%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP131^1 : 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 : n018.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 10:24:14 AM UTC 2026
% Result : Theorem 55.49s 9.56s
% Output : CNFRefutation 9.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 213
% Syntax : Number of formulae : 3201 (1309 unt; 0 typ; 0 def)
% Number of atoms : 19905 (9163 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 35632 (5675 ~;5037 |; 60 &;24473 @)
% ( 0 <=>; 387 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 411 ( 411 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 29 usr; 6 con; 0-3 aty)
% Number of variables : 8763 ( 110 ^;8635 !; 18 ?;8763 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_nat,type,
nat: $tType ).
thf(tp_i,type,
i: nat ).
thf(tp_k,type,
k: nat ).
thf(tp_minus_minus_nat,type,
minus_minus_nat: nat > nat > nat ).
thf(tp_n,type,
n: nat ).
thf(tp_number1551313001itions,type,
number1551313001itions: ( nat > nat ) > nat > $o ).
thf(tp_ord_less_eq_nat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(tp_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(tp_p,type,
p: nat > nat ).
thf(tp_plus_plus_nat,type,
plus_plus_nat: nat > nat > nat ).
thf(tp_sK10_SY751,type,
sK10_SY751: nat > nat > ( nat > $o ) > nat ).
thf(tp_sK11_SY1002,type,
sK11_SY1002: ( nat > $o ) > nat > nat > nat ).
thf(tp_sK12_SY1033,type,
sK12_SY1033: nat > nat > nat ).
thf(tp_sK13_SY1034,type,
sK13_SY1034: nat > nat > nat ).
thf(tp_sK14_SY1002,type,
sK14_SY1002: ( nat > $o ) > nat > nat > nat ).
thf(tp_sK15_SY1022,type,
sK15_SY1022: ( nat > $o ) > nat > nat > nat ).
thf(tp_sK16_SY1022,type,
sK16_SY1022: ( nat > $o ) > nat > nat > nat ).
thf(tp_sK17_SY1033,type,
sK17_SY1033: nat > nat > nat > nat ).
thf(tp_sK18_SY1034,type,
sK18_SY1034: nat > nat > nat > nat ).
thf(tp_sK1_SY712,type,
sK1_SY712: nat > ( nat > $o ) > nat ).
thf(tp_sK2_SY783,type,
sK2_SY783: nat > ( nat > $o ) > nat ).
thf(tp_sK3_SY609,type,
sK3_SY609: nat > nat > ( nat > nat ) > nat ).
thf(tp_sK4_SY975,type,
sK4_SY975: nat > nat > nat ).
thf(tp_sK5_SV515,type,
sK5_SV515: ( nat > nat ) > nat ).
thf(tp_sK6_SY1043,type,
sK6_SY1043: ( nat > nat ) > nat > nat > nat ).
thf(tp_sK7_SY655,type,
sK7_SY655: nat > ( nat > $o ) > nat ).
thf(tp_sK8_SY1015,type,
sK8_SY1015: nat > nat > ( nat > $o ) > nat ).
thf(tp_sK9_SY751,type,
sK9_SY751: nat > nat > ( nat > $o ) > nat ).
thf(tp_times_times_nat,type,
times_times_nat: nat > nat > nat ).
thf(tp_zero_zero_nat,type,
zero_zero_nat: nat ).
thf(1,axiom,
! [I2: nat,J: nat,K: nat,L: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ( ord_less_eq_nat @ K @ L )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_add__le__mono) ).
thf(2,axiom,
! [I2: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_add__le__mono1) ).
thf(3,axiom,
! [I2: nat,J: nat,M: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_trans__le__add1) ).
thf(4,axiom,
! [I2: nat,J: nat,M: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_trans__le__add2) ).
thf(5,axiom,
( ord_less_eq_nat
= ( ^ [M3: nat,N3: nat] :
? [K2: nat] :
( N3
= ( plus_plus_nat @ M3 @ K2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_nat__le__iff__add) ).
thf(6,axiom,
! [N: nat] :
( ( times_times_nat @ zero_zero_nat @ N )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_mult__0) ).
thf(7,axiom,
! [K: nat,M: nat,N: nat] :
( ( ( times_times_nat @ K @ M )
= ( times_times_nat @ K @ N ) )
= ( ( K = zero_zero_nat )
| ( M = N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_nat__mult__eq__cancel__disj) ).
thf(8,axiom,
! [I2: nat,J: nat,K: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
=> ( ord_less_nat @ I2 @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_add__lessD1) ).
thf(9,axiom,
! [I2: nat,J: nat,K: nat,L: nat] :
( ( ord_less_nat @ I2 @ J )
=> ( ( ord_less_nat @ K @ L )
=> ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_add__less__mono) ).
thf(10,axiom,
! [I2: nat,J: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ I2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_not__add__less1) ).
thf(11,axiom,
! [J: nat,I2: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ J @ I2 ) @ I2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_not__add__less2) ).
thf(12,axiom,
! [I2: nat,J: nat,K: nat] :
( ( ord_less_nat @ I2 @ J )
=> ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_add__less__mono1) ).
thf(13,axiom,
! [I2: nat,J: nat,M: nat] :
( ( ord_less_nat @ I2 @ J )
=> ( ord_less_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_trans__less__add1) ).
thf(14,axiom,
! [I2: nat,J: nat,M: nat] :
( ( ord_less_nat @ I2 @ J )
=> ( ord_less_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_trans__less__add2) ).
thf(15,axiom,
! [K: nat,L: nat,M: nat,N: nat] :
( ( ord_less_nat @ K @ L )
=> ( ( ( plus_plus_nat @ M @ L )
= ( plus_plus_nat @ K @ N ) )
=> ( ord_less_nat @ M @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_less__add__eq__less) ).
thf(16,axiom,
( ord_less_nat
= ( ^ [M3: nat,N3: nat] :
( ( ord_less_eq_nat @ M3 @ N3 )
& ( M3 != N3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_nat__less__le) ).
thf(17,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_eq_nat @ M @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_less__imp__le__nat) ).
thf(18,axiom,
( ord_less_eq_nat
= ( ^ [M3: nat,N3: nat] :
( ( ord_less_nat @ M3 @ N3 )
| ( M3 = N3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_le__eq__less__or__eq) ).
thf(19,axiom,
! [M: nat,N: nat] :
( ( ( ord_less_nat @ M @ N )
| ( M = N ) )
=> ( ord_less_eq_nat @ M @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_less__or__eq__imp__le) ).
thf(20,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( M != N )
=> ( ord_less_nat @ M @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_le__neq__implies__less) ).
thf(21,axiom,
! [F: nat > nat,I2: nat,J: nat] :
( ! [I3: nat,J2: nat] :
( ( ord_less_nat @ I3 @ J2 )
=> ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
=> ( ( ord_less_eq_nat @ I2 @ J )
=> ( ord_less_eq_nat @ ( F @ I2 ) @ ( F @ J ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_less__mono__imp__le__mono) ).
thf(22,axiom,
! [N: nat] :
( ( plus_plus_nat @ zero_zero_nat @ N )
= N ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_plus__nat_Oadd__0) ).
thf(23,axiom,
! [M: nat,N: nat] :
( ( ( plus_plus_nat @ M @ N )
= M )
=> ( N = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_add__eq__self__zero) ).
thf(24,axiom,
! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_less__eq__nat_Osimps_I1_J) ).
thf(25,axiom,
! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_le__0__eq) ).
thf(26,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_bot__nat__0_Oextremum__unique) ).
thf(27,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_bot__nat__0_Oextremum__uniqueI) ).
thf(28,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_gr0I) ).
thf(29,axiom,
! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_not__gr0) ).
thf(30,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_not__less0) ).
thf(31,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_less__zeroE) ).
thf(32,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_gr__implies__not0) ).
thf(33,axiom,
! [P2: nat > $o,N: nat] :
( ( P2 @ zero_zero_nat )
=> ( ! [N2: nat] :
( ( ord_less_nat @ zero_zero_nat @ N2 )
=> ( ~ ( P2 @ N2 )
=> ? [M2: nat] :
( ( ord_less_nat @ M2 @ N2 )
& ~ ( P2 @ M2 ) ) ) )
=> ( P2 @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_infinite__descent0) ).
thf(34,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_bot__nat__0_Oextremum__strict) ).
thf(35,axiom,
! [I2: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_nat @ I2 @ J )
& ( ord_less_nat @ K @ L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_add__mono__thms__linordered__field_I5_J) ).
thf(36,axiom,
! [I2: nat,J: nat,K: nat,L: nat] :
( ( ( I2 = J )
& ( ord_less_nat @ K @ L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_add__mono__thms__linordered__field_I2_J) ).
thf(37,axiom,
! [I2: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_nat @ I2 @ J )
& ( K = L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_add__mono__thms__linordered__field_I1_J) ).
thf(38,axiom,
! [A: nat,B: nat,C: nat,D2: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ C @ D2 )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_add__strict__mono) ).
thf(39,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_add__strict__left__mono) ).
thf(40,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_add__strict__right__mono) ).
thf(41,axiom,
! [C: nat,A: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_add__less__imp__less__left) ).
thf(42,axiom,
! [A: nat,C: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_add__less__imp__less__right) ).
thf(43,axiom,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_comm__monoid__add__class_Oadd__0) ).
thf(44,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_add_Ocomm__neutral) ).
thf(45,axiom,
! [I2: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_eq_nat @ I2 @ J )
& ( K = L ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_add__mono__thms__linordered__semiring_I3_J) ).
thf(46,axiom,
! [I2: nat,J: nat,K: nat,L: nat] :
( ( ( I2 = J )
& ( ord_less_eq_nat @ K @ L ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_add__mono__thms__linordered__semiring_I2_J) ).
thf(47,axiom,
! [I2: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_eq_nat @ I2 @ J )
& ( ord_less_eq_nat @ K @ L ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_add__mono__thms__linordered__semiring_I1_J) ).
thf(48,axiom,
! [A: nat,B: nat,C: nat,D2: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D2 )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_add__mono) ).
thf(49,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_add__left__mono) ).
thf(50,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ~ ! [C3: nat] :
( B
!= ( plus_plus_nat @ A @ C3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_less__eqE) ).
thf(51,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_add__right__mono) ).
thf(52,axiom,
( ord_less_eq_nat
= ( ^ [A2: nat,B2: nat] :
? [C2: nat] :
( B2
= ( plus_plus_nat @ A2 @ C2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_le__iff__add) ).
thf(53,axiom,
! [C: nat,A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_add__le__imp__le__left) ).
thf(54,axiom,
! [A: nat,C: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_add__le__imp__le__right) ).
thf(55,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_gr__zeroI) ).
thf(56,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_not__less__zero) ).
thf(57,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_gr__implies__not__zero) ).
thf(58,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( N != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_zero__less__iff__neq__zero) ).
thf(59,axiom,
! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_zero__le) ).
thf(60,axiom,
! [N: nat] : ( ord_less_eq_nat @ N @ N ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_le__refl) ).
thf(61,axiom,
! [I2: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ( ord_less_eq_nat @ J @ K )
=> ( ord_less_eq_nat @ I2 @ K ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_le__trans) ).
thf(62,axiom,
! [M: nat,N: nat] :
( ( M = N )
=> ( ord_less_eq_nat @ M @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_eq__imp__le) ).
thf(63,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( ord_less_eq_nat @ N @ M )
=> ( M = N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_le__antisym) ).
thf(64,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
| ( ord_less_eq_nat @ N @ M ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_nat__le__linear) ).
thf(65,axiom,
! [P2: nat > $o,K: nat,B: nat] :
( ( P2 @ K )
=> ( ! [Y2: nat] :
( ( P2 @ Y2 )
=> ( ord_less_eq_nat @ Y2 @ B ) )
=> ? [X2: nat] :
( ( P2 @ X2 )
& ! [Y3: nat] :
( ( P2 @ Y3 )
=> ( ord_less_eq_nat @ Y3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_Nat_Oex__has__greatest__nat) ).
thf(66,axiom,
! [M: nat,N: nat] :
( ( M != N )
= ( ( ord_less_nat @ M @ N )
| ( ord_less_nat @ N @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_nat__neq__iff) ).
thf(67,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ N ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_less__not__refl) ).
thf(68,axiom,
! [N: nat,M: nat] :
( ( ord_less_nat @ N @ M )
=> ( M != N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_less__not__refl2) ).
thf(69,axiom,
! [S: nat,T: nat] :
( ( ord_less_nat @ S @ T )
=> ( S != T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_less__not__refl3) ).
thf(70,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ N ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_less__irrefl__nat) ).
thf(71,axiom,
! [P2: nat > $o,N: nat] :
( ! [N2: nat] :
( ! [M2: nat] :
( ( ord_less_nat @ M2 @ N2 )
=> ( P2 @ M2 ) )
=> ( P2 @ N2 ) )
=> ( P2 @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_nat__less__induct) ).
thf(72,axiom,
! [P2: nat > $o,N: nat] :
( ! [N2: nat] :
( ~ ( P2 @ N2 )
=> ? [M2: nat] :
( ( ord_less_nat @ M2 @ N2 )
& ~ ( P2 @ M2 ) ) )
=> ( P2 @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_infinite__descent) ).
thf(73,axiom,
! [X: nat,Y: nat] :
( ( X != Y )
=> ( ~ ( ord_less_nat @ X @ Y )
=> ( ord_less_nat @ Y @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_linorder__neqE__nat) ).
thf(74,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(75,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_mult_Oassoc) ).
thf(76,axiom,
( times_times_nat
= ( ^ [A2: nat,B2: nat] : ( times_times_nat @ B2 @ A2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_mult_Ocommute) ).
thf(77,axiom,
! [B: nat,A: nat,C: nat] :
( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_mult_Oleft__commute) ).
thf(78,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(79,axiom,
! [I2: nat,J: nat,K: nat,L: nat] :
( ( ( I2 = J )
& ( K = L ) )
=> ( ( plus_plus_nat @ I2 @ K )
= ( plus_plus_nat @ J @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_add__mono__thms__linordered__semiring_I4_J) ).
thf(80,axiom,
! [A3: nat,K: nat,A: nat,B: nat] :
( ( A3
= ( plus_plus_nat @ K @ A ) )
=> ( ( plus_plus_nat @ A3 @ B )
= ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_group__cancel_Oadd1) ).
thf(81,axiom,
! [B3: nat,K: nat,B: nat,A: nat] :
( ( B3
= ( plus_plus_nat @ K @ B ) )
=> ( ( plus_plus_nat @ A @ B3 )
= ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_group__cancel_Oadd2) ).
thf(82,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_add_Oassoc) ).
thf(83,axiom,
( plus_plus_nat
= ( ^ [A2: nat,B2: nat] : ( plus_plus_nat @ B2 @ A2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_add_Ocommute) ).
thf(84,axiom,
! [B: nat,A: nat,C: nat] :
( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_add_Oleft__commute) ).
thf(85,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_add__left__imp__eq) ).
thf(86,axiom,
! [B: nat,A: nat,C: nat] :
( ( ( plus_plus_nat @ B @ A )
= ( plus_plus_nat @ C @ A ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_add__right__imp__eq) ).
thf(87,axiom,
! [X: nat] :
( ( zero_zero_nat = X )
= ( X = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_zero__reorient) ).
thf(88,axiom,
! [J: nat,I2: nat,U: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ J @ I2 )
=> ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
= ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_nat__less__add__iff1) ).
thf(89,axiom,
! [I2: nat,J: nat,U: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
= ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_nat__less__add__iff2) ).
thf(90,axiom,
! [J: nat,I2: nat,U: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ J @ I2 )
=> ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
= ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
= ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M )
= N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_nat__eq__add__iff1) ).
thf(91,axiom,
! [I2: nat,J: nat,U: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
= ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
= ( M
= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_nat__eq__add__iff2) ).
thf(92,axiom,
! [J: nat,I2: nat,U: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ J @ I2 )
=> ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_nat__le__add__iff1) ).
thf(93,axiom,
! [I2: nat,J: nat,U: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
= ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_nat__le__add__iff2) ).
thf(94,axiom,
! [J: nat,I2: nat,U: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ J @ I2 )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
= ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_nat__diff__add__eq1) ).
thf(95,axiom,
! [I2: nat,J: nat,U: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
= ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_nat__diff__add__eq2) ).
thf(96,axiom,
! [K: nat,J: nat,I2: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
= ( ord_less_nat @ J @ ( plus_plus_nat @ I2 @ K ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_less__diff__conv2) ).
thf(97,axiom,
! [P2: nat > $o,A: nat,B: nat] :
( ( P2 @ ( minus_minus_nat @ A @ B ) )
= ( ( ( ord_less_nat @ A @ B )
=> ( P2 @ zero_zero_nat ) )
& ! [D: nat] :
( ( A
= ( plus_plus_nat @ B @ D ) )
=> ( P2 @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_nat__diff__split) ).
thf(98,axiom,
! [P2: nat > $o,A: nat,B: nat] :
( ( P2 @ ( minus_minus_nat @ A @ B ) )
= ( ~ ( ( ( ord_less_nat @ A @ B )
& ~ ( P2 @ zero_zero_nat ) )
| ? [D: nat] :
( ( A
= ( plus_plus_nat @ B @ D ) )
& ~ ( P2 @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_nat__diff__split__asm) ).
thf(99,axiom,
! [J: nat,K: nat,I2: nat] :
( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
= ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I2 @ K ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_le__diff__conv) ).
thf(100,axiom,
! [K: nat,J: nat,I2: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_Nat_Ole__diff__conv2) ).
thf(101,axiom,
! [K: nat,J: nat,I2: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
= ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J @ K ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_Nat_Odiff__add__assoc) ).
thf(102,axiom,
! [K: nat,J: nat,I2: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I2 ) @ K )
= ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_Nat_Odiff__add__assoc2) ).
thf(103,axiom,
! [I2: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ( ( minus_minus_nat @ J @ I2 )
= K )
= ( J
= ( plus_plus_nat @ K @ I2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_Nat_Ole__imp__diff__is__add) ).
thf(104,axiom,
! [I2: nat,J: nat,K: nat] :
( ( ord_less_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
= ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_less__diff__conv) ).
thf(105,axiom,
! [M: nat,N: nat] :
( ~ ( ord_less_nat @ M @ N )
=> ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
= M ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_add__diff__inverse__nat) ).
thf(106,axiom,
! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ K @ M )
=> ( ( ord_less_eq_nat @ K @ N )
=> ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
= ( ord_less_nat @ M @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_less__diff__iff) ).
thf(107,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_diff__less__mono) ).
thf(108,axiom,
! [N: nat,M: nat] :
( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_diff__add__0) ).
thf(109,axiom,
! [N: nat,M: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( ord_less_nat @ zero_zero_nat @ M )
=> ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_diff__less) ).
thf(110,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_ordered__cancel__comm__monoid__diff__class_Odiff__add) ).
thf(111,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_le__add__diff) ).
thf(112,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2) ).
thf(113,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc) ).
thf(114,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
= ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc) ).
thf(115,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
= ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2) ).
thf(116,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
= ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2) ).
thf(117,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right) ).
thf(118,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse) ).
thf(119,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ( ( minus_minus_nat @ B @ A )
= C )
= ( B
= ( plus_plus_nat @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add) ).
thf(120,axiom,
! [M: nat,N: nat,K: nat] :
( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
= ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_diff__mult__distrib) ).
thf(121,axiom,
! [K: nat,M: nat,N: nat] :
( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
= ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_diff__mult__distrib2) ).
thf(122,axiom,
! [K: nat,M: nat,N: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
= ( minus_minus_nat @ M @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_Nat_Odiff__cancel) ).
thf(123,axiom,
! [M: nat,K: nat,N: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
= ( minus_minus_nat @ M @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_diff__cancel2) ).
thf(124,axiom,
! [N: nat,M: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
= M ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_diff__add__inverse) ).
thf(125,axiom,
! [M: nat,N: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
= M ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_diff__add__inverse2) ).
thf(126,axiom,
! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ K @ M )
=> ( ( ord_less_eq_nat @ K @ N )
=> ( ( ( minus_minus_nat @ M @ K )
= ( minus_minus_nat @ N @ K ) )
= ( M = N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_eq__diff__iff) ).
thf(127,axiom,
! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ K @ M )
=> ( ( ord_less_eq_nat @ K @ N )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
= ( ord_less_eq_nat @ M @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_le__diff__iff) ).
thf(128,axiom,
! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ K @ M )
=> ( ( ord_less_eq_nat @ K @ N )
=> ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
= ( minus_minus_nat @ M @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_Nat_Odiff__diff__eq) ).
thf(129,axiom,
! [M: nat,N: nat,L: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_diff__le__mono) ).
thf(130,axiom,
! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_diff__le__self) ).
thf(131,axiom,
! [A: nat,C: nat,B: nat] :
( ( ord_less_eq_nat @ A @ C )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
= ( ord_less_eq_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_le__diff__iff_H) ).
thf(132,axiom,
! [M: nat,N: nat,L: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_diff__le__mono2) ).
thf(133,axiom,
! [M: nat,N: nat,L: nat] :
( ( ord_less_nat @ M @ N )
=> ( ( ord_less_nat @ M @ L )
=> ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_diff__less__mono2) ).
thf(134,axiom,
! [J: nat,K: nat,N: nat] :
( ( ord_less_nat @ J @ K )
=> ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_less__imp__diff__less) ).
thf(135,axiom,
! [M: nat,N: nat] :
( ( ( minus_minus_nat @ M @ N )
= zero_zero_nat )
=> ( ( ( minus_minus_nat @ N @ M )
= zero_zero_nat )
=> ( M = N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_diffs0__imp__equal) ).
thf(136,axiom,
! [M: nat] :
( ( minus_minus_nat @ M @ zero_zero_nat )
= M ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_minus__nat_Odiff__0) ).
thf(137,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_diff__diff__add) ).
thf(138,axiom,
! [C: nat,B: nat,A: nat] :
( ( ( plus_plus_nat @ C @ B )
= A )
=> ( C
= ( minus_minus_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_add__implies__diff) ).
thf(139,axiom,
! [I2: nat,J: nat,K: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
= ( minus_minus_nat @ ( minus_minus_nat @ I2 @ K ) @ J ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_diff__commute) ).
thf(140,axiom,
! [A: nat,C: nat,B: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_cancel__ab__semigroup__add__class_Odiff__right__commute) ).
thf(141,axiom,
! [K: nat,J: nat,I2: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
= ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J ) @ K ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Nat_Oadd__diff__assoc) ).
thf(142,axiom,
! [K: nat,J: nat,I2: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
= ( minus_minus_nat @ ( plus_plus_nat @ J @ I2 ) @ K ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_Nat_Oadd__diff__assoc2) ).
thf(143,axiom,
! [K: nat,J: nat,I2: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( minus_minus_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
= ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_Nat_Odiff__diff__right) ).
thf(144,axiom,
! [M: nat,N: nat] :
( ( ( minus_minus_nat @ M @ N )
= zero_zero_nat )
= ( ord_less_eq_nat @ M @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_diff__is__0__eq) ).
thf(145,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( minus_minus_nat @ M @ N )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_diff__is__0__eq_H) ).
thf(146,axiom,
! [N: nat,M: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
= ( ord_less_nat @ M @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_zero__less__diff) ).
thf(147,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_diff__add__zero) ).
thf(148,axiom,
! [B: nat,A: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
= ( ord_less_eq_nat @ A @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_add__le__same__cancel1) ).
thf(149,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
= ( ord_less_eq_nat @ A @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_add__le__same__cancel2) ).
thf(150,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
= ( ord_less_eq_nat @ zero_zero_nat @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_le__add__same__cancel1) ).
thf(151,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
= ( ord_less_eq_nat @ zero_zero_nat @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_le__add__same__cancel2) ).
thf(152,axiom,
! [I2: nat,J: nat,K: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
= ( minus_minus_nat @ I2 @ ( plus_plus_nat @ J @ K ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_diff__diff__left) ).
thf(153,axiom,
! [I2: nat,N: nat] :
( ( ord_less_eq_nat @ I2 @ N )
=> ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I2 ) )
= I2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_diff__diff__cancel) ).
thf(154,axiom,
! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
= ( ord_less_eq_nat @ M @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_nat__add__left__cancel__le) ).
thf(155,axiom,
! [M: nat,N: nat] :
( ( ( times_times_nat @ M @ N )
= zero_zero_nat )
= ( ( M = zero_zero_nat )
| ( N = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_mult__is__0) ).
thf(156,axiom,
! [M: nat] :
( ( times_times_nat @ M @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_mult__0__right) ).
thf(157,axiom,
! [K: nat,M: nat,N: nat] :
( ( ( times_times_nat @ K @ M )
= ( times_times_nat @ K @ N ) )
= ( ( M = N )
| ( K = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_mult__cancel1) ).
thf(158,axiom,
! [M: nat,K: nat,N: nat] :
( ( ( times_times_nat @ M @ K )
= ( times_times_nat @ N @ K ) )
= ( ( M = N )
| ( K = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_mult__cancel2) ).
thf(159,axiom,
! [N: nat] :
( ( minus_minus_nat @ zero_zero_nat @ N )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_diff__0__eq__0) ).
thf(160,axiom,
! [M: nat] :
( ( minus_minus_nat @ M @ M )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_diff__self__eq__0) ).
thf(161,axiom,
! [K: nat,M: nat,N: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
= ( ord_less_nat @ M @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_nat__add__left__cancel__less) ).
thf(162,axiom,
! [M: nat,N: nat] :
( ( ( plus_plus_nat @ M @ N )
= zero_zero_nat )
= ( ( M = zero_zero_nat )
& ( N = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_add__is__0) ).
thf(163,axiom,
! [M: nat] :
( ( plus_plus_nat @ M @ zero_zero_nat )
= M ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_Nat_Oadd__0__right) ).
thf(164,axiom,
! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_le0) ).
thf(165,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_bot__nat__0_Oextremum) ).
thf(166,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_neq0__conv) ).
thf(167,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_less__nat__zero__code) ).
thf(168,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_bot__nat__0_Onot__eq__extremum) ).
thf(169,axiom,
! [C: nat,A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
= ( minus_minus_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_add__diff__cancel__left) ).
thf(170,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_add__diff__cancel__left_H) ).
thf(171,axiom,
! [A: nat,C: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
= ( minus_minus_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_add__diff__cancel__right) ).
thf(172,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_add__diff__cancel__right_H) ).
thf(173,axiom,
! [C: nat,A: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_add__less__cancel__left) ).
thf(174,axiom,
! [A: nat,C: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
= ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_add__less__cancel__right) ).
thf(175,axiom,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_zero__diff) ).
thf(176,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_diff__zero) ).
thf(177,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_cancel__comm__monoid__add__class_Odiff__cancel) ).
thf(178,axiom,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_add_Oleft__neutral) ).
thf(179,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_add_Oright__neutral) ).
thf(180,axiom,
! [B: nat,A: nat] :
( ( ( plus_plus_nat @ B @ A )
= A )
= ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_add__cancel__left__left) ).
thf(181,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= A )
= ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_add__cancel__left__right) ).
thf(182,axiom,
! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ B @ A ) )
= ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_add__cancel__right__left) ).
thf(183,axiom,
! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ A @ B ) )
= ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_add__cancel__right__right) ).
thf(184,axiom,
! [X: nat,Y: nat] :
( ( ( plus_plus_nat @ X @ Y )
= zero_zero_nat )
= ( ( X = zero_zero_nat )
& ( Y = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_add__eq__0__iff__both__eq__0) ).
thf(185,axiom,
! [X: nat,Y: nat] :
( ( zero_zero_nat
= ( plus_plus_nat @ X @ Y ) )
= ( ( X = zero_zero_nat )
& ( Y = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_zero__eq__add__iff__both__eq__0) ).
thf(186,axiom,
! [C: nat,A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_add__le__cancel__left) ).
thf(187,axiom,
! [A: nat,C: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_add__le__cancel__right) ).
thf(188,axiom,
! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_not__gr__zero) ).
thf(189,axiom,
! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_le__zero__eq) ).
thf(190,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_add__left__cancel) ).
thf(191,axiom,
! [B: nat,A: nat,C: nat] :
( ( ( plus_plus_nat @ B @ A )
= ( plus_plus_nat @ C @ A ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_add__right__cancel) ).
thf(192,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
= ( ord_less_nat @ zero_zero_nat @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_less__add__same__cancel2) ).
thf(193,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
= ( ord_less_nat @ zero_zero_nat @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_less__add__same__cancel1) ).
thf(194,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
= ( ord_less_nat @ A @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_add__less__same__cancel2) ).
thf(195,axiom,
! [B: nat,A: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
= ( ord_less_nat @ A @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_add__less__same__cancel1) ).
thf(196,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
= ( ( ord_less_nat @ zero_zero_nat @ M )
| ( ord_less_nat @ zero_zero_nat @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_add__gr__0) ).
thf(197,axiom,
! [K: nat,M: nat,N: nat] :
( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
= ( ( ord_less_nat @ zero_zero_nat @ K )
& ( ord_less_nat @ M @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_nat__mult__less__cancel__disj) ).
thf(198,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
= ( ( ord_less_nat @ zero_zero_nat @ M )
& ( ord_less_nat @ zero_zero_nat @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_nat__0__less__mult__iff) ).
thf(199,axiom,
! [M: nat,K: nat,N: nat] :
( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
= ( ( ord_less_nat @ zero_zero_nat @ K )
& ( ord_less_nat @ M @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_mult__less__cancel2) ).
thf(200,axiom,
! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
= ( ( ord_less_nat @ zero_zero_nat @ K )
=> ( ord_less_eq_nat @ M @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_nat__mult__le__cancel__disj) ).
thf(201,axiom,
! [M: nat,K: nat,N: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
= ( ( ord_less_nat @ zero_zero_nat @ K )
=> ( ord_less_eq_nat @ M @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_mult__le__cancel2) ).
thf(202,axiom,
! [P: nat > nat,N: nat,I2: nat] :
( ( number1551313001itions @ P @ N )
=> ( ord_less_eq_nat @ ( P @ I2 ) @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_partitions__bounds) ).
thf(203,axiom,
! [P: nat > nat] :
( ( number1551313001itions @ P @ zero_zero_nat )
= ( P
= ( ^ [I: nat] : zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_partitions__zero) ).
thf(204,axiom,
ord_less_nat @ ( minus_minus_nat @ n @ k ) @ i,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8__092_060open_062n_A_N_Ak_A_060_Ai_092_060close_062) ).
thf(205,axiom,
i != k,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7__092_060open_062i_A_092_060noteq_062_Ak_092_060close_062) ).
thf(206,axiom,
ord_less_nat @ zero_zero_nat @ ( p @ k ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_assms_I2_J) ).
thf(207,axiom,
( ( p @ i )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__092_060open_062p_Ai_A_092_060noteq_062_A0_092_060close_062) ).
thf(208,axiom,
ord_less_eq_nat @ k @ n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__092_060open_062k_A_092_060le_062_An_092_060close_062) ).
thf(209,axiom,
ord_less_nat @ n @ ( plus_plus_nat @ ( times_times_nat @ ( p @ i ) @ i ) @ ( times_times_nat @ ( p @ k ) @ k ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_lower__bound) ).
thf(210,axiom,
ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( p @ i ) @ i ) @ ( times_times_nat @ ( p @ k ) @ k ) ) @ n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_upper__bound) ).
thf(211,axiom,
number1551313001itions @ p @ n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_assms_I1_J) ).
thf(212,axiom,
ord_less_eq_nat @ i @ n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062i_A_092_060le_062_An_092_060close_062) ).
thf(213,conjecture,
$false,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(214,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[213]) ).
thf(215,plain,
$false = $false,
inference(unfold_def,[status(thm)],[214]) ).
thf(216,plain,
( ( ! [I2: nat,J: nat,K: nat,L: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ( ord_less_eq_nat @ K @ L )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(217,plain,
( ( ! [I2: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(218,plain,
( ( ! [I2: nat,J: nat,M: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(219,plain,
( ( ! [I2: nat,J: nat,M: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(220,plain,
( ( ord_less_eq_nat
= ( ^ [M3: nat,N3: nat] :
? [K2: nat] :
( N3
= ( plus_plus_nat @ M3 @ K2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(221,plain,
( ( ! [N: nat] :
( ( times_times_nat @ zero_zero_nat @ N )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(222,plain,
( ( ! [K: nat,M: nat,N: nat] :
( ( ( times_times_nat @ K @ M )
= ( times_times_nat @ K @ N ) )
= ( ( K = zero_zero_nat )
| ( M = N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(223,plain,
( ( ! [I2: nat,J: nat,K: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
=> ( ord_less_nat @ I2 @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(224,plain,
( ( ! [I2: nat,J: nat,K: nat,L: nat] :
( ( ord_less_nat @ I2 @ J )
=> ( ( ord_less_nat @ K @ L )
=> ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(225,plain,
( ( ! [I2: nat,J: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ I2 ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(226,plain,
( ( ! [J: nat,I2: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ J @ I2 ) @ I2 ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(227,plain,
( ( ! [I2: nat,J: nat,K: nat] :
( ( ord_less_nat @ I2 @ J )
=> ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(228,plain,
( ( ! [I2: nat,J: nat,M: nat] :
( ( ord_less_nat @ I2 @ J )
=> ( ord_less_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(229,plain,
( ( ! [I2: nat,J: nat,M: nat] :
( ( ord_less_nat @ I2 @ J )
=> ( ord_less_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(230,plain,
( ( ! [K: nat,L: nat,M: nat,N: nat] :
( ( ord_less_nat @ K @ L )
=> ( ( ( plus_plus_nat @ M @ L )
= ( plus_plus_nat @ K @ N ) )
=> ( ord_less_nat @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(231,plain,
( ( ord_less_nat
= ( ^ [M3: nat,N3: nat] :
( ( ord_less_eq_nat @ M3 @ N3 )
& ( M3 != N3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(232,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(233,plain,
( ( ord_less_eq_nat
= ( ^ [M3: nat,N3: nat] :
( ( ord_less_nat @ M3 @ N3 )
| ( M3 = N3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(234,plain,
( ( ! [M: nat,N: nat] :
( ( ( ord_less_nat @ M @ N )
| ( M = N ) )
=> ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(235,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( M != N )
=> ( ord_less_nat @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(236,plain,
( ( ! [F: nat > nat,I2: nat,J: nat] :
( ! [I3: nat,J2: nat] :
( ( ord_less_nat @ I3 @ J2 )
=> ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
=> ( ( ord_less_eq_nat @ I2 @ J )
=> ( ord_less_eq_nat @ ( F @ I2 ) @ ( F @ J ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(237,plain,
( ( ! [N: nat] :
( ( plus_plus_nat @ zero_zero_nat @ N )
= N ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(238,plain,
( ( ! [M: nat,N: nat] :
( ( ( plus_plus_nat @ M @ N )
= M )
=> ( N = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(239,plain,
( ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(240,plain,
( ( ! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(241,plain,
( ( ! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(242,plain,
( ( ! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(243,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(244,plain,
( ( ! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(245,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(246,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(247,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(248,plain,
( ( ! [P2: nat > $o,N: nat] :
( ( P2 @ zero_zero_nat )
=> ( ! [N2: nat] :
( ( ord_less_nat @ zero_zero_nat @ N2 )
=> ( ~ ( P2 @ N2 )
=> ? [M2: nat] :
( ( ord_less_nat @ M2 @ N2 )
& ~ ( P2 @ M2 ) ) ) )
=> ( P2 @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(249,plain,
( ( ! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(250,plain,
( ( ! [I2: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_nat @ I2 @ J )
& ( ord_less_nat @ K @ L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(251,plain,
( ( ! [I2: nat,J: nat,K: nat,L: nat] :
( ( ( I2 = J )
& ( ord_less_nat @ K @ L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(252,plain,
( ( ! [I2: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_nat @ I2 @ J )
& ( K = L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(253,plain,
( ( ! [A: nat,B: nat,C: nat,D2: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ C @ D2 )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(254,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(255,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(256,plain,
( ( ! [C: nat,A: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(257,plain,
( ( ! [A: nat,C: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
=> ( ord_less_nat @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(258,plain,
( ( ! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(259,plain,
( ( ! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(260,plain,
( ( ! [I2: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_eq_nat @ I2 @ J )
& ( K = L ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(261,plain,
( ( ! [I2: nat,J: nat,K: nat,L: nat] :
( ( ( I2 = J )
& ( ord_less_eq_nat @ K @ L ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(262,plain,
( ( ! [I2: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_eq_nat @ I2 @ J )
& ( ord_less_eq_nat @ K @ L ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(263,plain,
( ( ! [A: nat,B: nat,C: nat,D2: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D2 )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(264,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(265,plain,
( ( ! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ~ ! [C3: nat] :
( B
!= ( plus_plus_nat @ A @ C3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(266,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(267,plain,
( ( ord_less_eq_nat
= ( ^ [A2: nat,B2: nat] :
? [C2: nat] :
( B2
= ( plus_plus_nat @ A2 @ C2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(268,plain,
( ( ! [C: nat,A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_eq_nat @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(269,plain,
( ( ! [A: nat,C: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
=> ( ord_less_eq_nat @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(270,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(271,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(272,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(273,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( N != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(274,plain,
( ( ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(275,plain,
( ( ! [N: nat] : ( ord_less_eq_nat @ N @ N ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(276,plain,
( ( ! [I2: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ( ord_less_eq_nat @ J @ K )
=> ( ord_less_eq_nat @ I2 @ K ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(277,plain,
( ( ! [M: nat,N: nat] :
( ( M = N )
=> ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(278,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( ord_less_eq_nat @ N @ M )
=> ( M = N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(279,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
| ( ord_less_eq_nat @ N @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(280,plain,
( ( ! [P2: nat > $o,K: nat,B: nat] :
( ( P2 @ K )
=> ( ! [Y2: nat] :
( ( P2 @ Y2 )
=> ( ord_less_eq_nat @ Y2 @ B ) )
=> ? [X2: nat] :
( ( P2 @ X2 )
& ! [Y3: nat] :
( ( P2 @ Y3 )
=> ( ord_less_eq_nat @ Y3 @ X2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(281,plain,
( ( ! [M: nat,N: nat] :
( ( M != N )
= ( ( ord_less_nat @ M @ N )
| ( ord_less_nat @ N @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(282,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ N ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(283,plain,
( ( ! [N: nat,M: nat] :
( ( ord_less_nat @ N @ M )
=> ( M != N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(284,plain,
( ( ! [S: nat,T: nat] :
( ( ord_less_nat @ S @ T )
=> ( S != T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(285,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ N ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(286,plain,
( ( ! [P2: nat > $o,N: nat] :
( ! [N2: nat] :
( ! [M2: nat] :
( ( ord_less_nat @ M2 @ N2 )
=> ( P2 @ M2 ) )
=> ( P2 @ N2 ) )
=> ( P2 @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(287,plain,
( ( ! [P2: nat > $o,N: nat] :
( ! [N2: nat] :
( ~ ( P2 @ N2 )
=> ? [M2: nat] :
( ( ord_less_nat @ M2 @ N2 )
& ~ ( P2 @ M2 ) ) )
=> ( P2 @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(288,plain,
( ( ! [X: nat,Y: nat] :
( ( X != Y )
=> ( ~ ( ord_less_nat @ X @ Y )
=> ( ord_less_nat @ Y @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(289,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(290,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(291,plain,
( ( times_times_nat
= ( ^ [A2: nat,B2: nat] : ( times_times_nat @ B2 @ A2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(292,plain,
( ( ! [B: nat,A: nat,C: nat] :
( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(293,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(294,plain,
( ( ! [I2: nat,J: nat,K: nat,L: nat] :
( ( ( I2 = J )
& ( K = L ) )
=> ( ( plus_plus_nat @ I2 @ K )
= ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(295,plain,
( ( ! [A3: nat,K: nat,A: nat,B: nat] :
( ( A3
= ( plus_plus_nat @ K @ A ) )
=> ( ( plus_plus_nat @ A3 @ B )
= ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(296,plain,
( ( ! [B3: nat,K: nat,B: nat,A: nat] :
( ( B3
= ( plus_plus_nat @ K @ B ) )
=> ( ( plus_plus_nat @ A @ B3 )
= ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(297,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(298,plain,
( ( plus_plus_nat
= ( ^ [A2: nat,B2: nat] : ( plus_plus_nat @ B2 @ A2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(299,plain,
( ( ! [B: nat,A: nat,C: nat] :
( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(300,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
=> ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(301,plain,
( ( ! [B: nat,A: nat,C: nat] :
( ( ( plus_plus_nat @ B @ A )
= ( plus_plus_nat @ C @ A ) )
=> ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(302,plain,
( ( ! [X: nat] :
( ( zero_zero_nat = X )
= ( X = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(303,plain,
( ( ! [J: nat,I2: nat,U: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ J @ I2 )
=> ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
= ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(304,plain,
( ( ! [I2: nat,J: nat,U: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
= ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(305,plain,
( ( ! [J: nat,I2: nat,U: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ J @ I2 )
=> ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
= ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
= ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M )
= N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(306,plain,
( ( ! [I2: nat,J: nat,U: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
= ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
= ( M
= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(307,plain,
( ( ! [J: nat,I2: nat,U: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ J @ I2 )
=> ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(308,plain,
( ( ! [I2: nat,J: nat,U: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
= ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(309,plain,
( ( ! [J: nat,I2: nat,U: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ J @ I2 )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
= ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(310,plain,
( ( ! [I2: nat,J: nat,U: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
= ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(311,plain,
( ( ! [K: nat,J: nat,I2: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
= ( ord_less_nat @ J @ ( plus_plus_nat @ I2 @ K ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(312,plain,
( ( ! [P2: nat > $o,A: nat,B: nat] :
( ( P2 @ ( minus_minus_nat @ A @ B ) )
= ( ( ( ord_less_nat @ A @ B )
=> ( P2 @ zero_zero_nat ) )
& ! [D: nat] :
( ( A
= ( plus_plus_nat @ B @ D ) )
=> ( P2 @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(313,plain,
( ( ! [P2: nat > $o,A: nat,B: nat] :
( ( P2 @ ( minus_minus_nat @ A @ B ) )
= ( ~ ( ( ( ord_less_nat @ A @ B )
& ~ ( P2 @ zero_zero_nat ) )
| ? [D: nat] :
( ( A
= ( plus_plus_nat @ B @ D ) )
& ~ ( P2 @ D ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(314,plain,
( ( ! [J: nat,K: nat,I2: nat] :
( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
= ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I2 @ K ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(315,plain,
( ( ! [K: nat,J: nat,I2: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(316,plain,
( ( ! [K: nat,J: nat,I2: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
= ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J @ K ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(317,plain,
( ( ! [K: nat,J: nat,I2: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I2 ) @ K )
= ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(318,plain,
( ( ! [I2: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ( ( minus_minus_nat @ J @ I2 )
= K )
= ( J
= ( plus_plus_nat @ K @ I2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(319,plain,
( ( ! [I2: nat,J: nat,K: nat] :
( ( ord_less_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
= ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(320,plain,
( ( ! [M: nat,N: nat] :
( ~ ( ord_less_nat @ M @ N )
=> ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
= M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(321,plain,
( ( ! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ K @ M )
=> ( ( ord_less_eq_nat @ K @ N )
=> ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
= ( ord_less_nat @ M @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(322,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(323,plain,
( ( ! [N: nat,M: nat] :
( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(324,plain,
( ( ! [N: nat,M: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( ord_less_nat @ zero_zero_nat @ M )
=> ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(325,plain,
( ( ! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(326,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(327,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(328,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(329,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
= ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(330,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
= ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(331,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
= ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(332,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(333,plain,
( ( ! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(334,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ( ( minus_minus_nat @ B @ A )
= C )
= ( B
= ( plus_plus_nat @ C @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(335,plain,
( ( ! [M: nat,N: nat,K: nat] :
( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
= ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(336,plain,
( ( ! [K: nat,M: nat,N: nat] :
( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
= ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(337,plain,
( ( ! [K: nat,M: nat,N: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
= ( minus_minus_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(338,plain,
( ( ! [M: nat,K: nat,N: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
= ( minus_minus_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(339,plain,
( ( ! [N: nat,M: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
= M ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(340,plain,
( ( ! [M: nat,N: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
= M ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(341,plain,
( ( ! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ K @ M )
=> ( ( ord_less_eq_nat @ K @ N )
=> ( ( ( minus_minus_nat @ M @ K )
= ( minus_minus_nat @ N @ K ) )
= ( M = N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(342,plain,
( ( ! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ K @ M )
=> ( ( ord_less_eq_nat @ K @ N )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
= ( ord_less_eq_nat @ M @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(343,plain,
( ( ! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ K @ M )
=> ( ( ord_less_eq_nat @ K @ N )
=> ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
= ( minus_minus_nat @ M @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(344,plain,
( ( ! [M: nat,N: nat,L: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(345,plain,
( ( ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(346,plain,
( ( ! [A: nat,C: nat,B: nat] :
( ( ord_less_eq_nat @ A @ C )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
= ( ord_less_eq_nat @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(347,plain,
( ( ! [M: nat,N: nat,L: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(348,plain,
( ( ! [M: nat,N: nat,L: nat] :
( ( ord_less_nat @ M @ N )
=> ( ( ord_less_nat @ M @ L )
=> ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(349,plain,
( ( ! [J: nat,K: nat,N: nat] :
( ( ord_less_nat @ J @ K )
=> ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(350,plain,
( ( ! [M: nat,N: nat] :
( ( ( minus_minus_nat @ M @ N )
= zero_zero_nat )
=> ( ( ( minus_minus_nat @ N @ M )
= zero_zero_nat )
=> ( M = N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(351,plain,
( ( ! [M: nat] :
( ( minus_minus_nat @ M @ zero_zero_nat )
= M ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(352,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(353,plain,
( ( ! [C: nat,B: nat,A: nat] :
( ( ( plus_plus_nat @ C @ B )
= A )
=> ( C
= ( minus_minus_nat @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(354,plain,
( ( ! [I2: nat,J: nat,K: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
= ( minus_minus_nat @ ( minus_minus_nat @ I2 @ K ) @ J ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(355,plain,
( ( ! [A: nat,C: nat,B: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(356,plain,
( ( ! [K: nat,J: nat,I2: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
= ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J ) @ K ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(357,plain,
( ( ! [K: nat,J: nat,I2: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
= ( minus_minus_nat @ ( plus_plus_nat @ J @ I2 ) @ K ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(358,plain,
( ( ! [K: nat,J: nat,I2: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( minus_minus_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
= ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(359,plain,
( ( ! [M: nat,N: nat] :
( ( ( minus_minus_nat @ M @ N )
= zero_zero_nat )
= ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(360,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( minus_minus_nat @ M @ N )
= zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(361,plain,
( ( ! [N: nat,M: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
= ( ord_less_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(362,plain,
( ( ! [A: nat,B: nat] :
( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(363,plain,
( ( ! [B: nat,A: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
= ( ord_less_eq_nat @ A @ zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(364,plain,
( ( ! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
= ( ord_less_eq_nat @ A @ zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(365,plain,
( ( ! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
= ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(366,plain,
( ( ! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
= ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(367,plain,
( ( ! [I2: nat,J: nat,K: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
= ( minus_minus_nat @ I2 @ ( plus_plus_nat @ J @ K ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(368,plain,
( ( ! [I2: nat,N: nat] :
( ( ord_less_eq_nat @ I2 @ N )
=> ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I2 ) )
= I2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(369,plain,
( ( ! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
= ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(370,plain,
( ( ! [M: nat,N: nat] :
( ( ( times_times_nat @ M @ N )
= zero_zero_nat )
= ( ( M = zero_zero_nat )
| ( N = zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(371,plain,
( ( ! [M: nat] :
( ( times_times_nat @ M @ zero_zero_nat )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(372,plain,
( ( ! [K: nat,M: nat,N: nat] :
( ( ( times_times_nat @ K @ M )
= ( times_times_nat @ K @ N ) )
= ( ( M = N )
| ( K = zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(373,plain,
( ( ! [M: nat,K: nat,N: nat] :
( ( ( times_times_nat @ M @ K )
= ( times_times_nat @ N @ K ) )
= ( ( M = N )
| ( K = zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(374,plain,
( ( ! [N: nat] :
( ( minus_minus_nat @ zero_zero_nat @ N )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(375,plain,
( ( ! [M: nat] :
( ( minus_minus_nat @ M @ M )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(376,plain,
( ( ! [K: nat,M: nat,N: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
= ( ord_less_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(377,plain,
( ( ! [M: nat,N: nat] :
( ( ( plus_plus_nat @ M @ N )
= zero_zero_nat )
= ( ( M = zero_zero_nat )
& ( N = zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(378,plain,
( ( ! [M: nat] :
( ( plus_plus_nat @ M @ zero_zero_nat )
= M ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(379,plain,
( ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(380,plain,
( ( ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(381,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(382,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(383,plain,
( ( ! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(384,plain,
( ( ! [C: nat,A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
= ( minus_minus_nat @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(385,plain,
( ( ! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(386,plain,
( ( ! [A: nat,C: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
= ( minus_minus_nat @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(387,plain,
( ( ! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(388,plain,
( ( ! [C: nat,A: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_nat @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(389,plain,
( ( ! [A: nat,C: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
= ( ord_less_nat @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(390,plain,
( ( ! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(391,plain,
( ( ! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(392,plain,
( ( ! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(393,plain,
( ( ! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(394,plain,
( ( ! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(395,plain,
( ( ! [B: nat,A: nat] :
( ( ( plus_plus_nat @ B @ A )
= A )
= ( B = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(396,plain,
( ( ! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= A )
= ( B = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(397,plain,
( ( ! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ B @ A ) )
= ( B = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(398,plain,
( ( ! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ A @ B ) )
= ( B = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(399,plain,
( ( ! [X: nat,Y: nat] :
( ( ( plus_plus_nat @ X @ Y )
= zero_zero_nat )
= ( ( X = zero_zero_nat )
& ( Y = zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(400,plain,
( ( ! [X: nat,Y: nat] :
( ( zero_zero_nat
= ( plus_plus_nat @ X @ Y ) )
= ( ( X = zero_zero_nat )
& ( Y = zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(401,plain,
( ( ! [C: nat,A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_eq_nat @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(402,plain,
( ( ! [A: nat,C: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
= ( ord_less_eq_nat @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(403,plain,
( ( ! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(404,plain,
( ( ! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(405,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
= ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(406,plain,
( ( ! [B: nat,A: nat,C: nat] :
( ( ( plus_plus_nat @ B @ A )
= ( plus_plus_nat @ C @ A ) )
= ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(407,plain,
( ( ! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
= ( ord_less_nat @ zero_zero_nat @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(408,plain,
( ( ! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
= ( ord_less_nat @ zero_zero_nat @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(409,plain,
( ( ! [A: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
= ( ord_less_nat @ A @ zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(410,plain,
( ( ! [B: nat,A: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
= ( ord_less_nat @ A @ zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(411,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
= ( ( ord_less_nat @ zero_zero_nat @ M )
| ( ord_less_nat @ zero_zero_nat @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(412,plain,
( ( ! [K: nat,M: nat,N: nat] :
( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
= ( ( ord_less_nat @ zero_zero_nat @ K )
& ( ord_less_nat @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(413,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
= ( ( ord_less_nat @ zero_zero_nat @ M )
& ( ord_less_nat @ zero_zero_nat @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(414,plain,
( ( ! [M: nat,K: nat,N: nat] :
( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
= ( ( ord_less_nat @ zero_zero_nat @ K )
& ( ord_less_nat @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(415,plain,
( ( ! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
= ( ( ord_less_nat @ zero_zero_nat @ K )
=> ( ord_less_eq_nat @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(416,plain,
( ( ! [M: nat,K: nat,N: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
= ( ( ord_less_nat @ zero_zero_nat @ K )
=> ( ord_less_eq_nat @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(417,plain,
( ( ! [P: nat > nat,N: nat,I2: nat] :
( ( number1551313001itions @ P @ N )
=> ( ord_less_eq_nat @ ( P @ I2 ) @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(418,plain,
( ( ! [P: nat > nat] :
( ( number1551313001itions @ P @ zero_zero_nat )
= ( P
= ( ^ [I: nat] : zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(419,plain,
( ( ord_less_nat @ ( minus_minus_nat @ n @ k ) @ i )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(420,plain,
( ( i != k )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(421,plain,
( ( ord_less_nat @ zero_zero_nat @ ( p @ k ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(422,plain,
( ( ( p @ i )
!= zero_zero_nat )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(423,plain,
( ( ord_less_eq_nat @ k @ n )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(424,plain,
( ( ord_less_nat @ n @ ( plus_plus_nat @ ( times_times_nat @ ( p @ i ) @ i ) @ ( times_times_nat @ ( p @ k ) @ k ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(425,plain,
( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( p @ i ) @ i ) @ ( times_times_nat @ ( p @ k ) @ k ) ) @ n )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(426,plain,
( ( number1551313001itions @ p @ n )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(427,plain,
( ( ord_less_eq_nat @ i @ n )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(428,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[215]) ).
thf(429,plain,
( ( ord_less_eq_nat @ i @ n )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(430,plain,
( ( number1551313001itions @ p @ n )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(431,plain,
( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( p @ i ) @ i ) @ ( times_times_nat @ ( p @ k ) @ k ) ) @ n )
= $true ),
inference(copy,[status(thm)],[425]) ).
thf(432,plain,
( ( ord_less_nat @ n @ ( plus_plus_nat @ ( times_times_nat @ ( p @ i ) @ i ) @ ( times_times_nat @ ( p @ k ) @ k ) ) )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(433,plain,
( ( ord_less_eq_nat @ k @ n )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(434,plain,
( ( ( p @ i )
!= zero_zero_nat )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(435,plain,
( ( ord_less_nat @ zero_zero_nat @ ( p @ k ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(436,plain,
( ( i != k )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(437,plain,
( ( ord_less_nat @ ( minus_minus_nat @ n @ k ) @ i )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(438,plain,
( ( ! [P: nat > nat] :
( ( number1551313001itions @ P @ zero_zero_nat )
= ( P
= ( ^ [I: nat] : zero_zero_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(439,plain,
( ( ! [P: nat > nat,N: nat,I2: nat] :
( ( number1551313001itions @ P @ N )
=> ( ord_less_eq_nat @ ( P @ I2 ) @ N ) ) )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(440,plain,
( ( ! [M: nat,K: nat,N: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
= ( ( ord_less_nat @ zero_zero_nat @ K )
=> ( ord_less_eq_nat @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(441,plain,
( ( ! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
= ( ( ord_less_nat @ zero_zero_nat @ K )
=> ( ord_less_eq_nat @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(442,plain,
( ( ! [M: nat,K: nat,N: nat] :
( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
= ( ( ord_less_nat @ zero_zero_nat @ K )
& ( ord_less_nat @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(443,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
= ( ( ord_less_nat @ zero_zero_nat @ M )
& ( ord_less_nat @ zero_zero_nat @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(444,plain,
( ( ! [K: nat,M: nat,N: nat] :
( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
= ( ( ord_less_nat @ zero_zero_nat @ K )
& ( ord_less_nat @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(445,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
= ( ( ord_less_nat @ zero_zero_nat @ M )
| ( ord_less_nat @ zero_zero_nat @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(446,plain,
( ( ! [B: nat,A: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
= ( ord_less_nat @ A @ zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(447,plain,
( ( ! [A: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
= ( ord_less_nat @ A @ zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(448,plain,
( ( ! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
= ( ord_less_nat @ zero_zero_nat @ B ) ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(449,plain,
( ( ! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
= ( ord_less_nat @ zero_zero_nat @ B ) ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(450,plain,
( ( ! [B: nat,A: nat,C: nat] :
( ( ( plus_plus_nat @ B @ A )
= ( plus_plus_nat @ C @ A ) )
= ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(451,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
= ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(452,plain,
( ( ! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(453,plain,
( ( ! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(454,plain,
( ( ! [A: nat,C: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
= ( ord_less_eq_nat @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(455,plain,
( ( ! [C: nat,A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_eq_nat @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(456,plain,
( ( ! [X: nat,Y: nat] :
( ( zero_zero_nat
= ( plus_plus_nat @ X @ Y ) )
= ( ( X = zero_zero_nat )
& ( Y = zero_zero_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(457,plain,
( ( ! [X: nat,Y: nat] :
( ( ( plus_plus_nat @ X @ Y )
= zero_zero_nat )
= ( ( X = zero_zero_nat )
& ( Y = zero_zero_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(458,plain,
( ( ! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ A @ B ) )
= ( B = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(459,plain,
( ( ! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ B @ A ) )
= ( B = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(460,plain,
( ( ! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= A )
= ( B = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(461,plain,
( ( ! [B: nat,A: nat] :
( ( ( plus_plus_nat @ B @ A )
= A )
= ( B = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[395]) ).
thf(462,plain,
( ( ! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ) )
= $true ),
inference(copy,[status(thm)],[394]) ).
thf(463,plain,
( ( ! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(464,plain,
( ( ! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(465,plain,
( ( ! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ) )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(466,plain,
( ( ! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(467,plain,
( ( ! [A: nat,C: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
= ( ord_less_nat @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(468,plain,
( ( ! [C: nat,A: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_nat @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[388]) ).
thf(469,plain,
( ( ! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[387]) ).
thf(470,plain,
( ( ! [A: nat,C: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
= ( minus_minus_nat @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(471,plain,
( ( ! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
= B ) )
= $true ),
inference(copy,[status(thm)],[385]) ).
thf(472,plain,
( ( ! [C: nat,A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
= ( minus_minus_nat @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(473,plain,
( ( ! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(474,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(475,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(476,plain,
( ( ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) )
= $true ),
inference(copy,[status(thm)],[380]) ).
thf(477,plain,
( ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(478,plain,
( ( ! [M: nat] :
( ( plus_plus_nat @ M @ zero_zero_nat )
= M ) )
= $true ),
inference(copy,[status(thm)],[378]) ).
thf(479,plain,
( ( ! [M: nat,N: nat] :
( ( ( plus_plus_nat @ M @ N )
= zero_zero_nat )
= ( ( M = zero_zero_nat )
& ( N = zero_zero_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(480,plain,
( ( ! [K: nat,M: nat,N: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
= ( ord_less_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(481,plain,
( ( ! [M: nat] :
( ( minus_minus_nat @ M @ M )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(482,plain,
( ( ! [N: nat] :
( ( minus_minus_nat @ zero_zero_nat @ N )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(483,plain,
( ( ! [M: nat,K: nat,N: nat] :
( ( ( times_times_nat @ M @ K )
= ( times_times_nat @ N @ K ) )
= ( ( M = N )
| ( K = zero_zero_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(484,plain,
( ( ! [K: nat,M: nat,N: nat] :
( ( ( times_times_nat @ K @ M )
= ( times_times_nat @ K @ N ) )
= ( ( M = N )
| ( K = zero_zero_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(485,plain,
( ( ! [M: nat] :
( ( times_times_nat @ M @ zero_zero_nat )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(486,plain,
( ( ! [M: nat,N: nat] :
( ( ( times_times_nat @ M @ N )
= zero_zero_nat )
= ( ( M = zero_zero_nat )
| ( N = zero_zero_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(487,plain,
( ( ! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
= ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(488,plain,
( ( ! [I2: nat,N: nat] :
( ( ord_less_eq_nat @ I2 @ N )
=> ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I2 ) )
= I2 ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(489,plain,
( ( ! [I2: nat,J: nat,K: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
= ( minus_minus_nat @ I2 @ ( plus_plus_nat @ J @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(490,plain,
( ( ! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
= ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(491,plain,
( ( ! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
= ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(492,plain,
( ( ! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
= ( ord_less_eq_nat @ A @ zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(493,plain,
( ( ! [B: nat,A: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
= ( ord_less_eq_nat @ A @ zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(494,plain,
( ( ! [A: nat,B: nat] :
( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(495,plain,
( ( ! [N: nat,M: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
= ( ord_less_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(496,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( minus_minus_nat @ M @ N )
= zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(497,plain,
( ( ! [M: nat,N: nat] :
( ( ( minus_minus_nat @ M @ N )
= zero_zero_nat )
= ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(498,plain,
( ( ! [K: nat,J: nat,I2: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( minus_minus_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
= ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(499,plain,
( ( ! [K: nat,J: nat,I2: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
= ( minus_minus_nat @ ( plus_plus_nat @ J @ I2 ) @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[357]) ).
thf(500,plain,
( ( ! [K: nat,J: nat,I2: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
= ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J ) @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[356]) ).
thf(501,plain,
( ( ! [A: nat,C: nat,B: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[355]) ).
thf(502,plain,
( ( ! [I2: nat,J: nat,K: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
= ( minus_minus_nat @ ( minus_minus_nat @ I2 @ K ) @ J ) ) )
= $true ),
inference(copy,[status(thm)],[354]) ).
thf(503,plain,
( ( ! [C: nat,B: nat,A: nat] :
( ( ( plus_plus_nat @ C @ B )
= A )
=> ( C
= ( minus_minus_nat @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[353]) ).
thf(504,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[352]) ).
thf(505,plain,
( ( ! [M: nat] :
( ( minus_minus_nat @ M @ zero_zero_nat )
= M ) )
= $true ),
inference(copy,[status(thm)],[351]) ).
thf(506,plain,
( ( ! [M: nat,N: nat] :
( ( ( minus_minus_nat @ M @ N )
= zero_zero_nat )
=> ( ( ( minus_minus_nat @ N @ M )
= zero_zero_nat )
=> ( M = N ) ) ) )
= $true ),
inference(copy,[status(thm)],[350]) ).
thf(507,plain,
( ( ! [J: nat,K: nat,N: nat] :
( ( ord_less_nat @ J @ K )
=> ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(508,plain,
( ( ! [M: nat,N: nat,L: nat] :
( ( ord_less_nat @ M @ N )
=> ( ( ord_less_nat @ M @ L )
=> ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[348]) ).
thf(509,plain,
( ( ! [M: nat,N: nat,L: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[347]) ).
thf(510,plain,
( ( ! [A: nat,C: nat,B: nat] :
( ( ord_less_eq_nat @ A @ C )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
= ( ord_less_eq_nat @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[346]) ).
thf(511,plain,
( ( ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) )
= $true ),
inference(copy,[status(thm)],[345]) ).
thf(512,plain,
( ( ! [M: nat,N: nat,L: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[344]) ).
thf(513,plain,
( ( ! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ K @ M )
=> ( ( ord_less_eq_nat @ K @ N )
=> ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
= ( minus_minus_nat @ M @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[343]) ).
thf(514,plain,
( ( ! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ K @ M )
=> ( ( ord_less_eq_nat @ K @ N )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
= ( ord_less_eq_nat @ M @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[342]) ).
thf(515,plain,
( ( ! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ K @ M )
=> ( ( ord_less_eq_nat @ K @ N )
=> ( ( ( minus_minus_nat @ M @ K )
= ( minus_minus_nat @ N @ K ) )
= ( M = N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[341]) ).
thf(516,plain,
( ( ! [M: nat,N: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
= M ) )
= $true ),
inference(copy,[status(thm)],[340]) ).
thf(517,plain,
( ( ! [N: nat,M: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
= M ) )
= $true ),
inference(copy,[status(thm)],[339]) ).
thf(518,plain,
( ( ! [M: nat,K: nat,N: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
= ( minus_minus_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[338]) ).
thf(519,plain,
( ( ! [K: nat,M: nat,N: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
= ( minus_minus_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[337]) ).
thf(520,plain,
( ( ! [K: nat,M: nat,N: nat] :
( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
= ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[336]) ).
thf(521,plain,
( ( ! [M: nat,N: nat,K: nat] :
( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
= ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[335]) ).
thf(522,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ( ( minus_minus_nat @ B @ A )
= C )
= ( B
= ( plus_plus_nat @ C @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[334]) ).
thf(523,plain,
( ( ! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[333]) ).
thf(524,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[332]) ).
thf(525,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
= ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[331]) ).
thf(526,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
= ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[330]) ).
thf(527,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
= ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[329]) ).
thf(528,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[328]) ).
thf(529,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[327]) ).
thf(530,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[326]) ).
thf(531,plain,
( ( ! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[325]) ).
thf(532,plain,
( ( ! [N: nat,M: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( ord_less_nat @ zero_zero_nat @ M )
=> ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[324]) ).
thf(533,plain,
( ( ! [N: nat,M: nat] :
( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[323]) ).
thf(534,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[322]) ).
thf(535,plain,
( ( ! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ K @ M )
=> ( ( ord_less_eq_nat @ K @ N )
=> ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
= ( ord_less_nat @ M @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[321]) ).
thf(536,plain,
( ( ! [M: nat,N: nat] :
( ~ ( ord_less_nat @ M @ N )
=> ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
= M ) ) )
= $true ),
inference(copy,[status(thm)],[320]) ).
thf(537,plain,
( ( ! [I2: nat,J: nat,K: nat] :
( ( ord_less_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
= ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) )
= $true ),
inference(copy,[status(thm)],[319]) ).
thf(538,plain,
( ( ! [I2: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ( ( minus_minus_nat @ J @ I2 )
= K )
= ( J
= ( plus_plus_nat @ K @ I2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[318]) ).
thf(539,plain,
( ( ! [K: nat,J: nat,I2: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I2 ) @ K )
= ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[317]) ).
thf(540,plain,
( ( ! [K: nat,J: nat,I2: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
= ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J @ K ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[316]) ).
thf(541,plain,
( ( ! [K: nat,J: nat,I2: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ) )
= $true ),
inference(copy,[status(thm)],[315]) ).
thf(542,plain,
( ( ! [J: nat,K: nat,I2: nat] :
( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
= ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I2 @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[314]) ).
thf(543,plain,
( ( ! [P2: nat > $o,A: nat,B: nat] :
( ( P2 @ ( minus_minus_nat @ A @ B ) )
= ( ~ ( ( ( ord_less_nat @ A @ B )
& ~ ( P2 @ zero_zero_nat ) )
| ? [D: nat] :
( ( A
= ( plus_plus_nat @ B @ D ) )
& ~ ( P2 @ D ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[313]) ).
thf(544,plain,
( ( ! [P2: nat > $o,A: nat,B: nat] :
( ( P2 @ ( minus_minus_nat @ A @ B ) )
= ( ( ( ord_less_nat @ A @ B )
=> ( P2 @ zero_zero_nat ) )
& ! [D: nat] :
( ( A
= ( plus_plus_nat @ B @ D ) )
=> ( P2 @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[312]) ).
thf(545,plain,
( ( ! [K: nat,J: nat,I2: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
= ( ord_less_nat @ J @ ( plus_plus_nat @ I2 @ K ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[311]) ).
thf(546,plain,
( ( ! [I2: nat,J: nat,U: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
= ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[310]) ).
thf(547,plain,
( ( ! [J: nat,I2: nat,U: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ J @ I2 )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
= ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[309]) ).
thf(548,plain,
( ( ! [I2: nat,J: nat,U: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
= ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[308]) ).
thf(549,plain,
( ( ! [J: nat,I2: nat,U: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ J @ I2 )
=> ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[307]) ).
thf(550,plain,
( ( ! [I2: nat,J: nat,U: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
= ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
= ( M
= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[306]) ).
thf(551,plain,
( ( ! [J: nat,I2: nat,U: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ J @ I2 )
=> ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
= ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
= ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M )
= N ) ) ) )
= $true ),
inference(copy,[status(thm)],[305]) ).
thf(552,plain,
( ( ! [I2: nat,J: nat,U: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
= ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[304]) ).
thf(553,plain,
( ( ! [J: nat,I2: nat,U: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ J @ I2 )
=> ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
= ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[303]) ).
thf(554,plain,
( ( ! [X: nat] :
( ( zero_zero_nat = X )
= ( X = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[302]) ).
thf(555,plain,
( ( ! [B: nat,A: nat,C: nat] :
( ( ( plus_plus_nat @ B @ A )
= ( plus_plus_nat @ C @ A ) )
=> ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[301]) ).
thf(556,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
=> ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[300]) ).
thf(557,plain,
( ( ! [B: nat,A: nat,C: nat] :
( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[299]) ).
thf(558,plain,
( ( plus_plus_nat
= ( ^ [A2: nat,B2: nat] : ( plus_plus_nat @ B2 @ A2 ) ) )
= $true ),
inference(copy,[status(thm)],[298]) ).
thf(559,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[297]) ).
thf(560,plain,
( ( ! [B3: nat,K: nat,B: nat,A: nat] :
( ( B3
= ( plus_plus_nat @ K @ B ) )
=> ( ( plus_plus_nat @ A @ B3 )
= ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[296]) ).
thf(561,plain,
( ( ! [A3: nat,K: nat,A: nat,B: nat] :
( ( A3
= ( plus_plus_nat @ K @ A ) )
=> ( ( plus_plus_nat @ A3 @ B )
= ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[295]) ).
thf(562,plain,
( ( ! [I2: nat,J: nat,K: nat,L: nat] :
( ( ( I2 = J )
& ( K = L ) )
=> ( ( plus_plus_nat @ I2 @ K )
= ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[294]) ).
thf(563,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[293]) ).
thf(564,plain,
( ( ! [B: nat,A: nat,C: nat] :
( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[292]) ).
thf(565,plain,
( ( times_times_nat
= ( ^ [A2: nat,B2: nat] : ( times_times_nat @ B2 @ A2 ) ) )
= $true ),
inference(copy,[status(thm)],[291]) ).
thf(566,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[290]) ).
thf(567,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[289]) ).
thf(568,plain,
( ( ! [X: nat,Y: nat] :
( ( X != Y )
=> ( ~ ( ord_less_nat @ X @ Y )
=> ( ord_less_nat @ Y @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[288]) ).
thf(569,plain,
( ( ! [P2: nat > $o,N: nat] :
( ! [N2: nat] :
( ~ ( P2 @ N2 )
=> ? [M2: nat] :
( ( ord_less_nat @ M2 @ N2 )
& ~ ( P2 @ M2 ) ) )
=> ( P2 @ N ) ) )
= $true ),
inference(copy,[status(thm)],[287]) ).
thf(570,plain,
( ( ! [P2: nat > $o,N: nat] :
( ! [N2: nat] :
( ! [M2: nat] :
( ( ord_less_nat @ M2 @ N2 )
=> ( P2 @ M2 ) )
=> ( P2 @ N2 ) )
=> ( P2 @ N ) ) )
= $true ),
inference(copy,[status(thm)],[286]) ).
thf(571,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ N ) )
= $true ),
inference(copy,[status(thm)],[285]) ).
thf(572,plain,
( ( ! [S: nat,T: nat] :
( ( ord_less_nat @ S @ T )
=> ( S != T ) ) )
= $true ),
inference(copy,[status(thm)],[284]) ).
thf(573,plain,
( ( ! [N: nat,M: nat] :
( ( ord_less_nat @ N @ M )
=> ( M != N ) ) )
= $true ),
inference(copy,[status(thm)],[283]) ).
thf(574,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ N ) )
= $true ),
inference(copy,[status(thm)],[282]) ).
thf(575,plain,
( ( ! [M: nat,N: nat] :
( ( M != N )
= ( ( ord_less_nat @ M @ N )
| ( ord_less_nat @ N @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[281]) ).
thf(576,plain,
( ( ! [P2: nat > $o,K: nat,B: nat] :
( ( P2 @ K )
=> ( ! [Y2: nat] :
( ( P2 @ Y2 )
=> ( ord_less_eq_nat @ Y2 @ B ) )
=> ? [X2: nat] :
( ( P2 @ X2 )
& ! [Y3: nat] :
( ( P2 @ Y3 )
=> ( ord_less_eq_nat @ Y3 @ X2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[280]) ).
thf(577,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
| ( ord_less_eq_nat @ N @ M ) ) )
= $true ),
inference(copy,[status(thm)],[279]) ).
thf(578,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( ord_less_eq_nat @ N @ M )
=> ( M = N ) ) ) )
= $true ),
inference(copy,[status(thm)],[278]) ).
thf(579,plain,
( ( ! [M: nat,N: nat] :
( ( M = N )
=> ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[277]) ).
thf(580,plain,
( ( ! [I2: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ( ord_less_eq_nat @ J @ K )
=> ( ord_less_eq_nat @ I2 @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[276]) ).
thf(581,plain,
( ( ! [N: nat] : ( ord_less_eq_nat @ N @ N ) )
= $true ),
inference(copy,[status(thm)],[275]) ).
thf(582,plain,
( ( ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) )
= $true ),
inference(copy,[status(thm)],[274]) ).
thf(583,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( N != zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[273]) ).
thf(584,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[272]) ).
thf(585,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[271]) ).
thf(586,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(copy,[status(thm)],[270]) ).
thf(587,plain,
( ( ! [A: nat,C: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
=> ( ord_less_eq_nat @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[269]) ).
thf(588,plain,
( ( ! [C: nat,A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_eq_nat @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[268]) ).
thf(589,plain,
( ( ord_less_eq_nat
= ( ^ [A2: nat,B2: nat] :
? [C2: nat] :
( B2
= ( plus_plus_nat @ A2 @ C2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[267]) ).
thf(590,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[266]) ).
thf(591,plain,
( ( ! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ~ ! [C3: nat] :
( B
!= ( plus_plus_nat @ A @ C3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[265]) ).
thf(592,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(593,plain,
( ( ! [A: nat,B: nat,C: nat,D2: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D2 )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[263]) ).
thf(594,plain,
( ( ! [I2: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_eq_nat @ I2 @ J )
& ( ord_less_eq_nat @ K @ L ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[262]) ).
thf(595,plain,
( ( ! [I2: nat,J: nat,K: nat,L: nat] :
( ( ( I2 = J )
& ( ord_less_eq_nat @ K @ L ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[261]) ).
thf(596,plain,
( ( ! [I2: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_eq_nat @ I2 @ J )
& ( K = L ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[260]) ).
thf(597,plain,
( ( ! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ) )
= $true ),
inference(copy,[status(thm)],[259]) ).
thf(598,plain,
( ( ! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(599,plain,
( ( ! [A: nat,C: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
=> ( ord_less_nat @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[257]) ).
thf(600,plain,
( ( ! [C: nat,A: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[256]) ).
thf(601,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(602,plain,
( ( ! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(603,plain,
( ( ! [A: nat,B: nat,C: nat,D2: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ C @ D2 )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[253]) ).
thf(604,plain,
( ( ! [I2: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_nat @ I2 @ J )
& ( K = L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[252]) ).
thf(605,plain,
( ( ! [I2: nat,J: nat,K: nat,L: nat] :
( ( ( I2 = J )
& ( ord_less_nat @ K @ L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[251]) ).
thf(606,plain,
( ( ! [I2: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_nat @ I2 @ J )
& ( ord_less_nat @ K @ L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[250]) ).
thf(607,plain,
( ( ! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[249]) ).
thf(608,plain,
( ( ! [P2: nat > $o,N: nat] :
( ( P2 @ zero_zero_nat )
=> ( ! [N2: nat] :
( ( ord_less_nat @ zero_zero_nat @ N2 )
=> ( ~ ( P2 @ N2 )
=> ? [M2: nat] :
( ( ord_less_nat @ M2 @ N2 )
& ~ ( P2 @ M2 ) ) ) )
=> ( P2 @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[248]) ).
thf(609,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[247]) ).
thf(610,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(611,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[245]) ).
thf(612,plain,
( ( ! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[244]) ).
thf(613,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(614,plain,
( ( ! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(615,plain,
( ( ! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(616,plain,
( ( ! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[240]) ).
thf(617,plain,
( ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(618,plain,
( ( ! [M: nat,N: nat] :
( ( ( plus_plus_nat @ M @ N )
= M )
=> ( N = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(619,plain,
( ( ! [N: nat] :
( ( plus_plus_nat @ zero_zero_nat @ N )
= N ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(620,plain,
( ( ! [F: nat > nat,I2: nat,J: nat] :
( ! [I3: nat,J2: nat] :
( ( ord_less_nat @ I3 @ J2 )
=> ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
=> ( ( ord_less_eq_nat @ I2 @ J )
=> ( ord_less_eq_nat @ ( F @ I2 ) @ ( F @ J ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(621,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( M != N )
=> ( ord_less_nat @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(622,plain,
( ( ! [M: nat,N: nat] :
( ( ( ord_less_nat @ M @ N )
| ( M = N ) )
=> ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(623,plain,
( ( ord_less_eq_nat
= ( ^ [M3: nat,N3: nat] :
( ( ord_less_nat @ M3 @ N3 )
| ( M3 = N3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(624,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(625,plain,
( ( ord_less_nat
= ( ^ [M3: nat,N3: nat] :
( ( ord_less_eq_nat @ M3 @ N3 )
& ( M3 != N3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[231]) ).
thf(626,plain,
( ( ! [K: nat,L: nat,M: nat,N: nat] :
( ( ord_less_nat @ K @ L )
=> ( ( ( plus_plus_nat @ M @ L )
= ( plus_plus_nat @ K @ N ) )
=> ( ord_less_nat @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(627,plain,
( ( ! [I2: nat,J: nat,M: nat] :
( ( ord_less_nat @ I2 @ J )
=> ( ord_less_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(628,plain,
( ( ! [I2: nat,J: nat,M: nat] :
( ( ord_less_nat @ I2 @ J )
=> ( ord_less_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(629,plain,
( ( ! [I2: nat,J: nat,K: nat] :
( ( ord_less_nat @ I2 @ J )
=> ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(630,plain,
( ( ! [J: nat,I2: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ J @ I2 ) @ I2 ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(631,plain,
( ( ! [I2: nat,J: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ I2 ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(632,plain,
( ( ! [I2: nat,J: nat,K: nat,L: nat] :
( ( ord_less_nat @ I2 @ J )
=> ( ( ord_less_nat @ K @ L )
=> ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(633,plain,
( ( ! [I2: nat,J: nat,K: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
=> ( ord_less_nat @ I2 @ K ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(634,plain,
( ( ! [K: nat,M: nat,N: nat] :
( ( ( times_times_nat @ K @ M )
= ( times_times_nat @ K @ N ) )
= ( ( K = zero_zero_nat )
| ( M = N ) ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(635,plain,
( ( ! [N: nat] :
( ( times_times_nat @ zero_zero_nat @ N )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(636,plain,
( ( ord_less_eq_nat
= ( ^ [M3: nat,N3: nat] :
? [K2: nat] :
( N3
= ( plus_plus_nat @ M3 @ K2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(637,plain,
( ( ! [I2: nat,J: nat,M: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(638,plain,
( ( ! [I2: nat,J: nat,M: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(639,plain,
( ( ! [I2: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(640,plain,
( ( ! [I2: nat,J: nat,K: nat,L: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ( ord_less_eq_nat @ K @ L )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(641,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[428]) ).
thf(642,plain,
( ( ! [SX0: nat > nat,SX1: nat,SX2: nat] :
( ~ ! [SX3: nat,SX4: nat] :
( ~ ( ord_less_nat @ SX3 @ SX4 )
| ( ord_less_nat @ ( SX0 @ SX3 ) @ ( SX0 @ SX4 ) ) )
| ~ ( ord_less_eq_nat @ SX1 @ SX2 )
| ( ord_less_eq_nat @ ( SX0 @ SX1 ) @ ( SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[620]) ).
thf(643,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) )
| ( ord_less_nat @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[621]) ).
thf(644,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ~ ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX2 @ SX3 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[594]) ).
thf(645,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX2 @ SX1 )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SX1 @ SX0 ) @ ( minus_minus_nat @ SX1 @ SX2 ) )
= ( ord_less_eq_nat @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[510]) ).
thf(646,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( minus_minus_nat @ SX2 @ ( minus_minus_nat @ SX1 @ SX0 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ SX2 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[524]) ).
thf(647,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( plus_plus_nat @ ( minus_minus_nat @ SX1 @ SX0 ) @ SX0 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[531]) ).
thf(648,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ~ ( ( SX0 != SX1 )
| ~ ( ord_less_eq_nat @ SX2 @ SX3 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[595]) ).
thf(649,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat,SX4: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SX1 @ SX2 ) @ SX3 ) @ ( plus_plus_nat @ ( times_times_nat @ SX0 @ SX2 ) @ SX4 ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SX1 @ SX0 ) @ SX2 ) @ SX3 ) @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[549]) ).
thf(650,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( minus_minus_nat @ ( plus_plus_nat @ SX2 @ SX1 ) @ SX0 )
= ( plus_plus_nat @ SX2 @ ( minus_minus_nat @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[527]) ).
thf(651,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[601]) ).
thf(652,plain,
( ( ! [SX0: nat] :
( ( SX0 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473]) ).
thf(653,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[572]) ).
thf(654,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( ( plus_plus_nat @ SX0 @ SX1 )
!= SX0 )
| ( SX1 = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[618]) ).
thf(655,plain,
( ( i != k )
= $true ),
inference(unfold_def,[status(thm)],[436]) ).
thf(656,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ~ ( ord_less_nat @ SX2 @ SX3 )
| ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[632]) ).
thf(657,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX1 ) @ SX2 )
| ( ord_less_nat @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[633]) ).
thf(658,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat,SX4: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ SX0 @ SX2 ) @ SX3 ) @ ( plus_plus_nat @ ( times_times_nat @ SX1 @ SX2 ) @ SX4 ) )
= ( minus_minus_nat @ SX3 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SX1 @ SX0 ) @ SX2 ) @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[546]) ).
thf(659,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( minus_minus_nat @ ( plus_plus_nat @ SX1 @ SX2 ) @ SX0 )
= ( plus_plus_nat @ ( minus_minus_nat @ SX1 @ SX0 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[525]) ).
thf(660,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ~ ( ~ ( ord_less_nat @ SX0 @ SX1 )
| ~ ( ord_less_nat @ SX2 @ SX3 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[606]) ).
thf(661,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX0 @ SX2 )
| ( ( ( minus_minus_nat @ SX1 @ SX0 )
= ( minus_minus_nat @ SX2 @ SX0 ) )
= ( SX1 = SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[515]) ).
thf(662,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_nat @ ( plus_plus_nat @ SX2 @ SX0 ) @ ( plus_plus_nat @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[602]) ).
thf(663,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( ( minus_minus_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( ( minus_minus_nat @ SX1 @ SX0 )
!= zero_zero_nat )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[506]) ).
thf(664,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( ord_less_eq_nat @ SX2 @ ( minus_minus_nat @ SX1 @ SX0 ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ SX2 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[541]) ).
thf(665,plain,
( ( ! [SX0: nat > $o,SX1: nat] :
( ~ ( SX0 @ zero_zero_nat )
| ~ ! [SX2: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX2 )
| ~ ~ ( SX0 @ SX2 )
| ~ ! [SX3: nat] :
~ ~ ( ~ ( ord_less_nat @ SX3 @ SX2 )
| ~ ~ ( SX0 @ SX3 ) ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[608]) ).
thf(666,plain,
( ( ! [SX0: nat] :
( ( SX0 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[475]) ).
thf(667,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( plus_plus_nat @ SX2 @ ( minus_minus_nat @ SX1 @ SX0 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ SX2 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[528]) ).
thf(668,plain,
( ( ! [SX0: nat > $o,SX1: nat,SX2: nat] :
( ( SX0 @ ( minus_minus_nat @ SX1 @ SX2 ) )
= ( ~ ( ~ ( ~ ( ord_less_nat @ SX1 @ SX2 )
| ( SX0 @ zero_zero_nat ) )
| ~ ! [SX3: nat] :
( ( SX1
!= ( plus_plus_nat @ SX2 @ SX3 ) )
| ( SX0 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[544]) ).
thf(669,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ~ ( ord_less_nat @ SX0 @ SX2 )
| ( ord_less_nat @ ( minus_minus_nat @ SX2 @ SX1 ) @ ( minus_minus_nat @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[508]) ).
thf(670,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ~ ( ord_less_nat @ zero_zero_nat @ SX1 )
| ( ord_less_nat @ ( minus_minus_nat @ SX1 @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[532]) ).
thf(671,plain,
( ( ord_less_eq_nat
= ( ^ [SX0: nat,SX1: nat] :
~ ! [SX2: nat] :
( SX1
!= ( plus_plus_nat @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[589]) ).
thf(672,plain,
( ( ord_less_eq_nat
= ( ^ [SX0: nat,SX1: nat] :
~ ! [SX2: nat] :
( SX1
!= ( plus_plus_nat @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[636]) ).
thf(673,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( ( minus_minus_nat @ SX1 @ SX0 )
= SX2 )
= ( SX1
= ( plus_plus_nat @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[538]) ).
thf(674,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat,SX4: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ SX1 @ SX2 ) @ SX3 ) @ ( plus_plus_nat @ ( times_times_nat @ SX0 @ SX2 ) @ SX4 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SX1 @ SX0 ) @ SX2 ) @ SX3 ) @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[547]) ).
thf(675,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ord_less_eq_nat @ SX2 @ ( minus_minus_nat @ ( plus_plus_nat @ SX1 @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[530]) ).
thf(676,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX1 ) @ ( plus_plus_nat @ SX2 @ SX1 ) )
| ( ord_less_nat @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[599]) ).
thf(677,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( ( plus_plus_nat @ SX0 @ SX1 )
= zero_zero_nat )
= ( ~ ( ( SX0 != zero_zero_nat )
| ( SX1 != zero_zero_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(678,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat,SX4: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SX0 @ SX2 ) @ SX3 ) @ ( plus_plus_nat @ ( times_times_nat @ SX1 @ SX2 ) @ SX4 ) )
= ( ord_less_nat @ SX3 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SX1 @ SX0 ) @ SX2 ) @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[552]) ).
thf(679,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_nat @ ( minus_minus_nat @ SX0 @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[507]) ).
thf(680,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ord_less_eq_nat @ ( minus_minus_nat @ SX2 @ SX1 ) @ ( minus_minus_nat @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[509]) ).
thf(681,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[590]) ).
thf(682,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( SX1 != SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[573]) ).
thf(683,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ( plus_plus_nat @ SX2 @ SX1 )
!= ( plus_plus_nat @ SX0 @ SX3 ) )
| ( ord_less_nat @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[626]) ).
thf(684,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ord_less_eq_nat @ SX0 @ ( plus_plus_nat @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[637]) ).
thf(685,plain,
( ( ! [SX0: nat] :
( ( ord_less_nat @ zero_zero_nat @ SX0 )
= ( SX0 != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[583]) ).
thf(686,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( minus_minus_nat @ SX2 @ ( minus_minus_nat @ SX1 @ SX0 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ SX2 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[498]) ).
thf(687,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( minus_minus_nat @ ( plus_plus_nat @ SX2 @ SX1 ) @ SX0 )
= ( plus_plus_nat @ SX2 @ ( minus_minus_nat @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[540]) ).
thf(688,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX2 @ SX3 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[593]) ).
thf(689,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( minus_minus_nat @ ( plus_plus_nat @ SX1 @ SX2 ) @ SX0 )
= ( plus_plus_nat @ ( minus_minus_nat @ SX1 @ SX0 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[539]) ).
thf(690,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX1 ) @ ( plus_plus_nat @ SX0 @ SX2 ) )
| ( ord_less_nat @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[600]) ).
thf(691,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX1 ) @ ( plus_plus_nat @ SX2 @ SX1 ) )
| ( ord_less_eq_nat @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[587]) ).
thf(692,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( plus_plus_nat @ ( minus_minus_nat @ SX1 @ SX0 ) @ SX2 )
= ( minus_minus_nat @ ( plus_plus_nat @ SX1 @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[499]) ).
thf(693,plain,
( ( ( p @ i )
!= zero_zero_nat )
= $true ),
inference(unfold_def,[status(thm)],[434]) ).
thf(694,plain,
( ( ! [SX0: nat > $o,SX1: nat] :
( ~ ! [SX2: nat] :
( ~ ~ ( SX0 @ SX2 )
| ~ ! [SX3: nat] :
~ ~ ( ~ ( ord_less_nat @ SX3 @ SX2 )
| ~ ~ ( SX0 @ SX3 ) ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[569]) ).
thf(695,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ( ( plus_plus_nat @ SX0 @ SX1 )
!= ( plus_plus_nat @ SX2 @ SX1 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[555]) ).
thf(696,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_nat @ SX0 @ ( plus_plus_nat @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[628]) ).
thf(697,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( SX0 != SX1 )
| ( ord_less_eq_nat @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[579]) ).
thf(698,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat,SX4: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SX0 @ SX2 ) @ SX3 ) @ ( plus_plus_nat @ ( times_times_nat @ SX1 @ SX2 ) @ SX4 ) )
= ( ord_less_eq_nat @ SX3 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SX1 @ SX0 ) @ SX2 ) @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[548]) ).
thf(699,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[639]) ).
thf(700,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ~ ( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( SX2 != SX3 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[604]) ).
thf(701,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_eq_nat @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[624]) ).
thf(702,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ~ ( ord_less_nat @ SX2 @ SX3 )
| ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[603]) ).
thf(703,plain,
( ( ! [SX0: nat] :
( ~ ( ( SX0 != zero_zero_nat ) )
| ( ord_less_nat @ zero_zero_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[586]) ).
thf(704,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ( ord_less_nat @ ( times_times_nat @ SX0 @ SX1 ) @ ( times_times_nat @ SX2 @ SX1 ) )
= ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SX1 )
| ~ ( ord_less_nat @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[442]) ).
thf(705,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ( plus_plus_nat @ SX1 @ ( minus_minus_nat @ SX0 @ SX1 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[536]) ).
thf(706,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( SX1 != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[584]) ).
thf(707,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( SX0 != SX1 )
= ( ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_nat @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[575]) ).
thf(708,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( SX1 != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[609]) ).
thf(709,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( plus_plus_nat @ SX2 @ ( minus_minus_nat @ SX1 @ SX0 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ SX2 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[500]) ).
thf(710,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( plus_plus_nat @ ( minus_minus_nat @ SX1 @ SX0 ) @ SX2 )
= ( minus_minus_nat @ ( plus_plus_nat @ SX1 @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[526]) ).
thf(711,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SX0 @ SX1 ) )
= ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ~ ( ord_less_nat @ zero_zero_nat @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(712,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( ( plus_plus_nat @ SX0 @ SX1 )
= zero_zero_nat )
= ( ~ ( ( SX0 != zero_zero_nat )
| ( SX1 != zero_zero_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[479]) ).
thf(713,plain,
( ( ord_less_nat
= ( ^ [SX0: nat,SX1: nat] :
~ ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[625]) ).
thf(714,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( zero_zero_nat
= ( plus_plus_nat @ SX0 @ SX1 ) )
= ( ~ ( ( SX0 != zero_zero_nat )
| ( SX1 != zero_zero_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(715,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ SX0 @ SX1 ) @ ( times_times_nat @ SX2 @ SX1 ) )
= ( ~ ( ord_less_nat @ zero_zero_nat @ SX1 )
| ( ord_less_eq_nat @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[440]) ).
thf(716,plain,
( ( ! [SX0: nat > $o,SX1: nat,SX2: nat] :
( ~ ( SX0 @ SX1 )
| ~ ! [SX3: nat] :
( ~ ( SX0 @ SX3 )
| ( ord_less_eq_nat @ SX3 @ SX2 ) )
| ~ ! [SX3: nat] :
~ ~ ( ~ ( SX0 @ SX3 )
| ~ ! [SX4: nat] :
( ~ ( SX0 @ SX4 )
| ( ord_less_eq_nat @ SX4 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[576]) ).
thf(717,plain,
( ( ! [SX0: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[614]) ).
thf(718,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[629]) ).
thf(719,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX0 @ SX2 )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SX1 @ SX0 ) @ ( minus_minus_nat @ SX2 @ SX0 ) )
= ( ord_less_eq_nat @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[514]) ).
thf(720,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ( ( plus_plus_nat @ SX0 @ SX1 )
!= SX2 )
| ( SX0
= ( minus_minus_nat @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[503]) ).
thf(721,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( ord_less_nat @ ( minus_minus_nat @ SX1 @ SX0 ) @ SX2 )
= ( ord_less_nat @ SX1 @ ( plus_plus_nat @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[545]) ).
thf(722,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ( SX0
!= ( plus_plus_nat @ SX1 @ SX2 ) )
| ( ( plus_plus_nat @ SX0 @ SX3 )
= ( plus_plus_nat @ SX1 @ ( plus_plus_nat @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[561]) ).
thf(723,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX0 @ SX2 )
| ( ( minus_minus_nat @ ( minus_minus_nat @ SX1 @ SX0 ) @ ( minus_minus_nat @ SX2 @ SX0 ) )
= ( minus_minus_nat @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[513]) ).
thf(724,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ord_less_eq_nat @ SX0 @ ( plus_plus_nat @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[638]) ).
thf(725,plain,
( ( ! [SX0: nat] :
( ~ ( ( SX0 != zero_zero_nat ) )
| ( ord_less_nat @ zero_zero_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[613]) ).
thf(726,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat,SX4: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SX1 @ SX2 ) @ SX3 ) @ ( plus_plus_nat @ ( times_times_nat @ SX0 @ SX2 ) @ SX4 ) )
= ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SX1 @ SX0 ) @ SX2 ) @ SX3 ) @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[553]) ).
thf(727,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ( SX0
!= ( plus_plus_nat @ SX1 @ SX2 ) )
| ( ( plus_plus_nat @ SX3 @ SX0 )
= ( plus_plus_nat @ SX1 @ ( plus_plus_nat @ SX3 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[560]) ).
thf(728,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( plus_plus_nat @ SX0 @ ( minus_minus_nat @ SX1 @ SX0 ) )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[523]) ).
thf(729,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ( ord_less_nat @ ( times_times_nat @ SX0 @ SX1 ) @ ( times_times_nat @ SX0 @ SX2 ) )
= ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ~ ( ord_less_nat @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[444]) ).
thf(730,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ( SX0 != SX1 ) )
| ~ ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_nat @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[568]) ).
thf(731,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ord_less_eq_nat @ ( minus_minus_nat @ SX0 @ SX2 ) @ ( minus_minus_nat @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[512]) ).
thf(732,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( minus_minus_nat @ SX0 @ SX1 )
= zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[496]) ).
thf(733,plain,
( ( ! [SX0: nat > $o,SX1: nat] :
( ~ ! [SX2: nat] :
( ~ ! [SX3: nat] :
( ~ ( ord_less_nat @ SX3 @ SX2 )
| ( SX0 @ SX3 ) )
| ( SX0 @ SX2 ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[570]) ).
thf(734,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( ( minus_minus_nat @ SX1 @ SX0 )
= SX2 )
= ( SX1
= ( plus_plus_nat @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[522]) ).
thf(735,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SX2 @ SX0 ) @ ( plus_plus_nat @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[592]) ).
thf(736,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX0 @ SX2 )
| ( ( ord_less_nat @ ( minus_minus_nat @ SX1 @ SX0 ) @ ( minus_minus_nat @ SX2 @ SX0 ) )
= ( ord_less_nat @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[535]) ).
thf(737,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( ord_less_eq_nat @ SX2 @ ( minus_minus_nat @ SX1 @ SX0 ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ SX2 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[529]) ).
thf(738,plain,
( ( ! [SX0: nat > $o,SX1: nat,SX2: nat] :
( ( SX0 @ ( minus_minus_nat @ SX1 @ SX2 ) )
= ( ~ ( ~ ( ~ ( ord_less_nat @ SX1 @ SX2 )
| ~ ~ ( SX0 @ zero_zero_nat ) )
| ~ ! [SX3: nat] :
~ ~ ( ( SX1
!= ( plus_plus_nat @ SX2 @ SX3 ) )
| ~ ~ ( SX0 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[543]) ).
thf(739,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ( ( plus_plus_nat @ SX0 @ SX1 )
!= ( plus_plus_nat @ SX0 @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[556]) ).
thf(740,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX2 @ SX0 )
| ( ord_less_nat @ ( minus_minus_nat @ SX0 @ SX2 ) @ ( minus_minus_nat @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[534]) ).
thf(741,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[578]) ).
thf(742,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat,SX4: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SX1 @ SX2 ) @ SX3 )
= ( plus_plus_nat @ ( times_times_nat @ SX0 @ SX2 ) @ SX4 ) )
= ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SX1 @ SX0 ) @ SX2 ) @ SX3 )
= SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[551]) ).
thf(743,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ! [SX2: nat] :
( SX1
!= ( plus_plus_nat @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[591]) ).
thf(744,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ~ ( ( SX0 != SX1 )
| ~ ( ord_less_nat @ SX2 @ SX3 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[605]) ).
thf(745,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ~ ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( SX2 != SX3 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[596]) ).
thf(746,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ SX0 @ SX1 ) @ ( times_times_nat @ SX0 @ SX2 ) )
= ( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ( ord_less_eq_nat @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[441]) ).
thf(747,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX1 @ SX2 )
| ( ord_less_eq_nat @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[580]) ).
thf(748,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ~ ( ( SX0 != SX1 )
| ( SX2 != SX3 ) )
| ( ( plus_plus_nat @ SX0 @ SX2 )
= ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[562]) ).
thf(749,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat,SX4: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SX0 @ SX2 ) @ SX3 )
= ( plus_plus_nat @ ( times_times_nat @ SX1 @ SX2 ) @ SX4 ) )
= ( SX3
= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SX1 @ SX0 ) @ SX2 ) @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[550]) ).
thf(750,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX2 @ SX3 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[640]) ).
thf(751,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_nat @ SX0 @ ( plus_plus_nat @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[627]) ).
