ord_less_nat @ SV327 @ SV87 )
| ( SV214 @ ( suc @ SV327 ) ) )
= $true )
| ( ( ord_less_nat @ ( sK27_SY649 @ SV214 @ SV87 ) @ ( suc @ SV87 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2576]) ).
thf(2650,plain,
! [SV214: nat > $o,SV87: nat,SV325: nat] :
( ( ( ~ ( ord_less_nat @ SV325 @ SV87 ) )
= $true )
| ( ( SV214 @ ( suc @ SV325 ) )
= $true )
| ( ( SV214 @ ( sK27_SY649 @ SV214 @ SV87 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2577]) ).
thf(2651,plain,
! [SV214: nat > $o,SV87: nat] :
( ( ( ! [SY649: nat] :
( ~ ( ord_less_nat @ SY649 @ ( suc @ SV87 ) )
| ( SV214 @ SY649 ) ) )
= $true )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK44_SY650 @ SV214 @ SV87 ) @ SV87 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2578]) ).
thf(2652,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( ~ ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) ) )
= $true )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK44_SY650 @ SV214 @ SV87 ) @ SV87 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2579]) ).
thf(2653,plain,
! [SV214: nat > $o,SV87: nat,SV328: nat] :
( ( ( ~ ( ord_less_nat @ SV328 @ ( suc @ SV87 ) )
| ( SV214 @ SV328 ) )
= $true )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( SV214 @ ( suc @ ( sK44_SY650 @ SV214 @ SV87 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2580]) ).
thf(2654,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) )
= $false )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( SV214 @ ( suc @ ( sK44_SY650 @ SV214 @ SV87 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2581]) ).
thf(2655,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2582]) ).
thf(2656,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2583]) ).
thf(2657,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( ~ ( ( SV228 != zero_zero_real ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2584]) ).
thf(2658,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ord_less_real @ SV228 @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( ~ ( ( SV228 != zero_zero_real ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2585]) ).
thf(2659,plain,
! [SV228: real,SV103: real,SV297: real] :
( ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( ~ ( ( SV228 != zero_zero_real ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2585]) ).
thf(2660,plain,
! [SV314: nat,SV233: nat > $o,SV110: nat] :
( ( ( ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) ) )
= $true )
| ( ( ord_less_nat @ SV314 @ ( suc @ SV110 ) )
= $false )
| ( ( SV233 @ SV314 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2586]) ).
thf(2661,plain,
! [SV314: nat,SV110: nat,SV233: nat > $o] :
( ( ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) )
= $true )
| ( ( ord_less_nat @ SV314 @ ( suc @ SV110 ) )
= $false )
| ( ( SV233 @ SV314 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2587]) ).
thf(2662,plain,
! [SV110: nat,SV233: nat > $o] :
( ( ( ord_less_nat @ ( sK53_SY665 @ SV233 @ SV110 ) @ ( suc @ SV110 ) )
= $true )
| ( ( SV233 @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2588]) ).
thf(2663,plain,
! [SV110: nat,SV233: nat > $o] :
( ( ( SV233 @ ( sK53_SY665 @ SV233 @ SV110 ) )
= $true )
| ( ( SV233 @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2589]) ).
thf(2664,plain,
! [SV110: nat,SV233: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK61_SY666 @ SV233 @ SV110 ) @ SV110 ) )
= $false )
| ( ( SV233 @ SV110 )
= $true )
| ( ( SV233 @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2590]) ).
thf(2665,plain,
! [SV110: nat,SV233: nat > $o] :
( ( ( ~ ( SV233 @ ( sK61_SY666 @ SV233 @ SV110 ) ) )
= $false )
| ( ( SV233 @ SV110 )
= $true )
| ( ( SV233 @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2590]) ).
thf(2666,plain,
! [SV318: nat,SV233: nat > $o,SV110: nat] :
( ( ( ~ ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) ) )
= $false )
| ( ( ord_less_nat @ SV318 @ SV110 )
= $false )
| ( ( SV233 @ SV318 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2591]) ).
thf(2667,plain,
! [SV318: nat,SV110: nat,SV233: nat > $o] :
( ( ( ~ ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV318 @ SV110 )
= $false )
| ( ( SV233 @ SV318 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2591]) ).
thf(2668,plain,
! [SV315: nat,SV113: nat > $o] :
( ( ( SV113 @ ( sK45_SY536 @ SV315 @ SV113 ) )
= $false )
| ( ( SV113 @ SV315 )
= $false )
| ( ( SV113 @ zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2592]) ).
thf(2669,plain,
! [SV239: nat > $o,SV117: nat,SV329: nat] :
( ( ( ~ ( ord_less_nat @ SV329 @ SV117 )
| ( SV239 @ SV329 ) )
= $true )
| ( ( ord_less_nat @ ( sK30_SY669 @ SV239 @ SV117 ) @ ( suc @ SV117 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2596]) ).
thf(2670,plain,
! [SV239: nat > $o,SV117: nat,SV326: nat] :
( ( ( ~ ( ord_less_nat @ SV326 @ SV117 ) )
= $true )
| ( ( SV239 @ SV326 )
= $true )
| ( ( SV239 @ ( sK30_SY669 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2597]) ).
thf(2671,plain,
! [SV239: nat > $o,SV117: nat] :
( ( ( ! [SY669: nat] :
( ~ ( ord_less_nat @ SY669 @ ( suc @ SV117 ) )
| ( SV239 @ SY669 ) ) )
= $true )
| ( ( SV239 @ SV117 )
= $false )
| ( ( ord_less_nat @ ( sK46_SY670 @ SV239 @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2598]) ).
thf(2672,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( ~ ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) ) )
= $true )
| ( ( SV239 @ SV117 )
= $false )
| ( ( ord_less_nat @ ( sK46_SY670 @ SV239 @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2599]) ).
thf(2673,plain,
! [SV239: nat > $o,SV117: nat,SV330: nat] :
( ( ( ~ ( ord_less_nat @ SV330 @ ( suc @ SV117 ) )
| ( SV239 @ SV330 ) )
= $true )
| ( ( SV239 @ SV117 )
= $false )
| ( ( SV239 @ ( sK46_SY670 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2600]) ).
thf(2674,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) )
= $false )
| ( ( SV239 @ SV117 )
= $false )
| ( ( SV239 @ ( sK46_SY670 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2601]) ).
thf(2675,plain,
! [SV244: nat,SV122: nat > $o] :
( ( ( ord_less_nat @ ( sK38_SY677 @ SV122 @ SV244 ) @ SV244 )
= $true )
| ( ( SV122 @ zero_zero_nat )
= $true )
| ( ( SV122 @ SV244 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2602]) ).
thf(2676,plain,
! [SV244: nat,SV122: nat > $o] :
( ( ( ! [SY727: nat] :
( ~ ( ord_less_eq_nat @ SY727 @ ( sK38_SY677 @ SV122 @ SV244 ) )
| ~ ( SV122 @ SY727 ) ) )
= $true )
| ( ( SV122 @ zero_zero_nat )
= $true )
| ( ( SV122 @ SV244 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2603]) ).
thf(2677,plain,
! [SV316: nat,SV245: nat,SV123: nat] :
( ( ( ord_less_nat @ ( suc @ SV123 ) @ SV245 )
= $true )
| ( ( SV245
= ( suc @ SV316 ) )
= $false )
| ( ( ord_less_nat @ SV123 @ SV316 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2606]) ).
thf(2678,plain,
! [SV316: nat,SV123: nat,SV245: nat] :
( ( ( ~ ! [SY679: nat] :
~ ~ ( ( SV245
!= ( suc @ SY679 ) )
| ~ ( ord_less_nat @ SV123 @ SY679 ) ) )
= $true )
| ( ( SV245
= ( suc @ SV316 ) )
= $false )
| ( ( ord_less_nat @ SV123 @ SV316 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2607]) ).
thf(2679,plain,
! [SV248: nat,SV127: nat,SV303: nat > nat > $o] :
( ( ( ~ ! [SY722: nat] : ( SV303 @ SY722 @ ( suc @ SY722 ) ) )
= $true )
| ( ( SV303 @ SV127 @ SV248 )
= $true )
| ( ( SV303 @ ( sK48_SY719 @ SV248 @ SV127 @ SV303 ) @ ( sK54_SY730 @ SV127 @ SV248 @ SV303 ) )
= $true )
| ( ( SV303 @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV248 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2608]) ).
thf(2680,plain,
! [SV248: nat,SV127: nat,SV303: nat > nat > $o] :
( ( ( SV303 @ ( sK54_SY730 @ SV127 @ SV248 @ SV303 ) @ ( sK62_SY734 @ SV127 @ SV248 @ SV303 ) )
= $true )
| ( ( ~ ! [SY722: nat] : ( SV303 @ SY722 @ ( suc @ SY722 ) )
| ( SV303 @ SV127 @ SV248 ) )
= $true )
| ( ( SV303 @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV248 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2609]) ).
thf(2681,plain,
! [SV248: nat,SV127: nat,SV303: nat > nat > $o] :
( ( ( ~ ! [SY722: nat] : ( SV303 @ SY722 @ ( suc @ SY722 ) ) )
= $true )
| ( ( SV303 @ SV127 @ SV248 )
= $true )
| ( ( SV303 @ ( sK48_SY719 @ SV248 @ SV127 @ SV303 ) @ ( sK62_SY734 @ SV127 @ SV248 @ SV303 ) )
= $false )
| ( ( SV303 @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV248 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2610]) ).
thf(2682,plain,
! [SV249: real,SV128: real] :
( ( ( ord_less_real @ SV128 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2611]) ).
thf(2683,plain,
! [SV128: real,SV249: real] :
( ( ( ord_less_real @ SV249 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2612]) ).
thf(2684,plain,
! [SV249: real,SV128: real] :
( ( ( ord_less_real @ SV128 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2613]) ).
thf(2685,plain,
! [SV128: real,SV249: real] :
( ( ( ord_less_real @ SV249 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ SV128 @ SV249 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2614]) ).
thf(2686,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2615]) ).
thf(2687,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV128 )
| ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ SV128 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV249 @ zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2616]) ).
thf(2688,plain,
! [SV251: nat,SV133: nat] :
( ( ( SV133
= ( suc @ ( sK55_SY686 @ SV251 @ SV133 ) ) )
= $true )
| ( ( SV133 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2617]) ).
thf(2689,plain,
! [SV133: nat,SV251: nat] :
( ( ( ord_less_nat @ ( sK55_SY686 @ SV251 @ SV133 ) @ SV251 )
= $true )
| ( ( SV133 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2618]) ).
thf(2690,plain,
! [SV251: nat,SV133: nat] :
( ( ( SV133
!= ( suc @ ( sK63_SY686 @ SV251 @ SV133 ) ) )
= $false )
| ( ( SV133 = zero_zero_nat )
= $true )
| ( ( SV133 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2619]) ).
thf(2691,plain,
! [SV133: nat,SV251: nat] :
( ( ( ~ ( ord_less_nat @ ( sK63_SY686 @ SV251 @ SV133 ) @ SV251 ) )
= $false )
| ( ( SV133 = zero_zero_nat )
= $true )
| ( ( SV133 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2619]) ).
thf(2692,plain,
! [SV319: nat,SV251: nat,SV133: nat] :
( ( ( ~ ( ord_less_nat @ SV133 @ ( suc @ SV251 ) ) )
= $false )
| ( ( SV133
= ( suc @ SV319 ) )
= $false )
| ( ( ord_less_nat @ SV319 @ SV251 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2620]) ).
thf(2693,plain,
! [SV319: nat,SV251: nat,SV133: nat] :
( ( ( ~ ( ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) ) )
= $false )
| ( ( SV133
= ( suc @ SV319 ) )
= $false )
| ( ( ord_less_nat @ SV319 @ SV251 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2620]) ).
thf(2694,plain,
! [SV257: real,SV141: real] :
( ( ( ord_less_real @ SV141 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2621]) ).
thf(2695,plain,
! [SV141: real,SV257: real] :
( ( ( ord_less_real @ zero_zero_real @ SV257 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2622]) ).
thf(2696,plain,
! [SV257: real,SV141: real] :
( ( ( ord_less_real @ SV141 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2623]) ).
thf(2697,plain,
! [SV141: real,SV257: real] :
( ( ( ord_less_real @ zero_zero_real @ SV257 )
= $true )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV141 @ SV257 ) @ zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2624]) ).
thf(2698,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2625]) ).
thf(2699,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV141 )
| ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) )
= $true )
| ( ( ord_less_real @ SV141 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV257 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2626]) ).
thf(2700,plain,
! [SV312: nat,SV178: nat > $o,SV47: nat] :
( ( ( ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) ) )
= $false )
| ( ( ord_less_nat @ SV312 @ ( suc @ SV47 ) )
= $false )
| ( ( SV178 @ SV312 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2627]) ).
