%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP133^1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/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 10:24:15 AM UTC 2026
% Result : Theorem 69.46s 14.13s
% Output : CNFRefutation 69.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 163
% Syntax : Number of formulae : 3230 (1004 unt; 0 typ; 0 def)
% Number of atoms : 29272 (12419 equ; 0 cnn)
% Maximal formula atoms : 12 ( 9 avg)
% Number of connectives : 54154 (7985 ~;9063 |; 91 &;36398 @)
% ( 0 <=>; 617 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 1875 (1875 >; 0 *; 0 +; 0 <<)
% Number of symbols : 111 ( 108 usr; 7 con; 0-6 aty)
% Number of variables : 10283 ( 473 ^;9801 !; 9 ?;10283 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_nat,type,
nat: $tType ).
thf(tp_set_nat,type,
set_nat: $tType ).
thf(tp_set_set_nat,type,
set_set_nat: $tType ).
thf(tp_collect_nat,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(tp_collect_set_nat,type,
collect_set_nat: ( set_nat > $o ) > set_set_nat ).
thf(tp_groups1842438620at_nat,type,
groups1842438620at_nat: ( nat > nat ) > set_nat > nat ).
thf(tp_member_nat,type,
member_nat: nat > set_nat > $o ).
thf(tp_member_set_nat,type,
member_set_nat: set_nat > set_set_nat > $o ).
thf(tp_number1551313001itions,type,
number1551313001itions: ( nat > nat ) > nat > $o ).
thf(tp_one_one_nat,type,
one_one_nat: nat ).
thf(tp_ord_le1613022364et_nat,type,
ord_le1613022364et_nat: set_set_nat > set_set_nat > $o ).
thf(tp_ord_less_eq_nat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(tp_ord_less_eq_nat_o,type,
ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
thf(tp_ord_less_eq_set_nat,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(tp_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(tp_ord_less_set_nat,type,
ord_less_set_nat: set_nat > set_nat > $o ).
thf(tp_p,type,
p: nat > nat ).
thf(tp_sK10_SY608,type,
sK10_SY608: nat > ( nat > $o ) > nat ).
thf(tp_sK11_SY815,type,
sK11_SY815: ( nat > nat ) > set_nat > nat ).
thf(tp_sK12_SY884,type,
sK12_SY884: nat > nat > ( nat > $o ) > nat ).
thf(tp_sK13_SY900,type,
sK13_SY900: ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > set_nat > nat ).
thf(tp_sK14_SY920,type,
sK14_SY920: nat > nat > ( nat > $o ) > nat ).
thf(tp_sK15_SY876,type,
sK15_SY876: ( nat > nat ) > ( nat > nat ) > set_nat > ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(tp_sK16_SY972,type,
sK16_SY972: set_nat > ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(tp_sK17_SY981,type,
sK17_SY981: ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > ( nat > nat ) > set_nat > nat ).
thf(tp_sK18_SX0,type,
sK18_SX0: nat ).
thf(tp_sK19_SY882,type,
sK19_SY882: set_nat > nat > set_nat > ( set_nat > nat ) > set_nat ).
thf(tp_sK1_SY736,type,
sK1_SY736: ( nat > nat ) > set_nat > nat ).
thf(tp_sK20_SY505,type,
sK20_SY505: nat > nat > ( nat > $o ) > nat ).
thf(tp_sK21_SY891,type,
sK21_SY891: nat > set_nat > nat > ( nat > set_nat ) > nat ).
thf(tp_sK22_SY525,type,
sK22_SY525: nat > nat > ( nat > nat > $o ) > nat ).
thf(tp_sK23_SY776,type,
sK23_SY776: nat > nat > set_nat > ( nat > set_nat ) > nat ).
thf(tp_sK24_SY780,type,
sK24_SY780: set_nat > set_nat > nat > ( set_nat > nat ) > set_nat ).
thf(tp_sK25_SY789,type,
sK25_SY789: set_nat > set_nat > nat > ( set_nat > nat ) > set_nat ).
thf(tp_sK26_SY798,type,
sK26_SY798: nat > nat > nat > ( nat > nat ) > nat ).
thf(tp_sK27_SY590,type,
sK27_SY590: nat > nat > ( nat > $o ) > nat ).
thf(tp_sK28_SY924,type,
sK28_SY924: nat > nat > nat > ( nat > nat ) > nat ).
thf(tp_sK29_SY932,type,
sK29_SY932: nat > set_nat > nat > ( nat > set_nat ) > nat ).
thf(tp_sK2_SY791,type,
sK2_SY791: ( nat > nat ) > set_nat > nat ).
thf(tp_sK30_SY830,type,
sK30_SY830: nat > nat > nat > ( nat > nat ) > nat ).
thf(tp_sK31_SY838,type,
sK31_SY838: nat > nat > set_nat > ( nat > set_nat ) > nat ).
thf(tp_sK32_SY942,type,
sK32_SY942: nat > nat > nat > ( nat > nat ) > nat ).
thf(tp_sK33_SY946,type,
sK33_SY946: set_nat > nat > set_nat > ( set_nat > nat ) > set_nat ).
thf(tp_sK34_SY1018,type,
sK34_SY1018: ( set_nat > nat ) > set_nat > nat > set_nat > set_nat ).
thf(tp_sK35_SY505,type,
sK35_SY505: nat > nat > ( nat > $o ) > nat ).
thf(tp_sK36_SY959,type,
sK36_SY959: nat > ( nat > nat ) > nat ).