thf(752,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ( ord_less_nat @ SX0 @ SX1 )
| ( SX0 = SX1 ) )
| ( ord_less_eq_nat @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[622]) ).
thf(753,plain,
( ( ! [SX0: nat > nat,SX1: nat,SX2: nat] :
( ~ ( number1551313001itions @ SX0 @ SX1 )
| ( ord_less_eq_nat @ ( SX0 @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439]) ).
thf(754,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( minus_minus_nat @ SX1 @ ( minus_minus_nat @ SX1 @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[488]) ).
thf(755,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX1 ) @ ( plus_plus_nat @ SX0 @ SX2 ) )
| ( ord_less_eq_nat @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[588]) ).
thf(756,plain,
! [SV1: nat > nat] :
( ( ( number1551313001itions @ SV1 @ zero_zero_nat )
= ( SV1
= ( ^ [I: nat] : zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(757,plain,
! [SV2: nat] :
( ( ! [SY520: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SY520 ) )
= ( ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( ord_less_nat @ zero_zero_nat @ SY520 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(758,plain,
! [SV3: nat] :
( ( ! [SY521: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ SV3 @ SY521 ) @ SV3 )
= ( ord_less_nat @ SY521 @ zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(759,plain,
! [SV4: nat] :
( ( ! [SY522: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ SV4 @ SY522 ) @ SY522 )
= ( ord_less_nat @ SV4 @ zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(760,plain,
! [SV5: nat] :
( ( ! [SY523: nat] :
( ( ord_less_nat @ SV5 @ ( plus_plus_nat @ SV5 @ SY523 ) )
= ( ord_less_nat @ zero_zero_nat @ SY523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(761,plain,
! [SV6: nat] :
( ( ! [SY524: nat] :
( ( ord_less_nat @ SV6 @ ( plus_plus_nat @ SY524 @ SV6 ) )
= ( ord_less_nat @ zero_zero_nat @ SY524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(762,plain,
! [SV7: nat] :
( ( ! [SY525: nat,SY526: nat] :
( ( ( plus_plus_nat @ SV7 @ SY525 )
= ( plus_plus_nat @ SY526 @ SY525 ) )
= ( SV7 = SY526 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(763,plain,
! [SV8: nat] :
( ( ! [SY527: nat,SY528: nat] :
( ( ( plus_plus_nat @ SV8 @ SY527 )
= ( plus_plus_nat @ SV8 @ SY528 ) )
= ( SY527 = SY528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(764,plain,
! [SV9: nat] :
( ( ( ord_less_eq_nat @ SV9 @ zero_zero_nat )
= ( SV9 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(765,plain,
! [SV10: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV10 ) )
= ( SV10 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(766,plain,
! [SV11: nat] :
( ( ! [SY529: nat,SY530: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ SV11 @ SY529 ) @ ( plus_plus_nat @ SY530 @ SY529 ) )
= ( ord_less_eq_nat @ SV11 @ SY530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(767,plain,
! [SV12: nat] :
( ( ! [SY531: nat,SY532: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SY531 ) @ ( plus_plus_nat @ SV12 @ SY532 ) )
= ( ord_less_eq_nat @ SY531 @ SY532 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(768,plain,
! [SV13: nat] :
( ( ! [SY533: nat] :
( ( SV13
= ( plus_plus_nat @ SV13 @ SY533 ) )
= ( SY533 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(769,plain,
! [SV14: nat] :
( ( ! [SY534: nat] :
( ( SV14
= ( plus_plus_nat @ SY534 @ SV14 ) )
= ( SY534 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(770,plain,
! [SV15: nat] :
( ( ! [SY535: nat] :
( ( ( plus_plus_nat @ SV15 @ SY535 )
= SV15 )
= ( SY535 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(771,plain,
! [SV16: nat] :
( ( ! [SY536: nat] :
( ( ( plus_plus_nat @ SV16 @ SY536 )
= SY536 )
= ( SV16 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(772,plain,
! [SV17: nat] :
( ( ( plus_plus_nat @ SV17 @ zero_zero_nat )
= SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(773,plain,
! [SV18: nat] :
( ( ( plus_plus_nat @ zero_zero_nat @ SV18 )
= SV18 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(774,plain,
! [SV19: nat] :
( ( ( minus_minus_nat @ SV19 @ SV19 )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(775,plain,
! [SV20: nat] :
( ( ( minus_minus_nat @ SV20 @ zero_zero_nat )
= SV20 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(776,plain,
! [SV21: nat] :
( ( ( minus_minus_nat @ zero_zero_nat @ SV21 )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(777,plain,
! [SV22: nat] :
( ( ! [SY537: nat,SY538: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ SV22 @ SY537 ) @ ( plus_plus_nat @ SY538 @ SY537 ) )
= ( ord_less_nat @ SV22 @ SY538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(778,plain,
! [SV23: nat] :
( ( ! [SY539: nat,SY540: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ SV23 @ SY539 ) @ ( plus_plus_nat @ SV23 @ SY540 ) )
= ( ord_less_nat @ SY539 @ SY540 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(779,plain,
! [SV24: nat] :
( ( ! [SY541: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ SV24 @ SY541 ) @ SY541 )
= SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(780,plain,
! [SV25: nat] :
( ( ! [SY542: nat,SY543: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ SV25 @ SY542 ) @ ( plus_plus_nat @ SY543 @ SY542 ) )
= ( minus_minus_nat @ SV25 @ SY543 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(781,plain,
! [SV26: nat] :
( ( ! [SY544: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ SV26 @ SY544 ) @ SV26 )
= SY544 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(782,plain,
! [SV27: nat] :
( ( ! [SY545: nat,SY546: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ SV27 @ SY545 ) @ ( plus_plus_nat @ SV27 @ SY546 ) )
= ( minus_minus_nat @ SY545 @ SY546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(783,plain,
! [SV28: nat] :
( ( ~ ( ord_less_nat @ SV28 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(784,plain,
! [SV29: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ SV29 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(785,plain,
! [SV30: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ SV30 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(786,plain,
! [SV31: nat] :
( ( ( plus_plus_nat @ SV31 @ zero_zero_nat )
= SV31 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(787,plain,
! [SV32: nat] :
( ( ! [SY547: nat,SY548: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ SV32 @ SY547 ) @ ( plus_plus_nat @ SV32 @ SY548 ) )
= ( ord_less_nat @ SY547 @ SY548 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(788,plain,
! [SV33: nat] :
( ( ( minus_minus_nat @ SV33 @ SV33 )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(789,plain,
! [SV34: nat] :
( ( ( minus_minus_nat @ zero_zero_nat @ SV34 )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(790,plain,
! [SV35: nat] :
( ( ! [SY549: nat,SY550: nat] :
( ( ( times_times_nat @ SV35 @ SY549 )
= ( times_times_nat @ SY550 @ SY549 ) )
= ( ( SV35 = SY550 )
| ( SY549 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(791,plain,
! [SV36: nat] :
( ( ! [SY551: nat,SY552: nat] :
( ( ( times_times_nat @ SV36 @ SY551 )
= ( times_times_nat @ SV36 @ SY552 ) )
= ( ( SY551 = SY552 )
| ( SV36 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(792,plain,
! [SV37: nat] :
( ( ( times_times_nat @ SV37 @ zero_zero_nat )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(793,plain,
! [SV38: nat] :
( ( ! [SY553: nat] :
( ( ( times_times_nat @ SV38 @ SY553 )
= zero_zero_nat )
= ( ( SV38 = zero_zero_nat )
| ( SY553 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(794,plain,
! [SV39: nat] :
( ( ! [SY554: nat,SY555: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ SV39 @ SY554 ) @ ( plus_plus_nat @ SV39 @ SY555 ) )
= ( ord_less_eq_nat @ SY554 @ SY555 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(795,plain,
! [SV40: nat] :
( ( ! [SY556: nat,SY557: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ SV40 @ SY556 ) @ SY557 )
= ( minus_minus_nat @ SV40 @ ( plus_plus_nat @ SY556 @ SY557 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(796,plain,
! [SV41: nat] :
( ( ! [SY558: nat] :
( ( ord_less_eq_nat @ SV41 @ ( plus_plus_nat @ SY558 @ SV41 ) )
= ( ord_less_eq_nat @ zero_zero_nat @ SY558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(797,plain,
! [SV42: nat] :
( ( ! [SY559: nat] :
( ( ord_less_eq_nat @ SV42 @ ( plus_plus_nat @ SV42 @ SY559 ) )
= ( ord_less_eq_nat @ zero_zero_nat @ SY559 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(798,plain,
! [SV43: nat] :
( ( ! [SY560: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ SV43 @ SY560 ) @ SY560 )
= ( ord_less_eq_nat @ SV43 @ zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(799,plain,
! [SV44: nat] :
( ( ! [SY561: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ SV44 @ SY561 ) @ SV44 )
= ( ord_less_eq_nat @ SY561 @ zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(800,plain,
! [SV45: nat] :
( ( ! [SY562: nat] :
( ( minus_minus_nat @ SV45 @ ( plus_plus_nat @ SV45 @ SY562 ) )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(801,plain,
! [SV46: nat] :
( ( ! [SY563: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV46 @ SY563 ) )
= ( ord_less_nat @ SY563 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(802,plain,
! [SV47: nat] :
( ( ! [SY564: nat] :
( ( ( minus_minus_nat @ SV47 @ SY564 )
= zero_zero_nat )
= ( ord_less_eq_nat @ SV47 @ SY564 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(803,plain,
! [SV48: nat] :
( ( ! [SY565: nat,SY566: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ SV48 @ SY565 ) @ SY566 )
= ( minus_minus_nat @ ( minus_minus_nat @ SV48 @ SY566 ) @ SY565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(804,plain,
! [SV49: nat] :
( ( ! [SY567: nat,SY568: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ SV49 @ SY567 ) @ SY568 )
= ( minus_minus_nat @ ( minus_minus_nat @ SV49 @ SY568 ) @ SY567 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(805,plain,
! [SV50: nat] :
( ( ! [SY569: nat,SY570: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ SV50 @ SY569 ) @ SY570 )
= ( minus_minus_nat @ SV50 @ ( plus_plus_nat @ SY569 @ SY570 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(806,plain,
! [SV51: nat] :
( ( ( minus_minus_nat @ SV51 @ zero_zero_nat )
= SV51 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(807,plain,
! [SV52: nat] :
( ( ! [SY571: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ SV52 @ SY571 ) @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(808,plain,
! [SV53: nat] :
( ( ! [SY572: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ SV53 @ SY572 ) @ SY572 )
= SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(809,plain,
! [SV54: nat] :
( ( ! [SY573: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ SV54 @ SY573 ) @ SV54 )
= SY573 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(810,plain,
! [SV55: nat] :
( ( ! [SY574: nat,SY575: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ SV55 @ SY574 ) @ ( plus_plus_nat @ SY575 @ SY574 ) )
= ( minus_minus_nat @ SV55 @ SY575 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(811,plain,
! [SV56: nat] :
( ( ! [SY576: nat,SY577: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ SV56 @ SY576 ) @ ( plus_plus_nat @ SV56 @ SY577 ) )
= ( minus_minus_nat @ SY576 @ SY577 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(812,plain,
! [SV57: nat] :
( ( ! [SY578: nat,SY579: nat] :
( ( times_times_nat @ SV57 @ ( minus_minus_nat @ SY578 @ SY579 ) )
= ( minus_minus_nat @ ( times_times_nat @ SV57 @ SY578 ) @ ( times_times_nat @ SV57 @ SY579 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(813,plain,
! [SV58: nat] :
( ( ! [SY580: nat,SY581: nat] :
( ( times_times_nat @ ( minus_minus_nat @ SV58 @ SY580 ) @ SY581 )
= ( minus_minus_nat @ ( times_times_nat @ SV58 @ SY581 ) @ ( times_times_nat @ SY580 @ SY581 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(814,plain,
! [SV59: nat] :
( ( ! [SY582: nat] :
( ( minus_minus_nat @ SV59 @ ( plus_plus_nat @ SV59 @ SY582 ) )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(815,plain,
! [SV60: nat] :
( ( ! [SY583: nat,SY584: nat] :
( ( ord_less_nat @ SV60 @ ( minus_minus_nat @ SY583 @ SY584 ) )
= ( ord_less_nat @ ( plus_plus_nat @ SV60 @ SY584 ) @ SY583 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(816,plain,
! [SV61: nat] :
( ( ! [SY585: nat,SY586: nat] :
( ( ord_less_eq_nat @ ( minus_minus_nat @ SV61 @ SY585 ) @ SY586 )
= ( ord_less_eq_nat @ SV61 @ ( plus_plus_nat @ SY586 @ SY585 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(817,plain,
! [SV62: nat] :
( ( ( zero_zero_nat = SV62 )
= ( SV62 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(818,plain,
! [SV63: nat] :
( ( ! [SY587: nat,SY588: nat] :
( ( plus_plus_nat @ SV63 @ ( plus_plus_nat @ SY587 @ SY588 ) )
= ( plus_plus_nat @ SY587 @ ( plus_plus_nat @ SV63 @ SY588 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(819,plain,
( ( ! [SV64: nat] :
( ( plus_plus_nat @ SV64 )
= ( ^ [SY589: nat] : ( plus_plus_nat @ SY589 @ SV64 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[558]) ).
thf(820,plain,
( ( plus_plus_nat
= ( ^ [A2: nat,B2: nat] : ( plus_plus_nat @ B2 @ A2 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[558]) ).
thf(821,plain,
! [SV65: nat] :
( ( ! [SY590: nat,SY591: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ SV65 @ SY590 ) @ SY591 )
= ( plus_plus_nat @ SV65 @ ( plus_plus_nat @ SY590 @ SY591 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(822,plain,
! [SV66: nat] :
( ( ! [SY592: nat,SY593: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ SV66 @ SY592 ) @ SY593 )
= ( plus_plus_nat @ SV66 @ ( plus_plus_nat @ SY592 @ SY593 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(823,plain,
! [SV67: nat] :
( ( ! [SY594: nat,SY595: nat] :
( ( times_times_nat @ SV67 @ ( times_times_nat @ SY594 @ SY595 ) )
= ( times_times_nat @ SY594 @ ( times_times_nat @ SV67 @ SY595 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(824,plain,
( ( ! [SV68: nat] :
( ( times_times_nat @ SV68 )
= ( ^ [SY596: nat] : ( times_times_nat @ SY596 @ SV68 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[565]) ).
thf(825,plain,
( ( times_times_nat
= ( ^ [A2: nat,B2: nat] : ( times_times_nat @ B2 @ A2 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[565]) ).
thf(826,plain,
! [SV69: nat] :
( ( ! [SY597: nat,SY598: nat] :
( ( times_times_nat @ ( times_times_nat @ SV69 @ SY597 ) @ SY598 )
= ( times_times_nat @ SV69 @ ( times_times_nat @ SY597 @ SY598 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(827,plain,
! [SV70: nat] :
( ( ! [SY599: nat,SY600: nat] :
( ( times_times_nat @ ( times_times_nat @ SV70 @ SY599 ) @ SY600 )
= ( times_times_nat @ SV70 @ ( times_times_nat @ SY599 @ SY600 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(828,plain,
! [SV71: nat] :
( ( ~ ( ord_less_nat @ SV71 @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(829,plain,
! [SV72: nat] :
( ( ~ ( ord_less_nat @ SV72 @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(830,plain,
! [SV73: nat] :
( ( ! [SY601: nat] :
( ( ord_less_eq_nat @ SV73 @ SY601 )
| ( ord_less_eq_nat @ SY601 @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(831,plain,
! [SV74: nat] :
( ( ord_less_eq_nat @ SV74 @ SV74 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(832,plain,
! [SV75: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ SV75 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(833,plain,
! [SV76: nat] :
( ( ~ ( ord_less_nat @ SV76 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(834,plain,
! [SV77: nat] :
( ( ( plus_plus_nat @ SV77 @ zero_zero_nat )
= SV77 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(835,plain,
! [SV78: nat] :
( ( ( plus_plus_nat @ zero_zero_nat @ SV78 )
= SV78 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(836,plain,
! [SV79: nat] :
( ( ~ ( ord_less_nat @ SV79 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(837,plain,
! [SV80: nat] :
( ( ~ ( ord_less_nat @ SV80 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(838,plain,
! [SV81: nat] :
( ( ~ ( ord_less_nat @ SV81 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(839,plain,
! [SV82: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV82 ) )
= ( SV82 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(840,plain,
! [SV83: nat] :
( ( ( ord_less_eq_nat @ SV83 @ zero_zero_nat )
= ( SV83 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(841,plain,
! [SV84: nat] :
( ( ( ord_less_eq_nat @ SV84 @ zero_zero_nat )
= ( SV84 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(842,plain,
! [SV85: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ SV85 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(843,plain,
! [SV86: nat] :
( ( ( plus_plus_nat @ zero_zero_nat @ SV86 )
= SV86 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(844,plain,
( ( ! [SV87: nat] :
( ( ord_less_eq_nat @ SV87 )
= ( ^ [SY602: nat] :
( ( ord_less_nat @ SV87 @ SY602 )
| ( SV87 = SY602 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[623]) ).
thf(845,plain,
( ( ord_less_eq_nat
= ( ^ [M3: nat,N3: nat] :
( ( ord_less_nat @ M3 @ N3 )
| ( M3 = N3 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[623]) ).
thf(846,plain,
! [SV88: nat] :
( ( ! [SY603: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ SV88 @ SY603 ) @ SY603 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(847,plain,
! [SV89: nat] :
( ( ! [SY604: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ SV89 @ SY604 ) @ SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(848,plain,
! [SV90: nat] :
( ( ! [SY605: nat,SY606: nat] :
( ( ( times_times_nat @ SV90 @ SY605 )
= ( times_times_nat @ SV90 @ SY606 ) )
= ( ( SV90 = zero_zero_nat )
| ( SY605 = SY606 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(849,plain,
! [SV91: nat] :
( ( ( times_times_nat @ zero_zero_nat @ SV91 )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(850,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[641]) ).
thf(851,plain,
! [SV92: nat > nat] :
( ( ! [SY607: nat,SY608: nat] :
( ~ ! [SY609: nat,SY610: nat] :
( ~ ( ord_less_nat @ SY609 @ SY610 )
| ( ord_less_nat @ ( SV92 @ SY609 ) @ ( SV92 @ SY610 ) ) )
| ~ ( ord_less_eq_nat @ SY607 @ SY608 )
| ( ord_less_eq_nat @ ( SV92 @ SY607 ) @ ( SV92 @ SY608 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(852,plain,
! [SV93: nat] :
( ( ! [SY611: nat] :
( ~ ( ord_less_eq_nat @ SV93 @ SY611 )
| ~ ( ( SV93 != SY611 ) )
| ( ord_less_nat @ SV93 @ SY611 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(853,plain,
! [SV94: nat] :
( ( ! [SY612: nat,SY613: nat,SY614: nat] :
( ~ ~ ( ~ ( ord_less_eq_nat @ SV94 @ SY612 )
| ~ ( ord_less_eq_nat @ SY613 @ SY614 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV94 @ SY613 ) @ ( plus_plus_nat @ SY612 @ SY614 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(854,plain,
! [SV95: nat] :
( ( ! [SY615: nat,SY616: nat] :
( ~ ( ord_less_eq_nat @ SV95 @ SY615 )
| ~ ( ord_less_eq_nat @ SY616 @ SY615 )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SY615 @ SV95 ) @ ( minus_minus_nat @ SY615 @ SY616 ) )
= ( ord_less_eq_nat @ SY616 @ SV95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(855,plain,
! [SV96: nat] :
( ( ! [SY617: nat,SY618: nat] :
( ~ ( ord_less_eq_nat @ SV96 @ SY617 )
| ( ( minus_minus_nat @ SY618 @ ( minus_minus_nat @ SY617 @ SV96 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ SY618 @ SV96 ) @ SY617 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(856,plain,
! [SV97: nat] :
( ( ! [SY619: nat] :
( ~ ( ord_less_eq_nat @ SV97 @ SY619 )
| ( ( plus_plus_nat @ ( minus_minus_nat @ SY619 @ SV97 ) @ SV97 )
= SY619 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(857,plain,
! [SV98: nat] :
( ( ! [SY620: nat,SY621: nat,SY622: nat] :
( ~ ~ ( ( SV98 != SY620 )
| ~ ( ord_less_eq_nat @ SY621 @ SY622 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV98 @ SY621 ) @ ( plus_plus_nat @ SY620 @ SY622 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(858,plain,
! [SV99: nat] :
( ( ! [SY623: nat,SY624: nat,SY625: nat,SY626: nat] :
( ~ ( ord_less_eq_nat @ SV99 @ SY623 )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SY623 @ SY624 ) @ SY625 ) @ ( plus_plus_nat @ ( times_times_nat @ SV99 @ SY624 ) @ SY626 ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SY623 @ SV99 ) @ SY624 ) @ SY625 ) @ SY626 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(859,plain,
! [SV100: nat] :
( ( ! [SY627: nat,SY628: nat] :
( ~ ( ord_less_eq_nat @ SV100 @ SY627 )
| ( ( minus_minus_nat @ ( plus_plus_nat @ SY628 @ SY627 ) @ SV100 )
= ( plus_plus_nat @ SY628 @ ( minus_minus_nat @ SY627 @ SV100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(860,plain,
! [SV101: nat] :
( ( ! [SY629: nat,SY630: nat] :
( ~ ( ord_less_nat @ SV101 @ SY629 )
| ( ord_less_nat @ ( plus_plus_nat @ SV101 @ SY630 ) @ ( plus_plus_nat @ SY629 @ SY630 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(861,plain,
! [SV102: nat] :
( ( ( SV102 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(862,plain,
! [SV103: nat] :
( ( ! [SY631: nat] :
( ~ ( ord_less_nat @ SV103 @ SY631 )
| ( SV103 != SY631 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(863,plain,
! [SV104: nat] :
( ( ! [SY632: nat] :
( ( ( plus_plus_nat @ SV104 @ SY632 )
!= SV104 )
| ( SY632 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(864,plain,
( ( i = k )
= $false ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(865,plain,
! [SV105: nat] :
( ( ! [SY633: nat,SY634: nat,SY635: nat] :
( ~ ( ord_less_nat @ SV105 @ SY633 )
| ~ ( ord_less_nat @ SY634 @ SY635 )
| ( ord_less_nat @ ( plus_plus_nat @ SV105 @ SY634 ) @ ( plus_plus_nat @ SY633 @ SY635 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(866,plain,
! [SV106: nat] :
( ( ! [SY636: nat,SY637: nat] :
( ~ ( ord_less_nat @ ( plus_plus_nat @ SV106 @ SY636 ) @ SY637 )
| ( ord_less_nat @ SV106 @ SY637 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(867,plain,
! [SV107: nat] :
( ( ! [SY638: nat,SY639: nat,SY640: nat,SY641: nat] :
( ~ ( ord_less_eq_nat @ SV107 @ SY638 )
| ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ SV107 @ SY639 ) @ SY640 ) @ ( plus_plus_nat @ ( times_times_nat @ SY638 @ SY639 ) @ SY641 ) )
= ( minus_minus_nat @ SY640 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SY638 @ SV107 ) @ SY639 ) @ SY641 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(868,plain,
! [SV108: nat] :
( ( ! [SY642: nat,SY643: nat] :
( ~ ( ord_less_eq_nat @ SV108 @ SY642 )
| ( ( minus_minus_nat @ ( plus_plus_nat @ SY642 @ SY643 ) @ SV108 )
= ( plus_plus_nat @ ( minus_minus_nat @ SY642 @ SV108 ) @ SY643 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(869,plain,
! [SV109: nat] :
( ( ! [SY644: nat,SY645: nat,SY646: nat] :
( ~ ~ ( ~ ( ord_less_nat @ SV109 @ SY644 )
| ~ ( ord_less_nat @ SY645 @ SY646 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV109 @ SY645 ) @ ( plus_plus_nat @ SY644 @ SY646 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(870,plain,
! [SV110: nat] :
( ( ! [SY647: nat,SY648: nat] :
( ~ ( ord_less_eq_nat @ SV110 @ SY647 )
| ~ ( ord_less_eq_nat @ SV110 @ SY648 )
| ( ( ( minus_minus_nat @ SY647 @ SV110 )
= ( minus_minus_nat @ SY648 @ SV110 ) )
= ( SY647 = SY648 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(871,plain,
! [SV111: nat] :
( ( ! [SY649: nat,SY650: nat] :
( ~ ( ord_less_nat @ SV111 @ SY649 )
| ( ord_less_nat @ ( plus_plus_nat @ SY650 @ SV111 ) @ ( plus_plus_nat @ SY650 @ SY649 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(872,plain,
! [SV112: nat] :
( ( ! [SY651: nat] :
( ( ( minus_minus_nat @ SV112 @ SY651 )
!= zero_zero_nat )
| ( ( minus_minus_nat @ SY651 @ SV112 )
!= zero_zero_nat )
| ( SV112 = SY651 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(873,plain,
! [SV113: nat] :
( ( ! [SY652: nat,SY653: nat] :
( ~ ( ord_less_eq_nat @ SV113 @ SY652 )
| ( ( ord_less_eq_nat @ SY653 @ ( minus_minus_nat @ SY652 @ SV113 ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ SY653 @ SV113 ) @ SY652 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(874,plain,
! [SV114: nat > $o] :
( ( ! [SY654: nat] :
( ~ ( SV114 @ zero_zero_nat )
| ~ ! [SY655: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY655 )
| ~ ~ ( SV114 @ SY655 )
| ~ ! [SY656: nat] :
~ ~ ( ~ ( ord_less_nat @ SY656 @ SY655 )
| ~ ~ ( SV114 @ SY656 ) ) )
| ( SV114 @ SY654 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(875,plain,
! [SV115: nat] :
( ( ( SV115 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(876,plain,
! [SV116: nat] :
( ( ! [SY657: nat,SY658: nat] :
( ~ ( ord_less_eq_nat @ SV116 @ SY657 )
| ( ( plus_plus_nat @ SY658 @ ( minus_minus_nat @ SY657 @ SV116 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ SY658 @ SY657 ) @ SV116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(877,plain,
! [SV117: nat > $o] :
( ( ! [SY659: nat,SY660: nat] :
( ( SV117 @ ( minus_minus_nat @ SY659 @ SY660 ) )
= ( ~ ( ~ ( ~ ( ord_less_nat @ SY659 @ SY660 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY661: nat] :
( ( SY659
!= ( plus_plus_nat @ SY660 @ SY661 ) )
| ( SV117 @ SY661 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(878,plain,
! [SV118: nat] :
( ( ! [SY662: nat,SY663: nat] :
( ~ ( ord_less_nat @ SV118 @ SY662 )
| ~ ( ord_less_nat @ SV118 @ SY663 )
| ( ord_less_nat @ ( minus_minus_nat @ SY663 @ SY662 ) @ ( minus_minus_nat @ SY663 @ SV118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(879,plain,
! [SV119: nat] :
( ( ! [SY664: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SV119 )
| ~ ( ord_less_nat @ zero_zero_nat @ SY664 )
| ( ord_less_nat @ ( minus_minus_nat @ SY664 @ SV119 ) @ SY664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(880,plain,
( ( ! [SV120: nat] :
( ( ord_less_eq_nat @ SV120 )
= ( ^ [SY665: nat] :
~ ! [SY666: nat] :
( SY665
!= ( plus_plus_nat @ SV120 @ SY666 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[671]) ).
thf(881,plain,
( ( ord_less_eq_nat
= ( ^ [SX0: nat,SX1: nat] :
~ ! [SX2: nat] :
( SX1
!= ( plus_plus_nat @ SX0 @ SX2 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[671]) ).
thf(882,plain,
( ( ! [SV121: nat] :
( ( ord_less_eq_nat @ SV121 )
= ( ^ [SY667: nat] :
~ ! [SY668: nat] :
( SY667
!= ( plus_plus_nat @ SV121 @ SY668 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[672]) ).
thf(883,plain,
( ( ord_less_eq_nat
= ( ^ [SX0: nat,SX1: nat] :
~ ! [SX2: nat] :
( SX1
!= ( plus_plus_nat @ SX0 @ SX2 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[672]) ).
thf(884,plain,
! [SV122: nat] :
( ( ! [SY669: nat,SY670: nat] :
( ~ ( ord_less_eq_nat @ SV122 @ SY669 )
| ( ( ( minus_minus_nat @ SY669 @ SV122 )
= SY670 )
= ( SY669
= ( plus_plus_nat @ SY670 @ SV122 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(885,plain,
! [SV123: nat] :
( ( ! [SY671: nat,SY672: nat,SY673: nat,SY674: nat] :
( ~ ( ord_less_eq_nat @ SV123 @ SY671 )
| ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ SY671 @ SY672 ) @ SY673 ) @ ( plus_plus_nat @ ( times_times_nat @ SV123 @ SY672 ) @ SY674 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SY671 @ SV123 ) @ SY672 ) @ SY673 ) @ SY674 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(886,plain,
! [SV124: nat] :
( ( ! [SY675: nat,SY676: nat] :
( ~ ( ord_less_eq_nat @ SV124 @ SY675 )
| ( ord_less_eq_nat @ SY676 @ ( minus_minus_nat @ ( plus_plus_nat @ SY675 @ SY676 ) @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(887,plain,
! [SV125: nat] :
( ( ! [SY677: nat,SY678: nat] :
( ~ ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SY677 ) @ ( plus_plus_nat @ SY678 @ SY677 ) )
| ( ord_less_nat @ SV125 @ SY678 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(888,plain,
! [SV126: nat] :
( ( ! [SY679: nat] :
( ( ( plus_plus_nat @ SV126 @ SY679 )
= zero_zero_nat )
= ( ~ ( ( SV126 != zero_zero_nat )
| ( SY679 != zero_zero_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(889,plain,
! [SV127: nat] :
( ( ! [SY680: nat,SY681: nat,SY682: nat,SY683: nat] :
( ~ ( ord_less_eq_nat @ SV127 @ SY680 )
| ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV127 @ SY681 ) @ SY682 ) @ ( plus_plus_nat @ ( times_times_nat @ SY680 @ SY681 ) @ SY683 ) )
= ( ord_less_nat @ SY682 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SY680 @ SV127 ) @ SY681 ) @ SY683 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(890,plain,
! [SV128: nat] :
( ( ! [SY684: nat,SY685: nat] :
( ~ ( ord_less_nat @ SV128 @ SY684 )
| ( ord_less_nat @ ( minus_minus_nat @ SV128 @ SY685 ) @ SY684 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(891,plain,
! [SV129: nat] :
( ( ! [SY686: nat,SY687: nat] :
( ~ ( ord_less_eq_nat @ SV129 @ SY686 )
| ( ord_less_eq_nat @ ( minus_minus_nat @ SY687 @ SY686 ) @ ( minus_minus_nat @ SY687 @ SV129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(892,plain,
! [SV130: nat] :
( ( ! [SY688: nat,SY689: nat] :
( ~ ( ord_less_eq_nat @ SV130 @ SY688 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV130 @ SY689 ) @ ( plus_plus_nat @ SY688 @ SY689 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(893,plain,
! [SV131: nat] :
( ( ! [SY690: nat] :
( ~ ( ord_less_nat @ SV131 @ SY690 )
| ( SY690 != SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(894,plain,
! [SV132: nat] :
( ( ! [SY691: nat,SY692: nat,SY693: nat] :
( ~ ( ord_less_nat @ SV132 @ SY691 )
| ( ( plus_plus_nat @ SY692 @ SY691 )
!= ( plus_plus_nat @ SV132 @ SY693 ) )
| ( ord_less_nat @ SY692 @ SY693 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(895,plain,
! [SV133: nat] :
( ( ! [SY694: nat,SY695: nat] :
( ~ ( ord_less_eq_nat @ SV133 @ SY694 )
| ( ord_less_eq_nat @ SV133 @ ( plus_plus_nat @ SY695 @ SY694 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(896,plain,
! [SV134: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV134 )
= ( SV134 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(897,plain,
! [SV135: nat] :
( ( ! [SY696: nat,SY697: nat] :
( ~ ( ord_less_eq_nat @ SV135 @ SY696 )
| ( ( minus_minus_nat @ SY697 @ ( minus_minus_nat @ SY696 @ SV135 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ SY697 @ SV135 ) @ SY696 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(898,plain,
! [SV136: nat] :
( ( ! [SY698: nat,SY699: nat] :
( ~ ( ord_less_eq_nat @ SV136 @ SY698 )
| ( ( minus_minus_nat @ ( plus_plus_nat @ SY699 @ SY698 ) @ SV136 )
= ( plus_plus_nat @ SY699 @ ( minus_minus_nat @ SY698 @ SV136 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(899,plain,
! [SV137: nat] :
( ( ! [SY700: nat,SY701: nat,SY702: nat] :
( ~ ( ord_less_eq_nat @ SV137 @ SY700 )
| ~ ( ord_less_eq_nat @ SY701 @ SY702 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV137 @ SY701 ) @ ( plus_plus_nat @ SY700 @ SY702 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(900,plain,
! [SV138: nat] :
( ( ! [SY703: nat,SY704: nat] :
( ~ ( ord_less_eq_nat @ SV138 @ SY703 )
| ( ( minus_minus_nat @ ( plus_plus_nat @ SY703 @ SY704 ) @ SV138 )
= ( plus_plus_nat @ ( minus_minus_nat @ SY703 @ SV138 ) @ SY704 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(901,plain,
! [SV139: nat] :
( ( ! [SY705: nat,SY706: nat] :
( ~ ( ord_less_nat @ ( plus_plus_nat @ SV139 @ SY705 ) @ ( plus_plus_nat @ SV139 @ SY706 ) )
| ( ord_less_nat @ SY705 @ SY706 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(902,plain,
! [SV140: nat] :
( ( ! [SY707: nat,SY708: nat] :
( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV140 @ SY707 ) @ ( plus_plus_nat @ SY708 @ SY707 ) )
| ( ord_less_eq_nat @ SV140 @ SY708 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(903,plain,
! [SV141: nat] :
( ( ! [SY709: nat,SY710: nat] :
( ~ ( ord_less_eq_nat @ SV141 @ SY709 )
| ( ( plus_plus_nat @ ( minus_minus_nat @ SY709 @ SV141 ) @ SY710 )
= ( minus_minus_nat @ ( plus_plus_nat @ SY709 @ SY710 ) @ SV141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(904,plain,
( ( ( p @ i )
= zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[693]) ).
thf(905,plain,
! [SV142: nat > $o] :
( ( ! [SY711: nat] :
( ~ ! [SY712: nat] :
( ~ ~ ( SV142 @ SY712 )
| ~ ! [SY713: nat] :
~ ~ ( ~ ( ord_less_nat @ SY713 @ SY712 )
| ~ ~ ( SV142 @ SY713 ) ) )
| ( SV142 @ SY711 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(906,plain,
! [SV143: nat] :
( ( ! [SY714: nat,SY715: nat] :
( ( ( plus_plus_nat @ SV143 @ SY714 )
!= ( plus_plus_nat @ SY715 @ SY714 ) )
| ( SV143 = SY715 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(907,plain,
! [SV144: nat] :
( ( ! [SY716: nat,SY717: nat] :
( ~ ( ord_less_nat @ SV144 @ SY716 )
| ( ord_less_nat @ SV144 @ ( plus_plus_nat @ SY716 @ SY717 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(908,plain,
! [SV145: nat] :
( ( ! [SY718: nat] :
( ( SV145 != SY718 )
| ( ord_less_eq_nat @ SV145 @ SY718 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(909,plain,
! [SV146: nat] :
( ( ! [SY719: nat,SY720: nat,SY721: nat,SY722: nat] :
( ~ ( ord_less_eq_nat @ SV146 @ SY719 )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV146 @ SY720 ) @ SY721 ) @ ( plus_plus_nat @ ( times_times_nat @ SY719 @ SY720 ) @ SY722 ) )
= ( ord_less_eq_nat @ SY721 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SY719 @ SV146 ) @ SY720 ) @ SY722 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(910,plain,
! [SV147: nat] :
( ( ! [SY723: nat,SY724: nat] :
( ~ ( ord_less_eq_nat @ SV147 @ SY723 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV147 @ SY724 ) @ ( plus_plus_nat @ SY723 @ SY724 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(911,plain,
! [SV148: nat] :
( ( ! [SY725: nat,SY726: nat,SY727: nat] :
( ~ ~ ( ~ ( ord_less_nat @ SV148 @ SY725 )
| ( SY726 != SY727 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV148 @ SY726 ) @ ( plus_plus_nat @ SY725 @ SY727 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(912,plain,
! [SV149: nat] :
( ( ! [SY728: nat] :
( ~ ( ord_less_nat @ SV149 @ SY728 )
| ( ord_less_eq_nat @ SV149 @ SY728 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(913,plain,
! [SV150: nat] :
( ( ! [SY729: nat,SY730: nat,SY731: nat] :
( ~ ( ord_less_nat @ SV150 @ SY729 )
| ~ ( ord_less_nat @ SY730 @ SY731 )
| ( ord_less_nat @ ( plus_plus_nat @ SV150 @ SY730 ) @ ( plus_plus_nat @ SY729 @ SY731 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(914,plain,
! [SV151: nat] :
( ( ~ ( ( SV151 != zero_zero_nat ) )
| ( ord_less_nat @ zero_zero_nat @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(915,plain,
! [SV152: nat] :
( ( ! [SY732: nat,SY733: nat] :
( ( ord_less_nat @ ( times_times_nat @ SV152 @ SY732 ) @ ( times_times_nat @ SY733 @ SY732 ) )
= ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SY732 )
| ~ ( ord_less_nat @ SV152 @ SY733 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(916,plain,
! [SV153: nat] :
( ( ! [SY734: nat] :
( ~ ~ ( ord_less_nat @ SV153 @ SY734 )
| ( ( plus_plus_nat @ SY734 @ ( minus_minus_nat @ SV153 @ SY734 ) )
= SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(917,plain,
! [SV154: nat] :
( ( ! [SY735: nat] :
( ~ ( ord_less_nat @ SV154 @ SY735 )
| ( SY735 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(918,plain,
! [SV155: nat] :
( ( ! [SY736: nat] :
( ( SV155 != SY736 )
= ( ( ord_less_nat @ SV155 @ SY736 )
| ( ord_less_nat @ SY736 @ SV155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(919,plain,
! [SV156: nat] :
( ( ! [SY737: nat] :
( ~ ( ord_less_nat @ SV156 @ SY737 )
| ( SY737 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(920,plain,
! [SV157: nat] :
( ( ! [SY738: nat,SY739: nat] :
( ~ ( ord_less_eq_nat @ SV157 @ SY738 )
| ( ( plus_plus_nat @ SY739 @ ( minus_minus_nat @ SY738 @ SV157 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ SY739 @ SY738 ) @ SV157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(921,plain,
! [SV158: nat] :
( ( ! [SY740: nat,SY741: nat] :
( ~ ( ord_less_eq_nat @ SV158 @ SY740 )
| ( ( plus_plus_nat @ ( minus_minus_nat @ SY740 @ SV158 ) @ SY741 )
= ( minus_minus_nat @ ( plus_plus_nat @ SY740 @ SY741 ) @ SV158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(922,plain,
! [SV159: nat] :
( ( ! [SY742: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SY742 ) )
= ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV159 )
| ~ ( ord_less_nat @ zero_zero_nat @ SY742 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(923,plain,
! [SV160: nat] :
( ( ! [SY743: nat] :
( ( ( plus_plus_nat @ SV160 @ SY743 )
= zero_zero_nat )
= ( ~ ( ( SV160 != zero_zero_nat )
| ( SY743 != zero_zero_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(924,plain,
( ( ! [SV161: nat] :
( ( ord_less_nat @ SV161 )
= ( ^ [SY744: nat] :
~ ( ~ ( ord_less_eq_nat @ SV161 @ SY744 )
| ~ ( ( SV161 != SY744 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[713]) ).
thf(925,plain,
( ( ord_less_nat
= ( ^ [SX0: nat,SX1: nat] :
~ ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[713]) ).
thf(926,plain,
! [SV162: nat] :
( ( ! [SY745: nat] :
( ( zero_zero_nat
= ( plus_plus_nat @ SV162 @ SY745 ) )
= ( ~ ( ( SV162 != zero_zero_nat )
| ( SY745 != zero_zero_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(927,plain,
! [SV163: nat] :
( ( ! [SY746: nat,SY747: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SY746 ) @ ( times_times_nat @ SY747 @ SY746 ) )
= ( ~ ( ord_less_nat @ zero_zero_nat @ SY746 )
| ( ord_less_eq_nat @ SV163 @ SY747 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(928,plain,
! [SV164: nat > $o] :
( ( ! [SY748: nat,SY749: nat] :
( ~ ( SV164 @ SY748 )
| ~ ! [SY750: nat] :
( ~ ( SV164 @ SY750 )
| ( ord_less_eq_nat @ SY750 @ SY749 ) )
| ~ ! [SY751: nat] :
~ ~ ( ~ ( SV164 @ SY751 )
| ~ ! [SY752: nat] :
( ~ ( SV164 @ SY752 )
| ( ord_less_eq_nat @ SY752 @ SY751 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(929,plain,
! [SV165: nat] :
( ( ~ ( ord_less_eq_nat @ SV165 @ zero_zero_nat )
| ( SV165 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(930,plain,
! [SV166: nat] :
( ( ! [SY753: nat,SY754: nat] :
( ~ ( ord_less_nat @ SV166 @ SY753 )
| ( ord_less_nat @ ( plus_plus_nat @ SV166 @ SY754 ) @ ( plus_plus_nat @ SY753 @ SY754 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(931,plain,
! [SV167: nat] :
( ( ! [SY755: nat,SY756: nat] :
( ~ ( ord_less_eq_nat @ SV167 @ SY755 )
| ~ ( ord_less_eq_nat @ SV167 @ SY756 )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SY755 @ SV167 ) @ ( minus_minus_nat @ SY756 @ SV167 ) )
= ( ord_less_eq_nat @ SY755 @ SY756 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(932,plain,
! [SV168: nat] :
( ( ! [SY757: nat,SY758: nat] :
( ( ( plus_plus_nat @ SV168 @ SY757 )
!= SY758 )
| ( SV168
= ( minus_minus_nat @ SY758 @ SY757 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(933,plain,
! [SV169: nat] :
( ( ! [SY759: nat,SY760: nat] :
( ~ ( ord_less_eq_nat @ SV169 @ SY759 )
| ( ( ord_less_nat @ ( minus_minus_nat @ SY759 @ SV169 ) @ SY760 )
= ( ord_less_nat @ SY759 @ ( plus_plus_nat @ SY760 @ SV169 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(934,plain,
! [SV170: nat] :
( ( ! [SY761: nat,SY762: nat,SY763: nat] :
( ( SV170
!= ( plus_plus_nat @ SY761 @ SY762 ) )
| ( ( plus_plus_nat @ SV170 @ SY763 )
= ( plus_plus_nat @ SY761 @ ( plus_plus_nat @ SY762 @ SY763 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(935,plain,
! [SV171: nat] :
( ( ! [SY764: nat,SY765: nat] :
( ~ ( ord_less_eq_nat @ SV171 @ SY764 )
| ~ ( ord_less_eq_nat @ SV171 @ SY765 )
| ( ( minus_minus_nat @ ( minus_minus_nat @ SY764 @ SV171 ) @ ( minus_minus_nat @ SY765 @ SV171 ) )
= ( minus_minus_nat @ SY764 @ SY765 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(936,plain,
! [SV172: nat] :
( ( ! [SY766: nat,SY767: nat] :
( ~ ( ord_less_eq_nat @ SV172 @ SY766 )
| ( ord_less_eq_nat @ SV172 @ ( plus_plus_nat @ SY766 @ SY767 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(937,plain,
! [SV173: nat] :
( ( ~ ( ( SV173 != zero_zero_nat ) )
| ( ord_less_nat @ zero_zero_nat @ SV173 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(938,plain,
! [SV174: nat] :
( ( ! [SY768: nat,SY769: nat,SY770: nat,SY771: nat] :
( ~ ( ord_less_eq_nat @ SV174 @ SY768 )
| ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SY768 @ SY769 ) @ SY770 ) @ ( plus_plus_nat @ ( times_times_nat @ SV174 @ SY769 ) @ SY771 ) )
= ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SY768 @ SV174 ) @ SY769 ) @ SY770 ) @ SY771 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(939,plain,
! [SV175: nat] :
( ( ! [SY772: nat,SY773: nat,SY774: nat] :
( ( SV175
!= ( plus_plus_nat @ SY772 @ SY773 ) )
| ( ( plus_plus_nat @ SY774 @ SV175 )
= ( plus_plus_nat @ SY772 @ ( plus_plus_nat @ SY774 @ SY773 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(940,plain,
! [SV176: nat] :
( ( ! [SY775: nat] :
( ~ ( ord_less_eq_nat @ SV176 @ SY775 )
| ( ( plus_plus_nat @ SV176 @ ( minus_minus_nat @ SY775 @ SV176 ) )
= SY775 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(941,plain,
! [SV177: nat] :
( ( ! [SY776: nat,SY777: nat] :
( ( ord_less_nat @ ( times_times_nat @ SV177 @ SY776 ) @ ( times_times_nat @ SV177 @ SY777 ) )
= ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 )
| ~ ( ord_less_nat @ SY776 @ SY777 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(942,plain,
! [SV178: nat] :
( ( ! [SY778: nat] :
( ~ ( ( SV178 != SY778 ) )
| ~ ~ ( ord_less_nat @ SV178 @ SY778 )
| ( ord_less_nat @ SY778 @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(943,plain,
! [SV179: nat] :
( ( ! [SY779: nat,SY780: nat] :
( ~ ( ord_less_eq_nat @ SV179 @ SY779 )
| ( ord_less_eq_nat @ ( minus_minus_nat @ SV179 @ SY780 ) @ ( minus_minus_nat @ SY779 @ SY780 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(944,plain,
! [SV180: nat] :
( ( ! [SY781: nat] :
( ~ ( ord_less_eq_nat @ SV180 @ SY781 )
| ( ( minus_minus_nat @ SV180 @ SY781 )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(945,plain,
! [SV181: nat > $o] :
( ( ! [SY782: nat] :
( ~ ! [SY783: nat] :
( ~ ! [SY784: nat] :
( ~ ( ord_less_nat @ SY784 @ SY783 )
| ( SV181 @ SY784 ) )
| ( SV181 @ SY783 ) )
| ( SV181 @ SY782 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(946,plain,
! [SV182: nat] :
( ( ! [SY785: nat,SY786: nat] :
( ~ ( ord_less_eq_nat @ SV182 @ SY785 )
| ~ ( ord_less_eq_nat @ SV182 @ SY785 )
| ( ( ( minus_minus_nat @ SY785 @ SV182 )
= SY786 )
= ( SY785
= ( plus_plus_nat @ SY786 @ SV182 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(947,plain,
! [SV183: nat] :
( ( ! [SY787: nat,SY788: nat] :
( ~ ( ord_less_eq_nat @ SV183 @ SY787 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SY788 @ SV183 ) @ ( plus_plus_nat @ SY788 @ SY787 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(948,plain,
! [SV184: nat] :
( ( ! [SY789: nat,SY790: nat] :
( ~ ( ord_less_eq_nat @ SV184 @ SY789 )
| ~ ( ord_less_eq_nat @ SV184 @ SY790 )
| ( ( ord_less_nat @ ( minus_minus_nat @ SY789 @ SV184 ) @ ( minus_minus_nat @ SY790 @ SV184 ) )
= ( ord_less_nat @ SY789 @ SY790 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(949,plain,
! [SV185: nat] :
( ( ! [SY791: nat,SY792: nat] :
( ~ ( ord_less_eq_nat @ SV185 @ SY791 )
| ( ( ord_less_eq_nat @ SY792 @ ( minus_minus_nat @ SY791 @ SV185 ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ SY792 @ SV185 ) @ SY791 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(950,plain,
! [SV186: nat > $o] :
( ( ! [SY793: nat,SY794: nat] :
( ( SV186 @ ( minus_minus_nat @ SY793 @ SY794 ) )
= ( ~ ( ~ ( ~ ( ord_less_nat @ SY793 @ SY794 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY795: nat] :
~ ~ ( ( SY793
!= ( plus_plus_nat @ SY794 @ SY795 ) )
| ~ ~ ( SV186 @ SY795 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(951,plain,
! [SV187: nat] :
( ( ! [SY796: nat,SY797: nat] :
( ( ( plus_plus_nat @ SV187 @ SY796 )
!= ( plus_plus_nat @ SV187 @ SY797 ) )
| ( SY796 = SY797 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(952,plain,
! [SV188: nat] :
( ( ! [SY798: nat,SY799: nat] :
( ~ ( ord_less_nat @ SV188 @ SY798 )
| ~ ( ord_less_eq_nat @ SY799 @ SV188 )
| ( ord_less_nat @ ( minus_minus_nat @ SV188 @ SY799 ) @ ( minus_minus_nat @ SY798 @ SY799 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(953,plain,
! [SV189: nat] :
( ( ! [SY800: nat] :
( ~ ( ord_less_eq_nat @ SV189 @ SY800 )
| ~ ( ord_less_eq_nat @ SY800 @ SV189 )
| ( SV189 = SY800 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(954,plain,
! [SV190: nat] :
( ( ! [SY801: nat,SY802: nat,SY803: nat,SY804: nat] :
( ~ ( ord_less_eq_nat @ SV190 @ SY801 )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SY801 @ SY802 ) @ SY803 )
= ( plus_plus_nat @ ( times_times_nat @ SV190 @ SY802 ) @ SY804 ) )
= ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SY801 @ SV190 ) @ SY802 ) @ SY803 )
= SY804 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(955,plain,
! [SV191: nat] :
( ( ! [SY805: nat] :
( ~ ( ord_less_eq_nat @ SV191 @ SY805 )
| ~ ! [SY806: nat] :
( SY805
!= ( plus_plus_nat @ SV191 @ SY806 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(956,plain,
! [SV192: nat] :
( ( ! [SY807: nat,SY808: nat,SY809: nat] :
( ~ ~ ( ( SV192 != SY807 )
| ~ ( ord_less_nat @ SY808 @ SY809 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV192 @ SY808 ) @ ( plus_plus_nat @ SY807 @ SY809 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(957,plain,
! [SV193: nat] :
( ( ! [SY810: nat,SY811: nat,SY812: nat] :
( ~ ~ ( ~ ( ord_less_eq_nat @ SV193 @ SY810 )
| ( SY811 != SY812 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV193 @ SY811 ) @ ( plus_plus_nat @ SY810 @ SY812 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(958,plain,
! [SV194: nat] :
( ( ! [SY813: nat,SY814: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SY813 ) @ ( times_times_nat @ SV194 @ SY814 ) )
= ( ~ ( ord_less_nat @ zero_zero_nat @ SV194 )
| ( ord_less_eq_nat @ SY813 @ SY814 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(959,plain,
! [SV195: nat] :
( ( ! [SY815: nat,SY816: nat] :
( ~ ( ord_less_eq_nat @ SV195 @ SY815 )
| ~ ( ord_less_eq_nat @ SY815 @ SY816 )
| ( ord_less_eq_nat @ SV195 @ SY816 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(960,plain,
! [SV196: nat] :
( ( ! [SY817: nat,SY818: nat,SY819: nat] :
( ~ ~ ( ( SV196 != SY817 )
| ( SY818 != SY819 ) )
| ( ( plus_plus_nat @ SV196 @ SY818 )
= ( plus_plus_nat @ SY817 @ SY819 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(961,plain,
! [SV197: nat] :
( ( ! [SY820: nat,SY821: nat,SY822: nat,SY823: nat] :
( ~ ( ord_less_eq_nat @ SV197 @ SY820 )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SV197 @ SY821 ) @ SY822 )
= ( plus_plus_nat @ ( times_times_nat @ SY820 @ SY821 ) @ SY823 ) )
= ( SY822
= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SY820 @ SV197 ) @ SY821 ) @ SY823 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(962,plain,
! [SV198: nat] :
( ( ! [SY824: nat,SY825: nat,SY826: nat] :
( ~ ( ord_less_eq_nat @ SV198 @ SY824 )
| ~ ( ord_less_eq_nat @ SY825 @ SY826 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV198 @ SY825 ) @ ( plus_plus_nat @ SY824 @ SY826 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(963,plain,
! [SV199: nat] :
( ( ! [SY827: nat,SY828: nat] :
( ~ ( ord_less_nat @ SV199 @ SY827 )
| ( ord_less_nat @ SV199 @ ( plus_plus_nat @ SY828 @ SY827 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(964,plain,
! [SV200: nat] :
( ( ! [SY829: nat] :
( ~ ( ( ord_less_nat @ SV200 @ SY829 )
| ( SV200 = SY829 ) )
| ( ord_less_eq_nat @ SV200 @ SY829 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(965,plain,
! [SV201: nat > nat] :
( ( ! [SY830: nat,SY831: nat] :
( ~ ( number1551313001itions @ SV201 @ SY830 )
| ( ord_less_eq_nat @ ( SV201 @ SY831 ) @ SY830 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(966,plain,
! [SV202: nat] :
( ( ! [SY832: nat] :
( ~ ( ord_less_eq_nat @ SV202 @ SY832 )
| ( ( minus_minus_nat @ SY832 @ ( minus_minus_nat @ SY832 @ SV202 ) )
= SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(967,plain,
! [SV203: nat] :
( ( ! [SY833: nat,SY834: nat] :
( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV203 @ SY833 ) @ ( plus_plus_nat @ SV203 @ SY834 ) )
| ( ord_less_eq_nat @ SY833 @ SY834 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(968,plain,
! [SV1: nat > nat] :
( ( ~ ( ( number1551313001itions @ SV1 @ zero_zero_nat )
| ( SV1
= ( ^ [I: nat] : zero_zero_nat ) ) )
| ~ ( ~ ( number1551313001itions @ SV1 @ zero_zero_nat )
| ( SV1
!= ( ^ [I: nat] : zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[756]) ).
thf(969,plain,
! [SV1: nat > nat] :
( ( ( number1551313001itions @ SV1 @ zero_zero_nat )
= ( SV1
= ( ^ [I: nat] : zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[756]) ).
thf(970,plain,
! [SV204: nat,SV2: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SV204 ) )
= ( ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( ord_less_nat @ zero_zero_nat @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(971,plain,
! [SV205: nat,SV3: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV3 @ SV205 ) @ SV3 )
= ( ord_less_nat @ SV205 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(972,plain,
! [SV206: nat,SV4: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV4 @ SV206 ) @ SV206 )
= ( ord_less_nat @ SV4 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(973,plain,
! [SV207: nat,SV5: nat] :
( ( ( ord_less_nat @ SV5 @ ( plus_plus_nat @ SV5 @ SV207 ) )
= ( ord_less_nat @ zero_zero_nat @ SV207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(974,plain,
! [SV208: nat,SV6: nat] :
( ( ( ord_less_nat @ SV6 @ ( plus_plus_nat @ SV208 @ SV6 ) )
= ( ord_less_nat @ zero_zero_nat @ SV208 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(975,plain,
! [SV209: nat,SV7: nat] :
( ( ! [SY835: nat] :
( ( ( plus_plus_nat @ SV7 @ SV209 )
= ( plus_plus_nat @ SY835 @ SV209 ) )
= ( SV7 = SY835 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(976,plain,
! [SV210: nat,SV8: nat] :
( ( ! [SY836: nat] :
( ( ( plus_plus_nat @ SV8 @ SV210 )
= ( plus_plus_nat @ SV8 @ SY836 ) )
= ( SV210 = SY836 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(977,plain,
! [SV9: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV9 @ zero_zero_nat )
| ( SV9 = zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ SV9 @ zero_zero_nat )
| ( SV9 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[764]) ).
thf(978,plain,
! [SV9: nat] :
( ( ( ord_less_eq_nat @ SV9 @ zero_zero_nat )
= ( SV9 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[764]) ).
thf(979,plain,
! [SV10: nat] :
( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV10 )
| ( SV10 = zero_zero_nat ) )
| ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV10 )
| ( SV10 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[765]) ).
thf(980,plain,
! [SV10: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV10 ) )
= ( SV10 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[765]) ).
thf(981,plain,
! [SV211: nat,SV11: nat] :
( ( ! [SY837: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ SV11 @ SV211 ) @ ( plus_plus_nat @ SY837 @ SV211 ) )
= ( ord_less_eq_nat @ SV11 @ SY837 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(982,plain,
! [SV212: nat,SV12: nat] :
( ( ! [SY838: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV212 ) @ ( plus_plus_nat @ SV12 @ SY838 ) )
= ( ord_less_eq_nat @ SV212 @ SY838 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(983,plain,
! [SV213: nat,SV13: nat] :
( ( ( SV13
= ( plus_plus_nat @ SV13 @ SV213 ) )
= ( SV213 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(984,plain,
! [SV214: nat,SV14: nat] :
( ( ( SV14
= ( plus_plus_nat @ SV214 @ SV14 ) )
= ( SV214 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(985,plain,
! [SV215: nat,SV15: nat] :
( ( ( ( plus_plus_nat @ SV15 @ SV215 )
= SV15 )
= ( SV215 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(986,plain,
! [SV216: nat,SV16: nat] :
( ( ( ( plus_plus_nat @ SV16 @ SV216 )
= SV216 )
= ( SV16 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(987,plain,
! [SV217: nat,SV22: nat] :
( ( ! [SY839: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ SV22 @ SV217 ) @ ( plus_plus_nat @ SY839 @ SV217 ) )
= ( ord_less_nat @ SV22 @ SY839 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(988,plain,
! [SV218: nat,SV23: nat] :
( ( ! [SY840: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ SV23 @ SV218 ) @ ( plus_plus_nat @ SV23 @ SY840 ) )
= ( ord_less_nat @ SV218 @ SY840 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(989,plain,
! [SV219: nat,SV24: nat] :
( ( ( minus_minus_nat @ ( plus_plus_nat @ SV24 @ SV219 ) @ SV219 )
= SV24 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(990,plain,
! [SV220: nat,SV25: nat] :
( ( ! [SY841: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ SV25 @ SV220 ) @ ( plus_plus_nat @ SY841 @ SV220 ) )
= ( minus_minus_nat @ SV25 @ SY841 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(991,plain,
! [SV221: nat,SV26: nat] :
( ( ( minus_minus_nat @ ( plus_plus_nat @ SV26 @ SV221 ) @ SV26 )
= SV221 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(992,plain,
! [SV222: nat,SV27: nat] :
( ( ! [SY842: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ SV27 @ SV222 ) @ ( plus_plus_nat @ SV27 @ SY842 ) )
= ( minus_minus_nat @ SV222 @ SY842 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(993,plain,
! [SV28: nat] :
( ( ord_less_nat @ SV28 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[783]) ).
thf(994,plain,
! [SV223: nat,SV32: nat] :
( ( ! [SY843: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ SV32 @ SV223 ) @ ( plus_plus_nat @ SV32 @ SY843 ) )
= ( ord_less_nat @ SV223 @ SY843 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(995,plain,
! [SV224: nat,SV35: nat] :
( ( ! [SY844: nat] :
( ( ( times_times_nat @ SV35 @ SV224 )
= ( times_times_nat @ SY844 @ SV224 ) )
= ( ( SV35 = SY844 )
| ( SV224 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(996,plain,
! [SV225: nat,SV36: nat] :
( ( ! [SY845: nat] :
( ( ( times_times_nat @ SV36 @ SV225 )
= ( times_times_nat @ SV36 @ SY845 ) )
= ( ( SV225 = SY845 )
| ( SV36 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(997,plain,
! [SV226: nat,SV38: nat] :
( ( ( ( times_times_nat @ SV38 @ SV226 )
= zero_zero_nat )
= ( ( SV38 = zero_zero_nat )
| ( SV226 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(998,plain,
! [SV227: nat,SV39: nat] :
( ( ! [SY846: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ SV39 @ SV227 ) @ ( plus_plus_nat @ SV39 @ SY846 ) )
= ( ord_less_eq_nat @ SV227 @ SY846 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(999,plain,
! [SV228: nat,SV40: nat] :
( ( ! [SY847: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ SV40 @ SV228 ) @ SY847 )
= ( minus_minus_nat @ SV40 @ ( plus_plus_nat @ SV228 @ SY847 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(1000,plain,
! [SV229: nat,SV41: nat] :
( ( ( ord_less_eq_nat @ SV41 @ ( plus_plus_nat @ SV229 @ SV41 ) )
= ( ord_less_eq_nat @ zero_zero_nat @ SV229 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(1001,plain,
! [SV230: nat,SV42: nat] :
( ( ( ord_less_eq_nat @ SV42 @ ( plus_plus_nat @ SV42 @ SV230 ) )
= ( ord_less_eq_nat @ zero_zero_nat @ SV230 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(1002,plain,
! [SV231: nat,SV43: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV43 @ SV231 ) @ SV231 )
= ( ord_less_eq_nat @ SV43 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(1003,plain,
! [SV232: nat,SV44: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV44 @ SV232 ) @ SV44 )
= ( ord_less_eq_nat @ SV232 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(1004,plain,
! [SV233: nat,SV45: nat] :
( ( ( minus_minus_nat @ SV45 @ ( plus_plus_nat @ SV45 @ SV233 ) )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(1005,plain,
! [SV234: nat,SV46: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV46 @ SV234 ) )
= ( ord_less_nat @ SV234 @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(1006,plain,
! [SV235: nat,SV47: nat] :
( ( ( ( minus_minus_nat @ SV47 @ SV235 )
= zero_zero_nat )
= ( ord_less_eq_nat @ SV47 @ SV235 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(1007,plain,
! [SV236: nat,SV48: nat] :
( ( ! [SY848: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ SV48 @ SV236 ) @ SY848 )
= ( minus_minus_nat @ ( minus_minus_nat @ SV48 @ SY848 ) @ SV236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(1008,plain,
! [SV237: nat,SV49: nat] :
( ( ! [SY849: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ SV49 @ SV237 ) @ SY849 )
= ( minus_minus_nat @ ( minus_minus_nat @ SV49 @ SY849 ) @ SV237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(1009,plain,
! [SV238: nat,SV50: nat] :
( ( ! [SY850: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ SV50 @ SV238 ) @ SY850 )
= ( minus_minus_nat @ SV50 @ ( plus_plus_nat @ SV238 @ SY850 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(1010,plain,
! [SV239: nat,SV52: nat] :
( ( ord_less_eq_nat @ ( minus_minus_nat @ SV52 @ SV239 ) @ SV52 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(1011,plain,
! [SV240: nat,SV53: nat] :
( ( ( minus_minus_nat @ ( plus_plus_nat @ SV53 @ SV240 ) @ SV240 )
= SV53 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(1012,plain,
! [SV241: nat,SV54: nat] :
( ( ( minus_minus_nat @ ( plus_plus_nat @ SV54 @ SV241 ) @ SV54 )
= SV241 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(1013,plain,
! [SV242: nat,SV55: nat] :
( ( ! [SY851: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ SV55 @ SV242 ) @ ( plus_plus_nat @ SY851 @ SV242 ) )
= ( minus_minus_nat @ SV55 @ SY851 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(1014,plain,
! [SV243: nat,SV56: nat] :
( ( ! [SY852: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ SV56 @ SV243 ) @ ( plus_plus_nat @ SV56 @ SY852 ) )
= ( minus_minus_nat @ SV243 @ SY852 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(1015,plain,
! [SV244: nat,SV57: nat] :
( ( ! [SY853: nat] :
( ( times_times_nat @ SV57 @ ( minus_minus_nat @ SV244 @ SY853 ) )
= ( minus_minus_nat @ ( times_times_nat @ SV57 @ SV244 ) @ ( times_times_nat @ SV57 @ SY853 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(1016,plain,
! [SV245: nat,SV58: nat] :
( ( ! [SY854: nat] :
( ( times_times_nat @ ( minus_minus_nat @ SV58 @ SV245 ) @ SY854 )
= ( minus_minus_nat @ ( times_times_nat @ SV58 @ SY854 ) @ ( times_times_nat @ SV245 @ SY854 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(1017,plain,
! [SV246: nat,SV59: nat] :
( ( ( minus_minus_nat @ SV59 @ ( plus_plus_nat @ SV59 @ SV246 ) )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(1018,plain,
! [SV247: nat,SV60: nat] :
( ( ! [SY855: nat] :
( ( ord_less_nat @ SV60 @ ( minus_minus_nat @ SV247 @ SY855 ) )
= ( ord_less_nat @ ( plus_plus_nat @ SV60 @ SY855 ) @ SV247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(1019,plain,
! [SV248: nat,SV61: nat] :
( ( ! [SY856: nat] :
( ( ord_less_eq_nat @ ( minus_minus_nat @ SV61 @ SV248 ) @ SY856 )
= ( ord_less_eq_nat @ SV61 @ ( plus_plus_nat @ SY856 @ SV248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(1020,plain,
! [SV62: nat] :
( ( ~ ( ( zero_zero_nat = SV62 )
| ( SV62 = zero_zero_nat ) )
| ~ ( ( zero_zero_nat != SV62 )
| ( SV62 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[817]) ).
thf(1021,plain,
! [SV62: nat] :
( ( ( zero_zero_nat = SV62 )
= ( SV62 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[817]) ).
thf(1022,plain,
! [SV249: nat,SV63: nat] :
( ( ! [SY857: nat] :
( ( plus_plus_nat @ SV63 @ ( plus_plus_nat @ SV249 @ SY857 ) )
= ( plus_plus_nat @ SV249 @ ( plus_plus_nat @ SV63 @ SY857 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(1023,plain,
! [SV250: nat] :
( ( ( plus_plus_nat @ SV250 )
= ( ^ [SY858: nat] : ( plus_plus_nat @ SY858 @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(1024,plain,
! [SV251: nat,SV65: nat] :
( ( ! [SY859: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ SV65 @ SV251 ) @ SY859 )
= ( plus_plus_nat @ SV65 @ ( plus_plus_nat @ SV251 @ SY859 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(1025,plain,
! [SV252: nat,SV66: nat] :
( ( ! [SY860: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ SV66 @ SV252 ) @ SY860 )
= ( plus_plus_nat @ SV66 @ ( plus_plus_nat @ SV252 @ SY860 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(1026,plain,
! [SV253: nat,SV67: nat] :
( ( ! [SY861: nat] :
( ( times_times_nat @ SV67 @ ( times_times_nat @ SV253 @ SY861 ) )
= ( times_times_nat @ SV253 @ ( times_times_nat @ SV67 @ SY861 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(1027,plain,
! [SV254: nat] :
( ( ( times_times_nat @ SV254 )
= ( ^ [SY862: nat] : ( times_times_nat @ SY862 @ SV254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(1028,plain,
! [SV255: nat,SV69: nat] :
( ( ! [SY863: nat] :
( ( times_times_nat @ ( times_times_nat @ SV69 @ SV255 ) @ SY863 )
= ( times_times_nat @ SV69 @ ( times_times_nat @ SV255 @ SY863 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(1029,plain,
! [SV256: nat,SV70: nat] :
( ( ! [SY864: nat] :
( ( times_times_nat @ ( times_times_nat @ SV70 @ SV256 ) @ SY864 )
= ( times_times_nat @ SV70 @ ( times_times_nat @ SV256 @ SY864 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(1030,plain,
! [SV71: nat] :
( ( ord_less_nat @ SV71 @ SV71 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[828]) ).
thf(1031,plain,
! [SV72: nat] :
( ( ord_less_nat @ SV72 @ SV72 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[829]) ).
thf(1032,plain,
! [SV257: nat,SV73: nat] :
( ( ( ord_less_eq_nat @ SV73 @ SV257 )
| ( ord_less_eq_nat @ SV257 @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(1033,plain,
! [SV76: nat] :
( ( ord_less_nat @ SV76 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[833]) ).
thf(1034,plain,
! [SV79: nat] :
( ( ord_less_nat @ SV79 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[836]) ).
thf(1035,plain,
! [SV80: nat] :
( ( ord_less_nat @ SV80 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[837]) ).
thf(1036,plain,
! [SV81: nat] :
( ( ord_less_nat @ SV81 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[838]) ).
thf(1037,plain,
! [SV82: nat] :
( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV82 )
| ( SV82 = zero_zero_nat ) )
| ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV82 )
| ( SV82 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[839]) ).
thf(1038,plain,
! [SV82: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV82 ) )
= ( SV82 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[839]) ).
thf(1039,plain,
! [SV83: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV83 @ zero_zero_nat )
| ( SV83 = zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ SV83 @ zero_zero_nat )
| ( SV83 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[840]) ).
thf(1040,plain,
! [SV83: nat] :
( ( ( ord_less_eq_nat @ SV83 @ zero_zero_nat )
= ( SV83 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[840]) ).
thf(1041,plain,
! [SV84: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV84 @ zero_zero_nat )
| ( SV84 = zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ SV84 @ zero_zero_nat )
| ( SV84 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[841]) ).
thf(1042,plain,
! [SV84: nat] :
( ( ( ord_less_eq_nat @ SV84 @ zero_zero_nat )
= ( SV84 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[841]) ).
thf(1043,plain,
! [SV258: nat] :
( ( ( ord_less_eq_nat @ SV258 )
= ( ^ [SY865: nat] :
( ( ord_less_nat @ SV258 @ SY865 )
| ( SV258 = SY865 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(1044,plain,
! [SV259: nat,SV88: nat] :
( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV88 @ SV259 ) @ SV259 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(1045,plain,
! [SV260: nat,SV89: nat] :
( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV89 @ SV260 ) @ SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(1046,plain,
! [SV261: nat,SV90: nat] :
( ( ! [SY866: nat] :
( ( ( times_times_nat @ SV90 @ SV261 )
= ( times_times_nat @ SV90 @ SY866 ) )
= ( ( SV90 = zero_zero_nat )
| ( SV261 = SY866 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(1047,plain,
! [SV262: nat,SV92: nat > nat] :
( ( ! [SY867: nat] :
( ~ ! [SY609: nat,SY610: nat] :
( ~ ( ord_less_nat @ SY609 @ SY610 )
| ( ord_less_nat @ ( SV92 @ SY609 ) @ ( SV92 @ SY610 ) ) )
| ~ ( ord_less_eq_nat @ SV262 @ SY867 )
| ( ord_less_eq_nat @ ( SV92 @ SV262 ) @ ( SV92 @ SY867 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(1048,plain,
! [SV263: nat,SV93: nat] :
( ( ~ ( ord_less_eq_nat @ SV93 @ SV263 )
| ~ ( ( SV93 != SV263 ) )
| ( ord_less_nat @ SV93 @ SV263 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(1049,plain,
! [SV264: nat,SV94: nat] :
( ( ! [SY870: nat,SY871: nat] :
( ~ ~ ( ~ ( ord_less_eq_nat @ SV94 @ SV264 )
| ~ ( ord_less_eq_nat @ SY870 @ SY871 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV94 @ SY870 ) @ ( plus_plus_nat @ SV264 @ SY871 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(1050,plain,
! [SV265: nat,SV95: nat] :
( ( ! [SY872: nat] :
( ~ ( ord_less_eq_nat @ SV95 @ SV265 )
| ~ ( ord_less_eq_nat @ SY872 @ SV265 )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV265 @ SV95 ) @ ( minus_minus_nat @ SV265 @ SY872 ) )
= ( ord_less_eq_nat @ SY872 @ SV95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(1051,plain,
! [SV266: nat,SV96: nat] :
( ( ! [SY873: nat] :
( ~ ( ord_less_eq_nat @ SV96 @ SV266 )
| ( ( minus_minus_nat @ SY873 @ ( minus_minus_nat @ SV266 @ SV96 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ SY873 @ SV96 ) @ SV266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(1052,plain,
! [SV267: nat,SV97: nat] :
( ( ~ ( ord_less_eq_nat @ SV97 @ SV267 )
| ( ( plus_plus_nat @ ( minus_minus_nat @ SV267 @ SV97 ) @ SV97 )
= SV267 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(1053,plain,
! [SV268: nat,SV98: nat] :
( ( ! [SY874: nat,SY875: nat] :
( ~ ~ ( ( SV98 != SV268 )
| ~ ( ord_less_eq_nat @ SY874 @ SY875 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV98 @ SY874 ) @ ( plus_plus_nat @ SV268 @ SY875 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1054,plain,
! [SV269: nat,SV99: nat] :
( ( ! [SY876: nat,SY877: nat,SY878: nat] :
( ~ ( ord_less_eq_nat @ SV99 @ SV269 )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV269 @ SY876 ) @ SY877 ) @ ( plus_plus_nat @ ( times_times_nat @ SV99 @ SY876 ) @ SY878 ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV269 @ SV99 ) @ SY876 ) @ SY877 ) @ SY878 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(1055,plain,
! [SV270: nat,SV100: nat] :
( ( ! [SY879: nat] :
( ~ ( ord_less_eq_nat @ SV100 @ SV270 )
| ( ( minus_minus_nat @ ( plus_plus_nat @ SY879 @ SV270 ) @ SV100 )
= ( plus_plus_nat @ SY879 @ ( minus_minus_nat @ SV270 @ SV100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1056,plain,
! [SV271: nat,SV101: nat] :
( ( ! [SY880: nat] :
( ~ ( ord_less_nat @ SV101 @ SV271 )
| ( ord_less_nat @ ( plus_plus_nat @ SV101 @ SY880 ) @ ( plus_plus_nat @ SV271 @ SY880 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(1057,plain,
! [SV102: nat] :
( ( ~ ( ( SV102 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV102 ) )
| ~ ( ~ ( ( SV102 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV102 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[861]) ).
thf(1058,plain,
! [SV102: nat] :
( ( ( SV102 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SV102 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[861]) ).
thf(1059,plain,
! [SV272: nat,SV103: nat] :
( ( ~ ( ord_less_nat @ SV103 @ SV272 )
| ( SV103 != SV272 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1060,plain,
! [SV273: nat,SV104: nat] :
( ( ( ( plus_plus_nat @ SV104 @ SV273 )
!= SV104 )
| ( SV273 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[863]) ).
thf(1061,plain,
! [SV274: nat,SV105: nat] :
( ( ! [SY881: nat,SY882: nat] :
( ~ ( ord_less_nat @ SV105 @ SV274 )
| ~ ( ord_less_nat @ SY881 @ SY882 )
| ( ord_less_nat @ ( plus_plus_nat @ SV105 @ SY881 ) @ ( plus_plus_nat @ SV274 @ SY882 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(1062,plain,
! [SV275: nat,SV106: nat] :
( ( ! [SY883: nat] :
( ~ ( ord_less_nat @ ( plus_plus_nat @ SV106 @ SV275 ) @ SY883 )
| ( ord_less_nat @ SV106 @ SY883 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(1063,plain,
! [SV276: nat,SV107: nat] :
( ( ! [SY884: nat,SY885: nat,SY886: nat] :
( ~ ( ord_less_eq_nat @ SV107 @ SV276 )
| ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ SV107 @ SY884 ) @ SY885 ) @ ( plus_plus_nat @ ( times_times_nat @ SV276 @ SY884 ) @ SY886 ) )
= ( minus_minus_nat @ SY885 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV276 @ SV107 ) @ SY884 ) @ SY886 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(1064,plain,
! [SV277: nat,SV108: nat] :
( ( ! [SY887: nat] :
( ~ ( ord_less_eq_nat @ SV108 @ SV277 )
| ( ( minus_minus_nat @ ( plus_plus_nat @ SV277 @ SY887 ) @ SV108 )
= ( plus_plus_nat @ ( minus_minus_nat @ SV277 @ SV108 ) @ SY887 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(1065,plain,
! [SV278: nat,SV109: nat] :
( ( ! [SY888: nat,SY889: nat] :
( ~ ~ ( ~ ( ord_less_nat @ SV109 @ SV278 )
| ~ ( ord_less_nat @ SY888 @ SY889 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV109 @ SY888 ) @ ( plus_plus_nat @ SV278 @ SY889 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(1066,plain,
! [SV279: nat,SV110: nat] :
( ( ! [SY890: nat] :
( ~ ( ord_less_eq_nat @ SV110 @ SV279 )
| ~ ( ord_less_eq_nat @ SV110 @ SY890 )
| ( ( ( minus_minus_nat @ SV279 @ SV110 )
= ( minus_minus_nat @ SY890 @ SV110 ) )
= ( SV279 = SY890 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(1067,plain,
! [SV280: nat,SV111: nat] :
( ( ! [SY891: nat] :
( ~ ( ord_less_nat @ SV111 @ SV280 )
| ( ord_less_nat @ ( plus_plus_nat @ SY891 @ SV111 ) @ ( plus_plus_nat @ SY891 @ SV280 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(1068,plain,
! [SV281: nat,SV112: nat] :
( ( ( ( minus_minus_nat @ SV112 @ SV281 )
!= zero_zero_nat )
| ( ( minus_minus_nat @ SV281 @ SV112 )
!= zero_zero_nat )
| ( SV112 = SV281 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(1069,plain,
! [SV282: nat,SV113: nat] :
( ( ! [SY892: nat] :
( ~ ( ord_less_eq_nat @ SV113 @ SV282 )
| ( ( ord_less_eq_nat @ SY892 @ ( minus_minus_nat @ SV282 @ SV113 ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ SY892 @ SV113 ) @ SV282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(1070,plain,
! [SV283: nat,SV114: nat > $o] :
( ( ~ ( SV114 @ zero_zero_nat )
| ~ ! [SY655: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY655 )
| ~ ~ ( SV114 @ SY655 )
| ~ ! [SY656: nat] :
~ ~ ( ~ ( ord_less_nat @ SY656 @ SY655 )
| ~ ~ ( SV114 @ SY656 ) ) )
| ( SV114 @ SV283 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(1071,plain,
! [SV115: nat] :
( ( ~ ( ( SV115 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV115 ) )
| ~ ( ~ ( ( SV115 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV115 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[875]) ).
thf(1072,plain,
! [SV115: nat] :
( ( ( SV115 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SV115 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[875]) ).
thf(1073,plain,
! [SV284: nat,SV116: nat] :
( ( ! [SY895: nat] :
( ~ ( ord_less_eq_nat @ SV116 @ SV284 )
| ( ( plus_plus_nat @ SY895 @ ( minus_minus_nat @ SV284 @ SV116 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ SY895 @ SV284 ) @ SV116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(1074,plain,
! [SV285: nat,SV117: nat > $o] :
( ( ! [SY896: nat] :
( ( SV117 @ ( minus_minus_nat @ SV285 @ SY896 ) )
= ( ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SY896 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY897: nat] :
( ( SV285
!= ( plus_plus_nat @ SY896 @ SY897 ) )
| ( SV117 @ SY897 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[877]) ).
thf(1075,plain,
! [SV286: nat,SV118: nat] :
( ( ! [SY898: nat] :
( ~ ( ord_less_nat @ SV118 @ SV286 )
| ~ ( ord_less_nat @ SV118 @ SY898 )
| ( ord_less_nat @ ( minus_minus_nat @ SY898 @ SV286 ) @ ( minus_minus_nat @ SY898 @ SV118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[878]) ).
thf(1076,plain,
! [SV287: nat,SV119: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ SV119 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV287 )
| ( ord_less_nat @ ( minus_minus_nat @ SV287 @ SV119 ) @ SV287 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(1077,plain,
! [SV288: nat] :
( ( ( ord_less_eq_nat @ SV288 )
= ( ^ [SY899: nat] :
~ ! [SY900: nat] :
( SY899
!= ( plus_plus_nat @ SV288 @ SY900 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(1078,plain,
! [SV289: nat] :
( ( ( ord_less_eq_nat @ SV289 )
= ( ^ [SY901: nat] :
~ ! [SY902: nat] :
( SY901
!= ( plus_plus_nat @ SV289 @ SY902 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(1079,plain,
! [SV290: nat,SV122: nat] :
( ( ! [SY903: nat] :
( ~ ( ord_less_eq_nat @ SV122 @ SV290 )
| ( ( ( minus_minus_nat @ SV290 @ SV122 )
= SY903 )
= ( SV290
= ( plus_plus_nat @ SY903 @ SV122 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(1080,plain,
! [SV291: nat,SV123: nat] :
( ( ! [SY904: nat,SY905: nat,SY906: nat] :
( ~ ( ord_less_eq_nat @ SV123 @ SV291 )
| ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ SV291 @ SY904 ) @ SY905 ) @ ( plus_plus_nat @ ( times_times_nat @ SV123 @ SY904 ) @ SY906 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV291 @ SV123 ) @ SY904 ) @ SY905 ) @ SY906 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(1081,plain,
! [SV292: nat,SV124: nat] :
( ( ! [SY907: nat] :
( ~ ( ord_less_eq_nat @ SV124 @ SV292 )
| ( ord_less_eq_nat @ SY907 @ ( minus_minus_nat @ ( plus_plus_nat @ SV292 @ SY907 ) @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(1082,plain,
! [SV293: nat,SV125: nat] :
( ( ! [SY908: nat] :
( ~ ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SV293 ) @ ( plus_plus_nat @ SY908 @ SV293 ) )
| ( ord_less_nat @ SV125 @ SY908 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(1083,plain,
! [SV294: nat,SV126: nat] :
( ( ( ( plus_plus_nat @ SV126 @ SV294 )
= zero_zero_nat )
= ( ~ ( ( SV126 != zero_zero_nat )
| ( SV294 != zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(1084,plain,
! [SV295: nat,SV127: nat] :
( ( ! [SY909: nat,SY910: nat,SY911: nat] :
( ~ ( ord_less_eq_nat @ SV127 @ SV295 )
| ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV127 @ SY909 ) @ SY910 ) @ ( plus_plus_nat @ ( times_times_nat @ SV295 @ SY909 ) @ SY911 ) )
= ( ord_less_nat @ SY910 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV295 @ SV127 ) @ SY909 ) @ SY911 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1085,plain,
! [SV296: nat,SV128: nat] :
( ( ! [SY912: nat] :
( ~ ( ord_less_nat @ SV128 @ SV296 )
| ( ord_less_nat @ ( minus_minus_nat @ SV128 @ SY912 ) @ SV296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(1086,plain,
! [SV297: nat,SV129: nat] :
( ( ! [SY913: nat] :
( ~ ( ord_less_eq_nat @ SV129 @ SV297 )
| ( ord_less_eq_nat @ ( minus_minus_nat @ SY913 @ SV297 ) @ ( minus_minus_nat @ SY913 @ SV129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1087,plain,
! [SV298: nat,SV130: nat] :
( ( ! [SY914: nat] :
( ~ ( ord_less_eq_nat @ SV130 @ SV298 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV130 @ SY914 ) @ ( plus_plus_nat @ SV298 @ SY914 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(1088,plain,
! [SV299: nat,SV131: nat] :
( ( ~ ( ord_less_nat @ SV131 @ SV299 )
| ( SV299 != SV131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1089,plain,
! [SV300: nat,SV132: nat] :
( ( ! [SY915: nat,SY916: nat] :
( ~ ( ord_less_nat @ SV132 @ SV300 )
| ( ( plus_plus_nat @ SY915 @ SV300 )
!= ( plus_plus_nat @ SV132 @ SY916 ) )
| ( ord_less_nat @ SY915 @ SY916 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1090,plain,
! [SV301: nat,SV133: nat] :
( ( ! [SY917: nat] :
( ~ ( ord_less_eq_nat @ SV133 @ SV301 )
| ( ord_less_eq_nat @ SV133 @ ( plus_plus_nat @ SY917 @ SV301 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(1091,plain,
! [SV134: nat] :
( ( ~ ( ( ord_less_nat @ zero_zero_nat @ SV134 )
| ( SV134 != zero_zero_nat ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV134 )
| ~ ( ( SV134 != zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[896]) ).
thf(1092,plain,
! [SV134: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV134 )
= ( SV134 != zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[896]) ).
thf(1093,plain,
! [SV302: nat,SV135: nat] :
( ( ! [SY918: nat] :
( ~ ( ord_less_eq_nat @ SV135 @ SV302 )
| ( ( minus_minus_nat @ SY918 @ ( minus_minus_nat @ SV302 @ SV135 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ SY918 @ SV135 ) @ SV302 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1094,plain,
! [SV303: nat,SV136: nat] :
( ( ! [SY919: nat] :
( ~ ( ord_less_eq_nat @ SV136 @ SV303 )
| ( ( minus_minus_nat @ ( plus_plus_nat @ SY919 @ SV303 ) @ SV136 )
= ( plus_plus_nat @ SY919 @ ( minus_minus_nat @ SV303 @ SV136 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1095,plain,
! [SV304: nat,SV137: nat] :
( ( ! [SY920: nat,SY921: nat] :
( ~ ( ord_less_eq_nat @ SV137 @ SV304 )
| ~ ( ord_less_eq_nat @ SY920 @ SY921 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV137 @ SY920 ) @ ( plus_plus_nat @ SV304 @ SY921 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(1096,plain,
! [SV305: nat,SV138: nat] :
( ( ! [SY922: nat] :
( ~ ( ord_less_eq_nat @ SV138 @ SV305 )
| ( ( minus_minus_nat @ ( plus_plus_nat @ SV305 @ SY922 ) @ SV138 )
= ( plus_plus_nat @ ( minus_minus_nat @ SV305 @ SV138 ) @ SY922 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(1097,plain,
! [SV306: nat,SV139: nat] :
( ( ! [SY923: nat] :
( ~ ( ord_less_nat @ ( plus_plus_nat @ SV139 @ SV306 ) @ ( plus_plus_nat @ SV139 @ SY923 ) )
| ( ord_less_nat @ SV306 @ SY923 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(1098,plain,
! [SV307: nat,SV140: nat] :
( ( ! [SY924: nat] :
( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV140 @ SV307 ) @ ( plus_plus_nat @ SY924 @ SV307 ) )
| ( ord_less_eq_nat @ SV140 @ SY924 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(1099,plain,
! [SV308: nat,SV141: nat] :
( ( ! [SY925: nat] :
( ~ ( ord_less_eq_nat @ SV141 @ SV308 )
| ( ( plus_plus_nat @ ( minus_minus_nat @ SV308 @ SV141 ) @ SY925 )
= ( minus_minus_nat @ ( plus_plus_nat @ SV308 @ SY925 ) @ SV141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1100,plain,
! [SV309: nat,SV142: nat > $o] :
( ( ~ ! [SY712: nat] :
( ~ ~ ( SV142 @ SY712 )
| ~ ! [SY713: nat] :
~ ~ ( ~ ( ord_less_nat @ SY713 @ SY712 )
| ~ ~ ( SV142 @ SY713 ) ) )
| ( SV142 @ SV309 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(1101,plain,
! [SV310: nat,SV143: nat] :
( ( ! [SY928: nat] :
( ( ( plus_plus_nat @ SV143 @ SV310 )
!= ( plus_plus_nat @ SY928 @ SV310 ) )
| ( SV143 = SY928 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(1102,plain,
! [SV311: nat,SV144: nat] :
( ( ! [SY929: nat] :
( ~ ( ord_less_nat @ SV144 @ SV311 )
| ( ord_less_nat @ SV144 @ ( plus_plus_nat @ SV311 @ SY929 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(1103,plain,
! [SV312: nat,SV145: nat] :
( ( ( SV145 != SV312 )
| ( ord_less_eq_nat @ SV145 @ SV312 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(1104,plain,
! [SV313: nat,SV146: nat] :
( ( ! [SY930: nat,SY931: nat,SY932: nat] :
( ~ ( ord_less_eq_nat @ SV146 @ SV313 )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV146 @ SY930 ) @ SY931 ) @ ( plus_plus_nat @ ( times_times_nat @ SV313 @ SY930 ) @ SY932 ) )
= ( ord_less_eq_nat @ SY931 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV313 @ SV146 ) @ SY930 ) @ SY932 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1105,plain,
! [SV314: nat,SV147: nat] :
( ( ! [SY933: nat] :
( ~ ( ord_less_eq_nat @ SV147 @ SV314 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV147 @ SY933 ) @ ( plus_plus_nat @ SV314 @ SY933 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1106,plain,
! [SV315: nat,SV148: nat] :
( ( ! [SY934: nat,SY935: nat] :
( ~ ~ ( ~ ( ord_less_nat @ SV148 @ SV315 )
| ( SY934 != SY935 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV148 @ SY934 ) @ ( plus_plus_nat @ SV315 @ SY935 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1107,plain,
! [SV316: nat,SV149: nat] :
( ( ~ ( ord_less_nat @ SV149 @ SV316 )
| ( ord_less_eq_nat @ SV149 @ SV316 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[912]) ).
thf(1108,plain,
! [SV317: nat,SV150: nat] :
( ( ! [SY936: nat,SY937: nat] :
( ~ ( ord_less_nat @ SV150 @ SV317 )
| ~ ( ord_less_nat @ SY936 @ SY937 )
| ( ord_less_nat @ ( plus_plus_nat @ SV150 @ SY936 ) @ ( plus_plus_nat @ SV317 @ SY937 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1109,plain,
! [SV151: nat] :
( ( ( ~ ( ( SV151 != zero_zero_nat ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV151 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[914]) ).
thf(1110,plain,
! [SV318: nat,SV152: nat] :
( ( ! [SY938: nat] :
( ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SY938 @ SV318 ) )
= ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV318 )
| ~ ( ord_less_nat @ SV152 @ SY938 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1111,plain,
! [SV319: nat,SV153: nat] :
( ( ~ ~ ( ord_less_nat @ SV153 @ SV319 )
| ( ( plus_plus_nat @ SV319 @ ( minus_minus_nat @ SV153 @ SV319 ) )
= SV153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1112,plain,
! [SV320: nat,SV154: nat] :
( ( ~ ( ord_less_nat @ SV154 @ SV320 )
| ( SV320 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1113,plain,
! [SV321: nat,SV155: nat] :
( ( ( SV155 != SV321 )
= ( ( ord_less_nat @ SV155 @ SV321 )
| ( ord_less_nat @ SV321 @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1114,plain,
! [SV322: nat,SV156: nat] :
( ( ~ ( ord_less_nat @ SV156 @ SV322 )
| ( SV322 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1115,plain,
! [SV323: nat,SV157: nat] :
( ( ! [SY939: nat] :
( ~ ( ord_less_eq_nat @ SV157 @ SV323 )
| ( ( plus_plus_nat @ SY939 @ ( minus_minus_nat @ SV323 @ SV157 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ SY939 @ SV323 ) @ SV157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1116,plain,
! [SV324: nat,SV158: nat] :
( ( ! [SY940: nat] :
( ~ ( ord_less_eq_nat @ SV158 @ SV324 )
| ( ( plus_plus_nat @ ( minus_minus_nat @ SV324 @ SV158 ) @ SY940 )
= ( minus_minus_nat @ ( plus_plus_nat @ SV324 @ SY940 ) @ SV158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1117,plain,
! [SV325: nat,SV159: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
= ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV159 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV325 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[922]) ).
thf(1118,plain,
! [SV326: nat,SV160: nat] :
( ( ( ( plus_plus_nat @ SV160 @ SV326 )
= zero_zero_nat )
= ( ~ ( ( SV160 != zero_zero_nat )
| ( SV326 != zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1119,plain,
! [SV327: nat] :
( ( ( ord_less_nat @ SV327 )
= ( ^ [SY941: nat] :
~ ( ~ ( ord_less_eq_nat @ SV327 @ SY941 )
| ~ ( ( SV327 != SY941 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1120,plain,
! [SV328: nat,SV162: nat] :
( ( ( zero_zero_nat
= ( plus_plus_nat @ SV162 @ SV328 ) )
= ( ~ ( ( SV162 != zero_zero_nat )
| ( SV328 != zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1121,plain,
! [SV329: nat,SV163: nat] :
( ( ! [SY942: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SY942 @ SV329 ) )
= ( ~ ( ord_less_nat @ zero_zero_nat @ SV329 )
| ( ord_less_eq_nat @ SV163 @ SY942 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1122,plain,
! [SV330: nat,SV164: nat > $o] :
( ( ! [SY943: nat] :
( ~ ( SV164 @ SV330 )
| ~ ! [SY750: nat] :
( ~ ( SV164 @ SY750 )
| ( ord_less_eq_nat @ SY750 @ SY943 ) )
| ~ ! [SY751: nat] :
~ ~ ( ~ ( SV164 @ SY751 )
| ~ ! [SY752: nat] :
( ~ ( SV164 @ SY752 )
| ( ord_less_eq_nat @ SY752 @ SY751 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1123,plain,
! [SV165: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV165 @ zero_zero_nat ) )
= $true )
| ( ( SV165 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[929]) ).
thf(1124,plain,
! [SV331: nat,SV166: nat] :
( ( ! [SY947: nat] :
( ~ ( ord_less_nat @ SV166 @ SV331 )
| ( ord_less_nat @ ( plus_plus_nat @ SV166 @ SY947 ) @ ( plus_plus_nat @ SV331 @ SY947 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(1125,plain,
! [SV332: nat,SV167: nat] :
( ( ! [SY948: nat] :
( ~ ( ord_less_eq_nat @ SV167 @ SV332 )
| ~ ( ord_less_eq_nat @ SV167 @ SY948 )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV332 @ SV167 ) @ ( minus_minus_nat @ SY948 @ SV167 ) )
= ( ord_less_eq_nat @ SV332 @ SY948 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1126,plain,
! [SV333: nat,SV168: nat] :
( ( ! [SY949: nat] :
( ( ( plus_plus_nat @ SV168 @ SV333 )
!= SY949 )
| ( SV168
= ( minus_minus_nat @ SY949 @ SV333 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1127,plain,
! [SV334: nat,SV169: nat] :
( ( ! [SY950: nat] :
( ~ ( ord_less_eq_nat @ SV169 @ SV334 )
| ( ( ord_less_nat @ ( minus_minus_nat @ SV334 @ SV169 ) @ SY950 )
= ( ord_less_nat @ SV334 @ ( plus_plus_nat @ SY950 @ SV169 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1128,plain,
! [SV335: nat,SV170: nat] :
( ( ! [SY951: nat,SY952: nat] :
( ( SV170
!= ( plus_plus_nat @ SV335 @ SY951 ) )
| ( ( plus_plus_nat @ SV170 @ SY952 )
= ( plus_plus_nat @ SV335 @ ( plus_plus_nat @ SY951 @ SY952 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1129,plain,
! [SV336: nat,SV171: nat] :
( ( ! [SY953: nat] :
( ~ ( ord_less_eq_nat @ SV171 @ SV336 )
| ~ ( ord_less_eq_nat @ SV171 @ SY953 )
| ( ( minus_minus_nat @ ( minus_minus_nat @ SV336 @ SV171 ) @ ( minus_minus_nat @ SY953 @ SV171 ) )
= ( minus_minus_nat @ SV336 @ SY953 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1130,plain,
! [SV337: nat,SV172: nat] :
( ( ! [SY954: nat] :
( ~ ( ord_less_eq_nat @ SV172 @ SV337 )
| ( ord_less_eq_nat @ SV172 @ ( plus_plus_nat @ SV337 @ SY954 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1131,plain,
! [SV173: nat] :
( ( ( ~ ( ( SV173 != zero_zero_nat ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV173 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[937]) ).