thf(2701,plain,
! [SV312: nat,SV47: nat,SV178: nat > $o] :
( ( ( SV178 @ zero_zero_nat )
= $true )
| ( ( ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV312 @ ( suc @ SV47 ) )
= $false )
| ( ( SV178 @ SV312 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2628]) ).
thf(2702,plain,
! [SV47: nat,SV178: nat > $o] :
( ( ( ord_less_nat @ ( sK57_SY602 @ SV178 @ SV47 ) @ SV47 )
= $true )
| ( ( SV178 @ zero_zero_nat )
= $true )
| ( ( SV178 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2631]) ).
thf(2703,plain,
! [SV47: nat,SV178: nat > $o] :
( ( ( SV178 @ ( suc @ ( sK57_SY602 @ SV178 @ SV47 ) ) )
= $true )
| ( ( SV178 @ zero_zero_nat )
= $true )
| ( ( SV178 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2632]) ).
thf(2704,plain,
! [SV317: nat,SV178: nat > $o,SV47: nat] :
( ( ( ~ ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) ) )
= $true )
| ( ( ord_less_nat @ SV317 @ SV47 )
= $false )
| ( ( SV178 @ ( suc @ SV317 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2633]) ).
thf(2705,plain,
! [SV317: nat,SV47: nat,SV178: nat > $o] :
( ( ( ( SV178 @ zero_zero_nat )
| ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV317 @ SV47 )
= $false )
| ( ( SV178 @ ( suc @ SV317 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2634]) ).
thf(2706,plain,
! [SV274: real,SV182: real,SV51: real] :
( ( ( ~ ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2635]) ).
thf(2707,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2635]) ).
thf(2708,plain,
! [SV274: real,SV182: real,SV51: real] :
( ( ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2636]) ).
thf(2709,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2637]) ).
thf(2710,plain,
! [SV274: real,SV182: real,SV51: real] :
( ( ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
= $true )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2638]) ).
thf(2711,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) )
= $true )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2639]) ).
thf(2712,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) )
= $false )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2641]) ).
thf(2713,plain,
! [SV192: real,SV62: nat,SV322: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV322 ) )
= $true )
| ( ( ( power_power_real @ SV322 @ SV62 )
!= SV192 )
= $true )
| ( ( SV322
= ( sK31_SY616 @ SV192 @ SV62 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV192 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2644]) ).
thf(2714,plain,
! [SV79: nat,SV207: nat,SV285: nat > nat > $o] :
( ( ( SV285 @ ( sK43_SY702 @ SV207 @ SV79 @ SV285 ) @ ( sK51_SY728 @ SV285 @ SV79 @ SV207 ) )
= $true )
| ( ( SV285 @ SV79 @ SV207 )
= $true )
| ( ( SV285 @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) @ ( suc @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) ) )
= $false )
| ( ( ord_less_nat @ SV79 @ SV207 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2647]) ).
thf(2715,plain,
! [SV207: nat,SV79: nat,SV285: nat > nat > $o] :
( ( ( ~ ( SV285 @ ( sK51_SY728 @ SV285 @ SV79 @ SV207 ) @ ( sK59_SY732 @ SV285 @ SV79 @ SV207 ) ) )
= $false )
| ( ( SV285 @ SV79 @ SV207 )
= $true )
| ( ( SV285 @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) @ ( suc @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) ) )
= $false )
| ( ( ord_less_nat @ SV79 @ SV207 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2648]) ).
thf(2716,plain,
! [SV79: nat,SV207: nat,SV285: nat > nat > $o] :
( ( ( SV285 @ ( sK43_SY702 @ SV207 @ SV79 @ SV285 ) @ ( sK59_SY732 @ SV285 @ SV79 @ SV207 ) )
= $false )
| ( ( SV285 @ SV79 @ SV207 )
= $true )
| ( ( SV285 @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) @ ( suc @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) ) )
= $false )
| ( ( ord_less_nat @ SV79 @ SV207 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2648]) ).
thf(2717,plain,
! [SV214: nat > $o,SV87: nat,SV327: nat] :
( ( ( ~ ( ord_less_nat @ SV327 @ SV87 ) )
= $true )
| ( ( SV214 @ ( suc @ SV327 ) )
= $true )
| ( ( ord_less_nat @ ( sK27_SY649 @ SV214 @ SV87 ) @ ( suc @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2649]) ).
thf(2718,plain,
! [SV214: nat > $o,SV87: nat,SV325: nat] :
( ( ( ord_less_nat @ SV325 @ SV87 )
= $false )
| ( ( SV214 @ ( suc @ SV325 ) )
= $true )
| ( ( SV214 @ ( sK27_SY649 @ SV214 @ SV87 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2650]) ).
thf(2719,plain,
! [SV214: nat > $o,SV87: nat,SV331: nat] :
( ( ( ~ ( ord_less_nat @ SV331 @ ( suc @ SV87 ) )
| ( SV214 @ SV331 ) )
= $true )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK44_SY650 @ SV214 @ SV87 ) @ SV87 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2651]) ).
thf(2720,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( ~ ( SV214 @ zero_zero_nat )
| ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) )
= $false )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK44_SY650 @ SV214 @ SV87 ) @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2652]) ).
thf(2721,plain,
! [SV214: nat > $o,SV87: nat,SV328: nat] :
( ( ( ~ ( ord_less_nat @ SV328 @ ( suc @ SV87 ) ) )
= $true )
| ( ( SV214 @ SV328 )
= $true )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( SV214 @ ( suc @ ( sK44_SY650 @ SV214 @ SV87 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2653]) ).
thf(2722,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( ~ ( SV214 @ zero_zero_nat ) )
= $false )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( SV214 @ ( suc @ ( sK44_SY650 @ SV214 @ SV87 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2654]) ).
thf(2723,plain,
! [SV214: nat > $o,SV87: nat] :
( ( ( ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) )
= $false )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( SV214 @ ( suc @ ( sK44_SY650 @ SV214 @ SV87 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2654]) ).
thf(2724,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV228 ) )
= $true )
| ( ( ord_less_real @ SV103 @ SV297 )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2655]) ).
thf(2725,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( ~ ( ord_less_real @ SV228 @ zero_zero_real ) )
= $true )
| ( ( ord_less_real @ SV297 @ SV103 )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2656]) ).
thf(2726,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ord_less_real @ SV228 @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( ~ ( ( SV228 != zero_zero_real ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2657]) ).
thf(2727,plain,
! [SV228: real,SV103: real,SV297: real] :
( ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( ~ ( ( SV228 != zero_zero_real ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2657]) ).
thf(2728,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( ~ ( ( SV228 != zero_zero_real ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2658]) ).
thf(2729,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( SV228 != zero_zero_real )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2659]) ).
thf(2730,plain,
! [SV314: nat,SV233: nat > $o,SV110: nat] :
( ( ( ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) ) )
= $false )
| ( ( ord_less_nat @ SV314 @ ( suc @ SV110 ) )
= $false )
| ( ( SV233 @ SV314 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2660]) ).
thf(2731,plain,
! [SV314: nat,SV110: nat,SV233: nat > $o] :
( ( ( SV233 @ SV110 )
= $true )
| ( ( ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) )
= $true )
| ( ( ord_less_nat @ SV314 @ ( suc @ SV110 ) )
= $false )
| ( ( SV233 @ SV314 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2661]) ).
thf(2732,plain,
! [SV110: nat,SV233: nat > $o] :
( ( ( ord_less_nat @ ( sK61_SY666 @ SV233 @ SV110 ) @ SV110 )
= $true )
| ( ( SV233 @ SV110 )
= $true )
| ( ( SV233 @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2664]) ).
thf(2733,plain,
! [SV110: nat,SV233: nat > $o] :
( ( ( SV233 @ ( sK61_SY666 @ SV233 @ SV110 ) )
= $true )
| ( ( SV233 @ SV110 )
= $true )
| ( ( SV233 @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2665]) ).
thf(2734,plain,
! [SV318: nat,SV233: nat > $o,SV110: nat] :
( ( ( ~ ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) ) )
= $true )
| ( ( ord_less_nat @ SV318 @ SV110 )
= $false )
| ( ( SV233 @ SV318 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2666]) ).
thf(2735,plain,
! [SV318: nat,SV110: nat,SV233: nat > $o] :
( ( ( ( SV233 @ SV110 )
| ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) )
= $true )
| ( ( ord_less_nat @ SV318 @ SV110 )
= $false )
| ( ( SV233 @ SV318 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2667]) ).
thf(2736,plain,
! [SV239: nat > $o,SV117: nat,SV329: nat] :
( ( ( ~ ( ord_less_nat @ SV329 @ SV117 ) )
= $true )
| ( ( SV239 @ SV329 )
= $true )
| ( ( ord_less_nat @ ( sK30_SY669 @ SV239 @ SV117 ) @ ( suc @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2669]) ).
thf(2737,plain,
! [SV239: nat > $o,SV117: nat,SV326: nat] :
( ( ( ord_less_nat @ SV326 @ SV117 )
= $false )
| ( ( SV239 @ SV326 )
= $true )
| ( ( SV239 @ ( sK30_SY669 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2670]) ).
thf(2738,plain,
! [SV239: nat > $o,SV117: nat,SV332: nat] :
( ( ( ~ ( ord_less_nat @ SV332 @ ( suc @ SV117 ) )
| ( SV239 @ SV332 ) )
= $true )
| ( ( SV239 @ SV117 )
= $false )
| ( ( ord_less_nat @ ( sK46_SY670 @ SV239 @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2671]) ).
thf(2739,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( ~ ( SV239 @ SV117 )
| ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) )
= $false )
| ( ( SV239 @ SV117 )
= $false )
| ( ( ord_less_nat @ ( sK46_SY670 @ SV239 @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2672]) ).
thf(2740,plain,
! [SV239: nat > $o,SV117: nat,SV330: nat] :
( ( ( ~ ( ord_less_nat @ SV330 @ ( suc @ SV117 ) ) )
= $true )
| ( ( SV239 @ SV330 )
= $true )
| ( ( SV239 @ SV117 )
= $false )
| ( ( SV239 @ ( sK46_SY670 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2673]) ).
thf(2741,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( ~ ( SV239 @ SV117 ) )
= $false )
| ( ( SV239 @ SV117 )
= $false )
| ( ( SV239 @ ( sK46_SY670 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2674]) ).
thf(2742,plain,
! [SV239: nat > $o,SV117: nat] :
( ( ( ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) )
= $false )
| ( ( SV239 @ SV117 )
= $false )
| ( ( SV239 @ ( sK46_SY670 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2674]) ).
thf(2743,plain,
! [SV244: nat,SV122: nat > $o,SV333: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV333 @ ( sK38_SY677 @ SV122 @ SV244 ) )
| ~ ( SV122 @ SV333 ) )
= $true )
| ( ( SV122 @ zero_zero_nat )
= $true )
| ( ( SV122 @ SV244 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2676]) ).
thf(2744,plain,
! [SV316: nat,SV123: nat,SV245: nat] :
( ( ( ! [SY679: nat] :
~ ~ ( ( SV245
!= ( suc @ SY679 ) )
| ~ ( ord_less_nat @ SV123 @ SY679 ) ) )
= $false )
| ( ( SV245
= ( suc @ SV316 ) )
= $false )
| ( ( ord_less_nat @ SV123 @ SV316 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2678]) ).
thf(2745,plain,
! [SV248: nat,SV127: nat,SV303: nat > nat > $o] :
( ( ( ! [SY722: nat] : ( SV303 @ SY722 @ ( suc @ SY722 ) ) )
= $false )
| ( ( SV303 @ SV127 @ SV248 )
= $true )
| ( ( SV303 @ ( sK48_SY719 @ SV248 @ SV127 @ SV303 ) @ ( sK54_SY730 @ SV127 @ SV248 @ SV303 ) )
= $true )
| ( ( SV303 @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV248 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2679]) ).
thf(2746,plain,
! [SV248: nat,SV127: nat,SV303: nat > nat > $o] :
( ( ( ~ ! [SY722: nat] : ( SV303 @ SY722 @ ( suc @ SY722 ) ) )
= $true )
| ( ( SV303 @ SV127 @ SV248 )
= $true )
| ( ( SV303 @ ( sK54_SY730 @ SV127 @ SV248 @ SV303 ) @ ( sK62_SY734 @ SV127 @ SV248 @ SV303 ) )
= $true )
| ( ( SV303 @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV248 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2680]) ).
thf(2747,plain,
! [SV248: nat,SV127: nat,SV303: nat > nat > $o] :
( ( ( ! [SY722: nat] : ( SV303 @ SY722 @ ( suc @ SY722 ) ) )
= $false )
| ( ( SV303 @ SV127 @ SV248 )
= $true )
| ( ( SV303 @ ( sK48_SY719 @ SV248 @ SV127 @ SV303 ) @ ( sK62_SY734 @ SV127 @ SV248 @ SV303 ) )
= $false )
| ( ( SV303 @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV248 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2681]) ).