thf(1132,plain,
! [SV338: nat,SV174: nat] :
( ( ! [SY955: nat,SY956: nat,SY957: nat] :
( ~ ( ord_less_eq_nat @ SV174 @ SV338 )
| ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV338 @ SY955 ) @ SY956 ) @ ( plus_plus_nat @ ( times_times_nat @ SV174 @ SY955 ) @ SY957 ) )
= ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV338 @ SV174 ) @ SY955 ) @ SY956 ) @ SY957 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1133,plain,
! [SV339: nat,SV175: nat] :
( ( ! [SY958: nat,SY959: nat] :
( ( SV175
!= ( plus_plus_nat @ SV339 @ SY958 ) )
| ( ( plus_plus_nat @ SY959 @ SV175 )
= ( plus_plus_nat @ SV339 @ ( plus_plus_nat @ SY959 @ SY958 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1134,plain,
! [SV340: nat,SV176: nat] :
( ( ~ ( ord_less_eq_nat @ SV176 @ SV340 )
| ( ( plus_plus_nat @ SV176 @ ( minus_minus_nat @ SV340 @ SV176 ) )
= SV340 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1135,plain,
! [SV341: nat,SV177: nat] :
( ( ! [SY960: nat] :
( ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SY960 ) )
= ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 )
| ~ ( ord_less_nat @ SV341 @ SY960 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1136,plain,
! [SV342: nat,SV178: nat] :
( ( ~ ( ( SV178 != SV342 ) )
| ~ ~ ( ord_less_nat @ SV178 @ SV342 )
| ( ord_less_nat @ SV342 @ SV178 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1137,plain,
! [SV343: nat,SV179: nat] :
( ( ! [SY961: nat] :
( ~ ( ord_less_eq_nat @ SV179 @ SV343 )
| ( ord_less_eq_nat @ ( minus_minus_nat @ SV179 @ SY961 ) @ ( minus_minus_nat @ SV343 @ SY961 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1138,plain,
! [SV344: nat,SV180: nat] :
( ( ~ ( ord_less_eq_nat @ SV180 @ SV344 )
| ( ( minus_minus_nat @ SV180 @ SV344 )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1139,plain,
! [SV345: nat,SV181: nat > $o] :
( ( ~ ! [SY783: nat] :
( ~ ! [SY784: nat] :
( ~ ( ord_less_nat @ SY784 @ SY783 )
| ( SV181 @ SY784 ) )
| ( SV181 @ SY783 ) )
| ( SV181 @ SV345 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1140,plain,
! [SV346: nat,SV182: nat] :
( ( ! [SY964: nat] :
( ~ ( ord_less_eq_nat @ SV182 @ SV346 )
| ~ ( ord_less_eq_nat @ SV182 @ SV346 )
| ( ( ( minus_minus_nat @ SV346 @ SV182 )
= SY964 )
= ( SV346
= ( plus_plus_nat @ SY964 @ SV182 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1141,plain,
! [SV347: nat,SV183: nat] :
( ( ! [SY965: nat] :
( ~ ( ord_less_eq_nat @ SV183 @ SV347 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SY965 @ SV183 ) @ ( plus_plus_nat @ SY965 @ SV347 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1142,plain,
! [SV348: nat,SV184: nat] :
( ( ! [SY966: nat] :
( ~ ( ord_less_eq_nat @ SV184 @ SV348 )
| ~ ( ord_less_eq_nat @ SV184 @ SY966 )
| ( ( ord_less_nat @ ( minus_minus_nat @ SV348 @ SV184 ) @ ( minus_minus_nat @ SY966 @ SV184 ) )
= ( ord_less_nat @ SV348 @ SY966 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1143,plain,
! [SV349: nat,SV185: nat] :
( ( ! [SY967: nat] :
( ~ ( ord_less_eq_nat @ SV185 @ SV349 )
| ( ( ord_less_eq_nat @ SY967 @ ( minus_minus_nat @ SV349 @ SV185 ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ SY967 @ SV185 ) @ SV349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1144,plain,
! [SV350: nat,SV186: nat > $o] :
( ( ! [SY968: nat] :
( ( SV186 @ ( minus_minus_nat @ SV350 @ SY968 ) )
= ( ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SY968 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY969: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SY968 @ SY969 ) )
| ~ ~ ( SV186 @ SY969 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1145,plain,
! [SV351: nat,SV187: nat] :
( ( ! [SY970: nat] :
( ( ( plus_plus_nat @ SV187 @ SV351 )
!= ( plus_plus_nat @ SV187 @ SY970 ) )
| ( SV351 = SY970 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1146,plain,
! [SV352: nat,SV188: nat] :
( ( ! [SY971: nat] :
( ~ ( ord_less_nat @ SV188 @ SV352 )
| ~ ( ord_less_eq_nat @ SY971 @ SV188 )
| ( ord_less_nat @ ( minus_minus_nat @ SV188 @ SY971 ) @ ( minus_minus_nat @ SV352 @ SY971 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1147,plain,
! [SV353: nat,SV189: nat] :
( ( ~ ( ord_less_eq_nat @ SV189 @ SV353 )
| ~ ( ord_less_eq_nat @ SV353 @ SV189 )
| ( SV189 = SV353 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1148,plain,
! [SV354: nat,SV190: nat] :
( ( ! [SY972: nat,SY973: nat,SY974: nat] :
( ~ ( ord_less_eq_nat @ SV190 @ SV354 )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SV354 @ SY972 ) @ SY973 )
= ( plus_plus_nat @ ( times_times_nat @ SV190 @ SY972 ) @ SY974 ) )
= ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV354 @ SV190 ) @ SY972 ) @ SY973 )
= SY974 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1149,plain,
! [SV355: nat,SV191: nat] :
( ( ~ ( ord_less_eq_nat @ SV191 @ SV355 )
| ~ ! [SY975: nat] :
( SV355
!= ( plus_plus_nat @ SV191 @ SY975 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1150,plain,
! [SV356: nat,SV192: nat] :
( ( ! [SY976: nat,SY977: nat] :
( ~ ~ ( ( SV192 != SV356 )
| ~ ( ord_less_nat @ SY976 @ SY977 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV192 @ SY976 ) @ ( plus_plus_nat @ SV356 @ SY977 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1151,plain,
! [SV357: nat,SV193: nat] :
( ( ! [SY978: nat,SY979: nat] :
( ~ ~ ( ~ ( ord_less_eq_nat @ SV193 @ SV357 )
| ( SY978 != SY979 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV193 @ SY978 ) @ ( plus_plus_nat @ SV357 @ SY979 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1152,plain,
! [SV358: nat,SV194: nat] :
( ( ! [SY980: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SY980 ) )
= ( ~ ( ord_less_nat @ zero_zero_nat @ SV194 )
| ( ord_less_eq_nat @ SV358 @ SY980 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1153,plain,
! [SV359: nat,SV195: nat] :
( ( ! [SY981: nat] :
( ~ ( ord_less_eq_nat @ SV195 @ SV359 )
| ~ ( ord_less_eq_nat @ SV359 @ SY981 )
| ( ord_less_eq_nat @ SV195 @ SY981 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1154,plain,
! [SV360: nat,SV196: nat] :
( ( ! [SY982: nat,SY983: nat] :
( ~ ~ ( ( SV196 != SV360 )
| ( SY982 != SY983 ) )
| ( ( plus_plus_nat @ SV196 @ SY982 )
= ( plus_plus_nat @ SV360 @ SY983 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1155,plain,
! [SV361: nat,SV197: nat] :
( ( ! [SY984: nat,SY985: nat,SY986: nat] :
( ~ ( ord_less_eq_nat @ SV197 @ SV361 )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SV197 @ SY984 ) @ SY985 )
= ( plus_plus_nat @ ( times_times_nat @ SV361 @ SY984 ) @ SY986 ) )
= ( SY985
= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV361 @ SV197 ) @ SY984 ) @ SY986 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1156,plain,
! [SV362: nat,SV198: nat] :
( ( ! [SY987: nat,SY988: nat] :
( ~ ( ord_less_eq_nat @ SV198 @ SV362 )
| ~ ( ord_less_eq_nat @ SY987 @ SY988 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV198 @ SY987 ) @ ( plus_plus_nat @ SV362 @ SY988 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1157,plain,
! [SV363: nat,SV199: nat] :
( ( ! [SY989: nat] :
( ~ ( ord_less_nat @ SV199 @ SV363 )
| ( ord_less_nat @ SV199 @ ( plus_plus_nat @ SY989 @ SV363 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(1158,plain,
! [SV364: nat,SV200: nat] :
( ( ~ ( ( ord_less_nat @ SV200 @ SV364 )
| ( SV200 = SV364 ) )
| ( ord_less_eq_nat @ SV200 @ SV364 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1159,plain,
! [SV365: nat,SV201: nat > nat] :
( ( ! [SY990: nat] :
( ~ ( number1551313001itions @ SV201 @ SV365 )
| ( ord_less_eq_nat @ ( SV201 @ SY990 ) @ SV365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1160,plain,
! [SV366: nat,SV202: nat] :
( ( ~ ( ord_less_eq_nat @ SV202 @ SV366 )
| ( ( minus_minus_nat @ SV366 @ ( minus_minus_nat @ SV366 @ SV202 ) )
= SV202 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1161,plain,
! [SV367: nat,SV203: nat] :
( ( ! [SY991: nat] :
( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV203 @ SV367 ) @ ( plus_plus_nat @ SV203 @ SY991 ) )
| ( ord_less_eq_nat @ SV367 @ SY991 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1162,plain,
! [SV1: nat > nat] :
( ( ( ~ ( ( number1551313001itions @ SV1 @ zero_zero_nat )
| ( SV1
= ( ^ [I: nat] : zero_zero_nat ) ) ) )
= $true )
| ( ( ~ ( ~ ( number1551313001itions @ SV1 @ zero_zero_nat )
| ( SV1
!= ( ^ [I: nat] : zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[968]) ).
thf(1163,plain,
! [SV204: nat,SV2: nat] :
( ( ~ ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SV204 ) )
| ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( ord_less_nat @ zero_zero_nat @ SV204 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SV204 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( ord_less_nat @ zero_zero_nat @ SV204 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[970]) ).
thf(1164,plain,
! [SV204: nat,SV2: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SV204 ) )
= ( ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( ord_less_nat @ zero_zero_nat @ SV204 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[970]) ).
thf(1165,plain,
! [SV205: nat,SV3: nat] :
( ( ~ ( ( ord_less_nat @ ( plus_plus_nat @ SV3 @ SV205 ) @ SV3 )
| ( ord_less_nat @ SV205 @ zero_zero_nat ) )
| ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV3 @ SV205 ) @ SV3 )
| ~ ( ord_less_nat @ SV205 @ zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[971]) ).
thf(1166,plain,
! [SV205: nat,SV3: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV3 @ SV205 ) @ SV3 )
= ( ord_less_nat @ SV205 @ zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[971]) ).
thf(1167,plain,
! [SV206: nat,SV4: nat] :
( ( ~ ( ( ord_less_nat @ ( plus_plus_nat @ SV4 @ SV206 ) @ SV206 )
| ( ord_less_nat @ SV4 @ zero_zero_nat ) )
| ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV4 @ SV206 ) @ SV206 )
| ~ ( ord_less_nat @ SV4 @ zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[972]) ).
thf(1168,plain,
! [SV206: nat,SV4: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV4 @ SV206 ) @ SV206 )
= ( ord_less_nat @ SV4 @ zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[972]) ).
thf(1169,plain,
! [SV207: nat,SV5: nat] :
( ( ~ ( ( ord_less_nat @ SV5 @ ( plus_plus_nat @ SV5 @ SV207 ) )
| ( ord_less_nat @ zero_zero_nat @ SV207 ) )
| ~ ( ~ ( ord_less_nat @ SV5 @ ( plus_plus_nat @ SV5 @ SV207 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV207 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[973]) ).
thf(1170,plain,
! [SV207: nat,SV5: nat] :
( ( ( ord_less_nat @ SV5 @ ( plus_plus_nat @ SV5 @ SV207 ) )
= ( ord_less_nat @ zero_zero_nat @ SV207 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[973]) ).
thf(1171,plain,
! [SV208: nat,SV6: nat] :
( ( ~ ( ( ord_less_nat @ SV6 @ ( plus_plus_nat @ SV208 @ SV6 ) )
| ( ord_less_nat @ zero_zero_nat @ SV208 ) )
| ~ ( ~ ( ord_less_nat @ SV6 @ ( plus_plus_nat @ SV208 @ SV6 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV208 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[974]) ).
thf(1172,plain,
! [SV208: nat,SV6: nat] :
( ( ( ord_less_nat @ SV6 @ ( plus_plus_nat @ SV208 @ SV6 ) )
= ( ord_less_nat @ zero_zero_nat @ SV208 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[974]) ).
thf(1173,plain,
! [SV368: nat,SV209: nat,SV7: nat] :
( ( ( ( plus_plus_nat @ SV7 @ SV209 )
= ( plus_plus_nat @ SV368 @ SV209 ) )
= ( SV7 = SV368 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1174,plain,
! [SV369: nat,SV210: nat,SV8: nat] :
( ( ( ( plus_plus_nat @ SV8 @ SV210 )
= ( plus_plus_nat @ SV8 @ SV369 ) )
= ( SV210 = SV369 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1175,plain,
! [SV9: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV9 @ zero_zero_nat )
| ( SV9 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV9 @ zero_zero_nat )
| ( SV9 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[977]) ).
thf(1176,plain,
! [SV10: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV10 )
| ( SV10 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV10 )
| ( SV10 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[979]) ).
thf(1177,plain,
! [SV370: nat,SV211: nat,SV11: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV11 @ SV211 ) @ ( plus_plus_nat @ SV370 @ SV211 ) )
= ( ord_less_eq_nat @ SV11 @ SV370 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1178,plain,
! [SV371: nat,SV212: nat,SV12: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV212 ) @ ( plus_plus_nat @ SV12 @ SV371 ) )
= ( ord_less_eq_nat @ SV212 @ SV371 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1179,plain,
! [SV213: nat,SV13: nat] :
( ( ~ ( ( SV13
= ( plus_plus_nat @ SV13 @ SV213 ) )
| ( SV213 = zero_zero_nat ) )
| ~ ( ( SV13
!= ( plus_plus_nat @ SV13 @ SV213 ) )
| ( SV213 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[983]) ).
thf(1180,plain,
! [SV213: nat,SV13: nat] :
( ( ( SV13
= ( plus_plus_nat @ SV13 @ SV213 ) )
= ( SV213 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[983]) ).
thf(1181,plain,
! [SV214: nat,SV14: nat] :
( ( ~ ( ( SV14
= ( plus_plus_nat @ SV214 @ SV14 ) )
| ( SV214 = zero_zero_nat ) )
| ~ ( ( SV14
!= ( plus_plus_nat @ SV214 @ SV14 ) )
| ( SV214 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[984]) ).
thf(1182,plain,
! [SV214: nat,SV14: nat] :
( ( ( SV14
= ( plus_plus_nat @ SV214 @ SV14 ) )
= ( SV214 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[984]) ).
thf(1183,plain,
! [SV215: nat,SV15: nat] :
( ( ~ ( ( ( plus_plus_nat @ SV15 @ SV215 )
= SV15 )
| ( SV215 = zero_zero_nat ) )
| ~ ( ( ( plus_plus_nat @ SV15 @ SV215 )
!= SV15 )
| ( SV215 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[985]) ).
thf(1184,plain,
! [SV215: nat,SV15: nat] :
( ( ( ( plus_plus_nat @ SV15 @ SV215 )
= SV15 )
= ( SV215 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[985]) ).
thf(1185,plain,
! [SV216: nat,SV16: nat] :
( ( ~ ( ( ( plus_plus_nat @ SV16 @ SV216 )
= SV216 )
| ( SV16 = zero_zero_nat ) )
| ~ ( ( ( plus_plus_nat @ SV16 @ SV216 )
!= SV216 )
| ( SV16 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[986]) ).
thf(1186,plain,
! [SV216: nat,SV16: nat] :
( ( ( ( plus_plus_nat @ SV16 @ SV216 )
= SV216 )
= ( SV16 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[986]) ).
thf(1187,plain,
! [SV372: nat,SV217: nat,SV22: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV22 @ SV217 ) @ ( plus_plus_nat @ SV372 @ SV217 ) )
= ( ord_less_nat @ SV22 @ SV372 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1188,plain,
! [SV373: nat,SV218: nat,SV23: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV23 @ SV218 ) @ ( plus_plus_nat @ SV23 @ SV373 ) )
= ( ord_less_nat @ SV218 @ SV373 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1189,plain,
! [SV374: nat,SV220: nat,SV25: nat] :
( ( ( minus_minus_nat @ ( plus_plus_nat @ SV25 @ SV220 ) @ ( plus_plus_nat @ SV374 @ SV220 ) )
= ( minus_minus_nat @ SV25 @ SV374 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1190,plain,
! [SV375: nat,SV222: nat,SV27: nat] :
( ( ( minus_minus_nat @ ( plus_plus_nat @ SV27 @ SV222 ) @ ( plus_plus_nat @ SV27 @ SV375 ) )
= ( minus_minus_nat @ SV222 @ SV375 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1191,plain,
! [SV376: nat,SV223: nat,SV32: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV32 @ SV223 ) @ ( plus_plus_nat @ SV32 @ SV376 ) )
= ( ord_less_nat @ SV223 @ SV376 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1192,plain,
! [SV377: nat,SV224: nat,SV35: nat] :
( ( ( ( times_times_nat @ SV35 @ SV224 )
= ( times_times_nat @ SV377 @ SV224 ) )
= ( ( SV35 = SV377 )
| ( SV224 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1193,plain,
! [SV378: nat,SV225: nat,SV36: nat] :
( ( ( ( times_times_nat @ SV36 @ SV225 )
= ( times_times_nat @ SV36 @ SV378 ) )
= ( ( SV225 = SV378 )
| ( SV36 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1194,plain,
! [SV226: nat,SV38: nat] :
( ( ~ ( ( ( times_times_nat @ SV38 @ SV226 )
= zero_zero_nat )
| ( SV38 = zero_zero_nat )
| ( SV226 = zero_zero_nat ) )
| ~ ( ( ( times_times_nat @ SV38 @ SV226 )
!= zero_zero_nat )
| ~ ( ( SV38 = zero_zero_nat )
| ( SV226 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[997]) ).
thf(1195,plain,
! [SV226: nat,SV38: nat] :
( ( ( ( times_times_nat @ SV38 @ SV226 )
= zero_zero_nat )
= ( ( SV38 = zero_zero_nat )
| ( SV226 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[997]) ).
thf(1196,plain,
! [SV379: nat,SV227: nat,SV39: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV39 @ SV227 ) @ ( plus_plus_nat @ SV39 @ SV379 ) )
= ( ord_less_eq_nat @ SV227 @ SV379 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1197,plain,
! [SV380: nat,SV228: nat,SV40: nat] :
( ( ( minus_minus_nat @ ( minus_minus_nat @ SV40 @ SV228 ) @ SV380 )
= ( minus_minus_nat @ SV40 @ ( plus_plus_nat @ SV228 @ SV380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1198,plain,
! [SV229: nat,SV41: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV41 @ ( plus_plus_nat @ SV229 @ SV41 ) )
| ( ord_less_eq_nat @ zero_zero_nat @ SV229 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV41 @ ( plus_plus_nat @ SV229 @ SV41 ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV229 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1000]) ).
thf(1199,plain,
! [SV229: nat,SV41: nat] :
( ( ( ord_less_eq_nat @ SV41 @ ( plus_plus_nat @ SV229 @ SV41 ) )
= ( ord_less_eq_nat @ zero_zero_nat @ SV229 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1000]) ).
thf(1200,plain,
! [SV230: nat,SV42: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV42 @ ( plus_plus_nat @ SV42 @ SV230 ) )
| ( ord_less_eq_nat @ zero_zero_nat @ SV230 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV42 @ ( plus_plus_nat @ SV42 @ SV230 ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV230 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1001]) ).
thf(1201,plain,
! [SV230: nat,SV42: nat] :
( ( ( ord_less_eq_nat @ SV42 @ ( plus_plus_nat @ SV42 @ SV230 ) )
= ( ord_less_eq_nat @ zero_zero_nat @ SV230 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1001]) ).
thf(1202,plain,
! [SV231: nat,SV43: nat] :
( ( ~ ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV43 @ SV231 ) @ SV231 )
| ( ord_less_eq_nat @ SV43 @ zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV43 @ SV231 ) @ SV231 )
| ~ ( ord_less_eq_nat @ SV43 @ zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1002]) ).
thf(1203,plain,
! [SV231: nat,SV43: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV43 @ SV231 ) @ SV231 )
= ( ord_less_eq_nat @ SV43 @ zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1002]) ).
thf(1204,plain,
! [SV232: nat,SV44: nat] :
( ( ~ ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV44 @ SV232 ) @ SV44 )
| ( ord_less_eq_nat @ SV232 @ zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV44 @ SV232 ) @ SV44 )
| ~ ( ord_less_eq_nat @ SV232 @ zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1003]) ).
thf(1205,plain,
! [SV232: nat,SV44: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV44 @ SV232 ) @ SV44 )
= ( ord_less_eq_nat @ SV232 @ zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1003]) ).
thf(1206,plain,
! [SV234: nat,SV46: nat] :
( ( ~ ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV46 @ SV234 ) )
| ( ord_less_nat @ SV234 @ SV46 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV46 @ SV234 ) )
| ~ ( ord_less_nat @ SV234 @ SV46 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1005]) ).
thf(1207,plain,
! [SV234: nat,SV46: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV46 @ SV234 ) )
= ( ord_less_nat @ SV234 @ SV46 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1005]) ).
thf(1208,plain,
! [SV235: nat,SV47: nat] :
( ( ~ ( ( ( minus_minus_nat @ SV47 @ SV235 )
= zero_zero_nat )
| ( ord_less_eq_nat @ SV47 @ SV235 ) )
| ~ ( ( ( minus_minus_nat @ SV47 @ SV235 )
!= zero_zero_nat )
| ~ ( ord_less_eq_nat @ SV47 @ SV235 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1006]) ).
thf(1209,plain,
! [SV235: nat,SV47: nat] :
( ( ( ( minus_minus_nat @ SV47 @ SV235 )
= zero_zero_nat )
= ( ord_less_eq_nat @ SV47 @ SV235 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1006]) ).
thf(1210,plain,
! [SV381: nat,SV236: nat,SV48: nat] :
( ( ( minus_minus_nat @ ( minus_minus_nat @ SV48 @ SV236 ) @ SV381 )
= ( minus_minus_nat @ ( minus_minus_nat @ SV48 @ SV381 ) @ SV236 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1211,plain,
! [SV382: nat,SV237: nat,SV49: nat] :
( ( ( minus_minus_nat @ ( minus_minus_nat @ SV49 @ SV237 ) @ SV382 )
= ( minus_minus_nat @ ( minus_minus_nat @ SV49 @ SV382 ) @ SV237 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1212,plain,
! [SV383: nat,SV238: nat,SV50: nat] :
( ( ( minus_minus_nat @ ( minus_minus_nat @ SV50 @ SV238 ) @ SV383 )
= ( minus_minus_nat @ SV50 @ ( plus_plus_nat @ SV238 @ SV383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1213,plain,
! [SV384: nat,SV242: nat,SV55: nat] :
( ( ( minus_minus_nat @ ( plus_plus_nat @ SV55 @ SV242 ) @ ( plus_plus_nat @ SV384 @ SV242 ) )
= ( minus_minus_nat @ SV55 @ SV384 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1214,plain,
! [SV385: nat,SV243: nat,SV56: nat] :
( ( ( minus_minus_nat @ ( plus_plus_nat @ SV56 @ SV243 ) @ ( plus_plus_nat @ SV56 @ SV385 ) )
= ( minus_minus_nat @ SV243 @ SV385 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1215,plain,
! [SV386: nat,SV244: nat,SV57: nat] :
( ( ( times_times_nat @ SV57 @ ( minus_minus_nat @ SV244 @ SV386 ) )
= ( minus_minus_nat @ ( times_times_nat @ SV57 @ SV244 ) @ ( times_times_nat @ SV57 @ SV386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1216,plain,
! [SV387: nat,SV245: nat,SV58: nat] :
( ( ( times_times_nat @ ( minus_minus_nat @ SV58 @ SV245 ) @ SV387 )
= ( minus_minus_nat @ ( times_times_nat @ SV58 @ SV387 ) @ ( times_times_nat @ SV245 @ SV387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1217,plain,
! [SV388: nat,SV247: nat,SV60: nat] :
( ( ( ord_less_nat @ SV60 @ ( minus_minus_nat @ SV247 @ SV388 ) )
= ( ord_less_nat @ ( plus_plus_nat @ SV60 @ SV388 ) @ SV247 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1218,plain,
! [SV389: nat,SV248: nat,SV61: nat] :
( ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV61 @ SV248 ) @ SV389 )
= ( ord_less_eq_nat @ SV61 @ ( plus_plus_nat @ SV389 @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1219,plain,
! [SV62: nat] :
( ( ( ~ ( ( zero_zero_nat = SV62 )
| ( SV62 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( zero_zero_nat != SV62 )
| ( SV62 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1020]) ).
thf(1220,plain,
! [SV390: nat,SV249: nat,SV63: nat] :
( ( ( plus_plus_nat @ SV63 @ ( plus_plus_nat @ SV249 @ SV390 ) )
= ( plus_plus_nat @ SV249 @ ( plus_plus_nat @ SV63 @ SV390 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1221,plain,
! [SV250: nat] :
( ( ! [SV391: nat] :
( ( plus_plus_nat @ SV250 @ SV391 )
= ( plus_plus_nat @ SV391 @ SV250 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1023]) ).
thf(1222,plain,
! [SV250: nat] :
( ( ( plus_plus_nat @ SV250 )
= ( ^ [SY858: nat] : ( plus_plus_nat @ SY858 @ SV250 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1023]) ).
thf(1223,plain,
! [SV392: nat,SV251: nat,SV65: nat] :
( ( ( plus_plus_nat @ ( plus_plus_nat @ SV65 @ SV251 ) @ SV392 )
= ( plus_plus_nat @ SV65 @ ( plus_plus_nat @ SV251 @ SV392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1224,plain,
! [SV393: nat,SV252: nat,SV66: nat] :
( ( ( plus_plus_nat @ ( plus_plus_nat @ SV66 @ SV252 ) @ SV393 )
= ( plus_plus_nat @ SV66 @ ( plus_plus_nat @ SV252 @ SV393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1225,plain,
! [SV394: nat,SV253: nat,SV67: nat] :
( ( ( times_times_nat @ SV67 @ ( times_times_nat @ SV253 @ SV394 ) )
= ( times_times_nat @ SV253 @ ( times_times_nat @ SV67 @ SV394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1226,plain,
! [SV254: nat] :
( ( ! [SV395: nat] :
( ( times_times_nat @ SV254 @ SV395 )
= ( times_times_nat @ SV395 @ SV254 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1027]) ).
thf(1227,plain,
! [SV254: nat] :
( ( ( times_times_nat @ SV254 )
= ( ^ [SY862: nat] : ( times_times_nat @ SY862 @ SV254 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1027]) ).
thf(1228,plain,
! [SV396: nat,SV255: nat,SV69: nat] :
( ( ( times_times_nat @ ( times_times_nat @ SV69 @ SV255 ) @ SV396 )
= ( times_times_nat @ SV69 @ ( times_times_nat @ SV255 @ SV396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1229,plain,
! [SV397: nat,SV256: nat,SV70: nat] :
( ( ( times_times_nat @ ( times_times_nat @ SV70 @ SV256 ) @ SV397 )
= ( times_times_nat @ SV70 @ ( times_times_nat @ SV256 @ SV397 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1230,plain,
! [SV257: nat,SV73: nat] :
( ( ( ord_less_eq_nat @ SV73 @ SV257 )
= $true )
| ( ( ord_less_eq_nat @ SV257 @ SV73 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1032]) ).
thf(1231,plain,
! [SV82: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV82 )
| ( SV82 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV82 )
| ( SV82 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1037]) ).
thf(1232,plain,
! [SV83: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV83 @ zero_zero_nat )
| ( SV83 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV83 @ zero_zero_nat )
| ( SV83 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1039]) ).
thf(1233,plain,
! [SV84: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV84 @ zero_zero_nat )
| ( SV84 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV84 @ zero_zero_nat )
| ( SV84 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1041]) ).
thf(1234,plain,
! [SV258: nat] :
( ( ! [SV398: nat] :
( ( ord_less_eq_nat @ SV258 @ SV398 )
= ( ( ord_less_nat @ SV258 @ SV398 )
| ( SV258 = SV398 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1043]) ).
thf(1235,plain,
! [SV258: nat] :
( ( ( ord_less_eq_nat @ SV258 )
= ( ^ [SY865: nat] :
( ( ord_less_nat @ SV258 @ SY865 )
| ( SV258 = SY865 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1043]) ).
thf(1236,plain,
! [SV259: nat,SV88: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ SV88 @ SV259 ) @ SV259 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1044]) ).
thf(1237,plain,
! [SV260: nat,SV89: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ SV89 @ SV260 ) @ SV89 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1045]) ).
thf(1238,plain,
! [SV399: nat,SV261: nat,SV90: nat] :
( ( ( ( times_times_nat @ SV90 @ SV261 )
= ( times_times_nat @ SV90 @ SV399 ) )
= ( ( SV90 = zero_zero_nat )
| ( SV261 = SV399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1239,plain,
! [SV400: nat,SV262: nat,SV92: nat > nat] :
( ( ~ ! [SY609: nat,SY610: nat] :
( ~ ( ord_less_nat @ SY609 @ SY610 )
| ( ord_less_nat @ ( SV92 @ SY609 ) @ ( SV92 @ SY610 ) ) )
| ~ ( ord_less_eq_nat @ SV262 @ SV400 )
| ( ord_less_eq_nat @ ( SV92 @ SV262 ) @ ( SV92 @ SV400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1240,plain,
! [SV263: nat,SV93: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV93 @ SV263 ) )
= $true )
| ( ( ~ ( ( SV93 != SV263 ) )
| ( ord_less_nat @ SV93 @ SV263 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1048]) ).
thf(1241,plain,
! [SV401: nat,SV264: nat,SV94: nat] :
( ( ! [SY994: nat] :
( ~ ~ ( ~ ( ord_less_eq_nat @ SV94 @ SV264 )
| ~ ( ord_less_eq_nat @ SV401 @ SY994 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV94 @ SV401 ) @ ( plus_plus_nat @ SV264 @ SY994 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1242,plain,
! [SV402: nat,SV265: nat,SV95: nat] :
( ( ~ ( ord_less_eq_nat @ SV95 @ SV265 )
| ~ ( ord_less_eq_nat @ SV402 @ SV265 )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV265 @ SV95 ) @ ( minus_minus_nat @ SV265 @ SV402 ) )
= ( ord_less_eq_nat @ SV402 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1243,plain,
! [SV403: nat,SV266: nat,SV96: nat] :
( ( ~ ( ord_less_eq_nat @ SV96 @ SV266 )
| ( ( minus_minus_nat @ SV403 @ ( minus_minus_nat @ SV266 @ SV96 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ SV403 @ SV96 ) @ SV266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1244,plain,
! [SV267: nat,SV97: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV97 @ SV267 ) )
= $true )
| ( ( ( plus_plus_nat @ ( minus_minus_nat @ SV267 @ SV97 ) @ SV97 )
= SV267 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1052]) ).
thf(1245,plain,
! [SV404: nat,SV268: nat,SV98: nat] :
( ( ! [SY995: nat] :
( ~ ~ ( ( SV98 != SV268 )
| ~ ( ord_less_eq_nat @ SV404 @ SY995 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV98 @ SV404 ) @ ( plus_plus_nat @ SV268 @ SY995 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1246,plain,
! [SV405: nat,SV269: nat,SV99: nat] :
( ( ! [SY996: nat,SY997: nat] :
( ~ ( ord_less_eq_nat @ SV99 @ SV269 )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV269 @ SV405 ) @ SY996 ) @ ( plus_plus_nat @ ( times_times_nat @ SV99 @ SV405 ) @ SY997 ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV269 @ SV99 ) @ SV405 ) @ SY996 ) @ SY997 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1247,plain,
! [SV406: nat,SV270: nat,SV100: nat] :
( ( ~ ( ord_less_eq_nat @ SV100 @ SV270 )
| ( ( minus_minus_nat @ ( plus_plus_nat @ SV406 @ SV270 ) @ SV100 )
= ( plus_plus_nat @ SV406 @ ( minus_minus_nat @ SV270 @ SV100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1248,plain,
! [SV407: nat,SV271: nat,SV101: nat] :
( ( ~ ( ord_less_nat @ SV101 @ SV271 )
| ( ord_less_nat @ ( plus_plus_nat @ SV101 @ SV407 ) @ ( plus_plus_nat @ SV271 @ SV407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1249,plain,
! [SV102: nat] :
( ( ( ~ ( ( SV102 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV102 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV102 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV102 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1057]) ).
thf(1250,plain,
! [SV272: nat,SV103: nat] :
( ( ( ~ ( ord_less_nat @ SV103 @ SV272 ) )
= $true )
| ( ( SV103 != SV272 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1059]) ).
thf(1251,plain,
! [SV273: nat,SV104: nat] :
( ( ( ( plus_plus_nat @ SV104 @ SV273 )
!= SV104 )
= $true )
| ( ( SV273 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1060]) ).
thf(1252,plain,
! [SV408: nat,SV274: nat,SV105: nat] :
( ( ! [SY998: nat] :
( ~ ( ord_less_nat @ SV105 @ SV274 )
| ~ ( ord_less_nat @ SV408 @ SY998 )
| ( ord_less_nat @ ( plus_plus_nat @ SV105 @ SV408 ) @ ( plus_plus_nat @ SV274 @ SY998 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1253,plain,
! [SV409: nat,SV275: nat,SV106: nat] :
( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV106 @ SV275 ) @ SV409 )
| ( ord_less_nat @ SV106 @ SV409 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1254,plain,
! [SV410: nat,SV276: nat,SV107: nat] :
( ( ! [SY999: nat,SY1000: nat] :
( ~ ( ord_less_eq_nat @ SV107 @ SV276 )
| ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ SV107 @ SV410 ) @ SY999 ) @ ( plus_plus_nat @ ( times_times_nat @ SV276 @ SV410 ) @ SY1000 ) )
= ( minus_minus_nat @ SY999 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV276 @ SV107 ) @ SV410 ) @ SY1000 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1255,plain,
! [SV411: nat,SV277: nat,SV108: nat] :
( ( ~ ( ord_less_eq_nat @ SV108 @ SV277 )
| ( ( minus_minus_nat @ ( plus_plus_nat @ SV277 @ SV411 ) @ SV108 )
= ( plus_plus_nat @ ( minus_minus_nat @ SV277 @ SV108 ) @ SV411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1256,plain,
! [SV412: nat,SV278: nat,SV109: nat] :
( ( ! [SY1001: nat] :
( ~ ~ ( ~ ( ord_less_nat @ SV109 @ SV278 )
| ~ ( ord_less_nat @ SV412 @ SY1001 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV109 @ SV412 ) @ ( plus_plus_nat @ SV278 @ SY1001 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1257,plain,
! [SV413: nat,SV279: nat,SV110: nat] :
( ( ~ ( ord_less_eq_nat @ SV110 @ SV279 )
| ~ ( ord_less_eq_nat @ SV110 @ SV413 )
| ( ( ( minus_minus_nat @ SV279 @ SV110 )
= ( minus_minus_nat @ SV413 @ SV110 ) )
= ( SV279 = SV413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1258,plain,
! [SV414: nat,SV280: nat,SV111: nat] :
( ( ~ ( ord_less_nat @ SV111 @ SV280 )
| ( ord_less_nat @ ( plus_plus_nat @ SV414 @ SV111 ) @ ( plus_plus_nat @ SV414 @ SV280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1259,plain,
! [SV281: nat,SV112: nat] :
( ( ( ( minus_minus_nat @ SV112 @ SV281 )
!= zero_zero_nat )
= $true )
| ( ( ( ( minus_minus_nat @ SV281 @ SV112 )
!= zero_zero_nat )
| ( SV112 = SV281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1068]) ).
thf(1260,plain,
! [SV415: nat,SV282: nat,SV113: nat] :
( ( ~ ( ord_less_eq_nat @ SV113 @ SV282 )
| ( ( ord_less_eq_nat @ SV415 @ ( minus_minus_nat @ SV282 @ SV113 ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ SV415 @ SV113 ) @ SV282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1261,plain,
! [SV283: nat,SV114: nat > $o] :
( ( ( ~ ( SV114 @ zero_zero_nat ) )
= $true )
| ( ( ~ ! [SY655: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY655 )
| ~ ~ ( SV114 @ SY655 )
| ~ ! [SY656: nat] :
~ ~ ( ~ ( ord_less_nat @ SY656 @ SY655 )
| ~ ~ ( SV114 @ SY656 ) ) )
| ( SV114 @ SV283 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1070]) ).
thf(1262,plain,
! [SV115: nat] :
( ( ( ~ ( ( SV115 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV115 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV115 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV115 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1071]) ).
thf(1263,plain,
! [SV416: nat,SV284: nat,SV116: nat] :
( ( ~ ( ord_less_eq_nat @ SV116 @ SV284 )
| ( ( plus_plus_nat @ SV416 @ ( minus_minus_nat @ SV284 @ SV116 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ SV416 @ SV284 ) @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1264,plain,
! [SV417: nat,SV285: nat,SV117: nat > $o] :
( ( ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
= ( ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1265,plain,
! [SV418: nat,SV286: nat,SV118: nat] :
( ( ~ ( ord_less_nat @ SV118 @ SV286 )
| ~ ( ord_less_nat @ SV118 @ SV418 )
| ( ord_less_nat @ ( minus_minus_nat @ SV418 @ SV286 ) @ ( minus_minus_nat @ SV418 @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1266,plain,
! [SV287: nat,SV119: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV119 ) )
= $true )
| ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV287 )
| ( ord_less_nat @ ( minus_minus_nat @ SV287 @ SV119 ) @ SV287 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1076]) ).
thf(1267,plain,
! [SV288: nat] :
( ( ! [SV419: nat] :
( ( ord_less_eq_nat @ SV288 @ SV419 )
= ( ~ ! [SY1003: nat] :
( SV419
!= ( plus_plus_nat @ SV288 @ SY1003 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1077]) ).
thf(1268,plain,
! [SV288: nat] :
( ( ( ord_less_eq_nat @ SV288 )
= ( ^ [SY899: nat] :
~ ! [SY900: nat] :
( SY899
!= ( plus_plus_nat @ SV288 @ SY900 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1077]) ).
thf(1269,plain,
! [SV289: nat] :
( ( ! [SV420: nat] :
( ( ord_less_eq_nat @ SV289 @ SV420 )
= ( ~ ! [SY1004: nat] :
( SV420
!= ( plus_plus_nat @ SV289 @ SY1004 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1078]) ).
thf(1270,plain,
! [SV289: nat] :
( ( ( ord_less_eq_nat @ SV289 )
= ( ^ [SY901: nat] :
~ ! [SY902: nat] :
( SY901
!= ( plus_plus_nat @ SV289 @ SY902 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1078]) ).
thf(1271,plain,
! [SV421: nat,SV290: nat,SV122: nat] :
( ( ~ ( ord_less_eq_nat @ SV122 @ SV290 )
| ( ( ( minus_minus_nat @ SV290 @ SV122 )
= SV421 )
= ( SV290
= ( plus_plus_nat @ SV421 @ SV122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1272,plain,
! [SV422: nat,SV291: nat,SV123: nat] :
( ( ! [SY1005: nat,SY1006: nat] :
( ~ ( ord_less_eq_nat @ SV123 @ SV291 )
| ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ SV291 @ SV422 ) @ SY1005 ) @ ( plus_plus_nat @ ( times_times_nat @ SV123 @ SV422 ) @ SY1006 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV291 @ SV123 ) @ SV422 ) @ SY1005 ) @ SY1006 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1273,plain,
! [SV423: nat,SV292: nat,SV124: nat] :
( ( ~ ( ord_less_eq_nat @ SV124 @ SV292 )
| ( ord_less_eq_nat @ SV423 @ ( minus_minus_nat @ ( plus_plus_nat @ SV292 @ SV423 ) @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1274,plain,
! [SV424: nat,SV293: nat,SV125: nat] :
( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SV293 ) @ ( plus_plus_nat @ SV424 @ SV293 ) )
| ( ord_less_nat @ SV125 @ SV424 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1275,plain,
! [SV294: nat,SV126: nat] :
( ( ~ ( ( ( plus_plus_nat @ SV126 @ SV294 )
= zero_zero_nat )
| ~ ( ( SV126 != zero_zero_nat )
| ( SV294 != zero_zero_nat ) ) )
| ~ ( ( ( plus_plus_nat @ SV126 @ SV294 )
!= zero_zero_nat )
| ~ ~ ( ( SV126 != zero_zero_nat )
| ( SV294 != zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1083]) ).
thf(1276,plain,
! [SV294: nat,SV126: nat] :
( ( ( ( plus_plus_nat @ SV126 @ SV294 )
= zero_zero_nat )
= ( ~ ( ( SV126 != zero_zero_nat )
| ( SV294 != zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1083]) ).
thf(1277,plain,
! [SV425: nat,SV295: nat,SV127: nat] :
( ( ! [SY1007: nat,SY1008: nat] :
( ~ ( ord_less_eq_nat @ SV127 @ SV295 )
| ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV127 @ SV425 ) @ SY1007 ) @ ( plus_plus_nat @ ( times_times_nat @ SV295 @ SV425 ) @ SY1008 ) )
= ( ord_less_nat @ SY1007 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV295 @ SV127 ) @ SV425 ) @ SY1008 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1278,plain,
! [SV426: nat,SV296: nat,SV128: nat] :
( ( ~ ( ord_less_nat @ SV128 @ SV296 )
| ( ord_less_nat @ ( minus_minus_nat @ SV128 @ SV426 ) @ SV296 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1279,plain,
! [SV427: nat,SV297: nat,SV129: nat] :
( ( ~ ( ord_less_eq_nat @ SV129 @ SV297 )
| ( ord_less_eq_nat @ ( minus_minus_nat @ SV427 @ SV297 ) @ ( minus_minus_nat @ SV427 @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1280,plain,
! [SV428: nat,SV298: nat,SV130: nat] :
( ( ~ ( ord_less_eq_nat @ SV130 @ SV298 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV130 @ SV428 ) @ ( plus_plus_nat @ SV298 @ SV428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1281,plain,
! [SV299: nat,SV131: nat] :
( ( ( ~ ( ord_less_nat @ SV131 @ SV299 ) )
= $true )
| ( ( SV299 != SV131 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1088]) ).
thf(1282,plain,
! [SV429: nat,SV300: nat,SV132: nat] :
( ( ! [SY1009: nat] :
( ~ ( ord_less_nat @ SV132 @ SV300 )
| ( ( plus_plus_nat @ SV429 @ SV300 )
!= ( plus_plus_nat @ SV132 @ SY1009 ) )
| ( ord_less_nat @ SV429 @ SY1009 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1283,plain,
! [SV430: nat,SV301: nat,SV133: nat] :
( ( ~ ( ord_less_eq_nat @ SV133 @ SV301 )
| ( ord_less_eq_nat @ SV133 @ ( plus_plus_nat @ SV430 @ SV301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1284,plain,
! [SV134: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ SV134 )
| ( SV134 != zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV134 )
| ~ ( ( SV134 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1091]) ).
thf(1285,plain,
! [SV431: nat,SV302: nat,SV135: nat] :
( ( ~ ( ord_less_eq_nat @ SV135 @ SV302 )
| ( ( minus_minus_nat @ SV431 @ ( minus_minus_nat @ SV302 @ SV135 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ SV431 @ SV135 ) @ SV302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1286,plain,
! [SV432: nat,SV303: nat,SV136: nat] :
( ( ~ ( ord_less_eq_nat @ SV136 @ SV303 )
| ( ( minus_minus_nat @ ( plus_plus_nat @ SV432 @ SV303 ) @ SV136 )
= ( plus_plus_nat @ SV432 @ ( minus_minus_nat @ SV303 @ SV136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1287,plain,
! [SV433: nat,SV304: nat,SV137: nat] :
( ( ! [SY1010: nat] :
( ~ ( ord_less_eq_nat @ SV137 @ SV304 )
| ~ ( ord_less_eq_nat @ SV433 @ SY1010 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV137 @ SV433 ) @ ( plus_plus_nat @ SV304 @ SY1010 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1288,plain,
! [SV434: nat,SV305: nat,SV138: nat] :
( ( ~ ( ord_less_eq_nat @ SV138 @ SV305 )
| ( ( minus_minus_nat @ ( plus_plus_nat @ SV305 @ SV434 ) @ SV138 )
= ( plus_plus_nat @ ( minus_minus_nat @ SV305 @ SV138 ) @ SV434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1289,plain,
! [SV435: nat,SV306: nat,SV139: nat] :
( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV139 @ SV306 ) @ ( plus_plus_nat @ SV139 @ SV435 ) )
| ( ord_less_nat @ SV306 @ SV435 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1290,plain,
! [SV436: nat,SV307: nat,SV140: nat] :
( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV140 @ SV307 ) @ ( plus_plus_nat @ SV436 @ SV307 ) )
| ( ord_less_eq_nat @ SV140 @ SV436 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1291,plain,
! [SV437: nat,SV308: nat,SV141: nat] :
( ( ~ ( ord_less_eq_nat @ SV141 @ SV308 )
| ( ( plus_plus_nat @ ( minus_minus_nat @ SV308 @ SV141 ) @ SV437 )
= ( minus_minus_nat @ ( plus_plus_nat @ SV308 @ SV437 ) @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1292,plain,
! [SV309: nat,SV142: nat > $o] :
( ( ( ~ ! [SY712: nat] :
( ~ ~ ( SV142 @ SY712 )
| ~ ! [SY713: nat] :
~ ~ ( ~ ( ord_less_nat @ SY713 @ SY712 )
| ~ ~ ( SV142 @ SY713 ) ) ) )
= $true )
| ( ( SV142 @ SV309 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1100]) ).
thf(1293,plain,
! [SV438: nat,SV310: nat,SV143: nat] :
( ( ( ( plus_plus_nat @ SV143 @ SV310 )
!= ( plus_plus_nat @ SV438 @ SV310 ) )
| ( SV143 = SV438 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1294,plain,
! [SV439: nat,SV311: nat,SV144: nat] :
( ( ~ ( ord_less_nat @ SV144 @ SV311 )
| ( ord_less_nat @ SV144 @ ( plus_plus_nat @ SV311 @ SV439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1295,plain,
! [SV312: nat,SV145: nat] :
( ( ( SV145 != SV312 )
= $true )
| ( ( ord_less_eq_nat @ SV145 @ SV312 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1103]) ).
thf(1296,plain,
! [SV440: nat,SV313: nat,SV146: nat] :
( ( ! [SY1011: nat,SY1012: nat] :
( ~ ( ord_less_eq_nat @ SV146 @ SV313 )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV146 @ SV440 ) @ SY1011 ) @ ( plus_plus_nat @ ( times_times_nat @ SV313 @ SV440 ) @ SY1012 ) )
= ( ord_less_eq_nat @ SY1011 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV313 @ SV146 ) @ SV440 ) @ SY1012 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1297,plain,
! [SV441: nat,SV314: nat,SV147: nat] :
( ( ~ ( ord_less_eq_nat @ SV147 @ SV314 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV147 @ SV441 ) @ ( plus_plus_nat @ SV314 @ SV441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1298,plain,
! [SV442: nat,SV315: nat,SV148: nat] :
( ( ! [SY1013: nat] :
( ~ ~ ( ~ ( ord_less_nat @ SV148 @ SV315 )
| ( SV442 != SY1013 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV148 @ SV442 ) @ ( plus_plus_nat @ SV315 @ SY1013 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1299,plain,
! [SV316: nat,SV149: nat] :
( ( ( ~ ( ord_less_nat @ SV149 @ SV316 ) )
= $true )
| ( ( ord_less_eq_nat @ SV149 @ SV316 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1107]) ).
thf(1300,plain,
! [SV443: nat,SV317: nat,SV150: nat] :
( ( ! [SY1014: nat] :
( ~ ( ord_less_nat @ SV150 @ SV317 )
| ~ ( ord_less_nat @ SV443 @ SY1014 )
| ( ord_less_nat @ ( plus_plus_nat @ SV150 @ SV443 ) @ ( plus_plus_nat @ SV317 @ SY1014 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1301,plain,
! [SV151: nat] :
( ( ( SV151 != zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV151 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1109]) ).
thf(1302,plain,
! [SV444: nat,SV318: nat,SV152: nat] :
( ( ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
= ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV318 )
| ~ ( ord_less_nat @ SV152 @ SV444 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1303,plain,
! [SV319: nat,SV153: nat] :
( ( ( ~ ~ ( ord_less_nat @ SV153 @ SV319 ) )
= $true )
| ( ( ( plus_plus_nat @ SV319 @ ( minus_minus_nat @ SV153 @ SV319 ) )
= SV153 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1111]) ).
thf(1304,plain,
! [SV320: nat,SV154: nat] :
( ( ( ~ ( ord_less_nat @ SV154 @ SV320 ) )
= $true )
| ( ( SV320 != zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1112]) ).
thf(1305,plain,
! [SV321: nat,SV155: nat] :
( ( ~ ( ( SV155 != SV321 )
| ( ord_less_nat @ SV155 @ SV321 )
| ( ord_less_nat @ SV321 @ SV155 ) )
| ~ ( ~ ( ( SV155 != SV321 ) )
| ~ ( ( ord_less_nat @ SV155 @ SV321 )
| ( ord_less_nat @ SV321 @ SV155 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1113]) ).
thf(1306,plain,
! [SV321: nat,SV155: nat] :
( ( ( SV155 != SV321 )
= ( ( ord_less_nat @ SV155 @ SV321 )
| ( ord_less_nat @ SV321 @ SV155 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1113]) ).
thf(1307,plain,
! [SV322: nat,SV156: nat] :
( ( ( ~ ( ord_less_nat @ SV156 @ SV322 ) )
= $true )
| ( ( SV322 != zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1114]) ).
thf(1308,plain,
! [SV445: nat,SV323: nat,SV157: nat] :
( ( ~ ( ord_less_eq_nat @ SV157 @ SV323 )
| ( ( plus_plus_nat @ SV445 @ ( minus_minus_nat @ SV323 @ SV157 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ SV445 @ SV323 ) @ SV157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1309,plain,
! [SV446: nat,SV324: nat,SV158: nat] :
( ( ~ ( ord_less_eq_nat @ SV158 @ SV324 )
| ( ( plus_plus_nat @ ( minus_minus_nat @ SV324 @ SV158 ) @ SV446 )
= ( minus_minus_nat @ ( plus_plus_nat @ SV324 @ SV446 ) @ SV158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1310,plain,
! [SV325: nat,SV159: nat] :
( ( ~ ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV159 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV325 ) ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV159 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV325 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1117]) ).
thf(1311,plain,
! [SV325: nat,SV159: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
= ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV159 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV325 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1117]) ).
thf(1312,plain,
! [SV326: nat,SV160: nat] :
( ( ~ ( ( ( plus_plus_nat @ SV160 @ SV326 )
= zero_zero_nat )
| ~ ( ( SV160 != zero_zero_nat )
| ( SV326 != zero_zero_nat ) ) )
| ~ ( ( ( plus_plus_nat @ SV160 @ SV326 )
!= zero_zero_nat )
| ~ ~ ( ( SV160 != zero_zero_nat )
| ( SV326 != zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1118]) ).
thf(1313,plain,
! [SV326: nat,SV160: nat] :
( ( ( ( plus_plus_nat @ SV160 @ SV326 )
= zero_zero_nat )
= ( ~ ( ( SV160 != zero_zero_nat )
| ( SV326 != zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1118]) ).
thf(1314,plain,
! [SV327: nat] :
( ( ! [SV447: nat] :
( ( ord_less_nat @ SV327 @ SV447 )
= ( ~ ( ~ ( ord_less_eq_nat @ SV327 @ SV447 )
| ~ ( ( SV327 != SV447 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1119]) ).
thf(1315,plain,
! [SV327: nat] :
( ( ( ord_less_nat @ SV327 )
= ( ^ [SY941: nat] :
~ ( ~ ( ord_less_eq_nat @ SV327 @ SY941 )
| ~ ( ( SV327 != SY941 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1119]) ).
thf(1316,plain,
! [SV328: nat,SV162: nat] :
( ( ~ ( ( zero_zero_nat
= ( plus_plus_nat @ SV162 @ SV328 ) )
| ~ ( ( SV162 != zero_zero_nat )
| ( SV328 != zero_zero_nat ) ) )
| ~ ( ( zero_zero_nat
!= ( plus_plus_nat @ SV162 @ SV328 ) )
| ~ ~ ( ( SV162 != zero_zero_nat )
| ( SV328 != zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1120]) ).
thf(1317,plain,
! [SV328: nat,SV162: nat] :
( ( ( zero_zero_nat
= ( plus_plus_nat @ SV162 @ SV328 ) )
= ( ~ ( ( SV162 != zero_zero_nat )
| ( SV328 != zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1120]) ).
thf(1318,plain,
! [SV448: nat,SV329: nat,SV163: nat] :
( ( ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) )
= ( ~ ( ord_less_nat @ zero_zero_nat @ SV329 )
| ( ord_less_eq_nat @ SV163 @ SV448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1319,plain,
! [SV449: nat,SV330: nat,SV164: nat > $o] :
( ( ~ ( SV164 @ SV330 )
| ~ ! [SY1015: nat] :
( ~ ( SV164 @ SY1015 )
| ( ord_less_eq_nat @ SY1015 @ SV449 ) )
| ~ ! [SY751: nat] :
~ ~ ( ~ ( SV164 @ SY751 )
| ~ ! [SY752: nat] :
( ~ ( SV164 @ SY752 )
| ( ord_less_eq_nat @ SY752 @ SY751 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1320,plain,
! [SV165: nat] :
( ( ( ord_less_eq_nat @ SV165 @ zero_zero_nat )
= $false )
| ( ( SV165 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1123]) ).
thf(1321,plain,
! [SV450: nat,SV331: nat,SV166: nat] :
( ( ~ ( ord_less_nat @ SV166 @ SV331 )
| ( ord_less_nat @ ( plus_plus_nat @ SV166 @ SV450 ) @ ( plus_plus_nat @ SV331 @ SV450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1322,plain,
! [SV451: nat,SV332: nat,SV167: nat] :
( ( ~ ( ord_less_eq_nat @ SV167 @ SV332 )
| ~ ( ord_less_eq_nat @ SV167 @ SV451 )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV332 @ SV167 ) @ ( minus_minus_nat @ SV451 @ SV167 ) )
= ( ord_less_eq_nat @ SV332 @ SV451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1125]) ).
thf(1323,plain,
! [SV452: nat,SV333: nat,SV168: nat] :
( ( ( ( plus_plus_nat @ SV168 @ SV333 )
!= SV452 )
| ( SV168
= ( minus_minus_nat @ SV452 @ SV333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1324,plain,
! [SV453: nat,SV334: nat,SV169: nat] :
( ( ~ ( ord_less_eq_nat @ SV169 @ SV334 )
| ( ( ord_less_nat @ ( minus_minus_nat @ SV334 @ SV169 ) @ SV453 )
= ( ord_less_nat @ SV334 @ ( plus_plus_nat @ SV453 @ SV169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1325,plain,
! [SV454: nat,SV335: nat,SV170: nat] :
( ( ! [SY1018: nat] :
( ( SV170
!= ( plus_plus_nat @ SV335 @ SV454 ) )
| ( ( plus_plus_nat @ SV170 @ SY1018 )
= ( plus_plus_nat @ SV335 @ ( plus_plus_nat @ SV454 @ SY1018 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1326,plain,
! [SV455: nat,SV336: nat,SV171: nat] :
( ( ~ ( ord_less_eq_nat @ SV171 @ SV336 )
| ~ ( ord_less_eq_nat @ SV171 @ SV455 )
| ( ( minus_minus_nat @ ( minus_minus_nat @ SV336 @ SV171 ) @ ( minus_minus_nat @ SV455 @ SV171 ) )
= ( minus_minus_nat @ SV336 @ SV455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1327,plain,
! [SV456: nat,SV337: nat,SV172: nat] :
( ( ~ ( ord_less_eq_nat @ SV172 @ SV337 )
| ( ord_less_eq_nat @ SV172 @ ( plus_plus_nat @ SV337 @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1328,plain,
! [SV173: nat] :
( ( ( SV173 != zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV173 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1131]) ).
thf(1329,plain,
! [SV457: nat,SV338: nat,SV174: nat] :
( ( ! [SY1019: nat,SY1020: nat] :
( ~ ( ord_less_eq_nat @ SV174 @ SV338 )
| ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV338 @ SV457 ) @ SY1019 ) @ ( plus_plus_nat @ ( times_times_nat @ SV174 @ SV457 ) @ SY1020 ) )
= ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV338 @ SV174 ) @ SV457 ) @ SY1019 ) @ SY1020 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1330,plain,
! [SV458: nat,SV339: nat,SV175: nat] :
( ( ! [SY1021: nat] :
( ( SV175
!= ( plus_plus_nat @ SV339 @ SV458 ) )
| ( ( plus_plus_nat @ SY1021 @ SV175 )
= ( plus_plus_nat @ SV339 @ ( plus_plus_nat @ SY1021 @ SV458 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1331,plain,
! [SV340: nat,SV176: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV176 @ SV340 ) )
= $true )
| ( ( ( plus_plus_nat @ SV176 @ ( minus_minus_nat @ SV340 @ SV176 ) )
= SV340 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1134]) ).
thf(1332,plain,
! [SV459: nat,SV341: nat,SV177: nat] :
( ( ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
= ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 )
| ~ ( ord_less_nat @ SV341 @ SV459 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1333,plain,
! [SV342: nat,SV178: nat] :
( ( ( ~ ( ( SV178 != SV342 ) ) )
= $true )
| ( ( ~ ~ ( ord_less_nat @ SV178 @ SV342 )
| ( ord_less_nat @ SV342 @ SV178 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1136]) ).
thf(1334,plain,
! [SV460: nat,SV343: nat,SV179: nat] :
( ( ~ ( ord_less_eq_nat @ SV179 @ SV343 )
| ( ord_less_eq_nat @ ( minus_minus_nat @ SV179 @ SV460 ) @ ( minus_minus_nat @ SV343 @ SV460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1335,plain,
! [SV344: nat,SV180: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV180 @ SV344 ) )
= $true )
| ( ( ( minus_minus_nat @ SV180 @ SV344 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1138]) ).
thf(1336,plain,
! [SV345: nat,SV181: nat > $o] :
( ( ( ~ ! [SY783: nat] :
( ~ ! [SY784: nat] :
( ~ ( ord_less_nat @ SY784 @ SY783 )
| ( SV181 @ SY784 ) )
| ( SV181 @ SY783 ) ) )
= $true )
| ( ( SV181 @ SV345 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1139]) ).
thf(1337,plain,
! [SV461: nat,SV346: nat,SV182: nat] :
( ( ~ ( ord_less_eq_nat @ SV182 @ SV346 )
| ~ ( ord_less_eq_nat @ SV182 @ SV346 )
| ( ( ( minus_minus_nat @ SV346 @ SV182 )
= SV461 )
= ( SV346
= ( plus_plus_nat @ SV461 @ SV182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1338,plain,
! [SV462: nat,SV347: nat,SV183: nat] :
( ( ~ ( ord_less_eq_nat @ SV183 @ SV347 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV462 @ SV183 ) @ ( plus_plus_nat @ SV462 @ SV347 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1339,plain,
! [SV463: nat,SV348: nat,SV184: nat] :
( ( ~ ( ord_less_eq_nat @ SV184 @ SV348 )
| ~ ( ord_less_eq_nat @ SV184 @ SV463 )
| ( ( ord_less_nat @ ( minus_minus_nat @ SV348 @ SV184 ) @ ( minus_minus_nat @ SV463 @ SV184 ) )
= ( ord_less_nat @ SV348 @ SV463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1340,plain,
! [SV464: nat,SV349: nat,SV185: nat] :
( ( ~ ( ord_less_eq_nat @ SV185 @ SV349 )
| ( ( ord_less_eq_nat @ SV464 @ ( minus_minus_nat @ SV349 @ SV185 ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ SV464 @ SV185 ) @ SV349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1341,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= ( ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1342,plain,
! [SV466: nat,SV351: nat,SV187: nat] :
( ( ( ( plus_plus_nat @ SV187 @ SV351 )
!= ( plus_plus_nat @ SV187 @ SV466 ) )
| ( SV351 = SV466 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1343,plain,
! [SV467: nat,SV352: nat,SV188: nat] :
( ( ~ ( ord_less_nat @ SV188 @ SV352 )
| ~ ( ord_less_eq_nat @ SV467 @ SV188 )
| ( ord_less_nat @ ( minus_minus_nat @ SV188 @ SV467 ) @ ( minus_minus_nat @ SV352 @ SV467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1344,plain,
! [SV353: nat,SV189: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV189 @ SV353 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV353 @ SV189 )
| ( SV189 = SV353 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1147]) ).
thf(1345,plain,
! [SV468: nat,SV354: nat,SV190: nat] :
( ( ! [SY1023: nat,SY1024: nat] :
( ~ ( ord_less_eq_nat @ SV190 @ SV354 )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SV354 @ SV468 ) @ SY1023 )
= ( plus_plus_nat @ ( times_times_nat @ SV190 @ SV468 ) @ SY1024 ) )
= ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV354 @ SV190 ) @ SV468 ) @ SY1023 )
= SY1024 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1148]) ).
thf(1346,plain,
! [SV355: nat,SV191: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV191 @ SV355 ) )
= $true )
| ( ( ~ ! [SY975: nat] :
( SV355
!= ( plus_plus_nat @ SV191 @ SY975 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1149]) ).
thf(1347,plain,
! [SV469: nat,SV356: nat,SV192: nat] :
( ( ! [SY1025: nat] :
( ~ ~ ( ( SV192 != SV356 )
| ~ ( ord_less_nat @ SV469 @ SY1025 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV192 @ SV469 ) @ ( plus_plus_nat @ SV356 @ SY1025 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1150]) ).
thf(1348,plain,
! [SV470: nat,SV357: nat,SV193: nat] :
( ( ! [SY1026: nat] :
( ~ ~ ( ~ ( ord_less_eq_nat @ SV193 @ SV357 )
| ( SV470 != SY1026 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV193 @ SV470 ) @ ( plus_plus_nat @ SV357 @ SY1026 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1349,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) )
= ( ~ ( ord_less_nat @ zero_zero_nat @ SV194 )
| ( ord_less_eq_nat @ SV358 @ SV471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1350,plain,
! [SV472: nat,SV359: nat,SV195: nat] :
( ( ~ ( ord_less_eq_nat @ SV195 @ SV359 )
| ~ ( ord_less_eq_nat @ SV359 @ SV472 )
| ( ord_less_eq_nat @ SV195 @ SV472 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1351,plain,
! [SV473: nat,SV360: nat,SV196: nat] :
( ( ! [SY1027: nat] :
( ~ ~ ( ( SV196 != SV360 )
| ( SV473 != SY1027 ) )
| ( ( plus_plus_nat @ SV196 @ SV473 )
= ( plus_plus_nat @ SV360 @ SY1027 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1352,plain,
! [SV474: nat,SV361: nat,SV197: nat] :
( ( ! [SY1028: nat,SY1029: nat] :
( ~ ( ord_less_eq_nat @ SV197 @ SV361 )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SV197 @ SV474 ) @ SY1028 )
= ( plus_plus_nat @ ( times_times_nat @ SV361 @ SV474 ) @ SY1029 ) )
= ( SY1028
= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV361 @ SV197 ) @ SV474 ) @ SY1029 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1353,plain,
! [SV475: nat,SV362: nat,SV198: nat] :
( ( ! [SY1030: nat] :
( ~ ( ord_less_eq_nat @ SV198 @ SV362 )
| ~ ( ord_less_eq_nat @ SV475 @ SY1030 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV198 @ SV475 ) @ ( plus_plus_nat @ SV362 @ SY1030 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1354,plain,
! [SV476: nat,SV363: nat,SV199: nat] :
( ( ~ ( ord_less_nat @ SV199 @ SV363 )
| ( ord_less_nat @ SV199 @ ( plus_plus_nat @ SV476 @ SV363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1355,plain,
! [SV364: nat,SV200: nat] :
( ( ( ~ ( ( ord_less_nat @ SV200 @ SV364 )
| ( SV200 = SV364 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV200 @ SV364 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1158]) ).
thf(1356,plain,
! [SV477: nat,SV365: nat,SV201: nat > nat] :
( ( ~ ( number1551313001itions @ SV201 @ SV365 )
| ( ord_less_eq_nat @ ( SV201 @ SV477 ) @ SV365 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1357,plain,
! [SV366: nat,SV202: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV202 @ SV366 ) )
= $true )
| ( ( ( minus_minus_nat @ SV366 @ ( minus_minus_nat @ SV366 @ SV202 ) )
= SV202 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1160]) ).
thf(1358,plain,
! [SV478: nat,SV367: nat,SV203: nat] :
( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV203 @ SV367 ) @ ( plus_plus_nat @ SV203 @ SV478 ) )
| ( ord_less_eq_nat @ SV367 @ SV478 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1359,plain,
! [SV1: nat > nat] :
( ( ( ( number1551313001itions @ SV1 @ zero_zero_nat )
| ( SV1
= ( ^ [I: nat] : zero_zero_nat ) ) )
= $false )
| ( ( ~ ( ~ ( number1551313001itions @ SV1 @ zero_zero_nat )
| ( SV1
!= ( ^ [I: nat] : zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1162]) ).
thf(1360,plain,
! [SV204: nat,SV2: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SV204 ) )
| ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( ord_less_nat @ zero_zero_nat @ SV204 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SV204 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( ord_less_nat @ zero_zero_nat @ SV204 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1163]) ).
thf(1361,plain,
! [SV205: nat,SV3: nat] :
( ( ( ~ ( ( ord_less_nat @ ( plus_plus_nat @ SV3 @ SV205 ) @ SV3 )
| ( ord_less_nat @ SV205 @ zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV3 @ SV205 ) @ SV3 )
| ~ ( ord_less_nat @ SV205 @ zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1165]) ).
thf(1362,plain,
! [SV206: nat,SV4: nat] :
( ( ( ~ ( ( ord_less_nat @ ( plus_plus_nat @ SV4 @ SV206 ) @ SV206 )
| ( ord_less_nat @ SV4 @ zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV4 @ SV206 ) @ SV206 )
| ~ ( ord_less_nat @ SV4 @ zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1167]) ).
thf(1363,plain,
! [SV207: nat,SV5: nat] :
( ( ( ~ ( ( ord_less_nat @ SV5 @ ( plus_plus_nat @ SV5 @ SV207 ) )
| ( ord_less_nat @ zero_zero_nat @ SV207 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV5 @ ( plus_plus_nat @ SV5 @ SV207 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV207 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1169]) ).
thf(1364,plain,
! [SV208: nat,SV6: nat] :
( ( ( ~ ( ( ord_less_nat @ SV6 @ ( plus_plus_nat @ SV208 @ SV6 ) )
| ( ord_less_nat @ zero_zero_nat @ SV208 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV6 @ ( plus_plus_nat @ SV208 @ SV6 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV208 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1171]) ).
thf(1365,plain,
! [SV368: nat,SV209: nat,SV7: nat] :
( ( ~ ( ( ( plus_plus_nat @ SV7 @ SV209 )
= ( plus_plus_nat @ SV368 @ SV209 ) )
| ( SV7 = SV368 ) )
| ~ ( ( ( plus_plus_nat @ SV7 @ SV209 )
!= ( plus_plus_nat @ SV368 @ SV209 ) )
| ( SV7 != SV368 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1173]) ).
thf(1366,plain,
! [SV368: nat,SV209: nat,SV7: nat] :
( ( ( ( plus_plus_nat @ SV7 @ SV209 )
= ( plus_plus_nat @ SV368 @ SV209 ) )
= ( SV7 = SV368 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1173]) ).
thf(1367,plain,
! [SV369: nat,SV210: nat,SV8: nat] :
( ( ~ ( ( ( plus_plus_nat @ SV8 @ SV210 )
= ( plus_plus_nat @ SV8 @ SV369 ) )
| ( SV210 = SV369 ) )
| ~ ( ( ( plus_plus_nat @ SV8 @ SV210 )
!= ( plus_plus_nat @ SV8 @ SV369 ) )
| ( SV210 != SV369 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1174]) ).
thf(1368,plain,
! [SV369: nat,SV210: nat,SV8: nat] :
( ( ( ( plus_plus_nat @ SV8 @ SV210 )
= ( plus_plus_nat @ SV8 @ SV369 ) )
= ( SV210 = SV369 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1174]) ).
thf(1369,plain,
! [SV9: nat] :
( ( ( ( ord_less_eq_nat @ SV9 @ zero_zero_nat )
| ( SV9 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV9 @ zero_zero_nat )
| ( SV9 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1370,plain,
! [SV10: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV10 )
| ( SV10 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV10 )
| ( SV10 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1371,plain,
! [SV370: nat,SV211: nat,SV11: nat] :
( ( ~ ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV11 @ SV211 ) @ ( plus_plus_nat @ SV370 @ SV211 ) )
| ( ord_less_eq_nat @ SV11 @ SV370 ) )
| ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV11 @ SV211 ) @ ( plus_plus_nat @ SV370 @ SV211 ) )
| ~ ( ord_less_eq_nat @ SV11 @ SV370 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1177]) ).
thf(1372,plain,
! [SV370: nat,SV211: nat,SV11: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV11 @ SV211 ) @ ( plus_plus_nat @ SV370 @ SV211 ) )
= ( ord_less_eq_nat @ SV11 @ SV370 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1177]) ).
thf(1373,plain,
! [SV371: nat,SV212: nat,SV12: nat] :
( ( ~ ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV212 ) @ ( plus_plus_nat @ SV12 @ SV371 ) )
| ( ord_less_eq_nat @ SV212 @ SV371 ) )
| ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV212 ) @ ( plus_plus_nat @ SV12 @ SV371 ) )
| ~ ( ord_less_eq_nat @ SV212 @ SV371 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1178]) ).
thf(1374,plain,
! [SV371: nat,SV212: nat,SV12: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV212 ) @ ( plus_plus_nat @ SV12 @ SV371 ) )
= ( ord_less_eq_nat @ SV212 @ SV371 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1178]) ).
thf(1375,plain,
! [SV213: nat,SV13: nat] :
( ( ( ~ ( ( SV13
= ( plus_plus_nat @ SV13 @ SV213 ) )
| ( SV213 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( SV13
!= ( plus_plus_nat @ SV13 @ SV213 ) )
| ( SV213 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1179]) ).
thf(1376,plain,
! [SV214: nat,SV14: nat] :
( ( ( ~ ( ( SV14
= ( plus_plus_nat @ SV214 @ SV14 ) )
| ( SV214 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( SV14
!= ( plus_plus_nat @ SV214 @ SV14 ) )
| ( SV214 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1181]) ).
thf(1377,plain,
! [SV215: nat,SV15: nat] :
( ( ( ~ ( ( ( plus_plus_nat @ SV15 @ SV215 )
= SV15 )
| ( SV215 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( ( plus_plus_nat @ SV15 @ SV215 )
!= SV15 )
| ( SV215 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1183]) ).
thf(1378,plain,
! [SV216: nat,SV16: nat] :
( ( ( ~ ( ( ( plus_plus_nat @ SV16 @ SV216 )
= SV216 )
| ( SV16 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( ( plus_plus_nat @ SV16 @ SV216 )
!= SV216 )
| ( SV16 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1185]) ).
thf(1379,plain,
! [SV372: nat,SV217: nat,SV22: nat] :
( ( ~ ( ( ord_less_nat @ ( plus_plus_nat @ SV22 @ SV217 ) @ ( plus_plus_nat @ SV372 @ SV217 ) )
| ( ord_less_nat @ SV22 @ SV372 ) )
| ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV22 @ SV217 ) @ ( plus_plus_nat @ SV372 @ SV217 ) )
| ~ ( ord_less_nat @ SV22 @ SV372 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1187]) ).
thf(1380,plain,
! [SV372: nat,SV217: nat,SV22: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV22 @ SV217 ) @ ( plus_plus_nat @ SV372 @ SV217 ) )
= ( ord_less_nat @ SV22 @ SV372 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1187]) ).
thf(1381,plain,
! [SV373: nat,SV218: nat,SV23: nat] :
( ( ~ ( ( ord_less_nat @ ( plus_plus_nat @ SV23 @ SV218 ) @ ( plus_plus_nat @ SV23 @ SV373 ) )
| ( ord_less_nat @ SV218 @ SV373 ) )
| ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV23 @ SV218 ) @ ( plus_plus_nat @ SV23 @ SV373 ) )
| ~ ( ord_less_nat @ SV218 @ SV373 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1188]) ).
thf(1382,plain,
! [SV373: nat,SV218: nat,SV23: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV23 @ SV218 ) @ ( plus_plus_nat @ SV23 @ SV373 ) )
= ( ord_less_nat @ SV218 @ SV373 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1188]) ).
thf(1383,plain,
! [SV376: nat,SV223: nat,SV32: nat] :
( ( ~ ( ( ord_less_nat @ ( plus_plus_nat @ SV32 @ SV223 ) @ ( plus_plus_nat @ SV32 @ SV376 ) )
| ( ord_less_nat @ SV223 @ SV376 ) )
| ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV32 @ SV223 ) @ ( plus_plus_nat @ SV32 @ SV376 ) )
| ~ ( ord_less_nat @ SV223 @ SV376 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1191]) ).
thf(1384,plain,
! [SV376: nat,SV223: nat,SV32: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV32 @ SV223 ) @ ( plus_plus_nat @ SV32 @ SV376 ) )
= ( ord_less_nat @ SV223 @ SV376 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1191]) ).
thf(1385,plain,
! [SV377: nat,SV224: nat,SV35: nat] :
( ( ~ ( ( ( times_times_nat @ SV35 @ SV224 )
= ( times_times_nat @ SV377 @ SV224 ) )
| ( SV35 = SV377 )
| ( SV224 = zero_zero_nat ) )
| ~ ( ( ( times_times_nat @ SV35 @ SV224 )
!= ( times_times_nat @ SV377 @ SV224 ) )
| ~ ( ( SV35 = SV377 )
| ( SV224 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1192]) ).
thf(1386,plain,
! [SV377: nat,SV224: nat,SV35: nat] :
( ( ( ( times_times_nat @ SV35 @ SV224 )
= ( times_times_nat @ SV377 @ SV224 ) )
= ( ( SV35 = SV377 )
| ( SV224 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1192]) ).
thf(1387,plain,
! [SV378: nat,SV225: nat,SV36: nat] :
( ( ~ ( ( ( times_times_nat @ SV36 @ SV225 )
= ( times_times_nat @ SV36 @ SV378 ) )
| ( SV225 = SV378 )
| ( SV36 = zero_zero_nat ) )
| ~ ( ( ( times_times_nat @ SV36 @ SV225 )
!= ( times_times_nat @ SV36 @ SV378 ) )
| ~ ( ( SV225 = SV378 )
| ( SV36 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1193]) ).
thf(1388,plain,
! [SV378: nat,SV225: nat,SV36: nat] :
( ( ( ( times_times_nat @ SV36 @ SV225 )
= ( times_times_nat @ SV36 @ SV378 ) )
= ( ( SV225 = SV378 )
| ( SV36 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1193]) ).
thf(1389,plain,
! [SV226: nat,SV38: nat] :
( ( ( ~ ( ( ( times_times_nat @ SV38 @ SV226 )
= zero_zero_nat )
| ( SV38 = zero_zero_nat )
| ( SV226 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( ( times_times_nat @ SV38 @ SV226 )
!= zero_zero_nat )
| ~ ( ( SV38 = zero_zero_nat )
| ( SV226 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1194]) ).
thf(1390,plain,
! [SV379: nat,SV227: nat,SV39: nat] :
( ( ~ ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV39 @ SV227 ) @ ( plus_plus_nat @ SV39 @ SV379 ) )
| ( ord_less_eq_nat @ SV227 @ SV379 ) )
| ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV39 @ SV227 ) @ ( plus_plus_nat @ SV39 @ SV379 ) )
| ~ ( ord_less_eq_nat @ SV227 @ SV379 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1196]) ).
thf(1391,plain,
! [SV379: nat,SV227: nat,SV39: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV39 @ SV227 ) @ ( plus_plus_nat @ SV39 @ SV379 ) )
= ( ord_less_eq_nat @ SV227 @ SV379 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1196]) ).
thf(1392,plain,
! [SV229: nat,SV41: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV41 @ ( plus_plus_nat @ SV229 @ SV41 ) )
| ( ord_less_eq_nat @ zero_zero_nat @ SV229 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV41 @ ( plus_plus_nat @ SV229 @ SV41 ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV229 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1198]) ).
thf(1393,plain,
! [SV230: nat,SV42: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV42 @ ( plus_plus_nat @ SV42 @ SV230 ) )
| ( ord_less_eq_nat @ zero_zero_nat @ SV230 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV42 @ ( plus_plus_nat @ SV42 @ SV230 ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV230 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1200]) ).
thf(1394,plain,
! [SV231: nat,SV43: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV43 @ SV231 ) @ SV231 )
| ( ord_less_eq_nat @ SV43 @ zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV43 @ SV231 ) @ SV231 )
| ~ ( ord_less_eq_nat @ SV43 @ zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1202]) ).
thf(1395,plain,
! [SV232: nat,SV44: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV44 @ SV232 ) @ SV44 )
| ( ord_less_eq_nat @ SV232 @ zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV44 @ SV232 ) @ SV44 )
| ~ ( ord_less_eq_nat @ SV232 @ zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1204]) ).
thf(1396,plain,
! [SV234: nat,SV46: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV46 @ SV234 ) )
| ( ord_less_nat @ SV234 @ SV46 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV46 @ SV234 ) )
| ~ ( ord_less_nat @ SV234 @ SV46 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1206]) ).
thf(1397,plain,
! [SV235: nat,SV47: nat] :
( ( ( ~ ( ( ( minus_minus_nat @ SV47 @ SV235 )
= zero_zero_nat )
| ( ord_less_eq_nat @ SV47 @ SV235 ) ) )
= $true )
| ( ( ~ ( ( ( minus_minus_nat @ SV47 @ SV235 )
!= zero_zero_nat )
| ~ ( ord_less_eq_nat @ SV47 @ SV235 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1208]) ).
thf(1398,plain,
! [SV388: nat,SV247: nat,SV60: nat] :
( ( ~ ( ( ord_less_nat @ SV60 @ ( minus_minus_nat @ SV247 @ SV388 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV60 @ SV388 ) @ SV247 ) )
| ~ ( ~ ( ord_less_nat @ SV60 @ ( minus_minus_nat @ SV247 @ SV388 ) )
| ~ ( ord_less_nat @ ( plus_plus_nat @ SV60 @ SV388 ) @ SV247 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1217]) ).
thf(1399,plain,
! [SV388: nat,SV247: nat,SV60: nat] :
( ( ( ord_less_nat @ SV60 @ ( minus_minus_nat @ SV247 @ SV388 ) )
= ( ord_less_nat @ ( plus_plus_nat @ SV60 @ SV388 ) @ SV247 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1217]) ).
thf(1400,plain,
! [SV389: nat,SV248: nat,SV61: nat] :
( ( ~ ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV61 @ SV248 ) @ SV389 )
| ( ord_less_eq_nat @ SV61 @ ( plus_plus_nat @ SV389 @ SV248 ) ) )
| ~ ( ~ ( ord_less_eq_nat @ ( minus_minus_nat @ SV61 @ SV248 ) @ SV389 )
| ~ ( ord_less_eq_nat @ SV61 @ ( plus_plus_nat @ SV389 @ SV248 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1218]) ).
thf(1401,plain,
! [SV389: nat,SV248: nat,SV61: nat] :
( ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV61 @ SV248 ) @ SV389 )
= ( ord_less_eq_nat @ SV61 @ ( plus_plus_nat @ SV389 @ SV248 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1218]) ).
thf(1402,plain,
! [SV62: nat] :
( ( ( ( zero_zero_nat = SV62 )
| ( SV62 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( zero_zero_nat != SV62 )
| ( SV62 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1219]) ).
thf(1403,plain,
! [SV479: nat,SV250: nat] :
( ( ( plus_plus_nat @ SV250 @ SV479 )
= ( plus_plus_nat @ SV479 @ SV250 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1404,plain,
! [SV480: nat,SV254: nat] :
( ( ( times_times_nat @ SV254 @ SV480 )
= ( times_times_nat @ SV480 @ SV254 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1405,plain,
! [SV82: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV82 )
| ( SV82 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV82 )
| ( SV82 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1231]) ).
thf(1406,plain,
! [SV83: nat] :
( ( ( ( ord_less_eq_nat @ SV83 @ zero_zero_nat )
| ( SV83 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV83 @ zero_zero_nat )
| ( SV83 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1407,plain,
! [SV84: nat] :
( ( ( ( ord_less_eq_nat @ SV84 @ zero_zero_nat )
| ( SV84 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV84 @ zero_zero_nat )
| ( SV84 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1233]) ).
thf(1408,plain,
! [SV481: nat,SV258: nat] :
( ( ( ord_less_eq_nat @ SV258 @ SV481 )
= ( ( ord_less_nat @ SV258 @ SV481 )
| ( SV258 = SV481 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1234]) ).
thf(1409,plain,
! [SV399: nat,SV261: nat,SV90: nat] :
( ( ~ ( ( ( times_times_nat @ SV90 @ SV261 )
= ( times_times_nat @ SV90 @ SV399 ) )
| ( SV90 = zero_zero_nat )
| ( SV261 = SV399 ) )
| ~ ( ( ( times_times_nat @ SV90 @ SV261 )
!= ( times_times_nat @ SV90 @ SV399 ) )
| ~ ( ( SV90 = zero_zero_nat )
| ( SV261 = SV399 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1238]) ).
thf(1410,plain,
! [SV399: nat,SV261: nat,SV90: nat] :
( ( ( ( times_times_nat @ SV90 @ SV261 )
= ( times_times_nat @ SV90 @ SV399 ) )
= ( ( SV90 = zero_zero_nat )
| ( SV261 = SV399 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1238]) ).
thf(1411,plain,
! [SV400: nat,SV262: nat,SV92: nat > nat] :
( ( ( ~ ! [SY609: nat,SY610: nat] :
( ~ ( ord_less_nat @ SY609 @ SY610 )
| ( ord_less_nat @ ( SV92 @ SY609 ) @ ( SV92 @ SY610 ) ) ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV262 @ SV400 )
| ( ord_less_eq_nat @ ( SV92 @ SV262 ) @ ( SV92 @ SV400 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1412,plain,
! [SV263: nat,SV93: nat] :
( ( ( ord_less_eq_nat @ SV93 @ SV263 )
= $false )
| ( ( ~ ( ( SV93 != SV263 ) )
| ( ord_less_nat @ SV93 @ SV263 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1240]) ).
thf(1413,plain,
! [SV482: nat,SV401: nat,SV264: nat,SV94: nat] :
( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV94 @ SV264 )
| ~ ( ord_less_eq_nat @ SV401 @ SV482 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV94 @ SV401 ) @ ( plus_plus_nat @ SV264 @ SV482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1414,plain,
! [SV402: nat,SV265: nat,SV95: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV95 @ SV265 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV402 @ SV265 )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV265 @ SV95 ) @ ( minus_minus_nat @ SV265 @ SV402 ) )
= ( ord_less_eq_nat @ SV402 @ SV95 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1242]) ).
thf(1415,plain,
! [SV403: nat,SV266: nat,SV96: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV96 @ SV266 ) )
= $true )
| ( ( ( minus_minus_nat @ SV403 @ ( minus_minus_nat @ SV266 @ SV96 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ SV403 @ SV96 ) @ SV266 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1243]) ).
thf(1416,plain,
! [SV267: nat,SV97: nat] :
( ( ( ord_less_eq_nat @ SV97 @ SV267 )
= $false )
| ( ( ( plus_plus_nat @ ( minus_minus_nat @ SV267 @ SV97 ) @ SV97 )
= SV267 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1244]) ).
thf(1417,plain,
! [SV483: nat,SV404: nat,SV268: nat,SV98: nat] :
( ( ~ ~ ( ( SV98 != SV268 )
| ~ ( ord_less_eq_nat @ SV404 @ SV483 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV98 @ SV404 ) @ ( plus_plus_nat @ SV268 @ SV483 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1418,plain,
! [SV484: nat,SV405: nat,SV269: nat,SV99: nat] :
( ( ! [SY1031: nat] :
( ~ ( ord_less_eq_nat @ SV99 @ SV269 )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV269 @ SV405 ) @ SV484 ) @ ( plus_plus_nat @ ( times_times_nat @ SV99 @ SV405 ) @ SY1031 ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV269 @ SV99 ) @ SV405 ) @ SV484 ) @ SY1031 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1419,plain,
! [SV406: nat,SV270: nat,SV100: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV100 @ SV270 ) )
= $true )
| ( ( ( minus_minus_nat @ ( plus_plus_nat @ SV406 @ SV270 ) @ SV100 )
= ( plus_plus_nat @ SV406 @ ( minus_minus_nat @ SV270 @ SV100 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1247]) ).
thf(1420,plain,
! [SV407: nat,SV271: nat,SV101: nat] :
( ( ( ~ ( ord_less_nat @ SV101 @ SV271 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV101 @ SV407 ) @ ( plus_plus_nat @ SV271 @ SV407 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1248]) ).
thf(1421,plain,
! [SV102: nat] :
( ( ( ( SV102 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV102 ) )
= $false )
| ( ( ~ ( ~ ( ( SV102 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV102 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1249]) ).
thf(1422,plain,
! [SV272: nat,SV103: nat] :
( ( ( ord_less_nat @ SV103 @ SV272 )
= $false )
| ( ( SV103 != SV272 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1250]) ).
thf(1423,plain,
! [SV273: nat,SV104: nat] :
( ( ( ( plus_plus_nat @ SV104 @ SV273 )
= SV104 )
= $false )
| ( ( SV273 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1251]) ).
thf(1424,plain,
! [SV485: nat,SV408: nat,SV274: nat,SV105: nat] :
( ( ~ ( ord_less_nat @ SV105 @ SV274 )
| ~ ( ord_less_nat @ SV408 @ SV485 )
| ( ord_less_nat @ ( plus_plus_nat @ SV105 @ SV408 ) @ ( plus_plus_nat @ SV274 @ SV485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1425,plain,
! [SV409: nat,SV275: nat,SV106: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV106 @ SV275 ) @ SV409 ) )
= $true )
| ( ( ord_less_nat @ SV106 @ SV409 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1253]) ).
thf(1426,plain,
! [SV486: nat,SV410: nat,SV276: nat,SV107: nat] :
( ( ! [SY1032: nat] :
( ~ ( ord_less_eq_nat @ SV107 @ SV276 )
| ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ SV107 @ SV410 ) @ SV486 ) @ ( plus_plus_nat @ ( times_times_nat @ SV276 @ SV410 ) @ SY1032 ) )
= ( minus_minus_nat @ SV486 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV276 @ SV107 ) @ SV410 ) @ SY1032 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1427,plain,
! [SV411: nat,SV277: nat,SV108: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV108 @ SV277 ) )
= $true )
| ( ( ( minus_minus_nat @ ( plus_plus_nat @ SV277 @ SV411 ) @ SV108 )
= ( plus_plus_nat @ ( minus_minus_nat @ SV277 @ SV108 ) @ SV411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1255]) ).
thf(1428,plain,
! [SV487: nat,SV412: nat,SV278: nat,SV109: nat] :
( ( ~ ~ ( ~ ( ord_less_nat @ SV109 @ SV278 )
| ~ ( ord_less_nat @ SV412 @ SV487 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV109 @ SV412 ) @ ( plus_plus_nat @ SV278 @ SV487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1429,plain,
! [SV413: nat,SV279: nat,SV110: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV110 @ SV279 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV110 @ SV413 )
| ( ( ( minus_minus_nat @ SV279 @ SV110 )
= ( minus_minus_nat @ SV413 @ SV110 ) )
= ( SV279 = SV413 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1257]) ).
thf(1430,plain,
! [SV414: nat,SV280: nat,SV111: nat] :
( ( ( ~ ( ord_less_nat @ SV111 @ SV280 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV414 @ SV111 ) @ ( plus_plus_nat @ SV414 @ SV280 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1258]) ).
thf(1431,plain,
! [SV281: nat,SV112: nat] :
( ( ( ( minus_minus_nat @ SV112 @ SV281 )
= zero_zero_nat )
= $false )
| ( ( ( ( minus_minus_nat @ SV281 @ SV112 )
!= zero_zero_nat )
| ( SV112 = SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1259]) ).
thf(1432,plain,
! [SV415: nat,SV282: nat,SV113: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV113 @ SV282 ) )
= $true )
| ( ( ( ord_less_eq_nat @ SV415 @ ( minus_minus_nat @ SV282 @ SV113 ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ SV415 @ SV113 ) @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1260]) ).
thf(1433,plain,
! [SV283: nat,SV114: nat > $o] :
( ( ( SV114 @ zero_zero_nat )
= $false )
| ( ( ~ ! [SY655: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY655 )
| ~ ~ ( SV114 @ SY655 )
| ~ ! [SY656: nat] :
~ ~ ( ~ ( ord_less_nat @ SY656 @ SY655 )
| ~ ~ ( SV114 @ SY656 ) ) )
| ( SV114 @ SV283 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1261]) ).
thf(1434,plain,
! [SV115: nat] :
( ( ( ( SV115 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV115 ) )
= $false )
| ( ( ~ ( ~ ( ( SV115 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV115 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1262]) ).
thf(1435,plain,
! [SV416: nat,SV284: nat,SV116: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV116 @ SV284 ) )
= $true )
| ( ( ( plus_plus_nat @ SV416 @ ( minus_minus_nat @ SV284 @ SV116 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ SV416 @ SV284 ) @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1263]) ).
thf(1436,plain,
! [SV417: nat,SV285: nat,SV117: nat > $o] :
( ( ~ ( ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) )
| ~ ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1264]) ).
thf(1437,plain,
! [SV417: nat,SV285: nat,SV117: nat > $o] :
( ( ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
= ( ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1264]) ).
thf(1438,plain,
! [SV418: nat,SV286: nat,SV118: nat] :
( ( ( ~ ( ord_less_nat @ SV118 @ SV286 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV118 @ SV418 )
| ( ord_less_nat @ ( minus_minus_nat @ SV418 @ SV286 ) @ ( minus_minus_nat @ SV418 @ SV118 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1265]) ).
thf(1439,plain,
! [SV287: nat,SV119: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV119 )
= $false )
| ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV287 )
| ( ord_less_nat @ ( minus_minus_nat @ SV287 @ SV119 ) @ SV287 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1266]) ).
thf(1440,plain,
! [SV488: nat,SV288: nat] :
( ( ( ord_less_eq_nat @ SV288 @ SV488 )
= ( ~ ! [SY1033: nat] :
( SV488
!= ( plus_plus_nat @ SV288 @ SY1033 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1441,plain,
! [SV489: nat,SV289: nat] :
( ( ( ord_less_eq_nat @ SV289 @ SV489 )
= ( ~ ! [SY1034: nat] :
( SV489
!= ( plus_plus_nat @ SV289 @ SY1034 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1442,plain,
! [SV421: nat,SV290: nat,SV122: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV122 @ SV290 ) )
= $true )
| ( ( ( ( minus_minus_nat @ SV290 @ SV122 )
= SV421 )
= ( SV290
= ( plus_plus_nat @ SV421 @ SV122 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1271]) ).
thf(1443,plain,
! [SV490: nat,SV422: nat,SV291: nat,SV123: nat] :
( ( ! [SY1035: nat] :
( ~ ( ord_less_eq_nat @ SV123 @ SV291 )
| ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ SV291 @ SV422 ) @ SV490 ) @ ( plus_plus_nat @ ( times_times_nat @ SV123 @ SV422 ) @ SY1035 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV291 @ SV123 ) @ SV422 ) @ SV490 ) @ SY1035 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1444,plain,
! [SV423: nat,SV292: nat,SV124: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV124 @ SV292 ) )
= $true )
| ( ( ord_less_eq_nat @ SV423 @ ( minus_minus_nat @ ( plus_plus_nat @ SV292 @ SV423 ) @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1273]) ).
thf(1445,plain,
! [SV424: nat,SV293: nat,SV125: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SV293 ) @ ( plus_plus_nat @ SV424 @ SV293 ) ) )
= $true )
| ( ( ord_less_nat @ SV125 @ SV424 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1274]) ).
thf(1446,plain,
! [SV294: nat,SV126: nat] :
( ( ( ~ ( ( ( plus_plus_nat @ SV126 @ SV294 )
= zero_zero_nat )
| ~ ( ( SV126 != zero_zero_nat )
| ( SV294 != zero_zero_nat ) ) ) )
= $true )
| ( ( ~ ( ( ( plus_plus_nat @ SV126 @ SV294 )
!= zero_zero_nat )
| ~ ~ ( ( SV126 != zero_zero_nat )
| ( SV294 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1275]) ).
thf(1447,plain,
! [SV491: nat,SV425: nat,SV295: nat,SV127: nat] :
( ( ! [SY1036: nat] :
( ~ ( ord_less_eq_nat @ SV127 @ SV295 )
| ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV127 @ SV425 ) @ SV491 ) @ ( plus_plus_nat @ ( times_times_nat @ SV295 @ SV425 ) @ SY1036 ) )
= ( ord_less_nat @ SV491 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV295 @ SV127 ) @ SV425 ) @ SY1036 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1448,plain,
! [SV426: nat,SV296: nat,SV128: nat] :
( ( ( ~ ( ord_less_nat @ SV128 @ SV296 ) )
= $true )
| ( ( ord_less_nat @ ( minus_minus_nat @ SV128 @ SV426 ) @ SV296 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1278]) ).
thf(1449,plain,
! [SV427: nat,SV297: nat,SV129: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV129 @ SV297 ) )
= $true )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV427 @ SV297 ) @ ( minus_minus_nat @ SV427 @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1279]) ).
thf(1450,plain,
! [SV428: nat,SV298: nat,SV130: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV130 @ SV298 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV130 @ SV428 ) @ ( plus_plus_nat @ SV298 @ SV428 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1280]) ).
thf(1451,plain,
! [SV299: nat,SV131: nat] :
( ( ( ord_less_nat @ SV131 @ SV299 )
= $false )
| ( ( SV299 != SV131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1452,plain,
! [SV492: nat,SV429: nat,SV300: nat,SV132: nat] :
( ( ~ ( ord_less_nat @ SV132 @ SV300 )
| ( ( plus_plus_nat @ SV429 @ SV300 )
!= ( plus_plus_nat @ SV132 @ SV492 ) )
| ( ord_less_nat @ SV429 @ SV492 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1453,plain,
! [SV430: nat,SV301: nat,SV133: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV133 @ SV301 ) )
= $true )
| ( ( ord_less_eq_nat @ SV133 @ ( plus_plus_nat @ SV430 @ SV301 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1283]) ).
thf(1454,plain,
! [SV134: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ SV134 )
| ( SV134 != zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV134 )
| ~ ( ( SV134 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1284]) ).
thf(1455,plain,
! [SV431: nat,SV302: nat,SV135: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV135 @ SV302 ) )
= $true )
| ( ( ( minus_minus_nat @ SV431 @ ( minus_minus_nat @ SV302 @ SV135 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ SV431 @ SV135 ) @ SV302 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1285]) ).
thf(1456,plain,
! [SV432: nat,SV303: nat,SV136: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV136 @ SV303 ) )
= $true )
| ( ( ( minus_minus_nat @ ( plus_plus_nat @ SV432 @ SV303 ) @ SV136 )
= ( plus_plus_nat @ SV432 @ ( minus_minus_nat @ SV303 @ SV136 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1286]) ).
thf(1457,plain,
! [SV493: nat,SV433: nat,SV304: nat,SV137: nat] :
( ( ~ ( ord_less_eq_nat @ SV137 @ SV304 )
| ~ ( ord_less_eq_nat @ SV433 @ SV493 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV137 @ SV433 ) @ ( plus_plus_nat @ SV304 @ SV493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1458,plain,
! [SV434: nat,SV305: nat,SV138: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV138 @ SV305 ) )
= $true )
| ( ( ( minus_minus_nat @ ( plus_plus_nat @ SV305 @ SV434 ) @ SV138 )
= ( plus_plus_nat @ ( minus_minus_nat @ SV305 @ SV138 ) @ SV434 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1288]) ).
thf(1459,plain,
! [SV435: nat,SV306: nat,SV139: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV139 @ SV306 ) @ ( plus_plus_nat @ SV139 @ SV435 ) ) )
= $true )
| ( ( ord_less_nat @ SV306 @ SV435 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1289]) ).
thf(1460,plain,
! [SV436: nat,SV307: nat,SV140: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV140 @ SV307 ) @ ( plus_plus_nat @ SV436 @ SV307 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV140 @ SV436 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1290]) ).
thf(1461,plain,
! [SV437: nat,SV308: nat,SV141: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV141 @ SV308 ) )
= $true )
| ( ( ( plus_plus_nat @ ( minus_minus_nat @ SV308 @ SV141 ) @ SV437 )
= ( minus_minus_nat @ ( plus_plus_nat @ SV308 @ SV437 ) @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1291]) ).
thf(1462,plain,
! [SV309: nat,SV142: nat > $o] :
( ( ( ! [SY712: nat] :
( ~ ~ ( SV142 @ SY712 )
| ~ ! [SY713: nat] :
~ ~ ( ~ ( ord_less_nat @ SY713 @ SY712 )
| ~ ~ ( SV142 @ SY713 ) ) ) )
= $false )
| ( ( SV142 @ SV309 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1292]) ).
thf(1463,plain,
! [SV438: nat,SV310: nat,SV143: nat] :
( ( ( ( plus_plus_nat @ SV143 @ SV310 )
!= ( plus_plus_nat @ SV438 @ SV310 ) )
= $true )
| ( ( SV143 = SV438 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1293]) ).
thf(1464,plain,
! [SV439: nat,SV311: nat,SV144: nat] :
( ( ( ~ ( ord_less_nat @ SV144 @ SV311 ) )
= $true )
| ( ( ord_less_nat @ SV144 @ ( plus_plus_nat @ SV311 @ SV439 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1294]) ).
thf(1465,plain,
! [SV312: nat,SV145: nat] :
( ( ( SV145 = SV312 )
= $false )
| ( ( ord_less_eq_nat @ SV145 @ SV312 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1466,plain,
! [SV494: nat,SV440: nat,SV313: nat,SV146: nat] :
( ( ! [SY1037: nat] :
( ~ ( ord_less_eq_nat @ SV146 @ SV313 )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV146 @ SV440 ) @ SV494 ) @ ( plus_plus_nat @ ( times_times_nat @ SV313 @ SV440 ) @ SY1037 ) )
= ( ord_less_eq_nat @ SV494 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV313 @ SV146 ) @ SV440 ) @ SY1037 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1467,plain,
! [SV441: nat,SV314: nat,SV147: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV147 @ SV314 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV147 @ SV441 ) @ ( plus_plus_nat @ SV314 @ SV441 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1297]) ).
thf(1468,plain,
! [SV495: nat,SV442: nat,SV315: nat,SV148: nat] :
( ( ~ ~ ( ~ ( ord_less_nat @ SV148 @ SV315 )
| ( SV442 != SV495 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV148 @ SV442 ) @ ( plus_plus_nat @ SV315 @ SV495 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1298]) ).
thf(1469,plain,
! [SV316: nat,SV149: nat] :
( ( ( ord_less_nat @ SV149 @ SV316 )
= $false )
| ( ( ord_less_eq_nat @ SV149 @ SV316 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1299]) ).
thf(1470,plain,
! [SV496: nat,SV443: nat,SV317: nat,SV150: nat] :
( ( ~ ( ord_less_nat @ SV150 @ SV317 )
| ~ ( ord_less_nat @ SV443 @ SV496 )
| ( ord_less_nat @ ( plus_plus_nat @ SV150 @ SV443 ) @ ( plus_plus_nat @ SV317 @ SV496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1471,plain,
! [SV151: nat] :
( ( ( SV151 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV151 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1301]) ).
thf(1472,plain,
! [SV444: nat,SV318: nat,SV152: nat] :
( ( ~ ( ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV318 )
| ~ ( ord_less_nat @ SV152 @ SV444 ) ) )
| ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV318 )
| ~ ( ord_less_nat @ SV152 @ SV444 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1302]) ).
thf(1473,plain,
! [SV444: nat,SV318: nat,SV152: nat] :
( ( ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
= ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV318 )
| ~ ( ord_less_nat @ SV152 @ SV444 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1302]) ).
thf(1474,plain,
! [SV319: nat,SV153: nat] :
( ( ( ~ ( ord_less_nat @ SV153 @ SV319 ) )
= $false )
| ( ( ( plus_plus_nat @ SV319 @ ( minus_minus_nat @ SV153 @ SV319 ) )
= SV153 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1303]) ).
thf(1475,plain,
! [SV320: nat,SV154: nat] :
( ( ( ord_less_nat @ SV154 @ SV320 )
= $false )
| ( ( SV320 != zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1304]) ).
thf(1476,plain,
! [SV321: nat,SV155: nat] :
( ( ( ~ ( ( SV155 != SV321 )
| ( ord_less_nat @ SV155 @ SV321 )
| ( ord_less_nat @ SV321 @ SV155 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV155 != SV321 ) )
| ~ ( ( ord_less_nat @ SV155 @ SV321 )
| ( ord_less_nat @ SV321 @ SV155 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1305]) ).
thf(1477,plain,
! [SV322: nat,SV156: nat] :
( ( ( ord_less_nat @ SV156 @ SV322 )
= $false )
| ( ( SV322 != zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1307]) ).
thf(1478,plain,
! [SV445: nat,SV323: nat,SV157: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV157 @ SV323 ) )
= $true )
| ( ( ( plus_plus_nat @ SV445 @ ( minus_minus_nat @ SV323 @ SV157 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ SV445 @ SV323 ) @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1308]) ).
thf(1479,plain,
! [SV446: nat,SV324: nat,SV158: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV158 @ SV324 ) )
= $true )
| ( ( ( plus_plus_nat @ ( minus_minus_nat @ SV324 @ SV158 ) @ SV446 )
= ( minus_minus_nat @ ( plus_plus_nat @ SV324 @ SV446 ) @ SV158 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1309]) ).
thf(1480,plain,
! [SV325: nat,SV159: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV159 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV325 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV159 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV325 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1310]) ).
thf(1481,plain,
! [SV326: nat,SV160: nat] :
( ( ( ~ ( ( ( plus_plus_nat @ SV160 @ SV326 )
= zero_zero_nat )
| ~ ( ( SV160 != zero_zero_nat )
| ( SV326 != zero_zero_nat ) ) ) )
= $true )
| ( ( ~ ( ( ( plus_plus_nat @ SV160 @ SV326 )
!= zero_zero_nat )
| ~ ~ ( ( SV160 != zero_zero_nat )
| ( SV326 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1312]) ).
thf(1482,plain,
! [SV497: nat,SV327: nat] :
( ( ( ord_less_nat @ SV327 @ SV497 )
= ( ~ ( ~ ( ord_less_eq_nat @ SV327 @ SV497 )
| ~ ( ( SV327 != SV497 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1483,plain,
! [SV328: nat,SV162: nat] :
( ( ( ~ ( ( zero_zero_nat
= ( plus_plus_nat @ SV162 @ SV328 ) )
| ~ ( ( SV162 != zero_zero_nat )
| ( SV328 != zero_zero_nat ) ) ) )
= $true )
| ( ( ~ ( ( zero_zero_nat
!= ( plus_plus_nat @ SV162 @ SV328 ) )
| ~ ~ ( ( SV162 != zero_zero_nat )
| ( SV328 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1316]) ).
thf(1484,plain,
! [SV448: nat,SV329: nat,SV163: nat] :
( ( ~ ( ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV329 )
| ( ord_less_eq_nat @ SV163 @ SV448 ) )
| ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV329 )
| ( ord_less_eq_nat @ SV163 @ SV448 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1318]) ).
thf(1485,plain,
! [SV448: nat,SV329: nat,SV163: nat] :
( ( ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) )
= ( ~ ( ord_less_nat @ zero_zero_nat @ SV329 )
| ( ord_less_eq_nat @ SV163 @ SV448 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1318]) ).
thf(1486,plain,
! [SV449: nat,SV330: nat,SV164: nat > $o] :
( ( ( ~ ( SV164 @ SV330 ) )
= $true )
| ( ( ~ ! [SY1015: nat] :
( ~ ( SV164 @ SY1015 )
| ( ord_less_eq_nat @ SY1015 @ SV449 ) )
| ~ ! [SY751: nat] :
~ ~ ( ~ ( SV164 @ SY751 )
| ~ ! [SY752: nat] :
( ~ ( SV164 @ SY752 )
| ( ord_less_eq_nat @ SY752 @ SY751 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1319]) ).
thf(1487,plain,
! [SV450: nat,SV331: nat,SV166: nat] :
( ( ( ~ ( ord_less_nat @ SV166 @ SV331 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV166 @ SV450 ) @ ( plus_plus_nat @ SV331 @ SV450 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1321]) ).
thf(1488,plain,
! [SV451: nat,SV332: nat,SV167: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV167 @ SV332 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV167 @ SV451 )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV332 @ SV167 ) @ ( minus_minus_nat @ SV451 @ SV167 ) )
= ( ord_less_eq_nat @ SV332 @ SV451 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1322]) ).
thf(1489,plain,
! [SV452: nat,SV333: nat,SV168: nat] :
( ( ( ( plus_plus_nat @ SV168 @ SV333 )
!= SV452 )
= $true )
| ( ( SV168
= ( minus_minus_nat @ SV452 @ SV333 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1323]) ).
thf(1490,plain,
! [SV453: nat,SV334: nat,SV169: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV169 @ SV334 ) )
= $true )
| ( ( ( ord_less_nat @ ( minus_minus_nat @ SV334 @ SV169 ) @ SV453 )
= ( ord_less_nat @ SV334 @ ( plus_plus_nat @ SV453 @ SV169 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1324]) ).
thf(1491,plain,
! [SV498: nat,SV454: nat,SV335: nat,SV170: nat] :
( ( ( SV170
!= ( plus_plus_nat @ SV335 @ SV454 ) )
| ( ( plus_plus_nat @ SV170 @ SV498 )
= ( plus_plus_nat @ SV335 @ ( plus_plus_nat @ SV454 @ SV498 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1492,plain,
! [SV455: nat,SV336: nat,SV171: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV171 @ SV336 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV171 @ SV455 )
| ( ( minus_minus_nat @ ( minus_minus_nat @ SV336 @ SV171 ) @ ( minus_minus_nat @ SV455 @ SV171 ) )
= ( minus_minus_nat @ SV336 @ SV455 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1326]) ).
thf(1493,plain,
! [SV456: nat,SV337: nat,SV172: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV172 @ SV337 ) )
= $true )
| ( ( ord_less_eq_nat @ SV172 @ ( plus_plus_nat @ SV337 @ SV456 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1327]) ).
thf(1494,plain,
! [SV173: nat] :
( ( ( SV173 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV173 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1328]) ).
thf(1495,plain,
! [SV499: nat,SV457: nat,SV338: nat,SV174: nat] :
( ( ! [SY1038: nat] :
( ~ ( ord_less_eq_nat @ SV174 @ SV338 )
| ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV338 @ SV457 ) @ SV499 ) @ ( plus_plus_nat @ ( times_times_nat @ SV174 @ SV457 ) @ SY1038 ) )
= ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV338 @ SV174 ) @ SV457 ) @ SV499 ) @ SY1038 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1496,plain,
! [SV500: nat,SV458: nat,SV339: nat,SV175: nat] :
( ( ( SV175
!= ( plus_plus_nat @ SV339 @ SV458 ) )
| ( ( plus_plus_nat @ SV500 @ SV175 )
= ( plus_plus_nat @ SV339 @ ( plus_plus_nat @ SV500 @ SV458 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1330]) ).
thf(1497,plain,
! [SV340: nat,SV176: nat] :
( ( ( ord_less_eq_nat @ SV176 @ SV340 )
= $false )
| ( ( ( plus_plus_nat @ SV176 @ ( minus_minus_nat @ SV340 @ SV176 ) )
= SV340 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1331]) ).
thf(1498,plain,
! [SV459: nat,SV341: nat,SV177: nat] :
( ( ~ ( ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 )
| ~ ( ord_less_nat @ SV341 @ SV459 ) ) )
| ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 )
| ~ ( ord_less_nat @ SV341 @ SV459 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1332]) ).
thf(1499,plain,
! [SV459: nat,SV341: nat,SV177: nat] :
( ( ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
= ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 )
| ~ ( ord_less_nat @ SV341 @ SV459 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1332]) ).
thf(1500,plain,
! [SV342: nat,SV178: nat] :
( ( ( SV178 != SV342 )
= $false )
| ( ( ~ ~ ( ord_less_nat @ SV178 @ SV342 )
| ( ord_less_nat @ SV342 @ SV178 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1333]) ).
thf(1501,plain,
! [SV460: nat,SV343: nat,SV179: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV179 @ SV343 ) )
= $true )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV179 @ SV460 ) @ ( minus_minus_nat @ SV343 @ SV460 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1334]) ).
thf(1502,plain,
! [SV344: nat,SV180: nat] :
( ( ( ord_less_eq_nat @ SV180 @ SV344 )
= $false )
| ( ( ( minus_minus_nat @ SV180 @ SV344 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1335]) ).
thf(1503,plain,
! [SV345: nat,SV181: nat > $o] :
( ( ( ! [SY783: nat] :
( ~ ! [SY784: nat] :
( ~ ( ord_less_nat @ SY784 @ SY783 )
| ( SV181 @ SY784 ) )
| ( SV181 @ SY783 ) ) )
= $false )
| ( ( SV181 @ SV345 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1336]) ).
thf(1504,plain,
! [SV461: nat,SV346: nat,SV182: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV182 @ SV346 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV182 @ SV346 )
| ( ( ( minus_minus_nat @ SV346 @ SV182 )
= SV461 )
= ( SV346
= ( plus_plus_nat @ SV461 @ SV182 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1337]) ).
thf(1505,plain,
! [SV462: nat,SV347: nat,SV183: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV183 @ SV347 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV462 @ SV183 ) @ ( plus_plus_nat @ SV462 @ SV347 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1338]) ).
thf(1506,plain,
! [SV463: nat,SV348: nat,SV184: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV184 @ SV348 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV184 @ SV463 )
| ( ( ord_less_nat @ ( minus_minus_nat @ SV348 @ SV184 ) @ ( minus_minus_nat @ SV463 @ SV184 ) )
= ( ord_less_nat @ SV348 @ SV463 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1339]) ).
thf(1507,plain,
! [SV464: nat,SV349: nat,SV185: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV185 @ SV349 ) )
= $true )
| ( ( ( ord_less_eq_nat @ SV464 @ ( minus_minus_nat @ SV349 @ SV185 ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ SV464 @ SV185 ) @ SV349 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1340]) ).
thf(1508,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ~ ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) )
| ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1341]) ).
thf(1509,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= ( ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1341]) ).
thf(1510,plain,
! [SV466: nat,SV351: nat,SV187: nat] :
( ( ( ( plus_plus_nat @ SV187 @ SV351 )
!= ( plus_plus_nat @ SV187 @ SV466 ) )
= $true )
| ( ( SV351 = SV466 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1342]) ).
thf(1511,plain,
! [SV467: nat,SV352: nat,SV188: nat] :
( ( ( ~ ( ord_less_nat @ SV188 @ SV352 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV467 @ SV188 )
| ( ord_less_nat @ ( minus_minus_nat @ SV188 @ SV467 ) @ ( minus_minus_nat @ SV352 @ SV467 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1343]) ).
thf(1512,plain,
! [SV353: nat,SV189: nat] :
( ( ( ord_less_eq_nat @ SV189 @ SV353 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV353 @ SV189 )
| ( SV189 = SV353 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1344]) ).
thf(1513,plain,
! [SV501: nat,SV468: nat,SV354: nat,SV190: nat] :
( ( ! [SY1039: nat] :
( ~ ( ord_less_eq_nat @ SV190 @ SV354 )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SV354 @ SV468 ) @ SV501 )
= ( plus_plus_nat @ ( times_times_nat @ SV190 @ SV468 ) @ SY1039 ) )
= ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV354 @ SV190 ) @ SV468 ) @ SV501 )
= SY1039 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1345]) ).
thf(1514,plain,
! [SV355: nat,SV191: nat] :
( ( ( ord_less_eq_nat @ SV191 @ SV355 )
= $false )
| ( ( ~ ! [SY975: nat] :
( SV355
!= ( plus_plus_nat @ SV191 @ SY975 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1346]) ).
thf(1515,plain,
! [SV502: nat,SV469: nat,SV356: nat,SV192: nat] :
( ( ~ ~ ( ( SV192 != SV356 )
| ~ ( ord_less_nat @ SV469 @ SV502 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV192 @ SV469 ) @ ( plus_plus_nat @ SV356 @ SV502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1347]) ).
thf(1516,plain,
! [SV503: nat,SV470: nat,SV357: nat,SV193: nat] :
( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV193 @ SV357 )
| ( SV470 != SV503 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV193 @ SV470 ) @ ( plus_plus_nat @ SV357 @ SV503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1348]) ).
thf(1517,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ~ ( ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV194 )
| ( ord_less_eq_nat @ SV358 @ SV471 ) )
| ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV194 )
| ( ord_less_eq_nat @ SV358 @ SV471 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1349]) ).
thf(1518,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) )
= ( ~ ( ord_less_nat @ zero_zero_nat @ SV194 )
| ( ord_less_eq_nat @ SV358 @ SV471 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1349]) ).
thf(1519,plain,
! [SV472: nat,SV359: nat,SV195: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV195 @ SV359 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV359 @ SV472 )
| ( ord_less_eq_nat @ SV195 @ SV472 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1350]) ).
thf(1520,plain,
! [SV504: nat,SV473: nat,SV360: nat,SV196: nat] :
( ( ~ ~ ( ( SV196 != SV360 )
| ( SV473 != SV504 ) )
| ( ( plus_plus_nat @ SV196 @ SV473 )
= ( plus_plus_nat @ SV360 @ SV504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1351]) ).
thf(1521,plain,
! [SV505: nat,SV474: nat,SV361: nat,SV197: nat] :
( ( ! [SY1040: nat] :
( ~ ( ord_less_eq_nat @ SV197 @ SV361 )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SV197 @ SV474 ) @ SV505 )
= ( plus_plus_nat @ ( times_times_nat @ SV361 @ SV474 ) @ SY1040 ) )
= ( SV505
= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV361 @ SV197 ) @ SV474 ) @ SY1040 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1352]) ).
thf(1522,plain,
! [SV506: nat,SV475: nat,SV362: nat,SV198: nat] :
( ( ~ ( ord_less_eq_nat @ SV198 @ SV362 )
| ~ ( ord_less_eq_nat @ SV475 @ SV506 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV198 @ SV475 ) @ ( plus_plus_nat @ SV362 @ SV506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1353]) ).
thf(1523,plain,
! [SV476: nat,SV363: nat,SV199: nat] :
( ( ( ~ ( ord_less_nat @ SV199 @ SV363 ) )
= $true )
| ( ( ord_less_nat @ SV199 @ ( plus_plus_nat @ SV476 @ SV363 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1354]) ).
thf(1524,plain,
! [SV364: nat,SV200: nat] :
( ( ( ( ord_less_nat @ SV200 @ SV364 )
| ( SV200 = SV364 ) )
= $false )
| ( ( ord_less_eq_nat @ SV200 @ SV364 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1355]) ).
thf(1525,plain,
! [SV477: nat,SV365: nat,SV201: nat > nat] :
( ( ( ~ ( number1551313001itions @ SV201 @ SV365 ) )
= $true )
| ( ( ord_less_eq_nat @ ( SV201 @ SV477 ) @ SV365 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1356]) ).
thf(1526,plain,
! [SV366: nat,SV202: nat] :
( ( ( ord_less_eq_nat @ SV202 @ SV366 )
= $false )
| ( ( ( minus_minus_nat @ SV366 @ ( minus_minus_nat @ SV366 @ SV202 ) )
= SV202 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1357]) ).
thf(1527,plain,
! [SV478: nat,SV367: nat,SV203: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV203 @ SV367 ) @ ( plus_plus_nat @ SV203 @ SV478 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV367 @ SV478 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1358]) ).
thf(1528,plain,
! [SV1: nat > nat] :
( ( ( number1551313001itions @ SV1 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( number1551313001itions @ SV1 @ zero_zero_nat )
| ( SV1
!= ( ^ [I: nat] : zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1359]) ).
thf(1529,plain,
! [SV1: nat > nat] :
( ( ( SV1
= ( ^ [I: nat] : zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( number1551313001itions @ SV1 @ zero_zero_nat )
| ( SV1
!= ( ^ [I: nat] : zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1359]) ).
thf(1530,plain,
! [SV204: nat,SV2: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SV204 ) )
| ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( ord_less_nat @ zero_zero_nat @ SV204 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SV204 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( ord_less_nat @ zero_zero_nat @ SV204 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1360]) ).
thf(1531,plain,
! [SV205: nat,SV3: nat] :
( ( ( ( ord_less_nat @ ( plus_plus_nat @ SV3 @ SV205 ) @ SV3 )
| ( ord_less_nat @ SV205 @ zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV3 @ SV205 ) @ SV3 )
| ~ ( ord_less_nat @ SV205 @ zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1361]) ).
thf(1532,plain,
! [SV206: nat,SV4: nat] :
( ( ( ( ord_less_nat @ ( plus_plus_nat @ SV4 @ SV206 ) @ SV206 )
| ( ord_less_nat @ SV4 @ zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV4 @ SV206 ) @ SV206 )
| ~ ( ord_less_nat @ SV4 @ zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1362]) ).
thf(1533,plain,
! [SV207: nat,SV5: nat] :
( ( ( ( ord_less_nat @ SV5 @ ( plus_plus_nat @ SV5 @ SV207 ) )
| ( ord_less_nat @ zero_zero_nat @ SV207 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV5 @ ( plus_plus_nat @ SV5 @ SV207 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV207 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1534,plain,
! [SV208: nat,SV6: nat] :
( ( ( ( ord_less_nat @ SV6 @ ( plus_plus_nat @ SV208 @ SV6 ) )
| ( ord_less_nat @ zero_zero_nat @ SV208 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV6 @ ( plus_plus_nat @ SV208 @ SV6 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV208 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1364]) ).
thf(1535,plain,
! [SV368: nat,SV209: nat,SV7: nat] :
( ( ( ~ ( ( ( plus_plus_nat @ SV7 @ SV209 )
= ( plus_plus_nat @ SV368 @ SV209 ) )
| ( SV7 = SV368 ) ) )
= $true )
| ( ( ~ ( ( ( plus_plus_nat @ SV7 @ SV209 )
!= ( plus_plus_nat @ SV368 @ SV209 ) )
| ( SV7 != SV368 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1365]) ).
thf(1536,plain,
! [SV369: nat,SV210: nat,SV8: nat] :
( ( ( ~ ( ( ( plus_plus_nat @ SV8 @ SV210 )
= ( plus_plus_nat @ SV8 @ SV369 ) )
| ( SV210 = SV369 ) ) )
= $true )
| ( ( ~ ( ( ( plus_plus_nat @ SV8 @ SV210 )
!= ( plus_plus_nat @ SV8 @ SV369 ) )
| ( SV210 != SV369 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1367]) ).
thf(1537,plain,
! [SV9: nat] :
( ( ( ord_less_eq_nat @ SV9 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV9 @ zero_zero_nat )
| ( SV9 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1369]) ).
thf(1538,plain,
! [SV9: nat] :
( ( ( SV9 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV9 @ zero_zero_nat )
| ( SV9 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1369]) ).
thf(1539,plain,
! [SV10: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV10 ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV10 )
| ( SV10 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1370]) ).
thf(1540,plain,
! [SV10: nat] :
( ( ( SV10 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV10 )
| ( SV10 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1370]) ).
thf(1541,plain,
! [SV370: nat,SV211: nat,SV11: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV11 @ SV211 ) @ ( plus_plus_nat @ SV370 @ SV211 ) )
| ( ord_less_eq_nat @ SV11 @ SV370 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV11 @ SV211 ) @ ( plus_plus_nat @ SV370 @ SV211 ) )
| ~ ( ord_less_eq_nat @ SV11 @ SV370 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1371]) ).
thf(1542,plain,
! [SV371: nat,SV212: nat,SV12: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV212 ) @ ( plus_plus_nat @ SV12 @ SV371 ) )
| ( ord_less_eq_nat @ SV212 @ SV371 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV212 ) @ ( plus_plus_nat @ SV12 @ SV371 ) )
| ~ ( ord_less_eq_nat @ SV212 @ SV371 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1373]) ).
thf(1543,plain,
! [SV213: nat,SV13: nat] :
( ( ( ( SV13
= ( plus_plus_nat @ SV13 @ SV213 ) )
| ( SV213 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( SV13
!= ( plus_plus_nat @ SV13 @ SV213 ) )
| ( SV213 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1375]) ).
thf(1544,plain,
! [SV214: nat,SV14: nat] :
( ( ( ( SV14
= ( plus_plus_nat @ SV214 @ SV14 ) )
| ( SV214 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( SV14
!= ( plus_plus_nat @ SV214 @ SV14 ) )
| ( SV214 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1376]) ).
thf(1545,plain,
! [SV215: nat,SV15: nat] :
( ( ( ( ( plus_plus_nat @ SV15 @ SV215 )
= SV15 )
| ( SV215 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ SV15 @ SV215 )
!= SV15 )
| ( SV215 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1377]) ).
thf(1546,plain,
! [SV216: nat,SV16: nat] :
( ( ( ( ( plus_plus_nat @ SV16 @ SV216 )
= SV216 )
| ( SV16 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ SV16 @ SV216 )
!= SV216 )
| ( SV16 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1378]) ).
thf(1547,plain,
! [SV372: nat,SV217: nat,SV22: nat] :
( ( ( ~ ( ( ord_less_nat @ ( plus_plus_nat @ SV22 @ SV217 ) @ ( plus_plus_nat @ SV372 @ SV217 ) )
| ( ord_less_nat @ SV22 @ SV372 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV22 @ SV217 ) @ ( plus_plus_nat @ SV372 @ SV217 ) )
| ~ ( ord_less_nat @ SV22 @ SV372 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1379]) ).
thf(1548,plain,
! [SV373: nat,SV218: nat,SV23: nat] :
( ( ( ~ ( ( ord_less_nat @ ( plus_plus_nat @ SV23 @ SV218 ) @ ( plus_plus_nat @ SV23 @ SV373 ) )
| ( ord_less_nat @ SV218 @ SV373 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV23 @ SV218 ) @ ( plus_plus_nat @ SV23 @ SV373 ) )
| ~ ( ord_less_nat @ SV218 @ SV373 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1381]) ).
thf(1549,plain,
! [SV376: nat,SV223: nat,SV32: nat] :
( ( ( ~ ( ( ord_less_nat @ ( plus_plus_nat @ SV32 @ SV223 ) @ ( plus_plus_nat @ SV32 @ SV376 ) )
| ( ord_less_nat @ SV223 @ SV376 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV32 @ SV223 ) @ ( plus_plus_nat @ SV32 @ SV376 ) )
| ~ ( ord_less_nat @ SV223 @ SV376 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1383]) ).
thf(1550,plain,
! [SV377: nat,SV224: nat,SV35: nat] :
( ( ( ~ ( ( ( times_times_nat @ SV35 @ SV224 )
= ( times_times_nat @ SV377 @ SV224 ) )
| ( SV35 = SV377 )
| ( SV224 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( ( times_times_nat @ SV35 @ SV224 )
!= ( times_times_nat @ SV377 @ SV224 ) )
| ~ ( ( SV35 = SV377 )
| ( SV224 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1385]) ).
thf(1551,plain,
! [SV378: nat,SV225: nat,SV36: nat] :
( ( ( ~ ( ( ( times_times_nat @ SV36 @ SV225 )
= ( times_times_nat @ SV36 @ SV378 ) )
| ( SV225 = SV378 )
| ( SV36 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( ( times_times_nat @ SV36 @ SV225 )
!= ( times_times_nat @ SV36 @ SV378 ) )
| ~ ( ( SV225 = SV378 )
| ( SV36 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1387]) ).
thf(1552,plain,
! [SV226: nat,SV38: nat] :
( ( ( ( ( times_times_nat @ SV38 @ SV226 )
= zero_zero_nat )
| ( SV38 = zero_zero_nat )
| ( SV226 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV38 @ SV226 )
!= zero_zero_nat )
| ~ ( ( SV38 = zero_zero_nat )
| ( SV226 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1389]) ).
thf(1553,plain,
! [SV379: nat,SV227: nat,SV39: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV39 @ SV227 ) @ ( plus_plus_nat @ SV39 @ SV379 ) )
| ( ord_less_eq_nat @ SV227 @ SV379 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV39 @ SV227 ) @ ( plus_plus_nat @ SV39 @ SV379 ) )
| ~ ( ord_less_eq_nat @ SV227 @ SV379 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1390]) ).
thf(1554,plain,
! [SV229: nat,SV41: nat] :
( ( ( ( ord_less_eq_nat @ SV41 @ ( plus_plus_nat @ SV229 @ SV41 ) )
| ( ord_less_eq_nat @ zero_zero_nat @ SV229 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV41 @ ( plus_plus_nat @ SV229 @ SV41 ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV229 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1392]) ).
thf(1555,plain,
! [SV230: nat,SV42: nat] :
( ( ( ( ord_less_eq_nat @ SV42 @ ( plus_plus_nat @ SV42 @ SV230 ) )
| ( ord_less_eq_nat @ zero_zero_nat @ SV230 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV42 @ ( plus_plus_nat @ SV42 @ SV230 ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV230 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1393]) ).
thf(1556,plain,
! [SV231: nat,SV43: nat] :
( ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV43 @ SV231 ) @ SV231 )
| ( ord_less_eq_nat @ SV43 @ zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV43 @ SV231 ) @ SV231 )
| ~ ( ord_less_eq_nat @ SV43 @ zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1394]) ).
thf(1557,plain,
! [SV232: nat,SV44: nat] :
( ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV44 @ SV232 ) @ SV44 )
| ( ord_less_eq_nat @ SV232 @ zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV44 @ SV232 ) @ SV44 )
| ~ ( ord_less_eq_nat @ SV232 @ zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1395]) ).
thf(1558,plain,
! [SV234: nat,SV46: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV46 @ SV234 ) )
| ( ord_less_nat @ SV234 @ SV46 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV46 @ SV234 ) )
| ~ ( ord_less_nat @ SV234 @ SV46 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1396]) ).
thf(1559,plain,
! [SV235: nat,SV47: nat] :
( ( ( ( ( minus_minus_nat @ SV47 @ SV235 )
= zero_zero_nat )
| ( ord_less_eq_nat @ SV47 @ SV235 ) )
= $false )
| ( ( ~ ( ( ( minus_minus_nat @ SV47 @ SV235 )
!= zero_zero_nat )
| ~ ( ord_less_eq_nat @ SV47 @ SV235 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1397]) ).
thf(1560,plain,
! [SV388: nat,SV247: nat,SV60: nat] :
( ( ( ~ ( ( ord_less_nat @ SV60 @ ( minus_minus_nat @ SV247 @ SV388 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV60 @ SV388 ) @ SV247 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV60 @ ( minus_minus_nat @ SV247 @ SV388 ) )
| ~ ( ord_less_nat @ ( plus_plus_nat @ SV60 @ SV388 ) @ SV247 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1398]) ).
thf(1561,plain,
! [SV389: nat,SV248: nat,SV61: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV61 @ SV248 ) @ SV389 )
| ( ord_less_eq_nat @ SV61 @ ( plus_plus_nat @ SV389 @ SV248 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( minus_minus_nat @ SV61 @ SV248 ) @ SV389 )
| ~ ( ord_less_eq_nat @ SV61 @ ( plus_plus_nat @ SV389 @ SV248 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1400]) ).
thf(1562,plain,
! [SV62: nat] :
( ( ( zero_zero_nat = SV62 )
= $false )
| ( ( ~ ( ( zero_zero_nat != SV62 )
| ( SV62 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1402]) ).
thf(1563,plain,
! [SV62: nat] :
( ( ( SV62 = zero_zero_nat )
= $false )
| ( ( ~ ( ( zero_zero_nat != SV62 )
| ( SV62 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1402]) ).
thf(1564,plain,
! [SV82: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV82 ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV82 )
| ( SV82 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1405]) ).
thf(1565,plain,
! [SV82: nat] :
( ( ( SV82 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV82 )
| ( SV82 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1405]) ).
thf(1566,plain,
! [SV83: nat] :
( ( ( ord_less_eq_nat @ SV83 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV83 @ zero_zero_nat )
| ( SV83 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1406]) ).
thf(1567,plain,
! [SV83: nat] :
( ( ( SV83 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV83 @ zero_zero_nat )
| ( SV83 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1406]) ).
thf(1568,plain,
! [SV84: nat] :
( ( ( ord_less_eq_nat @ SV84 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV84 @ zero_zero_nat )
| ( SV84 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1407]) ).
thf(1569,plain,
! [SV84: nat] :
( ( ( SV84 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV84 @ zero_zero_nat )
| ( SV84 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1407]) ).
thf(1570,plain,
! [SV481: nat,SV258: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV258 @ SV481 )
| ( ord_less_nat @ SV258 @ SV481 )
| ( SV258 = SV481 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV258 @ SV481 )
| ~ ( ( ord_less_nat @ SV258 @ SV481 )
| ( SV258 = SV481 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1408]) ).
thf(1571,plain,
! [SV481: nat,SV258: nat] :
( ( ( ord_less_eq_nat @ SV258 @ SV481 )
= ( ( ord_less_nat @ SV258 @ SV481 )
| ( SV258 = SV481 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1408]) ).
thf(1572,plain,
! [SV399: nat,SV261: nat,SV90: nat] :
( ( ( ~ ( ( ( times_times_nat @ SV90 @ SV261 )
= ( times_times_nat @ SV90 @ SV399 ) )
| ( SV90 = zero_zero_nat )
| ( SV261 = SV399 ) ) )
= $true )
| ( ( ~ ( ( ( times_times_nat @ SV90 @ SV261 )
!= ( times_times_nat @ SV90 @ SV399 ) )
| ~ ( ( SV90 = zero_zero_nat )
| ( SV261 = SV399 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1409]) ).
thf(1573,plain,
! [SV400: nat,SV262: nat,SV92: nat > nat] :
( ( ( ! [SY609: nat,SY610: nat] :
( ~ ( ord_less_nat @ SY609 @ SY610 )
| ( ord_less_nat @ ( SV92 @ SY609 ) @ ( SV92 @ SY610 ) ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV262 @ SV400 )
| ( ord_less_eq_nat @ ( SV92 @ SV262 ) @ ( SV92 @ SV400 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1411]) ).
thf(1574,plain,
! [SV263: nat,SV93: nat] :
( ( ( ~ ( ( SV93 != SV263 ) ) )
= $true )
| ( ( ord_less_nat @ SV93 @ SV263 )
= $true )
| ( ( ord_less_eq_nat @ SV93 @ SV263 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1412]) ).
thf(1575,plain,
! [SV482: nat,SV401: nat,SV264: nat,SV94: nat] :
( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV94 @ SV264 )
| ~ ( ord_less_eq_nat @ SV401 @ SV482 ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV94 @ SV401 ) @ ( plus_plus_nat @ SV264 @ SV482 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1413]) ).
thf(1576,plain,
! [SV402: nat,SV265: nat,SV95: nat] :
( ( ( ord_less_eq_nat @ SV95 @ SV265 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV402 @ SV265 )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV265 @ SV95 ) @ ( minus_minus_nat @ SV265 @ SV402 ) )
= ( ord_less_eq_nat @ SV402 @ SV95 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1577,plain,
! [SV403: nat,SV266: nat,SV96: nat] :
( ( ( ord_less_eq_nat @ SV96 @ SV266 )
= $false )
| ( ( ( minus_minus_nat @ SV403 @ ( minus_minus_nat @ SV266 @ SV96 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ SV403 @ SV96 ) @ SV266 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1415]) ).
thf(1578,plain,
! [SV483: nat,SV404: nat,SV268: nat,SV98: nat] :
( ( ( ~ ~ ( ( SV98 != SV268 )
| ~ ( ord_less_eq_nat @ SV404 @ SV483 ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV98 @ SV404 ) @ ( plus_plus_nat @ SV268 @ SV483 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1417]) ).
thf(1579,plain,
! [SV507: nat,SV484: nat,SV405: nat,SV269: nat,SV99: nat] :
( ( ~ ( ord_less_eq_nat @ SV99 @ SV269 )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV269 @ SV405 ) @ SV484 ) @ ( plus_plus_nat @ ( times_times_nat @ SV99 @ SV405 ) @ SV507 ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV269 @ SV99 ) @ SV405 ) @ SV484 ) @ SV507 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1418]) ).
thf(1580,plain,
! [SV406: nat,SV270: nat,SV100: nat] :
( ( ( ord_less_eq_nat @ SV100 @ SV270 )
= $false )
| ( ( ( minus_minus_nat @ ( plus_plus_nat @ SV406 @ SV270 ) @ SV100 )
= ( plus_plus_nat @ SV406 @ ( minus_minus_nat @ SV270 @ SV100 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1419]) ).
thf(1581,plain,
! [SV407: nat,SV271: nat,SV101: nat] :
( ( ( ord_less_nat @ SV101 @ SV271 )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV101 @ SV407 ) @ ( plus_plus_nat @ SV271 @ SV407 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1420]) ).
thf(1582,plain,
! [SV102: nat] :
( ( ( SV102 != zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ( SV102 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV102 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1421]) ).
thf(1583,plain,
! [SV102: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV102 )
= $false )
| ( ( ~ ( ~ ( ( SV102 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV102 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1421]) ).
thf(1584,plain,
! [SV272: nat,SV103: nat] :
( ( ( SV103 = SV272 )
= $false )
| ( ( ord_less_nat @ SV103 @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1422]) ).
thf(1585,plain,
! [SV485: nat,SV408: nat,SV274: nat,SV105: nat] :
( ( ( ~ ( ord_less_nat @ SV105 @ SV274 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV408 @ SV485 )
| ( ord_less_nat @ ( plus_plus_nat @ SV105 @ SV408 ) @ ( plus_plus_nat @ SV274 @ SV485 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1424]) ).
thf(1586,plain,
! [SV409: nat,SV275: nat,SV106: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV106 @ SV275 ) @ SV409 )
= $false )
| ( ( ord_less_nat @ SV106 @ SV409 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1425]) ).
thf(1587,plain,
! [SV508: nat,SV486: nat,SV410: nat,SV276: nat,SV107: nat] :
( ( ~ ( ord_less_eq_nat @ SV107 @ SV276 )
| ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ SV107 @ SV410 ) @ SV486 ) @ ( plus_plus_nat @ ( times_times_nat @ SV276 @ SV410 ) @ SV508 ) )
= ( minus_minus_nat @ SV486 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV276 @ SV107 ) @ SV410 ) @ SV508 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1426]) ).
thf(1588,plain,
! [SV411: nat,SV277: nat,SV108: nat] :
( ( ( ord_less_eq_nat @ SV108 @ SV277 )
= $false )
| ( ( ( minus_minus_nat @ ( plus_plus_nat @ SV277 @ SV411 ) @ SV108 )
= ( plus_plus_nat @ ( minus_minus_nat @ SV277 @ SV108 ) @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1427]) ).
thf(1589,plain,
! [SV487: nat,SV412: nat,SV278: nat,SV109: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ SV109 @ SV278 )
| ~ ( ord_less_nat @ SV412 @ SV487 ) ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV109 @ SV412 ) @ ( plus_plus_nat @ SV278 @ SV487 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1428]) ).
thf(1590,plain,
! [SV413: nat,SV279: nat,SV110: nat] :
( ( ( ord_less_eq_nat @ SV110 @ SV279 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV110 @ SV413 )
| ( ( ( minus_minus_nat @ SV279 @ SV110 )
= ( minus_minus_nat @ SV413 @ SV110 ) )
= ( SV279 = SV413 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1429]) ).
thf(1591,plain,
! [SV414: nat,SV280: nat,SV111: nat] :
( ( ( ord_less_nat @ SV111 @ SV280 )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV414 @ SV111 ) @ ( plus_plus_nat @ SV414 @ SV280 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1430]) ).
thf(1592,plain,
! [SV112: nat,SV281: nat] :
( ( ( ( minus_minus_nat @ SV281 @ SV112 )
!= zero_zero_nat )
= $true )
| ( ( SV112 = SV281 )
= $true )
| ( ( ( minus_minus_nat @ SV112 @ SV281 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1431]) ).
thf(1593,plain,
! [SV415: nat,SV282: nat,SV113: nat] :
( ( ( ord_less_eq_nat @ SV113 @ SV282 )
= $false )
| ( ( ( ord_less_eq_nat @ SV415 @ ( minus_minus_nat @ SV282 @ SV113 ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ SV415 @ SV113 ) @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1432]) ).
thf(1594,plain,
! [SV283: nat,SV114: nat > $o] :
( ( ( ~ ! [SY655: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY655 )
| ~ ~ ( SV114 @ SY655 )
| ~ ! [SY656: nat] :
~ ~ ( ~ ( ord_less_nat @ SY656 @ SY655 )
| ~ ~ ( SV114 @ SY656 ) ) ) )
= $true )
| ( ( SV114 @ SV283 )
= $true )
| ( ( SV114 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1433]) ).
thf(1595,plain,
! [SV115: nat] :
( ( ( SV115 != zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ( SV115 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV115 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1434]) ).
thf(1596,plain,
! [SV115: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV115 )
= $false )
| ( ( ~ ( ~ ( ( SV115 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV115 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1434]) ).
thf(1597,plain,
! [SV416: nat,SV284: nat,SV116: nat] :
( ( ( ord_less_eq_nat @ SV116 @ SV284 )
= $false )
| ( ( ( plus_plus_nat @ SV416 @ ( minus_minus_nat @ SV284 @ SV116 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ SV416 @ SV284 ) @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1435]) ).
thf(1598,plain,
! [SV417: nat,SV285: nat,SV117: nat > $o] :
( ( ( ~ ( ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1436]) ).
thf(1599,plain,
! [SV418: nat,SV286: nat,SV118: nat] :
( ( ( ord_less_nat @ SV118 @ SV286 )
= $false )
| ( ( ~ ( ord_less_nat @ SV118 @ SV418 )
| ( ord_less_nat @ ( minus_minus_nat @ SV418 @ SV286 ) @ ( minus_minus_nat @ SV418 @ SV118 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1438]) ).
thf(1600,plain,
! [SV119: nat,SV287: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV287 ) )
= $true )
| ( ( ord_less_nat @ ( minus_minus_nat @ SV287 @ SV119 ) @ SV287 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV119 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1439]) ).
thf(1601,plain,
! [SV488: nat,SV288: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV288 @ SV488 )
| ~ ! [SY1033: nat] :
( SV488
!= ( plus_plus_nat @ SV288 @ SY1033 ) ) )
| ~ ( ~ ( ord_less_eq_nat @ SV288 @ SV488 )
| ~ ~ ! [SY1033: nat] :
( SV488
!= ( plus_plus_nat @ SV288 @ SY1033 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1440]) ).
thf(1602,plain,
! [SV488: nat,SV288: nat] :
( ( ( ord_less_eq_nat @ SV288 @ SV488 )
= ( ~ ! [SY1033: nat] :
( SV488
!= ( plus_plus_nat @ SV288 @ SY1033 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1440]) ).
thf(1603,plain,
! [SV489: nat,SV289: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV289 @ SV489 )
| ~ ! [SY1034: nat] :
( SV489
!= ( plus_plus_nat @ SV289 @ SY1034 ) ) )
| ~ ( ~ ( ord_less_eq_nat @ SV289 @ SV489 )
| ~ ~ ! [SY1034: nat] :
( SV489
!= ( plus_plus_nat @ SV289 @ SY1034 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1441]) ).
thf(1604,plain,
! [SV489: nat,SV289: nat] :
( ( ( ord_less_eq_nat @ SV289 @ SV489 )
= ( ~ ! [SY1034: nat] :
( SV489
!= ( plus_plus_nat @ SV289 @ SY1034 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1441]) ).
thf(1605,plain,
! [SV421: nat,SV290: nat,SV122: nat] :
( ( ( ord_less_eq_nat @ SV122 @ SV290 )
= $false )
| ( ( ( ( minus_minus_nat @ SV290 @ SV122 )
= SV421 )
= ( SV290
= ( plus_plus_nat @ SV421 @ SV122 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1442]) ).
thf(1606,plain,
! [SV509: nat,SV490: nat,SV422: nat,SV291: nat,SV123: nat] :
( ( ~ ( ord_less_eq_nat @ SV123 @ SV291 )
| ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ SV291 @ SV422 ) @ SV490 ) @ ( plus_plus_nat @ ( times_times_nat @ SV123 @ SV422 ) @ SV509 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV291 @ SV123 ) @ SV422 ) @ SV490 ) @ SV509 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1443]) ).
thf(1607,plain,
! [SV423: nat,SV292: nat,SV124: nat] :
( ( ( ord_less_eq_nat @ SV124 @ SV292 )
= $false )
| ( ( ord_less_eq_nat @ SV423 @ ( minus_minus_nat @ ( plus_plus_nat @ SV292 @ SV423 ) @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1444]) ).
thf(1608,plain,
! [SV424: nat,SV293: nat,SV125: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SV293 ) @ ( plus_plus_nat @ SV424 @ SV293 ) )
= $false )
| ( ( ord_less_nat @ SV125 @ SV424 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1445]) ).
thf(1609,plain,
! [SV294: nat,SV126: nat] :
( ( ( ( ( plus_plus_nat @ SV126 @ SV294 )
= zero_zero_nat )
| ~ ( ( SV126 != zero_zero_nat )
| ( SV294 != zero_zero_nat ) ) )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ SV126 @ SV294 )
!= zero_zero_nat )
| ~ ~ ( ( SV126 != zero_zero_nat )
| ( SV294 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1446]) ).
thf(1610,plain,
! [SV510: nat,SV491: nat,SV425: nat,SV295: nat,SV127: nat] :
( ( ~ ( ord_less_eq_nat @ SV127 @ SV295 )
| ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV127 @ SV425 ) @ SV491 ) @ ( plus_plus_nat @ ( times_times_nat @ SV295 @ SV425 ) @ SV510 ) )
= ( ord_less_nat @ SV491 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV295 @ SV127 ) @ SV425 ) @ SV510 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(1611,plain,
! [SV426: nat,SV296: nat,SV128: nat] :
( ( ( ord_less_nat @ SV128 @ SV296 )
= $false )
| ( ( ord_less_nat @ ( minus_minus_nat @ SV128 @ SV426 ) @ SV296 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1448]) ).
thf(1612,plain,
! [SV427: nat,SV297: nat,SV129: nat] :
( ( ( ord_less_eq_nat @ SV129 @ SV297 )
= $false )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV427 @ SV297 ) @ ( minus_minus_nat @ SV427 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1449]) ).
thf(1613,plain,
! [SV428: nat,SV298: nat,SV130: nat] :
( ( ( ord_less_eq_nat @ SV130 @ SV298 )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV130 @ SV428 ) @ ( plus_plus_nat @ SV298 @ SV428 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1450]) ).
thf(1614,plain,
! [SV131: nat,SV299: nat] :
( ( ( SV299 = SV131 )
= $false )
| ( ( ord_less_nat @ SV131 @ SV299 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1451]) ).
thf(1615,plain,
! [SV492: nat,SV429: nat,SV300: nat,SV132: nat] :
( ( ( ~ ( ord_less_nat @ SV132 @ SV300 ) )
= $true )
| ( ( ( ( plus_plus_nat @ SV429 @ SV300 )
!= ( plus_plus_nat @ SV132 @ SV492 ) )
| ( ord_less_nat @ SV429 @ SV492 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1452]) ).
thf(1616,plain,
! [SV430: nat,SV301: nat,SV133: nat] :
( ( ( ord_less_eq_nat @ SV133 @ SV301 )
= $false )
| ( ( ord_less_eq_nat @ SV133 @ ( plus_plus_nat @ SV430 @ SV301 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1453]) ).
thf(1617,plain,
! [SV134: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV134 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV134 )
| ~ ( ( SV134 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1454]) ).
thf(1618,plain,
! [SV134: nat] :
( ( ( SV134 != zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV134 )
| ~ ( ( SV134 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1454]) ).
thf(1619,plain,
! [SV431: nat,SV302: nat,SV135: nat] :
( ( ( ord_less_eq_nat @ SV135 @ SV302 )
= $false )
| ( ( ( minus_minus_nat @ SV431 @ ( minus_minus_nat @ SV302 @ SV135 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ SV431 @ SV135 ) @ SV302 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1455]) ).
thf(1620,plain,
! [SV432: nat,SV303: nat,SV136: nat] :
( ( ( ord_less_eq_nat @ SV136 @ SV303 )
= $false )
| ( ( ( minus_minus_nat @ ( plus_plus_nat @ SV432 @ SV303 ) @ SV136 )
= ( plus_plus_nat @ SV432 @ ( minus_minus_nat @ SV303 @ SV136 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1456]) ).
thf(1621,plain,
! [SV493: nat,SV433: nat,SV304: nat,SV137: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV137 @ SV304 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV433 @ SV493 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV137 @ SV433 ) @ ( plus_plus_nat @ SV304 @ SV493 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1457]) ).
thf(1622,plain,
! [SV434: nat,SV305: nat,SV138: nat] :
( ( ( ord_less_eq_nat @ SV138 @ SV305 )
= $false )
| ( ( ( minus_minus_nat @ ( plus_plus_nat @ SV305 @ SV434 ) @ SV138 )
= ( plus_plus_nat @ ( minus_minus_nat @ SV305 @ SV138 ) @ SV434 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1458]) ).
thf(1623,plain,
! [SV435: nat,SV306: nat,SV139: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV139 @ SV306 ) @ ( plus_plus_nat @ SV139 @ SV435 ) )
= $false )
| ( ( ord_less_nat @ SV306 @ SV435 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1459]) ).
thf(1624,plain,
! [SV436: nat,SV307: nat,SV140: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV140 @ SV307 ) @ ( plus_plus_nat @ SV436 @ SV307 ) )
= $false )
| ( ( ord_less_eq_nat @ SV140 @ SV436 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1460]) ).
thf(1625,plain,
! [SV437: nat,SV308: nat,SV141: nat] :
( ( ( ord_less_eq_nat @ SV141 @ SV308 )
= $false )
| ( ( ( plus_plus_nat @ ( minus_minus_nat @ SV308 @ SV141 ) @ SV437 )
= ( minus_minus_nat @ ( plus_plus_nat @ SV308 @ SV437 ) @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1461]) ).
thf(1626,plain,
! [SV309: nat,SV142: nat > $o] :
( ( ( ~ ~ ( SV142 @ ( sK1_SY712 @ SV309 @ SV142 ) )
| ~ ! [SY1041: nat] :
~ ~ ( ~ ( ord_less_nat @ SY1041 @ ( sK1_SY712 @ SV309 @ SV142 ) )
| ~ ~ ( SV142 @ SY1041 ) ) )
= $false )
| ( ( SV142 @ SV309 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1462]) ).
thf(1627,plain,
! [SV438: nat,SV310: nat,SV143: nat] :
( ( ( ( plus_plus_nat @ SV143 @ SV310 )
= ( plus_plus_nat @ SV438 @ SV310 ) )
= $false )
| ( ( SV143 = SV438 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1463]) ).
thf(1628,plain,
! [SV439: nat,SV311: nat,SV144: nat] :
( ( ( ord_less_nat @ SV144 @ SV311 )
= $false )
| ( ( ord_less_nat @ SV144 @ ( plus_plus_nat @ SV311 @ SV439 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1464]) ).
thf(1629,plain,
! [SV511: nat,SV494: nat,SV440: nat,SV313: nat,SV146: nat] :
( ( ~ ( ord_less_eq_nat @ SV146 @ SV313 )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV146 @ SV440 ) @ SV494 ) @ ( plus_plus_nat @ ( times_times_nat @ SV313 @ SV440 ) @ SV511 ) )
= ( ord_less_eq_nat @ SV494 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV313 @ SV146 ) @ SV440 ) @ SV511 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1466]) ).
thf(1630,plain,
! [SV441: nat,SV314: nat,SV147: nat] :
( ( ( ord_less_eq_nat @ SV147 @ SV314 )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV147 @ SV441 ) @ ( plus_plus_nat @ SV314 @ SV441 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1467]) ).
thf(1631,plain,
! [SV495: nat,SV442: nat,SV315: nat,SV148: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ SV148 @ SV315 )
| ( SV442 != SV495 ) ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV148 @ SV442 ) @ ( plus_plus_nat @ SV315 @ SV495 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1468]) ).
thf(1632,plain,
! [SV496: nat,SV443: nat,SV317: nat,SV150: nat] :
( ( ( ~ ( ord_less_nat @ SV150 @ SV317 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV443 @ SV496 )
| ( ord_less_nat @ ( plus_plus_nat @ SV150 @ SV443 ) @ ( plus_plus_nat @ SV317 @ SV496 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1470]) ).
thf(1633,plain,
! [SV444: nat,SV318: nat,SV152: nat] :
( ( ( ~ ( ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV318 )
| ~ ( ord_less_nat @ SV152 @ SV444 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV318 )
| ~ ( ord_less_nat @ SV152 @ SV444 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1472]) ).
thf(1634,plain,
! [SV319: nat,SV153: nat] :
( ( ( ord_less_nat @ SV153 @ SV319 )
= $true )
| ( ( ( plus_plus_nat @ SV319 @ ( minus_minus_nat @ SV153 @ SV319 ) )
= SV153 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1474]) ).
thf(1635,plain,
! [SV154: nat,SV320: nat] :
( ( ( SV320 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ SV154 @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1475]) ).
thf(1636,plain,
! [SV321: nat,SV155: nat] :
( ( ( ( SV155 != SV321 )
| ( ord_less_nat @ SV155 @ SV321 )
| ( ord_less_nat @ SV321 @ SV155 ) )
= $false )
| ( ( ~ ( ~ ( ( SV155 != SV321 ) )
| ~ ( ( ord_less_nat @ SV155 @ SV321 )
| ( ord_less_nat @ SV321 @ SV155 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1476]) ).
thf(1637,plain,
! [SV156: nat,SV322: nat] :
( ( ( SV322 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ SV156 @ SV322 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1477]) ).
thf(1638,plain,
! [SV445: nat,SV323: nat,SV157: nat] :
( ( ( ord_less_eq_nat @ SV157 @ SV323 )
= $false )
| ( ( ( plus_plus_nat @ SV445 @ ( minus_minus_nat @ SV323 @ SV157 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ SV445 @ SV323 ) @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1478]) ).
thf(1639,plain,
! [SV446: nat,SV324: nat,SV158: nat] :
( ( ( ord_less_eq_nat @ SV158 @ SV324 )
= $false )
| ( ( ( plus_plus_nat @ ( minus_minus_nat @ SV324 @ SV158 ) @ SV446 )
= ( minus_minus_nat @ ( plus_plus_nat @ SV324 @ SV446 ) @ SV158 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1479]) ).
thf(1640,plain,
! [SV325: nat,SV159: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV159 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV325 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV159 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV325 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1480]) ).
thf(1641,plain,
! [SV326: nat,SV160: nat] :
( ( ( ( ( plus_plus_nat @ SV160 @ SV326 )
= zero_zero_nat )
| ~ ( ( SV160 != zero_zero_nat )
| ( SV326 != zero_zero_nat ) ) )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ SV160 @ SV326 )
!= zero_zero_nat )
| ~ ~ ( ( SV160 != zero_zero_nat )
| ( SV326 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1481]) ).
thf(1642,plain,
! [SV497: nat,SV327: nat] :
( ( ~ ( ( ord_less_nat @ SV327 @ SV497 )
| ~ ( ~ ( ord_less_eq_nat @ SV327 @ SV497 )
| ~ ( ( SV327 != SV497 ) ) ) )
| ~ ( ~ ( ord_less_nat @ SV327 @ SV497 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV327 @ SV497 )
| ~ ( ( SV327 != SV497 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1482]) ).
thf(1643,plain,
! [SV497: nat,SV327: nat] :
( ( ( ord_less_nat @ SV327 @ SV497 )
= ( ~ ( ~ ( ord_less_eq_nat @ SV327 @ SV497 )
| ~ ( ( SV327 != SV497 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1482]) ).
thf(1644,plain,
! [SV328: nat,SV162: nat] :
( ( ( ( zero_zero_nat
= ( plus_plus_nat @ SV162 @ SV328 ) )
| ~ ( ( SV162 != zero_zero_nat )
| ( SV328 != zero_zero_nat ) ) )
= $false )
| ( ( ~ ( ( zero_zero_nat
!= ( plus_plus_nat @ SV162 @ SV328 ) )
| ~ ~ ( ( SV162 != zero_zero_nat )
| ( SV328 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1483]) ).
thf(1645,plain,
! [SV448: nat,SV329: nat,SV163: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV329 )
| ( ord_less_eq_nat @ SV163 @ SV448 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV329 )
| ( ord_less_eq_nat @ SV163 @ SV448 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1484]) ).
thf(1646,plain,
! [SV449: nat,SV330: nat,SV164: nat > $o] :
( ( ( SV164 @ SV330 )
= $false )
| ( ( ~ ! [SY1015: nat] :
( ~ ( SV164 @ SY1015 )
| ( ord_less_eq_nat @ SY1015 @ SV449 ) )
| ~ ! [SY751: nat] :
~ ~ ( ~ ( SV164 @ SY751 )
| ~ ! [SY752: nat] :
( ~ ( SV164 @ SY752 )
| ( ord_less_eq_nat @ SY752 @ SY751 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1486]) ).
thf(1647,plain,
! [SV450: nat,SV331: nat,SV166: nat] :
( ( ( ord_less_nat @ SV166 @ SV331 )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV166 @ SV450 ) @ ( plus_plus_nat @ SV331 @ SV450 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1487]) ).
thf(1648,plain,
! [SV451: nat,SV332: nat,SV167: nat] :
( ( ( ord_less_eq_nat @ SV167 @ SV332 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV167 @ SV451 )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV332 @ SV167 ) @ ( minus_minus_nat @ SV451 @ SV167 ) )
= ( ord_less_eq_nat @ SV332 @ SV451 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1488]) ).
thf(1649,plain,
! [SV452: nat,SV333: nat,SV168: nat] :
( ( ( ( plus_plus_nat @ SV168 @ SV333 )
= SV452 )
= $false )
| ( ( SV168
= ( minus_minus_nat @ SV452 @ SV333 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1489]) ).
thf(1650,plain,
! [SV453: nat,SV334: nat,SV169: nat] :
( ( ( ord_less_eq_nat @ SV169 @ SV334 )
= $false )
| ( ( ( ord_less_nat @ ( minus_minus_nat @ SV334 @ SV169 ) @ SV453 )
= ( ord_less_nat @ SV334 @ ( plus_plus_nat @ SV453 @ SV169 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1490]) ).
thf(1651,plain,
! [SV498: nat,SV454: nat,SV335: nat,SV170: nat] :
( ( ( SV170
!= ( plus_plus_nat @ SV335 @ SV454 ) )
= $true )
| ( ( ( plus_plus_nat @ SV170 @ SV498 )
= ( plus_plus_nat @ SV335 @ ( plus_plus_nat @ SV454 @ SV498 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1491]) ).
thf(1652,plain,
! [SV455: nat,SV336: nat,SV171: nat] :
( ( ( ord_less_eq_nat @ SV171 @ SV336 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV171 @ SV455 )
| ( ( minus_minus_nat @ ( minus_minus_nat @ SV336 @ SV171 ) @ ( minus_minus_nat @ SV455 @ SV171 ) )
= ( minus_minus_nat @ SV336 @ SV455 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1492]) ).
thf(1653,plain,
! [SV456: nat,SV337: nat,SV172: nat] :
( ( ( ord_less_eq_nat @ SV172 @ SV337 )
= $false )
| ( ( ord_less_eq_nat @ SV172 @ ( plus_plus_nat @ SV337 @ SV456 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1493]) ).
thf(1654,plain,
! [SV512: nat,SV499: nat,SV457: nat,SV338: nat,SV174: nat] :
( ( ~ ( ord_less_eq_nat @ SV174 @ SV338 )
| ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV338 @ SV457 ) @ SV499 ) @ ( plus_plus_nat @ ( times_times_nat @ SV174 @ SV457 ) @ SV512 ) )
= ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV338 @ SV174 ) @ SV457 ) @ SV499 ) @ SV512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1495]) ).
thf(1655,plain,
! [SV500: nat,SV458: nat,SV339: nat,SV175: nat] :
( ( ( SV175
!= ( plus_plus_nat @ SV339 @ SV458 ) )
= $true )
| ( ( ( plus_plus_nat @ SV500 @ SV175 )
= ( plus_plus_nat @ SV339 @ ( plus_plus_nat @ SV500 @ SV458 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1496]) ).
thf(1656,plain,
! [SV459: nat,SV341: nat,SV177: nat] :
( ( ( ~ ( ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 )
| ~ ( ord_less_nat @ SV341 @ SV459 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 )
| ~ ( ord_less_nat @ SV341 @ SV459 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1498]) ).
thf(1657,plain,
! [SV342: nat,SV178: nat] :
( ( ( SV178 = SV342 )
= $true )
| ( ( ~ ~ ( ord_less_nat @ SV178 @ SV342 )
| ( ord_less_nat @ SV342 @ SV178 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1500]) ).
thf(1658,plain,
! [SV460: nat,SV343: nat,SV179: nat] :
( ( ( ord_less_eq_nat @ SV179 @ SV343 )
= $false )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV179 @ SV460 ) @ ( minus_minus_nat @ SV343 @ SV460 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1501]) ).
thf(1659,plain,
! [SV181: nat > $o,SV345: nat] :
( ( ( ~ ! [SY1042: nat] :
( ~ ( ord_less_nat @ SY1042 @ ( sK2_SY783 @ SV345 @ SV181 ) )
| ( SV181 @ SY1042 ) )
| ( SV181 @ ( sK2_SY783 @ SV345 @ SV181 ) ) )
= $false )
| ( ( SV181 @ SV345 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1503]) ).
thf(1660,plain,
! [SV461: nat,SV346: nat,SV182: nat] :
( ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV182 @ SV346 )
| ( ( ( minus_minus_nat @ SV346 @ SV182 )
= SV461 )
= ( SV346
= ( plus_plus_nat @ SV461 @ SV182 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1504]) ).
thf(1661,plain,
! [SV462: nat,SV347: nat,SV183: nat] :
( ( ( ord_less_eq_nat @ SV183 @ SV347 )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV462 @ SV183 ) @ ( plus_plus_nat @ SV462 @ SV347 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1505]) ).
thf(1662,plain,
! [SV463: nat,SV348: nat,SV184: nat] :
( ( ( ord_less_eq_nat @ SV184 @ SV348 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV184 @ SV463 )
| ( ( ord_less_nat @ ( minus_minus_nat @ SV348 @ SV184 ) @ ( minus_minus_nat @ SV463 @ SV184 ) )
= ( ord_less_nat @ SV348 @ SV463 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1506]) ).
thf(1663,plain,
! [SV464: nat,SV349: nat,SV185: nat] :
( ( ( ord_less_eq_nat @ SV185 @ SV349 )
= $false )
| ( ( ( ord_less_eq_nat @ SV464 @ ( minus_minus_nat @ SV349 @ SV185 ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ SV464 @ SV185 ) @ SV349 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1507]) ).
thf(1664,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( ~ ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1508]) ).
thf(1665,plain,
! [SV466: nat,SV351: nat,SV187: nat] :
( ( ( ( plus_plus_nat @ SV187 @ SV351 )
= ( plus_plus_nat @ SV187 @ SV466 ) )
= $false )
| ( ( SV351 = SV466 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1510]) ).
thf(1666,plain,
! [SV467: nat,SV352: nat,SV188: nat] :
( ( ( ord_less_nat @ SV188 @ SV352 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV467 @ SV188 )
| ( ord_less_nat @ ( minus_minus_nat @ SV188 @ SV467 ) @ ( minus_minus_nat @ SV352 @ SV467 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1511]) ).
thf(1667,plain,
! [SV189: nat,SV353: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV353 @ SV189 ) )
= $true )
| ( ( SV189 = SV353 )
= $true )
| ( ( ord_less_eq_nat @ SV189 @ SV353 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1512]) ).
thf(1668,plain,
! [SV513: nat,SV501: nat,SV468: nat,SV354: nat,SV190: nat] :
( ( ~ ( ord_less_eq_nat @ SV190 @ SV354 )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SV354 @ SV468 ) @ SV501 )
= ( plus_plus_nat @ ( times_times_nat @ SV190 @ SV468 ) @ SV513 ) )
= ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV354 @ SV190 ) @ SV468 ) @ SV501 )
= SV513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(1669,plain,
! [SV191: nat,SV355: nat] :
( ( ( ! [SY975: nat] :
( SV355
!= ( plus_plus_nat @ SV191 @ SY975 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV191 @ SV355 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1514]) ).
thf(1670,plain,
! [SV502: nat,SV469: nat,SV356: nat,SV192: nat] :
( ( ( ~ ~ ( ( SV192 != SV356 )
| ~ ( ord_less_nat @ SV469 @ SV502 ) ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV192 @ SV469 ) @ ( plus_plus_nat @ SV356 @ SV502 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1515]) ).
thf(1671,plain,
! [SV503: nat,SV470: nat,SV357: nat,SV193: nat] :
( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV193 @ SV357 )
| ( SV470 != SV503 ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV193 @ SV470 ) @ ( plus_plus_nat @ SV357 @ SV503 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1516]) ).
thf(1672,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV194 )
| ( ord_less_eq_nat @ SV358 @ SV471 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV194 )
| ( ord_less_eq_nat @ SV358 @ SV471 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1517]) ).
thf(1673,plain,
! [SV472: nat,SV359: nat,SV195: nat] :
( ( ( ord_less_eq_nat @ SV195 @ SV359 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV359 @ SV472 )
| ( ord_less_eq_nat @ SV195 @ SV472 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1519]) ).
thf(1674,plain,
! [SV504: nat,SV473: nat,SV360: nat,SV196: nat] :
( ( ( ~ ~ ( ( SV196 != SV360 )
| ( SV473 != SV504 ) ) )
= $true )
| ( ( ( plus_plus_nat @ SV196 @ SV473 )
= ( plus_plus_nat @ SV360 @ SV504 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1520]) ).
thf(1675,plain,
! [SV514: nat,SV505: nat,SV474: nat,SV361: nat,SV197: nat] :
( ( ~ ( ord_less_eq_nat @ SV197 @ SV361 )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SV197 @ SV474 ) @ SV505 )
= ( plus_plus_nat @ ( times_times_nat @ SV361 @ SV474 ) @ SV514 ) )
= ( SV505
= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV361 @ SV197 ) @ SV474 ) @ SV514 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(1676,plain,
! [SV506: nat,SV475: nat,SV362: nat,SV198: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV198 @ SV362 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV475 @ SV506 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV198 @ SV475 ) @ ( plus_plus_nat @ SV362 @ SV506 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1522]) ).
thf(1677,plain,
! [SV476: nat,SV363: nat,SV199: nat] :
( ( ( ord_less_nat @ SV199 @ SV363 )
= $false )
| ( ( ord_less_nat @ SV199 @ ( plus_plus_nat @ SV476 @ SV363 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1523]) ).
thf(1678,plain,
! [SV364: nat,SV200: nat] :
( ( ( ord_less_nat @ SV200 @ SV364 )
= $false )
| ( ( ord_less_eq_nat @ SV200 @ SV364 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1524]) ).
thf(1679,plain,
! [SV364: nat,SV200: nat] :
( ( ( SV200 = SV364 )
= $false )
| ( ( ord_less_eq_nat @ SV200 @ SV364 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1524]) ).
thf(1680,plain,
! [SV477: nat,SV365: nat,SV201: nat > nat] :
( ( ( number1551313001itions @ SV201 @ SV365 )
= $false )
| ( ( ord_less_eq_nat @ ( SV201 @ SV477 ) @ SV365 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1525]) ).
thf(1681,plain,
! [SV478: nat,SV367: nat,SV203: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV203 @ SV367 ) @ ( plus_plus_nat @ SV203 @ SV478 ) )
= $false )
| ( ( ord_less_eq_nat @ SV367 @ SV478 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1527]) ).
thf(1682,plain,
! [SV1: nat > nat] :
( ( ( ~ ( number1551313001itions @ SV1 @ zero_zero_nat )
| ( SV1
!= ( ^ [I: nat] : zero_zero_nat ) ) )
= $false )
| ( ( number1551313001itions @ SV1 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1528]) ).
thf(1683,plain,
! [SV1: nat > nat] :
( ( ( ! [SV515: nat] :
( ( SV1 @ SV515 )
= zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( number1551313001itions @ SV1 @ zero_zero_nat )
| ( SV1
!= ( ^ [I: nat] : zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[1529]) ).
thf(1684,plain,
! [SV1: nat > nat] :
( ( ( SV1
= ( ^ [I: nat] : zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( number1551313001itions @ SV1 @ zero_zero_nat )
| ( SV1
!= ( ^ [I: nat] : zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[1529]) ).
thf(1685,plain,
! [SV204: nat,SV2: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SV204 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SV204 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( ord_less_nat @ zero_zero_nat @ SV204 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1530]) ).
thf(1686,plain,
! [SV204: nat,SV2: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( ord_less_nat @ zero_zero_nat @ SV204 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SV204 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( ord_less_nat @ zero_zero_nat @ SV204 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1530]) ).
thf(1687,plain,
! [SV205: nat,SV3: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV3 @ SV205 ) @ SV3 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV3 @ SV205 ) @ SV3 )
| ~ ( ord_less_nat @ SV205 @ zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1531]) ).
thf(1688,plain,
! [SV3: nat,SV205: nat] :
( ( ( ord_less_nat @ SV205 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV3 @ SV205 ) @ SV3 )
| ~ ( ord_less_nat @ SV205 @ zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1531]) ).
thf(1689,plain,
! [SV206: nat,SV4: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV4 @ SV206 ) @ SV206 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV4 @ SV206 ) @ SV206 )
| ~ ( ord_less_nat @ SV4 @ zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1532]) ).
thf(1690,plain,
! [SV206: nat,SV4: nat] :
( ( ( ord_less_nat @ SV4 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV4 @ SV206 ) @ SV206 )
| ~ ( ord_less_nat @ SV4 @ zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1532]) ).
thf(1691,plain,
! [SV207: nat,SV5: nat] :
( ( ( ord_less_nat @ SV5 @ ( plus_plus_nat @ SV5 @ SV207 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV5 @ ( plus_plus_nat @ SV5 @ SV207 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV207 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1533]) ).
thf(1692,plain,
! [SV5: nat,SV207: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV207 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV5 @ ( plus_plus_nat @ SV5 @ SV207 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV207 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1533]) ).
thf(1693,plain,
! [SV208: nat,SV6: nat] :
( ( ( ord_less_nat @ SV6 @ ( plus_plus_nat @ SV208 @ SV6 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV6 @ ( plus_plus_nat @ SV208 @ SV6 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV208 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1534]) ).
thf(1694,plain,
! [SV6: nat,SV208: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV208 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV6 @ ( plus_plus_nat @ SV208 @ SV6 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV208 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1534]) ).
thf(1695,plain,
! [SV368: nat,SV209: nat,SV7: nat] :
( ( ( ( ( plus_plus_nat @ SV7 @ SV209 )
= ( plus_plus_nat @ SV368 @ SV209 ) )
| ( SV7 = SV368 ) )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ SV7 @ SV209 )
!= ( plus_plus_nat @ SV368 @ SV209 ) )
| ( SV7 != SV368 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1535]) ).
thf(1696,plain,
! [SV369: nat,SV210: nat,SV8: nat] :
( ( ( ( ( plus_plus_nat @ SV8 @ SV210 )
= ( plus_plus_nat @ SV8 @ SV369 ) )
| ( SV210 = SV369 ) )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ SV8 @ SV210 )
!= ( plus_plus_nat @ SV8 @ SV369 ) )
| ( SV210 != SV369 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1536]) ).
thf(1697,plain,
! [SV9: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV9 @ zero_zero_nat )
| ( SV9 != zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV9 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1537]) ).
thf(1698,plain,
! [SV9: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV9 @ zero_zero_nat )
| ( SV9 != zero_zero_nat ) )
= $false )
| ( ( SV9 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1538]) ).
thf(1699,plain,
! [SV10: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV10 )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV10 )
| ( SV10 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1539]) ).
thf(1700,plain,
! [SV10: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV10 )
| ( SV10 != zero_zero_nat ) )
= $false )
| ( ( SV10 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1540]) ).
thf(1701,plain,
! [SV370: nat,SV211: nat,SV11: nat] :
( ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV11 @ SV211 ) @ ( plus_plus_nat @ SV370 @ SV211 ) )
| ( ord_less_eq_nat @ SV11 @ SV370 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV11 @ SV211 ) @ ( plus_plus_nat @ SV370 @ SV211 ) )
| ~ ( ord_less_eq_nat @ SV11 @ SV370 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1541]) ).
thf(1702,plain,
! [SV371: nat,SV212: nat,SV12: nat] :
( ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV212 ) @ ( plus_plus_nat @ SV12 @ SV371 ) )
| ( ord_less_eq_nat @ SV212 @ SV371 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV212 ) @ ( plus_plus_nat @ SV12 @ SV371 ) )
| ~ ( ord_less_eq_nat @ SV212 @ SV371 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1542]) ).
thf(1703,plain,
! [SV213: nat,SV13: nat] :
( ( ( SV13
= ( plus_plus_nat @ SV13 @ SV213 ) )
= $false )
| ( ( ~ ( ( SV13
!= ( plus_plus_nat @ SV13 @ SV213 ) )
| ( SV213 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1543]) ).
thf(1704,plain,
! [SV13: nat,SV213: nat] :
( ( ( SV213 = zero_zero_nat )
= $false )
| ( ( ~ ( ( SV13
!= ( plus_plus_nat @ SV13 @ SV213 ) )
| ( SV213 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1543]) ).
thf(1705,plain,
! [SV214: nat,SV14: nat] :
( ( ( SV14
= ( plus_plus_nat @ SV214 @ SV14 ) )
= $false )
| ( ( ~ ( ( SV14
!= ( plus_plus_nat @ SV214 @ SV14 ) )
| ( SV214 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1544]) ).
thf(1706,plain,
! [SV14: nat,SV214: nat] :
( ( ( SV214 = zero_zero_nat )
= $false )
| ( ( ~ ( ( SV14
!= ( plus_plus_nat @ SV214 @ SV14 ) )
| ( SV214 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1544]) ).
thf(1707,plain,
! [SV215: nat,SV15: nat] :
( ( ( ( plus_plus_nat @ SV15 @ SV215 )
= SV15 )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ SV15 @ SV215 )
!= SV15 )
| ( SV215 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1545]) ).
thf(1708,plain,
! [SV15: nat,SV215: nat] :
( ( ( SV215 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ SV15 @ SV215 )
!= SV15 )
| ( SV215 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1545]) ).
thf(1709,plain,
! [SV216: nat,SV16: nat] :
( ( ( ( plus_plus_nat @ SV16 @ SV216 )
= SV216 )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ SV16 @ SV216 )
!= SV216 )
| ( SV16 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1546]) ).
thf(1710,plain,
! [SV216: nat,SV16: nat] :
( ( ( SV16 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ SV16 @ SV216 )
!= SV216 )
| ( SV16 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1546]) ).
thf(1711,plain,
! [SV372: nat,SV217: nat,SV22: nat] :
( ( ( ( ord_less_nat @ ( plus_plus_nat @ SV22 @ SV217 ) @ ( plus_plus_nat @ SV372 @ SV217 ) )
| ( ord_less_nat @ SV22 @ SV372 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV22 @ SV217 ) @ ( plus_plus_nat @ SV372 @ SV217 ) )
| ~ ( ord_less_nat @ SV22 @ SV372 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1547]) ).
thf(1712,plain,
! [SV373: nat,SV218: nat,SV23: nat] :
( ( ( ( ord_less_nat @ ( plus_plus_nat @ SV23 @ SV218 ) @ ( plus_plus_nat @ SV23 @ SV373 ) )
| ( ord_less_nat @ SV218 @ SV373 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV23 @ SV218 ) @ ( plus_plus_nat @ SV23 @ SV373 ) )
| ~ ( ord_less_nat @ SV218 @ SV373 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1548]) ).
thf(1713,plain,
! [SV376: nat,SV223: nat,SV32: nat] :
( ( ( ( ord_less_nat @ ( plus_plus_nat @ SV32 @ SV223 ) @ ( plus_plus_nat @ SV32 @ SV376 ) )
| ( ord_less_nat @ SV223 @ SV376 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV32 @ SV223 ) @ ( plus_plus_nat @ SV32 @ SV376 ) )
| ~ ( ord_less_nat @ SV223 @ SV376 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1549]) ).
thf(1714,plain,
! [SV377: nat,SV224: nat,SV35: nat] :
( ( ( ( ( times_times_nat @ SV35 @ SV224 )
= ( times_times_nat @ SV377 @ SV224 ) )
| ( SV35 = SV377 )
| ( SV224 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV35 @ SV224 )
!= ( times_times_nat @ SV377 @ SV224 ) )
| ~ ( ( SV35 = SV377 )
| ( SV224 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1550]) ).
thf(1715,plain,
! [SV378: nat,SV225: nat,SV36: nat] :
( ( ( ( ( times_times_nat @ SV36 @ SV225 )
= ( times_times_nat @ SV36 @ SV378 ) )
| ( SV225 = SV378 )
| ( SV36 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV36 @ SV225 )
!= ( times_times_nat @ SV36 @ SV378 ) )
| ~ ( ( SV225 = SV378 )
| ( SV36 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1551]) ).
thf(1716,plain,
! [SV226: nat,SV38: nat] :
( ( ( ( times_times_nat @ SV38 @ SV226 )
= zero_zero_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV38 @ SV226 )
!= zero_zero_nat )
| ~ ( ( SV38 = zero_zero_nat )
| ( SV226 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1552]) ).
thf(1717,plain,
! [SV226: nat,SV38: nat] :
( ( ( ( SV38 = zero_zero_nat )
| ( SV226 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV38 @ SV226 )
!= zero_zero_nat )
| ~ ( ( SV38 = zero_zero_nat )
| ( SV226 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1552]) ).
thf(1718,plain,
! [SV379: nat,SV227: nat,SV39: nat] :
( ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV39 @ SV227 ) @ ( plus_plus_nat @ SV39 @ SV379 ) )
| ( ord_less_eq_nat @ SV227 @ SV379 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV39 @ SV227 ) @ ( plus_plus_nat @ SV39 @ SV379 ) )
| ~ ( ord_less_eq_nat @ SV227 @ SV379 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1553]) ).
thf(1719,plain,
! [SV229: nat,SV41: nat] :
( ( ( ord_less_eq_nat @ SV41 @ ( plus_plus_nat @ SV229 @ SV41 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV41 @ ( plus_plus_nat @ SV229 @ SV41 ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV229 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1554]) ).
thf(1720,plain,
! [SV41: nat,SV229: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV229 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV41 @ ( plus_plus_nat @ SV229 @ SV41 ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV229 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1554]) ).
thf(1721,plain,
! [SV230: nat,SV42: nat] :
( ( ( ord_less_eq_nat @ SV42 @ ( plus_plus_nat @ SV42 @ SV230 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV42 @ ( plus_plus_nat @ SV42 @ SV230 ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV230 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1555]) ).
thf(1722,plain,
! [SV42: nat,SV230: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV230 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV42 @ ( plus_plus_nat @ SV42 @ SV230 ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV230 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1555]) ).
thf(1723,plain,
! [SV231: nat,SV43: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV43 @ SV231 ) @ SV231 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV43 @ SV231 ) @ SV231 )
| ~ ( ord_less_eq_nat @ SV43 @ zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1556]) ).
thf(1724,plain,
! [SV231: nat,SV43: nat] :
( ( ( ord_less_eq_nat @ SV43 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV43 @ SV231 ) @ SV231 )
| ~ ( ord_less_eq_nat @ SV43 @ zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1556]) ).
thf(1725,plain,
! [SV232: nat,SV44: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV44 @ SV232 ) @ SV44 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV44 @ SV232 ) @ SV44 )
| ~ ( ord_less_eq_nat @ SV232 @ zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1557]) ).
thf(1726,plain,
! [SV44: nat,SV232: nat] :
( ( ( ord_less_eq_nat @ SV232 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV44 @ SV232 ) @ SV44 )
| ~ ( ord_less_eq_nat @ SV232 @ zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1557]) ).
thf(1727,plain,
! [SV234: nat,SV46: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV46 @ SV234 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV46 @ SV234 ) )
| ~ ( ord_less_nat @ SV234 @ SV46 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1558]) ).
thf(1728,plain,
! [SV46: nat,SV234: nat] :
( ( ( ord_less_nat @ SV234 @ SV46 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV46 @ SV234 ) )
| ~ ( ord_less_nat @ SV234 @ SV46 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1558]) ).
thf(1729,plain,
! [SV235: nat,SV47: nat] :
( ( ( ( minus_minus_nat @ SV47 @ SV235 )
= zero_zero_nat )
= $false )
| ( ( ~ ( ( ( minus_minus_nat @ SV47 @ SV235 )
!= zero_zero_nat )
| ~ ( ord_less_eq_nat @ SV47 @ SV235 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1559]) ).
thf(1730,plain,
! [SV235: nat,SV47: nat] :
( ( ( ord_less_eq_nat @ SV47 @ SV235 )
= $false )
| ( ( ~ ( ( ( minus_minus_nat @ SV47 @ SV235 )
!= zero_zero_nat )
| ~ ( ord_less_eq_nat @ SV47 @ SV235 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1559]) ).
thf(1731,plain,
! [SV388: nat,SV247: nat,SV60: nat] :
( ( ( ( ord_less_nat @ SV60 @ ( minus_minus_nat @ SV247 @ SV388 ) )
| ( ord_less_nat @ ( plus_plus_nat @ SV60 @ SV388 ) @ SV247 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV60 @ ( minus_minus_nat @ SV247 @ SV388 ) )
| ~ ( ord_less_nat @ ( plus_plus_nat @ SV60 @ SV388 ) @ SV247 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1560]) ).
thf(1732,plain,
! [SV389: nat,SV248: nat,SV61: nat] :
( ( ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV61 @ SV248 ) @ SV389 )
| ( ord_less_eq_nat @ SV61 @ ( plus_plus_nat @ SV389 @ SV248 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( minus_minus_nat @ SV61 @ SV248 ) @ SV389 )
| ~ ( ord_less_eq_nat @ SV61 @ ( plus_plus_nat @ SV389 @ SV248 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1561]) ).
thf(1733,plain,
! [SV62: nat] :
( ( ( ( zero_zero_nat != SV62 )
| ( SV62 != zero_zero_nat ) )
= $false )
| ( ( zero_zero_nat = SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1562]) ).
thf(1734,plain,
! [SV62: nat] :
( ( ( ( zero_zero_nat != SV62 )
| ( SV62 != zero_zero_nat ) )
= $false )
| ( ( SV62 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1563]) ).
thf(1735,plain,
! [SV82: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV82 )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV82 )
| ( SV82 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1564]) ).
thf(1736,plain,
! [SV82: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV82 )
| ( SV82 != zero_zero_nat ) )
= $false )
| ( ( SV82 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1565]) ).
thf(1737,plain,
! [SV83: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV83 @ zero_zero_nat )
| ( SV83 != zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV83 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1566]) ).
thf(1738,plain,
! [SV83: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV83 @ zero_zero_nat )
| ( SV83 != zero_zero_nat ) )
= $false )
| ( ( SV83 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1567]) ).
thf(1739,plain,
! [SV84: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV84 @ zero_zero_nat )
| ( SV84 != zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV84 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1568]) ).
thf(1740,plain,
! [SV84: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV84 @ zero_zero_nat )
| ( SV84 != zero_zero_nat ) )
= $false )
| ( ( SV84 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1569]) ).
thf(1741,plain,
! [SV481: nat,SV258: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV258 @ SV481 )
| ( ord_less_nat @ SV258 @ SV481 )
| ( SV258 = SV481 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV258 @ SV481 )
| ~ ( ( ord_less_nat @ SV258 @ SV481 )
| ( SV258 = SV481 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1570]) ).
thf(1742,plain,
! [SV399: nat,SV261: nat,SV90: nat] :
( ( ( ( ( times_times_nat @ SV90 @ SV261 )
= ( times_times_nat @ SV90 @ SV399 ) )
| ( SV90 = zero_zero_nat )
| ( SV261 = SV399 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV90 @ SV261 )
!= ( times_times_nat @ SV90 @ SV399 ) )
| ~ ( ( SV90 = zero_zero_nat )
| ( SV261 = SV399 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1572]) ).
thf(1743,plain,
! [SV92: nat > nat,SV262: nat,SV400: nat] :
( ( ( ! [SY1043: nat] :
( ~ ( ord_less_nat @ ( sK3_SY609 @ SV400 @ SV262 @ SV92 ) @ SY1043 )
| ( ord_less_nat @ ( SV92 @ ( sK3_SY609 @ SV400 @ SV262 @ SV92 ) ) @ ( SV92 @ SY1043 ) ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV262 @ SV400 )
| ( ord_less_eq_nat @ ( SV92 @ SV262 ) @ ( SV92 @ SV400 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1573]) ).
thf(1744,plain,
! [SV263: nat,SV93: nat] :
( ( ( SV93 != SV263 )
= $false )
| ( ( ord_less_nat @ SV93 @ SV263 )
= $true )
| ( ( ord_less_eq_nat @ SV93 @ SV263 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1574]) ).
thf(1745,plain,
! [SV482: nat,SV401: nat,SV264: nat,SV94: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV94 @ SV264 )
| ~ ( ord_less_eq_nat @ SV401 @ SV482 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV94 @ SV401 ) @ ( plus_plus_nat @ SV264 @ SV482 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1575]) ).
thf(1746,plain,
! [SV95: nat,SV265: nat,SV402: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV402 @ SV265 ) )
= $true )
| ( ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV265 @ SV95 ) @ ( minus_minus_nat @ SV265 @ SV402 ) )
= ( ord_less_eq_nat @ SV402 @ SV95 ) )
= $true )
| ( ( ord_less_eq_nat @ SV95 @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1576]) ).
thf(1747,plain,
! [SV483: nat,SV404: nat,SV268: nat,SV98: nat] :
( ( ( ~ ( ( SV98 != SV268 )
| ~ ( ord_less_eq_nat @ SV404 @ SV483 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV98 @ SV404 ) @ ( plus_plus_nat @ SV268 @ SV483 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1578]) ).
thf(1748,plain,
! [SV507: nat,SV484: nat,SV405: nat,SV269: nat,SV99: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV99 @ SV269 ) )
= $true )
| ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV269 @ SV405 ) @ SV484 ) @ ( plus_plus_nat @ ( times_times_nat @ SV99 @ SV405 ) @ SV507 ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV269 @ SV99 ) @ SV405 ) @ SV484 ) @ SV507 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1579]) ).
thf(1749,plain,
! [SV102: nat] :
( ( ( SV102 = zero_zero_nat )
= $true )
| ( ( ~ ( ~ ( ( SV102 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV102 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1582]) ).
thf(1750,plain,
! [SV102: nat] :
( ( ( ~ ( ( SV102 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV102 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1583]) ).
thf(1751,plain,
! [SV485: nat,SV408: nat,SV274: nat,SV105: nat] :
( ( ( ord_less_nat @ SV105 @ SV274 )
= $false )
| ( ( ~ ( ord_less_nat @ SV408 @ SV485 )
| ( ord_less_nat @ ( plus_plus_nat @ SV105 @ SV408 ) @ ( plus_plus_nat @ SV274 @ SV485 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1585]) ).
thf(1752,plain,
! [SV508: nat,SV486: nat,SV410: nat,SV276: nat,SV107: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV107 @ SV276 ) )
= $true )
| ( ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ SV107 @ SV410 ) @ SV486 ) @ ( plus_plus_nat @ ( times_times_nat @ SV276 @ SV410 ) @ SV508 ) )
= ( minus_minus_nat @ SV486 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV276 @ SV107 ) @ SV410 ) @ SV508 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1587]) ).
thf(1753,plain,
! [SV487: nat,SV412: nat,SV278: nat,SV109: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV109 @ SV278 )
| ~ ( ord_less_nat @ SV412 @ SV487 ) ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV109 @ SV412 ) @ ( plus_plus_nat @ SV278 @ SV487 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1589]) ).
thf(1754,plain,
! [SV279: nat,SV413: nat,SV110: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV110 @ SV413 ) )
= $true )
| ( ( ( ( minus_minus_nat @ SV279 @ SV110 )
= ( minus_minus_nat @ SV413 @ SV110 ) )
= ( SV279 = SV413 ) )
= $true )
| ( ( ord_less_eq_nat @ SV110 @ SV279 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1590]) ).
thf(1755,plain,
! [SV112: nat,SV281: nat] :
( ( ( ( minus_minus_nat @ SV281 @ SV112 )
= zero_zero_nat )
= $false )
| ( ( SV112 = SV281 )
= $true )
| ( ( ( minus_minus_nat @ SV112 @ SV281 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1592]) ).
thf(1756,plain,
! [SV113: nat,SV282: nat,SV415: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV415 @ ( minus_minus_nat @ SV282 @ SV113 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV415 @ SV113 ) @ SV282 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV415 @ ( minus_minus_nat @ SV282 @ SV113 ) )
| ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV415 @ SV113 ) @ SV282 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV113 @ SV282 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1593]) ).
thf(1757,plain,
! [SV113: nat,SV282: nat,SV415: nat] :
( ( ( ( ord_less_eq_nat @ SV415 @ ( minus_minus_nat @ SV282 @ SV113 ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ SV415 @ SV113 ) @ SV282 ) )
= $true )
| ( ( ord_less_eq_nat @ SV113 @ SV282 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1593]) ).
thf(1758,plain,
! [SV283: nat,SV114: nat > $o] :
( ( ( ! [SY655: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY655 )
| ~ ~ ( SV114 @ SY655 )
| ~ ! [SY656: nat] :
~ ~ ( ~ ( ord_less_nat @ SY656 @ SY655 )
| ~ ~ ( SV114 @ SY656 ) ) ) )
= $false )
| ( ( SV114 @ SV283 )
= $true )
| ( ( SV114 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1594]) ).
thf(1759,plain,
! [SV115: nat] :
( ( ( SV115 = zero_zero_nat )
= $true )
| ( ( ~ ( ~ ( ( SV115 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV115 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1595]) ).
thf(1760,plain,
! [SV115: nat] :
( ( ( ~ ( ( SV115 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV115 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1596]) ).
thf(1761,plain,
! [SV417: nat,SV285: nat,SV117: nat > $o] :
( ( ( ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1598]) ).
thf(1762,plain,
! [SV286: nat,SV418: nat,SV118: nat] :
( ( ( ~ ( ord_less_nat @ SV118 @ SV418 ) )
= $true )
| ( ( ord_less_nat @ ( minus_minus_nat @ SV418 @ SV286 ) @ ( minus_minus_nat @ SV418 @ SV118 ) )
= $true )
| ( ( ord_less_nat @ SV118 @ SV286 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1599]) ).
thf(1763,plain,
! [SV119: nat,SV287: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV287 )
= $false )
| ( ( ord_less_nat @ ( minus_minus_nat @ SV287 @ SV119 ) @ SV287 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1600]) ).
thf(1764,plain,
! [SV488: nat,SV288: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV288 @ SV488 )
| ~ ! [SY1033: nat] :
( SV488
!= ( plus_plus_nat @ SV288 @ SY1033 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV288 @ SV488 )
| ~ ~ ! [SY1033: nat] :
( SV488
!= ( plus_plus_nat @ SV288 @ SY1033 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1601]) ).
thf(1765,plain,
! [SV489: nat,SV289: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV289 @ SV489 )
| ~ ! [SY1034: nat] :
( SV489
!= ( plus_plus_nat @ SV289 @ SY1034 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV289 @ SV489 )
| ~ ~ ! [SY1034: nat] :
( SV489
!= ( plus_plus_nat @ SV289 @ SY1034 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1603]) ).
thf(1766,plain,
! [SV421: nat,SV122: nat,SV290: nat] :
( ( ( ~ ( ( ( minus_minus_nat @ SV290 @ SV122 )
= SV421 )
| ( SV290
= ( plus_plus_nat @ SV421 @ SV122 ) ) )
| ~ ( ( ( minus_minus_nat @ SV290 @ SV122 )
!= SV421 )
| ( SV290
!= ( plus_plus_nat @ SV421 @ SV122 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV122 @ SV290 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1605]) ).
thf(1767,plain,
! [SV421: nat,SV122: nat,SV290: nat] :
( ( ( ( ( minus_minus_nat @ SV290 @ SV122 )
= SV421 )
= ( SV290
= ( plus_plus_nat @ SV421 @ SV122 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV122 @ SV290 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1605]) ).
thf(1768,plain,
! [SV509: nat,SV490: nat,SV422: nat,SV291: nat,SV123: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV123 @ SV291 ) )
= $true )
| ( ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ SV291 @ SV422 ) @ SV490 ) @ ( plus_plus_nat @ ( times_times_nat @ SV123 @ SV422 ) @ SV509 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV291 @ SV123 ) @ SV422 ) @ SV490 ) @ SV509 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1606]) ).
thf(1769,plain,
! [SV294: nat,SV126: nat] :
( ( ( ( plus_plus_nat @ SV126 @ SV294 )
= zero_zero_nat )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ SV126 @ SV294 )
!= zero_zero_nat )
| ~ ~ ( ( SV126 != zero_zero_nat )
| ( SV294 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1609]) ).
thf(1770,plain,
! [SV294: nat,SV126: nat] :
( ( ( ~ ( ( SV126 != zero_zero_nat )
| ( SV294 != zero_zero_nat ) ) )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ SV126 @ SV294 )
!= zero_zero_nat )
| ~ ~ ( ( SV126 != zero_zero_nat )
| ( SV294 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1609]) ).
thf(1771,plain,
! [SV510: nat,SV491: nat,SV425: nat,SV295: nat,SV127: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV127 @ SV295 ) )
= $true )
| ( ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV127 @ SV425 ) @ SV491 ) @ ( plus_plus_nat @ ( times_times_nat @ SV295 @ SV425 ) @ SV510 ) )
= ( ord_less_nat @ SV491 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV295 @ SV127 ) @ SV425 ) @ SV510 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1610]) ).
thf(1772,plain,
! [SV492: nat,SV429: nat,SV300: nat,SV132: nat] :
( ( ( ord_less_nat @ SV132 @ SV300 )
= $false )
| ( ( ( ( plus_plus_nat @ SV429 @ SV300 )
!= ( plus_plus_nat @ SV132 @ SV492 ) )
| ( ord_less_nat @ SV429 @ SV492 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1615]) ).
thf(1773,plain,
! [SV134: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV134 )
| ~ ( ( SV134 != zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1617]) ).
thf(1774,plain,
! [SV134: nat] :
( ( ( SV134 = zero_zero_nat )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV134 )
| ~ ( ( SV134 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1618]) ).
thf(1775,plain,
! [SV493: nat,SV433: nat,SV304: nat,SV137: nat] :
( ( ( ord_less_eq_nat @ SV137 @ SV304 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV433 @ SV493 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV137 @ SV433 ) @ ( plus_plus_nat @ SV304 @ SV493 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1621]) ).
thf(1776,plain,
! [SV309: nat,SV142: nat > $o] :
( ( ( ~ ~ ( SV142 @ ( sK1_SY712 @ SV309 @ SV142 ) ) )
= $false )
| ( ( SV142 @ SV309 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1626]) ).
thf(1777,plain,
! [SV142: nat > $o,SV309: nat] :
( ( ( ~ ! [SY1041: nat] :
~ ~ ( ~ ( ord_less_nat @ SY1041 @ ( sK1_SY712 @ SV309 @ SV142 ) )
| ~ ~ ( SV142 @ SY1041 ) ) )
= $false )
| ( ( SV142 @ SV309 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1626]) ).
thf(1778,plain,
! [SV511: nat,SV494: nat,SV440: nat,SV313: nat,SV146: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV146 @ SV313 ) )
= $true )
| ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV146 @ SV440 ) @ SV494 ) @ ( plus_plus_nat @ ( times_times_nat @ SV313 @ SV440 ) @ SV511 ) )
= ( ord_less_eq_nat @ SV494 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV313 @ SV146 ) @ SV440 ) @ SV511 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1629]) ).
thf(1779,plain,
! [SV495: nat,SV442: nat,SV315: nat,SV148: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV148 @ SV315 )
| ( SV442 != SV495 ) ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV148 @ SV442 ) @ ( plus_plus_nat @ SV315 @ SV495 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1631]) ).
thf(1780,plain,
! [SV496: nat,SV443: nat,SV317: nat,SV150: nat] :
( ( ( ord_less_nat @ SV150 @ SV317 )
= $false )
| ( ( ~ ( ord_less_nat @ SV443 @ SV496 )
| ( ord_less_nat @ ( plus_plus_nat @ SV150 @ SV443 ) @ ( plus_plus_nat @ SV317 @ SV496 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1632]) ).
thf(1781,plain,
! [SV444: nat,SV318: nat,SV152: nat] :
( ( ( ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV318 )
| ~ ( ord_less_nat @ SV152 @ SV444 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV318 )
| ~ ( ord_less_nat @ SV152 @ SV444 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1633]) ).
thf(1782,plain,
! [SV321: nat,SV155: nat] :
( ( ( SV155 != SV321 )
= $false )
| ( ( ~ ( ~ ( ( SV155 != SV321 ) )
| ~ ( ( ord_less_nat @ SV155 @ SV321 )
| ( ord_less_nat @ SV321 @ SV155 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1636]) ).
thf(1783,plain,
! [SV321: nat,SV155: nat] :
( ( ( ( ord_less_nat @ SV155 @ SV321 )
| ( ord_less_nat @ SV321 @ SV155 ) )
= $false )
| ( ( ~ ( ~ ( ( SV155 != SV321 ) )
| ~ ( ( ord_less_nat @ SV155 @ SV321 )
| ( ord_less_nat @ SV321 @ SV155 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1636]) ).
thf(1784,plain,
! [SV325: nat,SV159: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV159 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV325 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1640]) ).
thf(1785,plain,
! [SV325: nat,SV159: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV159 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV325 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV159 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV325 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1640]) ).