thf(2748,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV128 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2686]) ).
thf(2749,plain,
! [SV128: real,SV249: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2686]) ).
thf(2750,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV128 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ SV128 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV249 @ zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2687]) ).
thf(2751,plain,
! [SV128: real,SV249: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV249 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ SV128 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV249 @ zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2687]) ).
thf(2752,plain,
! [SV251: nat,SV133: nat] :
( ( ( SV133
= ( suc @ ( sK63_SY686 @ SV251 @ SV133 ) ) )
= $true )
| ( ( SV133 = zero_zero_nat )
= $true )
| ( ( SV133 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2690]) ).
thf(2753,plain,
! [SV133: nat,SV251: nat] :
( ( ( ord_less_nat @ ( sK63_SY686 @ SV251 @ SV133 ) @ SV251 )
= $true )
| ( ( SV133 = zero_zero_nat )
= $true )
| ( ( SV133 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2691]) ).
thf(2754,plain,
! [SV319: nat,SV251: nat,SV133: nat] :
( ( ( ord_less_nat @ SV133 @ ( suc @ SV251 ) )
= $true )
| ( ( SV133
= ( suc @ SV319 ) )
= $false )
| ( ( ord_less_nat @ SV319 @ SV251 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2692]) ).
thf(2755,plain,
! [SV319: nat,SV251: nat,SV133: nat] :
( ( ( ( SV133 = zero_zero_nat )
| ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) )
= $true )
| ( ( SV133
= ( suc @ SV319 ) )
= $false )
| ( ( ord_less_nat @ SV319 @ SV251 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2693]) ).
thf(2756,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV141 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2698]) ).
thf(2757,plain,
! [SV141: real,SV257: real] :
( ( ( ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2698]) ).
thf(2758,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV141 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) )
= $true )
| ( ( ord_less_real @ SV141 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV257 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2699]) ).
thf(2759,plain,
! [SV141: real,SV257: real] :
( ( ( ~ ( ord_less_real @ SV257 @ zero_zero_real ) )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) )
= $true )
| ( ( ord_less_real @ SV141 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV257 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2699]) ).
thf(2760,plain,
! [SV47: nat,SV178: nat > $o,SV312: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ ( sK64_SY601 @ SV312 @ SV178 @ SV47 ) @ ( suc @ SV47 ) )
| ~ ( SV178 @ ( sK64_SY601 @ SV312 @ SV178 @ SV47 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV312 @ ( suc @ SV47 ) )
= $false )
| ( ( SV178 @ SV312 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2700]) ).
thf(2761,plain,
! [SV312: nat,SV178: nat > $o,SV47: nat] :
( ( ( ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) )
= $false )
| ( ( SV178 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV312 @ ( suc @ SV47 ) )
= $false )
| ( ( SV178 @ SV312 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2701]) ).
thf(2762,plain,
! [SV317: nat,SV178: nat > $o,SV47: nat] :
( ( ( ! [SY601: nat] :
~ ~ ( ~ ( ord_less_nat @ SY601 @ ( suc @ SV47 ) )
| ~ ( SV178 @ SY601 ) ) )
= $false )
| ( ( ord_less_nat @ SV317 @ SV47 )
= $false )
| ( ( SV178 @ ( suc @ SV317 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2704]) ).
thf(2763,plain,
! [SV317: nat,SV47: nat,SV178: nat > $o] :
( ( ( SV178 @ zero_zero_nat )
= $true )
| ( ( ~ ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV317 @ SV47 )
= $false )
| ( ( SV178 @ ( suc @ SV317 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2705]) ).
thf(2764,plain,
! [SV274: real,SV182: real,SV51: real] :
( ( ( ord_less_eq_real @ ( divide_divide_real @ SV51 @ SV182 ) @ ( divide_divide_real @ SV274 @ SV182 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2706]) ).
thf(2765,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2707]) ).
thf(2766,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2709]) ).
thf(2767,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) )
= $false )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2711]) ).
thf(2768,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) ) )
= $false )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2712]) ).
thf(2769,plain,
! [SV51: real,SV274: real,SV182: real] :
( ( ( ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) )
= $false )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2712]) ).
thf(2770,plain,
! [SV192: real,SV62: nat,SV322: real] :
( ( ( ord_less_real @ zero_zero_real @ SV322 )
= $false )
| ( ( ( power_power_real @ SV322 @ SV62 )
!= SV192 )
= $true )
| ( ( SV322
= ( sK31_SY616 @ SV192 @ SV62 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV192 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2713]) ).
thf(2771,plain,
! [SV207: nat,SV79: nat,SV285: nat > nat > $o] :
( ( ( SV285 @ ( sK51_SY728 @ SV285 @ SV79 @ SV207 ) @ ( sK59_SY732 @ SV285 @ SV79 @ SV207 ) )
= $true )
| ( ( SV285 @ SV79 @ SV207 )
= $true )
| ( ( SV285 @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) @ ( suc @ ( sK33_SY701 @ SV207 @ SV79 @ SV285 ) ) )
= $false )
| ( ( ord_less_nat @ SV79 @ SV207 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2715]) ).
thf(2772,plain,
! [SV214: nat > $o,SV87: nat,SV327: nat] :
( ( ( ord_less_nat @ SV327 @ SV87 )
= $false )
| ( ( SV214 @ ( suc @ SV327 ) )
= $true )
| ( ( ord_less_nat @ ( sK27_SY649 @ SV214 @ SV87 ) @ ( suc @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2717]) ).
thf(2773,plain,
! [SV214: nat > $o,SV87: nat,SV331: nat] :
( ( ( ~ ( ord_less_nat @ SV331 @ ( suc @ SV87 ) ) )
= $true )
| ( ( SV214 @ SV331 )
= $true )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK44_SY650 @ SV214 @ SV87 ) @ SV87 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2719]) ).
thf(2774,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( ~ ( SV214 @ zero_zero_nat ) )
= $false )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK44_SY650 @ SV214 @ SV87 ) @ SV87 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2720]) ).
thf(2775,plain,
! [SV214: nat > $o,SV87: nat] :
( ( ( ~ ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) )
= $false )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK44_SY650 @ SV214 @ SV87 ) @ SV87 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2720]) ).
thf(2776,plain,
! [SV214: nat > $o,SV87: nat,SV328: nat] :
( ( ( ord_less_nat @ SV328 @ ( suc @ SV87 ) )
= $false )
| ( ( SV214 @ SV328 )
= $true )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( SV214 @ ( suc @ ( sK44_SY650 @ SV214 @ SV87 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2721]) ).
thf(2777,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( SV214 @ zero_zero_nat )
= $true )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( SV214 @ ( suc @ ( sK44_SY650 @ SV214 @ SV87 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2722]) ).
thf(2778,plain,
! [SV214: nat > $o,SV87: nat] :
( ( ( ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) )
= $true )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( SV214 @ ( suc @ ( sK44_SY650 @ SV214 @ SV87 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2723]) ).
thf(2779,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ord_less_real @ zero_zero_real @ SV228 )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2724]) ).
thf(2780,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( ord_less_real @ SV228 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV297 @ SV103 )
= $true )
| ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2725]) ).
thf(2781,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( ~ ( ( SV228 != zero_zero_real ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2726]) ).
thf(2782,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( SV228 != zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2727]) ).
thf(2783,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( SV228 != zero_zero_real )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2728]) ).
thf(2784,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( SV228 = zero_zero_real )
= $true )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2729]) ).
thf(2785,plain,
! [SV110: nat,SV233: nat > $o,SV314: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ ( sK65_SY665 @ SV314 @ SV233 @ SV110 ) @ ( suc @ SV110 ) )
| ~ ( SV233 @ ( sK65_SY665 @ SV314 @ SV233 @ SV110 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV314 @ ( suc @ SV110 ) )
= $false )
| ( ( SV233 @ SV314 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2730]) ).
thf(2786,plain,
! [SV314: nat,SV233: nat > $o,SV110: nat] :
( ( ( ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) )
= $false )
| ( ( SV233 @ SV110 )
= $true )
| ( ( ord_less_nat @ SV314 @ ( suc @ SV110 ) )
= $false )
| ( ( SV233 @ SV314 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2731]) ).
thf(2787,plain,
! [SV318: nat,SV233: nat > $o,SV110: nat] :
( ( ( ! [SY665: nat] :
~ ~ ( ~ ( ord_less_nat @ SY665 @ ( suc @ SV110 ) )
| ~ ( SV233 @ SY665 ) ) )
= $false )
| ( ( ord_less_nat @ SV318 @ SV110 )
= $false )
| ( ( SV233 @ SV318 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2734]) ).
thf(2788,plain,
! [SV318: nat,SV110: nat,SV233: nat > $o] :
( ( ( SV233 @ SV110 )
= $true )
| ( ( ~ ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) )
= $true )
| ( ( ord_less_nat @ SV318 @ SV110 )
= $false )
| ( ( SV233 @ SV318 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2735]) ).
thf(2789,plain,
! [SV239: nat > $o,SV117: nat,SV329: nat] :
( ( ( ord_less_nat @ SV329 @ SV117 )
= $false )
| ( ( SV239 @ SV329 )
= $true )
| ( ( ord_less_nat @ ( sK30_SY669 @ SV239 @ SV117 ) @ ( suc @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2736]) ).
thf(2790,plain,
! [SV239: nat > $o,SV117: nat,SV332: nat] :
( ( ( ~ ( ord_less_nat @ SV332 @ ( suc @ SV117 ) ) )
= $true )
| ( ( SV239 @ SV332 )
= $true )
| ( ( SV239 @ SV117 )
= $false )
| ( ( ord_less_nat @ ( sK46_SY670 @ SV239 @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2738]) ).
thf(2791,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( ~ ( SV239 @ SV117 ) )
= $false )
| ( ( SV239 @ SV117 )
= $false )
| ( ( ord_less_nat @ ( sK46_SY670 @ SV239 @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2739]) ).
thf(2792,plain,
! [SV239: nat > $o,SV117: nat] :
( ( ( ~ ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) )
= $false )
| ( ( SV239 @ SV117 )
= $false )
| ( ( ord_less_nat @ ( sK46_SY670 @ SV239 @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2739]) ).
thf(2793,plain,
! [SV239: nat > $o,SV117: nat,SV330: nat] :
( ( ( ord_less_nat @ SV330 @ ( suc @ SV117 ) )
= $false )
| ( ( SV239 @ SV330 )
= $true )
| ( ( SV239 @ SV117 )
= $false )
| ( ( SV239 @ ( sK46_SY670 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2740]) ).
thf(2794,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( SV239 @ SV117 )
= $true )
| ( ( SV239 @ SV117 )
= $false )
| ( ( SV239 @ ( sK46_SY670 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2741]) ).
thf(2795,plain,
! [SV239: nat > $o,SV117: nat] :
( ( ( ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) )
= $true )
| ( ( SV239 @ SV117 )
= $false )
| ( ( SV239 @ ( sK46_SY670 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2742]) ).
thf(2796,plain,
! [SV244: nat,SV122: nat > $o,SV333: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV333 @ ( sK38_SY677 @ SV122 @ SV244 ) ) )
= $true )
| ( ( ~ ( SV122 @ SV333 ) )
= $true )
| ( ( SV122 @ zero_zero_nat )
= $true )
| ( ( SV122 @ SV244 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2743]) ).
thf(2797,plain,
! [SV123: nat,SV316: nat,SV245: nat] :
( ( ( ~ ~ ( ( SV245
!= ( suc @ ( sK66_SY679 @ SV316 @ SV123 @ SV245 ) ) )
| ~ ( ord_less_nat @ SV123 @ ( sK66_SY679 @ SV316 @ SV123 @ SV245 ) ) ) )
= $false )
| ( ( SV245
= ( suc @ SV316 ) )
= $false )
| ( ( ord_less_nat @ SV123 @ SV316 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2744]) ).
thf(2798,plain,
! [SV127: nat,SV248: nat,SV303: nat > nat > $o] :
( ( ( SV303 @ ( sK67_SY722 @ SV248 @ SV127 @ SV303 ) @ ( suc @ ( sK67_SY722 @ SV248 @ SV127 @ SV303 ) ) )
= $false )
| ( ( SV303 @ SV127 @ SV248 )
= $true )
| ( ( SV303 @ ( sK48_SY719 @ SV248 @ SV127 @ SV303 ) @ ( sK54_SY730 @ SV127 @ SV248 @ SV303 ) )
= $true )
| ( ( SV303 @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV248 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2745]) ).