thf(1786,plain,
! [SV326: nat,SV160: nat] :
( ( ( ( plus_plus_nat @ SV160 @ SV326 )
= zero_zero_nat )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ SV160 @ SV326 )
!= zero_zero_nat )
| ~ ~ ( ( SV160 != zero_zero_nat )
| ( SV326 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1641]) ).
thf(1787,plain,
! [SV326: nat,SV160: nat] :
( ( ( ~ ( ( SV160 != zero_zero_nat )
| ( SV326 != zero_zero_nat ) ) )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ SV160 @ SV326 )
!= zero_zero_nat )
| ~ ~ ( ( SV160 != zero_zero_nat )
| ( SV326 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1641]) ).
thf(1788,plain,
! [SV497: nat,SV327: nat] :
( ( ( ~ ( ( ord_less_nat @ SV327 @ SV497 )
| ~ ( ~ ( ord_less_eq_nat @ SV327 @ SV497 )
| ~ ( ( SV327 != SV497 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV327 @ SV497 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV327 @ SV497 )
| ~ ( ( SV327 != SV497 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1642]) ).
thf(1789,plain,
! [SV328: nat,SV162: nat] :
( ( ( zero_zero_nat
= ( plus_plus_nat @ SV162 @ SV328 ) )
= $false )
| ( ( ~ ( ( zero_zero_nat
!= ( plus_plus_nat @ SV162 @ SV328 ) )
| ~ ~ ( ( SV162 != zero_zero_nat )
| ( SV328 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1644]) ).
thf(1790,plain,
! [SV328: nat,SV162: nat] :
( ( ( ~ ( ( SV162 != zero_zero_nat )
| ( SV328 != zero_zero_nat ) ) )
= $false )
| ( ( ~ ( ( zero_zero_nat
!= ( plus_plus_nat @ SV162 @ SV328 ) )
| ~ ~ ( ( SV162 != zero_zero_nat )
| ( SV328 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1644]) ).
thf(1791,plain,
! [SV448: nat,SV329: nat,SV163: nat] :
( ( ( ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV329 )
| ( ord_less_eq_nat @ SV163 @ SV448 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV329 )
| ( ord_less_eq_nat @ SV163 @ SV448 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1645]) ).
thf(1792,plain,
! [SV330: nat,SV449: nat,SV164: nat > $o] :
( ( ( ~ ! [SY1015: nat] :
( ~ ( SV164 @ SY1015 )
| ( ord_less_eq_nat @ SY1015 @ SV449 ) ) )
= $true )
| ( ( ~ ! [SY751: nat] :
~ ~ ( ~ ( SV164 @ SY751 )
| ~ ! [SY752: nat] :
( ~ ( SV164 @ SY752 )
| ( ord_less_eq_nat @ SY752 @ SY751 ) ) ) )
= $true )
| ( ( SV164 @ SV330 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1646]) ).
thf(1793,plain,
! [SV332: nat,SV451: nat,SV167: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV167 @ SV451 ) )
= $true )
| ( ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV332 @ SV167 ) @ ( minus_minus_nat @ SV451 @ SV167 ) )
= ( ord_less_eq_nat @ SV332 @ SV451 ) )
= $true )
| ( ( ord_less_eq_nat @ SV167 @ SV332 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1648]) ).
thf(1794,plain,
! [SV453: nat,SV169: nat,SV334: nat] :
( ( ( ~ ( ( ord_less_nat @ ( minus_minus_nat @ SV334 @ SV169 ) @ SV453 )
| ( ord_less_nat @ SV334 @ ( plus_plus_nat @ SV453 @ SV169 ) ) )
| ~ ( ~ ( ord_less_nat @ ( minus_minus_nat @ SV334 @ SV169 ) @ SV453 )
| ~ ( ord_less_nat @ SV334 @ ( plus_plus_nat @ SV453 @ SV169 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV169 @ SV334 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1650]) ).
thf(1795,plain,
! [SV453: nat,SV169: nat,SV334: nat] :
( ( ( ( ord_less_nat @ ( minus_minus_nat @ SV334 @ SV169 ) @ SV453 )
= ( ord_less_nat @ SV334 @ ( plus_plus_nat @ SV453 @ SV169 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV169 @ SV334 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1650]) ).
thf(1796,plain,
! [SV498: nat,SV454: nat,SV335: nat,SV170: nat] :
( ( ( SV170
= ( plus_plus_nat @ SV335 @ SV454 ) )
= $false )
| ( ( ( plus_plus_nat @ SV170 @ SV498 )
= ( plus_plus_nat @ SV335 @ ( plus_plus_nat @ SV454 @ SV498 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1651]) ).
thf(1797,plain,
! [SV336: nat,SV455: nat,SV171: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV171 @ SV455 ) )
= $true )
| ( ( ( minus_minus_nat @ ( minus_minus_nat @ SV336 @ SV171 ) @ ( minus_minus_nat @ SV455 @ SV171 ) )
= ( minus_minus_nat @ SV336 @ SV455 ) )
= $true )
| ( ( ord_less_eq_nat @ SV171 @ SV336 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1652]) ).
thf(1798,plain,
! [SV512: nat,SV499: nat,SV457: nat,SV338: nat,SV174: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV174 @ SV338 ) )
= $true )
| ( ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV338 @ SV457 ) @ SV499 ) @ ( plus_plus_nat @ ( times_times_nat @ SV174 @ SV457 ) @ SV512 ) )
= ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV338 @ SV174 ) @ SV457 ) @ SV499 ) @ SV512 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1654]) ).
thf(1799,plain,
! [SV500: nat,SV458: nat,SV339: nat,SV175: nat] :
( ( ( SV175
= ( plus_plus_nat @ SV339 @ SV458 ) )
= $false )
| ( ( ( plus_plus_nat @ SV500 @ SV175 )
= ( plus_plus_nat @ SV339 @ ( plus_plus_nat @ SV500 @ SV458 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1655]) ).
thf(1800,plain,
! [SV459: nat,SV341: nat,SV177: nat] :
( ( ( ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 )
| ~ ( ord_less_nat @ SV341 @ SV459 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 )
| ~ ( ord_less_nat @ SV341 @ SV459 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1656]) ).
thf(1801,plain,
! [SV342: nat,SV178: nat] :
( ( ( ~ ~ ( ord_less_nat @ SV178 @ SV342 ) )
= $true )
| ( ( ord_less_nat @ SV342 @ SV178 )
= $true )
| ( ( SV178 = SV342 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1657]) ).
thf(1802,plain,
! [SV181: nat > $o,SV345: nat] :
( ( ( ~ ! [SY1042: nat] :
( ~ ( ord_less_nat @ SY1042 @ ( sK2_SY783 @ SV345 @ SV181 ) )
| ( SV181 @ SY1042 ) ) )
= $false )
| ( ( SV181 @ SV345 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1659]) ).
thf(1803,plain,
! [SV345: nat,SV181: nat > $o] :
( ( ( SV181 @ ( sK2_SY783 @ SV345 @ SV181 ) )
= $false )
| ( ( SV181 @ SV345 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1659]) ).
thf(1804,plain,
! [SV461: nat,SV346: nat,SV182: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV182 @ SV346 ) )
= $true )
| ( ( ( ( minus_minus_nat @ SV346 @ SV182 )
= SV461 )
= ( SV346
= ( plus_plus_nat @ SV461 @ SV182 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1660]) ).
thf(1805,plain,
! [SV348: nat,SV463: nat,SV184: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV184 @ SV463 ) )
= $true )
| ( ( ( ord_less_nat @ ( minus_minus_nat @ SV348 @ SV184 ) @ ( minus_minus_nat @ SV463 @ SV184 ) )
= ( ord_less_nat @ SV348 @ SV463 ) )
= $true )
| ( ( ord_less_eq_nat @ SV184 @ SV348 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1662]) ).
thf(1806,plain,
! [SV185: nat,SV349: nat,SV464: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV464 @ ( minus_minus_nat @ SV349 @ SV185 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV464 @ SV185 ) @ SV349 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV464 @ ( minus_minus_nat @ SV349 @ SV185 ) )
| ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV464 @ SV185 ) @ SV349 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV185 @ SV349 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1663]) ).
thf(1807,plain,
! [SV185: nat,SV349: nat,SV464: nat] :
( ( ( ( ord_less_eq_nat @ SV464 @ ( minus_minus_nat @ SV349 @ SV185 ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ SV464 @ SV185 ) @ SV349 ) )
= $true )
| ( ( ord_less_eq_nat @ SV185 @ SV349 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1663]) ).
thf(1808,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1664]) ).
thf(1809,plain,
! [SV352: nat,SV188: nat,SV467: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV467 @ SV188 ) )
= $true )
| ( ( ord_less_nat @ ( minus_minus_nat @ SV188 @ SV467 ) @ ( minus_minus_nat @ SV352 @ SV467 ) )
= $true )
| ( ( ord_less_nat @ SV188 @ SV352 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1666]) ).
thf(1810,plain,
! [SV189: nat,SV353: nat] :
( ( ( ord_less_eq_nat @ SV353 @ SV189 )
= $false )
| ( ( SV189 = SV353 )
= $true )
| ( ( ord_less_eq_nat @ SV189 @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1667]) ).
thf(1811,plain,
! [SV513: nat,SV501: nat,SV468: nat,SV354: nat,SV190: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV190 @ SV354 ) )
= $true )
| ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV354 @ SV468 ) @ SV501 )
= ( plus_plus_nat @ ( times_times_nat @ SV190 @ SV468 ) @ SV513 ) )
= ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV354 @ SV190 ) @ SV468 ) @ SV501 )
= SV513 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1668]) ).
thf(1812,plain,
! [SV191: nat,SV355: nat] :
( ( ( SV355
!= ( plus_plus_nat @ SV191 @ ( sK4_SY975 @ SV191 @ SV355 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV191 @ SV355 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1669]) ).
thf(1813,plain,
! [SV502: nat,SV469: nat,SV356: nat,SV192: nat] :
( ( ( ~ ( ( SV192 != SV356 )
| ~ ( ord_less_nat @ SV469 @ SV502 ) ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV192 @ SV469 ) @ ( plus_plus_nat @ SV356 @ SV502 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1670]) ).
thf(1814,plain,
! [SV503: nat,SV470: nat,SV357: nat,SV193: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV193 @ SV357 )
| ( SV470 != SV503 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV193 @ SV470 ) @ ( plus_plus_nat @ SV357 @ SV503 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1671]) ).
thf(1815,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV194 )
| ( ord_less_eq_nat @ SV358 @ SV471 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV194 )
| ( ord_less_eq_nat @ SV358 @ SV471 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1672]) ).
thf(1816,plain,
! [SV195: nat,SV472: nat,SV359: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV359 @ SV472 ) )
= $true )
| ( ( ord_less_eq_nat @ SV195 @ SV472 )
= $true )
| ( ( ord_less_eq_nat @ SV195 @ SV359 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1673]) ).
thf(1817,plain,
! [SV504: nat,SV473: nat,SV360: nat,SV196: nat] :
( ( ( ~ ( ( SV196 != SV360 )
| ( SV473 != SV504 ) ) )
= $false )
| ( ( ( plus_plus_nat @ SV196 @ SV473 )
= ( plus_plus_nat @ SV360 @ SV504 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1674]) ).
thf(1818,plain,
! [SV514: nat,SV505: nat,SV474: nat,SV361: nat,SV197: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV197 @ SV361 ) )
= $true )
| ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV197 @ SV474 ) @ SV505 )
= ( plus_plus_nat @ ( times_times_nat @ SV361 @ SV474 ) @ SV514 ) )
= ( SV505
= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV361 @ SV197 ) @ SV474 ) @ SV514 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1675]) ).
thf(1819,plain,
! [SV506: nat,SV475: nat,SV362: nat,SV198: nat] :
( ( ( ord_less_eq_nat @ SV198 @ SV362 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV475 @ SV506 )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV198 @ SV475 ) @ ( plus_plus_nat @ SV362 @ SV506 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1676]) ).
thf(1820,plain,
! [SV1: nat > nat] :
( ( ( ~ ( number1551313001itions @ SV1 @ zero_zero_nat ) )
= $false )
| ( ( number1551313001itions @ SV1 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1682]) ).
thf(1821,plain,
! [SV1: nat > nat] :
( ( ( SV1
!= ( ^ [I: nat] : zero_zero_nat ) )
= $false )
| ( ( number1551313001itions @ SV1 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1682]) ).
thf(1822,plain,
! [SV1: nat > nat] :
( ( ( ( SV1 @ ( sK5_SV515 @ SV1 ) )
= zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( number1551313001itions @ SV1 @ zero_zero_nat )
| ( SV1
!= ( ^ [I: nat] : zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1683]) ).
thf(1823,plain,
! [SV1: nat > nat] :
( ( ( ~ ( number1551313001itions @ SV1 @ zero_zero_nat )
| ( SV1
!= ( ^ [I: nat] : zero_zero_nat ) ) )
= $false )
| ( ( SV1
= ( ^ [I: nat] : zero_zero_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1684]) ).
thf(1824,plain,
! [SV204: nat,SV2: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SV204 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( ord_less_nat @ zero_zero_nat @ SV204 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SV204 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1685]) ).
thf(1825,plain,
! [SV204: nat,SV2: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV2 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SV204 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( ord_less_nat @ zero_zero_nat @ SV204 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1686]) ).
thf(1826,plain,
! [SV2: nat,SV204: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV204 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SV204 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( ord_less_nat @ zero_zero_nat @ SV204 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1686]) ).
thf(1827,plain,
! [SV205: nat,SV3: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV3 @ SV205 ) @ SV3 )
| ~ ( ord_less_nat @ SV205 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV3 @ SV205 ) @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1687]) ).
thf(1828,plain,
! [SV205: nat,SV3: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV3 @ SV205 ) @ SV3 )
| ~ ( ord_less_nat @ SV205 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ SV205 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1688]) ).
thf(1829,plain,
! [SV206: nat,SV4: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV4 @ SV206 ) @ SV206 )
| ~ ( ord_less_nat @ SV4 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV4 @ SV206 ) @ SV206 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1689]) ).
thf(1830,plain,
! [SV206: nat,SV4: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV4 @ SV206 ) @ SV206 )
| ~ ( ord_less_nat @ SV4 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ SV4 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1690]) ).
thf(1831,plain,
! [SV207: nat,SV5: nat] :
( ( ( ~ ( ord_less_nat @ SV5 @ ( plus_plus_nat @ SV5 @ SV207 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV207 ) )
= $false )
| ( ( ord_less_nat @ SV5 @ ( plus_plus_nat @ SV5 @ SV207 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1691]) ).
thf(1832,plain,
! [SV207: nat,SV5: nat] :
( ( ( ~ ( ord_less_nat @ SV5 @ ( plus_plus_nat @ SV5 @ SV207 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV207 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV207 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1692]) ).
thf(1833,plain,
! [SV208: nat,SV6: nat] :
( ( ( ~ ( ord_less_nat @ SV6 @ ( plus_plus_nat @ SV208 @ SV6 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV208 ) )
= $false )
| ( ( ord_less_nat @ SV6 @ ( plus_plus_nat @ SV208 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1693]) ).
thf(1834,plain,
! [SV208: nat,SV6: nat] :
( ( ( ~ ( ord_less_nat @ SV6 @ ( plus_plus_nat @ SV208 @ SV6 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV208 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV208 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1694]) ).
thf(1835,plain,
! [SV368: nat,SV209: nat,SV7: nat] :
( ( ( ( plus_plus_nat @ SV7 @ SV209 )
= ( plus_plus_nat @ SV368 @ SV209 ) )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ SV7 @ SV209 )
!= ( plus_plus_nat @ SV368 @ SV209 ) )
| ( SV7 != SV368 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1695]) ).
thf(1836,plain,
! [SV209: nat,SV368: nat,SV7: nat] :
( ( ( SV7 = SV368 )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ SV7 @ SV209 )
!= ( plus_plus_nat @ SV368 @ SV209 ) )
| ( SV7 != SV368 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1695]) ).
thf(1837,plain,
! [SV369: nat,SV210: nat,SV8: nat] :
( ( ( ( plus_plus_nat @ SV8 @ SV210 )
= ( plus_plus_nat @ SV8 @ SV369 ) )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ SV8 @ SV210 )
!= ( plus_plus_nat @ SV8 @ SV369 ) )
| ( SV210 != SV369 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1696]) ).
thf(1838,plain,
! [SV8: nat,SV369: nat,SV210: nat] :
( ( ( SV210 = SV369 )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ SV8 @ SV210 )
!= ( plus_plus_nat @ SV8 @ SV369 ) )
| ( SV210 != SV369 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1696]) ).
thf(1839,plain,
! [SV9: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV9 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV9 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1697]) ).
thf(1840,plain,
! [SV9: nat] :
( ( ( SV9 != zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ SV9 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1697]) ).
thf(1841,plain,
! [SV9: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV9 @ zero_zero_nat ) )
= $false )
| ( ( SV9 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1698]) ).
thf(1842,plain,
! [SV9: nat] :
( ( ( SV9 != zero_zero_nat )
= $false )
| ( ( SV9 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1698]) ).
thf(1843,plain,
! [SV10: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV10 )
| ( SV10 != zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1699]) ).
thf(1844,plain,
! [SV10: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV10 ) )
= $false )
| ( ( SV10 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1700]) ).
thf(1845,plain,
! [SV10: nat] :
( ( ( SV10 != zero_zero_nat )
= $false )
| ( ( SV10 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1700]) ).
thf(1846,plain,
! [SV370: nat,SV211: nat,SV11: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV11 @ SV211 ) @ ( plus_plus_nat @ SV370 @ SV211 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV11 @ SV211 ) @ ( plus_plus_nat @ SV370 @ SV211 ) )
| ~ ( ord_less_eq_nat @ SV11 @ SV370 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1701]) ).
thf(1847,plain,
! [SV211: nat,SV370: nat,SV11: nat] :
( ( ( ord_less_eq_nat @ SV11 @ SV370 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV11 @ SV211 ) @ ( plus_plus_nat @ SV370 @ SV211 ) )
| ~ ( ord_less_eq_nat @ SV11 @ SV370 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1701]) ).
thf(1848,plain,
! [SV371: nat,SV212: nat,SV12: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV212 ) @ ( plus_plus_nat @ SV12 @ SV371 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV212 ) @ ( plus_plus_nat @ SV12 @ SV371 ) )
| ~ ( ord_less_eq_nat @ SV212 @ SV371 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1702]) ).
thf(1849,plain,
! [SV12: nat,SV371: nat,SV212: nat] :
( ( ( ord_less_eq_nat @ SV212 @ SV371 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV212 ) @ ( plus_plus_nat @ SV12 @ SV371 ) )
| ~ ( ord_less_eq_nat @ SV212 @ SV371 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1702]) ).
thf(1850,plain,
! [SV213: nat,SV13: nat] :
( ( ( ( SV13
!= ( plus_plus_nat @ SV13 @ SV213 ) )
| ( SV213 != zero_zero_nat ) )
= $false )
| ( ( SV13
= ( plus_plus_nat @ SV13 @ SV213 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1703]) ).
thf(1851,plain,
! [SV213: nat,SV13: nat] :
( ( ( ( SV13
!= ( plus_plus_nat @ SV13 @ SV213 ) )
| ( SV213 != zero_zero_nat ) )
= $false )
| ( ( SV213 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1704]) ).
thf(1852,plain,
! [SV214: nat,SV14: nat] :
( ( ( ( SV14
!= ( plus_plus_nat @ SV214 @ SV14 ) )
| ( SV214 != zero_zero_nat ) )
= $false )
| ( ( SV14
= ( plus_plus_nat @ SV214 @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1705]) ).
thf(1853,plain,
! [SV214: nat,SV14: nat] :
( ( ( ( SV14
!= ( plus_plus_nat @ SV214 @ SV14 ) )
| ( SV214 != zero_zero_nat ) )
= $false )
| ( ( SV214 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1706]) ).
thf(1854,plain,
! [SV215: nat,SV15: nat] :
( ( ( ( ( plus_plus_nat @ SV15 @ SV215 )
!= SV15 )
| ( SV215 != zero_zero_nat ) )
= $false )
| ( ( ( plus_plus_nat @ SV15 @ SV215 )
= SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1707]) ).
thf(1855,plain,
! [SV215: nat,SV15: nat] :
( ( ( ( ( plus_plus_nat @ SV15 @ SV215 )
!= SV15 )
| ( SV215 != zero_zero_nat ) )
= $false )
| ( ( SV215 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1708]) ).
thf(1856,plain,
! [SV216: nat,SV16: nat] :
( ( ( ( ( plus_plus_nat @ SV16 @ SV216 )
!= SV216 )
| ( SV16 != zero_zero_nat ) )
= $false )
| ( ( ( plus_plus_nat @ SV16 @ SV216 )
= SV216 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1709]) ).
thf(1857,plain,
! [SV216: nat,SV16: nat] :
( ( ( ( ( plus_plus_nat @ SV16 @ SV216 )
!= SV216 )
| ( SV16 != zero_zero_nat ) )
= $false )
| ( ( SV16 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1710]) ).
thf(1858,plain,
! [SV372: nat,SV217: nat,SV22: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV22 @ SV217 ) @ ( plus_plus_nat @ SV372 @ SV217 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV22 @ SV217 ) @ ( plus_plus_nat @ SV372 @ SV217 ) )
| ~ ( ord_less_nat @ SV22 @ SV372 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1711]) ).
thf(1859,plain,
! [SV217: nat,SV372: nat,SV22: nat] :
( ( ( ord_less_nat @ SV22 @ SV372 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV22 @ SV217 ) @ ( plus_plus_nat @ SV372 @ SV217 ) )
| ~ ( ord_less_nat @ SV22 @ SV372 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1711]) ).
thf(1860,plain,
! [SV373: nat,SV218: nat,SV23: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV23 @ SV218 ) @ ( plus_plus_nat @ SV23 @ SV373 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV23 @ SV218 ) @ ( plus_plus_nat @ SV23 @ SV373 ) )
| ~ ( ord_less_nat @ SV218 @ SV373 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1712]) ).
thf(1861,plain,
! [SV23: nat,SV373: nat,SV218: nat] :
( ( ( ord_less_nat @ SV218 @ SV373 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV23 @ SV218 ) @ ( plus_plus_nat @ SV23 @ SV373 ) )
| ~ ( ord_less_nat @ SV218 @ SV373 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1712]) ).
thf(1862,plain,
! [SV376: nat,SV223: nat,SV32: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV32 @ SV223 ) @ ( plus_plus_nat @ SV32 @ SV376 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV32 @ SV223 ) @ ( plus_plus_nat @ SV32 @ SV376 ) )
| ~ ( ord_less_nat @ SV223 @ SV376 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1713]) ).
thf(1863,plain,
! [SV32: nat,SV376: nat,SV223: nat] :
( ( ( ord_less_nat @ SV223 @ SV376 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV32 @ SV223 ) @ ( plus_plus_nat @ SV32 @ SV376 ) )
| ~ ( ord_less_nat @ SV223 @ SV376 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1713]) ).
thf(1864,plain,
! [SV377: nat,SV224: nat,SV35: nat] :
( ( ( ( times_times_nat @ SV35 @ SV224 )
= ( times_times_nat @ SV377 @ SV224 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV35 @ SV224 )
!= ( times_times_nat @ SV377 @ SV224 ) )
| ~ ( ( SV35 = SV377 )
| ( SV224 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1714]) ).
thf(1865,plain,
! [SV224: nat,SV377: nat,SV35: nat] :
( ( ( ( SV35 = SV377 )
| ( SV224 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV35 @ SV224 )
!= ( times_times_nat @ SV377 @ SV224 ) )
| ~ ( ( SV35 = SV377 )
| ( SV224 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1714]) ).
thf(1866,plain,
! [SV378: nat,SV225: nat,SV36: nat] :
( ( ( ( times_times_nat @ SV36 @ SV225 )
= ( times_times_nat @ SV36 @ SV378 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV36 @ SV225 )
!= ( times_times_nat @ SV36 @ SV378 ) )
| ~ ( ( SV225 = SV378 )
| ( SV36 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1715]) ).
thf(1867,plain,
! [SV36: nat,SV378: nat,SV225: nat] :
( ( ( ( SV225 = SV378 )
| ( SV36 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV36 @ SV225 )
!= ( times_times_nat @ SV36 @ SV378 ) )
| ~ ( ( SV225 = SV378 )
| ( SV36 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1715]) ).
thf(1868,plain,
! [SV226: nat,SV38: nat] :
( ( ( ( ( times_times_nat @ SV38 @ SV226 )
!= zero_zero_nat )
| ~ ( ( SV38 = zero_zero_nat )
| ( SV226 = zero_zero_nat ) ) )
= $false )
| ( ( ( times_times_nat @ SV38 @ SV226 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1716]) ).
thf(1869,plain,
! [SV226: nat,SV38: nat] :
( ( ( SV38 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV38 @ SV226 )
!= zero_zero_nat )
| ~ ( ( SV38 = zero_zero_nat )
| ( SV226 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1717]) ).
thf(1870,plain,
! [SV38: nat,SV226: nat] :
( ( ( SV226 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV38 @ SV226 )
!= zero_zero_nat )
| ~ ( ( SV38 = zero_zero_nat )
| ( SV226 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1717]) ).
thf(1871,plain,
! [SV379: nat,SV227: nat,SV39: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV39 @ SV227 ) @ ( plus_plus_nat @ SV39 @ SV379 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV39 @ SV227 ) @ ( plus_plus_nat @ SV39 @ SV379 ) )
| ~ ( ord_less_eq_nat @ SV227 @ SV379 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1718]) ).
thf(1872,plain,
! [SV39: nat,SV379: nat,SV227: nat] :
( ( ( ord_less_eq_nat @ SV227 @ SV379 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV39 @ SV227 ) @ ( plus_plus_nat @ SV39 @ SV379 ) )
| ~ ( ord_less_eq_nat @ SV227 @ SV379 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1718]) ).
thf(1873,plain,
! [SV229: nat,SV41: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV41 @ ( plus_plus_nat @ SV229 @ SV41 ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV229 ) )
= $false )
| ( ( ord_less_eq_nat @ SV41 @ ( plus_plus_nat @ SV229 @ SV41 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1719]) ).
thf(1874,plain,
! [SV229: nat,SV41: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV41 @ ( plus_plus_nat @ SV229 @ SV41 ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV229 ) )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV229 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1720]) ).
thf(1875,plain,
! [SV230: nat,SV42: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV42 @ ( plus_plus_nat @ SV42 @ SV230 ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV230 ) )
= $false )
| ( ( ord_less_eq_nat @ SV42 @ ( plus_plus_nat @ SV42 @ SV230 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1721]) ).
thf(1876,plain,
! [SV230: nat,SV42: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV42 @ ( plus_plus_nat @ SV42 @ SV230 ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV230 ) )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1722]) ).
thf(1877,plain,
! [SV231: nat,SV43: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV43 @ SV231 ) @ SV231 )
| ~ ( ord_less_eq_nat @ SV43 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV43 @ SV231 ) @ SV231 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1723]) ).
thf(1878,plain,
! [SV231: nat,SV43: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV43 @ SV231 ) @ SV231 )
| ~ ( ord_less_eq_nat @ SV43 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV43 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1724]) ).
thf(1879,plain,
! [SV232: nat,SV44: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV44 @ SV232 ) @ SV44 )
| ~ ( ord_less_eq_nat @ SV232 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV44 @ SV232 ) @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1725]) ).
thf(1880,plain,
! [SV232: nat,SV44: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV44 @ SV232 ) @ SV44 )
| ~ ( ord_less_eq_nat @ SV232 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV232 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1726]) ).
thf(1881,plain,
! [SV234: nat,SV46: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV46 @ SV234 ) )
| ~ ( ord_less_nat @ SV234 @ SV46 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV46 @ SV234 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1727]) ).
thf(1882,plain,
! [SV234: nat,SV46: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV46 @ SV234 ) )
| ~ ( ord_less_nat @ SV234 @ SV46 ) )
= $false )
| ( ( ord_less_nat @ SV234 @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1728]) ).
thf(1883,plain,
! [SV235: nat,SV47: nat] :
( ( ( ( ( minus_minus_nat @ SV47 @ SV235 )
!= zero_zero_nat )
| ~ ( ord_less_eq_nat @ SV47 @ SV235 ) )
= $false )
| ( ( ( minus_minus_nat @ SV47 @ SV235 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1729]) ).
thf(1884,plain,
! [SV235: nat,SV47: nat] :
( ( ( ( ( minus_minus_nat @ SV47 @ SV235 )
!= zero_zero_nat )
| ~ ( ord_less_eq_nat @ SV47 @ SV235 ) )
= $false )
| ( ( ord_less_eq_nat @ SV47 @ SV235 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1730]) ).
thf(1885,plain,
! [SV388: nat,SV247: nat,SV60: nat] :
( ( ( ord_less_nat @ SV60 @ ( minus_minus_nat @ SV247 @ SV388 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV60 @ ( minus_minus_nat @ SV247 @ SV388 ) )
| ~ ( ord_less_nat @ ( plus_plus_nat @ SV60 @ SV388 ) @ SV247 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1731]) ).
thf(1886,plain,
! [SV247: nat,SV388: nat,SV60: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV60 @ SV388 ) @ SV247 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV60 @ ( minus_minus_nat @ SV247 @ SV388 ) )
| ~ ( ord_less_nat @ ( plus_plus_nat @ SV60 @ SV388 ) @ SV247 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1731]) ).
thf(1887,plain,
! [SV389: nat,SV248: nat,SV61: nat] :
( ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV61 @ SV248 ) @ SV389 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( minus_minus_nat @ SV61 @ SV248 ) @ SV389 )
| ~ ( ord_less_eq_nat @ SV61 @ ( plus_plus_nat @ SV389 @ SV248 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1732]) ).
thf(1888,plain,
! [SV248: nat,SV389: nat,SV61: nat] :
( ( ( ord_less_eq_nat @ SV61 @ ( plus_plus_nat @ SV389 @ SV248 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( minus_minus_nat @ SV61 @ SV248 ) @ SV389 )
| ~ ( ord_less_eq_nat @ SV61 @ ( plus_plus_nat @ SV389 @ SV248 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1732]) ).
thf(1889,plain,
! [SV62: nat] :
( ( ( zero_zero_nat != SV62 )
= $false )
| ( ( zero_zero_nat = SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1733]) ).
thf(1890,plain,
! [SV62: nat] :
( ( ( SV62 != zero_zero_nat )
= $false )
| ( ( zero_zero_nat = SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1733]) ).
thf(1891,plain,
! [SV62: nat] :
( ( ( zero_zero_nat != SV62 )
= $false )
| ( ( SV62 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1734]) ).
thf(1892,plain,
! [SV62: nat] :
( ( ( SV62 != zero_zero_nat )
= $false )
| ( ( SV62 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1734]) ).
thf(1893,plain,
! [SV82: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV82 )
| ( SV82 != zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1735]) ).
thf(1894,plain,
! [SV82: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV82 ) )
= $false )
| ( ( SV82 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1736]) ).
thf(1895,plain,
! [SV82: nat] :
( ( ( SV82 != zero_zero_nat )
= $false )
| ( ( SV82 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1736]) ).
thf(1896,plain,
! [SV83: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV83 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV83 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1737]) ).
thf(1897,plain,
! [SV83: nat] :
( ( ( SV83 != zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ SV83 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1737]) ).
thf(1898,plain,
! [SV83: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV83 @ zero_zero_nat ) )
= $false )
| ( ( SV83 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1738]) ).
thf(1899,plain,
! [SV83: nat] :
( ( ( SV83 != zero_zero_nat )
= $false )
| ( ( SV83 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1738]) ).
thf(1900,plain,
! [SV84: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV84 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV84 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1739]) ).
thf(1901,plain,
! [SV84: nat] :
( ( ( SV84 != zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ SV84 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1739]) ).
thf(1902,plain,
! [SV84: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV84 @ zero_zero_nat ) )
= $false )
| ( ( SV84 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1740]) ).
thf(1903,plain,
! [SV84: nat] :
( ( ( SV84 != zero_zero_nat )
= $false )
| ( ( SV84 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1740]) ).
thf(1904,plain,
! [SV481: nat,SV258: nat] :
( ( ( ( ord_less_eq_nat @ SV258 @ SV481 )
| ( ord_less_nat @ SV258 @ SV481 )
| ( SV258 = SV481 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV258 @ SV481 )
| ~ ( ( ord_less_nat @ SV258 @ SV481 )
| ( SV258 = SV481 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1741]) ).
thf(1905,plain,
! [SV399: nat,SV261: nat,SV90: nat] :
( ( ( ( times_times_nat @ SV90 @ SV261 )
= ( times_times_nat @ SV90 @ SV399 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV90 @ SV261 )
!= ( times_times_nat @ SV90 @ SV399 ) )
| ~ ( ( SV90 = zero_zero_nat )
| ( SV261 = SV399 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1742]) ).
thf(1906,plain,
! [SV399: nat,SV261: nat,SV90: nat] :
( ( ( ( SV90 = zero_zero_nat )
| ( SV261 = SV399 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV90 @ SV261 )
!= ( times_times_nat @ SV90 @ SV399 ) )
| ~ ( ( SV90 = zero_zero_nat )
| ( SV261 = SV399 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1742]) ).
thf(1907,plain,
! [SV92: nat > nat,SV262: nat,SV400: nat] :
( ( ( ~ ( ord_less_nat @ ( sK3_SY609 @ SV400 @ SV262 @ SV92 ) @ ( sK6_SY1043 @ SV92 @ SV262 @ SV400 ) )
| ( ord_less_nat @ ( SV92 @ ( sK3_SY609 @ SV400 @ SV262 @ SV92 ) ) @ ( SV92 @ ( sK6_SY1043 @ SV92 @ SV262 @ SV400 ) ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV262 @ SV400 )
| ( ord_less_eq_nat @ ( SV92 @ SV262 ) @ ( SV92 @ SV400 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1743]) ).
thf(1908,plain,
! [SV263: nat,SV93: nat] :
( ( ( SV93 = SV263 )
= $true )
| ( ( ord_less_nat @ SV93 @ SV263 )
= $true )
| ( ( ord_less_eq_nat @ SV93 @ SV263 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1744]) ).
thf(1909,plain,
! [SV482: nat,SV401: nat,SV264: nat,SV94: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV94 @ SV264 )
| ~ ( ord_less_eq_nat @ SV401 @ SV482 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV94 @ SV401 ) @ ( plus_plus_nat @ SV264 @ SV482 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1745]) ).
thf(1910,plain,
! [SV95: nat,SV265: nat,SV402: nat] :
( ( ( ord_less_eq_nat @ SV402 @ SV265 )
= $false )
| ( ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV265 @ SV95 ) @ ( minus_minus_nat @ SV265 @ SV402 ) )
= ( ord_less_eq_nat @ SV402 @ SV95 ) )
= $true )
| ( ( ord_less_eq_nat @ SV95 @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1746]) ).
thf(1911,plain,
! [SV483: nat,SV404: nat,SV268: nat,SV98: nat] :
( ( ( ( SV98 != SV268 )
| ~ ( ord_less_eq_nat @ SV404 @ SV483 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV98 @ SV404 ) @ ( plus_plus_nat @ SV268 @ SV483 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1747]) ).
thf(1912,plain,
! [SV507: nat,SV484: nat,SV405: nat,SV269: nat,SV99: nat] :
( ( ( ord_less_eq_nat @ SV99 @ SV269 )
= $false )
| ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV269 @ SV405 ) @ SV484 ) @ ( plus_plus_nat @ ( times_times_nat @ SV99 @ SV405 ) @ SV507 ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV269 @ SV99 ) @ SV405 ) @ SV484 ) @ SV507 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1748]) ).
thf(1913,plain,
! [SV102: nat] :
( ( ( ~ ( ( SV102 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV102 ) )
= $false )
| ( ( SV102 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1749]) ).
thf(1914,plain,
! [SV102: nat] :
( ( ( ~ ( ( SV102 != zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV102 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1750]) ).
thf(1915,plain,
! [SV102: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV102 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV102 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1750]) ).
thf(1916,plain,
! [SV274: nat,SV105: nat,SV485: nat,SV408: nat] :
( ( ( ~ ( ord_less_nat @ SV408 @ SV485 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV105 @ SV408 ) @ ( plus_plus_nat @ SV274 @ SV485 ) )
= $true )
| ( ( ord_less_nat @ SV105 @ SV274 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1751]) ).
thf(1917,plain,
! [SV508: nat,SV486: nat,SV410: nat,SV276: nat,SV107: nat] :
( ( ( ord_less_eq_nat @ SV107 @ SV276 )
= $false )
| ( ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ SV107 @ SV410 ) @ SV486 ) @ ( plus_plus_nat @ ( times_times_nat @ SV276 @ SV410 ) @ SV508 ) )
= ( minus_minus_nat @ SV486 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV276 @ SV107 ) @ SV410 ) @ SV508 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1752]) ).
thf(1918,plain,
! [SV487: nat,SV412: nat,SV278: nat,SV109: nat] :
( ( ( ~ ( ord_less_nat @ SV109 @ SV278 )
| ~ ( ord_less_nat @ SV412 @ SV487 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV109 @ SV412 ) @ ( plus_plus_nat @ SV278 @ SV487 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1753]) ).
thf(1919,plain,
! [SV279: nat,SV413: nat,SV110: nat] :
( ( ( ord_less_eq_nat @ SV110 @ SV413 )
= $false )
| ( ( ( ( minus_minus_nat @ SV279 @ SV110 )
= ( minus_minus_nat @ SV413 @ SV110 ) )
= ( SV279 = SV413 ) )
= $true )
| ( ( ord_less_eq_nat @ SV110 @ SV279 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1754]) ).
thf(1920,plain,
! [SV113: nat,SV282: nat,SV415: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV415 @ ( minus_minus_nat @ SV282 @ SV113 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV415 @ SV113 ) @ SV282 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV415 @ ( minus_minus_nat @ SV282 @ SV113 ) )
| ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV415 @ SV113 ) @ SV282 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV113 @ SV282 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1756]) ).
thf(1921,plain,
! [SV114: nat > $o,SV283: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( sK7_SY655 @ SV283 @ SV114 ) )
| ~ ~ ( SV114 @ ( sK7_SY655 @ SV283 @ SV114 ) )
| ~ ! [SY1044: nat] :
~ ~ ( ~ ( ord_less_nat @ SY1044 @ ( sK7_SY655 @ SV283 @ SV114 ) )
| ~ ~ ( SV114 @ SY1044 ) ) )
= $false )
| ( ( SV114 @ SV283 )
= $true )
| ( ( SV114 @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1758]) ).
thf(1922,plain,
! [SV115: nat] :
( ( ( ~ ( ( SV115 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV115 ) )
= $false )
| ( ( SV115 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1759]) ).
thf(1923,plain,
! [SV115: nat] :
( ( ( ~ ( ( SV115 != zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV115 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1760]) ).
thf(1924,plain,
! [SV115: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV115 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV115 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1760]) ).
thf(1925,plain,
! [SV417: nat,SV285: nat,SV117: nat > $o] :
( ( ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
= $false )
| ( ( ~ ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1761]) ).
thf(1926,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1761]) ).
thf(1927,plain,
! [SV286: nat,SV418: nat,SV118: nat] :
( ( ( ord_less_nat @ SV118 @ SV418 )
= $false )
| ( ( ord_less_nat @ ( minus_minus_nat @ SV418 @ SV286 ) @ ( minus_minus_nat @ SV418 @ SV118 ) )
= $true )
| ( ( ord_less_nat @ SV118 @ SV286 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1762]) ).
thf(1928,plain,
! [SV488: nat,SV288: nat] :
( ( ( ( ord_less_eq_nat @ SV288 @ SV488 )
| ~ ! [SY1033: nat] :
( SV488
!= ( plus_plus_nat @ SV288 @ SY1033 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV288 @ SV488 )
| ~ ~ ! [SY1033: nat] :
( SV488
!= ( plus_plus_nat @ SV288 @ SY1033 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1764]) ).
thf(1929,plain,
! [SV489: nat,SV289: nat] :
( ( ( ( ord_less_eq_nat @ SV289 @ SV489 )
| ~ ! [SY1034: nat] :
( SV489
!= ( plus_plus_nat @ SV289 @ SY1034 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV289 @ SV489 )
| ~ ~ ! [SY1034: nat] :
( SV489
!= ( plus_plus_nat @ SV289 @ SY1034 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1765]) ).
thf(1930,plain,
! [SV421: nat,SV122: nat,SV290: nat] :
( ( ( ~ ( ( ( minus_minus_nat @ SV290 @ SV122 )
= SV421 )
| ( SV290
= ( plus_plus_nat @ SV421 @ SV122 ) ) ) )
= $true )
| ( ( ~ ( ( ( minus_minus_nat @ SV290 @ SV122 )
!= SV421 )
| ( SV290
!= ( plus_plus_nat @ SV421 @ SV122 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV122 @ SV290 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1766]) ).
thf(1931,plain,
! [SV509: nat,SV490: nat,SV422: nat,SV291: nat,SV123: nat] :
( ( ( ord_less_eq_nat @ SV123 @ SV291 )
= $false )
| ( ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ SV291 @ SV422 ) @ SV490 ) @ ( plus_plus_nat @ ( times_times_nat @ SV123 @ SV422 ) @ SV509 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV291 @ SV123 ) @ SV422 ) @ SV490 ) @ SV509 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1768]) ).
thf(1932,plain,
! [SV294: nat,SV126: nat] :
( ( ( ( ( plus_plus_nat @ SV126 @ SV294 )
!= zero_zero_nat )
| ~ ~ ( ( SV126 != zero_zero_nat )
| ( SV294 != zero_zero_nat ) ) )
= $false )
| ( ( ( plus_plus_nat @ SV126 @ SV294 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1769]) ).
thf(1933,plain,
! [SV294: nat,SV126: nat] :
( ( ( ( SV126 != zero_zero_nat )
| ( SV294 != zero_zero_nat ) )
= $true )
| ( ( ~ ( ( ( plus_plus_nat @ SV126 @ SV294 )
!= zero_zero_nat )
| ~ ~ ( ( SV126 != zero_zero_nat )
| ( SV294 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1770]) ).
thf(1934,plain,
! [SV510: nat,SV491: nat,SV425: nat,SV295: nat,SV127: nat] :
( ( ( ord_less_eq_nat @ SV127 @ SV295 )
= $false )
| ( ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV127 @ SV425 ) @ SV491 ) @ ( plus_plus_nat @ ( times_times_nat @ SV295 @ SV425 ) @ SV510 ) )
= ( ord_less_nat @ SV491 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV295 @ SV127 ) @ SV425 ) @ SV510 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1771]) ).
thf(1935,plain,
! [SV492: nat,SV132: nat,SV300: nat,SV429: nat] :
( ( ( ( plus_plus_nat @ SV429 @ SV300 )
!= ( plus_plus_nat @ SV132 @ SV492 ) )
= $true )
| ( ( ord_less_nat @ SV429 @ SV492 )
= $true )
| ( ( ord_less_nat @ SV132 @ SV300 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1772]) ).
thf(1936,plain,
! [SV134: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV134 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1773]) ).
thf(1937,plain,
! [SV134: nat] :
( ( ( ~ ( ( SV134 != zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1773]) ).
thf(1938,plain,
! [SV134: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV134 )
| ~ ( ( SV134 != zero_zero_nat ) ) )
= $false )
| ( ( SV134 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1774]) ).
thf(1939,plain,
! [SV304: nat,SV137: nat,SV493: nat,SV433: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV433 @ SV493 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV137 @ SV433 ) @ ( plus_plus_nat @ SV304 @ SV493 ) )
= $true )
| ( ( ord_less_eq_nat @ SV137 @ SV304 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1775]) ).
thf(1940,plain,
! [SV309: nat,SV142: nat > $o] :
( ( ( ~ ( SV142 @ ( sK1_SY712 @ SV309 @ SV142 ) ) )
= $true )
| ( ( SV142 @ SV309 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1776]) ).
thf(1941,plain,
! [SV142: nat > $o,SV309: nat] :
( ( ( ! [SY1041: nat] :
~ ~ ( ~ ( ord_less_nat @ SY1041 @ ( sK1_SY712 @ SV309 @ SV142 ) )
| ~ ~ ( SV142 @ SY1041 ) ) )
= $true )
| ( ( SV142 @ SV309 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1777]) ).
thf(1942,plain,
! [SV511: nat,SV494: nat,SV440: nat,SV313: nat,SV146: nat] :
( ( ( ord_less_eq_nat @ SV146 @ SV313 )
= $false )
| ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV146 @ SV440 ) @ SV494 ) @ ( plus_plus_nat @ ( times_times_nat @ SV313 @ SV440 ) @ SV511 ) )
= ( ord_less_eq_nat @ SV494 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV313 @ SV146 ) @ SV440 ) @ SV511 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1778]) ).
thf(1943,plain,
! [SV495: nat,SV442: nat,SV315: nat,SV148: nat] :
( ( ( ~ ( ord_less_nat @ SV148 @ SV315 )
| ( SV442 != SV495 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV148 @ SV442 ) @ ( plus_plus_nat @ SV315 @ SV495 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1779]) ).
thf(1944,plain,
! [SV317: nat,SV150: nat,SV496: nat,SV443: nat] :
( ( ( ~ ( ord_less_nat @ SV443 @ SV496 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV150 @ SV443 ) @ ( plus_plus_nat @ SV317 @ SV496 ) )
= $true )
| ( ( ord_less_nat @ SV150 @ SV317 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1780]) ).
thf(1945,plain,
! [SV444: nat,SV318: nat,SV152: nat] :
( ( ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV318 )
| ~ ( ord_less_nat @ SV152 @ SV444 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1781]) ).
thf(1946,plain,
! [SV444: nat,SV152: nat,SV318: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV318 )
| ~ ( ord_less_nat @ SV152 @ SV444 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV318 )
| ~ ( ord_less_nat @ SV152 @ SV444 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1781]) ).
thf(1947,plain,
! [SV321: nat,SV155: nat] :
( ( ( SV155 = SV321 )
= $true )
| ( ( ~ ( ~ ( ( SV155 != SV321 ) )
| ~ ( ( ord_less_nat @ SV155 @ SV321 )
| ( ord_less_nat @ SV321 @ SV155 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1782]) ).
thf(1948,plain,
! [SV321: nat,SV155: nat] :
( ( ( ord_less_nat @ SV155 @ SV321 )
= $false )
| ( ( ~ ( ~ ( ( SV155 != SV321 ) )
| ~ ( ( ord_less_nat @ SV155 @ SV321 )
| ( ord_less_nat @ SV321 @ SV155 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1783]) ).
thf(1949,plain,
! [SV155: nat,SV321: nat] :
( ( ( ord_less_nat @ SV321 @ SV155 )
= $false )
| ( ( ~ ( ~ ( ( SV155 != SV321 ) )
| ~ ( ( ord_less_nat @ SV155 @ SV321 )
| ( ord_less_nat @ SV321 @ SV155 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1783]) ).
thf(1950,plain,
! [SV325: nat,SV159: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV159 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV325 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1784]) ).
thf(1951,plain,
! [SV325: nat,SV159: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV159 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV325 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV159 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV325 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1785]) ).
thf(1952,plain,
! [SV326: nat,SV160: nat] :
( ( ( ( ( plus_plus_nat @ SV160 @ SV326 )
!= zero_zero_nat )
| ~ ~ ( ( SV160 != zero_zero_nat )
| ( SV326 != zero_zero_nat ) ) )
= $false )
| ( ( ( plus_plus_nat @ SV160 @ SV326 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1786]) ).
thf(1953,plain,
! [SV326: nat,SV160: nat] :
( ( ( ( SV160 != zero_zero_nat )
| ( SV326 != zero_zero_nat ) )
= $true )
| ( ( ~ ( ( ( plus_plus_nat @ SV160 @ SV326 )
!= zero_zero_nat )
| ~ ~ ( ( SV160 != zero_zero_nat )
| ( SV326 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1787]) ).
thf(1954,plain,
! [SV497: nat,SV327: nat] :
( ( ( ( ord_less_nat @ SV327 @ SV497 )
| ~ ( ~ ( ord_less_eq_nat @ SV327 @ SV497 )
| ~ ( ( SV327 != SV497 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV327 @ SV497 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV327 @ SV497 )
| ~ ( ( SV327 != SV497 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1788]) ).
thf(1955,plain,
! [SV328: nat,SV162: nat] :
( ( ( ( zero_zero_nat
!= ( plus_plus_nat @ SV162 @ SV328 ) )
| ~ ~ ( ( SV162 != zero_zero_nat )
| ( SV328 != zero_zero_nat ) ) )
= $false )
| ( ( zero_zero_nat
= ( plus_plus_nat @ SV162 @ SV328 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1789]) ).
thf(1956,plain,
! [SV328: nat,SV162: nat] :
( ( ( ( SV162 != zero_zero_nat )
| ( SV328 != zero_zero_nat ) )
= $true )
| ( ( ~ ( ( zero_zero_nat
!= ( plus_plus_nat @ SV162 @ SV328 ) )
| ~ ~ ( ( SV162 != zero_zero_nat )
| ( SV328 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1790]) ).
thf(1957,plain,
! [SV448: nat,SV329: nat,SV163: nat] :
( ( ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV329 )
| ( ord_less_eq_nat @ SV163 @ SV448 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1791]) ).
thf(1958,plain,
! [SV448: nat,SV163: nat,SV329: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV329 )
| ( ord_less_eq_nat @ SV163 @ SV448 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV329 )
| ( ord_less_eq_nat @ SV163 @ SV448 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1791]) ).
thf(1959,plain,
! [SV330: nat,SV449: nat,SV164: nat > $o] :
( ( ( ! [SY1015: nat] :
( ~ ( SV164 @ SY1015 )
| ( ord_less_eq_nat @ SY1015 @ SV449 ) ) )
= $false )
| ( ( ~ ! [SY751: nat] :
~ ~ ( ~ ( SV164 @ SY751 )
| ~ ! [SY752: nat] :
( ~ ( SV164 @ SY752 )
| ( ord_less_eq_nat @ SY752 @ SY751 ) ) ) )
= $true )
| ( ( SV164 @ SV330 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1792]) ).
thf(1960,plain,
! [SV332: nat,SV451: nat,SV167: nat] :
( ( ( ord_less_eq_nat @ SV167 @ SV451 )
= $false )
| ( ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV332 @ SV167 ) @ ( minus_minus_nat @ SV451 @ SV167 ) )
= ( ord_less_eq_nat @ SV332 @ SV451 ) )
= $true )
| ( ( ord_less_eq_nat @ SV167 @ SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1793]) ).
thf(1961,plain,
! [SV453: nat,SV169: nat,SV334: nat] :
( ( ( ~ ( ( ord_less_nat @ ( minus_minus_nat @ SV334 @ SV169 ) @ SV453 )
| ( ord_less_nat @ SV334 @ ( plus_plus_nat @ SV453 @ SV169 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( minus_minus_nat @ SV334 @ SV169 ) @ SV453 )
| ~ ( ord_less_nat @ SV334 @ ( plus_plus_nat @ SV453 @ SV169 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV169 @ SV334 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1794]) ).
thf(1962,plain,
! [SV336: nat,SV455: nat,SV171: nat] :
( ( ( ord_less_eq_nat @ SV171 @ SV455 )
= $false )
| ( ( ( minus_minus_nat @ ( minus_minus_nat @ SV336 @ SV171 ) @ ( minus_minus_nat @ SV455 @ SV171 ) )
= ( minus_minus_nat @ SV336 @ SV455 ) )
= $true )
| ( ( ord_less_eq_nat @ SV171 @ SV336 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1797]) ).
thf(1963,plain,
! [SV512: nat,SV499: nat,SV457: nat,SV338: nat,SV174: nat] :
( ( ( ord_less_eq_nat @ SV174 @ SV338 )
= $false )
| ( ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV338 @ SV457 ) @ SV499 ) @ ( plus_plus_nat @ ( times_times_nat @ SV174 @ SV457 ) @ SV512 ) )
= ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV338 @ SV174 ) @ SV457 ) @ SV499 ) @ SV512 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1798]) ).
thf(1964,plain,
! [SV459: nat,SV341: nat,SV177: nat] :
( ( ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 )
| ~ ( ord_less_nat @ SV341 @ SV459 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1800]) ).
thf(1965,plain,
! [SV459: nat,SV341: nat,SV177: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 )
| ~ ( ord_less_nat @ SV341 @ SV459 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 )
| ~ ( ord_less_nat @ SV341 @ SV459 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1800]) ).
thf(1966,plain,
! [SV342: nat,SV178: nat] :
( ( ( ~ ( ord_less_nat @ SV178 @ SV342 ) )
= $false )
| ( ( ord_less_nat @ SV342 @ SV178 )
= $true )
| ( ( SV178 = SV342 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1801]) ).
thf(1967,plain,
! [SV181: nat > $o,SV345: nat] :
( ( ( ! [SY1042: nat] :
( ~ ( ord_less_nat @ SY1042 @ ( sK2_SY783 @ SV345 @ SV181 ) )
| ( SV181 @ SY1042 ) ) )
= $true )
| ( ( SV181 @ SV345 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1802]) ).
thf(1968,plain,
! [SV461: nat,SV346: nat,SV182: nat] :
( ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false )
| ( ( ( ( minus_minus_nat @ SV346 @ SV182 )
= SV461 )
= ( SV346
= ( plus_plus_nat @ SV461 @ SV182 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1804]) ).
thf(1969,plain,
! [SV348: nat,SV463: nat,SV184: nat] :
( ( ( ord_less_eq_nat @ SV184 @ SV463 )
= $false )
| ( ( ( ord_less_nat @ ( minus_minus_nat @ SV348 @ SV184 ) @ ( minus_minus_nat @ SV463 @ SV184 ) )
= ( ord_less_nat @ SV348 @ SV463 ) )
= $true )
| ( ( ord_less_eq_nat @ SV184 @ SV348 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1805]) ).
thf(1970,plain,
! [SV185: nat,SV349: nat,SV464: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV464 @ ( minus_minus_nat @ SV349 @ SV185 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV464 @ SV185 ) @ SV349 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV464 @ ( minus_minus_nat @ SV349 @ SV185 ) )
| ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV464 @ SV185 ) @ SV349 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV185 @ SV349 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1806]) ).
thf(1971,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= $false )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1808]) ).
thf(1972,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1808]) ).
thf(1973,plain,
! [SV352: nat,SV188: nat,SV467: nat] :
( ( ( ord_less_eq_nat @ SV467 @ SV188 )
= $false )
| ( ( ord_less_nat @ ( minus_minus_nat @ SV188 @ SV467 ) @ ( minus_minus_nat @ SV352 @ SV467 ) )
= $true )
| ( ( ord_less_nat @ SV188 @ SV352 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1809]) ).
thf(1974,plain,
! [SV513: nat,SV501: nat,SV468: nat,SV354: nat,SV190: nat] :
( ( ( ord_less_eq_nat @ SV190 @ SV354 )
= $false )
| ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV354 @ SV468 ) @ SV501 )
= ( plus_plus_nat @ ( times_times_nat @ SV190 @ SV468 ) @ SV513 ) )
= ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV354 @ SV190 ) @ SV468 ) @ SV501 )
= SV513 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1811]) ).
thf(1975,plain,
! [SV191: nat,SV355: nat] :
( ( ( SV355
= ( plus_plus_nat @ SV191 @ ( sK4_SY975 @ SV191 @ SV355 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV191 @ SV355 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1812]) ).
thf(1976,plain,
! [SV502: nat,SV469: nat,SV356: nat,SV192: nat] :
( ( ( ( SV192 != SV356 )
| ~ ( ord_less_nat @ SV469 @ SV502 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV192 @ SV469 ) @ ( plus_plus_nat @ SV356 @ SV502 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1813]) ).
thf(1977,plain,
! [SV503: nat,SV470: nat,SV357: nat,SV193: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV193 @ SV357 )
| ( SV470 != SV503 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV193 @ SV470 ) @ ( plus_plus_nat @ SV357 @ SV503 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1814]) ).
thf(1978,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV194 )
| ( ord_less_eq_nat @ SV358 @ SV471 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1815]) ).
thf(1979,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV194 )
| ( ord_less_eq_nat @ SV358 @ SV471 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV194 )
| ( ord_less_eq_nat @ SV358 @ SV471 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1815]) ).
thf(1980,plain,
! [SV195: nat,SV472: nat,SV359: nat] :
( ( ( ord_less_eq_nat @ SV359 @ SV472 )
= $false )
| ( ( ord_less_eq_nat @ SV195 @ SV472 )
= $true )
| ( ( ord_less_eq_nat @ SV195 @ SV359 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1816]) ).
thf(1981,plain,
! [SV504: nat,SV473: nat,SV360: nat,SV196: nat] :
( ( ( ( SV196 != SV360 )
| ( SV473 != SV504 ) )
= $true )
| ( ( ( plus_plus_nat @ SV196 @ SV473 )
= ( plus_plus_nat @ SV360 @ SV504 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1817]) ).
thf(1982,plain,
! [SV514: nat,SV505: nat,SV474: nat,SV361: nat,SV197: nat] :
( ( ( ord_less_eq_nat @ SV197 @ SV361 )
= $false )
| ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV197 @ SV474 ) @ SV505 )
= ( plus_plus_nat @ ( times_times_nat @ SV361 @ SV474 ) @ SV514 ) )
= ( SV505
= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV361 @ SV197 ) @ SV474 ) @ SV514 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1818]) ).
thf(1983,plain,
! [SV362: nat,SV198: nat,SV506: nat,SV475: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV475 @ SV506 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV198 @ SV475 ) @ ( plus_plus_nat @ SV362 @ SV506 ) )
= $true )
| ( ( ord_less_eq_nat @ SV198 @ SV362 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1819]) ).
thf(1984,plain,
! [SV1: nat > nat] :
( ( ( number1551313001itions @ SV1 @ zero_zero_nat )
= $true )
| ( ( number1551313001itions @ SV1 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1820]) ).
thf(1985,plain,
! [SV1: nat > nat] :
( ( ( SV1
= ( ^ [I: nat] : zero_zero_nat ) )
= $true )
| ( ( number1551313001itions @ SV1 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1821]) ).
thf(1986,plain,
! [SV1: nat > nat] :
( ( ( ~ ( number1551313001itions @ SV1 @ zero_zero_nat )
| ( SV1
!= ( ^ [I: nat] : zero_zero_nat ) ) )
= $false )
| ( ( ( SV1 @ ( sK5_SV515 @ SV1 ) )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1822]) ).
thf(1987,plain,
! [SV1: nat > nat] :
( ( ( ~ ( number1551313001itions @ SV1 @ zero_zero_nat ) )
= $false )
| ( ( SV1
= ( ^ [I: nat] : zero_zero_nat ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1823]) ).
thf(1988,plain,
! [SV1: nat > nat] :
( ( ( SV1
!= ( ^ [I: nat] : zero_zero_nat ) )
= $false )
| ( ( SV1
= ( ^ [I: nat] : zero_zero_nat ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1823]) ).
thf(1989,plain,
! [SV204: nat,SV2: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SV204 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SV204 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1824]) ).
thf(1990,plain,
! [SV204: nat,SV2: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( ord_less_nat @ zero_zero_nat @ SV204 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SV204 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1824]) ).
thf(1991,plain,
! [SV204: nat,SV2: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SV204 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( ord_less_nat @ zero_zero_nat @ SV204 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1825]) ).
thf(1992,plain,
! [SV204: nat,SV2: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SV204 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( ord_less_nat @ zero_zero_nat @ SV204 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1826]) ).
thf(1993,plain,
! [SV205: nat,SV3: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV3 @ SV205 ) @ SV3 ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV3 @ SV205 ) @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1827]) ).
thf(1994,plain,
! [SV3: nat,SV205: nat] :
( ( ( ~ ( ord_less_nat @ SV205 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV3 @ SV205 ) @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1827]) ).
thf(1995,plain,
! [SV205: nat,SV3: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV3 @ SV205 ) @ SV3 ) )
= $false )
| ( ( ord_less_nat @ SV205 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1828]) ).
thf(1996,plain,
! [SV205: nat] :
( ( ( ~ ( ord_less_nat @ SV205 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ SV205 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1828]) ).
thf(1997,plain,
! [SV206: nat,SV4: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV4 @ SV206 ) @ SV206 ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV4 @ SV206 ) @ SV206 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1829]) ).
thf(1998,plain,
! [SV206: nat,SV4: nat] :
( ( ( ~ ( ord_less_nat @ SV4 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV4 @ SV206 ) @ SV206 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1829]) ).
thf(1999,plain,
! [SV206: nat,SV4: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV4 @ SV206 ) @ SV206 ) )
= $false )
| ( ( ord_less_nat @ SV4 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1830]) ).
thf(2000,plain,
! [SV4: nat] :
( ( ( ~ ( ord_less_nat @ SV4 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ SV4 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1830]) ).
thf(2001,plain,
! [SV207: nat,SV5: nat] :
( ( ( ~ ( ord_less_nat @ SV5 @ ( plus_plus_nat @ SV5 @ SV207 ) ) )
= $false )
| ( ( ord_less_nat @ SV5 @ ( plus_plus_nat @ SV5 @ SV207 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1831]) ).
thf(2002,plain,
! [SV5: nat,SV207: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV207 ) )
= $false )
| ( ( ord_less_nat @ SV5 @ ( plus_plus_nat @ SV5 @ SV207 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1831]) ).
thf(2003,plain,
! [SV207: nat,SV5: nat] :
( ( ( ~ ( ord_less_nat @ SV5 @ ( plus_plus_nat @ SV5 @ SV207 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV207 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1832]) ).
thf(2004,plain,
! [SV207: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV207 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV207 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1832]) ).
thf(2005,plain,
! [SV208: nat,SV6: nat] :
( ( ( ~ ( ord_less_nat @ SV6 @ ( plus_plus_nat @ SV208 @ SV6 ) ) )
= $false )
| ( ( ord_less_nat @ SV6 @ ( plus_plus_nat @ SV208 @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1833]) ).
thf(2006,plain,
! [SV6: nat,SV208: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV208 ) )
= $false )
| ( ( ord_less_nat @ SV6 @ ( plus_plus_nat @ SV208 @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1833]) ).
thf(2007,plain,
! [SV208: nat,SV6: nat] :
( ( ( ~ ( ord_less_nat @ SV6 @ ( plus_plus_nat @ SV208 @ SV6 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV208 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1834]) ).
thf(2008,plain,
! [SV208: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV208 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV208 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1834]) ).
thf(2009,plain,
! [SV368: nat,SV209: nat,SV7: nat] :
( ( ( ( ( plus_plus_nat @ SV7 @ SV209 )
!= ( plus_plus_nat @ SV368 @ SV209 ) )
| ( SV7 != SV368 ) )
= $false )
| ( ( ( plus_plus_nat @ SV7 @ SV209 )
= ( plus_plus_nat @ SV368 @ SV209 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1835]) ).
thf(2010,plain,
! [SV368: nat,SV209: nat,SV7: nat] :
( ( ( ( ( plus_plus_nat @ SV7 @ SV209 )
!= ( plus_plus_nat @ SV368 @ SV209 ) )
| ( SV7 != SV368 ) )
= $false )
| ( ( SV7 = SV368 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1836]) ).
thf(2011,plain,
! [SV369: nat,SV210: nat,SV8: nat] :
( ( ( ( ( plus_plus_nat @ SV8 @ SV210 )
!= ( plus_plus_nat @ SV8 @ SV369 ) )
| ( SV210 != SV369 ) )
= $false )
| ( ( ( plus_plus_nat @ SV8 @ SV210 )
= ( plus_plus_nat @ SV8 @ SV369 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1837]) ).
thf(2012,plain,
! [SV369: nat,SV210: nat,SV8: nat] :
( ( ( ( ( plus_plus_nat @ SV8 @ SV210 )
!= ( plus_plus_nat @ SV8 @ SV369 ) )
| ( SV210 != SV369 ) )
= $false )
| ( ( SV210 = SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1838]) ).
thf(2013,plain,
! [SV9: nat] :
( ( ( ord_less_eq_nat @ SV9 @ zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV9 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1839]) ).
thf(2014,plain,
! [SV9: nat] :
( ( ( SV9 = zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV9 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1840]) ).
thf(2015,plain,
! [SV9: nat] :
( ( ( ord_less_eq_nat @ SV9 @ zero_zero_nat )
= $true )
| ( ( SV9 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1841]) ).
thf(2016,plain,
! [SV9: nat] :
( ( ( SV9 = zero_zero_nat )
= $true )
| ( ( SV9 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1842]) ).
thf(2017,plain,
! [SV10: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV10 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1843]) ).
thf(2018,plain,
! [SV10: nat] :
( ( ( SV10 != zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1843]) ).
thf(2019,plain,
! [SV10: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV10 ) )
= $true )
| ( ( SV10 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1844]) ).
thf(2020,plain,
! [SV10: nat] :
( ( ( SV10 = zero_zero_nat )
= $true )
| ( ( SV10 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1845]) ).
thf(2021,plain,
! [SV370: nat,SV211: nat,SV11: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV11 @ SV211 ) @ ( plus_plus_nat @ SV370 @ SV211 ) )
| ~ ( ord_less_eq_nat @ SV11 @ SV370 ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV11 @ SV211 ) @ ( plus_plus_nat @ SV370 @ SV211 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1846]) ).
thf(2022,plain,
! [SV370: nat,SV211: nat,SV11: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV11 @ SV211 ) @ ( plus_plus_nat @ SV370 @ SV211 ) )
| ~ ( ord_less_eq_nat @ SV11 @ SV370 ) )
= $false )
| ( ( ord_less_eq_nat @ SV11 @ SV370 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1847]) ).
thf(2023,plain,
! [SV371: nat,SV212: nat,SV12: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV212 ) @ ( plus_plus_nat @ SV12 @ SV371 ) )
| ~ ( ord_less_eq_nat @ SV212 @ SV371 ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV212 ) @ ( plus_plus_nat @ SV12 @ SV371 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1848]) ).
thf(2024,plain,
! [SV371: nat,SV212: nat,SV12: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV212 ) @ ( plus_plus_nat @ SV12 @ SV371 ) )
| ~ ( ord_less_eq_nat @ SV212 @ SV371 ) )
= $false )
| ( ( ord_less_eq_nat @ SV212 @ SV371 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1849]) ).
thf(2025,plain,
! [SV213: nat,SV13: nat] :
( ( ( SV13
!= ( plus_plus_nat @ SV13 @ SV213 ) )
= $false )
| ( ( SV13
= ( plus_plus_nat @ SV13 @ SV213 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1850]) ).
thf(2026,plain,
! [SV13: nat,SV213: nat] :
( ( ( SV213 != zero_zero_nat )
= $false )
| ( ( SV13
= ( plus_plus_nat @ SV13 @ SV213 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1850]) ).
thf(2027,plain,
! [SV213: nat,SV13: nat] :
( ( ( SV13
!= ( plus_plus_nat @ SV13 @ SV213 ) )
= $false )
| ( ( SV213 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1851]) ).
thf(2028,plain,
! [SV213: nat] :
( ( ( SV213 != zero_zero_nat )
= $false )
| ( ( SV213 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1851]) ).
thf(2029,plain,
! [SV214: nat,SV14: nat] :
( ( ( SV14
!= ( plus_plus_nat @ SV214 @ SV14 ) )
= $false )
| ( ( SV14
= ( plus_plus_nat @ SV214 @ SV14 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1852]) ).
thf(2030,plain,
! [SV14: nat,SV214: nat] :
( ( ( SV214 != zero_zero_nat )
= $false )
| ( ( SV14
= ( plus_plus_nat @ SV214 @ SV14 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1852]) ).
thf(2031,plain,
! [SV214: nat,SV14: nat] :
( ( ( SV14
!= ( plus_plus_nat @ SV214 @ SV14 ) )
= $false )
| ( ( SV214 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1853]) ).
thf(2032,plain,
! [SV214: nat] :
( ( ( SV214 != zero_zero_nat )
= $false )
| ( ( SV214 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1853]) ).
thf(2033,plain,
! [SV215: nat,SV15: nat] :
( ( ( ( plus_plus_nat @ SV15 @ SV215 )
!= SV15 )
= $false )
| ( ( ( plus_plus_nat @ SV15 @ SV215 )
= SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1854]) ).
thf(2034,plain,
! [SV15: nat,SV215: nat] :
( ( ( SV215 != zero_zero_nat )
= $false )
| ( ( ( plus_plus_nat @ SV15 @ SV215 )
= SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1854]) ).
thf(2035,plain,
! [SV215: nat,SV15: nat] :
( ( ( ( plus_plus_nat @ SV15 @ SV215 )
!= SV15 )
= $false )
| ( ( SV215 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1855]) ).
thf(2036,plain,
! [SV215: nat] :
( ( ( SV215 != zero_zero_nat )
= $false )
| ( ( SV215 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1855]) ).
thf(2037,plain,
! [SV216: nat,SV16: nat] :
( ( ( ( plus_plus_nat @ SV16 @ SV216 )
!= SV216 )
= $false )
| ( ( ( plus_plus_nat @ SV16 @ SV216 )
= SV216 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1856]) ).
thf(2038,plain,
! [SV216: nat,SV16: nat] :
( ( ( SV16 != zero_zero_nat )
= $false )
| ( ( ( plus_plus_nat @ SV16 @ SV216 )
= SV216 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1856]) ).
thf(2039,plain,
! [SV216: nat,SV16: nat] :
( ( ( ( plus_plus_nat @ SV16 @ SV216 )
!= SV216 )
= $false )
| ( ( SV16 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1857]) ).
thf(2040,plain,
! [SV16: nat] :
( ( ( SV16 != zero_zero_nat )
= $false )
| ( ( SV16 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1857]) ).
thf(2041,plain,
! [SV372: nat,SV217: nat,SV22: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV22 @ SV217 ) @ ( plus_plus_nat @ SV372 @ SV217 ) )
| ~ ( ord_less_nat @ SV22 @ SV372 ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV22 @ SV217 ) @ ( plus_plus_nat @ SV372 @ SV217 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1858]) ).
thf(2042,plain,
! [SV372: nat,SV217: nat,SV22: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV22 @ SV217 ) @ ( plus_plus_nat @ SV372 @ SV217 ) )
| ~ ( ord_less_nat @ SV22 @ SV372 ) )
= $false )
| ( ( ord_less_nat @ SV22 @ SV372 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1859]) ).
thf(2043,plain,
! [SV373: nat,SV218: nat,SV23: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV23 @ SV218 ) @ ( plus_plus_nat @ SV23 @ SV373 ) )
| ~ ( ord_less_nat @ SV218 @ SV373 ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV23 @ SV218 ) @ ( plus_plus_nat @ SV23 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1860]) ).
thf(2044,plain,
! [SV373: nat,SV218: nat,SV23: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV23 @ SV218 ) @ ( plus_plus_nat @ SV23 @ SV373 ) )
| ~ ( ord_less_nat @ SV218 @ SV373 ) )
= $false )
| ( ( ord_less_nat @ SV218 @ SV373 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1861]) ).
thf(2045,plain,
! [SV376: nat,SV223: nat,SV32: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV32 @ SV223 ) @ ( plus_plus_nat @ SV32 @ SV376 ) )
| ~ ( ord_less_nat @ SV223 @ SV376 ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV32 @ SV223 ) @ ( plus_plus_nat @ SV32 @ SV376 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1862]) ).
thf(2046,plain,
! [SV376: nat,SV223: nat,SV32: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV32 @ SV223 ) @ ( plus_plus_nat @ SV32 @ SV376 ) )
| ~ ( ord_less_nat @ SV223 @ SV376 ) )
= $false )
| ( ( ord_less_nat @ SV223 @ SV376 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1863]) ).
thf(2047,plain,
! [SV377: nat,SV224: nat,SV35: nat] :
( ( ( ( ( times_times_nat @ SV35 @ SV224 )
!= ( times_times_nat @ SV377 @ SV224 ) )
| ~ ( ( SV35 = SV377 )
| ( SV224 = zero_zero_nat ) ) )
= $false )
| ( ( ( times_times_nat @ SV35 @ SV224 )
= ( times_times_nat @ SV377 @ SV224 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1864]) ).
thf(2048,plain,
! [SV224: nat,SV377: nat,SV35: nat] :
( ( ( SV35 = SV377 )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV35 @ SV224 )
!= ( times_times_nat @ SV377 @ SV224 ) )
| ~ ( ( SV35 = SV377 )
| ( SV224 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1865]) ).
thf(2049,plain,
! [SV377: nat,SV35: nat,SV224: nat] :
( ( ( SV224 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV35 @ SV224 )
!= ( times_times_nat @ SV377 @ SV224 ) )
| ~ ( ( SV35 = SV377 )
| ( SV224 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1865]) ).
thf(2050,plain,
! [SV378: nat,SV225: nat,SV36: nat] :
( ( ( ( ( times_times_nat @ SV36 @ SV225 )
!= ( times_times_nat @ SV36 @ SV378 ) )
| ~ ( ( SV225 = SV378 )
| ( SV36 = zero_zero_nat ) ) )
= $false )
| ( ( ( times_times_nat @ SV36 @ SV225 )
= ( times_times_nat @ SV36 @ SV378 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1866]) ).
thf(2051,plain,
! [SV36: nat,SV378: nat,SV225: nat] :
( ( ( SV225 = SV378 )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV36 @ SV225 )
!= ( times_times_nat @ SV36 @ SV378 ) )
| ~ ( ( SV225 = SV378 )
| ( SV36 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1867]) ).
thf(2052,plain,
! [SV378: nat,SV225: nat,SV36: nat] :
( ( ( SV36 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV36 @ SV225 )
!= ( times_times_nat @ SV36 @ SV378 ) )
| ~ ( ( SV225 = SV378 )
| ( SV36 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1867]) ).
thf(2053,plain,
! [SV226: nat,SV38: nat] :
( ( ( ( times_times_nat @ SV38 @ SV226 )
!= zero_zero_nat )
= $false )
| ( ( ( times_times_nat @ SV38 @ SV226 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1868]) ).
thf(2054,plain,
! [SV226: nat,SV38: nat] :
( ( ( ~ ( ( SV38 = zero_zero_nat )
| ( SV226 = zero_zero_nat ) ) )
= $false )
| ( ( ( times_times_nat @ SV38 @ SV226 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1868]) ).
thf(2055,plain,
! [SV226: nat,SV38: nat] :
( ( ( ( ( times_times_nat @ SV38 @ SV226 )
!= zero_zero_nat )
| ~ ( ( SV38 = zero_zero_nat )
| ( SV226 = zero_zero_nat ) ) )
= $false )
| ( ( SV38 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(2056,plain,
! [SV226: nat,SV38: nat] :
( ( ( ( ( times_times_nat @ SV38 @ SV226 )
!= zero_zero_nat )
| ~ ( ( SV38 = zero_zero_nat )
| ( SV226 = zero_zero_nat ) ) )
= $false )
| ( ( SV226 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1870]) ).
thf(2057,plain,
! [SV379: nat,SV227: nat,SV39: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV39 @ SV227 ) @ ( plus_plus_nat @ SV39 @ SV379 ) )
| ~ ( ord_less_eq_nat @ SV227 @ SV379 ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV39 @ SV227 ) @ ( plus_plus_nat @ SV39 @ SV379 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1871]) ).
thf(2058,plain,
! [SV379: nat,SV227: nat,SV39: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV39 @ SV227 ) @ ( plus_plus_nat @ SV39 @ SV379 ) )
| ~ ( ord_less_eq_nat @ SV227 @ SV379 ) )
= $false )
| ( ( ord_less_eq_nat @ SV227 @ SV379 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1872]) ).
thf(2059,plain,
! [SV229: nat,SV41: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV41 @ ( plus_plus_nat @ SV229 @ SV41 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV41 @ ( plus_plus_nat @ SV229 @ SV41 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1873]) ).
thf(2060,plain,
! [SV41: nat,SV229: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV229 ) )
= $false )
| ( ( ord_less_eq_nat @ SV41 @ ( plus_plus_nat @ SV229 @ SV41 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1873]) ).
thf(2061,plain,
! [SV229: nat,SV41: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV41 @ ( plus_plus_nat @ SV229 @ SV41 ) ) )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV229 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1874]) ).
thf(2062,plain,
! [SV229: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV229 ) )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV229 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1874]) ).
thf(2063,plain,
! [SV230: nat,SV42: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV42 @ ( plus_plus_nat @ SV42 @ SV230 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV42 @ ( plus_plus_nat @ SV42 @ SV230 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1875]) ).
thf(2064,plain,
! [SV42: nat,SV230: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV230 ) )
= $false )
| ( ( ord_less_eq_nat @ SV42 @ ( plus_plus_nat @ SV42 @ SV230 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1875]) ).
thf(2065,plain,
! [SV230: nat,SV42: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV42 @ ( plus_plus_nat @ SV42 @ SV230 ) ) )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV230 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1876]) ).
thf(2066,plain,
! [SV230: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV230 ) )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV230 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1876]) ).
thf(2067,plain,
! [SV231: nat,SV43: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV43 @ SV231 ) @ SV231 ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV43 @ SV231 ) @ SV231 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1877]) ).
thf(2068,plain,
! [SV231: nat,SV43: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV43 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV43 @ SV231 ) @ SV231 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1877]) ).
thf(2069,plain,
! [SV231: nat,SV43: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV43 @ SV231 ) @ SV231 ) )
= $false )
| ( ( ord_less_eq_nat @ SV43 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1878]) ).
thf(2070,plain,
! [SV43: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV43 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV43 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1878]) ).
thf(2071,plain,
! [SV232: nat,SV44: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV44 @ SV232 ) @ SV44 ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV44 @ SV232 ) @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1879]) ).
thf(2072,plain,
! [SV44: nat,SV232: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV232 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV44 @ SV232 ) @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1879]) ).
thf(2073,plain,
! [SV232: nat,SV44: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV44 @ SV232 ) @ SV44 ) )
= $false )
| ( ( ord_less_eq_nat @ SV232 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1880]) ).
thf(2074,plain,
! [SV232: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV232 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV232 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1880]) ).
thf(2075,plain,
! [SV234: nat,SV46: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV46 @ SV234 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV46 @ SV234 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1881]) ).
thf(2076,plain,
! [SV46: nat,SV234: nat] :
( ( ( ~ ( ord_less_nat @ SV234 @ SV46 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV46 @ SV234 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1881]) ).
thf(2077,plain,
! [SV234: nat,SV46: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV46 @ SV234 ) ) )
= $false )
| ( ( ord_less_nat @ SV234 @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1882]) ).
thf(2078,plain,
! [SV46: nat,SV234: nat] :
( ( ( ~ ( ord_less_nat @ SV234 @ SV46 ) )
= $false )
| ( ( ord_less_nat @ SV234 @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1882]) ).
thf(2079,plain,
! [SV235: nat,SV47: nat] :
( ( ( ( minus_minus_nat @ SV47 @ SV235 )
!= zero_zero_nat )
= $false )
| ( ( ( minus_minus_nat @ SV47 @ SV235 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1883]) ).
thf(2080,plain,
! [SV235: nat,SV47: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV47 @ SV235 ) )
= $false )
| ( ( ( minus_minus_nat @ SV47 @ SV235 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1883]) ).
thf(2081,plain,
! [SV235: nat,SV47: nat] :
( ( ( ( minus_minus_nat @ SV47 @ SV235 )
!= zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ SV47 @ SV235 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1884]) ).
thf(2082,plain,
! [SV235: nat,SV47: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV47 @ SV235 ) )
= $false )
| ( ( ord_less_eq_nat @ SV47 @ SV235 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1884]) ).
thf(2083,plain,
! [SV388: nat,SV247: nat,SV60: nat] :
( ( ( ~ ( ord_less_nat @ SV60 @ ( minus_minus_nat @ SV247 @ SV388 ) )
| ~ ( ord_less_nat @ ( plus_plus_nat @ SV60 @ SV388 ) @ SV247 ) )
= $false )
| ( ( ord_less_nat @ SV60 @ ( minus_minus_nat @ SV247 @ SV388 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1885]) ).
thf(2084,plain,
! [SV388: nat,SV247: nat,SV60: nat] :
( ( ( ~ ( ord_less_nat @ SV60 @ ( minus_minus_nat @ SV247 @ SV388 ) )
| ~ ( ord_less_nat @ ( plus_plus_nat @ SV60 @ SV388 ) @ SV247 ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV60 @ SV388 ) @ SV247 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1886]) ).
thf(2085,plain,
! [SV389: nat,SV248: nat,SV61: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( minus_minus_nat @ SV61 @ SV248 ) @ SV389 )
| ~ ( ord_less_eq_nat @ SV61 @ ( plus_plus_nat @ SV389 @ SV248 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV61 @ SV248 ) @ SV389 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1887]) ).
thf(2086,plain,
! [SV389: nat,SV248: nat,SV61: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( minus_minus_nat @ SV61 @ SV248 ) @ SV389 )
| ~ ( ord_less_eq_nat @ SV61 @ ( plus_plus_nat @ SV389 @ SV248 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV61 @ ( plus_plus_nat @ SV389 @ SV248 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1888]) ).
thf(2087,plain,
! [SV62: nat] :
( ( ( zero_zero_nat = SV62 )
= $true )
| ( ( zero_zero_nat = SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1889]) ).
thf(2088,plain,
! [SV62: nat] :
( ( ( SV62 = zero_zero_nat )
= $true )
| ( ( zero_zero_nat = SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1890]) ).
thf(2089,plain,
! [SV62: nat] :
( ( ( zero_zero_nat = SV62 )
= $true )
| ( ( SV62 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1891]) ).
thf(2090,plain,
! [SV62: nat] :
( ( ( SV62 = zero_zero_nat )
= $true )
| ( ( SV62 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1892]) ).
thf(2091,plain,
! [SV82: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV82 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV82 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1893]) ).
thf(2092,plain,
! [SV82: nat] :
( ( ( SV82 != zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV82 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1893]) ).
thf(2093,plain,
! [SV82: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV82 ) )
= $true )
| ( ( SV82 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1894]) ).
thf(2094,plain,
! [SV82: nat] :
( ( ( SV82 = zero_zero_nat )
= $true )
| ( ( SV82 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1895]) ).
thf(2095,plain,
! [SV83: nat] :
( ( ( ord_less_eq_nat @ SV83 @ zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV83 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1896]) ).
thf(2096,plain,
! [SV83: nat] :
( ( ( SV83 = zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV83 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1897]) ).
thf(2097,plain,
! [SV83: nat] :
( ( ( ord_less_eq_nat @ SV83 @ zero_zero_nat )
= $true )
| ( ( SV83 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1898]) ).
thf(2098,plain,
! [SV83: nat] :
( ( ( SV83 = zero_zero_nat )
= $true )
| ( ( SV83 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1899]) ).
thf(2099,plain,
! [SV84: nat] :
( ( ( ord_less_eq_nat @ SV84 @ zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV84 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1900]) ).
thf(2100,plain,
! [SV84: nat] :
( ( ( SV84 = zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV84 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1901]) ).
thf(2101,plain,
! [SV84: nat] :
( ( ( ord_less_eq_nat @ SV84 @ zero_zero_nat )
= $true )
| ( ( SV84 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1902]) ).
thf(2102,plain,
! [SV84: nat] :
( ( ( SV84 = zero_zero_nat )
= $true )
| ( ( SV84 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1903]) ).
thf(2103,plain,
! [SV481: nat,SV258: nat] :
( ( ( ord_less_eq_nat @ SV258 @ SV481 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV258 @ SV481 )
| ~ ( ( ord_less_nat @ SV258 @ SV481 )
| ( SV258 = SV481 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1904]) ).
thf(2104,plain,
! [SV481: nat,SV258: nat] :
( ( ( ( ord_less_nat @ SV258 @ SV481 )
| ( SV258 = SV481 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV258 @ SV481 )
| ~ ( ( ord_less_nat @ SV258 @ SV481 )
| ( SV258 = SV481 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1904]) ).
thf(2105,plain,
! [SV399: nat,SV261: nat,SV90: nat] :
( ( ( ( ( times_times_nat @ SV90 @ SV261 )
!= ( times_times_nat @ SV90 @ SV399 ) )
| ~ ( ( SV90 = zero_zero_nat )
| ( SV261 = SV399 ) ) )
= $false )
| ( ( ( times_times_nat @ SV90 @ SV261 )
= ( times_times_nat @ SV90 @ SV399 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1905]) ).
thf(2106,plain,
! [SV399: nat,SV261: nat,SV90: nat] :
( ( ( SV90 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV90 @ SV261 )
!= ( times_times_nat @ SV90 @ SV399 ) )
| ~ ( ( SV90 = zero_zero_nat )
| ( SV261 = SV399 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1906]) ).
thf(2107,plain,
! [SV90: nat,SV399: nat,SV261: nat] :
( ( ( SV261 = SV399 )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV90 @ SV261 )
!= ( times_times_nat @ SV90 @ SV399 ) )
| ~ ( ( SV90 = zero_zero_nat )
| ( SV261 = SV399 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1906]) ).
thf(2108,plain,
! [SV92: nat > nat,SV262: nat,SV400: nat] :
( ( ( ~ ( ord_less_nat @ ( sK3_SY609 @ SV400 @ SV262 @ SV92 ) @ ( sK6_SY1043 @ SV92 @ SV262 @ SV400 ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV262 @ SV400 )
| ( ord_less_eq_nat @ ( SV92 @ SV262 ) @ ( SV92 @ SV400 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1907]) ).
thf(2109,plain,
! [SV262: nat,SV400: nat,SV92: nat > nat] :
( ( ( ord_less_nat @ ( SV92 @ ( sK3_SY609 @ SV400 @ SV262 @ SV92 ) ) @ ( SV92 @ ( sK6_SY1043 @ SV92 @ SV262 @ SV400 ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV262 @ SV400 )
| ( ord_less_eq_nat @ ( SV92 @ SV262 ) @ ( SV92 @ SV400 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1907]) ).
thf(2110,plain,
! [SV482: nat,SV401: nat,SV264: nat,SV94: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV94 @ SV264 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV401 @ SV482 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV94 @ SV401 ) @ ( plus_plus_nat @ SV264 @ SV482 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1909]) ).
thf(2111,plain,
! [SV402: nat,SV95: nat,SV265: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV265 @ SV95 ) @ ( minus_minus_nat @ SV265 @ SV402 ) )
| ( ord_less_eq_nat @ SV402 @ SV95 ) )
| ~ ( ~ ( ord_less_eq_nat @ ( minus_minus_nat @ SV265 @ SV95 ) @ ( minus_minus_nat @ SV265 @ SV402 ) )
| ~ ( ord_less_eq_nat @ SV402 @ SV95 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV402 @ SV265 )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ SV265 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1910]) ).
thf(2112,plain,
! [SV402: nat,SV95: nat,SV265: nat] :
( ( ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV265 @ SV95 ) @ ( minus_minus_nat @ SV265 @ SV402 ) )
= ( ord_less_eq_nat @ SV402 @ SV95 ) )
= $true )
| ( ( ord_less_eq_nat @ SV402 @ SV265 )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ SV265 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1910]) ).
thf(2113,plain,
! [SV483: nat,SV404: nat,SV268: nat,SV98: nat] :
( ( ( SV98 != SV268 )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV404 @ SV483 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV98 @ SV404 ) @ ( plus_plus_nat @ SV268 @ SV483 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1911]) ).
thf(2114,plain,
! [SV507: nat,SV99: nat,SV484: nat,SV405: nat,SV269: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV269 @ SV405 ) @ SV484 ) @ ( plus_plus_nat @ ( times_times_nat @ SV99 @ SV405 ) @ SV507 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV269 @ SV99 ) @ SV405 ) @ SV484 ) @ SV507 ) )
| ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV269 @ SV405 ) @ SV484 ) @ ( plus_plus_nat @ ( times_times_nat @ SV99 @ SV405 ) @ SV507 ) )
| ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV269 @ SV99 ) @ SV405 ) @ SV484 ) @ SV507 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV99 @ SV269 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1912]) ).
thf(2115,plain,
! [SV507: nat,SV99: nat,SV484: nat,SV405: nat,SV269: nat] :
( ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV269 @ SV405 ) @ SV484 ) @ ( plus_plus_nat @ ( times_times_nat @ SV99 @ SV405 ) @ SV507 ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV269 @ SV99 ) @ SV405 ) @ SV484 ) @ SV507 ) )
= $true )
| ( ( ord_less_eq_nat @ SV99 @ SV269 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1912]) ).
thf(2116,plain,
! [SV102: nat] :
( ( ( ~ ( ( SV102 != zero_zero_nat ) ) )
= $false )
| ( ( SV102 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1913]) ).
thf(2117,plain,
! [SV102: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV102 ) )
= $false )
| ( ( SV102 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1913]) ).
thf(2118,plain,
! [SV102: nat] :
( ( ( SV102 != zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV102 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1914]) ).
thf(2119,plain,
! [SV102: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV102 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV102 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1915]) ).
thf(2120,plain,
! [SV274: nat,SV105: nat,SV485: nat,SV408: nat] :
( ( ( ord_less_nat @ SV408 @ SV485 )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV105 @ SV408 ) @ ( plus_plus_nat @ SV274 @ SV485 ) )
= $true )
| ( ( ord_less_nat @ SV105 @ SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1916]) ).
thf(2121,plain,
! [SV487: nat,SV412: nat,SV278: nat,SV109: nat] :
( ( ( ~ ( ord_less_nat @ SV109 @ SV278 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV412 @ SV487 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV109 @ SV412 ) @ ( plus_plus_nat @ SV278 @ SV487 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1918]) ).
thf(2122,plain,
! [SV413: nat,SV110: nat,SV279: nat] :
( ( ( ~ ( ( ( minus_minus_nat @ SV279 @ SV110 )
= ( minus_minus_nat @ SV413 @ SV110 ) )
| ( SV279 = SV413 ) )
| ~ ( ( ( minus_minus_nat @ SV279 @ SV110 )
!= ( minus_minus_nat @ SV413 @ SV110 ) )
| ( SV279 != SV413 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV110 @ SV413 )
= $false )
| ( ( ord_less_eq_nat @ SV110 @ SV279 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1919]) ).
thf(2123,plain,
! [SV413: nat,SV110: nat,SV279: nat] :
( ( ( ( ( minus_minus_nat @ SV279 @ SV110 )
= ( minus_minus_nat @ SV413 @ SV110 ) )
= ( SV279 = SV413 ) )
= $true )
| ( ( ord_less_eq_nat @ SV110 @ SV413 )
= $false )
| ( ( ord_less_eq_nat @ SV110 @ SV279 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1919]) ).
thf(2124,plain,
! [SV113: nat,SV282: nat,SV415: nat] :
( ( ( ( ord_less_eq_nat @ SV415 @ ( minus_minus_nat @ SV282 @ SV113 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV415 @ SV113 ) @ SV282 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV415 @ ( minus_minus_nat @ SV282 @ SV113 ) )
| ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV415 @ SV113 ) @ SV282 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV113 @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1920]) ).
thf(2125,plain,
! [SV114: nat > $o,SV283: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( sK7_SY655 @ SV283 @ SV114 ) ) )
= $false )
| ( ( SV114 @ SV283 )
= $true )
| ( ( SV114 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1921]) ).
thf(2126,plain,
! [SV283: nat,SV114: nat > $o] :
( ( ( ~ ~ ( SV114 @ ( sK7_SY655 @ SV283 @ SV114 ) )
| ~ ! [SY1044: nat] :
~ ~ ( ~ ( ord_less_nat @ SY1044 @ ( sK7_SY655 @ SV283 @ SV114 ) )
| ~ ~ ( SV114 @ SY1044 ) ) )
= $false )
| ( ( SV114 @ SV283 )
= $true )
| ( ( SV114 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1921]) ).
thf(2127,plain,
! [SV115: nat] :
( ( ( ~ ( ( SV115 != zero_zero_nat ) ) )
= $false )
| ( ( SV115 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1922]) ).
thf(2128,plain,
! [SV115: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV115 ) )
= $false )
| ( ( SV115 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1922]) ).
thf(2129,plain,
! [SV115: nat] :
( ( ( SV115 != zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV115 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1923]) ).
thf(2130,plain,
! [SV115: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV115 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV115 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1924]) ).
thf(2131,plain,
! [SV417: nat,SV285: nat,SV117: nat > $o] :
( ( ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) )
= $false )
| ( ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1925]) ).
thf(2132,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) )
= $true )
| ( ( ~ ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1926]) ).
thf(2133,plain,
! [SV488: nat,SV288: nat] :
( ( ( ord_less_eq_nat @ SV288 @ SV488 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV288 @ SV488 )
| ~ ~ ! [SY1033: nat] :
( SV488
!= ( plus_plus_nat @ SV288 @ SY1033 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1928]) ).
thf(2134,plain,
! [SV288: nat,SV488: nat] :
( ( ( ~ ! [SY1033: nat] :
( SV488
!= ( plus_plus_nat @ SV288 @ SY1033 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV288 @ SV488 )
| ~ ~ ! [SY1033: nat] :
( SV488
!= ( plus_plus_nat @ SV288 @ SY1033 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1928]) ).
thf(2135,plain,
! [SV489: nat,SV289: nat] :
( ( ( ord_less_eq_nat @ SV289 @ SV489 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV289 @ SV489 )
| ~ ~ ! [SY1034: nat] :
( SV489
!= ( plus_plus_nat @ SV289 @ SY1034 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1929]) ).
thf(2136,plain,
! [SV289: nat,SV489: nat] :
( ( ( ~ ! [SY1034: nat] :
( SV489
!= ( plus_plus_nat @ SV289 @ SY1034 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV289 @ SV489 )
| ~ ~ ! [SY1034: nat] :
( SV489
!= ( plus_plus_nat @ SV289 @ SY1034 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1929]) ).
thf(2137,plain,
! [SV421: nat,SV122: nat,SV290: nat] :
( ( ( ( ( minus_minus_nat @ SV290 @ SV122 )
= SV421 )
| ( SV290
= ( plus_plus_nat @ SV421 @ SV122 ) ) )
= $false )
| ( ( ~ ( ( ( minus_minus_nat @ SV290 @ SV122 )
!= SV421 )
| ( SV290
!= ( plus_plus_nat @ SV421 @ SV122 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV122 @ SV290 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1930]) ).
thf(2138,plain,
! [SV294: nat,SV126: nat] :
( ( ( ( plus_plus_nat @ SV126 @ SV294 )
!= zero_zero_nat )
= $false )
| ( ( ( plus_plus_nat @ SV126 @ SV294 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1932]) ).
thf(2139,plain,
! [SV294: nat,SV126: nat] :
( ( ( ~ ~ ( ( SV126 != zero_zero_nat )
| ( SV294 != zero_zero_nat ) ) )
= $false )
| ( ( ( plus_plus_nat @ SV126 @ SV294 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1932]) ).
thf(2140,plain,
! [SV294: nat,SV126: nat] :
( ( ( SV126 != zero_zero_nat )
= $true )
| ( ( SV294 != zero_zero_nat )
= $true )
| ( ( ~ ( ( ( plus_plus_nat @ SV126 @ SV294 )
!= zero_zero_nat )
| ~ ~ ( ( SV126 != zero_zero_nat )
| ( SV294 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1933]) ).
thf(2141,plain,
! [SV510: nat,SV295: nat,SV491: nat,SV425: nat,SV127: nat] :
( ( ( ~ ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV127 @ SV425 ) @ SV491 ) @ ( plus_plus_nat @ ( times_times_nat @ SV295 @ SV425 ) @ SV510 ) )
| ( ord_less_nat @ SV491 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV295 @ SV127 ) @ SV425 ) @ SV510 ) ) )
| ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV127 @ SV425 ) @ SV491 ) @ ( plus_plus_nat @ ( times_times_nat @ SV295 @ SV425 ) @ SV510 ) )
| ~ ( ord_less_nat @ SV491 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV295 @ SV127 ) @ SV425 ) @ SV510 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV127 @ SV295 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1934]) ).
thf(2142,plain,
! [SV510: nat,SV295: nat,SV491: nat,SV425: nat,SV127: nat] :
( ( ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV127 @ SV425 ) @ SV491 ) @ ( plus_plus_nat @ ( times_times_nat @ SV295 @ SV425 ) @ SV510 ) )
= ( ord_less_nat @ SV491 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV295 @ SV127 ) @ SV425 ) @ SV510 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV127 @ SV295 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1934]) ).
thf(2143,plain,
! [SV492: nat,SV132: nat,SV300: nat,SV429: nat] :
( ( ( ( plus_plus_nat @ SV429 @ SV300 )
= ( plus_plus_nat @ SV132 @ SV492 ) )
= $false )
| ( ( ord_less_nat @ SV429 @ SV492 )
= $true )
| ( ( ord_less_nat @ SV132 @ SV300 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1935]) ).
thf(2144,plain,
! [SV134: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV134 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1936]) ).
thf(2145,plain,
! [SV134: nat] :
( ( ( SV134 != zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1937]) ).
thf(2146,plain,
! [SV134: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV134 ) )
= $false )
| ( ( SV134 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1938]) ).
thf(2147,plain,
! [SV134: nat] :
( ( ( ~ ( ( SV134 != zero_zero_nat ) ) )
= $false )
| ( ( SV134 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1938]) ).
thf(2148,plain,
! [SV304: nat,SV137: nat,SV493: nat,SV433: nat] :
( ( ( ord_less_eq_nat @ SV433 @ SV493 )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV137 @ SV433 ) @ ( plus_plus_nat @ SV304 @ SV493 ) )
= $true )
| ( ( ord_less_eq_nat @ SV137 @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1939]) ).
thf(2149,plain,
! [SV309: nat,SV142: nat > $o] :
( ( ( SV142 @ ( sK1_SY712 @ SV309 @ SV142 ) )
= $false )
| ( ( SV142 @ SV309 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1940]) ).
thf(2150,plain,
! [SV142: nat > $o,SV309: nat,SV516: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ SV516 @ ( sK1_SY712 @ SV309 @ SV142 ) )
| ~ ~ ( SV142 @ SV516 ) ) )
= $true )
| ( ( SV142 @ SV309 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1941]) ).
thf(2151,plain,
! [SV511: nat,SV313: nat,SV494: nat,SV440: nat,SV146: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV146 @ SV440 ) @ SV494 ) @ ( plus_plus_nat @ ( times_times_nat @ SV313 @ SV440 ) @ SV511 ) )
| ( ord_less_eq_nat @ SV494 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV313 @ SV146 ) @ SV440 ) @ SV511 ) ) )
| ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV146 @ SV440 ) @ SV494 ) @ ( plus_plus_nat @ ( times_times_nat @ SV313 @ SV440 ) @ SV511 ) )
| ~ ( ord_less_eq_nat @ SV494 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV313 @ SV146 ) @ SV440 ) @ SV511 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV146 @ SV313 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1942]) ).
thf(2152,plain,
! [SV511: nat,SV313: nat,SV494: nat,SV440: nat,SV146: nat] :
( ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV146 @ SV440 ) @ SV494 ) @ ( plus_plus_nat @ ( times_times_nat @ SV313 @ SV440 ) @ SV511 ) )
= ( ord_less_eq_nat @ SV494 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV313 @ SV146 ) @ SV440 ) @ SV511 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV146 @ SV313 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1942]) ).
thf(2153,plain,
! [SV495: nat,SV442: nat,SV315: nat,SV148: nat] :
( ( ( ~ ( ord_less_nat @ SV148 @ SV315 ) )
= $true )
| ( ( SV442 != SV495 )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV148 @ SV442 ) @ ( plus_plus_nat @ SV315 @ SV495 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1943]) ).
thf(2154,plain,
! [SV317: nat,SV150: nat,SV496: nat,SV443: nat] :
( ( ( ord_less_nat @ SV443 @ SV496 )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV150 @ SV443 ) @ ( plus_plus_nat @ SV317 @ SV496 ) )
= $true )
| ( ( ord_less_nat @ SV150 @ SV317 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1944]) ).
thf(2155,plain,
! [SV444: nat,SV318: nat,SV152: nat] :
( ( ( ~ ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV318 )
| ~ ( ord_less_nat @ SV152 @ SV444 ) ) )
= $false )
| ( ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1945]) ).
thf(2156,plain,
! [SV444: nat,SV152: nat,SV318: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV318 )
| ~ ( ord_less_nat @ SV152 @ SV444 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV318 )
| ~ ( ord_less_nat @ SV152 @ SV444 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1946]) ).
thf(2157,plain,
! [SV321: nat,SV155: nat] :
( ( ( ~ ( ( SV155 != SV321 ) )
| ~ ( ( ord_less_nat @ SV155 @ SV321 )
| ( ord_less_nat @ SV321 @ SV155 ) ) )
= $false )
| ( ( SV155 = SV321 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1947]) ).
thf(2158,plain,
! [SV321: nat,SV155: nat] :
( ( ( ~ ( ( SV155 != SV321 ) )
| ~ ( ( ord_less_nat @ SV155 @ SV321 )
| ( ord_less_nat @ SV321 @ SV155 ) ) )
= $false )
| ( ( ord_less_nat @ SV155 @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1948]) ).
thf(2159,plain,
! [SV321: nat,SV155: nat] :
( ( ( ~ ( ( SV155 != SV321 ) )
| ~ ( ( ord_less_nat @ SV155 @ SV321 )
| ( ord_less_nat @ SV321 @ SV155 ) ) )
= $false )
| ( ( ord_less_nat @ SV321 @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1949]) ).
thf(2160,plain,
! [SV325: nat,SV159: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1950]) ).
thf(2161,plain,
! [SV325: nat,SV159: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV159 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV325 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1950]) ).
thf(2162,plain,
! [SV325: nat,SV159: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV159 ) )
= $true )
| ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV325 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV159 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV325 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1951]) ).
thf(2163,plain,
! [SV326: nat,SV160: nat] :
( ( ( ( plus_plus_nat @ SV160 @ SV326 )
!= zero_zero_nat )
= $false )
| ( ( ( plus_plus_nat @ SV160 @ SV326 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1952]) ).
thf(2164,plain,
! [SV326: nat,SV160: nat] :
( ( ( ~ ~ ( ( SV160 != zero_zero_nat )
| ( SV326 != zero_zero_nat ) ) )
= $false )
| ( ( ( plus_plus_nat @ SV160 @ SV326 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1952]) ).
thf(2165,plain,
! [SV326: nat,SV160: nat] :
( ( ( SV160 != zero_zero_nat )
= $true )
| ( ( SV326 != zero_zero_nat )
= $true )
| ( ( ~ ( ( ( plus_plus_nat @ SV160 @ SV326 )
!= zero_zero_nat )
| ~ ~ ( ( SV160 != zero_zero_nat )
| ( SV326 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1953]) ).
thf(2166,plain,
! [SV497: nat,SV327: nat] :
( ( ( ord_less_nat @ SV327 @ SV497 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV327 @ SV497 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV327 @ SV497 )
| ~ ( ( SV327 != SV497 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1954]) ).
thf(2167,plain,
! [SV497: nat,SV327: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV327 @ SV497 )
| ~ ( ( SV327 != SV497 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV327 @ SV497 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV327 @ SV497 )
| ~ ( ( SV327 != SV497 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1954]) ).
thf(2168,plain,
! [SV328: nat,SV162: nat] :
( ( ( zero_zero_nat
!= ( plus_plus_nat @ SV162 @ SV328 ) )
= $false )
| ( ( zero_zero_nat
= ( plus_plus_nat @ SV162 @ SV328 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1955]) ).
thf(2169,plain,
! [SV328: nat,SV162: nat] :
( ( ( ~ ~ ( ( SV162 != zero_zero_nat )
| ( SV328 != zero_zero_nat ) ) )
= $false )
| ( ( zero_zero_nat
= ( plus_plus_nat @ SV162 @ SV328 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1955]) ).
thf(2170,plain,
! [SV328: nat,SV162: nat] :
( ( ( SV162 != zero_zero_nat )
= $true )
| ( ( SV328 != zero_zero_nat )
= $true )
| ( ( ~ ( ( zero_zero_nat
!= ( plus_plus_nat @ SV162 @ SV328 ) )
| ~ ~ ( ( SV162 != zero_zero_nat )
| ( SV328 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1956]) ).
thf(2171,plain,
! [SV448: nat,SV329: nat,SV163: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV329 )
| ( ord_less_eq_nat @ SV163 @ SV448 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1957]) ).
thf(2172,plain,
! [SV448: nat,SV163: nat,SV329: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV329 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV329 )
| ( ord_less_eq_nat @ SV163 @ SV448 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1958]) ).
thf(2173,plain,
! [SV329: nat,SV448: nat,SV163: nat] :
( ( ( ord_less_eq_nat @ SV163 @ SV448 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV329 )
| ( ord_less_eq_nat @ SV163 @ SV448 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1958]) ).
thf(2174,plain,
! [SV449: nat,SV330: nat,SV164: nat > $o] :
( ( ( ~ ( SV164 @ ( sK8_SY1015 @ SV330 @ SV449 @ SV164 ) )
| ( ord_less_eq_nat @ ( sK8_SY1015 @ SV330 @ SV449 @ SV164 ) @ SV449 ) )
= $false )
| ( ( ~ ! [SY751: nat] :
~ ~ ( ~ ( SV164 @ SY751 )
| ~ ! [SY752: nat] :
( ~ ( SV164 @ SY752 )
| ( ord_less_eq_nat @ SY752 @ SY751 ) ) ) )
= $true )
| ( ( SV164 @ SV330 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1959]) ).
thf(2175,plain,
! [SV451: nat,SV167: nat,SV332: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV332 @ SV167 ) @ ( minus_minus_nat @ SV451 @ SV167 ) )
| ( ord_less_eq_nat @ SV332 @ SV451 ) )
| ~ ( ~ ( ord_less_eq_nat @ ( minus_minus_nat @ SV332 @ SV167 ) @ ( minus_minus_nat @ SV451 @ SV167 ) )
| ~ ( ord_less_eq_nat @ SV332 @ SV451 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV167 @ SV451 )
= $false )
| ( ( ord_less_eq_nat @ SV167 @ SV332 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1960]) ).
thf(2176,plain,
! [SV451: nat,SV167: nat,SV332: nat] :
( ( ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV332 @ SV167 ) @ ( minus_minus_nat @ SV451 @ SV167 ) )
= ( ord_less_eq_nat @ SV332 @ SV451 ) )
= $true )
| ( ( ord_less_eq_nat @ SV167 @ SV451 )
= $false )
| ( ( ord_less_eq_nat @ SV167 @ SV332 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1960]) ).
thf(2177,plain,
! [SV453: nat,SV169: nat,SV334: nat] :
( ( ( ( ord_less_nat @ ( minus_minus_nat @ SV334 @ SV169 ) @ SV453 )
| ( ord_less_nat @ SV334 @ ( plus_plus_nat @ SV453 @ SV169 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( minus_minus_nat @ SV334 @ SV169 ) @ SV453 )
| ~ ( ord_less_nat @ SV334 @ ( plus_plus_nat @ SV453 @ SV169 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV169 @ SV334 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1961]) ).
thf(2178,plain,
! [SV512: nat,SV174: nat,SV499: nat,SV457: nat,SV338: nat] :
( ( ( ~ ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV338 @ SV457 ) @ SV499 ) @ ( plus_plus_nat @ ( times_times_nat @ SV174 @ SV457 ) @ SV512 ) )
| ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV338 @ SV174 ) @ SV457 ) @ SV499 ) @ SV512 ) )
| ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV338 @ SV457 ) @ SV499 ) @ ( plus_plus_nat @ ( times_times_nat @ SV174 @ SV457 ) @ SV512 ) )
| ~ ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV338 @ SV174 ) @ SV457 ) @ SV499 ) @ SV512 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV174 @ SV338 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1963]) ).
thf(2179,plain,
! [SV512: nat,SV174: nat,SV499: nat,SV457: nat,SV338: nat] :
( ( ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV338 @ SV457 ) @ SV499 ) @ ( plus_plus_nat @ ( times_times_nat @ SV174 @ SV457 ) @ SV512 ) )
= ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV338 @ SV174 ) @ SV457 ) @ SV499 ) @ SV512 ) )
= $true )
| ( ( ord_less_eq_nat @ SV174 @ SV338 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1963]) ).
thf(2180,plain,
! [SV459: nat,SV341: nat,SV177: nat] :
( ( ( ~ ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 )
| ~ ( ord_less_nat @ SV341 @ SV459 ) ) )
= $false )
| ( ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1964]) ).
thf(2181,plain,
! [SV459: nat,SV341: nat,SV177: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 )
| ~ ( ord_less_nat @ SV341 @ SV459 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 )
| ~ ( ord_less_nat @ SV341 @ SV459 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1965]) ).
thf(2182,plain,
! [SV342: nat,SV178: nat] :
( ( ( ord_less_nat @ SV178 @ SV342 )
= $true )
| ( ( ord_less_nat @ SV342 @ SV178 )
= $true )
| ( ( SV178 = SV342 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1966]) ).
thf(2183,plain,
! [SV181: nat > $o,SV345: nat,SV517: nat] :
( ( ( ~ ( ord_less_nat @ SV517 @ ( sK2_SY783 @ SV345 @ SV181 ) )
| ( SV181 @ SV517 ) )
= $true )
| ( ( SV181 @ SV345 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2184,plain,
! [SV461: nat,SV182: nat,SV346: nat] :
( ( ( ~ ( ( ( minus_minus_nat @ SV346 @ SV182 )
= SV461 )
| ( SV346
= ( plus_plus_nat @ SV461 @ SV182 ) ) )
| ~ ( ( ( minus_minus_nat @ SV346 @ SV182 )
!= SV461 )
| ( SV346
!= ( plus_plus_nat @ SV461 @ SV182 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1968]) ).
thf(2185,plain,
! [SV461: nat,SV182: nat,SV346: nat] :
( ( ( ( ( minus_minus_nat @ SV346 @ SV182 )
= SV461 )
= ( SV346
= ( plus_plus_nat @ SV461 @ SV182 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1968]) ).
thf(2186,plain,
! [SV463: nat,SV184: nat,SV348: nat] :
( ( ( ~ ( ( ord_less_nat @ ( minus_minus_nat @ SV348 @ SV184 ) @ ( minus_minus_nat @ SV463 @ SV184 ) )
| ( ord_less_nat @ SV348 @ SV463 ) )
| ~ ( ~ ( ord_less_nat @ ( minus_minus_nat @ SV348 @ SV184 ) @ ( minus_minus_nat @ SV463 @ SV184 ) )
| ~ ( ord_less_nat @ SV348 @ SV463 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV184 @ SV463 )
= $false )
| ( ( ord_less_eq_nat @ SV184 @ SV348 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1969]) ).
thf(2187,plain,
! [SV463: nat,SV184: nat,SV348: nat] :
( ( ( ( ord_less_nat @ ( minus_minus_nat @ SV348 @ SV184 ) @ ( minus_minus_nat @ SV463 @ SV184 ) )
= ( ord_less_nat @ SV348 @ SV463 ) )
= $true )
| ( ( ord_less_eq_nat @ SV184 @ SV463 )
= $false )
| ( ( ord_less_eq_nat @ SV184 @ SV348 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1969]) ).
thf(2188,plain,
! [SV185: nat,SV349: nat,SV464: nat] :
( ( ( ( ord_less_eq_nat @ SV464 @ ( minus_minus_nat @ SV349 @ SV185 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ SV464 @ SV185 ) @ SV349 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV464 @ ( minus_minus_nat @ SV349 @ SV185 ) )
| ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV464 @ SV185 ) @ SV349 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV185 @ SV349 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1970]) ).
thf(2189,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) )
= $false )
| ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1971]) ).
thf(2190,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) )
= $true )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1972]) ).
thf(2191,plain,
! [SV513: nat,SV190: nat,SV501: nat,SV468: nat,SV354: nat] :
( ( ( ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV354 @ SV468 ) @ SV501 )
= ( plus_plus_nat @ ( times_times_nat @ SV190 @ SV468 ) @ SV513 ) )
| ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV354 @ SV190 ) @ SV468 ) @ SV501 )
= SV513 ) )
| ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV354 @ SV468 ) @ SV501 )
!= ( plus_plus_nat @ ( times_times_nat @ SV190 @ SV468 ) @ SV513 ) )
| ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV354 @ SV190 ) @ SV468 ) @ SV501 )
!= SV513 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV190 @ SV354 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1974]) ).
thf(2192,plain,
! [SV513: nat,SV190: nat,SV501: nat,SV468: nat,SV354: nat] :
( ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV354 @ SV468 ) @ SV501 )
= ( plus_plus_nat @ ( times_times_nat @ SV190 @ SV468 ) @ SV513 ) )
= ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV354 @ SV190 ) @ SV468 ) @ SV501 )
= SV513 ) )
= $true )
| ( ( ord_less_eq_nat @ SV190 @ SV354 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1974]) ).
thf(2193,plain,
! [SV502: nat,SV469: nat,SV356: nat,SV192: nat] :
( ( ( SV192 != SV356 )
= $true )
| ( ( ~ ( ord_less_nat @ SV469 @ SV502 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV192 @ SV469 ) @ ( plus_plus_nat @ SV356 @ SV502 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1976]) ).
thf(2194,plain,
! [SV503: nat,SV470: nat,SV357: nat,SV193: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV193 @ SV357 ) )
= $true )
| ( ( SV470 != SV503 )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV193 @ SV470 ) @ ( plus_plus_nat @ SV357 @ SV503 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1977]) ).
thf(2195,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV194 )
| ( ord_less_eq_nat @ SV358 @ SV471 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1978]) ).
thf(2196,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV194 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV194 )
| ( ord_less_eq_nat @ SV358 @ SV471 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1979]) ).
thf(2197,plain,
! [SV194: nat,SV471: nat,SV358: nat] :
( ( ( ord_less_eq_nat @ SV358 @ SV471 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV194 )
| ( ord_less_eq_nat @ SV358 @ SV471 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1979]) ).
thf(2198,plain,
! [SV504: nat,SV473: nat,SV360: nat,SV196: nat] :
( ( ( SV196 != SV360 )
= $true )
| ( ( SV473 != SV504 )
= $true )
| ( ( ( plus_plus_nat @ SV196 @ SV473 )
= ( plus_plus_nat @ SV360 @ SV504 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1981]) ).
thf(2199,plain,
! [SV514: nat,SV361: nat,SV505: nat,SV474: nat,SV197: nat] :
( ( ( ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV197 @ SV474 ) @ SV505 )
= ( plus_plus_nat @ ( times_times_nat @ SV361 @ SV474 ) @ SV514 ) )
| ( SV505
= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV361 @ SV197 ) @ SV474 ) @ SV514 ) ) )
| ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV197 @ SV474 ) @ SV505 )
!= ( plus_plus_nat @ ( times_times_nat @ SV361 @ SV474 ) @ SV514 ) )
| ( SV505
!= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV361 @ SV197 ) @ SV474 ) @ SV514 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV197 @ SV361 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1982]) ).
thf(2200,plain,
! [SV514: nat,SV361: nat,SV505: nat,SV474: nat,SV197: nat] :
( ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV197 @ SV474 ) @ SV505 )
= ( plus_plus_nat @ ( times_times_nat @ SV361 @ SV474 ) @ SV514 ) )
= ( SV505
= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV361 @ SV197 ) @ SV474 ) @ SV514 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV197 @ SV361 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1982]) ).
thf(2201,plain,
! [SV362: nat,SV198: nat,SV506: nat,SV475: nat] :
( ( ( ord_less_eq_nat @ SV475 @ SV506 )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV198 @ SV475 ) @ ( plus_plus_nat @ SV362 @ SV506 ) )
= $true )
| ( ( ord_less_eq_nat @ SV198 @ SV362 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1983]) ).
thf(2202,plain,
! [SV1: nat > nat] :
( ( ( ! [SV518: nat] :
( ( SV1 @ SV518 )
= zero_zero_nat ) )
= $true )
| ( ( number1551313001itions @ SV1 @ zero_zero_nat )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1985]) ).
thf(2203,plain,
! [SV1: nat > nat] :
( ( ( SV1
= ( ^ [I: nat] : zero_zero_nat ) )
= $true )
| ( ( number1551313001itions @ SV1 @ zero_zero_nat )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1985]) ).
thf(2204,plain,
! [SV1: nat > nat] :
( ( ( ~ ( number1551313001itions @ SV1 @ zero_zero_nat ) )
= $false )
| ( ( ( SV1 @ ( sK5_SV515 @ SV1 ) )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1986]) ).
thf(2205,plain,
! [SV1: nat > nat] :
( ( ( SV1
!= ( ^ [I: nat] : zero_zero_nat ) )
= $false )
| ( ( ( SV1 @ ( sK5_SV515 @ SV1 ) )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1986]) ).
thf(2206,plain,
! [SV1: nat > nat] :
( ( ( number1551313001itions @ SV1 @ zero_zero_nat )
= $true )
| ( ( SV1
= ( ^ [I: nat] : zero_zero_nat ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1987]) ).
thf(2207,plain,
! [SV1: nat > nat] :
( ( ( SV1
= ( ^ [I: nat] : zero_zero_nat ) )
= $true )
| ( ( SV1
= ( ^ [I: nat] : zero_zero_nat ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1988]) ).
thf(2208,plain,
! [SV204: nat,SV2: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SV204 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SV204 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1989]) ).
thf(2209,plain,
! [SV204: nat,SV2: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( ord_less_nat @ zero_zero_nat @ SV204 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SV204 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1990]) ).
thf(2210,plain,
! [SV204: nat,SV2: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SV204 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1991]) ).
thf(2211,plain,
! [SV204: nat,SV2: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( ord_less_nat @ zero_zero_nat @ SV204 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1991]) ).
thf(2212,plain,
! [SV204: nat,SV2: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SV204 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV204 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1992]) ).
thf(2213,plain,
! [SV204: nat,SV2: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( ord_less_nat @ zero_zero_nat @ SV204 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV204 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1992]) ).
thf(2214,plain,
! [SV205: nat,SV3: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV3 @ SV205 ) @ SV3 )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV3 @ SV205 ) @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1993]) ).
thf(2215,plain,
! [SV3: nat,SV205: nat] :
( ( ( ord_less_nat @ SV205 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV3 @ SV205 ) @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1994]) ).
thf(2216,plain,
! [SV205: nat,SV3: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV3 @ SV205 ) @ SV3 )
= $true )
| ( ( ord_less_nat @ SV205 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1995]) ).
thf(2217,plain,
! [SV205: nat] :
( ( ( ord_less_nat @ SV205 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV205 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1996]) ).
thf(2218,plain,
! [SV206: nat,SV4: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV4 @ SV206 ) @ SV206 )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV4 @ SV206 ) @ SV206 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1997]) ).
thf(2219,plain,
! [SV206: nat,SV4: nat] :
( ( ( ord_less_nat @ SV4 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV4 @ SV206 ) @ SV206 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1998]) ).
thf(2220,plain,
! [SV206: nat,SV4: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV4 @ SV206 ) @ SV206 )
= $true )
| ( ( ord_less_nat @ SV4 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1999]) ).
thf(2221,plain,
! [SV4: nat] :
( ( ( ord_less_nat @ SV4 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV4 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2000]) ).
thf(2222,plain,
! [SV207: nat,SV5: nat] :
( ( ( ord_less_nat @ SV5 @ ( plus_plus_nat @ SV5 @ SV207 ) )
= $true )
| ( ( ord_less_nat @ SV5 @ ( plus_plus_nat @ SV5 @ SV207 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2001]) ).
thf(2223,plain,
! [SV5: nat,SV207: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV207 )
= $true )
| ( ( ord_less_nat @ SV5 @ ( plus_plus_nat @ SV5 @ SV207 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2002]) ).
thf(2224,plain,
! [SV207: nat,SV5: nat] :
( ( ( ord_less_nat @ SV5 @ ( plus_plus_nat @ SV5 @ SV207 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV207 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2003]) ).
thf(2225,plain,
! [SV207: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV207 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV207 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2004]) ).
thf(2226,plain,
! [SV208: nat,SV6: nat] :
( ( ( ord_less_nat @ SV6 @ ( plus_plus_nat @ SV208 @ SV6 ) )
= $true )
| ( ( ord_less_nat @ SV6 @ ( plus_plus_nat @ SV208 @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2005]) ).
thf(2227,plain,
! [SV6: nat,SV208: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV208 )
= $true )
| ( ( ord_less_nat @ SV6 @ ( plus_plus_nat @ SV208 @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2006]) ).
thf(2228,plain,
! [SV208: nat,SV6: nat] :
( ( ( ord_less_nat @ SV6 @ ( plus_plus_nat @ SV208 @ SV6 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV208 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2007]) ).
thf(2229,plain,
! [SV208: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV208 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV208 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2008]) ).
thf(2230,plain,
! [SV368: nat,SV209: nat,SV7: nat] :
( ( ( ( plus_plus_nat @ SV7 @ SV209 )
!= ( plus_plus_nat @ SV368 @ SV209 ) )
= $false )
| ( ( ( plus_plus_nat @ SV7 @ SV209 )
= ( plus_plus_nat @ SV368 @ SV209 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2009]) ).
thf(2231,plain,
! [SV209: nat,SV368: nat,SV7: nat] :
( ( ( SV7 != SV368 )
= $false )
| ( ( ( plus_plus_nat @ SV7 @ SV209 )
= ( plus_plus_nat @ SV368 @ SV209 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2009]) ).
thf(2232,plain,
! [SV368: nat,SV209: nat,SV7: nat] :
( ( ( ( plus_plus_nat @ SV7 @ SV209 )
!= ( plus_plus_nat @ SV368 @ SV209 ) )
= $false )
| ( ( SV7 = SV368 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2010]) ).
thf(2233,plain,
! [SV368: nat,SV7: nat] :
( ( ( SV7 != SV368 )
= $false )
| ( ( SV7 = SV368 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2010]) ).
thf(2234,plain,
! [SV369: nat,SV210: nat,SV8: nat] :
( ( ( ( plus_plus_nat @ SV8 @ SV210 )
!= ( plus_plus_nat @ SV8 @ SV369 ) )
= $false )
| ( ( ( plus_plus_nat @ SV8 @ SV210 )
= ( plus_plus_nat @ SV8 @ SV369 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2011]) ).
thf(2235,plain,
! [SV8: nat,SV369: nat,SV210: nat] :
( ( ( SV210 != SV369 )
= $false )
| ( ( ( plus_plus_nat @ SV8 @ SV210 )
= ( plus_plus_nat @ SV8 @ SV369 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2011]) ).
thf(2236,plain,
! [SV369: nat,SV210: nat,SV8: nat] :
( ( ( ( plus_plus_nat @ SV8 @ SV210 )
!= ( plus_plus_nat @ SV8 @ SV369 ) )
= $false )
| ( ( SV210 = SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2012]) ).
thf(2237,plain,
! [SV369: nat,SV210: nat] :
( ( ( SV210 != SV369 )
= $false )
| ( ( SV210 = SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2012]) ).
thf(2238,plain,
! [SV10: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV10 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2017]) ).
thf(2239,plain,
! [SV10: nat] :
( ( ( SV10 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2018]) ).
thf(2240,plain,
! [SV10: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV10 )
= $false )
| ( ( SV10 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2019]) ).
thf(2241,plain,
! [SV370: nat,SV211: nat,SV11: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV11 @ SV211 ) @ ( plus_plus_nat @ SV370 @ SV211 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV11 @ SV211 ) @ ( plus_plus_nat @ SV370 @ SV211 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2021]) ).
thf(2242,plain,
! [SV211: nat,SV370: nat,SV11: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV11 @ SV370 ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV11 @ SV211 ) @ ( plus_plus_nat @ SV370 @ SV211 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2021]) ).
thf(2243,plain,
! [SV370: nat,SV211: nat,SV11: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV11 @ SV211 ) @ ( plus_plus_nat @ SV370 @ SV211 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV11 @ SV370 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2022]) ).
thf(2244,plain,
! [SV370: nat,SV11: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV11 @ SV370 ) )
= $false )
| ( ( ord_less_eq_nat @ SV11 @ SV370 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2022]) ).
thf(2245,plain,
! [SV371: nat,SV212: nat,SV12: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV212 ) @ ( plus_plus_nat @ SV12 @ SV371 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV212 ) @ ( plus_plus_nat @ SV12 @ SV371 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2023]) ).
thf(2246,plain,
! [SV12: nat,SV371: nat,SV212: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV212 @ SV371 ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV212 ) @ ( plus_plus_nat @ SV12 @ SV371 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2023]) ).
thf(2247,plain,
! [SV371: nat,SV212: nat,SV12: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV212 ) @ ( plus_plus_nat @ SV12 @ SV371 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV212 @ SV371 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2024]) ).
thf(2248,plain,
! [SV371: nat,SV212: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV212 @ SV371 ) )
= $false )
| ( ( ord_less_eq_nat @ SV212 @ SV371 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2024]) ).
thf(2249,plain,
! [SV213: nat,SV13: nat] :
( ( ( SV13
= ( plus_plus_nat @ SV13 @ SV213 ) )
= $true )
| ( ( SV13
= ( plus_plus_nat @ SV13 @ SV213 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2025]) ).
thf(2250,plain,
! [SV13: nat,SV213: nat] :
( ( ( SV213 = zero_zero_nat )
= $true )
| ( ( SV13
= ( plus_plus_nat @ SV13 @ SV213 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2026]) ).
thf(2251,plain,
! [SV213: nat,SV13: nat] :
( ( ( SV13
= ( plus_plus_nat @ SV13 @ SV213 ) )
= $true )
| ( ( SV213 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2027]) ).
thf(2252,plain,
! [SV213: nat] :
( ( ( SV213 = zero_zero_nat )
= $true )
| ( ( SV213 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2028]) ).
thf(2253,plain,
! [SV214: nat,SV14: nat] :
( ( ( SV14
= ( plus_plus_nat @ SV214 @ SV14 ) )
= $true )
| ( ( SV14
= ( plus_plus_nat @ SV214 @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2029]) ).
thf(2254,plain,
! [SV14: nat,SV214: nat] :
( ( ( SV214 = zero_zero_nat )
= $true )
| ( ( SV14
= ( plus_plus_nat @ SV214 @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2030]) ).
thf(2255,plain,
! [SV214: nat,SV14: nat] :
( ( ( SV14
= ( plus_plus_nat @ SV214 @ SV14 ) )
= $true )
| ( ( SV214 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2031]) ).
thf(2256,plain,
! [SV214: nat] :
( ( ( SV214 = zero_zero_nat )
= $true )
| ( ( SV214 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2032]) ).
thf(2257,plain,
! [SV215: nat,SV15: nat] :
( ( ( ( plus_plus_nat @ SV15 @ SV215 )
= SV15 )
= $true )
| ( ( ( plus_plus_nat @ SV15 @ SV215 )
= SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2033]) ).
thf(2258,plain,
! [SV15: nat,SV215: nat] :
( ( ( SV215 = zero_zero_nat )
= $true )
| ( ( ( plus_plus_nat @ SV15 @ SV215 )
= SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2034]) ).
thf(2259,plain,
! [SV215: nat,SV15: nat] :
( ( ( ( plus_plus_nat @ SV15 @ SV215 )
= SV15 )
= $true )
| ( ( SV215 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2035]) ).
thf(2260,plain,
! [SV215: nat] :
( ( ( SV215 = zero_zero_nat )
= $true )
| ( ( SV215 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2036]) ).
thf(2261,plain,
! [SV216: nat,SV16: nat] :
( ( ( ( plus_plus_nat @ SV16 @ SV216 )
= SV216 )
= $true )
| ( ( ( plus_plus_nat @ SV16 @ SV216 )
= SV216 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2037]) ).
thf(2262,plain,
! [SV216: nat,SV16: nat] :
( ( ( SV16 = zero_zero_nat )
= $true )
| ( ( ( plus_plus_nat @ SV16 @ SV216 )
= SV216 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2038]) ).
thf(2263,plain,
! [SV216: nat,SV16: nat] :
( ( ( ( plus_plus_nat @ SV16 @ SV216 )
= SV216 )
= $true )
| ( ( SV16 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2039]) ).
thf(2264,plain,
! [SV16: nat] :
( ( ( SV16 = zero_zero_nat )
= $true )
| ( ( SV16 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2040]) ).
thf(2265,plain,
! [SV372: nat,SV217: nat,SV22: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV22 @ SV217 ) @ ( plus_plus_nat @ SV372 @ SV217 ) ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV22 @ SV217 ) @ ( plus_plus_nat @ SV372 @ SV217 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2041]) ).
thf(2266,plain,
! [SV217: nat,SV372: nat,SV22: nat] :
( ( ( ~ ( ord_less_nat @ SV22 @ SV372 ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV22 @ SV217 ) @ ( plus_plus_nat @ SV372 @ SV217 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2041]) ).
thf(2267,plain,
! [SV372: nat,SV217: nat,SV22: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV22 @ SV217 ) @ ( plus_plus_nat @ SV372 @ SV217 ) ) )
= $false )
| ( ( ord_less_nat @ SV22 @ SV372 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2042]) ).
thf(2268,plain,
! [SV372: nat,SV22: nat] :
( ( ( ~ ( ord_less_nat @ SV22 @ SV372 ) )
= $false )
| ( ( ord_less_nat @ SV22 @ SV372 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2042]) ).
thf(2269,plain,
! [SV373: nat,SV218: nat,SV23: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV23 @ SV218 ) @ ( plus_plus_nat @ SV23 @ SV373 ) ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV23 @ SV218 ) @ ( plus_plus_nat @ SV23 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2043]) ).
thf(2270,plain,
! [SV23: nat,SV373: nat,SV218: nat] :
( ( ( ~ ( ord_less_nat @ SV218 @ SV373 ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV23 @ SV218 ) @ ( plus_plus_nat @ SV23 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2043]) ).
thf(2271,plain,
! [SV373: nat,SV218: nat,SV23: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV23 @ SV218 ) @ ( plus_plus_nat @ SV23 @ SV373 ) ) )
= $false )
| ( ( ord_less_nat @ SV218 @ SV373 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2044]) ).
thf(2272,plain,
! [SV373: nat,SV218: nat] :
( ( ( ~ ( ord_less_nat @ SV218 @ SV373 ) )
= $false )
| ( ( ord_less_nat @ SV218 @ SV373 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2044]) ).
thf(2273,plain,
! [SV376: nat,SV223: nat,SV32: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV32 @ SV223 ) @ ( plus_plus_nat @ SV32 @ SV376 ) ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV32 @ SV223 ) @ ( plus_plus_nat @ SV32 @ SV376 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2045]) ).
thf(2274,plain,
! [SV32: nat,SV376: nat,SV223: nat] :
( ( ( ~ ( ord_less_nat @ SV223 @ SV376 ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV32 @ SV223 ) @ ( plus_plus_nat @ SV32 @ SV376 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2045]) ).
thf(2275,plain,
! [SV376: nat,SV223: nat,SV32: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV32 @ SV223 ) @ ( plus_plus_nat @ SV32 @ SV376 ) ) )
= $false )
| ( ( ord_less_nat @ SV223 @ SV376 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2046]) ).
thf(2276,plain,
! [SV376: nat,SV223: nat] :
( ( ( ~ ( ord_less_nat @ SV223 @ SV376 ) )
= $false )
| ( ( ord_less_nat @ SV223 @ SV376 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2046]) ).
thf(2277,plain,
! [SV377: nat,SV224: nat,SV35: nat] :
( ( ( ( times_times_nat @ SV35 @ SV224 )
!= ( times_times_nat @ SV377 @ SV224 ) )
= $false )
| ( ( ( times_times_nat @ SV35 @ SV224 )
= ( times_times_nat @ SV377 @ SV224 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2047]) ).
thf(2278,plain,
! [SV224: nat,SV377: nat,SV35: nat] :
( ( ( ~ ( ( SV35 = SV377 )
| ( SV224 = zero_zero_nat ) ) )
= $false )
| ( ( ( times_times_nat @ SV35 @ SV224 )
= ( times_times_nat @ SV377 @ SV224 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2047]) ).
thf(2279,plain,
! [SV377: nat,SV224: nat,SV35: nat] :
( ( ( ( ( times_times_nat @ SV35 @ SV224 )
!= ( times_times_nat @ SV377 @ SV224 ) )
| ~ ( ( SV35 = SV377 )
| ( SV224 = zero_zero_nat ) ) )
= $false )
| ( ( SV35 = SV377 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2048]) ).
thf(2280,plain,
! [SV377: nat,SV224: nat,SV35: nat] :
( ( ( ( ( times_times_nat @ SV35 @ SV224 )
!= ( times_times_nat @ SV377 @ SV224 ) )
| ~ ( ( SV35 = SV377 )
| ( SV224 = zero_zero_nat ) ) )
= $false )
| ( ( SV224 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2049]) ).
thf(2281,plain,
! [SV378: nat,SV225: nat,SV36: nat] :
( ( ( ( times_times_nat @ SV36 @ SV225 )
!= ( times_times_nat @ SV36 @ SV378 ) )
= $false )
| ( ( ( times_times_nat @ SV36 @ SV225 )
= ( times_times_nat @ SV36 @ SV378 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2050]) ).
thf(2282,plain,
! [SV36: nat,SV378: nat,SV225: nat] :
( ( ( ~ ( ( SV225 = SV378 )
| ( SV36 = zero_zero_nat ) ) )
= $false )
| ( ( ( times_times_nat @ SV36 @ SV225 )
= ( times_times_nat @ SV36 @ SV378 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2050]) ).
thf(2283,plain,
! [SV378: nat,SV225: nat,SV36: nat] :
( ( ( ( ( times_times_nat @ SV36 @ SV225 )
!= ( times_times_nat @ SV36 @ SV378 ) )
| ~ ( ( SV225 = SV378 )
| ( SV36 = zero_zero_nat ) ) )
= $false )
| ( ( SV225 = SV378 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2051]) ).
thf(2284,plain,
! [SV378: nat,SV225: nat,SV36: nat] :
( ( ( ( ( times_times_nat @ SV36 @ SV225 )
!= ( times_times_nat @ SV36 @ SV378 ) )
| ~ ( ( SV225 = SV378 )
| ( SV36 = zero_zero_nat ) ) )
= $false )
| ( ( SV36 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2052]) ).
thf(2285,plain,
! [SV226: nat,SV38: nat] :
( ( ( ( times_times_nat @ SV38 @ SV226 )
= zero_zero_nat )
= $true )
| ( ( ( times_times_nat @ SV38 @ SV226 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2053]) ).
thf(2286,plain,
! [SV226: nat,SV38: nat] :
( ( ( ( SV38 = zero_zero_nat )
| ( SV226 = zero_zero_nat ) )
= $true )
| ( ( ( times_times_nat @ SV38 @ SV226 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2054]) ).
thf(2287,plain,
! [SV226: nat,SV38: nat] :
( ( ( ( times_times_nat @ SV38 @ SV226 )
!= zero_zero_nat )
= $false )
| ( ( SV38 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2055]) ).
thf(2288,plain,
! [SV226: nat,SV38: nat] :
( ( ( ~ ( ( SV38 = zero_zero_nat )
| ( SV226 = zero_zero_nat ) ) )
= $false )
| ( ( SV38 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2055]) ).
thf(2289,plain,
! [SV226: nat,SV38: nat] :
( ( ( ( times_times_nat @ SV38 @ SV226 )
!= zero_zero_nat )
= $false )
| ( ( SV226 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2056]) ).
thf(2290,plain,
! [SV226: nat,SV38: nat] :
( ( ( ~ ( ( SV38 = zero_zero_nat )
| ( SV226 = zero_zero_nat ) ) )
= $false )
| ( ( SV226 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2056]) ).
thf(2291,plain,
! [SV379: nat,SV227: nat,SV39: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV39 @ SV227 ) @ ( plus_plus_nat @ SV39 @ SV379 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV39 @ SV227 ) @ ( plus_plus_nat @ SV39 @ SV379 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2057]) ).
thf(2292,plain,
! [SV39: nat,SV379: nat,SV227: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV227 @ SV379 ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV39 @ SV227 ) @ ( plus_plus_nat @ SV39 @ SV379 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2057]) ).
thf(2293,plain,
! [SV379: nat,SV227: nat,SV39: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV39 @ SV227 ) @ ( plus_plus_nat @ SV39 @ SV379 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV227 @ SV379 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2058]) ).
thf(2294,plain,
! [SV379: nat,SV227: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV227 @ SV379 ) )
= $false )
| ( ( ord_less_eq_nat @ SV227 @ SV379 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2058]) ).
thf(2295,plain,
! [SV229: nat,SV41: nat] :
( ( ( ord_less_eq_nat @ SV41 @ ( plus_plus_nat @ SV229 @ SV41 ) )
= $true )
| ( ( ord_less_eq_nat @ SV41 @ ( plus_plus_nat @ SV229 @ SV41 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2059]) ).
thf(2296,plain,
! [SV41: nat,SV229: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV229 )
= $true )
| ( ( ord_less_eq_nat @ SV41 @ ( plus_plus_nat @ SV229 @ SV41 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2060]) ).
thf(2297,plain,
! [SV229: nat,SV41: nat] :
( ( ( ord_less_eq_nat @ SV41 @ ( plus_plus_nat @ SV229 @ SV41 ) )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV229 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2061]) ).
thf(2298,plain,
! [SV229: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV229 )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV229 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2062]) ).
thf(2299,plain,
! [SV230: nat,SV42: nat] :
( ( ( ord_less_eq_nat @ SV42 @ ( plus_plus_nat @ SV42 @ SV230 ) )
= $true )
| ( ( ord_less_eq_nat @ SV42 @ ( plus_plus_nat @ SV42 @ SV230 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2063]) ).
thf(2300,plain,
! [SV42: nat,SV230: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV230 )
= $true )
| ( ( ord_less_eq_nat @ SV42 @ ( plus_plus_nat @ SV42 @ SV230 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2064]) ).
thf(2301,plain,
! [SV230: nat,SV42: nat] :
( ( ( ord_less_eq_nat @ SV42 @ ( plus_plus_nat @ SV42 @ SV230 ) )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV230 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2065]) ).
thf(2302,plain,
! [SV230: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV230 )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV230 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2066]) ).
thf(2303,plain,
! [SV231: nat,SV43: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV43 @ SV231 ) @ SV231 )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV43 @ SV231 ) @ SV231 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2067]) ).
thf(2304,plain,
! [SV231: nat,SV43: nat] :
( ( ( ord_less_eq_nat @ SV43 @ zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV43 @ SV231 ) @ SV231 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2068]) ).
thf(2305,plain,
! [SV231: nat,SV43: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV43 @ SV231 ) @ SV231 )
= $true )
| ( ( ord_less_eq_nat @ SV43 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2069]) ).
thf(2306,plain,
! [SV43: nat] :
( ( ( ord_less_eq_nat @ SV43 @ zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV43 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2070]) ).
thf(2307,plain,
! [SV232: nat,SV44: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV44 @ SV232 ) @ SV44 )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV44 @ SV232 ) @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2071]) ).
thf(2308,plain,
! [SV44: nat,SV232: nat] :
( ( ( ord_less_eq_nat @ SV232 @ zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV44 @ SV232 ) @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2072]) ).
thf(2309,plain,
! [SV232: nat,SV44: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV44 @ SV232 ) @ SV44 )
= $true )
| ( ( ord_less_eq_nat @ SV232 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2073]) ).
thf(2310,plain,
! [SV232: nat] :
( ( ( ord_less_eq_nat @ SV232 @ zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV232 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2074]) ).
thf(2311,plain,
! [SV234: nat,SV46: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV46 @ SV234 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV46 @ SV234 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2075]) ).
thf(2312,plain,
! [SV46: nat,SV234: nat] :
( ( ( ord_less_nat @ SV234 @ SV46 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV46 @ SV234 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2076]) ).
thf(2313,plain,
! [SV234: nat,SV46: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV46 @ SV234 ) )
= $true )
| ( ( ord_less_nat @ SV234 @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2077]) ).
thf(2314,plain,
! [SV46: nat,SV234: nat] :
( ( ( ord_less_nat @ SV234 @ SV46 )
= $true )
| ( ( ord_less_nat @ SV234 @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2078]) ).
thf(2315,plain,
! [SV235: nat,SV47: nat] :
( ( ( ( minus_minus_nat @ SV47 @ SV235 )
= zero_zero_nat )
= $true )
| ( ( ( minus_minus_nat @ SV47 @ SV235 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2079]) ).
thf(2316,plain,
! [SV235: nat,SV47: nat] :
( ( ( ord_less_eq_nat @ SV47 @ SV235 )
= $true )
| ( ( ( minus_minus_nat @ SV47 @ SV235 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2080]) ).
thf(2317,plain,
! [SV235: nat,SV47: nat] :
( ( ( ( minus_minus_nat @ SV47 @ SV235 )
= zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV47 @ SV235 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2081]) ).
thf(2318,plain,
! [SV235: nat,SV47: nat] :
( ( ( ord_less_eq_nat @ SV47 @ SV235 )
= $true )
| ( ( ord_less_eq_nat @ SV47 @ SV235 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2082]) ).
thf(2319,plain,
! [SV388: nat,SV247: nat,SV60: nat] :
( ( ( ~ ( ord_less_nat @ SV60 @ ( minus_minus_nat @ SV247 @ SV388 ) ) )
= $false )
| ( ( ord_less_nat @ SV60 @ ( minus_minus_nat @ SV247 @ SV388 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2083]) ).
thf(2320,plain,
! [SV247: nat,SV388: nat,SV60: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV60 @ SV388 ) @ SV247 ) )
= $false )
| ( ( ord_less_nat @ SV60 @ ( minus_minus_nat @ SV247 @ SV388 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2083]) ).
thf(2321,plain,
! [SV388: nat,SV247: nat,SV60: nat] :
( ( ( ~ ( ord_less_nat @ SV60 @ ( minus_minus_nat @ SV247 @ SV388 ) ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV60 @ SV388 ) @ SV247 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2084]) ).
thf(2322,plain,
! [SV247: nat,SV388: nat,SV60: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV60 @ SV388 ) @ SV247 ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV60 @ SV388 ) @ SV247 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2084]) ).
thf(2323,plain,
! [SV389: nat,SV248: nat,SV61: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( minus_minus_nat @ SV61 @ SV248 ) @ SV389 ) )
= $false )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV61 @ SV248 ) @ SV389 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2085]) ).
thf(2324,plain,
! [SV248: nat,SV389: nat,SV61: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV61 @ ( plus_plus_nat @ SV389 @ SV248 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV61 @ SV248 ) @ SV389 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2085]) ).
thf(2325,plain,
! [SV389: nat,SV248: nat,SV61: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( minus_minus_nat @ SV61 @ SV248 ) @ SV389 ) )
= $false )
| ( ( ord_less_eq_nat @ SV61 @ ( plus_plus_nat @ SV389 @ SV248 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2086]) ).
thf(2326,plain,
! [SV248: nat,SV389: nat,SV61: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV61 @ ( plus_plus_nat @ SV389 @ SV248 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV61 @ ( plus_plus_nat @ SV389 @ SV248 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2086]) ).
thf(2327,plain,
! [SV82: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV82 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV82 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2091]) ).
thf(2328,plain,
! [SV82: nat] :
( ( ( SV82 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV82 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2092]) ).
thf(2329,plain,
! [SV82: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV82 )
= $false )
| ( ( SV82 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2093]) ).
thf(2330,plain,
! [SV481: nat,SV258: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV258 @ SV481 )
| ~ ( ( ord_less_nat @ SV258 @ SV481 )
| ( SV258 = SV481 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV258 @ SV481 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2103]) ).
thf(2331,plain,
! [SV481: nat,SV258: nat] :
( ( ( ord_less_nat @ SV258 @ SV481 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV258 @ SV481 )
| ~ ( ( ord_less_nat @ SV258 @ SV481 )
| ( SV258 = SV481 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2104]) ).
thf(2332,plain,
! [SV481: nat,SV258: nat] :
( ( ( SV258 = SV481 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV258 @ SV481 )
| ~ ( ( ord_less_nat @ SV258 @ SV481 )
| ( SV258 = SV481 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2104]) ).
thf(2333,plain,
! [SV399: nat,SV261: nat,SV90: nat] :
( ( ( ( times_times_nat @ SV90 @ SV261 )
!= ( times_times_nat @ SV90 @ SV399 ) )
= $false )
| ( ( ( times_times_nat @ SV90 @ SV261 )
= ( times_times_nat @ SV90 @ SV399 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2105]) ).
thf(2334,plain,
! [SV399: nat,SV261: nat,SV90: nat] :
( ( ( ~ ( ( SV90 = zero_zero_nat )
| ( SV261 = SV399 ) ) )
= $false )
| ( ( ( times_times_nat @ SV90 @ SV261 )
= ( times_times_nat @ SV90 @ SV399 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2105]) ).
thf(2335,plain,
! [SV399: nat,SV261: nat,SV90: nat] :
( ( ( ( ( times_times_nat @ SV90 @ SV261 )
!= ( times_times_nat @ SV90 @ SV399 ) )
| ~ ( ( SV90 = zero_zero_nat )
| ( SV261 = SV399 ) ) )
= $false )
| ( ( SV90 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2106]) ).
thf(2336,plain,
! [SV399: nat,SV261: nat,SV90: nat] :
( ( ( ( ( times_times_nat @ SV90 @ SV261 )
!= ( times_times_nat @ SV90 @ SV399 ) )
| ~ ( ( SV90 = zero_zero_nat )
| ( SV261 = SV399 ) ) )
= $false )
| ( ( SV261 = SV399 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2107]) ).
thf(2337,plain,
! [SV92: nat > nat,SV262: nat,SV400: nat] :
( ( ( ord_less_nat @ ( sK3_SY609 @ SV400 @ SV262 @ SV92 ) @ ( sK6_SY1043 @ SV92 @ SV262 @ SV400 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV262 @ SV400 )
| ( ord_less_eq_nat @ ( SV92 @ SV262 ) @ ( SV92 @ SV400 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2108]) ).
thf(2338,plain,
! [SV92: nat > nat,SV400: nat,SV262: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV262 @ SV400 ) )
= $true )
| ( ( ord_less_eq_nat @ ( SV92 @ SV262 ) @ ( SV92 @ SV400 ) )
= $true )
| ( ( ord_less_nat @ ( SV92 @ ( sK3_SY609 @ SV400 @ SV262 @ SV92 ) ) @ ( SV92 @ ( sK6_SY1043 @ SV92 @ SV262 @ SV400 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2109]) ).
thf(2339,plain,
! [SV482: nat,SV401: nat,SV264: nat,SV94: nat] :
( ( ( ord_less_eq_nat @ SV94 @ SV264 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV401 @ SV482 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV94 @ SV401 ) @ ( plus_plus_nat @ SV264 @ SV482 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2110]) ).
thf(2340,plain,
! [SV402: nat,SV95: nat,SV265: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV265 @ SV95 ) @ ( minus_minus_nat @ SV265 @ SV402 ) )
| ( ord_less_eq_nat @ SV402 @ SV95 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( minus_minus_nat @ SV265 @ SV95 ) @ ( minus_minus_nat @ SV265 @ SV402 ) )
| ~ ( ord_less_eq_nat @ SV402 @ SV95 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV402 @ SV265 )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2111]) ).
thf(2341,plain,
! [SV483: nat,SV404: nat,SV268: nat,SV98: nat] :
( ( ( SV98 = SV268 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV404 @ SV483 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV98 @ SV404 ) @ ( plus_plus_nat @ SV268 @ SV483 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2113]) ).
thf(2342,plain,
! [SV507: nat,SV99: nat,SV484: nat,SV405: nat,SV269: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV269 @ SV405 ) @ SV484 ) @ ( plus_plus_nat @ ( times_times_nat @ SV99 @ SV405 ) @ SV507 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV269 @ SV99 ) @ SV405 ) @ SV484 ) @ SV507 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV269 @ SV405 ) @ SV484 ) @ ( plus_plus_nat @ ( times_times_nat @ SV99 @ SV405 ) @ SV507 ) )
| ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV269 @ SV99 ) @ SV405 ) @ SV484 ) @ SV507 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV99 @ SV269 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2114]) ).
thf(2343,plain,
! [SV102: nat] :
( ( ( SV102 != zero_zero_nat )
= $true )
| ( ( SV102 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2116]) ).
thf(2344,plain,
! [SV102: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV102 )
= $true )
| ( ( SV102 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2117]) ).
thf(2345,plain,
! [SV102: nat] :
( ( ( SV102 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2118]) ).
thf(2346,plain,
! [SV487: nat,SV412: nat,SV278: nat,SV109: nat] :
( ( ( ord_less_nat @ SV109 @ SV278 )
= $false )
| ( ( ~ ( ord_less_nat @ SV412 @ SV487 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV109 @ SV412 ) @ ( plus_plus_nat @ SV278 @ SV487 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2121]) ).
thf(2347,plain,
! [SV413: nat,SV110: nat,SV279: nat] :
( ( ( ~ ( ( ( minus_minus_nat @ SV279 @ SV110 )
= ( minus_minus_nat @ SV413 @ SV110 ) )
| ( SV279 = SV413 ) ) )
= $true )
| ( ( ~ ( ( ( minus_minus_nat @ SV279 @ SV110 )
!= ( minus_minus_nat @ SV413 @ SV110 ) )
| ( SV279 != SV413 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV110 @ SV413 )
= $false )
| ( ( ord_less_eq_nat @ SV110 @ SV279 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2122]) ).
thf(2348,plain,
! [SV113: nat,SV282: nat,SV415: nat] :
( ( ( ord_less_eq_nat @ SV415 @ ( minus_minus_nat @ SV282 @ SV113 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV415 @ ( minus_minus_nat @ SV282 @ SV113 ) )
| ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV415 @ SV113 ) @ SV282 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV113 @ SV282 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2124]) ).
thf(2349,plain,
! [SV282: nat,SV113: nat,SV415: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV415 @ SV113 ) @ SV282 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV415 @ ( minus_minus_nat @ SV282 @ SV113 ) )
| ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV415 @ SV113 ) @ SV282 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV113 @ SV282 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2124]) ).
thf(2350,plain,
! [SV114: nat > $o,SV283: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( sK7_SY655 @ SV283 @ SV114 ) )
= $true )
| ( ( SV114 @ SV283 )
= $true )
| ( ( SV114 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2125]) ).
thf(2351,plain,
! [SV283: nat,SV114: nat > $o] :
( ( ( ~ ~ ( SV114 @ ( sK7_SY655 @ SV283 @ SV114 ) ) )
= $false )
| ( ( SV114 @ SV283 )
= $true )
| ( ( SV114 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2126]) ).
thf(2352,plain,
! [SV114: nat > $o,SV283: nat] :
( ( ( ~ ! [SY1044: nat] :
~ ~ ( ~ ( ord_less_nat @ SY1044 @ ( sK7_SY655 @ SV283 @ SV114 ) )
| ~ ~ ( SV114 @ SY1044 ) ) )
= $false )
| ( ( SV114 @ SV283 )
= $true )
| ( ( SV114 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2126]) ).
thf(2353,plain,
! [SV115: nat] :
( ( ( SV115 != zero_zero_nat )
= $true )
| ( ( SV115 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2127]) ).
thf(2354,plain,
! [SV115: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV115 )
= $true )
| ( ( SV115 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2128]) ).
thf(2355,plain,
! [SV115: nat] :
( ( ( SV115 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2129]) ).
thf(2356,plain,
! [SV417: nat,SV285: nat,SV117: nat > $o] :
( ( ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) ) )
= $false )
| ( ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2131]) ).
thf(2357,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) )
= $false )
| ( ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2131]) ).
thf(2358,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) ) )
= $true )
| ( ( ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) )
= $true )
| ( ( ~ ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2132]) ).
thf(2359,plain,
! [SV488: nat,SV288: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV288 @ SV488 )
| ~ ~ ! [SY1033: nat] :
( SV488
!= ( plus_plus_nat @ SV288 @ SY1033 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV288 @ SV488 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2133]) ).
thf(2360,plain,
! [SV288: nat,SV488: nat] :
( ( ( ! [SY1033: nat] :
( SV488
!= ( plus_plus_nat @ SV288 @ SY1033 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV288 @ SV488 )
| ~ ~ ! [SY1033: nat] :
( SV488
!= ( plus_plus_nat @ SV288 @ SY1033 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2134]) ).
thf(2361,plain,
! [SV489: nat,SV289: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV289 @ SV489 )
| ~ ~ ! [SY1034: nat] :
( SV489
!= ( plus_plus_nat @ SV289 @ SY1034 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV289 @ SV489 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2135]) ).
thf(2362,plain,
! [SV289: nat,SV489: nat] :
( ( ( ! [SY1034: nat] :
( SV489
!= ( plus_plus_nat @ SV289 @ SY1034 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV289 @ SV489 )
| ~ ~ ! [SY1034: nat] :
( SV489
!= ( plus_plus_nat @ SV289 @ SY1034 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2136]) ).
thf(2363,plain,
! [SV421: nat,SV122: nat,SV290: nat] :
( ( ( ( minus_minus_nat @ SV290 @ SV122 )
= SV421 )
= $false )
| ( ( ~ ( ( ( minus_minus_nat @ SV290 @ SV122 )
!= SV421 )
| ( SV290
!= ( plus_plus_nat @ SV421 @ SV122 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV122 @ SV290 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2137]) ).
thf(2364,plain,
! [SV122: nat,SV421: nat,SV290: nat] :
( ( ( SV290
= ( plus_plus_nat @ SV421 @ SV122 ) )
= $false )
| ( ( ~ ( ( ( minus_minus_nat @ SV290 @ SV122 )
!= SV421 )
| ( SV290
!= ( plus_plus_nat @ SV421 @ SV122 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV122 @ SV290 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2137]) ).
thf(2365,plain,
! [SV294: nat,SV126: nat] :
( ( ( ( plus_plus_nat @ SV126 @ SV294 )
= zero_zero_nat )
= $true )
| ( ( ( plus_plus_nat @ SV126 @ SV294 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2138]) ).
thf(2366,plain,
! [SV294: nat,SV126: nat] :
( ( ( ~ ( ( SV126 != zero_zero_nat )
| ( SV294 != zero_zero_nat ) ) )
= $true )
| ( ( ( plus_plus_nat @ SV126 @ SV294 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2139]) ).
thf(2367,plain,
! [SV294: nat,SV126: nat] :
( ( ( SV126 = zero_zero_nat )
= $false )
| ( ( SV294 != zero_zero_nat )
= $true )
| ( ( ~ ( ( ( plus_plus_nat @ SV126 @ SV294 )
!= zero_zero_nat )
| ~ ~ ( ( SV126 != zero_zero_nat )
| ( SV294 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2140]) ).
thf(2368,plain,
! [SV510: nat,SV295: nat,SV491: nat,SV425: nat,SV127: nat] :
( ( ( ~ ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV127 @ SV425 ) @ SV491 ) @ ( plus_plus_nat @ ( times_times_nat @ SV295 @ SV425 ) @ SV510 ) )
| ( ord_less_nat @ SV491 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV295 @ SV127 ) @ SV425 ) @ SV510 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV127 @ SV425 ) @ SV491 ) @ ( plus_plus_nat @ ( times_times_nat @ SV295 @ SV425 ) @ SV510 ) )
| ~ ( ord_less_nat @ SV491 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV295 @ SV127 ) @ SV425 ) @ SV510 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV127 @ SV295 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2141]) ).
thf(2369,plain,
! [SV134: nat] :
( ( ( SV134 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2145]) ).
thf(2370,plain,
! [SV134: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV134 )
= $true )
| ( ( SV134 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2146]) ).
thf(2371,plain,
! [SV134: nat] :
( ( ( SV134 != zero_zero_nat )
= $true )
| ( ( SV134 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2147]) ).
thf(2372,plain,
! [SV142: nat > $o,SV309: nat,SV516: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV516 @ ( sK1_SY712 @ SV309 @ SV142 ) )
| ~ ~ ( SV142 @ SV516 ) ) )
= $false )
| ( ( SV142 @ SV309 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2150]) ).
thf(2373,plain,
! [SV511: nat,SV313: nat,SV494: nat,SV440: nat,SV146: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV146 @ SV440 ) @ SV494 ) @ ( plus_plus_nat @ ( times_times_nat @ SV313 @ SV440 ) @ SV511 ) )
| ( ord_less_eq_nat @ SV494 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV313 @ SV146 ) @ SV440 ) @ SV511 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV146 @ SV440 ) @ SV494 ) @ ( plus_plus_nat @ ( times_times_nat @ SV313 @ SV440 ) @ SV511 ) )
| ~ ( ord_less_eq_nat @ SV494 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV313 @ SV146 ) @ SV440 ) @ SV511 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV146 @ SV313 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2151]) ).
thf(2374,plain,
! [SV495: nat,SV442: nat,SV315: nat,SV148: nat] :
( ( ( ord_less_nat @ SV148 @ SV315 )
= $false )
| ( ( SV442 != SV495 )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV148 @ SV442 ) @ ( plus_plus_nat @ SV315 @ SV495 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2153]) ).
thf(2375,plain,
! [SV444: nat,SV318: nat,SV152: nat] :
( ( ( ~ ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) ) )
= $false )
| ( ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2155]) ).
thf(2376,plain,
! [SV444: nat,SV152: nat,SV318: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV318 )
| ~ ( ord_less_nat @ SV152 @ SV444 ) ) )
= $false )
| ( ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2155]) ).
thf(2377,plain,
! [SV444: nat,SV152: nat,SV318: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV318 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV152 @ SV444 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV318 )
| ~ ( ord_less_nat @ SV152 @ SV444 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2156]) ).
thf(2378,plain,
! [SV321: nat,SV155: nat] :
( ( ( ~ ( ( SV155 != SV321 ) ) )
= $false )
| ( ( SV155 = SV321 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2157]) ).
thf(2379,plain,
! [SV321: nat,SV155: nat] :
( ( ( ~ ( ( ord_less_nat @ SV155 @ SV321 )
| ( ord_less_nat @ SV321 @ SV155 ) ) )
= $false )
| ( ( SV155 = SV321 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2157]) ).
thf(2380,plain,
! [SV321: nat,SV155: nat] :
( ( ( ~ ( ( SV155 != SV321 ) ) )
= $false )
| ( ( ord_less_nat @ SV155 @ SV321 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2158]) ).
thf(2381,plain,
! [SV321: nat,SV155: nat] :
( ( ( ~ ( ( ord_less_nat @ SV155 @ SV321 )
| ( ord_less_nat @ SV321 @ SV155 ) ) )
= $false )
| ( ( ord_less_nat @ SV155 @ SV321 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2158]) ).
thf(2382,plain,
! [SV321: nat,SV155: nat] :
( ( ( ~ ( ( SV155 != SV321 ) ) )
= $false )
| ( ( ord_less_nat @ SV321 @ SV155 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2159]) ).
thf(2383,plain,
! [SV321: nat,SV155: nat] :
( ( ( ~ ( ( ord_less_nat @ SV155 @ SV321 )
| ( ord_less_nat @ SV321 @ SV155 ) ) )
= $false )
| ( ( ord_less_nat @ SV321 @ SV155 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2159]) ).
thf(2384,plain,
! [SV325: nat,SV159: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2160]) ).
thf(2385,plain,
! [SV325: nat,SV159: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV159 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV325 ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2161]) ).
thf(2386,plain,
! [SV325: nat,SV159: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV159 )
= $false )
| ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV325 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV159 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV325 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2162]) ).
thf(2387,plain,
! [SV326: nat,SV160: nat] :
( ( ( ( plus_plus_nat @ SV160 @ SV326 )
= zero_zero_nat )
= $true )
| ( ( ( plus_plus_nat @ SV160 @ SV326 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2163]) ).
thf(2388,plain,
! [SV326: nat,SV160: nat] :
( ( ( ~ ( ( SV160 != zero_zero_nat )
| ( SV326 != zero_zero_nat ) ) )
= $true )
| ( ( ( plus_plus_nat @ SV160 @ SV326 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2164]) ).
thf(2389,plain,
! [SV326: nat,SV160: nat] :
( ( ( SV160 = zero_zero_nat )
= $false )
| ( ( SV326 != zero_zero_nat )
= $true )
| ( ( ~ ( ( ( plus_plus_nat @ SV160 @ SV326 )
!= zero_zero_nat )
| ~ ~ ( ( SV160 != zero_zero_nat )
| ( SV326 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2165]) ).
thf(2390,plain,
! [SV497: nat,SV327: nat] :
( ( ( ~ ( ord_less_nat @ SV327 @ SV497 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV327 @ SV497 )
| ~ ( ( SV327 != SV497 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV327 @ SV497 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2166]) ).
thf(2391,plain,
! [SV497: nat,SV327: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV327 @ SV497 )
| ~ ( ( SV327 != SV497 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV327 @ SV497 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV327 @ SV497 )
| ~ ( ( SV327 != SV497 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2167]) ).
thf(2392,plain,
! [SV328: nat,SV162: nat] :
( ( ( zero_zero_nat
= ( plus_plus_nat @ SV162 @ SV328 ) )
= $true )
| ( ( zero_zero_nat
= ( plus_plus_nat @ SV162 @ SV328 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2168]) ).
thf(2393,plain,
! [SV328: nat,SV162: nat] :
( ( ( ~ ( ( SV162 != zero_zero_nat )
| ( SV328 != zero_zero_nat ) ) )
= $true )
| ( ( zero_zero_nat
= ( plus_plus_nat @ SV162 @ SV328 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2169]) ).
thf(2394,plain,
! [SV328: nat,SV162: nat] :
( ( ( SV162 = zero_zero_nat )
= $false )
| ( ( SV328 != zero_zero_nat )
= $true )
| ( ( ~ ( ( zero_zero_nat
!= ( plus_plus_nat @ SV162 @ SV328 ) )
| ~ ~ ( ( SV162 != zero_zero_nat )
| ( SV328 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2170]) ).
thf(2395,plain,
! [SV448: nat,SV329: nat,SV163: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2171]) ).
thf(2396,plain,
! [SV448: nat,SV163: nat,SV329: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV329 )
| ( ord_less_eq_nat @ SV163 @ SV448 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2171]) ).
thf(2397,plain,
! [SV448: nat,SV163: nat,SV329: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV329 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV329 )
| ( ord_less_eq_nat @ SV163 @ SV448 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2172]) ).
thf(2398,plain,
! [SV448: nat,SV329: nat,SV163: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV329 )
| ( ord_less_eq_nat @ SV163 @ SV448 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV163 @ SV448 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2173]) ).
thf(2399,plain,
! [SV449: nat,SV330: nat,SV164: nat > $o] :
( ( ( ~ ( SV164 @ ( sK8_SY1015 @ SV330 @ SV449 @ SV164 ) ) )
= $false )
| ( ( ~ ! [SY751: nat] :
~ ~ ( ~ ( SV164 @ SY751 )
| ~ ! [SY752: nat] :
( ~ ( SV164 @ SY752 )
| ( ord_less_eq_nat @ SY752 @ SY751 ) ) ) )
= $true )
| ( ( SV164 @ SV330 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2174]) ).
thf(2400,plain,
! [SV164: nat > $o,SV449: nat,SV330: nat] :
( ( ( ord_less_eq_nat @ ( sK8_SY1015 @ SV330 @ SV449 @ SV164 ) @ SV449 )
= $false )
| ( ( ~ ! [SY751: nat] :
~ ~ ( ~ ( SV164 @ SY751 )
| ~ ! [SY752: nat] :
( ~ ( SV164 @ SY752 )
| ( ord_less_eq_nat @ SY752 @ SY751 ) ) ) )
= $true )
| ( ( SV164 @ SV330 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2174]) ).
thf(2401,plain,
! [SV451: nat,SV167: nat,SV332: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV332 @ SV167 ) @ ( minus_minus_nat @ SV451 @ SV167 ) )
| ( ord_less_eq_nat @ SV332 @ SV451 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( minus_minus_nat @ SV332 @ SV167 ) @ ( minus_minus_nat @ SV451 @ SV167 ) )
| ~ ( ord_less_eq_nat @ SV332 @ SV451 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV167 @ SV451 )
= $false )
| ( ( ord_less_eq_nat @ SV167 @ SV332 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2175]) ).
thf(2402,plain,
! [SV453: nat,SV169: nat,SV334: nat] :
( ( ( ord_less_nat @ ( minus_minus_nat @ SV334 @ SV169 ) @ SV453 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( minus_minus_nat @ SV334 @ SV169 ) @ SV453 )
| ~ ( ord_less_nat @ SV334 @ ( plus_plus_nat @ SV453 @ SV169 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV169 @ SV334 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2177]) ).
thf(2403,plain,
! [SV169: nat,SV453: nat,SV334: nat] :
( ( ( ord_less_nat @ SV334 @ ( plus_plus_nat @ SV453 @ SV169 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( minus_minus_nat @ SV334 @ SV169 ) @ SV453 )
| ~ ( ord_less_nat @ SV334 @ ( plus_plus_nat @ SV453 @ SV169 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV169 @ SV334 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2177]) ).
thf(2404,plain,
! [SV512: nat,SV174: nat,SV499: nat,SV457: nat,SV338: nat] :
( ( ( ~ ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV338 @ SV457 ) @ SV499 ) @ ( plus_plus_nat @ ( times_times_nat @ SV174 @ SV457 ) @ SV512 ) )
| ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV338 @ SV174 ) @ SV457 ) @ SV499 ) @ SV512 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV338 @ SV457 ) @ SV499 ) @ ( plus_plus_nat @ ( times_times_nat @ SV174 @ SV457 ) @ SV512 ) )
| ~ ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV338 @ SV174 ) @ SV457 ) @ SV499 ) @ SV512 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV174 @ SV338 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2178]) ).
thf(2405,plain,
! [SV459: nat,SV341: nat,SV177: nat] :
( ( ( ~ ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) ) )
= $false )
| ( ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2180]) ).
thf(2406,plain,
! [SV459: nat,SV341: nat,SV177: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 )
| ~ ( ord_less_nat @ SV341 @ SV459 ) ) )
= $false )
| ( ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2180]) ).
thf(2407,plain,
! [SV459: nat,SV341: nat,SV177: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV341 @ SV459 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 )
| ~ ( ord_less_nat @ SV341 @ SV459 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2181]) ).
thf(2408,plain,
! [SV181: nat > $o,SV345: nat,SV517: nat] :
( ( ( ~ ( ord_less_nat @ SV517 @ ( sK2_SY783 @ SV345 @ SV181 ) ) )
= $true )
| ( ( SV181 @ SV517 )
= $true )
| ( ( SV181 @ SV345 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2183]) ).
thf(2409,plain,
! [SV461: nat,SV182: nat,SV346: nat] :
( ( ( ~ ( ( ( minus_minus_nat @ SV346 @ SV182 )
= SV461 )
| ( SV346
= ( plus_plus_nat @ SV461 @ SV182 ) ) ) )
= $true )
| ( ( ~ ( ( ( minus_minus_nat @ SV346 @ SV182 )
!= SV461 )
| ( SV346
!= ( plus_plus_nat @ SV461 @ SV182 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2184]) ).
thf(2410,plain,
! [SV463: nat,SV184: nat,SV348: nat] :
( ( ( ~ ( ( ord_less_nat @ ( minus_minus_nat @ SV348 @ SV184 ) @ ( minus_minus_nat @ SV463 @ SV184 ) )
| ( ord_less_nat @ SV348 @ SV463 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( minus_minus_nat @ SV348 @ SV184 ) @ ( minus_minus_nat @ SV463 @ SV184 ) )
| ~ ( ord_less_nat @ SV348 @ SV463 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV184 @ SV463 )
= $false )
| ( ( ord_less_eq_nat @ SV184 @ SV348 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2186]) ).
thf(2411,plain,
! [SV185: nat,SV349: nat,SV464: nat] :
( ( ( ord_less_eq_nat @ SV464 @ ( minus_minus_nat @ SV349 @ SV185 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV464 @ ( minus_minus_nat @ SV349 @ SV185 ) )
| ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV464 @ SV185 ) @ SV349 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV185 @ SV349 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2188]) ).
thf(2412,plain,
! [SV349: nat,SV185: nat,SV464: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV464 @ SV185 ) @ SV349 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV464 @ ( minus_minus_nat @ SV349 @ SV185 ) )
| ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV464 @ SV185 ) @ SV349 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV185 @ SV349 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2188]) ).
thf(2413,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) ) )
= $false )
| ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2189]) ).
thf(2414,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) )
= $false )
| ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2189]) ).
thf(2415,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) ) )
= $true )
| ( ( ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) )
= $true )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2190]) ).
thf(2416,plain,
! [SV513: nat,SV190: nat,SV501: nat,SV468: nat,SV354: nat] :
( ( ( ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV354 @ SV468 ) @ SV501 )
= ( plus_plus_nat @ ( times_times_nat @ SV190 @ SV468 ) @ SV513 ) )
| ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV354 @ SV190 ) @ SV468 ) @ SV501 )
= SV513 ) ) )
= $true )
| ( ( ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV354 @ SV468 ) @ SV501 )
!= ( plus_plus_nat @ ( times_times_nat @ SV190 @ SV468 ) @ SV513 ) )
| ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV354 @ SV190 ) @ SV468 ) @ SV501 )
!= SV513 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV190 @ SV354 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2191]) ).
thf(2417,plain,
! [SV502: nat,SV469: nat,SV356: nat,SV192: nat] :
( ( ( SV192 = SV356 )
= $false )
| ( ( ~ ( ord_less_nat @ SV469 @ SV502 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV192 @ SV469 ) @ ( plus_plus_nat @ SV356 @ SV502 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2193]) ).
thf(2418,plain,
! [SV503: nat,SV470: nat,SV357: nat,SV193: nat] :
( ( ( ord_less_eq_nat @ SV193 @ SV357 )
= $false )
| ( ( SV470 != SV503 )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV193 @ SV470 ) @ ( plus_plus_nat @ SV357 @ SV503 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2194]) ).
thf(2419,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2195]) ).
thf(2420,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV194 )
| ( ord_less_eq_nat @ SV358 @ SV471 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2195]) ).
thf(2421,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV194 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV194 )
| ( ord_less_eq_nat @ SV358 @ SV471 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2196]) ).
thf(2422,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV194 )
| ( ord_less_eq_nat @ SV358 @ SV471 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV358 @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2197]) ).
thf(2423,plain,
! [SV504: nat,SV473: nat,SV360: nat,SV196: nat] :
( ( ( SV196 = SV360 )
= $false )
| ( ( SV473 != SV504 )
= $true )
| ( ( ( plus_plus_nat @ SV196 @ SV473 )
= ( plus_plus_nat @ SV360 @ SV504 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2198]) ).
thf(2424,plain,
! [SV514: nat,SV361: nat,SV505: nat,SV474: nat,SV197: nat] :
( ( ( ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV197 @ SV474 ) @ SV505 )
= ( plus_plus_nat @ ( times_times_nat @ SV361 @ SV474 ) @ SV514 ) )
| ( SV505
= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV361 @ SV197 ) @ SV474 ) @ SV514 ) ) ) )
= $true )
| ( ( ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV197 @ SV474 ) @ SV505 )
!= ( plus_plus_nat @ ( times_times_nat @ SV361 @ SV474 ) @ SV514 ) )
| ( SV505
!= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV361 @ SV197 ) @ SV474 ) @ SV514 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV197 @ SV361 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2199]) ).
thf(2425,plain,
! [SV519: nat,SV1: nat > nat] :
( ( ( ( SV1 @ SV519 )
= zero_zero_nat )
= $true )
| ( ( number1551313001itions @ SV1 @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2202]) ).
thf(2426,plain,
! [SV1: nat > nat] :
( ( ( number1551313001itions @ SV1 @ zero_zero_nat )
= $true )
| ( ( ( SV1 @ ( sK5_SV515 @ SV1 ) )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2204]) ).
thf(2427,plain,
! [SV1: nat > nat] :
( ( ( SV1
= ( ^ [I: nat] : zero_zero_nat ) )
= $true )
| ( ( ( SV1 @ ( sK5_SV515 @ SV1 ) )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2205]) ).
thf(2428,plain,
! [SV1: nat > nat] :
( ( ( ! [SV520: nat] :
( ( SV1 @ SV520 )
= zero_zero_nat ) )
= $true )
| ( ( SV1
= ( ^ [I: nat] : zero_zero_nat ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2207]) ).
thf(2429,plain,
! [SV1: nat > nat] :
( ( ( SV1
= ( ^ [I: nat] : zero_zero_nat ) )
= $true )
| ( ( SV1
= ( ^ [I: nat] : zero_zero_nat ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2207]) ).
thf(2430,plain,
! [SV204: nat,SV2: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV2 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV204 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SV204 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2209]) ).
thf(2431,plain,
! [SV204: nat,SV2: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SV204 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2210]) ).
thf(2432,plain,
! [SV204: nat,SV2: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( ord_less_nat @ zero_zero_nat @ SV204 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2211]) ).
thf(2433,plain,
! [SV204: nat,SV2: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ SV2 @ SV204 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV204 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2212]) ).
thf(2434,plain,
! [SV204: nat,SV2: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( ord_less_nat @ zero_zero_nat @ SV204 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV204 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2213]) ).
thf(2435,plain,
! [SV368: nat,SV209: nat,SV7: nat] :
( ( ( ( plus_plus_nat @ SV7 @ SV209 )
= ( plus_plus_nat @ SV368 @ SV209 ) )
= $true )
| ( ( ( plus_plus_nat @ SV7 @ SV209 )
= ( plus_plus_nat @ SV368 @ SV209 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2230]) ).
thf(2436,plain,
! [SV209: nat,SV368: nat,SV7: nat] :
( ( ( SV7 = SV368 )
= $true )
| ( ( ( plus_plus_nat @ SV7 @ SV209 )
= ( plus_plus_nat @ SV368 @ SV209 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2231]) ).
thf(2437,plain,
! [SV368: nat,SV209: nat,SV7: nat] :
( ( ( ( plus_plus_nat @ SV7 @ SV209 )
= ( plus_plus_nat @ SV368 @ SV209 ) )
= $true )
| ( ( SV7 = SV368 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2232]) ).
thf(2438,plain,
! [SV368: nat,SV7: nat] :
( ( ( SV7 = SV368 )
= $true )
| ( ( SV7 = SV368 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2233]) ).
thf(2439,plain,
! [SV369: nat,SV210: nat,SV8: nat] :
( ( ( ( plus_plus_nat @ SV8 @ SV210 )
= ( plus_plus_nat @ SV8 @ SV369 ) )
= $true )
| ( ( ( plus_plus_nat @ SV8 @ SV210 )
= ( plus_plus_nat @ SV8 @ SV369 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2234]) ).
thf(2440,plain,
! [SV8: nat,SV369: nat,SV210: nat] :
( ( ( SV210 = SV369 )
= $true )
| ( ( ( plus_plus_nat @ SV8 @ SV210 )
= ( plus_plus_nat @ SV8 @ SV369 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2235]) ).
thf(2441,plain,
! [SV369: nat,SV210: nat,SV8: nat] :
( ( ( ( plus_plus_nat @ SV8 @ SV210 )
= ( plus_plus_nat @ SV8 @ SV369 ) )
= $true )
| ( ( SV210 = SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2236]) ).
thf(2442,plain,
! [SV369: nat,SV210: nat] :
( ( ( SV210 = SV369 )
= $true )
| ( ( SV210 = SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2237]) ).
thf(2443,plain,
! [SV10: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV10 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2238]) ).
thf(2444,plain,
! [SV370: nat,SV211: nat,SV11: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV11 @ SV211 ) @ ( plus_plus_nat @ SV370 @ SV211 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV11 @ SV211 ) @ ( plus_plus_nat @ SV370 @ SV211 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2241]) ).
thf(2445,plain,
! [SV211: nat,SV370: nat,SV11: nat] :
( ( ( ord_less_eq_nat @ SV11 @ SV370 )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV11 @ SV211 ) @ ( plus_plus_nat @ SV370 @ SV211 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2242]) ).
thf(2446,plain,
! [SV370: nat,SV211: nat,SV11: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV11 @ SV211 ) @ ( plus_plus_nat @ SV370 @ SV211 ) )
= $true )
| ( ( ord_less_eq_nat @ SV11 @ SV370 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2243]) ).
thf(2447,plain,
! [SV370: nat,SV11: nat] :
( ( ( ord_less_eq_nat @ SV11 @ SV370 )
= $true )
| ( ( ord_less_eq_nat @ SV11 @ SV370 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2244]) ).
thf(2448,plain,
! [SV371: nat,SV212: nat,SV12: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV212 ) @ ( plus_plus_nat @ SV12 @ SV371 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV212 ) @ ( plus_plus_nat @ SV12 @ SV371 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2245]) ).
thf(2449,plain,
! [SV12: nat,SV371: nat,SV212: nat] :
( ( ( ord_less_eq_nat @ SV212 @ SV371 )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV212 ) @ ( plus_plus_nat @ SV12 @ SV371 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2246]) ).
thf(2450,plain,
! [SV371: nat,SV212: nat,SV12: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV12 @ SV212 ) @ ( plus_plus_nat @ SV12 @ SV371 ) )
= $true )
| ( ( ord_less_eq_nat @ SV212 @ SV371 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2247]) ).
thf(2451,plain,
! [SV371: nat,SV212: nat] :
( ( ( ord_less_eq_nat @ SV212 @ SV371 )
= $true )
| ( ( ord_less_eq_nat @ SV212 @ SV371 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2248]) ).
thf(2452,plain,
! [SV372: nat,SV217: nat,SV22: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV22 @ SV217 ) @ ( plus_plus_nat @ SV372 @ SV217 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV22 @ SV217 ) @ ( plus_plus_nat @ SV372 @ SV217 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2265]) ).
thf(2453,plain,
! [SV217: nat,SV372: nat,SV22: nat] :
( ( ( ord_less_nat @ SV22 @ SV372 )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV22 @ SV217 ) @ ( plus_plus_nat @ SV372 @ SV217 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2266]) ).
thf(2454,plain,
! [SV372: nat,SV217: nat,SV22: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV22 @ SV217 ) @ ( plus_plus_nat @ SV372 @ SV217 ) )
= $true )
| ( ( ord_less_nat @ SV22 @ SV372 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2267]) ).
thf(2455,plain,
! [SV372: nat,SV22: nat] :
( ( ( ord_less_nat @ SV22 @ SV372 )
= $true )
| ( ( ord_less_nat @ SV22 @ SV372 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2268]) ).
thf(2456,plain,
! [SV373: nat,SV218: nat,SV23: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV23 @ SV218 ) @ ( plus_plus_nat @ SV23 @ SV373 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV23 @ SV218 ) @ ( plus_plus_nat @ SV23 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2269]) ).
thf(2457,plain,
! [SV23: nat,SV373: nat,SV218: nat] :
( ( ( ord_less_nat @ SV218 @ SV373 )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV23 @ SV218 ) @ ( plus_plus_nat @ SV23 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2270]) ).
thf(2458,plain,
! [SV373: nat,SV218: nat,SV23: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV23 @ SV218 ) @ ( plus_plus_nat @ SV23 @ SV373 ) )
= $true )
| ( ( ord_less_nat @ SV218 @ SV373 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2271]) ).
thf(2459,plain,
! [SV373: nat,SV218: nat] :
( ( ( ord_less_nat @ SV218 @ SV373 )
= $true )
| ( ( ord_less_nat @ SV218 @ SV373 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2272]) ).
thf(2460,plain,
! [SV376: nat,SV223: nat,SV32: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV32 @ SV223 ) @ ( plus_plus_nat @ SV32 @ SV376 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV32 @ SV223 ) @ ( plus_plus_nat @ SV32 @ SV376 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2273]) ).
thf(2461,plain,
! [SV32: nat,SV376: nat,SV223: nat] :
( ( ( ord_less_nat @ SV223 @ SV376 )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV32 @ SV223 ) @ ( plus_plus_nat @ SV32 @ SV376 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2274]) ).
thf(2462,plain,
! [SV376: nat,SV223: nat,SV32: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV32 @ SV223 ) @ ( plus_plus_nat @ SV32 @ SV376 ) )
= $true )
| ( ( ord_less_nat @ SV223 @ SV376 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2275]) ).
thf(2463,plain,
! [SV376: nat,SV223: nat] :
( ( ( ord_less_nat @ SV223 @ SV376 )
= $true )
| ( ( ord_less_nat @ SV223 @ SV376 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2276]) ).
thf(2464,plain,
! [SV377: nat,SV224: nat,SV35: nat] :
( ( ( ( times_times_nat @ SV35 @ SV224 )
= ( times_times_nat @ SV377 @ SV224 ) )
= $true )
| ( ( ( times_times_nat @ SV35 @ SV224 )
= ( times_times_nat @ SV377 @ SV224 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2277]) ).
thf(2465,plain,
! [SV224: nat,SV377: nat,SV35: nat] :
( ( ( ( SV35 = SV377 )
| ( SV224 = zero_zero_nat ) )
= $true )
| ( ( ( times_times_nat @ SV35 @ SV224 )
= ( times_times_nat @ SV377 @ SV224 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2278]) ).
thf(2466,plain,
! [SV377: nat,SV224: nat,SV35: nat] :
( ( ( ( times_times_nat @ SV35 @ SV224 )
!= ( times_times_nat @ SV377 @ SV224 ) )
= $false )
| ( ( SV35 = SV377 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2279]) ).
thf(2467,plain,
! [SV224: nat,SV377: nat,SV35: nat] :
( ( ( ~ ( ( SV35 = SV377 )
| ( SV224 = zero_zero_nat ) ) )
= $false )
| ( ( SV35 = SV377 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2279]) ).
thf(2468,plain,
! [SV377: nat,SV224: nat,SV35: nat] :
( ( ( ( times_times_nat @ SV35 @ SV224 )
!= ( times_times_nat @ SV377 @ SV224 ) )
= $false )
| ( ( SV224 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2280]) ).
thf(2469,plain,
! [SV224: nat,SV377: nat,SV35: nat] :
( ( ( ~ ( ( SV35 = SV377 )
| ( SV224 = zero_zero_nat ) ) )
= $false )
| ( ( SV224 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2280]) ).
thf(2470,plain,
! [SV378: nat,SV225: nat,SV36: nat] :
( ( ( ( times_times_nat @ SV36 @ SV225 )
= ( times_times_nat @ SV36 @ SV378 ) )
= $true )
| ( ( ( times_times_nat @ SV36 @ SV225 )
= ( times_times_nat @ SV36 @ SV378 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2281]) ).
thf(2471,plain,
! [SV36: nat,SV378: nat,SV225: nat] :
( ( ( ( SV225 = SV378 )
| ( SV36 = zero_zero_nat ) )
= $true )
| ( ( ( times_times_nat @ SV36 @ SV225 )
= ( times_times_nat @ SV36 @ SV378 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2282]) ).
thf(2472,plain,
! [SV378: nat,SV225: nat,SV36: nat] :
( ( ( ( times_times_nat @ SV36 @ SV225 )
!= ( times_times_nat @ SV36 @ SV378 ) )
= $false )
| ( ( SV225 = SV378 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2283]) ).
thf(2473,plain,
! [SV36: nat,SV378: nat,SV225: nat] :
( ( ( ~ ( ( SV225 = SV378 )
| ( SV36 = zero_zero_nat ) ) )
= $false )
| ( ( SV225 = SV378 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2283]) ).
thf(2474,plain,
! [SV378: nat,SV225: nat,SV36: nat] :
( ( ( ( times_times_nat @ SV36 @ SV225 )
!= ( times_times_nat @ SV36 @ SV378 ) )
= $false )
| ( ( SV36 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2284]) ).
thf(2475,plain,
! [SV36: nat,SV378: nat,SV225: nat] :
( ( ( ~ ( ( SV225 = SV378 )
| ( SV36 = zero_zero_nat ) ) )
= $false )
| ( ( SV36 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2284]) ).
thf(2476,plain,
! [SV226: nat,SV38: nat] :
( ( ( SV38 = zero_zero_nat )
= $true )
| ( ( SV226 = zero_zero_nat )
= $true )
| ( ( ( times_times_nat @ SV38 @ SV226 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2286]) ).
thf(2477,plain,
! [SV226: nat,SV38: nat] :
( ( ( ( times_times_nat @ SV38 @ SV226 )
= zero_zero_nat )
= $true )
| ( ( SV38 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2287]) ).
thf(2478,plain,
! [SV226: nat,SV38: nat] :
( ( ( ( SV38 = zero_zero_nat )
| ( SV226 = zero_zero_nat ) )
= $true )
| ( ( SV38 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2288]) ).
thf(2479,plain,
! [SV226: nat,SV38: nat] :
( ( ( ( times_times_nat @ SV38 @ SV226 )
= zero_zero_nat )
= $true )
| ( ( SV226 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2289]) ).
thf(2480,plain,
! [SV226: nat,SV38: nat] :
( ( ( ( SV38 = zero_zero_nat )
| ( SV226 = zero_zero_nat ) )
= $true )
| ( ( SV226 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2290]) ).
thf(2481,plain,
! [SV379: nat,SV227: nat,SV39: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV39 @ SV227 ) @ ( plus_plus_nat @ SV39 @ SV379 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV39 @ SV227 ) @ ( plus_plus_nat @ SV39 @ SV379 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2291]) ).
thf(2482,plain,
! [SV39: nat,SV379: nat,SV227: nat] :
( ( ( ord_less_eq_nat @ SV227 @ SV379 )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV39 @ SV227 ) @ ( plus_plus_nat @ SV39 @ SV379 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2292]) ).
thf(2483,plain,
! [SV379: nat,SV227: nat,SV39: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV39 @ SV227 ) @ ( plus_plus_nat @ SV39 @ SV379 ) )
= $true )
| ( ( ord_less_eq_nat @ SV227 @ SV379 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2293]) ).
thf(2484,plain,
! [SV379: nat,SV227: nat] :
( ( ( ord_less_eq_nat @ SV227 @ SV379 )
= $true )
| ( ( ord_less_eq_nat @ SV227 @ SV379 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2294]) ).
thf(2485,plain,
! [SV388: nat,SV247: nat,SV60: nat] :
( ( ( ord_less_nat @ SV60 @ ( minus_minus_nat @ SV247 @ SV388 ) )
= $true )
| ( ( ord_less_nat @ SV60 @ ( minus_minus_nat @ SV247 @ SV388 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2319]) ).
thf(2486,plain,
! [SV247: nat,SV388: nat,SV60: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV60 @ SV388 ) @ SV247 )
= $true )
| ( ( ord_less_nat @ SV60 @ ( minus_minus_nat @ SV247 @ SV388 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2320]) ).
thf(2487,plain,
! [SV388: nat,SV247: nat,SV60: nat] :
( ( ( ord_less_nat @ SV60 @ ( minus_minus_nat @ SV247 @ SV388 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV60 @ SV388 ) @ SV247 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2321]) ).
thf(2488,plain,
! [SV247: nat,SV388: nat,SV60: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ SV60 @ SV388 ) @ SV247 )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV60 @ SV388 ) @ SV247 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2322]) ).
thf(2489,plain,
! [SV389: nat,SV248: nat,SV61: nat] :
( ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV61 @ SV248 ) @ SV389 )
= $true )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV61 @ SV248 ) @ SV389 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2323]) ).
thf(2490,plain,
! [SV248: nat,SV389: nat,SV61: nat] :
( ( ( ord_less_eq_nat @ SV61 @ ( plus_plus_nat @ SV389 @ SV248 ) )
= $true )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV61 @ SV248 ) @ SV389 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2324]) ).
thf(2491,plain,
! [SV389: nat,SV248: nat,SV61: nat] :
( ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV61 @ SV248 ) @ SV389 )
= $true )
| ( ( ord_less_eq_nat @ SV61 @ ( plus_plus_nat @ SV389 @ SV248 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2325]) ).
thf(2492,plain,
! [SV248: nat,SV389: nat,SV61: nat] :
( ( ( ord_less_eq_nat @ SV61 @ ( plus_plus_nat @ SV389 @ SV248 ) )
= $true )
| ( ( ord_less_eq_nat @ SV61 @ ( plus_plus_nat @ SV389 @ SV248 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2326]) ).
thf(2493,plain,
! [SV82: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV82 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2327]) ).
thf(2494,plain,
! [SV481: nat,SV258: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV258 @ SV481 ) )
= $false )
| ( ( ord_less_eq_nat @ SV258 @ SV481 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2330]) ).
thf(2495,plain,
! [SV481: nat,SV258: nat] :
( ( ( ~ ( ( ord_less_nat @ SV258 @ SV481 )
| ( SV258 = SV481 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV258 @ SV481 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2330]) ).
thf(2496,plain,
! [SV481: nat,SV258: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV258 @ SV481 )
| ~ ( ( ord_less_nat @ SV258 @ SV481 )
| ( SV258 = SV481 ) ) )
= $false )
| ( ( ord_less_nat @ SV258 @ SV481 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2331]) ).
thf(2497,plain,
! [SV481: nat,SV258: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV258 @ SV481 )
| ~ ( ( ord_less_nat @ SV258 @ SV481 )
| ( SV258 = SV481 ) ) )
= $false )
| ( ( SV258 = SV481 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2332]) ).
thf(2498,plain,
! [SV399: nat,SV261: nat,SV90: nat] :
( ( ( ( times_times_nat @ SV90 @ SV261 )
= ( times_times_nat @ SV90 @ SV399 ) )
= $true )
| ( ( ( times_times_nat @ SV90 @ SV261 )
= ( times_times_nat @ SV90 @ SV399 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2333]) ).
thf(2499,plain,
! [SV399: nat,SV261: nat,SV90: nat] :
( ( ( ( SV90 = zero_zero_nat )
| ( SV261 = SV399 ) )
= $true )
| ( ( ( times_times_nat @ SV90 @ SV261 )
= ( times_times_nat @ SV90 @ SV399 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2334]) ).
thf(2500,plain,
! [SV399: nat,SV261: nat,SV90: nat] :
( ( ( ( times_times_nat @ SV90 @ SV261 )
!= ( times_times_nat @ SV90 @ SV399 ) )
= $false )
| ( ( SV90 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2335]) ).
thf(2501,plain,
! [SV399: nat,SV261: nat,SV90: nat] :
( ( ( ~ ( ( SV90 = zero_zero_nat )
| ( SV261 = SV399 ) ) )
= $false )
| ( ( SV90 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2335]) ).
thf(2502,plain,
! [SV399: nat,SV261: nat,SV90: nat] :
( ( ( ( times_times_nat @ SV90 @ SV261 )
!= ( times_times_nat @ SV90 @ SV399 ) )
= $false )
| ( ( SV261 = SV399 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2336]) ).
thf(2503,plain,
! [SV399: nat,SV261: nat,SV90: nat] :
( ( ( ~ ( ( SV90 = zero_zero_nat )
| ( SV261 = SV399 ) ) )
= $false )
| ( ( SV261 = SV399 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2336]) ).
thf(2504,plain,
! [SV92: nat > nat,SV400: nat,SV262: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV262 @ SV400 ) )
= $true )
| ( ( ord_less_eq_nat @ ( SV92 @ SV262 ) @ ( SV92 @ SV400 ) )
= $true )
| ( ( ord_less_nat @ ( sK3_SY609 @ SV400 @ SV262 @ SV92 ) @ ( sK6_SY1043 @ SV92 @ SV262 @ SV400 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2337]) ).
thf(2505,plain,
! [SV92: nat > nat,SV400: nat,SV262: nat] :
( ( ( ord_less_eq_nat @ SV262 @ SV400 )
= $false )
| ( ( ord_less_eq_nat @ ( SV92 @ SV262 ) @ ( SV92 @ SV400 ) )
= $true )
| ( ( ord_less_nat @ ( SV92 @ ( sK3_SY609 @ SV400 @ SV262 @ SV92 ) ) @ ( SV92 @ ( sK6_SY1043 @ SV92 @ SV262 @ SV400 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2338]) ).
thf(2506,plain,
! [SV264: nat,SV94: nat,SV482: nat,SV401: nat] :
( ( ( ord_less_eq_nat @ SV401 @ SV482 )
= $false )
| ( ( ord_less_eq_nat @ SV94 @ SV264 )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV94 @ SV401 ) @ ( plus_plus_nat @ SV264 @ SV482 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2339]) ).
thf(2507,plain,
! [SV402: nat,SV95: nat,SV265: nat] :
( ( ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV265 @ SV95 ) @ ( minus_minus_nat @ SV265 @ SV402 ) )
| ( ord_less_eq_nat @ SV402 @ SV95 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( minus_minus_nat @ SV265 @ SV95 ) @ ( minus_minus_nat @ SV265 @ SV402 ) )
| ~ ( ord_less_eq_nat @ SV402 @ SV95 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV402 @ SV265 )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2340]) ).
thf(2508,plain,
! [SV268: nat,SV98: nat,SV483: nat,SV404: nat] :
( ( ( ord_less_eq_nat @ SV404 @ SV483 )
= $false )
| ( ( SV98 = SV268 )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV98 @ SV404 ) @ ( plus_plus_nat @ SV268 @ SV483 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2341]) ).
thf(2509,plain,
! [SV507: nat,SV99: nat,SV484: nat,SV405: nat,SV269: nat] :
( ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV269 @ SV405 ) @ SV484 ) @ ( plus_plus_nat @ ( times_times_nat @ SV99 @ SV405 ) @ SV507 ) )
| ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV269 @ SV99 ) @ SV405 ) @ SV484 ) @ SV507 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV269 @ SV405 ) @ SV484 ) @ ( plus_plus_nat @ ( times_times_nat @ SV99 @ SV405 ) @ SV507 ) )
| ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV269 @ SV99 ) @ SV405 ) @ SV484 ) @ SV507 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV99 @ SV269 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2342]) ).