thf(2799,plain,
! [SV248: nat,SV127: nat,SV303: nat > nat > $o] :
( ( ( ! [SY722: nat] : ( SV303 @ SY722 @ ( suc @ SY722 ) ) )
= $false )
| ( ( SV303 @ SV127 @ SV248 )
= $true )
| ( ( SV303 @ ( sK54_SY730 @ SV127 @ SV248 @ SV303 ) @ ( sK62_SY734 @ SV127 @ SV248 @ SV303 ) )
= $true )
| ( ( SV303 @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV248 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2746]) ).
thf(2800,plain,
! [SV127: nat,SV248: nat,SV303: nat > nat > $o] :
( ( ( SV303 @ ( sK68_SY722 @ SV248 @ SV127 @ SV303 ) @ ( suc @ ( sK68_SY722 @ SV248 @ SV127 @ SV303 ) ) )
= $false )
| ( ( SV303 @ SV127 @ SV248 )
= $true )
| ( ( SV303 @ ( sK48_SY719 @ SV248 @ SV127 @ SV303 ) @ ( sK62_SY734 @ SV127 @ SV248 @ SV303 ) )
= $false )
| ( ( SV303 @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV248 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2747]) ).
thf(2801,plain,
! [SV249: real,SV128: real] :
( ( ( ord_less_real @ zero_zero_real @ SV128 )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2748]) ).
thf(2802,plain,
! [SV128: real,SV249: real] :
( ( ( ord_less_real @ zero_zero_real @ SV249 )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2749]) ).
thf(2803,plain,
! [SV249: real,SV128: real] :
( ( ( ord_less_real @ zero_zero_real @ SV128 )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ SV128 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV249 @ zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2750]) ).
thf(2804,plain,
! [SV128: real,SV249: real] :
( ( ( ord_less_real @ zero_zero_real @ SV249 )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) ) )
= $true )
| ( ( ord_less_real @ SV128 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV249 @ zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2751]) ).
thf(2805,plain,
! [SV319: nat,SV251: nat,SV133: nat] :
( ( ( SV133 = zero_zero_nat )
= $true )
| ( ( ~ ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) )
= $true )
| ( ( SV133
= ( suc @ SV319 ) )
= $false )
| ( ( ord_less_nat @ SV319 @ SV251 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2755]) ).
thf(2806,plain,
! [SV257: real,SV141: real] :
( ( ( ord_less_real @ zero_zero_real @ SV141 )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2756]) ).
thf(2807,plain,
! [SV141: real,SV257: real] :
( ( ( ord_less_real @ SV257 @ zero_zero_real )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2757]) ).
thf(2808,plain,
! [SV257: real,SV141: real] :
( ( ( ord_less_real @ zero_zero_real @ SV141 )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) )
= $true )
| ( ( ord_less_real @ SV141 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV257 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2758]) ).
thf(2809,plain,
! [SV141: real,SV257: real] :
( ( ( ord_less_real @ SV257 @ zero_zero_real )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) ) )
= $true )
| ( ( ord_less_real @ SV141 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV257 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2759]) ).
thf(2810,plain,
! [SV47: nat,SV178: nat > $o,SV312: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ ( sK64_SY601 @ SV312 @ SV178 @ SV47 ) @ ( suc @ SV47 ) )
| ~ ( SV178 @ ( sK64_SY601 @ SV312 @ SV178 @ SV47 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV312 @ ( suc @ SV47 ) )
= $false )
| ( ( SV178 @ SV312 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2760]) ).
thf(2811,plain,
! [SV47: nat,SV178: nat > $o,SV312: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ ( sK69_SY602 @ SV312 @ SV178 @ SV47 ) @ SV47 )
| ~ ( SV178 @ ( suc @ ( sK69_SY602 @ SV312 @ SV178 @ SV47 ) ) ) ) )
= $false )
| ( ( SV178 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV312 @ ( suc @ SV47 ) )
= $false )
| ( ( SV178 @ SV312 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2761]) ).
thf(2812,plain,
! [SV47: nat,SV178: nat > $o,SV317: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ ( sK70_SY601 @ SV317 @ SV178 @ SV47 ) @ ( suc @ SV47 ) )
| ~ ( SV178 @ ( sK70_SY601 @ SV317 @ SV178 @ SV47 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV317 @ SV47 )
= $false )
| ( ( SV178 @ ( suc @ SV317 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2762]) ).
thf(2813,plain,
! [SV317: nat,SV178: nat > $o,SV47: nat] :
( ( ( ! [SY602: nat] :
~ ~ ( ~ ( ord_less_nat @ SY602 @ SV47 )
| ~ ( SV178 @ ( suc @ SY602 ) ) ) )
= $false )
| ( ( SV178 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV317 @ SV47 )
= $false )
| ( ( SV178 @ ( suc @ SV317 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2763]) ).
thf(2814,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
| ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2765]) ).
thf(2815,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2766]) ).
thf(2816,plain,
! [SV51: real,SV274: real,SV182: real] :
( ( ( ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2766]) ).
thf(2817,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) ) )
= $false )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2767]) ).
thf(2818,plain,
! [SV51: real,SV274: real,SV182: real] :
( ( ( ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) )
= $false )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2767]) ).
thf(2819,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
= $true )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2768]) ).
thf(2820,plain,
! [SV51: real,SV274: real,SV182: real] :
( ( ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) )
= $true )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2769]) ).
thf(2821,plain,
! [SV192: real,SV62: nat,SV322: real] :
( ( ( ( power_power_real @ SV322 @ SV62 )
= SV192 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV322 )
= $false )
| ( ( SV322
= ( sK31_SY616 @ SV192 @ SV62 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV192 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2770]) ).
thf(2822,plain,
! [SV214: nat > $o,SV87: nat,SV331: nat] :
( ( ( ord_less_nat @ SV331 @ ( suc @ SV87 ) )
= $false )
| ( ( SV214 @ SV331 )
= $true )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK44_SY650 @ SV214 @ SV87 ) @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2773]) ).
thf(2823,plain,
! [SV87: nat,SV214: nat > $o] :
( ( ( SV214 @ zero_zero_nat )
= $true )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK44_SY650 @ SV214 @ SV87 ) @ SV87 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2774]) ).
thf(2824,plain,
! [SV214: nat > $o,SV87: nat] :
( ( ( ! [SY650: nat] :
( ~ ( ord_less_nat @ SY650 @ SV87 )
| ( SV214 @ ( suc @ SY650 ) ) ) )
= $true )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK44_SY650 @ SV214 @ SV87 ) @ SV87 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2775]) ).
thf(2825,plain,
! [SV214: nat > $o,SV87: nat,SV334: nat] :
( ( ( ~ ( ord_less_nat @ SV334 @ SV87 )
| ( SV214 @ ( suc @ SV334 ) ) )
= $true )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( SV214 @ ( suc @ ( sK44_SY650 @ SV214 @ SV87 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2778]) ).
thf(2826,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( SV228 != zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2781]) ).
thf(2827,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( SV228 = zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2782]) ).
thf(2828,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( SV228 = zero_zero_real )
= $true )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2783]) ).
thf(2829,plain,
! [SV297: real,SV228: real,SV103: real] :
( ( ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) )
= $false )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2784]) ).
thf(2830,plain,
! [SV110: nat,SV233: nat > $o,SV314: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ ( sK65_SY665 @ SV314 @ SV233 @ SV110 ) @ ( suc @ SV110 ) )
| ~ ( SV233 @ ( sK65_SY665 @ SV314 @ SV233 @ SV110 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV314 @ ( suc @ SV110 ) )
= $false )
| ( ( SV233 @ SV314 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2785]) ).
thf(2831,plain,
! [SV110: nat,SV233: nat > $o,SV314: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ ( sK71_SY666 @ SV314 @ SV233 @ SV110 ) @ SV110 )
| ~ ( SV233 @ ( sK71_SY666 @ SV314 @ SV233 @ SV110 ) ) ) )
= $false )
| ( ( SV233 @ SV110 )
= $true )
| ( ( ord_less_nat @ SV314 @ ( suc @ SV110 ) )
= $false )
| ( ( SV233 @ SV314 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2786]) ).
thf(2832,plain,
! [SV110: nat,SV233: nat > $o,SV318: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ ( sK72_SY665 @ SV318 @ SV233 @ SV110 ) @ ( suc @ SV110 ) )
| ~ ( SV233 @ ( sK72_SY665 @ SV318 @ SV233 @ SV110 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV318 @ SV110 )
= $false )
| ( ( SV233 @ SV318 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2787]) ).
thf(2833,plain,
! [SV318: nat,SV233: nat > $o,SV110: nat] :
( ( ( ! [SY666: nat] :
~ ~ ( ~ ( ord_less_nat @ SY666 @ SV110 )
| ~ ( SV233 @ SY666 ) ) )
= $false )
| ( ( SV233 @ SV110 )
= $true )
| ( ( ord_less_nat @ SV318 @ SV110 )
= $false )
| ( ( SV233 @ SV318 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2788]) ).
thf(2834,plain,
! [SV239: nat > $o,SV117: nat,SV332: nat] :
( ( ( ord_less_nat @ SV332 @ ( suc @ SV117 ) )
= $false )
| ( ( SV239 @ SV332 )
= $true )
| ( ( SV239 @ SV117 )
= $false )
| ( ( ord_less_nat @ ( sK46_SY670 @ SV239 @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2790]) ).
thf(2835,plain,
! [SV117: nat,SV239: nat > $o] :
( ( ( SV239 @ SV117 )
= $true )
| ( ( SV239 @ SV117 )
= $false )
| ( ( ord_less_nat @ ( sK46_SY670 @ SV239 @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2791]) ).
thf(2836,plain,
! [SV239: nat > $o,SV117: nat] :
( ( ( ! [SY670: nat] :
( ~ ( ord_less_nat @ SY670 @ SV117 )
| ( SV239 @ SY670 ) ) )
= $true )
| ( ( SV239 @ SV117 )
= $false )
| ( ( ord_less_nat @ ( sK46_SY670 @ SV239 @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2792]) ).
thf(2837,plain,
! [SV239: nat > $o,SV117: nat,SV335: nat] :
( ( ( ~ ( ord_less_nat @ SV335 @ SV117 )
| ( SV239 @ SV335 ) )
= $true )
| ( ( SV239 @ SV117 )
= $false )
| ( ( SV239 @ ( sK46_SY670 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2795]) ).
thf(2838,plain,
! [SV244: nat,SV122: nat > $o,SV333: nat] :
( ( ( ord_less_eq_nat @ SV333 @ ( sK38_SY677 @ SV122 @ SV244 ) )
= $false )
| ( ( ~ ( SV122 @ SV333 ) )
= $true )
| ( ( SV122 @ zero_zero_nat )
= $true )
| ( ( SV122 @ SV244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2796]) ).
thf(2839,plain,
! [SV123: nat,SV316: nat,SV245: nat] :
( ( ( ~ ( ( SV245
!= ( suc @ ( sK66_SY679 @ SV316 @ SV123 @ SV245 ) ) )
| ~ ( ord_less_nat @ SV123 @ ( sK66_SY679 @ SV316 @ SV123 @ SV245 ) ) ) )
= $true )
| ( ( SV245
= ( suc @ SV316 ) )
= $false )
| ( ( ord_less_nat @ SV123 @ SV316 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2797]) ).
thf(2840,plain,
! [SV127: nat,SV248: nat,SV303: nat > nat > $o] :
( ( ( SV303 @ ( sK73_SY722 @ SV248 @ SV127 @ SV303 ) @ ( suc @ ( sK73_SY722 @ SV248 @ SV127 @ SV303 ) ) )
= $false )
| ( ( SV303 @ SV127 @ SV248 )
= $true )
| ( ( SV303 @ ( sK54_SY730 @ SV127 @ SV248 @ SV303 ) @ ( sK62_SY734 @ SV127 @ SV248 @ SV303 ) )
= $true )
| ( ( SV303 @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) @ ( sK34_SY718 @ SV248 @ SV127 @ SV303 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV248 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2799]) ).
thf(2841,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2801]) ).
thf(2842,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2802]) ).
thf(2843,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $true )
| ( ( ord_less_real @ SV128 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV249 @ zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2803]) ).
thf(2844,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ord_less_real @ SV128 @ zero_zero_real )
| ~ ( ord_less_real @ SV249 @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $true )
| ( ( ord_less_real @ SV128 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV249 @ zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2804]) ).
thf(2845,plain,
! [SV319: nat,SV251: nat,SV133: nat] :
( ( ( ! [SY686: nat] :
~ ~ ( ( SV133
!= ( suc @ SY686 ) )
| ~ ( ord_less_nat @ SY686 @ SV251 ) ) )
= $false )
| ( ( SV133 = zero_zero_nat )
= $true )
| ( ( SV133
= ( suc @ SV319 ) )
= $false )
| ( ( ord_less_nat @ SV319 @ SV251 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2805]) ).
thf(2846,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2806]) ).
thf(2847,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2807]) ).
thf(2848,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $true )
| ( ( ord_less_real @ SV141 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV257 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2808]) ).
thf(2849,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ord_less_real @ SV141 @ zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ SV257 ) )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV141 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV257 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2809]) ).
thf(2850,plain,
! [SV47: nat,SV178: nat > $o,SV312: nat] :
( ( ( ~ ( ord_less_nat @ ( sK64_SY601 @ SV312 @ SV178 @ SV47 ) @ ( suc @ SV47 ) )
| ~ ( SV178 @ ( sK64_SY601 @ SV312 @ SV178 @ SV47 ) ) )
= $false )
| ( ( ord_less_nat @ SV312 @ ( suc @ SV47 ) )
= $false )
| ( ( SV178 @ SV312 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2810]) ).
thf(2851,plain,
! [SV47: nat,SV178: nat > $o,SV312: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ ( sK69_SY602 @ SV312 @ SV178 @ SV47 ) @ SV47 )
| ~ ( SV178 @ ( suc @ ( sK69_SY602 @ SV312 @ SV178 @ SV47 ) ) ) ) )
= $true )
| ( ( SV178 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV312 @ ( suc @ SV47 ) )
= $false )
| ( ( SV178 @ SV312 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2811]) ).
thf(2852,plain,
! [SV47: nat,SV178: nat > $o,SV317: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ ( sK70_SY601 @ SV317 @ SV178 @ SV47 ) @ ( suc @ SV47 ) )
| ~ ( SV178 @ ( sK70_SY601 @ SV317 @ SV178 @ SV47 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV317 @ SV47 )
= $false )
| ( ( SV178 @ ( suc @ SV317 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2812]) ).
thf(2853,plain,
! [SV47: nat,SV178: nat > $o,SV317: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ ( sK74_SY602 @ SV317 @ SV178 @ SV47 ) @ SV47 )
| ~ ( SV178 @ ( suc @ ( sK74_SY602 @ SV317 @ SV178 @ SV47 ) ) ) ) )
= $false )
| ( ( SV178 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV317 @ SV47 )
= $false )
| ( ( SV178 @ ( suc @ SV317 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2813]) ).
thf(2854,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2814]) ).
thf(2855,plain,
! [SV51: real,SV274: real,SV182: real] :
( ( ( ~ ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2814]) ).
thf(2856,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2815]) ).
thf(2857,plain,
! [SV51: real,SV274: real,SV182: real] :
( ( ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2816]) ).
thf(2858,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
= $true )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2817]) ).
thf(2859,plain,
! [SV51: real,SV274: real,SV182: real] :
( ( ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) )
= $true )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2818]) ).
thf(2860,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV182 ) )
= $true )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $true )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2819]) ).
thf(2861,plain,
! [SV51: real,SV274: real,SV182: real] :
( ( ( ~ ( ord_less_real @ SV182 @ zero_zero_real ) )
= $true )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $true )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2820]) ).
thf(2862,plain,
! [SV214: nat > $o,SV87: nat,SV336: nat] :
( ( ( ~ ( ord_less_nat @ SV336 @ SV87 )
| ( SV214 @ ( suc @ SV336 ) ) )
= $true )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK44_SY650 @ SV214 @ SV87 ) @ SV87 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2824]) ).
thf(2863,plain,
! [SV214: nat > $o,SV87: nat,SV334: nat] :
( ( ( ~ ( ord_less_nat @ SV334 @ SV87 ) )
= $true )
| ( ( SV214 @ ( suc @ SV334 ) )
= $true )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( SV214 @ ( suc @ ( sK44_SY650 @ SV214 @ SV87 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2825]) ).
thf(2864,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( SV228 = zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ~ ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2826]) ).
thf(2865,plain,
! [SV297: real,SV228: real,SV103: real] :
( ( ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) )
= $false )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2827]) ).
thf(2866,plain,
! [SV297: real,SV228: real,SV103: real] :
( ( ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) )
= $false )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2828]) ).
thf(2867,plain,
! [SV297: real,SV228: real,SV103: real] :
( ( ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) ) )
= $false )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2829]) ).
thf(2868,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) )
= $false )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2829]) ).
thf(2869,plain,
! [SV110: nat,SV233: nat > $o,SV314: nat] :
( ( ( ~ ( ord_less_nat @ ( sK65_SY665 @ SV314 @ SV233 @ SV110 ) @ ( suc @ SV110 ) )
| ~ ( SV233 @ ( sK65_SY665 @ SV314 @ SV233 @ SV110 ) ) )
= $false )
| ( ( ord_less_nat @ SV314 @ ( suc @ SV110 ) )
= $false )
| ( ( SV233 @ SV314 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2830]) ).
thf(2870,plain,
! [SV110: nat,SV233: nat > $o,SV314: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ ( sK71_SY666 @ SV314 @ SV233 @ SV110 ) @ SV110 )
| ~ ( SV233 @ ( sK71_SY666 @ SV314 @ SV233 @ SV110 ) ) ) )
= $true )
| ( ( SV233 @ SV110 )
= $true )
| ( ( ord_less_nat @ SV314 @ ( suc @ SV110 ) )
= $false )
| ( ( SV233 @ SV314 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2831]) ).
thf(2871,plain,
! [SV110: nat,SV233: nat > $o,SV318: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ ( sK72_SY665 @ SV318 @ SV233 @ SV110 ) @ ( suc @ SV110 ) )
| ~ ( SV233 @ ( sK72_SY665 @ SV318 @ SV233 @ SV110 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV318 @ SV110 )
= $false )
| ( ( SV233 @ SV318 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2832]) ).
thf(2872,plain,
! [SV110: nat,SV233: nat > $o,SV318: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ ( sK75_SY666 @ SV318 @ SV233 @ SV110 ) @ SV110 )
| ~ ( SV233 @ ( sK75_SY666 @ SV318 @ SV233 @ SV110 ) ) ) )
= $false )
| ( ( SV233 @ SV110 )
= $true )
| ( ( ord_less_nat @ SV318 @ SV110 )
= $false )
| ( ( SV233 @ SV318 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2833]) ).
thf(2873,plain,
! [SV239: nat > $o,SV117: nat,SV337: nat] :
( ( ( ~ ( ord_less_nat @ SV337 @ SV117 )
| ( SV239 @ SV337 ) )
= $true )
| ( ( SV239 @ SV117 )
= $false )
| ( ( ord_less_nat @ ( sK46_SY670 @ SV239 @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2836]) ).
thf(2874,plain,
! [SV239: nat > $o,SV117: nat,SV335: nat] :
( ( ( ~ ( ord_less_nat @ SV335 @ SV117 ) )
= $true )
| ( ( SV239 @ SV335 )
= $true )
| ( ( SV239 @ SV117 )
= $false )
| ( ( SV239 @ ( sK46_SY670 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2837]) ).
thf(2875,plain,
! [SV244: nat,SV333: nat,SV122: nat > $o] :
( ( ( SV122 @ SV333 )
= $false )
| ( ( ord_less_eq_nat @ SV333 @ ( sK38_SY677 @ SV122 @ SV244 ) )
= $false )
| ( ( SV122 @ zero_zero_nat )
= $true )
| ( ( SV122 @ SV244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2838]) ).
thf(2876,plain,
! [SV123: nat,SV316: nat,SV245: nat] :
( ( ( ( SV245
!= ( suc @ ( sK66_SY679 @ SV316 @ SV123 @ SV245 ) ) )
| ~ ( ord_less_nat @ SV123 @ ( sK66_SY679 @ SV316 @ SV123 @ SV245 ) ) )
= $false )
| ( ( SV245
= ( suc @ SV316 ) )
= $false )
| ( ( ord_less_nat @ SV123 @ SV316 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2839]) ).
thf(2877,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ord_less_real @ SV128 @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2841]) ).
thf(2878,plain,
! [SV128: real,SV249: real] :
( ( ( ~ ( ord_less_real @ SV249 @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2841]) ).
thf(2879,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ord_less_real @ SV128 @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2842]) ).
thf(2880,plain,
! [SV128: real,SV249: real] :
( ( ( ~ ( ord_less_real @ SV249 @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2842]) ).
thf(2881,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ord_less_real @ SV128 @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $true )
| ( ( ord_less_real @ SV128 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV249 @ zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2843]) ).
thf(2882,plain,
! [SV128: real,SV249: real] :
( ( ( ~ ( ord_less_real @ SV249 @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $true )
| ( ( ord_less_real @ SV128 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV249 @ zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2843]) ).
thf(2883,plain,
! [SV249: real,SV128: real] :
( ( ( ~ ( ord_less_real @ SV128 @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $true )
| ( ( ord_less_real @ SV128 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV249 @ zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2844]) ).
thf(2884,plain,
! [SV128: real,SV249: real] :
( ( ( ~ ( ord_less_real @ SV249 @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $true )
| ( ( ord_less_real @ SV128 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV249 @ zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2844]) ).
thf(2885,plain,
! [SV251: nat,SV319: nat,SV133: nat] :
( ( ( ~ ~ ( ( SV133
!= ( suc @ ( sK76_SY686 @ SV319 @ SV251 @ SV133 ) ) )
| ~ ( ord_less_nat @ ( sK76_SY686 @ SV319 @ SV251 @ SV133 ) @ SV251 ) ) )
= $false )
| ( ( SV133 = zero_zero_nat )
= $true )
| ( ( SV133
= ( suc @ SV319 ) )
= $false )
| ( ( ord_less_nat @ SV319 @ SV251 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2845]) ).
thf(2886,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ord_less_real @ SV141 @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2846]) ).
thf(2887,plain,
! [SV141: real,SV257: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV257 ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2846]) ).
thf(2888,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ord_less_real @ SV141 @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2847]) ).
thf(2889,plain,
! [SV141: real,SV257: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV257 ) )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2847]) ).
thf(2890,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ord_less_real @ SV141 @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $true )
| ( ( ord_less_real @ SV141 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV257 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2848]) ).
thf(2891,plain,
! [SV141: real,SV257: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV257 ) )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $true )
| ( ( ord_less_real @ SV141 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV257 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2848]) ).
thf(2892,plain,
! [SV257: real,SV141: real] :
( ( ( ~ ( ord_less_real @ SV141 @ zero_zero_real ) )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV141 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV257 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2849]) ).
thf(2893,plain,
! [SV141: real,SV257: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV257 ) )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV141 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV257 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2849]) ).
thf(2894,plain,
! [SV47: nat,SV178: nat > $o,SV312: nat] :
( ( ( ~ ( ord_less_nat @ ( sK64_SY601 @ SV312 @ SV178 @ SV47 ) @ ( suc @ SV47 ) ) )
= $false )
| ( ( ord_less_nat @ SV312 @ ( suc @ SV47 ) )
= $false )
| ( ( SV178 @ SV312 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2850]) ).
thf(2895,plain,
! [SV47: nat,SV312: nat,SV178: nat > $o] :
( ( ( ~ ( SV178 @ ( sK64_SY601 @ SV312 @ SV178 @ SV47 ) ) )
= $false )
| ( ( ord_less_nat @ SV312 @ ( suc @ SV47 ) )
= $false )
| ( ( SV178 @ SV312 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2850]) ).
thf(2896,plain,
! [SV47: nat,SV178: nat > $o,SV312: nat] :
( ( ( ~ ( ord_less_nat @ ( sK69_SY602 @ SV312 @ SV178 @ SV47 ) @ SV47 )
| ~ ( SV178 @ ( suc @ ( sK69_SY602 @ SV312 @ SV178 @ SV47 ) ) ) )
= $false )
| ( ( SV178 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV312 @ ( suc @ SV47 ) )
= $false )
| ( ( SV178 @ SV312 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2851]) ).
thf(2897,plain,
! [SV47: nat,SV178: nat > $o,SV317: nat] :
( ( ( ~ ( ord_less_nat @ ( sK70_SY601 @ SV317 @ SV178 @ SV47 ) @ ( suc @ SV47 ) )
| ~ ( SV178 @ ( sK70_SY601 @ SV317 @ SV178 @ SV47 ) ) )
= $false )
| ( ( ord_less_nat @ SV317 @ SV47 )
= $false )
| ( ( SV178 @ ( suc @ SV317 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2852]) ).
thf(2898,plain,
! [SV47: nat,SV178: nat > $o,SV317: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ ( sK74_SY602 @ SV317 @ SV178 @ SV47 ) @ SV47 )
| ~ ( SV178 @ ( suc @ ( sK74_SY602 @ SV317 @ SV178 @ SV47 ) ) ) ) )
= $true )
| ( ( SV178 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV317 @ SV47 )
= $false )
| ( ( SV178 @ ( suc @ SV317 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2853]) ).
thf(2899,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV182 )
| ( ord_less_eq_real @ SV51 @ SV274 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2854]) ).