thf(2510,plain,
! [SV102: nat] :
( ( ( SV102 = zero_zero_nat )
= $false )
| ( ( SV102 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2343]) ).
thf(2511,plain,
! [SV278: nat,SV109: nat,SV487: nat,SV412: nat] :
( ( ( ord_less_nat @ SV412 @ SV487 )
= $false )
| ( ( ord_less_nat @ SV109 @ SV278 )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV109 @ SV412 ) @ ( plus_plus_nat @ SV278 @ SV487 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2346]) ).
thf(2512,plain,
! [SV413: nat,SV110: nat,SV279: nat] :
( ( ( ( ( minus_minus_nat @ SV279 @ SV110 )
= ( minus_minus_nat @ SV413 @ SV110 ) )
| ( SV279 = SV413 ) )
= $false )
| ( ( ~ ( ( ( minus_minus_nat @ SV279 @ SV110 )
!= ( minus_minus_nat @ SV413 @ SV110 ) )
| ( SV279 != SV413 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV110 @ SV413 )
= $false )
| ( ( ord_less_eq_nat @ SV110 @ SV279 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2347]) ).
thf(2513,plain,
! [SV113: nat,SV282: nat,SV415: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV415 @ ( minus_minus_nat @ SV282 @ SV113 ) )
| ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV415 @ SV113 ) @ SV282 ) )
= $false )
| ( ( ord_less_eq_nat @ SV415 @ ( minus_minus_nat @ SV282 @ SV113 ) )
= $false )
| ( ( ord_less_eq_nat @ SV113 @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2348]) ).
thf(2514,plain,
! [SV113: nat,SV282: nat,SV415: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV415 @ ( minus_minus_nat @ SV282 @ SV113 ) )
| ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV415 @ SV113 ) @ SV282 ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV415 @ SV113 ) @ SV282 )
= $false )
| ( ( ord_less_eq_nat @ SV113 @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2349]) ).
thf(2515,plain,
! [SV283: nat,SV114: nat > $o] :
( ( ( ~ ( SV114 @ ( sK7_SY655 @ SV283 @ SV114 ) ) )
= $true )
| ( ( SV114 @ SV283 )
= $true )
| ( ( SV114 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2351]) ).
thf(2516,plain,
! [SV114: nat > $o,SV283: nat] :
( ( ( ! [SY1044: nat] :
~ ~ ( ~ ( ord_less_nat @ SY1044 @ ( sK7_SY655 @ SV283 @ SV114 ) )
| ~ ~ ( SV114 @ SY1044 ) ) )
= $true )
| ( ( SV114 @ SV283 )
= $true )
| ( ( SV114 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2352]) ).
thf(2517,plain,
! [SV115: nat] :
( ( ( SV115 = zero_zero_nat )
= $false )
| ( ( SV115 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2353]) ).
thf(2518,plain,
! [SV417: nat,SV285: nat,SV117: nat > $o] :
( ( ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
= $true )
| ( ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2356]) ).
thf(2519,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) )
= $true )
| ( ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2357]) ).
thf(2520,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
= $false )
| ( ( ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) )
= $true )
| ( ( ~ ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2358]) ).
thf(2521,plain,
! [SV488: nat,SV288: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV288 @ SV488 ) )
= $false )
| ( ( ord_less_eq_nat @ SV288 @ SV488 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2359]) ).
thf(2522,plain,
! [SV288: nat,SV488: nat] :
( ( ( ~ ~ ! [SY1033: nat] :
( SV488
!= ( plus_plus_nat @ SV288 @ SY1033 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV288 @ SV488 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2359]) ).
thf(2523,plain,
! [SV521: nat,SV288: nat,SV488: nat] :
( ( ( SV488
!= ( plus_plus_nat @ SV288 @ SV521 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV288 @ SV488 )
| ~ ~ ! [SY1033: nat] :
( SV488
!= ( plus_plus_nat @ SV288 @ SY1033 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2360]) ).
thf(2524,plain,
! [SV489: nat,SV289: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV289 @ SV489 ) )
= $false )
| ( ( ord_less_eq_nat @ SV289 @ SV489 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2361]) ).
thf(2525,plain,
! [SV289: nat,SV489: nat] :
( ( ( ~ ~ ! [SY1034: nat] :
( SV489
!= ( plus_plus_nat @ SV289 @ SY1034 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV289 @ SV489 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2361]) ).
thf(2526,plain,
! [SV522: nat,SV289: nat,SV489: nat] :
( ( ( SV489
!= ( plus_plus_nat @ SV289 @ SV522 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV289 @ SV489 )
| ~ ~ ! [SY1034: nat] :
( SV489
!= ( plus_plus_nat @ SV289 @ SY1034 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2362]) ).
thf(2527,plain,
! [SV421: nat,SV122: nat,SV290: nat] :
( ( ( ( ( minus_minus_nat @ SV290 @ SV122 )
!= SV421 )
| ( SV290
!= ( plus_plus_nat @ SV421 @ SV122 ) ) )
= $false )
| ( ( ( minus_minus_nat @ SV290 @ SV122 )
= SV421 )
= $false )
| ( ( ord_less_eq_nat @ SV122 @ SV290 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2363]) ).
thf(2528,plain,
! [SV421: nat,SV122: nat,SV290: nat] :
( ( ( ( ( minus_minus_nat @ SV290 @ SV122 )
!= SV421 )
| ( SV290
!= ( plus_plus_nat @ SV421 @ SV122 ) ) )
= $false )
| ( ( SV290
= ( plus_plus_nat @ SV421 @ SV122 ) )
= $false )
| ( ( ord_less_eq_nat @ SV122 @ SV290 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2364]) ).
thf(2529,plain,
! [SV294: nat,SV126: nat] :
( ( ( ( SV126 != zero_zero_nat )
| ( SV294 != zero_zero_nat ) )
= $false )
| ( ( ( plus_plus_nat @ SV126 @ SV294 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2366]) ).
thf(2530,plain,
! [SV126: nat,SV294: nat] :
( ( ( SV294 = zero_zero_nat )
= $false )
| ( ( SV126 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ SV126 @ SV294 )
!= zero_zero_nat )
| ~ ~ ( ( SV126 != zero_zero_nat )
| ( SV294 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2367]) ).
thf(2531,plain,
! [SV510: nat,SV295: nat,SV491: nat,SV425: nat,SV127: nat] :
( ( ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV127 @ SV425 ) @ SV491 ) @ ( plus_plus_nat @ ( times_times_nat @ SV295 @ SV425 ) @ SV510 ) )
| ( ord_less_nat @ SV491 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV295 @ SV127 ) @ SV425 ) @ SV510 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV127 @ SV425 ) @ SV491 ) @ ( plus_plus_nat @ ( times_times_nat @ SV295 @ SV425 ) @ SV510 ) )
| ~ ( ord_less_nat @ SV491 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV295 @ SV127 ) @ SV425 ) @ SV510 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV127 @ SV295 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2368]) ).
thf(2532,plain,
! [SV134: nat] :
( ( ( SV134 = zero_zero_nat )
= $false )
| ( ( SV134 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2371]) ).
thf(2533,plain,
! [SV142: nat > $o,SV309: nat,SV516: nat] :
( ( ( ~ ( ord_less_nat @ SV516 @ ( sK1_SY712 @ SV309 @ SV142 ) )
| ~ ~ ( SV142 @ SV516 ) )
= $true )
| ( ( SV142 @ SV309 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2372]) ).
thf(2534,plain,
! [SV511: nat,SV313: nat,SV494: nat,SV440: nat,SV146: nat] :
( ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV146 @ SV440 ) @ SV494 ) @ ( plus_plus_nat @ ( times_times_nat @ SV313 @ SV440 ) @ SV511 ) )
| ( ord_less_eq_nat @ SV494 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV313 @ SV146 ) @ SV440 ) @ SV511 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV146 @ SV440 ) @ SV494 ) @ ( plus_plus_nat @ ( times_times_nat @ SV313 @ SV440 ) @ SV511 ) )
| ~ ( ord_less_eq_nat @ SV494 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV313 @ SV146 ) @ SV440 ) @ SV511 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV146 @ SV313 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2373]) ).
thf(2535,plain,
! [SV315: nat,SV148: nat,SV495: nat,SV442: nat] :
( ( ( SV442 = SV495 )
= $false )
| ( ( ord_less_nat @ SV148 @ SV315 )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV148 @ SV442 ) @ ( plus_plus_nat @ SV315 @ SV495 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2374]) ).
thf(2536,plain,
! [SV444: nat,SV318: nat,SV152: nat] :
( ( ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
= $true )
| ( ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2375]) ).
thf(2537,plain,
! [SV444: nat,SV152: nat,SV318: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV318 )
| ~ ( ord_less_nat @ SV152 @ SV444 ) ) )
= $true )
| ( ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2376]) ).
thf(2538,plain,
! [SV444: nat,SV152: nat,SV318: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV318 )
= $false )
| ( ( ~ ( ord_less_nat @ SV152 @ SV444 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV318 )
| ~ ( ord_less_nat @ SV152 @ SV444 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2377]) ).
thf(2539,plain,
! [SV321: nat,SV155: nat] :
( ( ( SV155 != SV321 )
= $true )
| ( ( SV155 = SV321 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2378]) ).
thf(2540,plain,
! [SV321: nat,SV155: nat] :
( ( ( ( ord_less_nat @ SV155 @ SV321 )
| ( ord_less_nat @ SV321 @ SV155 ) )
= $true )
| ( ( SV155 = SV321 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2379]) ).
thf(2541,plain,
! [SV321: nat,SV155: nat] :
( ( ( SV155 != SV321 )
= $true )
| ( ( ord_less_nat @ SV155 @ SV321 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2380]) ).
thf(2542,plain,
! [SV321: nat,SV155: nat] :
( ( ( ( ord_less_nat @ SV155 @ SV321 )
| ( ord_less_nat @ SV321 @ SV155 ) )
= $true )
| ( ( ord_less_nat @ SV155 @ SV321 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2381]) ).
thf(2543,plain,
! [SV321: nat,SV155: nat] :
( ( ( SV155 != SV321 )
= $true )
| ( ( ord_less_nat @ SV321 @ SV155 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2382]) ).
thf(2544,plain,
! [SV321: nat,SV155: nat] :
( ( ( ( ord_less_nat @ SV155 @ SV321 )
| ( ord_less_nat @ SV321 @ SV155 ) )
= $true )
| ( ( ord_less_nat @ SV321 @ SV155 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2383]) ).
thf(2545,plain,
! [SV325: nat,SV159: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV159 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV325 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2385]) ).
thf(2546,plain,
! [SV159: nat,SV325: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV325 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV159 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV159 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV325 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2386]) ).
thf(2547,plain,
! [SV326: nat,SV160: nat] :
( ( ( ( SV160 != zero_zero_nat )
| ( SV326 != zero_zero_nat ) )
= $false )
| ( ( ( plus_plus_nat @ SV160 @ SV326 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2388]) ).
thf(2548,plain,
! [SV160: nat,SV326: nat] :
( ( ( SV326 = zero_zero_nat )
= $false )
| ( ( SV160 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ SV160 @ SV326 )
!= zero_zero_nat )
| ~ ~ ( ( SV160 != zero_zero_nat )
| ( SV326 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2389]) ).
thf(2549,plain,
! [SV497: nat,SV327: nat] :
( ( ( ~ ( ord_less_nat @ SV327 @ SV497 ) )
= $false )
| ( ( ord_less_nat @ SV327 @ SV497 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2390]) ).
thf(2550,plain,
! [SV497: nat,SV327: nat] :
( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV327 @ SV497 )
| ~ ( ( SV327 != SV497 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV327 @ SV497 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2390]) ).
thf(2551,plain,
! [SV497: nat,SV327: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV327 @ SV497 ) )
= $true )
| ( ( ~ ( ( SV327 != SV497 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV327 @ SV497 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV327 @ SV497 )
| ~ ( ( SV327 != SV497 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2391]) ).
thf(2552,plain,
! [SV328: nat,SV162: nat] :
( ( ( ( SV162 != zero_zero_nat )
| ( SV328 != zero_zero_nat ) )
= $false )
| ( ( zero_zero_nat
= ( plus_plus_nat @ SV162 @ SV328 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2393]) ).
thf(2553,plain,
! [SV162: nat,SV328: nat] :
( ( ( SV328 = zero_zero_nat )
= $false )
| ( ( SV162 = zero_zero_nat )
= $false )
| ( ( ~ ( ( zero_zero_nat
!= ( plus_plus_nat @ SV162 @ SV328 ) )
| ~ ~ ( ( SV162 != zero_zero_nat )
| ( SV328 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2394]) ).
thf(2554,plain,
! [SV448: nat,SV329: nat,SV163: nat] :
( ( ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2395]) ).
thf(2555,plain,
! [SV448: nat,SV163: nat,SV329: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV329 )
| ( ord_less_eq_nat @ SV163 @ SV448 ) )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2396]) ).
thf(2556,plain,
! [SV448: nat,SV329: nat,SV163: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV329 )
| ( ord_less_eq_nat @ SV163 @ SV448 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV329 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2397]) ).
thf(2557,plain,
! [SV448: nat,SV329: nat,SV163: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV163 @ SV448 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2398]) ).
thf(2558,plain,
! [SV448: nat,SV163: nat,SV329: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV329 )
| ( ord_less_eq_nat @ SV163 @ SV448 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV163 @ SV448 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2398]) ).
thf(2559,plain,
! [SV449: nat,SV330: nat,SV164: nat > $o] :
( ( ( SV164 @ ( sK8_SY1015 @ SV330 @ SV449 @ SV164 ) )
= $true )
| ( ( ~ ! [SY751: nat] :
~ ~ ( ~ ( SV164 @ SY751 )
| ~ ! [SY752: nat] :
( ~ ( SV164 @ SY752 )
| ( ord_less_eq_nat @ SY752 @ SY751 ) ) ) )
= $true )
| ( ( SV164 @ SV330 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2399]) ).
thf(2560,plain,
! [SV449: nat,SV330: nat,SV164: nat > $o] :
( ( ( ! [SY751: nat] :
~ ~ ( ~ ( SV164 @ SY751 )
| ~ ! [SY752: nat] :
( ~ ( SV164 @ SY752 )
| ( ord_less_eq_nat @ SY752 @ SY751 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK8_SY1015 @ SV330 @ SV449 @ SV164 ) @ SV449 )
= $false )
| ( ( SV164 @ SV330 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2400]) ).
thf(2561,plain,
! [SV451: nat,SV167: nat,SV332: nat] :
( ( ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV332 @ SV167 ) @ ( minus_minus_nat @ SV451 @ SV167 ) )
| ( ord_less_eq_nat @ SV332 @ SV451 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( minus_minus_nat @ SV332 @ SV167 ) @ ( minus_minus_nat @ SV451 @ SV167 ) )
| ~ ( ord_less_eq_nat @ SV332 @ SV451 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV167 @ SV451 )
= $false )
| ( ( ord_less_eq_nat @ SV167 @ SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2401]) ).
thf(2562,plain,
! [SV453: nat,SV169: nat,SV334: nat] :
( ( ( ~ ( ord_less_nat @ ( minus_minus_nat @ SV334 @ SV169 ) @ SV453 )
| ~ ( ord_less_nat @ SV334 @ ( plus_plus_nat @ SV453 @ SV169 ) ) )
= $false )
| ( ( ord_less_nat @ ( minus_minus_nat @ SV334 @ SV169 ) @ SV453 )
= $false )
| ( ( ord_less_eq_nat @ SV169 @ SV334 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2402]) ).
thf(2563,plain,
! [SV453: nat,SV169: nat,SV334: nat] :
( ( ( ~ ( ord_less_nat @ ( minus_minus_nat @ SV334 @ SV169 ) @ SV453 )
| ~ ( ord_less_nat @ SV334 @ ( plus_plus_nat @ SV453 @ SV169 ) ) )
= $false )
| ( ( ord_less_nat @ SV334 @ ( plus_plus_nat @ SV453 @ SV169 ) )
= $false )
| ( ( ord_less_eq_nat @ SV169 @ SV334 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2403]) ).
thf(2564,plain,
! [SV512: nat,SV174: nat,SV499: nat,SV457: nat,SV338: nat] :
( ( ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV338 @ SV457 ) @ SV499 ) @ ( plus_plus_nat @ ( times_times_nat @ SV174 @ SV457 ) @ SV512 ) )
| ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV338 @ SV174 ) @ SV457 ) @ SV499 ) @ SV512 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV338 @ SV457 ) @ SV499 ) @ ( plus_plus_nat @ ( times_times_nat @ SV174 @ SV457 ) @ SV512 ) )
| ~ ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV338 @ SV174 ) @ SV457 ) @ SV499 ) @ SV512 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV174 @ SV338 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2404]) ).
thf(2565,plain,
! [SV459: nat,SV341: nat,SV177: nat] :
( ( ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
= $true )
| ( ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2405]) ).
thf(2566,plain,
! [SV459: nat,SV341: nat,SV177: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 )
| ~ ( ord_less_nat @ SV341 @ SV459 ) ) )
= $true )
| ( ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2406]) ).
thf(2567,plain,
! [SV459: nat,SV341: nat,SV177: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV177 )
= $false )
| ( ( ~ ( ord_less_nat @ SV341 @ SV459 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 )
| ~ ( ord_less_nat @ SV341 @ SV459 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2407]) ).
thf(2568,plain,
! [SV181: nat > $o,SV345: nat,SV517: nat] :
( ( ( ord_less_nat @ SV517 @ ( sK2_SY783 @ SV345 @ SV181 ) )
= $false )
| ( ( SV181 @ SV517 )
= $true )
| ( ( SV181 @ SV345 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2408]) ).
thf(2569,plain,
! [SV461: nat,SV182: nat,SV346: nat] :
( ( ( ( ( minus_minus_nat @ SV346 @ SV182 )
= SV461 )
| ( SV346
= ( plus_plus_nat @ SV461 @ SV182 ) ) )
= $false )
| ( ( ~ ( ( ( minus_minus_nat @ SV346 @ SV182 )
!= SV461 )
| ( SV346
!= ( plus_plus_nat @ SV461 @ SV182 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2409]) ).
thf(2570,plain,
! [SV463: nat,SV184: nat,SV348: nat] :
( ( ( ( ord_less_nat @ ( minus_minus_nat @ SV348 @ SV184 ) @ ( minus_minus_nat @ SV463 @ SV184 ) )
| ( ord_less_nat @ SV348 @ SV463 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( minus_minus_nat @ SV348 @ SV184 ) @ ( minus_minus_nat @ SV463 @ SV184 ) )
| ~ ( ord_less_nat @ SV348 @ SV463 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV184 @ SV463 )
= $false )
| ( ( ord_less_eq_nat @ SV184 @ SV348 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2410]) ).
thf(2571,plain,
! [SV185: nat,SV349: nat,SV464: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV464 @ ( minus_minus_nat @ SV349 @ SV185 ) )
| ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV464 @ SV185 ) @ SV349 ) )
= $false )
| ( ( ord_less_eq_nat @ SV464 @ ( minus_minus_nat @ SV349 @ SV185 ) )
= $false )
| ( ( ord_less_eq_nat @ SV185 @ SV349 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2411]) ).
thf(2572,plain,
! [SV185: nat,SV349: nat,SV464: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV464 @ ( minus_minus_nat @ SV349 @ SV185 ) )
| ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV464 @ SV185 ) @ SV349 ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV464 @ SV185 ) @ SV349 )
= $false )
| ( ( ord_less_eq_nat @ SV185 @ SV349 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2412]) ).
thf(2573,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= $true )
| ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2413]) ).
thf(2574,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) )
= $true )
| ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2414]) ).
thf(2575,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
= $false )
| ( ( ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) )
= $true )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2415]) ).
thf(2576,plain,
! [SV513: nat,SV190: nat,SV501: nat,SV468: nat,SV354: nat] :
( ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV354 @ SV468 ) @ SV501 )
= ( plus_plus_nat @ ( times_times_nat @ SV190 @ SV468 ) @ SV513 ) )
| ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV354 @ SV190 ) @ SV468 ) @ SV501 )
= SV513 ) )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV354 @ SV468 ) @ SV501 )
!= ( plus_plus_nat @ ( times_times_nat @ SV190 @ SV468 ) @ SV513 ) )
| ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV354 @ SV190 ) @ SV468 ) @ SV501 )
!= SV513 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV190 @ SV354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2416]) ).
thf(2577,plain,
! [SV356: nat,SV192: nat,SV502: nat,SV469: nat] :
( ( ( ord_less_nat @ SV469 @ SV502 )
= $false )
| ( ( SV192 = SV356 )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ SV192 @ SV469 ) @ ( plus_plus_nat @ SV356 @ SV502 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2417]) ).
thf(2578,plain,
! [SV357: nat,SV193: nat,SV503: nat,SV470: nat] :
( ( ( SV470 = SV503 )
= $false )
| ( ( ord_less_eq_nat @ SV193 @ SV357 )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV193 @ SV470 ) @ ( plus_plus_nat @ SV357 @ SV503 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2418]) ).
thf(2579,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2419]) ).
thf(2580,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV194 )
| ( ord_less_eq_nat @ SV358 @ SV471 ) )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2420]) ).
thf(2581,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV194 )
| ( ord_less_eq_nat @ SV358 @ SV471 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV194 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2421]) ).
thf(2582,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV358 @ SV471 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2422]) ).
thf(2583,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV194 )
| ( ord_less_eq_nat @ SV358 @ SV471 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV358 @ SV471 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2422]) ).
thf(2584,plain,
! [SV360: nat,SV196: nat,SV504: nat,SV473: nat] :
( ( ( SV473 = SV504 )
= $false )
| ( ( SV196 = SV360 )
= $false )
| ( ( ( plus_plus_nat @ SV196 @ SV473 )
= ( plus_plus_nat @ SV360 @ SV504 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2423]) ).
thf(2585,plain,
! [SV514: nat,SV361: nat,SV505: nat,SV474: nat,SV197: nat] :
( ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV197 @ SV474 ) @ SV505 )
= ( plus_plus_nat @ ( times_times_nat @ SV361 @ SV474 ) @ SV514 ) )
| ( SV505
= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV361 @ SV197 ) @ SV474 ) @ SV514 ) ) )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV197 @ SV474 ) @ SV505 )
!= ( plus_plus_nat @ ( times_times_nat @ SV361 @ SV474 ) @ SV514 ) )
| ( SV505
!= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV361 @ SV197 ) @ SV474 ) @ SV514 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV197 @ SV361 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2424]) ).
thf(2586,plain,
! [SV1: nat > nat] :
( ( ( ! [SV523: nat] :
( ( SV1 @ SV523 )
= zero_zero_nat ) )
= $true )
| ( ( ( SV1 @ ( sK5_SV515 @ SV1 ) )
= zero_zero_nat )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2427]) ).
thf(2587,plain,
! [SV1: nat > nat] :
( ( ( SV1
= ( ^ [I: nat] : zero_zero_nat ) )
= $true )
| ( ( ( SV1 @ ( sK5_SV515 @ SV1 ) )
= zero_zero_nat )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2427]) ).
thf(2588,plain,
! [SV524: nat,SV1: nat > nat] :
( ( ( ( SV1 @ SV524 )
= zero_zero_nat )
= $true )
| ( ( SV1
= ( ^ [I: nat] : zero_zero_nat ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2428]) ).
thf(2589,plain,
! [SV204: nat,SV2: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV2 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV204 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2432]) ).
thf(2590,plain,
! [SV204: nat,SV2: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV2 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV204 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2434]) ).
thf(2591,plain,
! [SV224: nat,SV377: nat,SV35: nat] :
( ( ( SV35 = SV377 )
= $true )
| ( ( SV224 = zero_zero_nat )
= $true )
| ( ( ( times_times_nat @ SV35 @ SV224 )
= ( times_times_nat @ SV377 @ SV224 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2465]) ).
thf(2592,plain,
! [SV377: nat,SV224: nat,SV35: nat] :
( ( ( ( times_times_nat @ SV35 @ SV224 )
= ( times_times_nat @ SV377 @ SV224 ) )
= $true )
| ( ( SV35 = SV377 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2466]) ).
thf(2593,plain,
! [SV224: nat,SV377: nat,SV35: nat] :
( ( ( ( SV35 = SV377 )
| ( SV224 = zero_zero_nat ) )
= $true )
| ( ( SV35 = SV377 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2467]) ).
thf(2594,plain,
! [SV377: nat,SV224: nat,SV35: nat] :
( ( ( ( times_times_nat @ SV35 @ SV224 )
= ( times_times_nat @ SV377 @ SV224 ) )
= $true )
| ( ( SV224 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2468]) ).
thf(2595,plain,
! [SV224: nat,SV377: nat,SV35: nat] :
( ( ( ( SV35 = SV377 )
| ( SV224 = zero_zero_nat ) )
= $true )
| ( ( SV224 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2469]) ).
thf(2596,plain,
! [SV36: nat,SV378: nat,SV225: nat] :
( ( ( SV225 = SV378 )
= $true )
| ( ( SV36 = zero_zero_nat )
= $true )
| ( ( ( times_times_nat @ SV36 @ SV225 )
= ( times_times_nat @ SV36 @ SV378 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2471]) ).
thf(2597,plain,
! [SV378: nat,SV225: nat,SV36: nat] :
( ( ( ( times_times_nat @ SV36 @ SV225 )
= ( times_times_nat @ SV36 @ SV378 ) )
= $true )
| ( ( SV225 = SV378 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2472]) ).
thf(2598,plain,
! [SV36: nat,SV378: nat,SV225: nat] :
( ( ( ( SV225 = SV378 )
| ( SV36 = zero_zero_nat ) )
= $true )
| ( ( SV225 = SV378 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2473]) ).
thf(2599,plain,
! [SV378: nat,SV225: nat,SV36: nat] :
( ( ( ( times_times_nat @ SV36 @ SV225 )
= ( times_times_nat @ SV36 @ SV378 ) )
= $true )
| ( ( SV36 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2474]) ).
thf(2600,plain,
! [SV36: nat,SV378: nat,SV225: nat] :
( ( ( ( SV225 = SV378 )
| ( SV36 = zero_zero_nat ) )
= $true )
| ( ( SV36 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2475]) ).
thf(2601,plain,
! [SV226: nat,SV38: nat] :
( ( ( SV38 = zero_zero_nat )
= $true )
| ( ( SV226 = zero_zero_nat )
= $true )
| ( ( SV38 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2478]) ).
thf(2602,plain,
! [SV226: nat,SV38: nat] :
( ( ( SV38 = zero_zero_nat )
= $true )
| ( ( SV226 = zero_zero_nat )
= $true )
| ( ( SV226 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2480]) ).
thf(2603,plain,
! [SV481: nat,SV258: nat] :
( ( ( ord_less_eq_nat @ SV258 @ SV481 )
= $true )
| ( ( ord_less_eq_nat @ SV258 @ SV481 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2494]) ).
thf(2604,plain,
! [SV481: nat,SV258: nat] :
( ( ( ( ord_less_nat @ SV258 @ SV481 )
| ( SV258 = SV481 ) )
= $true )
| ( ( ord_less_eq_nat @ SV258 @ SV481 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2495]) ).
thf(2605,plain,
! [SV481: nat,SV258: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV258 @ SV481 ) )
= $false )
| ( ( ord_less_nat @ SV258 @ SV481 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2496]) ).
thf(2606,plain,
! [SV481: nat,SV258: nat] :
( ( ( ~ ( ( ord_less_nat @ SV258 @ SV481 )
| ( SV258 = SV481 ) ) )
= $false )
| ( ( ord_less_nat @ SV258 @ SV481 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2496]) ).
thf(2607,plain,
! [SV481: nat,SV258: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV258 @ SV481 ) )
= $false )
| ( ( SV258 = SV481 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2497]) ).
thf(2608,plain,
! [SV481: nat,SV258: nat] :
( ( ( ~ ( ( ord_less_nat @ SV258 @ SV481 )
| ( SV258 = SV481 ) ) )
= $false )
| ( ( SV258 = SV481 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2497]) ).
thf(2609,plain,
! [SV399: nat,SV261: nat,SV90: nat] :
( ( ( SV90 = zero_zero_nat )
= $true )
| ( ( SV261 = SV399 )
= $true )
| ( ( ( times_times_nat @ SV90 @ SV261 )
= ( times_times_nat @ SV90 @ SV399 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2499]) ).
thf(2610,plain,
! [SV399: nat,SV261: nat,SV90: nat] :
( ( ( ( times_times_nat @ SV90 @ SV261 )
= ( times_times_nat @ SV90 @ SV399 ) )
= $true )
| ( ( SV90 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2500]) ).
thf(2611,plain,
! [SV399: nat,SV261: nat,SV90: nat] :
( ( ( ( SV90 = zero_zero_nat )
| ( SV261 = SV399 ) )
= $true )
| ( ( SV90 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2501]) ).
thf(2612,plain,
! [SV399: nat,SV261: nat,SV90: nat] :
( ( ( ( times_times_nat @ SV90 @ SV261 )
= ( times_times_nat @ SV90 @ SV399 ) )
= $true )
| ( ( SV261 = SV399 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2502]) ).
thf(2613,plain,
! [SV399: nat,SV261: nat,SV90: nat] :
( ( ( ( SV90 = zero_zero_nat )
| ( SV261 = SV399 ) )
= $true )
| ( ( SV261 = SV399 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2503]) ).
thf(2614,plain,
! [SV92: nat > nat,SV400: nat,SV262: nat] :
( ( ( ord_less_eq_nat @ SV262 @ SV400 )
= $false )
| ( ( ord_less_eq_nat @ ( SV92 @ SV262 ) @ ( SV92 @ SV400 ) )
= $true )
| ( ( ord_less_nat @ ( sK3_SY609 @ SV400 @ SV262 @ SV92 ) @ ( sK6_SY1043 @ SV92 @ SV262 @ SV400 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2504]) ).
thf(2615,plain,
! [SV402: nat,SV95: nat,SV265: nat] :
( ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV265 @ SV95 ) @ ( minus_minus_nat @ SV265 @ SV402 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( minus_minus_nat @ SV265 @ SV95 ) @ ( minus_minus_nat @ SV265 @ SV402 ) )
| ~ ( ord_less_eq_nat @ SV402 @ SV95 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV402 @ SV265 )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2507]) ).
thf(2616,plain,
! [SV265: nat,SV95: nat,SV402: nat] :
( ( ( ord_less_eq_nat @ SV402 @ SV95 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( minus_minus_nat @ SV265 @ SV95 ) @ ( minus_minus_nat @ SV265 @ SV402 ) )
| ~ ( ord_less_eq_nat @ SV402 @ SV95 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV402 @ SV265 )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2507]) ).
thf(2617,plain,
! [SV507: nat,SV99: nat,SV484: nat,SV405: nat,SV269: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV269 @ SV405 ) @ SV484 ) @ ( plus_plus_nat @ ( times_times_nat @ SV99 @ SV405 ) @ SV507 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV269 @ SV405 ) @ SV484 ) @ ( plus_plus_nat @ ( times_times_nat @ SV99 @ SV405 ) @ SV507 ) )
| ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV269 @ SV99 ) @ SV405 ) @ SV484 ) @ SV507 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV99 @ SV269 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2509]) ).
thf(2618,plain,
! [SV507: nat,SV484: nat,SV405: nat,SV99: nat,SV269: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV269 @ SV99 ) @ SV405 ) @ SV484 ) @ SV507 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV269 @ SV405 ) @ SV484 ) @ ( plus_plus_nat @ ( times_times_nat @ SV99 @ SV405 ) @ SV507 ) )
| ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV269 @ SV99 ) @ SV405 ) @ SV484 ) @ SV507 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV99 @ SV269 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2509]) ).
thf(2619,plain,
! [SV413: nat,SV110: nat,SV279: nat] :
( ( ( ( minus_minus_nat @ SV279 @ SV110 )
= ( minus_minus_nat @ SV413 @ SV110 ) )
= $false )
| ( ( ~ ( ( ( minus_minus_nat @ SV279 @ SV110 )
!= ( minus_minus_nat @ SV413 @ SV110 ) )
| ( SV279 != SV413 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV110 @ SV413 )
= $false )
| ( ( ord_less_eq_nat @ SV110 @ SV279 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2512]) ).
thf(2620,plain,
! [SV110: nat,SV413: nat,SV279: nat] :
( ( ( SV279 = SV413 )
= $false )
| ( ( ~ ( ( ( minus_minus_nat @ SV279 @ SV110 )
!= ( minus_minus_nat @ SV413 @ SV110 ) )
| ( SV279 != SV413 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV110 @ SV413 )
= $false )
| ( ( ord_less_eq_nat @ SV110 @ SV279 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2512]) ).
thf(2621,plain,
! [SV113: nat,SV282: nat,SV415: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV415 @ ( minus_minus_nat @ SV282 @ SV113 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV415 @ ( minus_minus_nat @ SV282 @ SV113 ) )
= $false )
| ( ( ord_less_eq_nat @ SV113 @ SV282 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2513]) ).
thf(2622,plain,
! [SV282: nat,SV113: nat,SV415: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV415 @ SV113 ) @ SV282 ) )
= $false )
| ( ( ord_less_eq_nat @ SV415 @ ( minus_minus_nat @ SV282 @ SV113 ) )
= $false )
| ( ( ord_less_eq_nat @ SV113 @ SV282 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2513]) ).
thf(2623,plain,
! [SV113: nat,SV282: nat,SV415: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV415 @ ( minus_minus_nat @ SV282 @ SV113 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV415 @ SV113 ) @ SV282 )
= $false )
| ( ( ord_less_eq_nat @ SV113 @ SV282 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2514]) ).
thf(2624,plain,
! [SV282: nat,SV113: nat,SV415: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV415 @ SV113 ) @ SV282 ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV415 @ SV113 ) @ SV282 )
= $false )
| ( ( ord_less_eq_nat @ SV113 @ SV282 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2514]) ).
thf(2625,plain,
! [SV283: nat,SV114: nat > $o] :
( ( ( SV114 @ ( sK7_SY655 @ SV283 @ SV114 ) )
= $false )
| ( ( SV114 @ SV283 )
= $true )
| ( ( SV114 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2515]) ).
thf(2626,plain,
! [SV114: nat > $o,SV283: nat,SV525: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ SV525 @ ( sK7_SY655 @ SV283 @ SV114 ) )
| ~ ~ ( SV114 @ SV525 ) ) )
= $true )
| ( ( SV114 @ SV283 )
= $true )
| ( ( SV114 @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2516]) ).
thf(2627,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) )
= $false )
| ( ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2519]) ).
thf(2628,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ord_less_nat @ SV285 @ SV417 ) )
= $false )
| ( ( ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) )
= $true )
| ( ( ~ ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2520]) ).
thf(2629,plain,
! [SV417: nat,SV285: nat,SV117: nat > $o] :
( ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) )
= $true )
| ( ( ~ ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2520]) ).
thf(2630,plain,
! [SV488: nat,SV288: nat] :
( ( ( ord_less_eq_nat @ SV288 @ SV488 )
= $true )
| ( ( ord_less_eq_nat @ SV288 @ SV488 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2521]) ).
thf(2631,plain,
! [SV288: nat,SV488: nat] :
( ( ( ~ ! [SY1033: nat] :
( SV488
!= ( plus_plus_nat @ SV288 @ SY1033 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV288 @ SV488 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2522]) ).
thf(2632,plain,
! [SV521: nat,SV288: nat,SV488: nat] :
( ( ( SV488
= ( plus_plus_nat @ SV288 @ SV521 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV288 @ SV488 )
| ~ ~ ! [SY1033: nat] :
( SV488
!= ( plus_plus_nat @ SV288 @ SY1033 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2523]) ).
thf(2633,plain,
! [SV489: nat,SV289: nat] :
( ( ( ord_less_eq_nat @ SV289 @ SV489 )
= $true )
| ( ( ord_less_eq_nat @ SV289 @ SV489 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2524]) ).
thf(2634,plain,
! [SV289: nat,SV489: nat] :
( ( ( ~ ! [SY1034: nat] :
( SV489
!= ( plus_plus_nat @ SV289 @ SY1034 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV289 @ SV489 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2525]) ).
thf(2635,plain,
! [SV522: nat,SV289: nat,SV489: nat] :
( ( ( SV489
= ( plus_plus_nat @ SV289 @ SV522 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV289 @ SV489 )
| ~ ~ ! [SY1034: nat] :
( SV489
!= ( plus_plus_nat @ SV289 @ SY1034 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2526]) ).
thf(2636,plain,
! [SV421: nat,SV122: nat,SV290: nat] :
( ( ( ( minus_minus_nat @ SV290 @ SV122 )
!= SV421 )
= $false )
| ( ( ( minus_minus_nat @ SV290 @ SV122 )
= SV421 )
= $false )
| ( ( ord_less_eq_nat @ SV122 @ SV290 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2527]) ).
thf(2637,plain,
! [SV122: nat,SV421: nat,SV290: nat] :
( ( ( SV290
!= ( plus_plus_nat @ SV421 @ SV122 ) )
= $false )
| ( ( ( minus_minus_nat @ SV290 @ SV122 )
= SV421 )
= $false )
| ( ( ord_less_eq_nat @ SV122 @ SV290 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2527]) ).
thf(2638,plain,
! [SV421: nat,SV122: nat,SV290: nat] :
( ( ( ( minus_minus_nat @ SV290 @ SV122 )
!= SV421 )
= $false )
| ( ( SV290
= ( plus_plus_nat @ SV421 @ SV122 ) )
= $false )
| ( ( ord_less_eq_nat @ SV122 @ SV290 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2528]) ).
thf(2639,plain,
! [SV122: nat,SV421: nat,SV290: nat] :
( ( ( SV290
!= ( plus_plus_nat @ SV421 @ SV122 ) )
= $false )
| ( ( SV290
= ( plus_plus_nat @ SV421 @ SV122 ) )
= $false )
| ( ( ord_less_eq_nat @ SV122 @ SV290 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2528]) ).
thf(2640,plain,
! [SV294: nat,SV126: nat] :
( ( ( SV126 != zero_zero_nat )
= $false )
| ( ( ( plus_plus_nat @ SV126 @ SV294 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2529]) ).
thf(2641,plain,
! [SV126: nat,SV294: nat] :
( ( ( SV294 != zero_zero_nat )
= $false )
| ( ( ( plus_plus_nat @ SV126 @ SV294 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2529]) ).
thf(2642,plain,
! [SV294: nat,SV126: nat] :
( ( ( ( ( plus_plus_nat @ SV126 @ SV294 )
!= zero_zero_nat )
| ~ ~ ( ( SV126 != zero_zero_nat )
| ( SV294 != zero_zero_nat ) ) )
= $false )
| ( ( SV126 = zero_zero_nat )
= $false )
| ( ( SV294 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2530]) ).
thf(2643,plain,
! [SV510: nat,SV295: nat,SV491: nat,SV425: nat,SV127: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV127 @ SV425 ) @ SV491 ) @ ( plus_plus_nat @ ( times_times_nat @ SV295 @ SV425 ) @ SV510 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV127 @ SV425 ) @ SV491 ) @ ( plus_plus_nat @ ( times_times_nat @ SV295 @ SV425 ) @ SV510 ) )
| ~ ( ord_less_nat @ SV491 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV295 @ SV127 ) @ SV425 ) @ SV510 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV127 @ SV295 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2531]) ).
thf(2644,plain,
! [SV510: nat,SV425: nat,SV127: nat,SV295: nat,SV491: nat] :
( ( ( ord_less_nat @ SV491 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV295 @ SV127 ) @ SV425 ) @ SV510 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV127 @ SV425 ) @ SV491 ) @ ( plus_plus_nat @ ( times_times_nat @ SV295 @ SV425 ) @ SV510 ) )
| ~ ( ord_less_nat @ SV491 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV295 @ SV127 ) @ SV425 ) @ SV510 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV127 @ SV295 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2531]) ).
thf(2645,plain,
! [SV142: nat > $o,SV309: nat,SV516: nat] :
( ( ( ~ ( ord_less_nat @ SV516 @ ( sK1_SY712 @ SV309 @ SV142 ) ) )
= $true )
| ( ( ~ ~ ( SV142 @ SV516 ) )
= $true )
| ( ( SV142 @ SV309 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2533]) ).
thf(2646,plain,
! [SV511: nat,SV313: nat,SV494: nat,SV440: nat,SV146: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV146 @ SV440 ) @ SV494 ) @ ( plus_plus_nat @ ( times_times_nat @ SV313 @ SV440 ) @ SV511 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV146 @ SV440 ) @ SV494 ) @ ( plus_plus_nat @ ( times_times_nat @ SV313 @ SV440 ) @ SV511 ) )
| ~ ( ord_less_eq_nat @ SV494 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV313 @ SV146 ) @ SV440 ) @ SV511 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV146 @ SV313 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2534]) ).
thf(2647,plain,
! [SV511: nat,SV440: nat,SV146: nat,SV313: nat,SV494: nat] :
( ( ( ord_less_eq_nat @ SV494 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV313 @ SV146 ) @ SV440 ) @ SV511 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV146 @ SV440 ) @ SV494 ) @ ( plus_plus_nat @ ( times_times_nat @ SV313 @ SV440 ) @ SV511 ) )
| ~ ( ord_less_eq_nat @ SV494 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV313 @ SV146 ) @ SV440 ) @ SV511 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV146 @ SV313 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2534]) ).
thf(2648,plain,
! [SV444: nat,SV152: nat,SV318: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV318 )
| ~ ( ord_less_nat @ SV152 @ SV444 ) )
= $false )
| ( ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2537]) ).
thf(2649,plain,
! [SV318: nat,SV444: nat,SV152: nat] :
( ( ( ord_less_nat @ SV152 @ SV444 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV318 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV318 )
| ~ ( ord_less_nat @ SV152 @ SV444 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2538]) ).
thf(2650,plain,
! [SV321: nat,SV155: nat] :
( ( ( SV155 = SV321 )
= $false )
| ( ( SV155 = SV321 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2539]) ).
thf(2651,plain,
! [SV321: nat,SV155: nat] :
( ( ( ord_less_nat @ SV155 @ SV321 )
= $true )
| ( ( ord_less_nat @ SV321 @ SV155 )
= $true )
| ( ( SV155 = SV321 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2540]) ).
thf(2652,plain,
! [SV321: nat,SV155: nat] :
( ( ( SV155 = SV321 )
= $false )
| ( ( ord_less_nat @ SV155 @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2541]) ).
thf(2653,plain,
! [SV321: nat,SV155: nat] :
( ( ( ord_less_nat @ SV155 @ SV321 )
= $true )
| ( ( ord_less_nat @ SV321 @ SV155 )
= $true )
| ( ( ord_less_nat @ SV155 @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2542]) ).
thf(2654,plain,
! [SV321: nat,SV155: nat] :
( ( ( SV155 = SV321 )
= $false )
| ( ( ord_less_nat @ SV321 @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2543]) ).
thf(2655,plain,
! [SV321: nat,SV155: nat] :
( ( ( ord_less_nat @ SV155 @ SV321 )
= $true )
| ( ( ord_less_nat @ SV321 @ SV155 )
= $true )
| ( ( ord_less_nat @ SV321 @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2544]) ).
thf(2656,plain,
! [SV325: nat,SV159: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV159 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2545]) ).
thf(2657,plain,
! [SV159: nat,SV325: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV325 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2545]) ).
thf(2658,plain,
! [SV325: nat,SV159: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV159 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV325 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV159 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV325 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2546]) ).
thf(2659,plain,
! [SV326: nat,SV160: nat] :
( ( ( SV160 != zero_zero_nat )
= $false )
| ( ( ( plus_plus_nat @ SV160 @ SV326 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2547]) ).
thf(2660,plain,
! [SV160: nat,SV326: nat] :
( ( ( SV326 != zero_zero_nat )
= $false )
| ( ( ( plus_plus_nat @ SV160 @ SV326 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2547]) ).
thf(2661,plain,
! [SV326: nat,SV160: nat] :
( ( ( ( ( plus_plus_nat @ SV160 @ SV326 )
!= zero_zero_nat )
| ~ ~ ( ( SV160 != zero_zero_nat )
| ( SV326 != zero_zero_nat ) ) )
= $false )
| ( ( SV160 = zero_zero_nat )
= $false )
| ( ( SV326 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2548]) ).
thf(2662,plain,
! [SV497: nat,SV327: nat] :
( ( ( ord_less_nat @ SV327 @ SV497 )
= $true )
| ( ( ord_less_nat @ SV327 @ SV497 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2549]) ).
thf(2663,plain,
! [SV497: nat,SV327: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV327 @ SV497 )
| ~ ( ( SV327 != SV497 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV327 @ SV497 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2550]) ).
thf(2664,plain,
! [SV497: nat,SV327: nat] :
( ( ( ord_less_eq_nat @ SV327 @ SV497 )
= $false )
| ( ( ~ ( ( SV327 != SV497 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV327 @ SV497 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV327 @ SV497 )
| ~ ( ( SV327 != SV497 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2551]) ).
thf(2665,plain,
! [SV328: nat,SV162: nat] :
( ( ( SV162 != zero_zero_nat )
= $false )
| ( ( zero_zero_nat
= ( plus_plus_nat @ SV162 @ SV328 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2552]) ).
thf(2666,plain,
! [SV162: nat,SV328: nat] :
( ( ( SV328 != zero_zero_nat )
= $false )
| ( ( zero_zero_nat
= ( plus_plus_nat @ SV162 @ SV328 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2552]) ).
thf(2667,plain,
! [SV328: nat,SV162: nat] :
( ( ( ( zero_zero_nat
!= ( plus_plus_nat @ SV162 @ SV328 ) )
| ~ ~ ( ( SV162 != zero_zero_nat )
| ( SV328 != zero_zero_nat ) ) )
= $false )
| ( ( SV162 = zero_zero_nat )
= $false )
| ( ( SV328 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2553]) ).
thf(2668,plain,
! [SV448: nat,SV163: nat,SV329: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV329 ) )
= $true )
| ( ( ord_less_eq_nat @ SV163 @ SV448 )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2555]) ).
thf(2669,plain,
! [SV448: nat,SV329: nat,SV163: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV329 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2556]) ).
thf(2670,plain,
! [SV448: nat,SV163: nat,SV329: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV329 )
| ( ord_less_eq_nat @ SV163 @ SV448 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV329 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2556]) ).
thf(2671,plain,
! [SV448: nat,SV329: nat,SV163: nat] :
( ( ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) )
= $true )
| ( ( ord_less_eq_nat @ SV163 @ SV448 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2557]) ).
thf(2672,plain,
! [SV448: nat,SV163: nat,SV329: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV329 )
| ( ord_less_eq_nat @ SV163 @ SV448 ) )
= $true )
| ( ( ord_less_eq_nat @ SV163 @ SV448 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2558]) ).
thf(2673,plain,
! [SV449: nat,SV330: nat,SV164: nat > $o] :
( ( ( ! [SY751: nat] :
~ ~ ( ~ ( SV164 @ SY751 )
| ~ ! [SY752: nat] :
( ~ ( SV164 @ SY752 )
| ( ord_less_eq_nat @ SY752 @ SY751 ) ) ) )
= $false )
| ( ( SV164 @ ( sK8_SY1015 @ SV330 @ SV449 @ SV164 ) )
= $true )
| ( ( SV164 @ SV330 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2559]) ).
thf(2674,plain,
! [SV330: nat,SV449: nat,SV164: nat > $o] :
( ( ( ~ ~ ( ~ ( SV164 @ ( sK9_SY751 @ SV449 @ SV330 @ SV164 ) )
| ~ ! [SY1045: nat] :
( ~ ( SV164 @ SY1045 )
| ( ord_less_eq_nat @ SY1045 @ ( sK9_SY751 @ SV449 @ SV330 @ SV164 ) ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK8_SY1015 @ SV330 @ SV449 @ SV164 ) @ SV449 )
= $false )
| ( ( SV164 @ SV330 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2560]) ).
thf(2675,plain,
! [SV451: nat,SV167: nat,SV332: nat] :
( ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV332 @ SV167 ) @ ( minus_minus_nat @ SV451 @ SV167 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( minus_minus_nat @ SV332 @ SV167 ) @ ( minus_minus_nat @ SV451 @ SV167 ) )
| ~ ( ord_less_eq_nat @ SV332 @ SV451 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV167 @ SV451 )
= $false )
| ( ( ord_less_eq_nat @ SV167 @ SV332 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2561]) ).
thf(2676,plain,
! [SV167: nat,SV451: nat,SV332: nat] :
( ( ( ord_less_eq_nat @ SV332 @ SV451 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( minus_minus_nat @ SV332 @ SV167 ) @ ( minus_minus_nat @ SV451 @ SV167 ) )
| ~ ( ord_less_eq_nat @ SV332 @ SV451 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV167 @ SV451 )
= $false )
| ( ( ord_less_eq_nat @ SV167 @ SV332 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2561]) ).
thf(2677,plain,
! [SV453: nat,SV169: nat,SV334: nat] :
( ( ( ~ ( ord_less_nat @ ( minus_minus_nat @ SV334 @ SV169 ) @ SV453 ) )
= $false )
| ( ( ord_less_nat @ ( minus_minus_nat @ SV334 @ SV169 ) @ SV453 )
= $false )
| ( ( ord_less_eq_nat @ SV169 @ SV334 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2562]) ).
thf(2678,plain,
! [SV169: nat,SV453: nat,SV334: nat] :
( ( ( ~ ( ord_less_nat @ SV334 @ ( plus_plus_nat @ SV453 @ SV169 ) ) )
= $false )
| ( ( ord_less_nat @ ( minus_minus_nat @ SV334 @ SV169 ) @ SV453 )
= $false )
| ( ( ord_less_eq_nat @ SV169 @ SV334 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2562]) ).
thf(2679,plain,
! [SV453: nat,SV169: nat,SV334: nat] :
( ( ( ~ ( ord_less_nat @ ( minus_minus_nat @ SV334 @ SV169 ) @ SV453 ) )
= $false )
| ( ( ord_less_nat @ SV334 @ ( plus_plus_nat @ SV453 @ SV169 ) )
= $false )
| ( ( ord_less_eq_nat @ SV169 @ SV334 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2563]) ).
thf(2680,plain,
! [SV169: nat,SV453: nat,SV334: nat] :
( ( ( ~ ( ord_less_nat @ SV334 @ ( plus_plus_nat @ SV453 @ SV169 ) ) )
= $false )
| ( ( ord_less_nat @ SV334 @ ( plus_plus_nat @ SV453 @ SV169 ) )
= $false )
| ( ( ord_less_eq_nat @ SV169 @ SV334 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2563]) ).
thf(2681,plain,
! [SV512: nat,SV174: nat,SV499: nat,SV457: nat,SV338: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV338 @ SV457 ) @ SV499 ) @ ( plus_plus_nat @ ( times_times_nat @ SV174 @ SV457 ) @ SV512 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV338 @ SV457 ) @ SV499 ) @ ( plus_plus_nat @ ( times_times_nat @ SV174 @ SV457 ) @ SV512 ) )
| ~ ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV338 @ SV174 ) @ SV457 ) @ SV499 ) @ SV512 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV174 @ SV338 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2564]) ).
thf(2682,plain,
! [SV512: nat,SV499: nat,SV457: nat,SV174: nat,SV338: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV338 @ SV174 ) @ SV457 ) @ SV499 ) @ SV512 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV338 @ SV457 ) @ SV499 ) @ ( plus_plus_nat @ ( times_times_nat @ SV174 @ SV457 ) @ SV512 ) )
| ~ ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV338 @ SV174 ) @ SV457 ) @ SV499 ) @ SV512 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV174 @ SV338 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2564]) ).
thf(2683,plain,
! [SV459: nat,SV341: nat,SV177: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 )
| ~ ( ord_less_nat @ SV341 @ SV459 ) )
= $false )
| ( ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2566]) ).
thf(2684,plain,
! [SV177: nat,SV459: nat,SV341: nat] :
( ( ( ord_less_nat @ SV341 @ SV459 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV177 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 )
| ~ ( ord_less_nat @ SV341 @ SV459 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2567]) ).
thf(2685,plain,
! [SV461: nat,SV182: nat,SV346: nat] :
( ( ( ( minus_minus_nat @ SV346 @ SV182 )
= SV461 )
= $false )
| ( ( ~ ( ( ( minus_minus_nat @ SV346 @ SV182 )
!= SV461 )
| ( SV346
!= ( plus_plus_nat @ SV461 @ SV182 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2569]) ).
thf(2686,plain,
! [SV182: nat,SV461: nat,SV346: nat] :
( ( ( SV346
= ( plus_plus_nat @ SV461 @ SV182 ) )
= $false )
| ( ( ~ ( ( ( minus_minus_nat @ SV346 @ SV182 )
!= SV461 )
| ( SV346
!= ( plus_plus_nat @ SV461 @ SV182 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2569]) ).
thf(2687,plain,
! [SV463: nat,SV184: nat,SV348: nat] :
( ( ( ord_less_nat @ ( minus_minus_nat @ SV348 @ SV184 ) @ ( minus_minus_nat @ SV463 @ SV184 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( minus_minus_nat @ SV348 @ SV184 ) @ ( minus_minus_nat @ SV463 @ SV184 ) )
| ~ ( ord_less_nat @ SV348 @ SV463 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV184 @ SV463 )
= $false )
| ( ( ord_less_eq_nat @ SV184 @ SV348 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2570]) ).
thf(2688,plain,
! [SV184: nat,SV463: nat,SV348: nat] :
( ( ( ord_less_nat @ SV348 @ SV463 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( minus_minus_nat @ SV348 @ SV184 ) @ ( minus_minus_nat @ SV463 @ SV184 ) )
| ~ ( ord_less_nat @ SV348 @ SV463 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV184 @ SV463 )
= $false )
| ( ( ord_less_eq_nat @ SV184 @ SV348 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2570]) ).
thf(2689,plain,
! [SV185: nat,SV349: nat,SV464: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV464 @ ( minus_minus_nat @ SV349 @ SV185 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV464 @ ( minus_minus_nat @ SV349 @ SV185 ) )
= $false )
| ( ( ord_less_eq_nat @ SV185 @ SV349 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2571]) ).
thf(2690,plain,
! [SV349: nat,SV185: nat,SV464: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV464 @ SV185 ) @ SV349 ) )
= $false )
| ( ( ord_less_eq_nat @ SV464 @ ( minus_minus_nat @ SV349 @ SV185 ) )
= $false )
| ( ( ord_less_eq_nat @ SV185 @ SV349 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2571]) ).
thf(2691,plain,
! [SV185: nat,SV349: nat,SV464: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV464 @ ( minus_minus_nat @ SV349 @ SV185 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV464 @ SV185 ) @ SV349 )
= $false )
| ( ( ord_less_eq_nat @ SV185 @ SV349 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2572]) ).
thf(2692,plain,
! [SV349: nat,SV185: nat,SV464: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV464 @ SV185 ) @ SV349 ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV464 @ SV185 ) @ SV349 )
= $false )
| ( ( ord_less_eq_nat @ SV185 @ SV349 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2572]) ).
thf(2693,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) )
= $false )
| ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2574]) ).
thf(2694,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ord_less_nat @ SV350 @ SV465 ) )
= $false )
| ( ( ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) )
= $true )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2575]) ).
thf(2695,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( ~ ~ ( SV186 @ zero_zero_nat ) )
= $false )
| ( ( ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) )
= $true )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2575]) ).
thf(2696,plain,
! [SV513: nat,SV190: nat,SV501: nat,SV468: nat,SV354: nat] :
( ( ( ( plus_plus_nat @ ( times_times_nat @ SV354 @ SV468 ) @ SV501 )
= ( plus_plus_nat @ ( times_times_nat @ SV190 @ SV468 ) @ SV513 ) )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV354 @ SV468 ) @ SV501 )
!= ( plus_plus_nat @ ( times_times_nat @ SV190 @ SV468 ) @ SV513 ) )
| ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV354 @ SV190 ) @ SV468 ) @ SV501 )
!= SV513 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV190 @ SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2576]) ).
thf(2697,plain,
! [SV513: nat,SV501: nat,SV468: nat,SV190: nat,SV354: nat] :
( ( ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV354 @ SV190 ) @ SV468 ) @ SV501 )
= SV513 )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV354 @ SV468 ) @ SV501 )
!= ( plus_plus_nat @ ( times_times_nat @ SV190 @ SV468 ) @ SV513 ) )
| ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV354 @ SV190 ) @ SV468 ) @ SV501 )
!= SV513 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV190 @ SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2576]) ).
thf(2698,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV194 ) )
= $true )
| ( ( ord_less_eq_nat @ SV358 @ SV471 )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2580]) ).
thf(2699,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV194 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2581]) ).
thf(2700,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV194 )
| ( ord_less_eq_nat @ SV358 @ SV471 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV194 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2581]) ).
thf(2701,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) )
= $true )
| ( ( ord_less_eq_nat @ SV358 @ SV471 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2582]) ).
thf(2702,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV194 )
| ( ord_less_eq_nat @ SV358 @ SV471 ) )
= $true )
| ( ( ord_less_eq_nat @ SV358 @ SV471 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2583]) ).
thf(2703,plain,
! [SV514: nat,SV361: nat,SV505: nat,SV474: nat,SV197: nat] :
( ( ( ( plus_plus_nat @ ( times_times_nat @ SV197 @ SV474 ) @ SV505 )
= ( plus_plus_nat @ ( times_times_nat @ SV361 @ SV474 ) @ SV514 ) )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV197 @ SV474 ) @ SV505 )
!= ( plus_plus_nat @ ( times_times_nat @ SV361 @ SV474 ) @ SV514 ) )
| ( SV505
!= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV361 @ SV197 ) @ SV474 ) @ SV514 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV197 @ SV361 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2585]) ).
thf(2704,plain,
! [SV514: nat,SV474: nat,SV197: nat,SV361: nat,SV505: nat] :
( ( ( SV505
= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV361 @ SV197 ) @ SV474 ) @ SV514 ) )
= $false )
| ( ( ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV197 @ SV474 ) @ SV505 )
!= ( plus_plus_nat @ ( times_times_nat @ SV361 @ SV474 ) @ SV514 ) )
| ( SV505
!= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV361 @ SV197 ) @ SV474 ) @ SV514 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV197 @ SV361 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2585]) ).
thf(2705,plain,
! [SV526: nat,SV1: nat > nat] :
( ( ( ( SV1 @ SV526 )
= zero_zero_nat )
= $true )
| ( ( ( SV1 @ ( sK5_SV515 @ SV1 ) )
= zero_zero_nat )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2586]) ).
thf(2706,plain,
! [SV224: nat,SV377: nat,SV35: nat] :
( ( ( SV35 = SV377 )
= $true )
| ( ( SV224 = zero_zero_nat )
= $true )
| ( ( SV35 = SV377 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2593]) ).
thf(2707,plain,
! [SV224: nat,SV377: nat,SV35: nat] :
( ( ( SV35 = SV377 )
= $true )
| ( ( SV224 = zero_zero_nat )
= $true )
| ( ( SV224 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2595]) ).
thf(2708,plain,
! [SV36: nat,SV378: nat,SV225: nat] :
( ( ( SV225 = SV378 )
= $true )
| ( ( SV36 = zero_zero_nat )
= $true )
| ( ( SV225 = SV378 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2598]) ).
thf(2709,plain,
! [SV36: nat,SV378: nat,SV225: nat] :
( ( ( SV225 = SV378 )
= $true )
| ( ( SV36 = zero_zero_nat )
= $true )
| ( ( SV36 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2600]) ).
thf(2710,plain,
! [SV481: nat,SV258: nat] :
( ( ( ord_less_nat @ SV258 @ SV481 )
= $true )
| ( ( SV258 = SV481 )
= $true )
| ( ( ord_less_eq_nat @ SV258 @ SV481 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2604]) ).
thf(2711,plain,
! [SV481: nat,SV258: nat] :
( ( ( ord_less_eq_nat @ SV258 @ SV481 )
= $true )
| ( ( ord_less_nat @ SV258 @ SV481 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2605]) ).
thf(2712,plain,
! [SV481: nat,SV258: nat] :
( ( ( ( ord_less_nat @ SV258 @ SV481 )
| ( SV258 = SV481 ) )
= $true )
| ( ( ord_less_nat @ SV258 @ SV481 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2606]) ).
thf(2713,plain,
! [SV481: nat,SV258: nat] :
( ( ( ord_less_eq_nat @ SV258 @ SV481 )
= $true )
| ( ( SV258 = SV481 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2607]) ).
thf(2714,plain,
! [SV481: nat,SV258: nat] :
( ( ( ( ord_less_nat @ SV258 @ SV481 )
| ( SV258 = SV481 ) )
= $true )
| ( ( SV258 = SV481 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2608]) ).
thf(2715,plain,
! [SV399: nat,SV261: nat,SV90: nat] :
( ( ( SV90 = zero_zero_nat )
= $true )
| ( ( SV261 = SV399 )
= $true )
| ( ( SV90 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2611]) ).
thf(2716,plain,
! [SV399: nat,SV261: nat,SV90: nat] :
( ( ( SV90 = zero_zero_nat )
= $true )
| ( ( SV261 = SV399 )
= $true )
| ( ( SV261 = SV399 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2613]) ).
thf(2717,plain,
! [SV402: nat,SV95: nat,SV265: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( minus_minus_nat @ SV265 @ SV95 ) @ ( minus_minus_nat @ SV265 @ SV402 ) )
| ~ ( ord_less_eq_nat @ SV402 @ SV95 ) )
= $false )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV265 @ SV95 ) @ ( minus_minus_nat @ SV265 @ SV402 ) )
= $false )
| ( ( ord_less_eq_nat @ SV402 @ SV265 )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2615]) ).
thf(2718,plain,
! [SV402: nat,SV95: nat,SV265: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( minus_minus_nat @ SV265 @ SV95 ) @ ( minus_minus_nat @ SV265 @ SV402 ) )
| ~ ( ord_less_eq_nat @ SV402 @ SV95 ) )
= $false )
| ( ( ord_less_eq_nat @ SV402 @ SV95 )
= $false )
| ( ( ord_less_eq_nat @ SV402 @ SV265 )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2616]) ).
thf(2719,plain,
! [SV507: nat,SV99: nat,SV484: nat,SV405: nat,SV269: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV269 @ SV405 ) @ SV484 ) @ ( plus_plus_nat @ ( times_times_nat @ SV99 @ SV405 ) @ SV507 ) )
| ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV269 @ SV99 ) @ SV405 ) @ SV484 ) @ SV507 ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV269 @ SV405 ) @ SV484 ) @ ( plus_plus_nat @ ( times_times_nat @ SV99 @ SV405 ) @ SV507 ) )
= $false )
| ( ( ord_less_eq_nat @ SV99 @ SV269 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2617]) ).
thf(2720,plain,
! [SV507: nat,SV99: nat,SV484: nat,SV405: nat,SV269: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV269 @ SV405 ) @ SV484 ) @ ( plus_plus_nat @ ( times_times_nat @ SV99 @ SV405 ) @ SV507 ) )
| ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV269 @ SV99 ) @ SV405 ) @ SV484 ) @ SV507 ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV269 @ SV99 ) @ SV405 ) @ SV484 ) @ SV507 )
= $false )
| ( ( ord_less_eq_nat @ SV99 @ SV269 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2618]) ).
thf(2721,plain,
! [SV413: nat,SV110: nat,SV279: nat] :
( ( ( ( ( minus_minus_nat @ SV279 @ SV110 )
!= ( minus_minus_nat @ SV413 @ SV110 ) )
| ( SV279 != SV413 ) )
= $false )
| ( ( ( minus_minus_nat @ SV279 @ SV110 )
= ( minus_minus_nat @ SV413 @ SV110 ) )
= $false )
| ( ( ord_less_eq_nat @ SV110 @ SV413 )
= $false )
| ( ( ord_less_eq_nat @ SV110 @ SV279 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2619]) ).
thf(2722,plain,
! [SV413: nat,SV110: nat,SV279: nat] :
( ( ( ( ( minus_minus_nat @ SV279 @ SV110 )
!= ( minus_minus_nat @ SV413 @ SV110 ) )
| ( SV279 != SV413 ) )
= $false )
| ( ( SV279 = SV413 )
= $false )
| ( ( ord_less_eq_nat @ SV110 @ SV413 )
= $false )
| ( ( ord_less_eq_nat @ SV110 @ SV279 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2620]) ).
thf(2723,plain,
! [SV113: nat,SV282: nat,SV415: nat] :
( ( ( ord_less_eq_nat @ SV415 @ ( minus_minus_nat @ SV282 @ SV113 ) )
= $true )
| ( ( ord_less_eq_nat @ SV415 @ ( minus_minus_nat @ SV282 @ SV113 ) )
= $false )
| ( ( ord_less_eq_nat @ SV113 @ SV282 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2621]) ).
thf(2724,plain,
! [SV282: nat,SV113: nat,SV415: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV415 @ SV113 ) @ SV282 )
= $true )
| ( ( ord_less_eq_nat @ SV415 @ ( minus_minus_nat @ SV282 @ SV113 ) )
= $false )
| ( ( ord_less_eq_nat @ SV113 @ SV282 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2622]) ).
thf(2725,plain,
! [SV113: nat,SV282: nat,SV415: nat] :
( ( ( ord_less_eq_nat @ SV415 @ ( minus_minus_nat @ SV282 @ SV113 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV415 @ SV113 ) @ SV282 )
= $false )
| ( ( ord_less_eq_nat @ SV113 @ SV282 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2623]) ).
thf(2726,plain,
! [SV282: nat,SV113: nat,SV415: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV415 @ SV113 ) @ SV282 )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV415 @ SV113 ) @ SV282 )
= $false )
| ( ( ord_less_eq_nat @ SV113 @ SV282 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2624]) ).
thf(2727,plain,
! [SV114: nat > $o,SV283: nat,SV525: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV525 @ ( sK7_SY655 @ SV283 @ SV114 ) )
| ~ ~ ( SV114 @ SV525 ) ) )
= $false )
| ( ( SV114 @ SV283 )
= $true )
| ( ( SV114 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2626]) ).
thf(2728,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) ) )
= $false )
| ( ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2627]) ).
thf(2729,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) )
= $false )
| ( ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2627]) ).
thf(2730,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) )
= $true )
| ( ( ~ ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2628]) ).
thf(2731,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) )
= $false )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2629]) ).
thf(2732,plain,
! [SV288: nat,SV488: nat] :
( ( ( ! [SY1033: nat] :
( SV488
!= ( plus_plus_nat @ SV288 @ SY1033 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV288 @ SV488 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2631]) ).
thf(2733,plain,
! [SV521: nat,SV488: nat,SV288: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV288 @ SV488 )
| ~ ~ ! [SY1033: nat] :
( SV488
!= ( plus_plus_nat @ SV288 @ SY1033 ) ) )
= $false )
| ( ( SV488
= ( plus_plus_nat @ SV288 @ SV521 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2632]) ).
thf(2734,plain,
! [SV289: nat,SV489: nat] :
( ( ( ! [SY1034: nat] :
( SV489
!= ( plus_plus_nat @ SV289 @ SY1034 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV289 @ SV489 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2634]) ).
thf(2735,plain,
! [SV522: nat,SV489: nat,SV289: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV289 @ SV489 )
| ~ ~ ! [SY1034: nat] :
( SV489
!= ( plus_plus_nat @ SV289 @ SY1034 ) ) )
= $false )
| ( ( SV489
= ( plus_plus_nat @ SV289 @ SV522 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2635]) ).
thf(2736,plain,
! [SV421: nat,SV122: nat,SV290: nat] :
( ( ( ( minus_minus_nat @ SV290 @ SV122 )
= SV421 )
= $true )
| ( ( ( minus_minus_nat @ SV290 @ SV122 )
= SV421 )
= $false )
| ( ( ord_less_eq_nat @ SV122 @ SV290 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2636]) ).
thf(2737,plain,
! [SV122: nat,SV421: nat,SV290: nat] :
( ( ( SV290
= ( plus_plus_nat @ SV421 @ SV122 ) )
= $true )
| ( ( ( minus_minus_nat @ SV290 @ SV122 )
= SV421 )
= $false )
| ( ( ord_less_eq_nat @ SV122 @ SV290 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2637]) ).
thf(2738,plain,
! [SV421: nat,SV122: nat,SV290: nat] :
( ( ( ( minus_minus_nat @ SV290 @ SV122 )
= SV421 )
= $true )
| ( ( SV290
= ( plus_plus_nat @ SV421 @ SV122 ) )
= $false )
| ( ( ord_less_eq_nat @ SV122 @ SV290 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2638]) ).
thf(2739,plain,
! [SV122: nat,SV421: nat,SV290: nat] :
( ( ( SV290
= ( plus_plus_nat @ SV421 @ SV122 ) )
= $true )
| ( ( SV290
= ( plus_plus_nat @ SV421 @ SV122 ) )
= $false )
| ( ( ord_less_eq_nat @ SV122 @ SV290 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2639]) ).
thf(2740,plain,
! [SV294: nat,SV126: nat] :
( ( ( SV126 = zero_zero_nat )
= $true )
| ( ( ( plus_plus_nat @ SV126 @ SV294 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2640]) ).
thf(2741,plain,
! [SV126: nat,SV294: nat] :
( ( ( SV294 = zero_zero_nat )
= $true )
| ( ( ( plus_plus_nat @ SV126 @ SV294 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2641]) ).
thf(2742,plain,
! [SV294: nat,SV126: nat] :
( ( ( ( plus_plus_nat @ SV126 @ SV294 )
!= zero_zero_nat )
= $false )
| ( ( SV126 = zero_zero_nat )
= $false )
| ( ( SV294 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2642]) ).
thf(2743,plain,
! [SV294: nat,SV126: nat] :
( ( ( ~ ~ ( ( SV126 != zero_zero_nat )
| ( SV294 != zero_zero_nat ) ) )
= $false )
| ( ( SV126 = zero_zero_nat )
= $false )
| ( ( SV294 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2642]) ).
thf(2744,plain,
! [SV510: nat,SV295: nat,SV491: nat,SV425: nat,SV127: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV127 @ SV425 ) @ SV491 ) @ ( plus_plus_nat @ ( times_times_nat @ SV295 @ SV425 ) @ SV510 ) )
| ~ ( ord_less_nat @ SV491 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV295 @ SV127 ) @ SV425 ) @ SV510 ) ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV127 @ SV425 ) @ SV491 ) @ ( plus_plus_nat @ ( times_times_nat @ SV295 @ SV425 ) @ SV510 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV295 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2643]) ).
thf(2745,plain,
! [SV510: nat,SV295: nat,SV491: nat,SV425: nat,SV127: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV127 @ SV425 ) @ SV491 ) @ ( plus_plus_nat @ ( times_times_nat @ SV295 @ SV425 ) @ SV510 ) )
| ~ ( ord_less_nat @ SV491 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV295 @ SV127 ) @ SV425 ) @ SV510 ) ) )
= $false )
| ( ( ord_less_nat @ SV491 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV295 @ SV127 ) @ SV425 ) @ SV510 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV295 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2644]) ).
thf(2746,plain,
! [SV142: nat > $o,SV309: nat,SV516: nat] :
( ( ( ord_less_nat @ SV516 @ ( sK1_SY712 @ SV309 @ SV142 ) )
= $false )
| ( ( ~ ~ ( SV142 @ SV516 ) )
= $true )
| ( ( SV142 @ SV309 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2645]) ).
thf(2747,plain,
! [SV511: nat,SV313: nat,SV494: nat,SV440: nat,SV146: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV146 @ SV440 ) @ SV494 ) @ ( plus_plus_nat @ ( times_times_nat @ SV313 @ SV440 ) @ SV511 ) )
| ~ ( ord_less_eq_nat @ SV494 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV313 @ SV146 ) @ SV440 ) @ SV511 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV146 @ SV440 ) @ SV494 ) @ ( plus_plus_nat @ ( times_times_nat @ SV313 @ SV440 ) @ SV511 ) )
= $false )
| ( ( ord_less_eq_nat @ SV146 @ SV313 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2646]) ).
thf(2748,plain,
! [SV511: nat,SV313: nat,SV494: nat,SV440: nat,SV146: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV146 @ SV440 ) @ SV494 ) @ ( plus_plus_nat @ ( times_times_nat @ SV313 @ SV440 ) @ SV511 ) )
| ~ ( ord_less_eq_nat @ SV494 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV313 @ SV146 ) @ SV440 ) @ SV511 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV494 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV313 @ SV146 ) @ SV440 ) @ SV511 ) )
= $false )
| ( ( ord_less_eq_nat @ SV146 @ SV313 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2647]) ).
thf(2749,plain,
! [SV444: nat,SV152: nat,SV318: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV318 ) )
= $false )
| ( ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2648]) ).
thf(2750,plain,
! [SV318: nat,SV444: nat,SV152: nat] :
( ( ( ~ ( ord_less_nat @ SV152 @ SV444 ) )
= $false )
| ( ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2648]) ).
thf(2751,plain,
! [SV444: nat,SV318: nat,SV152: nat] :
( ( ( ~ ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV318 )
| ~ ( ord_less_nat @ SV152 @ SV444 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV318 )
= $false )
| ( ( ord_less_nat @ SV152 @ SV444 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2649]) ).
thf(2752,plain,
! [SV325: nat,SV159: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV159 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2656]) ).
thf(2753,plain,
! [SV159: nat,SV325: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV325 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2657]) ).
thf(2754,plain,
! [SV325: nat,SV159: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV159 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV325 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2658]) ).
thf(2755,plain,
! [SV325: nat,SV159: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV159 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV325 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV159 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV325 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2658]) ).
thf(2756,plain,
! [SV326: nat,SV160: nat] :
( ( ( SV160 = zero_zero_nat )
= $true )
| ( ( ( plus_plus_nat @ SV160 @ SV326 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2659]) ).
thf(2757,plain,
! [SV160: nat,SV326: nat] :
( ( ( SV326 = zero_zero_nat )
= $true )
| ( ( ( plus_plus_nat @ SV160 @ SV326 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2660]) ).
thf(2758,plain,
! [SV326: nat,SV160: nat] :
( ( ( ( plus_plus_nat @ SV160 @ SV326 )
!= zero_zero_nat )
= $false )
| ( ( SV160 = zero_zero_nat )
= $false )
| ( ( SV326 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2661]) ).
thf(2759,plain,
! [SV326: nat,SV160: nat] :
( ( ( ~ ~ ( ( SV160 != zero_zero_nat )
| ( SV326 != zero_zero_nat ) ) )
= $false )
| ( ( SV160 = zero_zero_nat )
= $false )
| ( ( SV326 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2661]) ).
thf(2760,plain,
! [SV497: nat,SV327: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV327 @ SV497 )
| ~ ( ( SV327 != SV497 ) ) )
= $false )
| ( ( ord_less_nat @ SV327 @ SV497 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2663]) ).
thf(2761,plain,
! [SV497: nat,SV327: nat] :
( ( ( SV327 != SV497 )
= $false )
| ( ( ord_less_eq_nat @ SV327 @ SV497 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV327 @ SV497 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV327 @ SV497 )
| ~ ( ( SV327 != SV497 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2664]) ).
thf(2762,plain,
! [SV328: nat,SV162: nat] :
( ( ( SV162 = zero_zero_nat )
= $true )
| ( ( zero_zero_nat
= ( plus_plus_nat @ SV162 @ SV328 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2665]) ).
thf(2763,plain,
! [SV162: nat,SV328: nat] :
( ( ( SV328 = zero_zero_nat )
= $true )
| ( ( zero_zero_nat
= ( plus_plus_nat @ SV162 @ SV328 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2666]) ).
thf(2764,plain,
! [SV328: nat,SV162: nat] :
( ( ( zero_zero_nat
!= ( plus_plus_nat @ SV162 @ SV328 ) )
= $false )
| ( ( SV162 = zero_zero_nat )
= $false )
| ( ( SV328 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2667]) ).
thf(2765,plain,
! [SV328: nat,SV162: nat] :
( ( ( ~ ~ ( ( SV162 != zero_zero_nat )
| ( SV328 != zero_zero_nat ) ) )
= $false )
| ( ( SV162 = zero_zero_nat )
= $false )
| ( ( SV328 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2667]) ).
thf(2766,plain,
! [SV448: nat,SV163: nat,SV329: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV329 )
= $false )
| ( ( ord_less_eq_nat @ SV163 @ SV448 )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2668]) ).
thf(2767,plain,
! [SV448: nat,SV329: nat,SV163: nat] :
( ( ( ord_less_eq_nat @ ( times_times_nat @ SV163 @ SV329 ) @ ( times_times_nat @ SV448 @ SV329 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV329 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2669]) ).
thf(2768,plain,
! [SV448: nat,SV163: nat,SV329: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV329 )
| ( ord_less_eq_nat @ SV163 @ SV448 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV329 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2670]) ).
thf(2769,plain,
! [SV448: nat,SV163: nat,SV329: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV329 ) )
= $true )
| ( ( ord_less_eq_nat @ SV163 @ SV448 )
= $true )
| ( ( ord_less_eq_nat @ SV163 @ SV448 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2672]) ).
thf(2770,plain,
! [SV330: nat,SV449: nat,SV164: nat > $o] :
( ( ( ~ ~ ( ~ ( SV164 @ ( sK10_SY751 @ SV449 @ SV330 @ SV164 ) )
| ~ ! [SY1046: nat] :
( ~ ( SV164 @ SY1046 )
| ( ord_less_eq_nat @ SY1046 @ ( sK10_SY751 @ SV449 @ SV330 @ SV164 ) ) ) ) )
= $false )
| ( ( SV164 @ ( sK8_SY1015 @ SV330 @ SV449 @ SV164 ) )
= $true )
| ( ( SV164 @ SV330 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2673]) ).
thf(2771,plain,
! [SV330: nat,SV449: nat,SV164: nat > $o] :
( ( ( ~ ( ~ ( SV164 @ ( sK9_SY751 @ SV449 @ SV330 @ SV164 ) )
| ~ ! [SY1045: nat] :
( ~ ( SV164 @ SY1045 )
| ( ord_less_eq_nat @ SY1045 @ ( sK9_SY751 @ SV449 @ SV330 @ SV164 ) ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK8_SY1015 @ SV330 @ SV449 @ SV164 ) @ SV449 )
= $false )
| ( ( SV164 @ SV330 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2674]) ).
thf(2772,plain,
! [SV451: nat,SV167: nat,SV332: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( minus_minus_nat @ SV332 @ SV167 ) @ ( minus_minus_nat @ SV451 @ SV167 ) )
| ~ ( ord_less_eq_nat @ SV332 @ SV451 ) )
= $false )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV332 @ SV167 ) @ ( minus_minus_nat @ SV451 @ SV167 ) )
= $false )
| ( ( ord_less_eq_nat @ SV167 @ SV451 )
= $false )
| ( ( ord_less_eq_nat @ SV167 @ SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2675]) ).
thf(2773,plain,
! [SV451: nat,SV167: nat,SV332: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( minus_minus_nat @ SV332 @ SV167 ) @ ( minus_minus_nat @ SV451 @ SV167 ) )
| ~ ( ord_less_eq_nat @ SV332 @ SV451 ) )
= $false )
| ( ( ord_less_eq_nat @ SV332 @ SV451 )
= $false )
| ( ( ord_less_eq_nat @ SV167 @ SV451 )
= $false )
| ( ( ord_less_eq_nat @ SV167 @ SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2676]) ).
thf(2774,plain,
! [SV453: nat,SV169: nat,SV334: nat] :
( ( ( ord_less_nat @ ( minus_minus_nat @ SV334 @ SV169 ) @ SV453 )
= $true )
| ( ( ord_less_nat @ ( minus_minus_nat @ SV334 @ SV169 ) @ SV453 )
= $false )
| ( ( ord_less_eq_nat @ SV169 @ SV334 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2677]) ).
thf(2775,plain,
! [SV169: nat,SV453: nat,SV334: nat] :
( ( ( ord_less_nat @ SV334 @ ( plus_plus_nat @ SV453 @ SV169 ) )
= $true )
| ( ( ord_less_nat @ ( minus_minus_nat @ SV334 @ SV169 ) @ SV453 )
= $false )
| ( ( ord_less_eq_nat @ SV169 @ SV334 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2678]) ).
thf(2776,plain,
! [SV453: nat,SV169: nat,SV334: nat] :
( ( ( ord_less_nat @ ( minus_minus_nat @ SV334 @ SV169 ) @ SV453 )
= $true )
| ( ( ord_less_nat @ SV334 @ ( plus_plus_nat @ SV453 @ SV169 ) )
= $false )
| ( ( ord_less_eq_nat @ SV169 @ SV334 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2679]) ).
thf(2777,plain,
! [SV169: nat,SV453: nat,SV334: nat] :
( ( ( ord_less_nat @ SV334 @ ( plus_plus_nat @ SV453 @ SV169 ) )
= $true )
| ( ( ord_less_nat @ SV334 @ ( plus_plus_nat @ SV453 @ SV169 ) )
= $false )
| ( ( ord_less_eq_nat @ SV169 @ SV334 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2680]) ).
thf(2778,plain,
! [SV512: nat,SV174: nat,SV499: nat,SV457: nat,SV338: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV338 @ SV457 ) @ SV499 ) @ ( plus_plus_nat @ ( times_times_nat @ SV174 @ SV457 ) @ SV512 ) )
| ~ ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV338 @ SV174 ) @ SV457 ) @ SV499 ) @ SV512 ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV338 @ SV457 ) @ SV499 ) @ ( plus_plus_nat @ ( times_times_nat @ SV174 @ SV457 ) @ SV512 ) )
= $false )
| ( ( ord_less_eq_nat @ SV174 @ SV338 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2681]) ).
thf(2779,plain,
! [SV512: nat,SV174: nat,SV499: nat,SV457: nat,SV338: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV338 @ SV457 ) @ SV499 ) @ ( plus_plus_nat @ ( times_times_nat @ SV174 @ SV457 ) @ SV512 ) )
| ~ ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV338 @ SV174 ) @ SV457 ) @ SV499 ) @ SV512 ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV338 @ SV174 ) @ SV457 ) @ SV499 ) @ SV512 )
= $false )
| ( ( ord_less_eq_nat @ SV174 @ SV338 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2682]) ).
thf(2780,plain,
! [SV459: nat,SV341: nat,SV177: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 ) )
= $false )
| ( ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2683]) ).
thf(2781,plain,
! [SV177: nat,SV459: nat,SV341: nat] :
( ( ( ~ ( ord_less_nat @ SV341 @ SV459 ) )
= $false )
| ( ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2683]) ).
thf(2782,plain,
! [SV459: nat,SV341: nat,SV177: nat] :
( ( ( ~ ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 )
| ~ ( ord_less_nat @ SV341 @ SV459 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV177 )
= $false )
| ( ( ord_less_nat @ SV341 @ SV459 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2684]) ).
thf(2783,plain,
! [SV461: nat,SV182: nat,SV346: nat] :
( ( ( ( ( minus_minus_nat @ SV346 @ SV182 )
!= SV461 )
| ( SV346
!= ( plus_plus_nat @ SV461 @ SV182 ) ) )
= $false )
| ( ( ( minus_minus_nat @ SV346 @ SV182 )
= SV461 )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2685]) ).
thf(2784,plain,
! [SV461: nat,SV182: nat,SV346: nat] :
( ( ( ( ( minus_minus_nat @ SV346 @ SV182 )
!= SV461 )
| ( SV346
!= ( plus_plus_nat @ SV461 @ SV182 ) ) )
= $false )
| ( ( SV346
= ( plus_plus_nat @ SV461 @ SV182 ) )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2686]) ).
thf(2785,plain,
! [SV463: nat,SV184: nat,SV348: nat] :
( ( ( ~ ( ord_less_nat @ ( minus_minus_nat @ SV348 @ SV184 ) @ ( minus_minus_nat @ SV463 @ SV184 ) )
| ~ ( ord_less_nat @ SV348 @ SV463 ) )
= $false )
| ( ( ord_less_nat @ ( minus_minus_nat @ SV348 @ SV184 ) @ ( minus_minus_nat @ SV463 @ SV184 ) )
= $false )
| ( ( ord_less_eq_nat @ SV184 @ SV463 )
= $false )
| ( ( ord_less_eq_nat @ SV184 @ SV348 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2687]) ).
thf(2786,plain,
! [SV463: nat,SV184: nat,SV348: nat] :
( ( ( ~ ( ord_less_nat @ ( minus_minus_nat @ SV348 @ SV184 ) @ ( minus_minus_nat @ SV463 @ SV184 ) )
| ~ ( ord_less_nat @ SV348 @ SV463 ) )
= $false )
| ( ( ord_less_nat @ SV348 @ SV463 )
= $false )
| ( ( ord_less_eq_nat @ SV184 @ SV463 )
= $false )
| ( ( ord_less_eq_nat @ SV184 @ SV348 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2688]) ).
thf(2787,plain,
! [SV185: nat,SV349: nat,SV464: nat] :
( ( ( ord_less_eq_nat @ SV464 @ ( minus_minus_nat @ SV349 @ SV185 ) )
= $true )
| ( ( ord_less_eq_nat @ SV464 @ ( minus_minus_nat @ SV349 @ SV185 ) )
= $false )
| ( ( ord_less_eq_nat @ SV185 @ SV349 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2689]) ).
thf(2788,plain,
! [SV349: nat,SV185: nat,SV464: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV464 @ SV185 ) @ SV349 )
= $true )
| ( ( ord_less_eq_nat @ SV464 @ ( minus_minus_nat @ SV349 @ SV185 ) )
= $false )
| ( ( ord_less_eq_nat @ SV185 @ SV349 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2690]) ).
thf(2789,plain,
! [SV185: nat,SV349: nat,SV464: nat] :
( ( ( ord_less_eq_nat @ SV464 @ ( minus_minus_nat @ SV349 @ SV185 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV464 @ SV185 ) @ SV349 )
= $false )
| ( ( ord_less_eq_nat @ SV185 @ SV349 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2691]) ).
thf(2790,plain,
! [SV349: nat,SV185: nat,SV464: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV464 @ SV185 ) @ SV349 )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV464 @ SV185 ) @ SV349 )
= $false )
| ( ( ord_less_eq_nat @ SV185 @ SV349 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2692]) ).
thf(2791,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) ) )
= $false )
| ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2693]) ).
thf(2792,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) )
= $false )
| ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2693]) ).
thf(2793,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) )
= $true )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2694]) ).
thf(2794,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( ~ ( SV186 @ zero_zero_nat ) )
= $true )
| ( ( ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) )
= $true )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2695]) ).
thf(2795,plain,
! [SV513: nat,SV190: nat,SV501: nat,SV468: nat,SV354: nat] :
( ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV354 @ SV468 ) @ SV501 )
!= ( plus_plus_nat @ ( times_times_nat @ SV190 @ SV468 ) @ SV513 ) )
| ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV354 @ SV190 ) @ SV468 ) @ SV501 )
!= SV513 ) )
= $false )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SV354 @ SV468 ) @ SV501 )
= ( plus_plus_nat @ ( times_times_nat @ SV190 @ SV468 ) @ SV513 ) )
= $false )
| ( ( ord_less_eq_nat @ SV190 @ SV354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2696]) ).
thf(2796,plain,
! [SV513: nat,SV190: nat,SV501: nat,SV468: nat,SV354: nat] :
( ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV354 @ SV468 ) @ SV501 )
!= ( plus_plus_nat @ ( times_times_nat @ SV190 @ SV468 ) @ SV513 ) )
| ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV354 @ SV190 ) @ SV468 ) @ SV501 )
!= SV513 ) )
= $false )
| ( ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV354 @ SV190 ) @ SV468 ) @ SV501 )
= SV513 )
= $false )
| ( ( ord_less_eq_nat @ SV190 @ SV354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2697]) ).
thf(2797,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV194 )
= $false )
| ( ( ord_less_eq_nat @ SV358 @ SV471 )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2698]) ).
thf(2798,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ord_less_eq_nat @ ( times_times_nat @ SV194 @ SV358 ) @ ( times_times_nat @ SV194 @ SV471 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV194 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2699]) ).
thf(2799,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV194 )
| ( ord_less_eq_nat @ SV358 @ SV471 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV194 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2700]) ).
thf(2800,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV194 ) )
= $true )
| ( ( ord_less_eq_nat @ SV358 @ SV471 )
= $true )
| ( ( ord_less_eq_nat @ SV358 @ SV471 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2702]) ).
thf(2801,plain,
! [SV514: nat,SV361: nat,SV505: nat,SV474: nat,SV197: nat] :
( ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV197 @ SV474 ) @ SV505 )
!= ( plus_plus_nat @ ( times_times_nat @ SV361 @ SV474 ) @ SV514 ) )
| ( SV505
!= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV361 @ SV197 ) @ SV474 ) @ SV514 ) ) )
= $false )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SV197 @ SV474 ) @ SV505 )
= ( plus_plus_nat @ ( times_times_nat @ SV361 @ SV474 ) @ SV514 ) )
= $false )
| ( ( ord_less_eq_nat @ SV197 @ SV361 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2703]) ).
thf(2802,plain,
! [SV514: nat,SV361: nat,SV505: nat,SV474: nat,SV197: nat] :
( ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV197 @ SV474 ) @ SV505 )
!= ( plus_plus_nat @ ( times_times_nat @ SV361 @ SV474 ) @ SV514 ) )
| ( SV505
!= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV361 @ SV197 ) @ SV474 ) @ SV514 ) ) )
= $false )
| ( ( SV505
= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV361 @ SV197 ) @ SV474 ) @ SV514 ) )
= $false )
| ( ( ord_less_eq_nat @ SV197 @ SV361 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2704]) ).
thf(2803,plain,
! [SV481: nat,SV258: nat] :
( ( ( ord_less_nat @ SV258 @ SV481 )
= $true )
| ( ( SV258 = SV481 )
= $true )
| ( ( ord_less_nat @ SV258 @ SV481 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2712]) ).
thf(2804,plain,
! [SV481: nat,SV258: nat] :
( ( ( ord_less_nat @ SV258 @ SV481 )
= $true )
| ( ( SV258 = SV481 )
= $true )
| ( ( SV258 = SV481 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2714]) ).
thf(2805,plain,
! [SV402: nat,SV95: nat,SV265: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( minus_minus_nat @ SV265 @ SV95 ) @ ( minus_minus_nat @ SV265 @ SV402 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV265 @ SV95 ) @ ( minus_minus_nat @ SV265 @ SV402 ) )
= $false )
| ( ( ord_less_eq_nat @ SV402 @ SV265 )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2717]) ).
thf(2806,plain,
! [SV265: nat,SV95: nat,SV402: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV402 @ SV95 ) )
= $false )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV265 @ SV95 ) @ ( minus_minus_nat @ SV265 @ SV402 ) )
= $false )
| ( ( ord_less_eq_nat @ SV402 @ SV265 )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2717]) ).
thf(2807,plain,
! [SV402: nat,SV95: nat,SV265: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( minus_minus_nat @ SV265 @ SV95 ) @ ( minus_minus_nat @ SV265 @ SV402 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV402 @ SV95 )
= $false )
| ( ( ord_less_eq_nat @ SV402 @ SV265 )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2718]) ).
thf(2808,plain,
! [SV265: nat,SV95: nat,SV402: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV402 @ SV95 ) )
= $false )
| ( ( ord_less_eq_nat @ SV402 @ SV95 )
= $false )
| ( ( ord_less_eq_nat @ SV402 @ SV265 )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2718]) ).
thf(2809,plain,
! [SV507: nat,SV99: nat,SV484: nat,SV405: nat,SV269: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV269 @ SV405 ) @ SV484 ) @ ( plus_plus_nat @ ( times_times_nat @ SV99 @ SV405 ) @ SV507 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV269 @ SV405 ) @ SV484 ) @ ( plus_plus_nat @ ( times_times_nat @ SV99 @ SV405 ) @ SV507 ) )
= $false )
| ( ( ord_less_eq_nat @ SV99 @ SV269 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2719]) ).
thf(2810,plain,
! [SV507: nat,SV484: nat,SV405: nat,SV99: nat,SV269: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV269 @ SV99 ) @ SV405 ) @ SV484 ) @ SV507 ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV269 @ SV405 ) @ SV484 ) @ ( plus_plus_nat @ ( times_times_nat @ SV99 @ SV405 ) @ SV507 ) )
= $false )
| ( ( ord_less_eq_nat @ SV99 @ SV269 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2719]) ).
thf(2811,plain,
! [SV507: nat,SV99: nat,SV484: nat,SV405: nat,SV269: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV269 @ SV405 ) @ SV484 ) @ ( plus_plus_nat @ ( times_times_nat @ SV99 @ SV405 ) @ SV507 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV269 @ SV99 ) @ SV405 ) @ SV484 ) @ SV507 )
= $false )
| ( ( ord_less_eq_nat @ SV99 @ SV269 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2720]) ).
thf(2812,plain,
! [SV507: nat,SV484: nat,SV405: nat,SV99: nat,SV269: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV269 @ SV99 ) @ SV405 ) @ SV484 ) @ SV507 ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV269 @ SV99 ) @ SV405 ) @ SV484 ) @ SV507 )
= $false )
| ( ( ord_less_eq_nat @ SV99 @ SV269 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2720]) ).
thf(2813,plain,
! [SV413: nat,SV110: nat,SV279: nat] :
( ( ( ( minus_minus_nat @ SV279 @ SV110 )
!= ( minus_minus_nat @ SV413 @ SV110 ) )
= $false )
| ( ( ( minus_minus_nat @ SV279 @ SV110 )
= ( minus_minus_nat @ SV413 @ SV110 ) )
= $false )
| ( ( ord_less_eq_nat @ SV110 @ SV413 )
= $false )
| ( ( ord_less_eq_nat @ SV110 @ SV279 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2721]) ).
thf(2814,plain,
! [SV110: nat,SV413: nat,SV279: nat] :
( ( ( SV279 != SV413 )
= $false )
| ( ( ( minus_minus_nat @ SV279 @ SV110 )
= ( minus_minus_nat @ SV413 @ SV110 ) )
= $false )
| ( ( ord_less_eq_nat @ SV110 @ SV413 )
= $false )
| ( ( ord_less_eq_nat @ SV110 @ SV279 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2721]) ).
thf(2815,plain,
! [SV413: nat,SV110: nat,SV279: nat] :
( ( ( ( minus_minus_nat @ SV279 @ SV110 )
!= ( minus_minus_nat @ SV413 @ SV110 ) )
= $false )
| ( ( SV279 = SV413 )
= $false )
| ( ( ord_less_eq_nat @ SV110 @ SV413 )
= $false )
| ( ( ord_less_eq_nat @ SV110 @ SV279 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2722]) ).
thf(2816,plain,
! [SV110: nat,SV413: nat,SV279: nat] :
( ( ( SV279 != SV413 )
= $false )
| ( ( SV279 = SV413 )
= $false )
| ( ( ord_less_eq_nat @ SV110 @ SV413 )
= $false )
| ( ( ord_less_eq_nat @ SV110 @ SV279 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2722]) ).
thf(2817,plain,
! [SV114: nat > $o,SV283: nat,SV525: nat] :
( ( ( ~ ( ord_less_nat @ SV525 @ ( sK7_SY655 @ SV283 @ SV114 ) )
| ~ ~ ( SV114 @ SV525 ) )
= $true )
| ( ( SV114 @ SV283 )
= $true )
| ( ( SV114 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2727]) ).
thf(2818,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
= $true )
| ( ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2728]) ).
thf(2819,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) )
= $true )
| ( ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2729]) ).
thf(2820,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) )
= $false )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( ~ ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2730]) ).
thf(2821,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ( SV285
!= ( plus_plus_nat @ SV417 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
| ( SV117 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $false )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2731]) ).
thf(2822,plain,
! [SV288: nat,SV488: nat] :
( ( ( SV488
!= ( plus_plus_nat @ SV288 @ ( sK12_SY1033 @ SV288 @ SV488 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV288 @ SV488 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2732]) ).
thf(2823,plain,
! [SV521: nat,SV488: nat,SV288: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV288 @ SV488 ) )
= $false )
| ( ( SV488
= ( plus_plus_nat @ SV288 @ SV521 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2733]) ).
thf(2824,plain,
! [SV521: nat,SV288: nat,SV488: nat] :
( ( ( ~ ~ ! [SY1033: nat] :
( SV488
!= ( plus_plus_nat @ SV288 @ SY1033 ) ) )
= $false )
| ( ( SV488
= ( plus_plus_nat @ SV288 @ SV521 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2733]) ).
thf(2825,plain,
! [SV289: nat,SV489: nat] :
( ( ( SV489
!= ( plus_plus_nat @ SV289 @ ( sK13_SY1034 @ SV289 @ SV489 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV289 @ SV489 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2734]) ).
thf(2826,plain,
! [SV522: nat,SV489: nat,SV289: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV289 @ SV489 ) )
= $false )
| ( ( SV489
= ( plus_plus_nat @ SV289 @ SV522 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2735]) ).