thf(2900,plain,
! [SV51: real,SV274: real,SV182: real] :
( ( ( ~ ( ord_less_real @ SV182 @ zero_zero_real )
| ( ord_less_eq_real @ SV274 @ SV51 ) )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2855]) ).
thf(2901,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV182 ) )
= $true )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2856]) ).
thf(2902,plain,
! [SV51: real,SV274: real,SV182: real] :
( ( ( ~ ( ord_less_real @ SV182 @ zero_zero_real ) )
= $true )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2857]) ).
thf(2903,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV182 ) )
= $true )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $true )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2858]) ).
thf(2904,plain,
! [SV51: real,SV274: real,SV182: real] :
( ( ( ~ ( ord_less_real @ SV182 @ zero_zero_real ) )
= $true )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $true )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2859]) ).
thf(2905,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ord_less_real @ zero_zero_real @ SV182 )
= $false )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $true )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2860]) ).
thf(2906,plain,
! [SV51: real,SV274: real,SV182: real] :
( ( ( ord_less_real @ SV182 @ zero_zero_real )
= $false )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $true )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2861]) ).
thf(2907,plain,
! [SV214: nat > $o,SV87: nat,SV336: nat] :
( ( ( ~ ( ord_less_nat @ SV336 @ SV87 ) )
= $true )
| ( ( SV214 @ ( suc @ SV336 ) )
= $true )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK44_SY650 @ SV214 @ SV87 ) @ SV87 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2862]) ).
thf(2908,plain,
! [SV214: nat > $o,SV87: nat,SV334: nat] :
( ( ( ord_less_nat @ SV334 @ SV87 )
= $false )
| ( ( SV214 @ ( suc @ SV334 ) )
= $true )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( SV214 @ ( suc @ ( sK44_SY650 @ SV214 @ SV87 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2863]) ).
thf(2909,plain,
! [SV297: real,SV228: real,SV103: real] :
( ( ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) )
= $false )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2864]) ).
thf(2910,plain,
! [SV297: real,SV228: real,SV103: real] :
( ( ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) ) )
= $false )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2865]) ).
thf(2911,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) )
= $false )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2865]) ).
thf(2912,plain,
! [SV297: real,SV228: real,SV103: real] :
( ( ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) ) )
= $false )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2866]) ).
thf(2913,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) )
= $false )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2866]) ).
thf(2914,plain,
! [SV297: real,SV228: real,SV103: real] :
( ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
= $true )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2867]) ).
thf(2915,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) )
= $true )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2868]) ).
thf(2916,plain,
! [SV110: nat,SV233: nat > $o,SV314: nat] :
( ( ( ~ ( ord_less_nat @ ( sK65_SY665 @ SV314 @ SV233 @ SV110 ) @ ( suc @ SV110 ) ) )
= $false )
| ( ( ord_less_nat @ SV314 @ ( suc @ SV110 ) )
= $false )
| ( ( SV233 @ SV314 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2869]) ).
thf(2917,plain,
! [SV110: nat,SV314: nat,SV233: nat > $o] :
( ( ( ~ ( SV233 @ ( sK65_SY665 @ SV314 @ SV233 @ SV110 ) ) )
= $false )
| ( ( ord_less_nat @ SV314 @ ( suc @ SV110 ) )
= $false )
| ( ( SV233 @ SV314 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2869]) ).
thf(2918,plain,
! [SV110: nat,SV233: nat > $o,SV314: nat] :
( ( ( ~ ( ord_less_nat @ ( sK71_SY666 @ SV314 @ SV233 @ SV110 ) @ SV110 )
| ~ ( SV233 @ ( sK71_SY666 @ SV314 @ SV233 @ SV110 ) ) )
= $false )
| ( ( SV233 @ SV110 )
= $true )
| ( ( ord_less_nat @ SV314 @ ( suc @ SV110 ) )
= $false )
| ( ( SV233 @ SV314 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2870]) ).
thf(2919,plain,
! [SV110: nat,SV233: nat > $o,SV318: nat] :
( ( ( ~ ( ord_less_nat @ ( sK72_SY665 @ SV318 @ SV233 @ SV110 ) @ ( suc @ SV110 ) )
| ~ ( SV233 @ ( sK72_SY665 @ SV318 @ SV233 @ SV110 ) ) )
= $false )
| ( ( ord_less_nat @ SV318 @ SV110 )
= $false )
| ( ( SV233 @ SV318 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2871]) ).
thf(2920,plain,
! [SV110: nat,SV233: nat > $o,SV318: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ ( sK75_SY666 @ SV318 @ SV233 @ SV110 ) @ SV110 )
| ~ ( SV233 @ ( sK75_SY666 @ SV318 @ SV233 @ SV110 ) ) ) )
= $true )
| ( ( SV233 @ SV110 )
= $true )
| ( ( ord_less_nat @ SV318 @ SV110 )
= $false )
| ( ( SV233 @ SV318 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2872]) ).
thf(2921,plain,
! [SV239: nat > $o,SV117: nat,SV337: nat] :
( ( ( ~ ( ord_less_nat @ SV337 @ SV117 ) )
= $true )
| ( ( SV239 @ SV337 )
= $true )
| ( ( SV239 @ SV117 )
= $false )
| ( ( ord_less_nat @ ( sK46_SY670 @ SV239 @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2873]) ).
thf(2922,plain,
! [SV239: nat > $o,SV117: nat,SV335: nat] :
( ( ( ord_less_nat @ SV335 @ SV117 )
= $false )
| ( ( SV239 @ SV335 )
= $true )
| ( ( SV239 @ SV117 )
= $false )
| ( ( SV239 @ ( sK46_SY670 @ SV239 @ SV117 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2874]) ).
thf(2923,plain,
! [SV123: nat,SV316: nat,SV245: nat] :
( ( ( SV245
!= ( suc @ ( sK66_SY679 @ SV316 @ SV123 @ SV245 ) ) )
= $false )
| ( ( SV245
= ( suc @ SV316 ) )
= $false )
| ( ( ord_less_nat @ SV123 @ SV316 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2876]) ).
thf(2924,plain,
! [SV245: nat,SV316: nat,SV123: nat] :
( ( ( ~ ( ord_less_nat @ SV123 @ ( sK66_SY679 @ SV316 @ SV123 @ SV245 ) ) )
= $false )
| ( ( SV245
= ( suc @ SV316 ) )
= $false )
| ( ( ord_less_nat @ SV123 @ SV316 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2876]) ).
thf(2925,plain,
! [SV249: real,SV128: real] :
( ( ( ord_less_real @ SV128 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2877]) ).
thf(2926,plain,
! [SV128: real,SV249: real] :
( ( ( ord_less_real @ SV249 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2878]) ).
thf(2927,plain,
! [SV249: real,SV128: real] :
( ( ( ord_less_real @ SV128 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2879]) ).
thf(2928,plain,
! [SV128: real,SV249: real] :
( ( ( ord_less_real @ SV249 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2880]) ).
thf(2929,plain,
! [SV249: real,SV128: real] :
( ( ( ord_less_real @ SV128 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $true )
| ( ( ord_less_real @ SV128 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV249 @ zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2881]) ).
thf(2930,plain,
! [SV128: real,SV249: real] :
( ( ( ord_less_real @ SV249 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV128 )
= $true )
| ( ( ord_less_real @ SV128 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV249 @ zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2882]) ).
thf(2931,plain,
! [SV249: real,SV128: real] :
( ( ( ord_less_real @ SV128 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $true )
| ( ( ord_less_real @ SV128 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV249 @ zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2883]) ).
thf(2932,plain,
! [SV128: real,SV249: real] :
( ( ( ord_less_real @ SV249 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV249 )
= $true )
| ( ( ord_less_real @ SV128 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV249 @ zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2884]) ).
thf(2933,plain,
! [SV251: nat,SV319: nat,SV133: nat] :
( ( ( ~ ( ( SV133
!= ( suc @ ( sK76_SY686 @ SV319 @ SV251 @ SV133 ) ) )
| ~ ( ord_less_nat @ ( sK76_SY686 @ SV319 @ SV251 @ SV133 ) @ SV251 ) ) )
= $true )
| ( ( SV133 = zero_zero_nat )
= $true )
| ( ( SV133
= ( suc @ SV319 ) )
= $false )
| ( ( ord_less_nat @ SV319 @ SV251 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2885]) ).
thf(2934,plain,
! [SV257: real,SV141: real] :
( ( ( ord_less_real @ SV141 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2886]) ).
thf(2935,plain,
! [SV141: real,SV257: real] :
( ( ( ord_less_real @ zero_zero_real @ SV257 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2887]) ).
thf(2936,plain,
! [SV257: real,SV141: real] :
( ( ( ord_less_real @ SV141 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2888]) ).
thf(2937,plain,
! [SV141: real,SV257: real] :
( ( ( ord_less_real @ zero_zero_real @ SV257 )
= $true )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $false )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2889]) ).
thf(2938,plain,
! [SV257: real,SV141: real] :
( ( ( ord_less_real @ SV141 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $true )
| ( ( ord_less_real @ SV141 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV257 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2890]) ).
thf(2939,plain,
! [SV141: real,SV257: real] :
( ( ( ord_less_real @ zero_zero_real @ SV257 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV141 )
= $true )
| ( ( ord_less_real @ SV141 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV257 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2891]) ).
thf(2940,plain,
! [SV257: real,SV141: real] :
( ( ( ord_less_real @ SV141 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV141 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV257 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2892]) ).
thf(2941,plain,
! [SV141: real,SV257: real] :
( ( ( ord_less_real @ zero_zero_real @ SV257 )
= $true )
| ( ( ord_less_real @ SV257 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV141 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV257 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2893]) ).
thf(2942,plain,
! [SV47: nat,SV178: nat > $o,SV312: nat] :
( ( ( ord_less_nat @ ( sK64_SY601 @ SV312 @ SV178 @ SV47 ) @ ( suc @ SV47 ) )
= $true )
| ( ( ord_less_nat @ SV312 @ ( suc @ SV47 ) )
= $false )
| ( ( SV178 @ SV312 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2894]) ).
thf(2943,plain,
! [SV47: nat,SV312: nat,SV178: nat > $o] :
( ( ( SV178 @ ( sK64_SY601 @ SV312 @ SV178 @ SV47 ) )
= $true )
| ( ( ord_less_nat @ SV312 @ ( suc @ SV47 ) )
= $false )
| ( ( SV178 @ SV312 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2895]) ).
thf(2944,plain,
! [SV47: nat,SV178: nat > $o,SV312: nat] :
( ( ( ~ ( ord_less_nat @ ( sK69_SY602 @ SV312 @ SV178 @ SV47 ) @ SV47 ) )
= $false )
| ( ( SV178 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV312 @ ( suc @ SV47 ) )
= $false )
| ( ( SV178 @ SV312 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2896]) ).
thf(2945,plain,
! [SV47: nat,SV312: nat,SV178: nat > $o] :
( ( ( ~ ( SV178 @ ( suc @ ( sK69_SY602 @ SV312 @ SV178 @ SV47 ) ) ) )
= $false )
| ( ( SV178 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV312 @ ( suc @ SV47 ) )
= $false )
| ( ( SV178 @ SV312 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2896]) ).
thf(2946,plain,
! [SV47: nat,SV178: nat > $o,SV317: nat] :
( ( ( ~ ( ord_less_nat @ ( sK70_SY601 @ SV317 @ SV178 @ SV47 ) @ ( suc @ SV47 ) ) )
= $false )
| ( ( ord_less_nat @ SV317 @ SV47 )
= $false )
| ( ( SV178 @ ( suc @ SV317 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2897]) ).
thf(2947,plain,
! [SV47: nat,SV317: nat,SV178: nat > $o] :
( ( ( ~ ( SV178 @ ( sK70_SY601 @ SV317 @ SV178 @ SV47 ) ) )
= $false )
| ( ( ord_less_nat @ SV317 @ SV47 )
= $false )
| ( ( SV178 @ ( suc @ SV317 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2897]) ).
thf(2948,plain,
! [SV47: nat,SV178: nat > $o,SV317: nat] :
( ( ( ~ ( ord_less_nat @ ( sK74_SY602 @ SV317 @ SV178 @ SV47 ) @ SV47 )
| ~ ( SV178 @ ( suc @ ( sK74_SY602 @ SV317 @ SV178 @ SV47 ) ) ) )
= $false )
| ( ( SV178 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV317 @ SV47 )
= $false )
| ( ( SV178 @ ( suc @ SV317 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2898]) ).
thf(2949,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV182 ) )
= $true )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2899]) ).
thf(2950,plain,
! [SV51: real,SV274: real,SV182: real] :
( ( ( ~ ( ord_less_real @ SV182 @ zero_zero_real ) )
= $true )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2900]) ).
thf(2951,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ord_less_real @ zero_zero_real @ SV182 )
= $false )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2901]) ).
thf(2952,plain,
! [SV51: real,SV274: real,SV182: real] :
( ( ( ord_less_real @ SV182 @ zero_zero_real )
= $false )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2902]) ).
thf(2953,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ord_less_real @ zero_zero_real @ SV182 )
= $false )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $true )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2903]) ).
thf(2954,plain,
! [SV51: real,SV274: real,SV182: real] :
( ( ( ord_less_real @ SV182 @ zero_zero_real )
= $false )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $true )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $false )
| ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2904]) ).
thf(2955,plain,
! [SV214: nat > $o,SV87: nat,SV336: nat] :
( ( ( ord_less_nat @ SV336 @ SV87 )
= $false )
| ( ( SV214 @ ( suc @ SV336 ) )
= $true )
| ( ( SV214 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK44_SY650 @ SV214 @ SV87 ) @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2907]) ).
thf(2956,plain,
! [SV297: real,SV228: real,SV103: real] :
( ( ( ~ ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) ) )
= $false )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2909]) ).
thf(2957,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) )
= $false )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2909]) ).
thf(2958,plain,
! [SV297: real,SV228: real,SV103: real] :
( ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
= $true )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2910]) ).
thf(2959,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) )
= $true )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2911]) ).
thf(2960,plain,
! [SV297: real,SV228: real,SV103: real] :
( ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
= $true )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2912]) ).
thf(2961,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) )
= $true )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2913]) ).
thf(2962,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) )
= $false )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2915]) ).
thf(2963,plain,
! [SV110: nat,SV233: nat > $o,SV314: nat] :
( ( ( ord_less_nat @ ( sK65_SY665 @ SV314 @ SV233 @ SV110 ) @ ( suc @ SV110 ) )
= $true )
| ( ( ord_less_nat @ SV314 @ ( suc @ SV110 ) )
= $false )
| ( ( SV233 @ SV314 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2916]) ).
thf(2964,plain,
! [SV110: nat,SV314: nat,SV233: nat > $o] :
( ( ( SV233 @ ( sK65_SY665 @ SV314 @ SV233 @ SV110 ) )
= $true )
| ( ( ord_less_nat @ SV314 @ ( suc @ SV110 ) )
= $false )
| ( ( SV233 @ SV314 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2917]) ).
thf(2965,plain,
! [SV110: nat,SV233: nat > $o,SV314: nat] :
( ( ( ~ ( ord_less_nat @ ( sK71_SY666 @ SV314 @ SV233 @ SV110 ) @ SV110 ) )
= $false )
| ( ( SV233 @ SV110 )
= $true )
| ( ( ord_less_nat @ SV314 @ ( suc @ SV110 ) )
= $false )
| ( ( SV233 @ SV314 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2918]) ).
thf(2966,plain,
! [SV110: nat,SV314: nat,SV233: nat > $o] :
( ( ( ~ ( SV233 @ ( sK71_SY666 @ SV314 @ SV233 @ SV110 ) ) )
= $false )
| ( ( SV233 @ SV110 )
= $true )
| ( ( ord_less_nat @ SV314 @ ( suc @ SV110 ) )
= $false )
| ( ( SV233 @ SV314 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2918]) ).
thf(2967,plain,
! [SV110: nat,SV233: nat > $o,SV318: nat] :
( ( ( ~ ( ord_less_nat @ ( sK72_SY665 @ SV318 @ SV233 @ SV110 ) @ ( suc @ SV110 ) ) )
= $false )
| ( ( ord_less_nat @ SV318 @ SV110 )
= $false )
| ( ( SV233 @ SV318 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2919]) ).
thf(2968,plain,
! [SV110: nat,SV318: nat,SV233: nat > $o] :
( ( ( ~ ( SV233 @ ( sK72_SY665 @ SV318 @ SV233 @ SV110 ) ) )
= $false )
| ( ( ord_less_nat @ SV318 @ SV110 )
= $false )
| ( ( SV233 @ SV318 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2919]) ).
thf(2969,plain,
! [SV110: nat,SV233: nat > $o,SV318: nat] :
( ( ( ~ ( ord_less_nat @ ( sK75_SY666 @ SV318 @ SV233 @ SV110 ) @ SV110 )
| ~ ( SV233 @ ( sK75_SY666 @ SV318 @ SV233 @ SV110 ) ) )
= $false )
| ( ( SV233 @ SV110 )
= $true )
| ( ( ord_less_nat @ SV318 @ SV110 )
= $false )
| ( ( SV233 @ SV318 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2920]) ).
thf(2970,plain,
! [SV239: nat > $o,SV117: nat,SV337: nat] :
( ( ( ord_less_nat @ SV337 @ SV117 )
= $false )
| ( ( SV239 @ SV337 )
= $true )
| ( ( SV239 @ SV117 )
= $false )
| ( ( ord_less_nat @ ( sK46_SY670 @ SV239 @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2921]) ).
thf(2971,plain,
! [SV123: nat,SV316: nat,SV245: nat] :
( ( ( SV245
= ( suc @ ( sK66_SY679 @ SV316 @ SV123 @ SV245 ) ) )
= $true )
| ( ( SV245
= ( suc @ SV316 ) )
= $false )
| ( ( ord_less_nat @ SV123 @ SV316 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2923]) ).
thf(2972,plain,
! [SV245: nat,SV316: nat,SV123: nat] :
( ( ( ord_less_nat @ SV123 @ ( sK66_SY679 @ SV316 @ SV123 @ SV245 ) )
= $true )
| ( ( SV245
= ( suc @ SV316 ) )
= $false )
| ( ( ord_less_nat @ SV123 @ SV316 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2924]) ).
thf(2973,plain,
! [SV251: nat,SV319: nat,SV133: nat] :
( ( ( ( SV133
!= ( suc @ ( sK76_SY686 @ SV319 @ SV251 @ SV133 ) ) )
| ~ ( ord_less_nat @ ( sK76_SY686 @ SV319 @ SV251 @ SV133 ) @ SV251 ) )
= $false )
| ( ( SV133 = zero_zero_nat )
= $true )
| ( ( SV133
= ( suc @ SV319 ) )
= $false )
| ( ( ord_less_nat @ SV319 @ SV251 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2933]) ).
thf(2974,plain,
! [SV47: nat,SV178: nat > $o,SV312: nat] :
( ( ( ord_less_nat @ ( sK69_SY602 @ SV312 @ SV178 @ SV47 ) @ SV47 )
= $true )
| ( ( SV178 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV312 @ ( suc @ SV47 ) )
= $false )
| ( ( SV178 @ SV312 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2944]) ).
thf(2975,plain,
! [SV47: nat,SV312: nat,SV178: nat > $o] :
( ( ( SV178 @ ( suc @ ( sK69_SY602 @ SV312 @ SV178 @ SV47 ) ) )
= $true )
| ( ( SV178 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV312 @ ( suc @ SV47 ) )
= $false )
| ( ( SV178 @ SV312 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2945]) ).
thf(2976,plain,
! [SV47: nat,SV178: nat > $o,SV317: nat] :
( ( ( ord_less_nat @ ( sK70_SY601 @ SV317 @ SV178 @ SV47 ) @ ( suc @ SV47 ) )
= $true )
| ( ( ord_less_nat @ SV317 @ SV47 )
= $false )
| ( ( SV178 @ ( suc @ SV317 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2946]) ).
thf(2977,plain,
! [SV47: nat,SV317: nat,SV178: nat > $o] :
( ( ( SV178 @ ( sK70_SY601 @ SV317 @ SV178 @ SV47 ) )
= $true )
| ( ( ord_less_nat @ SV317 @ SV47 )
= $false )
| ( ( SV178 @ ( suc @ SV317 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2947]) ).
thf(2978,plain,
! [SV47: nat,SV178: nat > $o,SV317: nat] :
( ( ( ~ ( ord_less_nat @ ( sK74_SY602 @ SV317 @ SV178 @ SV47 ) @ SV47 ) )
= $false )
| ( ( SV178 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV317 @ SV47 )
= $false )
| ( ( SV178 @ ( suc @ SV317 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2948]) ).
thf(2979,plain,
! [SV47: nat,SV317: nat,SV178: nat > $o] :
( ( ( ~ ( SV178 @ ( suc @ ( sK74_SY602 @ SV317 @ SV178 @ SV47 ) ) ) )
= $false )
| ( ( SV178 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV317 @ SV47 )
= $false )
| ( ( SV178 @ ( suc @ SV317 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2948]) ).
thf(2980,plain,
! [SV274: real,SV51: real,SV182: real] :
( ( ( ord_less_real @ zero_zero_real @ SV182 )
= $false )
| ( ( ord_less_eq_real @ SV51 @ SV274 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2949]) ).
thf(2981,plain,
! [SV51: real,SV274: real,SV182: real] :
( ( ( ord_less_real @ SV182 @ zero_zero_real )
= $false )
| ( ( ord_less_eq_real @ SV274 @ SV51 )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV182 )
= $true )
| ( ( ord_less_real @ SV182 @ zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2950]) ).
thf(2982,plain,
! [SV297: real,SV228: real,SV103: real] :
( ( ( ord_less_real @ ( divide_divide_real @ SV103 @ SV228 ) @ ( divide_divide_real @ SV297 @ SV228 ) )
= $true )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2956]) ).
thf(2983,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) ) )
= $true )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2957]) ).
thf(2984,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) )
= $false )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2959]) ).
thf(2985,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) )
= $false )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2961]) ).
thf(2986,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) ) )
= $false )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2962]) ).
thf(2987,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( ~ ( ( SV228 != zero_zero_real ) ) )
= $false )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2962]) ).
thf(2988,plain,
! [SV110: nat,SV233: nat > $o,SV314: nat] :
( ( ( ord_less_nat @ ( sK71_SY666 @ SV314 @ SV233 @ SV110 ) @ SV110 )
= $true )
| ( ( SV233 @ SV110 )
= $true )
| ( ( ord_less_nat @ SV314 @ ( suc @ SV110 ) )
= $false )
| ( ( SV233 @ SV314 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2965]) ).
thf(2989,plain,
! [SV110: nat,SV314: nat,SV233: nat > $o] :
( ( ( SV233 @ ( sK71_SY666 @ SV314 @ SV233 @ SV110 ) )
= $true )
| ( ( SV233 @ SV110 )
= $true )
| ( ( ord_less_nat @ SV314 @ ( suc @ SV110 ) )
= $false )
| ( ( SV233 @ SV314 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2966]) ).
thf(2990,plain,
! [SV110: nat,SV233: nat > $o,SV318: nat] :
( ( ( ord_less_nat @ ( sK72_SY665 @ SV318 @ SV233 @ SV110 ) @ ( suc @ SV110 ) )
= $true )
| ( ( ord_less_nat @ SV318 @ SV110 )
= $false )
| ( ( SV233 @ SV318 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2967]) ).
thf(2991,plain,
! [SV110: nat,SV318: nat,SV233: nat > $o] :
( ( ( SV233 @ ( sK72_SY665 @ SV318 @ SV233 @ SV110 ) )
= $true )
| ( ( ord_less_nat @ SV318 @ SV110 )
= $false )
| ( ( SV233 @ SV318 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2968]) ).
thf(2992,plain,
! [SV110: nat,SV233: nat > $o,SV318: nat] :
( ( ( ~ ( ord_less_nat @ ( sK75_SY666 @ SV318 @ SV233 @ SV110 ) @ SV110 ) )
= $false )
| ( ( SV233 @ SV110 )
= $true )
| ( ( ord_less_nat @ SV318 @ SV110 )
= $false )
| ( ( SV233 @ SV318 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2969]) ).
thf(2993,plain,
! [SV110: nat,SV318: nat,SV233: nat > $o] :
( ( ( ~ ( SV233 @ ( sK75_SY666 @ SV318 @ SV233 @ SV110 ) ) )
= $false )
| ( ( SV233 @ SV110 )
= $true )
| ( ( ord_less_nat @ SV318 @ SV110 )
= $false )
| ( ( SV233 @ SV318 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2969]) ).
thf(2994,plain,
! [SV251: nat,SV319: nat,SV133: nat] :
( ( ( SV133
!= ( suc @ ( sK76_SY686 @ SV319 @ SV251 @ SV133 ) ) )
= $false )
| ( ( SV133 = zero_zero_nat )
= $true )
| ( ( SV133
= ( suc @ SV319 ) )
= $false )
| ( ( ord_less_nat @ SV319 @ SV251 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2973]) ).
thf(2995,plain,
! [SV133: nat,SV251: nat,SV319: nat] :
( ( ( ~ ( ord_less_nat @ ( sK76_SY686 @ SV319 @ SV251 @ SV133 ) @ SV251 ) )
= $false )
| ( ( SV133 = zero_zero_nat )
= $true )
| ( ( SV133
= ( suc @ SV319 ) )
= $false )
| ( ( ord_less_nat @ SV319 @ SV251 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2973]) ).