thf(2827,plain,
! [SV522: nat,SV289: nat,SV489: nat] :
( ( ( ~ ~ ! [SY1034: nat] :
( SV489
!= ( plus_plus_nat @ SV289 @ SY1034 ) ) )
= $false )
| ( ( SV489
= ( plus_plus_nat @ SV289 @ SV522 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2735]) ).
thf(2828,plain,
! [SV294: nat,SV126: nat] :
( ( ( ( plus_plus_nat @ SV126 @ SV294 )
= zero_zero_nat )
= $true )
| ( ( SV126 = zero_zero_nat )
= $false )
| ( ( SV294 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2742]) ).
thf(2829,plain,
! [SV294: nat,SV126: nat] :
( ( ( ~ ( ( SV126 != zero_zero_nat )
| ( SV294 != zero_zero_nat ) ) )
= $true )
| ( ( SV126 = zero_zero_nat )
= $false )
| ( ( SV294 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2743]) ).
thf(2830,plain,
! [SV510: nat,SV295: nat,SV491: nat,SV425: nat,SV127: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV127 @ SV425 ) @ SV491 ) @ ( plus_plus_nat @ ( times_times_nat @ SV295 @ SV425 ) @ SV510 ) ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV127 @ SV425 ) @ SV491 ) @ ( plus_plus_nat @ ( times_times_nat @ SV295 @ SV425 ) @ SV510 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV295 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2744]) ).
thf(2831,plain,
! [SV510: nat,SV425: nat,SV127: nat,SV295: nat,SV491: nat] :
( ( ( ~ ( ord_less_nat @ SV491 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV295 @ SV127 ) @ SV425 ) @ SV510 ) ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV127 @ SV425 ) @ SV491 ) @ ( plus_plus_nat @ ( times_times_nat @ SV295 @ SV425 ) @ SV510 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV295 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2744]) ).
thf(2832,plain,
! [SV510: nat,SV295: nat,SV491: nat,SV425: nat,SV127: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV127 @ SV425 ) @ SV491 ) @ ( plus_plus_nat @ ( times_times_nat @ SV295 @ SV425 ) @ SV510 ) ) )
= $false )
| ( ( ord_less_nat @ SV491 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV295 @ SV127 ) @ SV425 ) @ SV510 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV295 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2745]) ).
thf(2833,plain,
! [SV510: nat,SV425: nat,SV127: nat,SV295: nat,SV491: nat] :
( ( ( ~ ( ord_less_nat @ SV491 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV295 @ SV127 ) @ SV425 ) @ SV510 ) ) )
= $false )
| ( ( ord_less_nat @ SV491 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV295 @ SV127 ) @ SV425 ) @ SV510 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV295 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2745]) ).
thf(2834,plain,
! [SV309: nat,SV516: nat,SV142: nat > $o] :
( ( ( ~ ( SV142 @ SV516 ) )
= $false )
| ( ( ord_less_nat @ SV516 @ ( sK1_SY712 @ SV309 @ SV142 ) )
= $false )
| ( ( SV142 @ SV309 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2746]) ).
thf(2835,plain,
! [SV511: nat,SV313: nat,SV494: nat,SV440: nat,SV146: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV146 @ SV440 ) @ SV494 ) @ ( plus_plus_nat @ ( times_times_nat @ SV313 @ SV440 ) @ SV511 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV146 @ SV440 ) @ SV494 ) @ ( plus_plus_nat @ ( times_times_nat @ SV313 @ SV440 ) @ SV511 ) )
= $false )
| ( ( ord_less_eq_nat @ SV146 @ SV313 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2747]) ).
thf(2836,plain,
! [SV511: nat,SV440: nat,SV146: nat,SV313: nat,SV494: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV494 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV313 @ SV146 ) @ SV440 ) @ SV511 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV146 @ SV440 ) @ SV494 ) @ ( plus_plus_nat @ ( times_times_nat @ SV313 @ SV440 ) @ SV511 ) )
= $false )
| ( ( ord_less_eq_nat @ SV146 @ SV313 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2747]) ).
thf(2837,plain,
! [SV511: nat,SV313: nat,SV494: nat,SV440: nat,SV146: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV146 @ SV440 ) @ SV494 ) @ ( plus_plus_nat @ ( times_times_nat @ SV313 @ SV440 ) @ SV511 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV494 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV313 @ SV146 ) @ SV440 ) @ SV511 ) )
= $false )
| ( ( ord_less_eq_nat @ SV146 @ SV313 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2748]) ).
thf(2838,plain,
! [SV511: nat,SV440: nat,SV146: nat,SV313: nat,SV494: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV494 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV313 @ SV146 ) @ SV440 ) @ SV511 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV494 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV313 @ SV146 ) @ SV440 ) @ SV511 ) )
= $false )
| ( ( ord_less_eq_nat @ SV146 @ SV313 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2748]) ).
thf(2839,plain,
! [SV444: nat,SV152: nat,SV318: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV318 )
= $true )
| ( ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2749]) ).
thf(2840,plain,
! [SV318: nat,SV444: nat,SV152: nat] :
( ( ( ord_less_nat @ SV152 @ SV444 )
= $true )
| ( ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2750]) ).
thf(2841,plain,
! [SV444: nat,SV318: nat,SV152: nat] :
( ( ( ~ ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV318 )
= $false )
| ( ( ord_less_nat @ SV152 @ SV444 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2751]) ).
thf(2842,plain,
! [SV444: nat,SV152: nat,SV318: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV318 )
| ~ ( ord_less_nat @ SV152 @ SV444 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV318 )
= $false )
| ( ( ord_less_nat @ SV152 @ SV444 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2751]) ).
thf(2843,plain,
! [SV325: nat,SV159: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV159 @ SV325 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV159 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV325 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2754]) ).
thf(2844,plain,
! [SV325: nat,SV159: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV159 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV325 ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV159 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV325 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2755]) ).
thf(2845,plain,
! [SV326: nat,SV160: nat] :
( ( ( ( plus_plus_nat @ SV160 @ SV326 )
= zero_zero_nat )
= $true )
| ( ( SV160 = zero_zero_nat )
= $false )
| ( ( SV326 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2758]) ).
thf(2846,plain,
! [SV326: nat,SV160: nat] :
( ( ( ~ ( ( SV160 != zero_zero_nat )
| ( SV326 != zero_zero_nat ) ) )
= $true )
| ( ( SV160 = zero_zero_nat )
= $false )
| ( ( SV326 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2759]) ).
thf(2847,plain,
! [SV497: nat,SV327: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV327 @ SV497 ) )
= $false )
| ( ( ord_less_nat @ SV327 @ SV497 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2760]) ).
thf(2848,plain,
! [SV497: nat,SV327: nat] :
( ( ( ~ ( ( SV327 != SV497 ) ) )
= $false )
| ( ( ord_less_nat @ SV327 @ SV497 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2760]) ).
thf(2849,plain,
! [SV497: nat,SV327: nat] :
( ( ( SV327 = SV497 )
= $true )
| ( ( ord_less_eq_nat @ SV327 @ SV497 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV327 @ SV497 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV327 @ SV497 )
| ~ ( ( SV327 != SV497 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2761]) ).
thf(2850,plain,
! [SV328: nat,SV162: nat] :
( ( ( zero_zero_nat
= ( plus_plus_nat @ SV162 @ SV328 ) )
= $true )
| ( ( SV162 = zero_zero_nat )
= $false )
| ( ( SV328 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2764]) ).
thf(2851,plain,
! [SV328: nat,SV162: nat] :
( ( ( ~ ( ( SV162 != zero_zero_nat )
| ( SV328 != zero_zero_nat ) ) )
= $true )
| ( ( SV162 = zero_zero_nat )
= $false )
| ( ( SV328 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2765]) ).
thf(2852,plain,
! [SV448: nat,SV163: nat,SV329: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV329 ) )
= $true )
| ( ( ord_less_eq_nat @ SV163 @ SV448 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV329 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2768]) ).
thf(2853,plain,
! [SV448: nat,SV163: nat,SV329: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV329 )
= $false )
| ( ( ord_less_eq_nat @ SV163 @ SV448 )
= $true )
| ( ( ord_less_eq_nat @ SV163 @ SV448 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2769]) ).
thf(2854,plain,
! [SV330: nat,SV449: nat,SV164: nat > $o] :
( ( ( ~ ( ~ ( SV164 @ ( sK10_SY751 @ SV449 @ SV330 @ SV164 ) )
| ~ ! [SY1046: nat] :
( ~ ( SV164 @ SY1046 )
| ( ord_less_eq_nat @ SY1046 @ ( sK10_SY751 @ SV449 @ SV330 @ SV164 ) ) ) ) )
= $true )
| ( ( SV164 @ ( sK8_SY1015 @ SV330 @ SV449 @ SV164 ) )
= $true )
| ( ( SV164 @ SV330 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2770]) ).
thf(2855,plain,
! [SV330: nat,SV449: nat,SV164: nat > $o] :
( ( ( ~ ( SV164 @ ( sK9_SY751 @ SV449 @ SV330 @ SV164 ) )
| ~ ! [SY1045: nat] :
( ~ ( SV164 @ SY1045 )
| ( ord_less_eq_nat @ SY1045 @ ( sK9_SY751 @ SV449 @ SV330 @ SV164 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK8_SY1015 @ SV330 @ SV449 @ SV164 ) @ SV449 )
= $false )
| ( ( SV164 @ SV330 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2771]) ).
thf(2856,plain,
! [SV451: nat,SV167: nat,SV332: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( minus_minus_nat @ SV332 @ SV167 ) @ ( minus_minus_nat @ SV451 @ SV167 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV332 @ SV167 ) @ ( minus_minus_nat @ SV451 @ SV167 ) )
= $false )
| ( ( ord_less_eq_nat @ SV167 @ SV451 )
= $false )
| ( ( ord_less_eq_nat @ SV167 @ SV332 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2772]) ).
thf(2857,plain,
! [SV167: nat,SV451: nat,SV332: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV332 @ SV451 ) )
= $false )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV332 @ SV167 ) @ ( minus_minus_nat @ SV451 @ SV167 ) )
= $false )
| ( ( ord_less_eq_nat @ SV167 @ SV451 )
= $false )
| ( ( ord_less_eq_nat @ SV167 @ SV332 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2772]) ).
thf(2858,plain,
! [SV451: nat,SV167: nat,SV332: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( minus_minus_nat @ SV332 @ SV167 ) @ ( minus_minus_nat @ SV451 @ SV167 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV332 @ SV451 )
= $false )
| ( ( ord_less_eq_nat @ SV167 @ SV451 )
= $false )
| ( ( ord_less_eq_nat @ SV167 @ SV332 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2773]) ).
thf(2859,plain,
! [SV167: nat,SV451: nat,SV332: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV332 @ SV451 ) )
= $false )
| ( ( ord_less_eq_nat @ SV332 @ SV451 )
= $false )
| ( ( ord_less_eq_nat @ SV167 @ SV451 )
= $false )
| ( ( ord_less_eq_nat @ SV167 @ SV332 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2773]) ).
thf(2860,plain,
! [SV512: nat,SV174: nat,SV499: nat,SV457: nat,SV338: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV338 @ SV457 ) @ SV499 ) @ ( plus_plus_nat @ ( times_times_nat @ SV174 @ SV457 ) @ SV512 ) ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV338 @ SV457 ) @ SV499 ) @ ( plus_plus_nat @ ( times_times_nat @ SV174 @ SV457 ) @ SV512 ) )
= $false )
| ( ( ord_less_eq_nat @ SV174 @ SV338 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2778]) ).
thf(2861,plain,
! [SV512: nat,SV499: nat,SV457: nat,SV174: nat,SV338: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV338 @ SV174 ) @ SV457 ) @ SV499 ) @ SV512 ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV338 @ SV457 ) @ SV499 ) @ ( plus_plus_nat @ ( times_times_nat @ SV174 @ SV457 ) @ SV512 ) )
= $false )
| ( ( ord_less_eq_nat @ SV174 @ SV338 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2778]) ).
thf(2862,plain,
! [SV512: nat,SV174: nat,SV499: nat,SV457: nat,SV338: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV338 @ SV457 ) @ SV499 ) @ ( plus_plus_nat @ ( times_times_nat @ SV174 @ SV457 ) @ SV512 ) ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV338 @ SV174 ) @ SV457 ) @ SV499 ) @ SV512 )
= $false )
| ( ( ord_less_eq_nat @ SV174 @ SV338 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2779]) ).
thf(2863,plain,
! [SV512: nat,SV499: nat,SV457: nat,SV174: nat,SV338: nat] :
( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV338 @ SV174 ) @ SV457 ) @ SV499 ) @ SV512 ) )
= $false )
| ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV338 @ SV174 ) @ SV457 ) @ SV499 ) @ SV512 )
= $false )
| ( ( ord_less_eq_nat @ SV174 @ SV338 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2779]) ).
thf(2864,plain,
! [SV459: nat,SV341: nat,SV177: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV177 )
= $true )
| ( ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2780]) ).
thf(2865,plain,
! [SV177: nat,SV459: nat,SV341: nat] :
( ( ( ord_less_nat @ SV341 @ SV459 )
= $true )
| ( ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2781]) ).
thf(2866,plain,
! [SV459: nat,SV341: nat,SV177: nat] :
( ( ( ~ ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV177 )
= $false )
| ( ( ord_less_nat @ SV341 @ SV459 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2782]) ).
thf(2867,plain,
! [SV459: nat,SV341: nat,SV177: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 )
| ~ ( ord_less_nat @ SV341 @ SV459 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV177 )
= $false )
| ( ( ord_less_nat @ SV341 @ SV459 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2782]) ).
thf(2868,plain,
! [SV461: nat,SV182: nat,SV346: nat] :
( ( ( ( minus_minus_nat @ SV346 @ SV182 )
!= SV461 )
= $false )
| ( ( ( minus_minus_nat @ SV346 @ SV182 )
= SV461 )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2783]) ).
thf(2869,plain,
! [SV182: nat,SV461: nat,SV346: nat] :
( ( ( SV346
!= ( plus_plus_nat @ SV461 @ SV182 ) )
= $false )
| ( ( ( minus_minus_nat @ SV346 @ SV182 )
= SV461 )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2783]) ).
thf(2870,plain,
! [SV461: nat,SV182: nat,SV346: nat] :
( ( ( ( minus_minus_nat @ SV346 @ SV182 )
!= SV461 )
= $false )
| ( ( SV346
= ( plus_plus_nat @ SV461 @ SV182 ) )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2784]) ).
thf(2871,plain,
! [SV182: nat,SV461: nat,SV346: nat] :
( ( ( SV346
!= ( plus_plus_nat @ SV461 @ SV182 ) )
= $false )
| ( ( SV346
= ( plus_plus_nat @ SV461 @ SV182 ) )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2784]) ).
thf(2872,plain,
! [SV463: nat,SV184: nat,SV348: nat] :
( ( ( ~ ( ord_less_nat @ ( minus_minus_nat @ SV348 @ SV184 ) @ ( minus_minus_nat @ SV463 @ SV184 ) ) )
= $false )
| ( ( ord_less_nat @ ( minus_minus_nat @ SV348 @ SV184 ) @ ( minus_minus_nat @ SV463 @ SV184 ) )
= $false )
| ( ( ord_less_eq_nat @ SV184 @ SV463 )
= $false )
| ( ( ord_less_eq_nat @ SV184 @ SV348 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2785]) ).
thf(2873,plain,
! [SV184: nat,SV463: nat,SV348: nat] :
( ( ( ~ ( ord_less_nat @ SV348 @ SV463 ) )
= $false )
| ( ( ord_less_nat @ ( minus_minus_nat @ SV348 @ SV184 ) @ ( minus_minus_nat @ SV463 @ SV184 ) )
= $false )
| ( ( ord_less_eq_nat @ SV184 @ SV463 )
= $false )
| ( ( ord_less_eq_nat @ SV184 @ SV348 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2785]) ).
thf(2874,plain,
! [SV463: nat,SV184: nat,SV348: nat] :
( ( ( ~ ( ord_less_nat @ ( minus_minus_nat @ SV348 @ SV184 ) @ ( minus_minus_nat @ SV463 @ SV184 ) ) )
= $false )
| ( ( ord_less_nat @ SV348 @ SV463 )
= $false )
| ( ( ord_less_eq_nat @ SV184 @ SV463 )
= $false )
| ( ( ord_less_eq_nat @ SV184 @ SV348 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2786]) ).
thf(2875,plain,
! [SV184: nat,SV463: nat,SV348: nat] :
( ( ( ~ ( ord_less_nat @ SV348 @ SV463 ) )
= $false )
| ( ( ord_less_nat @ SV348 @ SV463 )
= $false )
| ( ( ord_less_eq_nat @ SV184 @ SV463 )
= $false )
| ( ( ord_less_eq_nat @ SV184 @ SV348 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2786]) ).
thf(2876,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
= $true )
| ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2791]) ).
thf(2877,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) )
= $true )
| ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2792]) ).
thf(2878,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2793]) ).
thf(2879,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) )
= $true )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2794]) ).
thf(2880,plain,
! [SV513: nat,SV190: nat,SV501: nat,SV468: nat,SV354: nat] :
( ( ( ( plus_plus_nat @ ( times_times_nat @ SV354 @ SV468 ) @ SV501 )
!= ( plus_plus_nat @ ( times_times_nat @ SV190 @ SV468 ) @ SV513 ) )
= $false )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SV354 @ SV468 ) @ SV501 )
= ( plus_plus_nat @ ( times_times_nat @ SV190 @ SV468 ) @ SV513 ) )
= $false )
| ( ( ord_less_eq_nat @ SV190 @ SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2795]) ).
thf(2881,plain,
! [SV513: nat,SV501: nat,SV468: nat,SV190: nat,SV354: nat] :
( ( ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV354 @ SV190 ) @ SV468 ) @ SV501 )
!= SV513 )
= $false )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SV354 @ SV468 ) @ SV501 )
= ( plus_plus_nat @ ( times_times_nat @ SV190 @ SV468 ) @ SV513 ) )
= $false )
| ( ( ord_less_eq_nat @ SV190 @ SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2795]) ).
thf(2882,plain,
! [SV513: nat,SV190: nat,SV501: nat,SV468: nat,SV354: nat] :
( ( ( ( plus_plus_nat @ ( times_times_nat @ SV354 @ SV468 ) @ SV501 )
!= ( plus_plus_nat @ ( times_times_nat @ SV190 @ SV468 ) @ SV513 ) )
= $false )
| ( ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV354 @ SV190 ) @ SV468 ) @ SV501 )
= SV513 )
= $false )
| ( ( ord_less_eq_nat @ SV190 @ SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2796]) ).
thf(2883,plain,
! [SV513: nat,SV501: nat,SV468: nat,SV190: nat,SV354: nat] :
( ( ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV354 @ SV190 ) @ SV468 ) @ SV501 )
!= SV513 )
= $false )
| ( ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV354 @ SV190 ) @ SV468 ) @ SV501 )
= SV513 )
= $false )
| ( ( ord_less_eq_nat @ SV190 @ SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2796]) ).
thf(2884,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV194 ) )
= $true )
| ( ( ord_less_eq_nat @ SV358 @ SV471 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV194 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2799]) ).
thf(2885,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV194 )
= $false )
| ( ( ord_less_eq_nat @ SV358 @ SV471 )
= $true )
| ( ( ord_less_eq_nat @ SV358 @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2800]) ).
thf(2886,plain,
! [SV514: nat,SV361: nat,SV505: nat,SV474: nat,SV197: nat] :
( ( ( ( plus_plus_nat @ ( times_times_nat @ SV197 @ SV474 ) @ SV505 )
!= ( plus_plus_nat @ ( times_times_nat @ SV361 @ SV474 ) @ SV514 ) )
= $false )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SV197 @ SV474 ) @ SV505 )
= ( plus_plus_nat @ ( times_times_nat @ SV361 @ SV474 ) @ SV514 ) )
= $false )
| ( ( ord_less_eq_nat @ SV197 @ SV361 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2801]) ).
thf(2887,plain,
! [SV514: nat,SV474: nat,SV197: nat,SV361: nat,SV505: nat] :
( ( ( SV505
!= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV361 @ SV197 ) @ SV474 ) @ SV514 ) )
= $false )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SV197 @ SV474 ) @ SV505 )
= ( plus_plus_nat @ ( times_times_nat @ SV361 @ SV474 ) @ SV514 ) )
= $false )
| ( ( ord_less_eq_nat @ SV197 @ SV361 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2801]) ).
thf(2888,plain,
! [SV514: nat,SV361: nat,SV505: nat,SV474: nat,SV197: nat] :
( ( ( ( plus_plus_nat @ ( times_times_nat @ SV197 @ SV474 ) @ SV505 )
!= ( plus_plus_nat @ ( times_times_nat @ SV361 @ SV474 ) @ SV514 ) )
= $false )
| ( ( SV505
= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV361 @ SV197 ) @ SV474 ) @ SV514 ) )
= $false )
| ( ( ord_less_eq_nat @ SV197 @ SV361 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2802]) ).
thf(2889,plain,
! [SV514: nat,SV474: nat,SV197: nat,SV361: nat,SV505: nat] :
( ( ( SV505
!= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV361 @ SV197 ) @ SV474 ) @ SV514 ) )
= $false )
| ( ( SV505
= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV361 @ SV197 ) @ SV474 ) @ SV514 ) )
= $false )
| ( ( ord_less_eq_nat @ SV197 @ SV361 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2802]) ).
thf(2890,plain,
! [SV402: nat,SV95: nat,SV265: nat] :
( ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV265 @ SV95 ) @ ( minus_minus_nat @ SV265 @ SV402 ) )
= $true )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV265 @ SV95 ) @ ( minus_minus_nat @ SV265 @ SV402 ) )
= $false )
| ( ( ord_less_eq_nat @ SV402 @ SV265 )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2805]) ).
thf(2891,plain,
! [SV265: nat,SV95: nat,SV402: nat] :
( ( ( ord_less_eq_nat @ SV402 @ SV95 )
= $true )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV265 @ SV95 ) @ ( minus_minus_nat @ SV265 @ SV402 ) )
= $false )
| ( ( ord_less_eq_nat @ SV402 @ SV265 )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2806]) ).
thf(2892,plain,
! [SV402: nat,SV95: nat,SV265: nat] :
( ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV265 @ SV95 ) @ ( minus_minus_nat @ SV265 @ SV402 ) )
= $true )
| ( ( ord_less_eq_nat @ SV402 @ SV95 )
= $false )
| ( ( ord_less_eq_nat @ SV402 @ SV265 )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2807]) ).
thf(2893,plain,
! [SV265: nat,SV95: nat,SV402: nat] :
( ( ( ord_less_eq_nat @ SV402 @ SV95 )
= $true )
| ( ( ord_less_eq_nat @ SV402 @ SV95 )
= $false )
| ( ( ord_less_eq_nat @ SV402 @ SV265 )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2808]) ).
thf(2894,plain,
! [SV507: nat,SV99: nat,SV484: nat,SV405: nat,SV269: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV269 @ SV405 ) @ SV484 ) @ ( plus_plus_nat @ ( times_times_nat @ SV99 @ SV405 ) @ SV507 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV269 @ SV405 ) @ SV484 ) @ ( plus_plus_nat @ ( times_times_nat @ SV99 @ SV405 ) @ SV507 ) )
= $false )
| ( ( ord_less_eq_nat @ SV99 @ SV269 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2809]) ).
thf(2895,plain,
! [SV507: nat,SV484: nat,SV405: nat,SV99: nat,SV269: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV269 @ SV99 ) @ SV405 ) @ SV484 ) @ SV507 )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV269 @ SV405 ) @ SV484 ) @ ( plus_plus_nat @ ( times_times_nat @ SV99 @ SV405 ) @ SV507 ) )
= $false )
| ( ( ord_less_eq_nat @ SV99 @ SV269 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2810]) ).
thf(2896,plain,
! [SV507: nat,SV99: nat,SV484: nat,SV405: nat,SV269: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV269 @ SV405 ) @ SV484 ) @ ( plus_plus_nat @ ( times_times_nat @ SV99 @ SV405 ) @ SV507 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV269 @ SV99 ) @ SV405 ) @ SV484 ) @ SV507 )
= $false )
| ( ( ord_less_eq_nat @ SV99 @ SV269 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2811]) ).
thf(2897,plain,
! [SV507: nat,SV484: nat,SV405: nat,SV99: nat,SV269: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV269 @ SV99 ) @ SV405 ) @ SV484 ) @ SV507 )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV269 @ SV99 ) @ SV405 ) @ SV484 ) @ SV507 )
= $false )
| ( ( ord_less_eq_nat @ SV99 @ SV269 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2812]) ).
thf(2898,plain,
! [SV413: nat,SV110: nat,SV279: nat] :
( ( ( ( minus_minus_nat @ SV279 @ SV110 )
= ( minus_minus_nat @ SV413 @ SV110 ) )
= $true )
| ( ( ( minus_minus_nat @ SV279 @ SV110 )
= ( minus_minus_nat @ SV413 @ SV110 ) )
= $false )
| ( ( ord_less_eq_nat @ SV110 @ SV413 )
= $false )
| ( ( ord_less_eq_nat @ SV110 @ SV279 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2813]) ).
thf(2899,plain,
! [SV110: nat,SV413: nat,SV279: nat] :
( ( ( SV279 = SV413 )
= $true )
| ( ( ( minus_minus_nat @ SV279 @ SV110 )
= ( minus_minus_nat @ SV413 @ SV110 ) )
= $false )
| ( ( ord_less_eq_nat @ SV110 @ SV413 )
= $false )
| ( ( ord_less_eq_nat @ SV110 @ SV279 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2814]) ).
thf(2900,plain,
! [SV413: nat,SV110: nat,SV279: nat] :
( ( ( ( minus_minus_nat @ SV279 @ SV110 )
= ( minus_minus_nat @ SV413 @ SV110 ) )
= $true )
| ( ( SV279 = SV413 )
= $false )
| ( ( ord_less_eq_nat @ SV110 @ SV413 )
= $false )
| ( ( ord_less_eq_nat @ SV110 @ SV279 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2815]) ).
thf(2901,plain,
! [SV110: nat,SV413: nat,SV279: nat] :
( ( ( SV279 = SV413 )
= $true )
| ( ( SV279 = SV413 )
= $false )
| ( ( ord_less_eq_nat @ SV110 @ SV413 )
= $false )
| ( ( ord_less_eq_nat @ SV110 @ SV279 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2816]) ).
thf(2902,plain,
! [SV114: nat > $o,SV283: nat,SV525: nat] :
( ( ( ~ ( ord_less_nat @ SV525 @ ( sK7_SY655 @ SV283 @ SV114 ) ) )
= $true )
| ( ( ~ ~ ( SV114 @ SV525 ) )
= $true )
| ( ( SV114 @ SV283 )
= $true )
| ( ( SV114 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2817]) ).
thf(2903,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ord_less_nat @ SV285 @ SV417 ) )
= $true )
| ( ( SV117 @ zero_zero_nat )
= $true )
| ( ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2818]) ).
thf(2904,plain,
! [SV117: nat > $o,SV527: nat,SV417: nat,SV285: nat] :
( ( ( ( SV285
!= ( plus_plus_nat @ SV417 @ SV527 ) )
| ( SV117 @ SV527 ) )
= $true )
| ( ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2819]) ).
thf(2905,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ( SV285
!= ( plus_plus_nat @ SV417 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
| ( SV117 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $false )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( ~ ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2820]) ).
thf(2906,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( SV285
!= ( plus_plus_nat @ SV417 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $false )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2821]) ).
thf(2907,plain,
! [SV285: nat,SV417: nat,SV117: nat > $o] :
( ( ( SV117 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2821]) ).
thf(2908,plain,
! [SV288: nat,SV488: nat] :
( ( ( SV488
= ( plus_plus_nat @ SV288 @ ( sK12_SY1033 @ SV288 @ SV488 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV288 @ SV488 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2822]) ).
thf(2909,plain,
! [SV521: nat,SV488: nat,SV288: nat] :
( ( ( ord_less_eq_nat @ SV288 @ SV488 )
= $true )
| ( ( SV488
= ( plus_plus_nat @ SV288 @ SV521 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2823]) ).
thf(2910,plain,
! [SV521: nat,SV288: nat,SV488: nat] :
( ( ( ~ ! [SY1033: nat] :
( SV488
!= ( plus_plus_nat @ SV288 @ SY1033 ) ) )
= $true )
| ( ( SV488
= ( plus_plus_nat @ SV288 @ SV521 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2824]) ).
thf(2911,plain,
! [SV289: nat,SV489: nat] :
( ( ( SV489
= ( plus_plus_nat @ SV289 @ ( sK13_SY1034 @ SV289 @ SV489 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV289 @ SV489 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2825]) ).
thf(2912,plain,
! [SV522: nat,SV489: nat,SV289: nat] :
( ( ( ord_less_eq_nat @ SV289 @ SV489 )
= $true )
| ( ( SV489
= ( plus_plus_nat @ SV289 @ SV522 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2826]) ).
thf(2913,plain,
! [SV522: nat,SV289: nat,SV489: nat] :
( ( ( ~ ! [SY1034: nat] :
( SV489
!= ( plus_plus_nat @ SV289 @ SY1034 ) ) )
= $true )
| ( ( SV489
= ( plus_plus_nat @ SV289 @ SV522 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2827]) ).
thf(2914,plain,
! [SV294: nat,SV126: nat] :
( ( ( ( SV126 != zero_zero_nat )
| ( SV294 != zero_zero_nat ) )
= $false )
| ( ( SV126 = zero_zero_nat )
= $false )
| ( ( SV294 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2829]) ).
thf(2915,plain,
! [SV510: nat,SV295: nat,SV491: nat,SV425: nat,SV127: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV127 @ SV425 ) @ SV491 ) @ ( plus_plus_nat @ ( times_times_nat @ SV295 @ SV425 ) @ SV510 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV127 @ SV425 ) @ SV491 ) @ ( plus_plus_nat @ ( times_times_nat @ SV295 @ SV425 ) @ SV510 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV295 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2830]) ).
thf(2916,plain,
! [SV510: nat,SV425: nat,SV127: nat,SV295: nat,SV491: nat] :
( ( ( ord_less_nat @ SV491 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV295 @ SV127 ) @ SV425 ) @ SV510 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV127 @ SV425 ) @ SV491 ) @ ( plus_plus_nat @ ( times_times_nat @ SV295 @ SV425 ) @ SV510 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV295 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2831]) ).
thf(2917,plain,
! [SV510: nat,SV295: nat,SV491: nat,SV425: nat,SV127: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV127 @ SV425 ) @ SV491 ) @ ( plus_plus_nat @ ( times_times_nat @ SV295 @ SV425 ) @ SV510 ) )
= $true )
| ( ( ord_less_nat @ SV491 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV295 @ SV127 ) @ SV425 ) @ SV510 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV295 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2832]) ).
thf(2918,plain,
! [SV510: nat,SV425: nat,SV127: nat,SV295: nat,SV491: nat] :
( ( ( ord_less_nat @ SV491 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV295 @ SV127 ) @ SV425 ) @ SV510 ) )
= $true )
| ( ( ord_less_nat @ SV491 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV295 @ SV127 ) @ SV425 ) @ SV510 ) )
= $false )
| ( ( ord_less_eq_nat @ SV127 @ SV295 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2833]) ).
thf(2919,plain,
! [SV309: nat,SV516: nat,SV142: nat > $o] :
( ( ( SV142 @ SV516 )
= $true )
| ( ( ord_less_nat @ SV516 @ ( sK1_SY712 @ SV309 @ SV142 ) )
= $false )
| ( ( SV142 @ SV309 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2834]) ).
thf(2920,plain,
! [SV511: nat,SV313: nat,SV494: nat,SV440: nat,SV146: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV146 @ SV440 ) @ SV494 ) @ ( plus_plus_nat @ ( times_times_nat @ SV313 @ SV440 ) @ SV511 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV146 @ SV440 ) @ SV494 ) @ ( plus_plus_nat @ ( times_times_nat @ SV313 @ SV440 ) @ SV511 ) )
= $false )
| ( ( ord_less_eq_nat @ SV146 @ SV313 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2835]) ).
thf(2921,plain,
! [SV511: nat,SV440: nat,SV146: nat,SV313: nat,SV494: nat] :
( ( ( ord_less_eq_nat @ SV494 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV313 @ SV146 ) @ SV440 ) @ SV511 ) )
= $true )
| ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV146 @ SV440 ) @ SV494 ) @ ( plus_plus_nat @ ( times_times_nat @ SV313 @ SV440 ) @ SV511 ) )
= $false )
| ( ( ord_less_eq_nat @ SV146 @ SV313 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2836]) ).
thf(2922,plain,
! [SV511: nat,SV313: nat,SV494: nat,SV440: nat,SV146: nat] :
( ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ SV146 @ SV440 ) @ SV494 ) @ ( plus_plus_nat @ ( times_times_nat @ SV313 @ SV440 ) @ SV511 ) )
= $true )
| ( ( ord_less_eq_nat @ SV494 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV313 @ SV146 ) @ SV440 ) @ SV511 ) )
= $false )
| ( ( ord_less_eq_nat @ SV146 @ SV313 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2837]) ).
thf(2923,plain,
! [SV511: nat,SV440: nat,SV146: nat,SV313: nat,SV494: nat] :
( ( ( ord_less_eq_nat @ SV494 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV313 @ SV146 ) @ SV440 ) @ SV511 ) )
= $true )
| ( ( ord_less_eq_nat @ SV494 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV313 @ SV146 ) @ SV440 ) @ SV511 ) )
= $false )
| ( ( ord_less_eq_nat @ SV146 @ SV313 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2838]) ).
thf(2924,plain,
! [SV444: nat,SV318: nat,SV152: nat] :
( ( ( ord_less_nat @ ( times_times_nat @ SV152 @ SV318 ) @ ( times_times_nat @ SV444 @ SV318 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV318 )
= $false )
| ( ( ord_less_nat @ SV152 @ SV444 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2841]) ).
thf(2925,plain,
! [SV444: nat,SV152: nat,SV318: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV318 )
| ~ ( ord_less_nat @ SV152 @ SV444 ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV318 )
= $false )
| ( ( ord_less_nat @ SV152 @ SV444 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2842]) ).
thf(2926,plain,
! [SV325: nat,SV159: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV159 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV325 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV159 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV325 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2844]) ).
thf(2927,plain,
! [SV326: nat,SV160: nat] :
( ( ( ( SV160 != zero_zero_nat )
| ( SV326 != zero_zero_nat ) )
= $false )
| ( ( SV160 = zero_zero_nat )
= $false )
| ( ( SV326 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2846]) ).
thf(2928,plain,
! [SV497: nat,SV327: nat] :
( ( ( ord_less_eq_nat @ SV327 @ SV497 )
= $true )
| ( ( ord_less_nat @ SV327 @ SV497 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2847]) ).
thf(2929,plain,
! [SV497: nat,SV327: nat] :
( ( ( SV327 != SV497 )
= $true )
| ( ( ord_less_nat @ SV327 @ SV497 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2848]) ).
thf(2930,plain,
! [SV497: nat,SV327: nat] :
( ( ( ~ ( ord_less_nat @ SV327 @ SV497 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV327 @ SV497 )
| ~ ( ( SV327 != SV497 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV327 @ SV497 )
= $false )
| ( ( SV327 = SV497 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2849]) ).
thf(2931,plain,
! [SV328: nat,SV162: nat] :
( ( ( ( SV162 != zero_zero_nat )
| ( SV328 != zero_zero_nat ) )
= $false )
| ( ( SV162 = zero_zero_nat )
= $false )
| ( ( SV328 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2851]) ).
thf(2932,plain,
! [SV448: nat,SV163: nat,SV329: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV329 )
= $false )
| ( ( ord_less_eq_nat @ SV163 @ SV448 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV329 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2852]) ).
thf(2933,plain,
! [SV330: nat,SV449: nat,SV164: nat > $o] :
( ( ( ~ ( SV164 @ ( sK10_SY751 @ SV449 @ SV330 @ SV164 ) )
| ~ ! [SY1046: nat] :
( ~ ( SV164 @ SY1046 )
| ( ord_less_eq_nat @ SY1046 @ ( sK10_SY751 @ SV449 @ SV330 @ SV164 ) ) ) )
= $false )
| ( ( SV164 @ ( sK8_SY1015 @ SV330 @ SV449 @ SV164 ) )
= $true )
| ( ( SV164 @ SV330 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2854]) ).
thf(2934,plain,
! [SV330: nat,SV449: nat,SV164: nat > $o] :
( ( ( ~ ( SV164 @ ( sK9_SY751 @ SV449 @ SV330 @ SV164 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK8_SY1015 @ SV330 @ SV449 @ SV164 ) @ SV449 )
= $false )
| ( ( SV164 @ SV330 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2855]) ).
thf(2935,plain,
! [SV330: nat,SV449: nat,SV164: nat > $o] :
( ( ( ~ ! [SY1045: nat] :
( ~ ( SV164 @ SY1045 )
| ( ord_less_eq_nat @ SY1045 @ ( sK9_SY751 @ SV449 @ SV330 @ SV164 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK8_SY1015 @ SV330 @ SV449 @ SV164 ) @ SV449 )
= $false )
| ( ( SV164 @ SV330 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2855]) ).
thf(2936,plain,
! [SV451: nat,SV167: nat,SV332: nat] :
( ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV332 @ SV167 ) @ ( minus_minus_nat @ SV451 @ SV167 ) )
= $true )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV332 @ SV167 ) @ ( minus_minus_nat @ SV451 @ SV167 ) )
= $false )
| ( ( ord_less_eq_nat @ SV167 @ SV451 )
= $false )
| ( ( ord_less_eq_nat @ SV167 @ SV332 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2856]) ).
thf(2937,plain,
! [SV167: nat,SV451: nat,SV332: nat] :
( ( ( ord_less_eq_nat @ SV332 @ SV451 )
= $true )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV332 @ SV167 ) @ ( minus_minus_nat @ SV451 @ SV167 ) )
= $false )
| ( ( ord_less_eq_nat @ SV167 @ SV451 )
= $false )
| ( ( ord_less_eq_nat @ SV167 @ SV332 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2857]) ).
thf(2938,plain,
! [SV451: nat,SV167: nat,SV332: nat] :
( ( ( ord_less_eq_nat @ ( minus_minus_nat @ SV332 @ SV167 ) @ ( minus_minus_nat @ SV451 @ SV167 ) )
= $true )
| ( ( ord_less_eq_nat @ SV332 @ SV451 )
= $false )
| ( ( ord_less_eq_nat @ SV167 @ SV451 )
= $false )
| ( ( ord_less_eq_nat @ SV167 @ SV332 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2858]) ).
thf(2939,plain,
! [SV167: nat,SV451: nat,SV332: nat] :
( ( ( ord_less_eq_nat @ SV332 @ SV451 )
= $true )
| ( ( ord_less_eq_nat @ SV332 @ SV451 )
= $false )
| ( ( ord_less_eq_nat @ SV167 @ SV451 )
= $false )
| ( ( ord_less_eq_nat @ SV167 @ SV332 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2859]) ).
thf(2940,plain,
! [SV512: nat,SV174: nat,SV499: nat,SV457: nat,SV338: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV338 @ SV457 ) @ SV499 ) @ ( plus_plus_nat @ ( times_times_nat @ SV174 @ SV457 ) @ SV512 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV338 @ SV457 ) @ SV499 ) @ ( plus_plus_nat @ ( times_times_nat @ SV174 @ SV457 ) @ SV512 ) )
= $false )
| ( ( ord_less_eq_nat @ SV174 @ SV338 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2860]) ).
thf(2941,plain,
! [SV512: nat,SV499: nat,SV457: nat,SV174: nat,SV338: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV338 @ SV174 ) @ SV457 ) @ SV499 ) @ SV512 )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV338 @ SV457 ) @ SV499 ) @ ( plus_plus_nat @ ( times_times_nat @ SV174 @ SV457 ) @ SV512 ) )
= $false )
| ( ( ord_less_eq_nat @ SV174 @ SV338 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2861]) ).
thf(2942,plain,
! [SV512: nat,SV174: nat,SV499: nat,SV457: nat,SV338: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ SV338 @ SV457 ) @ SV499 ) @ ( plus_plus_nat @ ( times_times_nat @ SV174 @ SV457 ) @ SV512 ) )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV338 @ SV174 ) @ SV457 ) @ SV499 ) @ SV512 )
= $false )
| ( ( ord_less_eq_nat @ SV174 @ SV338 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2862]) ).
thf(2943,plain,
! [SV512: nat,SV499: nat,SV457: nat,SV174: nat,SV338: nat] :
( ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV338 @ SV174 ) @ SV457 ) @ SV499 ) @ SV512 )
= $true )
| ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV338 @ SV174 ) @ SV457 ) @ SV499 ) @ SV512 )
= $false )
| ( ( ord_less_eq_nat @ SV174 @ SV338 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2863]) ).
thf(2944,plain,
! [SV459: nat,SV341: nat,SV177: nat] :
( ( ( ord_less_nat @ ( times_times_nat @ SV177 @ SV341 ) @ ( times_times_nat @ SV177 @ SV459 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV177 )
= $false )
| ( ( ord_less_nat @ SV341 @ SV459 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2866]) ).
thf(2945,plain,
! [SV459: nat,SV341: nat,SV177: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 )
| ~ ( ord_less_nat @ SV341 @ SV459 ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV177 )
= $false )
| ( ( ord_less_nat @ SV341 @ SV459 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2867]) ).
thf(2946,plain,
! [SV461: nat,SV182: nat,SV346: nat] :
( ( ( ( minus_minus_nat @ SV346 @ SV182 )
= SV461 )
= $true )
| ( ( ( minus_minus_nat @ SV346 @ SV182 )
= SV461 )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2868]) ).
thf(2947,plain,
! [SV182: nat,SV461: nat,SV346: nat] :
( ( ( SV346
= ( plus_plus_nat @ SV461 @ SV182 ) )
= $true )
| ( ( ( minus_minus_nat @ SV346 @ SV182 )
= SV461 )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2869]) ).
thf(2948,plain,
! [SV461: nat,SV182: nat,SV346: nat] :
( ( ( ( minus_minus_nat @ SV346 @ SV182 )
= SV461 )
= $true )
| ( ( SV346
= ( plus_plus_nat @ SV461 @ SV182 ) )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2870]) ).
thf(2949,plain,
! [SV182: nat,SV461: nat,SV346: nat] :
( ( ( SV346
= ( plus_plus_nat @ SV461 @ SV182 ) )
= $true )
| ( ( SV346
= ( plus_plus_nat @ SV461 @ SV182 ) )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false )
| ( ( ord_less_eq_nat @ SV182 @ SV346 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2871]) ).
thf(2950,plain,
! [SV463: nat,SV184: nat,SV348: nat] :
( ( ( ord_less_nat @ ( minus_minus_nat @ SV348 @ SV184 ) @ ( minus_minus_nat @ SV463 @ SV184 ) )
= $true )
| ( ( ord_less_nat @ ( minus_minus_nat @ SV348 @ SV184 ) @ ( minus_minus_nat @ SV463 @ SV184 ) )
= $false )
| ( ( ord_less_eq_nat @ SV184 @ SV463 )
= $false )
| ( ( ord_less_eq_nat @ SV184 @ SV348 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2872]) ).
thf(2951,plain,
! [SV184: nat,SV463: nat,SV348: nat] :
( ( ( ord_less_nat @ SV348 @ SV463 )
= $true )
| ( ( ord_less_nat @ ( minus_minus_nat @ SV348 @ SV184 ) @ ( minus_minus_nat @ SV463 @ SV184 ) )
= $false )
| ( ( ord_less_eq_nat @ SV184 @ SV463 )
= $false )
| ( ( ord_less_eq_nat @ SV184 @ SV348 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2873]) ).
thf(2952,plain,
! [SV463: nat,SV184: nat,SV348: nat] :
( ( ( ord_less_nat @ ( minus_minus_nat @ SV348 @ SV184 ) @ ( minus_minus_nat @ SV463 @ SV184 ) )
= $true )
| ( ( ord_less_nat @ SV348 @ SV463 )
= $false )
| ( ( ord_less_eq_nat @ SV184 @ SV463 )
= $false )
| ( ( ord_less_eq_nat @ SV184 @ SV348 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2874]) ).
thf(2953,plain,
! [SV184: nat,SV463: nat,SV348: nat] :
( ( ( ord_less_nat @ SV348 @ SV463 )
= $true )
| ( ( ord_less_nat @ SV348 @ SV463 )
= $false )
| ( ( ord_less_eq_nat @ SV184 @ SV463 )
= $false )
| ( ( ord_less_eq_nat @ SV184 @ SV348 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2875]) ).
thf(2954,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ord_less_nat @ SV350 @ SV465 ) )
= $true )
| ( ( ~ ~ ( SV186 @ zero_zero_nat ) )
= $true )
| ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2876]) ).
thf(2955,plain,
! [SV186: nat > $o,SV528: nat,SV465: nat,SV350: nat] :
( ( ( ~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SV528 ) )
| ~ ~ ( SV186 @ SV528 ) ) )
= $true )
| ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2877]) ).
thf(2956,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
| ~ ~ ( SV186 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2878]) ).
thf(2957,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) )
= $false )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2879]) ).
thf(2958,plain,
! [SV513: nat,SV190: nat,SV501: nat,SV468: nat,SV354: nat] :
( ( ( ( plus_plus_nat @ ( times_times_nat @ SV354 @ SV468 ) @ SV501 )
= ( plus_plus_nat @ ( times_times_nat @ SV190 @ SV468 ) @ SV513 ) )
= $true )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SV354 @ SV468 ) @ SV501 )
= ( plus_plus_nat @ ( times_times_nat @ SV190 @ SV468 ) @ SV513 ) )
= $false )
| ( ( ord_less_eq_nat @ SV190 @ SV354 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2880]) ).
thf(2959,plain,
! [SV513: nat,SV501: nat,SV468: nat,SV190: nat,SV354: nat] :
( ( ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV354 @ SV190 ) @ SV468 ) @ SV501 )
= SV513 )
= $true )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SV354 @ SV468 ) @ SV501 )
= ( plus_plus_nat @ ( times_times_nat @ SV190 @ SV468 ) @ SV513 ) )
= $false )
| ( ( ord_less_eq_nat @ SV190 @ SV354 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2881]) ).
thf(2960,plain,
! [SV513: nat,SV190: nat,SV501: nat,SV468: nat,SV354: nat] :
( ( ( ( plus_plus_nat @ ( times_times_nat @ SV354 @ SV468 ) @ SV501 )
= ( plus_plus_nat @ ( times_times_nat @ SV190 @ SV468 ) @ SV513 ) )
= $true )
| ( ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV354 @ SV190 ) @ SV468 ) @ SV501 )
= SV513 )
= $false )
| ( ( ord_less_eq_nat @ SV190 @ SV354 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2882]) ).
thf(2961,plain,
! [SV513: nat,SV501: nat,SV468: nat,SV190: nat,SV354: nat] :
( ( ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV354 @ SV190 ) @ SV468 ) @ SV501 )
= SV513 )
= $true )
| ( ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV354 @ SV190 ) @ SV468 ) @ SV501 )
= SV513 )
= $false )
| ( ( ord_less_eq_nat @ SV190 @ SV354 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2883]) ).
thf(2962,plain,
! [SV471: nat,SV358: nat,SV194: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV194 )
= $false )
| ( ( ord_less_eq_nat @ SV358 @ SV471 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV194 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2884]) ).
thf(2963,plain,
! [SV514: nat,SV361: nat,SV505: nat,SV474: nat,SV197: nat] :
( ( ( ( plus_plus_nat @ ( times_times_nat @ SV197 @ SV474 ) @ SV505 )
= ( plus_plus_nat @ ( times_times_nat @ SV361 @ SV474 ) @ SV514 ) )
= $true )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SV197 @ SV474 ) @ SV505 )
= ( plus_plus_nat @ ( times_times_nat @ SV361 @ SV474 ) @ SV514 ) )
= $false )
| ( ( ord_less_eq_nat @ SV197 @ SV361 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2886]) ).
thf(2964,plain,
! [SV514: nat,SV474: nat,SV197: nat,SV361: nat,SV505: nat] :
( ( ( SV505
= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV361 @ SV197 ) @ SV474 ) @ SV514 ) )
= $true )
| ( ( ( plus_plus_nat @ ( times_times_nat @ SV197 @ SV474 ) @ SV505 )
= ( plus_plus_nat @ ( times_times_nat @ SV361 @ SV474 ) @ SV514 ) )
= $false )
| ( ( ord_less_eq_nat @ SV197 @ SV361 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2887]) ).
thf(2965,plain,
! [SV514: nat,SV361: nat,SV505: nat,SV474: nat,SV197: nat] :
( ( ( ( plus_plus_nat @ ( times_times_nat @ SV197 @ SV474 ) @ SV505 )
= ( plus_plus_nat @ ( times_times_nat @ SV361 @ SV474 ) @ SV514 ) )
= $true )
| ( ( SV505
= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV361 @ SV197 ) @ SV474 ) @ SV514 ) )
= $false )
| ( ( ord_less_eq_nat @ SV197 @ SV361 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2888]) ).
thf(2966,plain,
! [SV514: nat,SV474: nat,SV197: nat,SV361: nat,SV505: nat] :
( ( ( SV505
= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV361 @ SV197 ) @ SV474 ) @ SV514 ) )
= $true )
| ( ( SV505
= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ SV361 @ SV197 ) @ SV474 ) @ SV514 ) )
= $false )
| ( ( ord_less_eq_nat @ SV197 @ SV361 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2889]) ).
thf(2967,plain,
! [SV114: nat > $o,SV283: nat,SV525: nat] :
( ( ( ord_less_nat @ SV525 @ ( sK7_SY655 @ SV283 @ SV114 ) )
= $false )
| ( ( ~ ~ ( SV114 @ SV525 ) )
= $true )
| ( ( SV114 @ SV283 )
= $true )
| ( ( SV114 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2902]) ).
thf(2968,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ord_less_nat @ SV285 @ SV417 )
= $false )
| ( ( SV117 @ zero_zero_nat )
= $true )
| ( ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2903]) ).
thf(2969,plain,
! [SV117: nat > $o,SV527: nat,SV417: nat,SV285: nat] :
( ( ( SV285
!= ( plus_plus_nat @ SV417 @ SV527 ) )
= $true )
| ( ( SV117 @ SV527 )
= $true )
| ( ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2904]) ).
thf(2970,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( SV285
!= ( plus_plus_nat @ SV417 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $false )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( ~ ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2905]) ).
thf(2971,plain,
! [SV285: nat,SV417: nat,SV117: nat > $o] :
( ( ( SV117 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( ~ ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2905]) ).
thf(2972,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2906]) ).
thf(2973,plain,
! [SV417: nat,SV285: nat,SV117: nat > $o] :
( ( ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) )
= $false )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV117 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2907]) ).
thf(2974,plain,
! [SV521: nat,SV288: nat,SV488: nat] :
( ( ( ! [SY1033: nat] :
( SV488
!= ( plus_plus_nat @ SV288 @ SY1033 ) ) )
= $false )
| ( ( SV488
= ( plus_plus_nat @ SV288 @ SV521 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2910]) ).
thf(2975,plain,
! [SV522: nat,SV289: nat,SV489: nat] :
( ( ( ! [SY1034: nat] :
( SV489
!= ( plus_plus_nat @ SV289 @ SY1034 ) ) )
= $false )
| ( ( SV489
= ( plus_plus_nat @ SV289 @ SV522 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2913]) ).
thf(2976,plain,
! [SV294: nat,SV126: nat] :
( ( ( SV126 != zero_zero_nat )
= $false )
| ( ( SV126 = zero_zero_nat )
= $false )
| ( ( SV294 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2914]) ).
thf(2977,plain,
! [SV126: nat,SV294: nat] :
( ( ( SV294 != zero_zero_nat )
= $false )
| ( ( SV126 = zero_zero_nat )
= $false )
| ( ( SV294 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2914]) ).
thf(2978,plain,
! [SV444: nat,SV152: nat,SV318: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV318 )
| ~ ( ord_less_nat @ SV152 @ SV444 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV318 )
= $false )
| ( ( ord_less_nat @ SV152 @ SV444 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2925]) ).
thf(2979,plain,
! [SV325: nat,SV159: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV159 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV159 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV325 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2926]) ).
thf(2980,plain,
! [SV159: nat,SV325: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV325 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV159 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV325 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2926]) ).
thf(2981,plain,
! [SV326: nat,SV160: nat] :
( ( ( SV160 != zero_zero_nat )
= $false )
| ( ( SV160 = zero_zero_nat )
= $false )
| ( ( SV326 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2927]) ).
thf(2982,plain,
! [SV160: nat,SV326: nat] :
( ( ( SV326 != zero_zero_nat )
= $false )
| ( ( SV160 = zero_zero_nat )
= $false )
| ( ( SV326 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2927]) ).
thf(2983,plain,
! [SV497: nat,SV327: nat] :
( ( ( SV327 = SV497 )
= $false )
| ( ( ord_less_nat @ SV327 @ SV497 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2929]) ).
thf(2984,plain,
! [SV497: nat,SV327: nat] :
( ( ( ~ ( ord_less_nat @ SV327 @ SV497 ) )
= $false )
| ( ( ord_less_eq_nat @ SV327 @ SV497 )
= $false )
| ( ( SV327 = SV497 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2930]) ).
thf(2985,plain,
! [SV497: nat,SV327: nat] :
( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV327 @ SV497 )
| ~ ( ( SV327 != SV497 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV327 @ SV497 )
= $false )
| ( ( SV327 = SV497 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2930]) ).
thf(2986,plain,
! [SV328: nat,SV162: nat] :
( ( ( SV162 != zero_zero_nat )
= $false )
| ( ( SV162 = zero_zero_nat )
= $false )
| ( ( SV328 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2931]) ).
thf(2987,plain,
! [SV162: nat,SV328: nat] :
( ( ( SV328 != zero_zero_nat )
= $false )
| ( ( SV162 = zero_zero_nat )
= $false )
| ( ( SV328 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2931]) ).
thf(2988,plain,
! [SV330: nat,SV449: nat,SV164: nat > $o] :
( ( ( ~ ( SV164 @ ( sK10_SY751 @ SV449 @ SV330 @ SV164 ) ) )
= $false )
| ( ( SV164 @ ( sK8_SY1015 @ SV330 @ SV449 @ SV164 ) )
= $true )
| ( ( SV164 @ SV330 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2933]) ).
thf(2989,plain,
! [SV330: nat,SV449: nat,SV164: nat > $o] :
( ( ( ~ ! [SY1046: nat] :
( ~ ( SV164 @ SY1046 )
| ( ord_less_eq_nat @ SY1046 @ ( sK10_SY751 @ SV449 @ SV330 @ SV164 ) ) ) )
= $false )
| ( ( SV164 @ ( sK8_SY1015 @ SV330 @ SV449 @ SV164 ) )
= $true )
| ( ( SV164 @ SV330 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2933]) ).
thf(2990,plain,
! [SV330: nat,SV449: nat,SV164: nat > $o] :
( ( ( SV164 @ ( sK9_SY751 @ SV449 @ SV330 @ SV164 ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK8_SY1015 @ SV330 @ SV449 @ SV164 ) @ SV449 )
= $false )
| ( ( SV164 @ SV330 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2934]) ).
thf(2991,plain,
! [SV330: nat,SV449: nat,SV164: nat > $o] :
( ( ( ! [SY1045: nat] :
( ~ ( SV164 @ SY1045 )
| ( ord_less_eq_nat @ SY1045 @ ( sK9_SY751 @ SV449 @ SV330 @ SV164 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK8_SY1015 @ SV330 @ SV449 @ SV164 ) @ SV449 )
= $false )
| ( ( SV164 @ SV330 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2935]) ).
thf(2992,plain,
! [SV459: nat,SV341: nat,SV177: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 )
| ~ ( ord_less_nat @ SV341 @ SV459 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV177 )
= $false )
| ( ( ord_less_nat @ SV341 @ SV459 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2945]) ).
thf(2993,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ord_less_nat @ SV350 @ SV465 )
= $false )
| ( ( ~ ~ ( SV186 @ zero_zero_nat ) )
= $true )
| ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2954]) ).
thf(2994,plain,
! [SV186: nat > $o,SV528: nat,SV465: nat,SV350: nat] :
( ( ( ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SV528 ) )
| ~ ~ ( SV186 @ SV528 ) ) )
= $false )
| ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2955]) ).
thf(2995,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
| ~ ~ ( SV186 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2956]) ).
thf(2996,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
| ~ ~ ( SV186 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) ) )
= $false )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2957]) ).
thf(2997,plain,
! [SV283: nat,SV525: nat,SV114: nat > $o] :
( ( ( ~ ( SV114 @ SV525 ) )
= $false )
| ( ( ord_less_nat @ SV525 @ ( sK7_SY655 @ SV283 @ SV114 ) )
= $false )
| ( ( SV114 @ SV283 )
= $true )
| ( ( SV114 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2967]) ).
thf(2998,plain,
! [SV117: nat > $o,SV527: nat,SV417: nat,SV285: nat] :
( ( ( SV285
= ( plus_plus_nat @ SV417 @ SV527 ) )
= $false )
| ( ( SV117 @ SV527 )
= $true )
| ( ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2969]) ).
thf(2999,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( ~ ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2970]) ).
thf(3000,plain,
! [SV417: nat,SV285: nat,SV117: nat > $o] :
( ( ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV117 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2971]) ).
thf(3001,plain,
! [SV417: nat,SV285: nat,SV117: nat > $o] :
( ( ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) )
= $false )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2972]) ).
thf(3002,plain,
! [SV417: nat,SV285: nat,SV117: nat > $o] :
( ( ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) ) )
= $false )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV117 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2973]) ).
thf(3003,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) )
= $false )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV117 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2973]) ).
thf(3004,plain,
! [SV521: nat,SV288: nat,SV488: nat] :
( ( ( SV488
!= ( plus_plus_nat @ SV288 @ ( sK17_SY1033 @ SV521 @ SV288 @ SV488 ) ) )
= $false )
| ( ( SV488
= ( plus_plus_nat @ SV288 @ SV521 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2974]) ).
thf(3005,plain,
! [SV522: nat,SV289: nat,SV489: nat] :
( ( ( SV489
!= ( plus_plus_nat @ SV289 @ ( sK18_SY1034 @ SV522 @ SV289 @ SV489 ) ) )
= $false )
| ( ( SV489
= ( plus_plus_nat @ SV289 @ SV522 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2975]) ).
thf(3006,plain,
! [SV294: nat,SV126: nat] :
( ( ( SV126 = zero_zero_nat )
= $true )
| ( ( SV126 = zero_zero_nat )
= $false )
| ( ( SV294 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2976]) ).
thf(3007,plain,
! [SV126: nat,SV294: nat] :
( ( ( SV294 = zero_zero_nat )
= $true )
| ( ( SV126 = zero_zero_nat )
= $false )
| ( ( SV294 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2977]) ).
thf(3008,plain,
! [SV444: nat,SV152: nat,SV318: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV318 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV318 )
= $false )
| ( ( ord_less_nat @ SV152 @ SV444 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2978]) ).
thf(3009,plain,
! [SV318: nat,SV444: nat,SV152: nat] :
( ( ( ~ ( ord_less_nat @ SV152 @ SV444 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV318 )
= $false )
| ( ( ord_less_nat @ SV152 @ SV444 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2978]) ).
thf(3010,plain,
! [SV325: nat,SV159: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV159 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV159 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV325 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2979]) ).
thf(3011,plain,
! [SV159: nat,SV325: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV325 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV159 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV325 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2980]) ).
thf(3012,plain,
! [SV326: nat,SV160: nat] :
( ( ( SV160 = zero_zero_nat )
= $true )
| ( ( SV160 = zero_zero_nat )
= $false )
| ( ( SV326 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2981]) ).
thf(3013,plain,
! [SV160: nat,SV326: nat] :
( ( ( SV326 = zero_zero_nat )
= $true )
| ( ( SV160 = zero_zero_nat )
= $false )
| ( ( SV326 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2982]) ).
thf(3014,plain,
! [SV497: nat,SV327: nat] :
( ( ( ord_less_nat @ SV327 @ SV497 )
= $true )
| ( ( ord_less_eq_nat @ SV327 @ SV497 )
= $false )
| ( ( SV327 = SV497 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2984]) ).
thf(3015,plain,
! [SV497: nat,SV327: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV327 @ SV497 )
| ~ ( ( SV327 != SV497 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV327 @ SV497 )
= $false )
| ( ( SV327 = SV497 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2985]) ).
thf(3016,plain,
! [SV328: nat,SV162: nat] :
( ( ( SV162 = zero_zero_nat )
= $true )
| ( ( SV162 = zero_zero_nat )
= $false )
| ( ( SV328 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2986]) ).
thf(3017,plain,
! [SV162: nat,SV328: nat] :
( ( ( SV328 = zero_zero_nat )
= $true )
| ( ( SV162 = zero_zero_nat )
= $false )
| ( ( SV328 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2987]) ).
thf(3018,plain,
! [SV330: nat,SV449: nat,SV164: nat > $o] :
( ( ( SV164 @ ( sK10_SY751 @ SV449 @ SV330 @ SV164 ) )
= $true )
| ( ( SV164 @ ( sK8_SY1015 @ SV330 @ SV449 @ SV164 ) )
= $true )
| ( ( SV164 @ SV330 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2988]) ).
thf(3019,plain,
! [SV330: nat,SV449: nat,SV164: nat > $o] :
( ( ( ! [SY1046: nat] :
( ~ ( SV164 @ SY1046 )
| ( ord_less_eq_nat @ SY1046 @ ( sK10_SY751 @ SV449 @ SV330 @ SV164 ) ) ) )
= $true )
| ( ( SV164 @ ( sK8_SY1015 @ SV330 @ SV449 @ SV164 ) )
= $true )
| ( ( SV164 @ SV330 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2989]) ).
thf(3020,plain,
! [SV330: nat,SV449: nat,SV529: nat,SV164: nat > $o] :
( ( ( ~ ( SV164 @ SV529 )
| ( ord_less_eq_nat @ SV529 @ ( sK9_SY751 @ SV449 @ SV330 @ SV164 ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK8_SY1015 @ SV330 @ SV449 @ SV164 ) @ SV449 )
= $false )
| ( ( SV164 @ SV330 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2991]) ).
thf(3021,plain,
! [SV459: nat,SV341: nat,SV177: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV177 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV177 )
= $false )
| ( ( ord_less_nat @ SV341 @ SV459 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2992]) ).
thf(3022,plain,
! [SV177: nat,SV459: nat,SV341: nat] :
( ( ( ~ ( ord_less_nat @ SV341 @ SV459 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV177 )
= $false )
| ( ( ord_less_nat @ SV341 @ SV459 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2992]) ).
thf(3023,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( ~ ( SV186 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $false )
| ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2993]) ).
thf(3024,plain,
! [SV186: nat > $o,SV528: nat,SV465: nat,SV350: nat] :
( ( ( ( SV350
!= ( plus_plus_nat @ SV465 @ SV528 ) )
| ~ ~ ( SV186 @ SV528 ) )
= $true )
| ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2994]) ).
thf(3025,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ( SV350
!= ( plus_plus_nat @ SV465 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
| ~ ~ ( SV186 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2995]) ).
thf(3026,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
| ~ ~ ( SV186 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) ) )
= $true )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2996]) ).
thf(3027,plain,
! [SV283: nat,SV525: nat,SV114: nat > $o] :
( ( ( SV114 @ SV525 )
= $true )
| ( ( ord_less_nat @ SV525 @ ( sK7_SY655 @ SV283 @ SV114 ) )
= $false )
| ( ( SV114 @ SV283 )
= $true )
| ( ( SV114 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2997]) ).
thf(3028,plain,
! [SV417: nat,SV285: nat,SV117: nat > $o] :
( ( ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2999]) ).
thf(3029,plain,
! [SV417: nat,SV285: nat,SV117: nat > $o] :
( ( ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) ) )
= $false )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV117 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3000]) ).
thf(3030,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV117 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3000]) ).
thf(3031,plain,
! [SV417: nat,SV285: nat,SV117: nat > $o] :
( ( ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) ) )
= $false )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3001]) ).
thf(3032,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) )
= $false )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3001]) ).
thf(3033,plain,
! [SV417: nat,SV285: nat,SV117: nat > $o] :
( ( ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
= $true )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV117 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3002]) ).
thf(3034,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) )
= $true )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV117 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3003]) ).
thf(3035,plain,
! [SV521: nat,SV288: nat,SV488: nat] :
( ( ( SV488
= ( plus_plus_nat @ SV288 @ ( sK17_SY1033 @ SV521 @ SV288 @ SV488 ) ) )
= $true )
| ( ( SV488
= ( plus_plus_nat @ SV288 @ SV521 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3004]) ).
thf(3036,plain,
! [SV522: nat,SV289: nat,SV489: nat] :
( ( ( SV489
= ( plus_plus_nat @ SV289 @ ( sK18_SY1034 @ SV522 @ SV289 @ SV489 ) ) )
= $true )
| ( ( SV489
= ( plus_plus_nat @ SV289 @ SV522 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3005]) ).
thf(3037,plain,
! [SV444: nat,SV152: nat,SV318: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV318 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV318 )
= $false )
| ( ( ord_less_nat @ SV152 @ SV444 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3008]) ).
thf(3038,plain,
! [SV318: nat,SV444: nat,SV152: nat] :
( ( ( ord_less_nat @ SV152 @ SV444 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV318 )
= $false )
| ( ( ord_less_nat @ SV152 @ SV444 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3009]) ).
thf(3039,plain,
! [SV497: nat,SV327: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV327 @ SV497 )
| ~ ( ( SV327 != SV497 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV327 @ SV497 )
= $false )
| ( ( SV327 = SV497 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3015]) ).
thf(3040,plain,
! [SV330: nat,SV449: nat,SV530: nat,SV164: nat > $o] :
( ( ( ~ ( SV164 @ SV530 )
| ( ord_less_eq_nat @ SV530 @ ( sK10_SY751 @ SV449 @ SV330 @ SV164 ) ) )
= $true )
| ( ( SV164 @ ( sK8_SY1015 @ SV330 @ SV449 @ SV164 ) )
= $true )
| ( ( SV164 @ SV330 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3019]) ).
thf(3041,plain,
! [SV330: nat,SV449: nat,SV529: nat,SV164: nat > $o] :
( ( ( ~ ( SV164 @ SV529 ) )
= $true )
| ( ( ord_less_eq_nat @ SV529 @ ( sK9_SY751 @ SV449 @ SV330 @ SV164 ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK8_SY1015 @ SV330 @ SV449 @ SV164 ) @ SV449 )
= $false )
| ( ( SV164 @ SV330 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3020]) ).
thf(3042,plain,
! [SV459: nat,SV341: nat,SV177: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV177 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV177 )
= $false )
| ( ( ord_less_nat @ SV341 @ SV459 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3021]) ).
thf(3043,plain,
! [SV177: nat,SV459: nat,SV341: nat] :
( ( ( ord_less_nat @ SV341 @ SV459 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV177 )
= $false )
| ( ( ord_less_nat @ SV341 @ SV459 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3022]) ).
thf(3044,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( SV186 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $false )
| ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3023]) ).
thf(3045,plain,
! [SV186: nat > $o,SV528: nat,SV465: nat,SV350: nat] :
( ( ( SV350
!= ( plus_plus_nat @ SV465 @ SV528 ) )
= $true )
| ( ( ~ ~ ( SV186 @ SV528 ) )
= $true )
| ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3024]) ).
thf(3046,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( SV350
!= ( plus_plus_nat @ SV465 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3025]) ).
thf(3047,plain,
! [SV350: nat,SV465: nat,SV186: nat > $o] :
( ( ( ~ ~ ( SV186 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3025]) ).
thf(3048,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ( SV350
!= ( plus_plus_nat @ SV465 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
| ~ ~ ( SV186 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $false )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3026]) ).
thf(3049,plain,
! [SV417: nat,SV285: nat,SV117: nat > $o] :
( ( ( ~ ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) ) )
= $false )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3028]) ).
thf(3050,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3028]) ).
thf(3051,plain,
! [SV417: nat,SV285: nat,SV117: nat > $o] :
( ( ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
= $true )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV117 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3029]) ).
thf(3052,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV117 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3030]) ).
thf(3053,plain,
! [SV417: nat,SV285: nat,SV117: nat > $o] :
( ( ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
= $true )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3031]) ).
thf(3054,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) )
= $true )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3032]) ).
thf(3055,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) )
= $false )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV117 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3034]) ).
thf(3056,plain,
! [SV497: nat,SV327: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV327 @ SV497 ) )
= $false )
| ( ( ord_less_eq_nat @ SV327 @ SV497 )
= $false )
| ( ( SV327 = SV497 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3039]) ).
thf(3057,plain,
! [SV497: nat,SV327: nat] :
( ( ( ~ ( ( SV327 != SV497 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV327 @ SV497 )
= $false )
| ( ( SV327 = SV497 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3039]) ).
thf(3058,plain,
! [SV330: nat,SV449: nat,SV530: nat,SV164: nat > $o] :
( ( ( ~ ( SV164 @ SV530 ) )
= $true )
| ( ( ord_less_eq_nat @ SV530 @ ( sK10_SY751 @ SV449 @ SV330 @ SV164 ) )
= $true )
| ( ( SV164 @ ( sK8_SY1015 @ SV330 @ SV449 @ SV164 ) )
= $true )
| ( ( SV164 @ SV330 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3040]) ).
thf(3059,plain,
! [SV330: nat,SV449: nat,SV529: nat,SV164: nat > $o] :
( ( ( SV164 @ SV529 )
= $false )
| ( ( ord_less_eq_nat @ SV529 @ ( sK9_SY751 @ SV449 @ SV330 @ SV164 ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK8_SY1015 @ SV330 @ SV449 @ SV164 ) @ SV449 )
= $false )
| ( ( SV164 @ SV330 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3041]) ).
thf(3060,plain,
! [SV186: nat > $o,SV528: nat,SV465: nat,SV350: nat] :
( ( ( SV350
= ( plus_plus_nat @ SV465 @ SV528 ) )
= $false )
| ( ( ~ ~ ( SV186 @ SV528 ) )
= $true )
| ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3045]) ).
thf(3061,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3046]) ).
thf(3062,plain,
! [SV350: nat,SV465: nat,SV186: nat > $o] :
( ( ( ~ ( SV186 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3047]) ).
thf(3063,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( SV350
!= ( plus_plus_nat @ SV465 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $false )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3048]) ).
thf(3064,plain,
! [SV350: nat,SV465: nat,SV186: nat > $o] :
( ( ( ~ ~ ( SV186 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $false )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3048]) ).
thf(3065,plain,
! [SV417: nat,SV285: nat,SV117: nat > $o] :
( ( ( SV117 @ ( minus_minus_nat @ SV285 @ SV417 ) )
= $true )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3049]) ).
thf(3066,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3050]) ).
thf(3067,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) )
= $false )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV117 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3052]) ).
thf(3068,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) )
= $false )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3054]) ).
thf(3069,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) ) )
= $false )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV117 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3055]) ).
thf(3070,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) )
= $false )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV117 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3055]) ).
thf(3071,plain,
! [SV497: nat,SV327: nat] :
( ( ( ord_less_eq_nat @ SV327 @ SV497 )
= $true )
| ( ( ord_less_eq_nat @ SV327 @ SV497 )
= $false )
| ( ( SV327 = SV497 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3056]) ).
thf(3072,plain,
! [SV497: nat,SV327: nat] :
( ( ( SV327 != SV497 )
= $true )
| ( ( ord_less_eq_nat @ SV327 @ SV497 )
= $false )
| ( ( SV327 = SV497 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3057]) ).
thf(3073,plain,
! [SV330: nat,SV449: nat,SV530: nat,SV164: nat > $o] :
( ( ( SV164 @ SV530 )
= $false )
| ( ( ord_less_eq_nat @ SV530 @ ( sK10_SY751 @ SV449 @ SV330 @ SV164 ) )
= $true )
| ( ( SV164 @ ( sK8_SY1015 @ SV330 @ SV449 @ SV164 ) )
= $true )
| ( ( SV164 @ SV330 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3058]) ).
thf(3074,plain,
! [SV465: nat,SV350: nat,SV528: nat,SV186: nat > $o] :
( ( ( ~ ( SV186 @ SV528 ) )
= $false )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ SV528 ) )
= $false )
| ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3060]) ).
thf(3075,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3061]) ).
thf(3076,plain,
! [SV350: nat,SV465: nat,SV186: nat > $o] :
( ( ( SV186 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3062]) ).
thf(3077,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3063]) ).
thf(3078,plain,
! [SV350: nat,SV465: nat,SV186: nat > $o] :
( ( ( ~ ( SV186 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3064]) ).
thf(3079,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
| ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) )
= $false )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3066]) ).
thf(3080,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV117 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3067]) ).
thf(3081,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) )
= $false )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV117 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3067]) ).
thf(3082,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) ) )
= $false )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3068]) ).
thf(3083,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) )
= $false )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3068]) ).
thf(3084,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
= $true )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV117 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3069]) ).
thf(3085,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) )
= $true )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV117 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3070]) ).
thf(3086,plain,
! [SV497: nat,SV327: nat] :
( ( ( SV327 = SV497 )
= $false )
| ( ( ord_less_eq_nat @ SV327 @ SV497 )
= $false )
| ( ( SV327 = SV497 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3072]) ).
thf(3087,plain,
! [SV465: nat,SV350: nat,SV528: nat,SV186: nat > $o] :
( ( ( SV186 @ SV528 )
= $true )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ SV528 ) )
= $false )
| ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3074]) ).
thf(3088,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3075]) ).
thf(3089,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3075]) ).
thf(3090,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV186 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3076]) ).
thf(3091,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) )
= $false )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3077]) ).
thf(3092,plain,
! [SV350: nat,SV465: nat,SV186: nat > $o] :
( ( ( SV186 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3078]) ).
thf(3093,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3079]) ).
thf(3094,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) )
= $false )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3079]) ).
thf(3095,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
= $true )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV117 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3080]) ).
thf(3096,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) )
= $true )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV117 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3081]) ).
thf(3097,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
= $true )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3082]) ).
thf(3098,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) )
= $true )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3083]) ).
thf(3099,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ord_less_nat @ SV285 @ SV417 ) )
= $true )
| ( ( SV117 @ zero_zero_nat )
= $true )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV117 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3084]) ).
thf(3100,plain,
! [SV117: nat > $o,SV531: nat,SV417: nat,SV285: nat] :
( ( ( ( SV285
!= ( plus_plus_nat @ SV417 @ SV531 ) )
| ( SV117 @ SV531 ) )
= $true )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV117 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3085]) ).
thf(3101,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= $true )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3088]) ).
thf(3102,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3089]) ).
thf(3103,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV186 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3090]) ).
thf(3104,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV186 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3090]) ).
thf(3105,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) ) )
= $false )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3091]) ).
thf(3106,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) )
= $false )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3091]) ).
thf(3107,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
| ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) )
= $false )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV186 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3092]) ).
thf(3108,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ord_less_nat @ SV285 @ SV417 )
| ( SV117 @ zero_zero_nat ) )
= $true )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3093]) ).
thf(3109,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ! [SY1002: nat] :
( ( SV285
!= ( plus_plus_nat @ SV417 @ SY1002 ) )
| ( SV117 @ SY1002 ) ) )
= $true )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3094]) ).
thf(3110,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ord_less_nat @ SV285 @ SV417 ) )
= $true )
| ( ( SV117 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV117 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3095]) ).
thf(3111,plain,
! [SV117: nat > $o,SV532: nat,SV417: nat,SV285: nat] :
( ( ( ( SV285
!= ( plus_plus_nat @ SV417 @ SV532 ) )
| ( SV117 @ SV532 ) )
= $true )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV117 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3096]) ).
thf(3112,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ord_less_nat @ SV285 @ SV417 ) )
= $true )
| ( ( SV117 @ zero_zero_nat )
= $true )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3097]) ).
thf(3113,plain,
! [SV117: nat > $o,SV533: nat,SV417: nat,SV285: nat] :
( ( ( ( SV285
!= ( plus_plus_nat @ SV417 @ SV533 ) )
| ( SV117 @ SV533 ) )
= $true )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3098]) ).
thf(3114,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ord_less_nat @ SV285 @ SV417 )
= $false )
| ( ( SV117 @ zero_zero_nat )
= $true )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV117 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3099]) ).
thf(3115,plain,
! [SV117: nat > $o,SV531: nat,SV417: nat,SV285: nat] :
( ( ( SV285
!= ( plus_plus_nat @ SV417 @ SV531 ) )
= $true )
| ( ( SV117 @ SV531 )
= $true )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV117 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3100]) ).
thf(3116,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3102]) ).
thf(3117,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= $true )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV186 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3103]) ).
thf(3118,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV186 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3104]) ).
thf(3119,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= $true )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3105]) ).
thf(3120,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) )
= $true )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3106]) ).
thf(3121,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( ~ ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) ) )
= $false )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV186 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3107]) ).
thf(3122,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) )
= $false )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV186 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3107]) ).
thf(3123,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ~ ( ord_less_nat @ SV285 @ SV417 ) )
= $true )
| ( ( SV117 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3108]) ).
thf(3124,plain,
! [SV117: nat > $o,SV534: nat,SV417: nat,SV285: nat] :
( ( ( ( SV285
!= ( plus_plus_nat @ SV417 @ SV534 ) )
| ( SV117 @ SV534 ) )
= $true )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3109]) ).
thf(3125,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ord_less_nat @ SV285 @ SV417 )
= $false )
| ( ( SV117 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV117 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3110]) ).
thf(3126,plain,
! [SV117: nat > $o,SV532: nat,SV417: nat,SV285: nat] :
( ( ( SV285
!= ( plus_plus_nat @ SV417 @ SV532 ) )
= $true )
| ( ( SV117 @ SV532 )
= $true )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV117 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3111]) ).
thf(3127,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ord_less_nat @ SV285 @ SV417 )
= $false )
| ( ( SV117 @ zero_zero_nat )
= $true )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3112]) ).
thf(3128,plain,
! [SV117: nat > $o,SV533: nat,SV417: nat,SV285: nat] :
( ( ( SV285
!= ( plus_plus_nat @ SV417 @ SV533 ) )
= $true )
| ( ( SV117 @ SV533 )
= $true )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3113]) ).
thf(3129,plain,
! [SV117: nat > $o,SV531: nat,SV417: nat,SV285: nat] :
( ( ( SV285
= ( plus_plus_nat @ SV417 @ SV531 ) )
= $false )
| ( ( SV117 @ SV531 )
= $true )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV117 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3115]) ).
thf(3130,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3116]) ).
thf(3131,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3116]) ).
thf(3132,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV186 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3118]) ).
thf(3133,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) )
= $false )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3120]) ).
thf(3134,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( SV186 @ ( minus_minus_nat @ SV350 @ SV465 ) )
= $true )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV186 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3121]) ).
thf(3135,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) ) )
= $true )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV186 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3122]) ).
thf(3136,plain,
! [SV117: nat > $o,SV417: nat,SV285: nat] :
( ( ( ord_less_nat @ SV285 @ SV417 )
= $false )
| ( ( SV117 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3123]) ).
thf(3137,plain,
! [SV117: nat > $o,SV534: nat,SV417: nat,SV285: nat] :
( ( ( SV285
!= ( plus_plus_nat @ SV417 @ SV534 ) )
= $true )
| ( ( SV117 @ SV534 )
= $true )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3124]) ).
thf(3138,plain,
! [SV117: nat > $o,SV532: nat,SV417: nat,SV285: nat] :
( ( ( SV285
= ( plus_plus_nat @ SV417 @ SV532 ) )
= $false )
| ( ( SV117 @ SV532 )
= $true )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV117 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3126]) ).
thf(3139,plain,
! [SV117: nat > $o,SV533: nat,SV417: nat,SV285: nat] :
( ( ( SV285
= ( plus_plus_nat @ SV417 @ SV533 ) )
= $false )
| ( ( SV117 @ SV533 )
= $true )
| ( ( SV117 @ zero_zero_nat )
= $false )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK11_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3128]) ).
thf(3140,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
= $true )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3130]) ).
thf(3141,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) )
= $true )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3131]) ).
thf(3142,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV186 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3132]) ).
thf(3143,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV186 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3132]) ).
thf(3144,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) ) )
= $false )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3133]) ).
thf(3145,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) )
= $false )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3133]) ).
thf(3146,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
| ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) )
= $false )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV186 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3135]) ).
thf(3147,plain,
! [SV117: nat > $o,SV534: nat,SV417: nat,SV285: nat] :
( ( ( SV285
= ( plus_plus_nat @ SV417 @ SV534 ) )
= $false )
| ( ( SV117 @ SV534 )
= $true )
| ( ( ord_less_nat @ SV285 @ SV417 )
= $true )
| ( ( SV285
= ( plus_plus_nat @ SV417 @ ( sK14_SY1002 @ SV117 @ SV417 @ SV285 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3137]) ).
thf(3148,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ord_less_nat @ SV350 @ SV465 ) )
= $true )
| ( ( ~ ~ ( SV186 @ zero_zero_nat ) )
= $true )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3140]) ).
thf(3149,plain,
! [SV186: nat > $o,SV535: nat,SV465: nat,SV350: nat] :
( ( ( ~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SV535 ) )
| ~ ~ ( SV186 @ SV535 ) ) )
= $true )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3141]) ).
thf(3150,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
= $true )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV186 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3142]) ).
thf(3151,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) )
= $true )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV186 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3143]) ).
thf(3152,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
= $true )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3144]) ).
thf(3153,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) )
= $true )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3145]) ).
thf(3154,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) ) )
= $false )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV186 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3146]) ).
thf(3155,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) )
= $false )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV186 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3146]) ).
thf(3156,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ord_less_nat @ SV350 @ SV465 )
= $false )
| ( ( ~ ~ ( SV186 @ zero_zero_nat ) )
= $true )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3148]) ).
thf(3157,plain,
! [SV186: nat > $o,SV535: nat,SV465: nat,SV350: nat] :
( ( ( ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SV535 ) )
| ~ ~ ( SV186 @ SV535 ) ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3149]) ).
thf(3158,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ord_less_nat @ SV350 @ SV465 ) )
= $true )
| ( ( ~ ~ ( SV186 @ zero_zero_nat ) )
= $true )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV186 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3150]) ).
thf(3159,plain,
! [SV186: nat > $o,SV536: nat,SV465: nat,SV350: nat] :
( ( ( ~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SV536 ) )
| ~ ~ ( SV186 @ SV536 ) ) )
= $true )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV186 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3151]) ).
thf(3160,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ord_less_nat @ SV350 @ SV465 ) )
= $true )
| ( ( ~ ~ ( SV186 @ zero_zero_nat ) )
= $true )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3152]) ).
thf(3161,plain,
! [SV186: nat > $o,SV537: nat,SV465: nat,SV350: nat] :
( ( ( ~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SV537 ) )
| ~ ~ ( SV186 @ SV537 ) ) )
= $true )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3153]) ).
thf(3162,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ord_less_nat @ SV350 @ SV465 )
| ~ ~ ( SV186 @ zero_zero_nat ) )
= $true )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV186 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3154]) ).
thf(3163,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ! [SY1022: nat] :
~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SY1022 ) )
| ~ ~ ( SV186 @ SY1022 ) ) )
= $true )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV186 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3155]) ).
thf(3164,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( ~ ( SV186 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3156]) ).
thf(3165,plain,
! [SV186: nat > $o,SV535: nat,SV465: nat,SV350: nat] :
( ( ( ( SV350
!= ( plus_plus_nat @ SV465 @ SV535 ) )
| ~ ~ ( SV186 @ SV535 ) )
= $true )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3157]) ).
thf(3166,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ord_less_nat @ SV350 @ SV465 )
= $false )
| ( ( ~ ~ ( SV186 @ zero_zero_nat ) )
= $true )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV186 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3158]) ).
thf(3167,plain,
! [SV186: nat > $o,SV536: nat,SV465: nat,SV350: nat] :
( ( ( ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SV536 ) )
| ~ ~ ( SV186 @ SV536 ) ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV186 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3159]) ).
thf(3168,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ord_less_nat @ SV350 @ SV465 )
= $false )
| ( ( ~ ~ ( SV186 @ zero_zero_nat ) )
= $true )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3160]) ).
thf(3169,plain,
! [SV186: nat > $o,SV537: nat,SV465: nat,SV350: nat] :
( ( ( ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SV537 ) )
| ~ ~ ( SV186 @ SV537 ) ) )
= $false )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3161]) ).
thf(3170,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ~ ( ord_less_nat @ SV350 @ SV465 ) )
= $true )
| ( ( ~ ~ ( SV186 @ zero_zero_nat ) )
= $true )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV186 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3162]) ).
thf(3171,plain,
! [SV186: nat > $o,SV538: nat,SV465: nat,SV350: nat] :
( ( ( ~ ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SV538 ) )
| ~ ~ ( SV186 @ SV538 ) ) )
= $true )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV186 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3163]) ).
thf(3172,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( SV186 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3164]) ).
thf(3173,plain,
! [SV186: nat > $o,SV535: nat,SV465: nat,SV350: nat] :
( ( ( SV350
!= ( plus_plus_nat @ SV465 @ SV535 ) )
= $true )
| ( ( ~ ~ ( SV186 @ SV535 ) )
= $true )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3165]) ).
thf(3174,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( ~ ( SV186 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV186 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3166]) ).
thf(3175,plain,
! [SV186: nat > $o,SV536: nat,SV465: nat,SV350: nat] :
( ( ( ( SV350
!= ( plus_plus_nat @ SV465 @ SV536 ) )
| ~ ~ ( SV186 @ SV536 ) )
= $true )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV186 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3167]) ).
thf(3176,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( ~ ( SV186 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $false )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3168]) ).
thf(3177,plain,
! [SV186: nat > $o,SV537: nat,SV465: nat,SV350: nat] :
( ( ( ( SV350
!= ( plus_plus_nat @ SV465 @ SV537 ) )
| ~ ~ ( SV186 @ SV537 ) )
= $true )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3169]) ).
thf(3178,plain,
! [SV186: nat > $o,SV465: nat,SV350: nat] :
( ( ( ord_less_nat @ SV350 @ SV465 )
= $false )
| ( ( ~ ~ ( SV186 @ zero_zero_nat ) )
= $true )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV186 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3170]) ).
thf(3179,plain,
! [SV186: nat > $o,SV538: nat,SV465: nat,SV350: nat] :
( ( ( ~ ( ( SV350
!= ( plus_plus_nat @ SV465 @ SV538 ) )
| ~ ~ ( SV186 @ SV538 ) ) )
= $false )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV186 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3171]) ).
thf(3180,plain,
! [SV186: nat > $o,SV535: nat,SV465: nat,SV350: nat] :
( ( ( SV350
= ( plus_plus_nat @ SV465 @ SV535 ) )
= $false )
| ( ( ~ ~ ( SV186 @ SV535 ) )
= $true )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3173]) ).
thf(3181,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( SV186 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV186 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3174]) ).
thf(3182,plain,
! [SV186: nat > $o,SV536: nat,SV465: nat,SV350: nat] :
( ( ( SV350
!= ( plus_plus_nat @ SV465 @ SV536 ) )
= $true )
| ( ( ~ ~ ( SV186 @ SV536 ) )
= $true )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV186 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3175]) ).
thf(3183,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( SV186 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $false )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3176]) ).
thf(3184,plain,
! [SV186: nat > $o,SV537: nat,SV465: nat,SV350: nat] :
( ( ( SV350
!= ( plus_plus_nat @ SV465 @ SV537 ) )
= $true )
| ( ( ~ ~ ( SV186 @ SV537 ) )
= $true )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3177]) ).
thf(3185,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( ~ ( SV186 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $false )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV186 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3178]) ).
thf(3186,plain,
! [SV186: nat > $o,SV538: nat,SV465: nat,SV350: nat] :
( ( ( ( SV350
!= ( plus_plus_nat @ SV465 @ SV538 ) )
| ~ ~ ( SV186 @ SV538 ) )
= $true )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV186 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3179]) ).
thf(3187,plain,
! [SV465: nat,SV350: nat,SV535: nat,SV186: nat > $o] :
( ( ( ~ ( SV186 @ SV535 ) )
= $false )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ SV535 ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3180]) ).
thf(3188,plain,
! [SV186: nat > $o,SV536: nat,SV465: nat,SV350: nat] :
( ( ( SV350
= ( plus_plus_nat @ SV465 @ SV536 ) )
= $false )
| ( ( ~ ~ ( SV186 @ SV536 ) )
= $true )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV186 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3182]) ).
thf(3189,plain,
! [SV186: nat > $o,SV537: nat,SV465: nat,SV350: nat] :
( ( ( SV350
= ( plus_plus_nat @ SV465 @ SV537 ) )
= $false )
| ( ( ~ ~ ( SV186 @ SV537 ) )
= $true )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3184]) ).
thf(3190,plain,
! [SV465: nat,SV350: nat,SV186: nat > $o] :
( ( ( SV186 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $false )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV186 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3185]) ).
thf(3191,plain,
! [SV186: nat > $o,SV538: nat,SV465: nat,SV350: nat] :
( ( ( SV350
!= ( plus_plus_nat @ SV465 @ SV538 ) )
= $true )
| ( ( ~ ~ ( SV186 @ SV538 ) )
= $true )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV186 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3186]) ).
thf(3192,plain,
! [SV465: nat,SV350: nat,SV535: nat,SV186: nat > $o] :
( ( ( SV186 @ SV535 )
= $true )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ SV535 ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3187]) ).
thf(3193,plain,
! [SV465: nat,SV350: nat,SV536: nat,SV186: nat > $o] :
( ( ( ~ ( SV186 @ SV536 ) )
= $false )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ SV536 ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV186 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3188]) ).
thf(3194,plain,
! [SV465: nat,SV350: nat,SV537: nat,SV186: nat > $o] :
( ( ( ~ ( SV186 @ SV537 ) )
= $false )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ SV537 ) )
= $false )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3189]) ).
thf(3195,plain,
! [SV186: nat > $o,SV538: nat,SV465: nat,SV350: nat] :
( ( ( SV350
= ( plus_plus_nat @ SV465 @ SV538 ) )
= $false )
| ( ( ~ ~ ( SV186 @ SV538 ) )
= $true )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV186 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3191]) ).
thf(3196,plain,
! [SV465: nat,SV350: nat,SV536: nat,SV186: nat > $o] :
( ( ( SV186 @ SV536 )
= $true )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ SV536 ) )
= $false )
| ( ( ord_less_nat @ SV350 @ SV465 )
= $true )
| ( ( SV186 @ ( sK15_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3193]) ).
thf(3197,plain,
! [SV465: nat,SV350: nat,SV537: nat,SV186: nat > $o] :
( ( ( SV186 @ SV537 )
= $true )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ SV537 ) )
= $false )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3194]) ).
thf(3198,plain,
! [SV465: nat,SV350: nat,SV538: nat,SV186: nat > $o] :
( ( ( ~ ( SV186 @ SV538 ) )
= $false )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ SV538 ) )
= $false )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV186 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3195]) ).
thf(3199,plain,
! [SV465: nat,SV350: nat,SV538: nat,SV186: nat > $o] :
( ( ( SV186 @ SV538 )
= $true )
| ( ( SV350
= ( plus_plus_nat @ SV465 @ SV538 ) )
= $false )
| ( ( SV186 @ zero_zero_nat )
= $false )
| ( ( SV186 @ ( sK16_SY1022 @ SV186 @ SV465 @ SV350 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3198]) ).
thf(3200,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[429,3199,3197,3196,3192,3190,3183,3181,3172,3147,3139,3138,3136,3134,3129,3127,3125,3119,3117,3114,3101,3087,3086,3073,3071,3065,3059,3053,3051,3044,3043,3042,3038,3037,3036,3035,3033,3027,3018,3017,3016,3014,3013,3012,3011,3010,3007,3006,2998,2990,2983,2968,2966,2965,2964,2963,2962,2961,2960,2959,2958,2953,2952,2951,2950,2949,2948,2947,2946,2944,2943,2942,2941,2940,2939,2938,2937,2936,2932,2928,2924,2923,2922,2921,2920,2919,2918,2917,2916,2915,2912,2911,2909,2908,2901,2900,2899,2898,2897,2896,2895,2894,2893,2892,2891,2890,2885,2865,2864,2853,2850,2845,2843,2840,2839,2828,2804,2803,2798,2797,2790,2789,2788,2787,2777,2776,2775,2774,2767,2766,2763,2762,2757,2756,2753,2752,2741,2740,2739,2738,2737,2736,2726,2725,2724,2723,2716,2715,2713,2711,2710,2709,2708,2707,2706,2705,2701,2671,2662,2655,2654,2653,2652,2651,2650,2633,2630,2625,2614,2612,2610,2609,2603,2602,2601,2599,2597,2596,2594,2592,2591,2590,2589,2588,2587,2584,2579,2578,2577,2573,2568,2565,2554,2536,2535,2532,2518,2517,2511,2510,2508,2506,2505,2498,2493,2492,2491,2490,2489,2488,2487,2486,2485,2484,2483,2482,2481,2479,2477,2476,2470,2464,2463,2462,2461,2460,2459,2458,2457,2456,2455,2454,2453,2452,2451,2450,2449,2448,2447,2446,2445,2444,2443,2442,2441,2440,2439,2438,2437,2436,2435,2433,2431,2430,2429,2426,2425,2392,2387,2384,2370,2369,2365,2355,2354,2350,2345,2344,2329,2328,2318,2317,2316,2315,2314,2313,2312,2311,2310,2309,2308,2307,2306,2305,2304,2303,2302,2301,2300,2299,2298,2297,2296,2295,2285,2264,2263,2262,2261,2260,2259,2258,2257,2256,2255,2254,2253,2252,2251,2250,2249,2240,2239,2229,2228,2227,2226,2225,2224,2223,2222,2221,2220,2219,2218,2217,2216,2215,2214,2208,2206,2203,2201,2200,2192,2187,2185,2182,2179,2176,2154,2152,2149,2148,2144,2143,2142,2130,2123,2120,2119,2115,2112,2102,2101,2100,2099,2098,2097,2096,2095,2094,2090,2089,2088,2087,2020,2016,2015,2014,2013,1984,1980,1975,1973,1962,1931,1927,1917,1908,1810,1807,1803,1799,1796,1795,1767,1763,1757,1755,1681,1680,1679,1678,1677,1665,1661,1658,1653,1649,1647,1643,1639,1638,1637,1635,1634,1630,1628,1627,1625,1624,1623,1622,1620,1619,1616,1614,1613,1612,1611,1608,1607,1604,1602,1597,1591,1588,1586,1584,1581,1580,1577,1571,1526,1518,1509,1502,1499,1497,1494,1485,1473,1471,1469,1465,1437,1423,1416,1410,1404,1403,1401,1399,1391,1388,1386,1384,1382,1380,1374,1372,1368,1366,1320,1317,1315,1313,1311,1306,1276,1270,1268,1237,1236,1235,1230,1229,1228,1227,1225,1224,1223,1222,1220,1216,1215,1214,1213,1212,1211,1210,1209,1207,1205,1203,1201,1199,1197,1195,1190,1189,1186,1184,1182,1180,1172,1170,1168,1166,1164,1092,1072,1058,1042,1040,1038,1036,1035,1034,1033,1031,1030,1021,1017,1012,1011,1010,1004,993,991,989,980,978,969,925,904,883,881,864,850,849,845,843,842,835,834,832,831,825,820,806,792,789,788,786,785,784,776,775,774,773,772,437,435,433,432,431,430]) ).
thf(3201,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[3200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP131^1 : 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
% 0.08/0.17 % Computer : n018.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 11:20:21 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 55.49/9.56 .
% 55.49/9.56
% 55.49/9.56 No.of.Axioms: 212
% 55.49/9.56
% 55.49/9.56 Length.of.Defs: 0
% 55.49/9.56
% 55.49/9.56 Contains.Choice.Funs: false
% 55.49/9.56 .........................................................................................
% 55.49/9.56
% 55.49/9.56 ********************************
% 55.49/9.56 * All subproblems solved! *
% 55.49/9.56 ********************************
% 55.49/9.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:212,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:3200,loop_count:0,foatp_calls:1,translation:fof_full)
% 55.49/9.56
% 55.49/9.56 %**** Beginning of derivation protocol ****
% 55.49/9.56 % SZS output start CNFRefutation
% See solution above
% 9.51/9.60
% 9.51/9.60 %**** End of derivation protocol ****
% 9.51/9.60 %**** no. of clauses in derivation: 3201 ****
% 9.51/9.60 %**** clause counter: 3200 ****
% 9.51/9.60
% 9.51/9.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:212,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:3200,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------