thf(2996,plain,
! [SV47: nat,SV178: nat > $o,SV317: nat] :
( ( ( ord_less_nat @ ( sK74_SY602 @ SV317 @ SV178 @ SV47 ) @ SV47 )
= $true )
| ( ( SV178 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV317 @ SV47 )
= $false )
| ( ( SV178 @ ( suc @ SV317 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2978]) ).
thf(2997,plain,
! [SV47: nat,SV317: nat,SV178: nat > $o] :
( ( ( SV178 @ ( suc @ ( sK74_SY602 @ SV317 @ SV178 @ SV47 ) ) )
= $true )
| ( ( SV178 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV317 @ SV47 )
= $false )
| ( ( SV178 @ ( suc @ SV317 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2979]) ).
thf(2998,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
| ~ ( ( SV228 != zero_zero_real ) ) )
= $false )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2983]) ).
thf(2999,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) ) )
= $false )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2984]) ).
thf(3000,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( ~ ( ( SV228 != zero_zero_real ) ) )
= $false )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2984]) ).
thf(3001,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) ) )
= $false )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2985]) ).
thf(3002,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ( SV228 != zero_zero_real ) ) )
= $false )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2985]) ).
thf(3003,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) ) )
= $true )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2986]) ).
thf(3004,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( SV228 != zero_zero_real )
= $true )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2987]) ).
thf(3005,plain,
! [SV110: nat,SV233: nat > $o,SV318: nat] :
( ( ( ord_less_nat @ ( sK75_SY666 @ SV318 @ SV233 @ SV110 ) @ SV110 )
= $true )
| ( ( SV233 @ SV110 )
= $true )
| ( ( ord_less_nat @ SV318 @ SV110 )
= $false )
| ( ( SV233 @ SV318 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2992]) ).
thf(3006,plain,
! [SV110: nat,SV318: nat,SV233: nat > $o] :
( ( ( SV233 @ ( sK75_SY666 @ SV318 @ SV233 @ SV110 ) )
= $true )
| ( ( SV233 @ SV110 )
= $true )
| ( ( ord_less_nat @ SV318 @ SV110 )
= $false )
| ( ( SV233 @ SV318 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2993]) ).
thf(3007,plain,
! [SV251: nat,SV319: nat,SV133: nat] :
( ( ( SV133
= ( suc @ ( sK76_SY686 @ SV319 @ SV251 @ SV133 ) ) )
= $true )
| ( ( SV133 = zero_zero_nat )
= $true )
| ( ( SV133
= ( suc @ SV319 ) )
= $false )
| ( ( ord_less_nat @ SV319 @ SV251 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2994]) ).
thf(3008,plain,
! [SV133: nat,SV251: nat,SV319: nat] :
( ( ( ord_less_nat @ ( sK76_SY686 @ SV319 @ SV251 @ SV133 ) @ SV251 )
= $true )
| ( ( SV133 = zero_zero_nat )
= $true )
| ( ( SV133
= ( suc @ SV319 ) )
= $false )
| ( ( ord_less_nat @ SV319 @ SV251 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2995]) ).
thf(3009,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) ) )
= $false )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2998]) ).
thf(3010,plain,
! [SV228: real] :
( ( ( ~ ( ( SV228 != zero_zero_real ) ) )
= $false )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2998]) ).
thf(3011,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) ) )
= $true )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2999]) ).
thf(3012,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( SV228 != zero_zero_real )
= $true )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3000]) ).
thf(3013,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) ) )
= $true )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3001]) ).
thf(3014,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( SV228 != zero_zero_real )
= $true )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3002]) ).
thf(3015,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
= $false )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3003]) ).
thf(3016,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( SV228 = zero_zero_real )
= $false )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3004]) ).
thf(3017,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) ) )
= $true )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3009]) ).
thf(3018,plain,
! [SV228: real] :
( ( ( SV228 != zero_zero_real )
= $true )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3010]) ).
thf(3019,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
= $false )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3011]) ).
thf(3020,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( SV228 = zero_zero_real )
= $false )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3012]) ).
thf(3021,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
= $false )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3013]) ).
thf(3022,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( SV228 = zero_zero_real )
= $false )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3014]) ).
thf(3023,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) ) )
= $false )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3015]) ).
thf(3024,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
= $false )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3015]) ).
thf(3025,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
| ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
= $false )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3017]) ).
thf(3026,plain,
! [SV228: real] :
( ( ( SV228 = zero_zero_real )
= $false )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3018]) ).
thf(3027,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) ) )
= $false )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3019]) ).
thf(3028,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
= $false )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3019]) ).
thf(3029,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) ) )
= $false )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3021]) ).
thf(3030,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
= $false )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3021]) ).
thf(3031,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
= $true )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3023]) ).
thf(3032,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) )
= $true )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3024]) ).
thf(3033,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) ) )
= $false )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3025]) ).
thf(3034,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( ~ ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) ) )
= $false )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3025]) ).
thf(3035,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
= $true )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3027]) ).
thf(3036,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) )
= $true )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3028]) ).
thf(3037,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
= $true )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3029]) ).
thf(3038,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) )
= $true )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3030]) ).
thf(3039,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV228 ) )
= $true )
| ( ( ord_less_real @ SV103 @ SV297 )
= $true )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3031]) ).
thf(3040,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( ~ ( ord_less_real @ SV228 @ zero_zero_real ) )
= $true )
| ( ( ord_less_real @ SV297 @ SV103 )
= $true )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3032]) ).
thf(3041,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV228 )
| ( ord_less_real @ SV103 @ SV297 ) )
= $true )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3033]) ).
thf(3042,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( ~ ( ord_less_real @ SV228 @ zero_zero_real )
| ( ord_less_real @ SV297 @ SV103 ) )
= $true )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3034]) ).
thf(3043,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV228 ) )
= $true )
| ( ( ord_less_real @ SV103 @ SV297 )
= $true )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3035]) ).
thf(3044,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( ~ ( ord_less_real @ SV228 @ zero_zero_real ) )
= $true )
| ( ( ord_less_real @ SV297 @ SV103 )
= $true )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3036]) ).
thf(3045,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV228 ) )
= $true )
| ( ( ord_less_real @ SV103 @ SV297 )
= $true )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3037]) ).
thf(3046,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( ~ ( ord_less_real @ SV228 @ zero_zero_real ) )
= $true )
| ( ( ord_less_real @ SV297 @ SV103 )
= $true )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3038]) ).
thf(3047,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ord_less_real @ zero_zero_real @ SV228 )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $true )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3039]) ).
thf(3048,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( ord_less_real @ SV228 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV297 @ SV103 )
= $true )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3040]) ).
thf(3049,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ~ ( ord_less_real @ zero_zero_real @ SV228 ) )
= $true )
| ( ( ord_less_real @ SV103 @ SV297 )
= $true )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3041]) ).
thf(3050,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( ~ ( ord_less_real @ SV228 @ zero_zero_real ) )
= $true )
| ( ( ord_less_real @ SV297 @ SV103 )
= $true )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3042]) ).
thf(3051,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ord_less_real @ zero_zero_real @ SV228 )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $true )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3043]) ).
thf(3052,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( ord_less_real @ SV228 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV297 @ SV103 )
= $true )
| ( ( ord_less_real @ SV297 @ SV103 )
= $false )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3044]) ).
thf(3053,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ord_less_real @ zero_zero_real @ SV228 )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $true )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3045]) ).
thf(3054,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( ord_less_real @ SV228 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV297 @ SV103 )
= $true )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ SV103 @ SV297 )
= $false )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3046]) ).
thf(3055,plain,
! [SV297: real,SV103: real,SV228: real] :
( ( ( ord_less_real @ zero_zero_real @ SV228 )
= $false )
| ( ( ord_less_real @ SV103 @ SV297 )
= $true )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3049]) ).
thf(3056,plain,
! [SV103: real,SV297: real,SV228: real] :
( ( ( ord_less_real @ SV228 @ zero_zero_real )
= $false )
| ( ( ord_less_real @ SV297 @ SV103 )
= $true )
| ( ( ord_less_real @ SV228 @ zero_zero_real )
= $true )
| ( ( ord_less_real @ zero_zero_real @ SV228 )
= $true )
| ( ( SV228 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3050]) ).
thf(3057,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[497,3056,3055,3054,3053,3052,3051,3048,3047,3026,3022,3020,3016,3008,3007,3006,3005,2997,2996,2991,2990,2989,2988,2982,2981,2980,2977,2976,2975,2974,2972,2971,2970,2964,2963,2960,2958,2955,2954,2953,2952,2951,2943,2942,2941,2940,2939,2938,2937,2936,2935,2934,2932,2931,2930,2929,2928,2927,2926,2925,2922,2914,2908,2906,2905,2875,2840,2835,2834,2823,2822,2821,2800,2798,2794,2793,2789,2780,2779,2777,2776,2772,2771,2764,2754,2753,2752,2737,2733,2732,2718,2716,2714,2710,2708,2703,2702,2697,2696,2695,2694,2689,2688,2685,2684,2683,2682,2677,2675,2668,2663,2662,2646,2645,2643,2642,2640,2630,2629,2605,2604,2595,2594,2593,2575,2574,2573,2570,2569,2568,2566,2564,2563,2555,2554,2547,2545,2543,2536,2534,2521,2520,2508,2502,2501,2497,2495,2492,2490,2473,2472,2470,2451,2437,2436,2435,2434,2422,2420,2415,2414,2413,2412,2411,2410,2409,2408,2404,2403,2390,2385,2384,2383,2370,2354,2353,2352,2351,2338,2322,2321,2320,2319,2317,2283,2282,2281,2280,2253,2252,2233,2232,2231,2230,2229,2228,2227,2226,2225,2224,2223,2222,2221,2220,2219,2218,2217,2216,2207,2178,2168,2167,2156,2152,2135,2133,2132,2131,2130,2128,2127,2126,2125,2124,2123,2122,2121,2119,2117,2116,2114,2112,2111,2110,2109,2107,2106,2105,2104,2103,2102,2101,2100,2099,2098,2097,2096,2095,2094,2093,2092,2087,2080,2076,2072,2059,2058,2051,2042,2038,2032,2025,2016,2015,2014,2013,2012,2011,2010,2009,2001,2000,1996,1995,1994,1993,1984,1983,1982,1981,1975,1969,1968,1964,1963,1962,1961,1960,1959,1958,1957,1956,1955,1954,1953,1952,1951,1950,1949,1948,1947,1946,1945,1907,1906,1899,1895,1893,1887,1885,1881,1878,1874,1873,1870,1866,1861,1860,1848,1816,1815,1814,1813,1801,1800,1799,1798,1797,1796,1795,1794,1793,1792,1791,1790,1789,1788,1787,1786,1757,1756,1742,1733,1729,1723,1718,1717,1716,1715,1705,1698,1694,1692,1690,1685,1677,1670,1598,1590,1586,1579,1569,1563,1561,1553,1543,1533,1528,1518,1449,1434,1391,1387,1356,1354,1353,1350,1348,1347,1343,1342,1338,1321,1317,1313,1310,1308,1298,1290,1282,1275,1274,1268,1264,1262,1258,1250,1248,1232,1230,1228,1226,1218,1210,1206,1200,1193,1185,1164,1147,1141,1137,1122,1115,1113,1111,1109,1107,1105,1103,1101,1098,1095,1093,1091,1085,1083,1081,1079,1077,1070,1061,1053,1052,1028,1019,1013,968,963,957,950,945,943,941,939,937,936,935,934,926,891,890,862,813,811,810,806,795,794,793,792,791,789,788,787,778,776,557,556,555,554,552,549,545,511,510,509,498]) ).
thf(3058,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[3057]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP130^1 : TPTP v9.3.1. Released v7.5.0.
% 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
% 0.09/0.17 % Computer : n013.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 11:17:21 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.97/5.74 ..
% 32.97/5.74
% 32.97/5.74 No.of.Axioms: 166
% 32.97/5.74
% 32.97/5.74 Length.of.Defs: 0
% 32.97/5.74
% 32.97/5.74 Contains.Choice.Funs: false
% 32.97/5.74 ..........................................................................
% 32.97/5.74
% 32.97/5.74 ********************************
% 32.97/5.74 * All subproblems solved! *
% 32.97/5.74 ********************************
% 32.97/5.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:166,ps:0,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:3057,loop_count:0,foatp_calls:1,translation:fof_full)
% 32.97/5.74
% 32.97/5.74 %**** Beginning of derivation protocol ****
% 32.97/5.74 % SZS output start CNFRefutation
% See solution above
% 32.97/5.77
% 32.97/5.77 %**** End of derivation protocol ****
% 32.97/5.77 %**** no. of clauses in derivation: 2905 ****
% 32.97/5.77 %**** clause counter: 3057 ****
% 32.97/5.77
% 32.97/5.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:166,ps:0,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:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:3057,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------