thf(tp_sK37_SY1020,type,
sK37_SY1020: ( nat > set_nat ) > nat > set_nat > nat > nat ).
thf(tp_sK38_SY525,type,
sK38_SY525: nat > nat > ( nat > nat > $o ) > nat ).
thf(tp_sK39_SY1021,type,
sK39_SY1021: nat > nat > ( nat > nat > $o ) > nat ).
thf(tp_sK3_SY816,type,
sK3_SY816: ( nat > nat ) > set_nat > nat ).
thf(tp_sK40_SY1023,type,
sK40_SY1023: ( nat > set_nat ) > set_nat > nat > nat > nat ).
thf(tp_sK41_SY1024,type,
sK41_SY1024: ( set_nat > nat ) > nat > set_nat > set_nat > set_nat ).
thf(tp_sK42_SY1025,type,
sK42_SY1025: ( set_nat > nat ) > nat > set_nat > set_nat > set_nat ).
thf(tp_sK43_SY1026,type,
sK43_SY1026: ( nat > nat ) > nat > nat > nat > nat ).
thf(tp_sK44_SY590,type,
sK44_SY590: nat > nat > ( nat > $o ) > nat ).
thf(tp_sK45_SY1028,type,
sK45_SY1028: ( nat > nat ) > nat > nat > nat > nat ).
thf(tp_sK46_SY1029,type,
sK46_SY1029: ( nat > set_nat ) > nat > set_nat > nat > nat ).
thf(tp_sK47_SY1030,type,
sK47_SY1030: ( nat > nat ) > nat > nat > nat > nat ).
thf(tp_sK48_SY1031,type,
sK48_SY1031: ( nat > set_nat ) > set_nat > nat > nat > nat ).
thf(tp_sK49_SY1032,type,
sK49_SY1032: ( nat > nat ) > nat > nat > nat > nat ).
thf(tp_sK4_SY856,type,
sK4_SY856: nat > ( nat > nat ) > nat ).
thf(tp_sK50_SY1033,type,
sK50_SY1033: ( set_nat > nat ) > set_nat > nat > set_nat > set_nat ).
thf(tp_sK51_SY953,type,
sK51_SY953: ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > ( nat > nat ) > set_nat > nat ).
thf(tp_sK52_SY1035,type,
sK52_SY1035: nat > nat > ( nat > nat > $o ) > nat ).
thf(tp_sK53_SY1002,type,
sK53_SY1002: ( nat > nat ) > ( nat > nat ) > set_nat > ( nat > nat ) > set_nat > nat ).
thf(tp_sK54_SY953,type,
sK54_SY953: ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > ( nat > nat ) > set_nat > nat ).
thf(tp_sK55_SY1014,type,
sK55_SY1014: ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > ( nat > nat ) > set_nat > nat ).
thf(tp_sK56_SY954,type,
sK56_SY954: ( nat > nat ) > ( nat > nat ) > set_nat > ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(tp_sK57_SV388,type,
sK57_SV388: nat ).
thf(tp_sK58_SY1014,type,
sK58_SY1014: ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > ( nat > nat ) > set_nat > nat ).
thf(tp_sK59_SY954,type,
sK59_SY954: ( nat > nat ) > ( nat > nat ) > set_nat > ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(tp_sK5_SY523,type,
sK5_SY523: nat > nat > ( nat > nat > $o ) > nat ).
thf(tp_sK60_SY954,type,
sK60_SY954: ( nat > nat ) > ( nat > nat ) > set_nat > ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(tp_sK61_SY954,type,
sK61_SY954: ( nat > nat ) > ( nat > nat ) > set_nat > ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(tp_sK62_SV393,type,
sK62_SV393: nat ).
thf(tp_sK63_SY955,type,
sK63_SY955: ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > ( nat > nat ) > set_nat > nat ).
thf(tp_sK64_SY1022,type,
sK64_SY1022: nat > set_nat > ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(tp_sK65_SY955,type,
sK65_SY955: ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > ( nat > nat ) > set_nat > nat ).
thf(tp_sK66_SY955,type,
sK66_SY955: ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > ( nat > nat ) > set_nat > nat ).
thf(tp_sK67_SY955,type,
sK67_SY955: ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > ( nat > nat ) > set_nat > nat ).
thf(tp_sK68_SY955,type,
sK68_SY955: ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > ( nat > nat ) > set_nat > nat ).
thf(tp_sK69_SY955,type,
sK69_SY955: ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > ( nat > nat ) > set_nat > nat ).
thf(tp_sK6_SY578,type,
sK6_SY578: nat > nat > ( nat > nat ) > nat ).
thf(tp_sK70_SY955,type,
sK70_SY955: ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > ( nat > nat ) > set_nat > nat ).
thf(tp_sK71_SY955,type,
sK71_SY955: ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > ( nat > nat ) > set_nat > nat ).
thf(tp_sK72_SY1010,type,
sK72_SY1010: ( nat > nat ) > set_nat > ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(tp_sK73_SY1002,type,
sK73_SY1002: nat > ( nat > nat ) > ( nat > nat ) > set_nat > ( nat > nat ) > set_nat > nat ).
thf(tp_sK74_SY1010,type,
sK74_SY1010: ( nat > nat ) > set_nat > ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(tp_sK75_SY1010,type,
sK75_SY1010: ( nat > nat ) > set_nat > ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(tp_sK76_SY1010,type,
sK76_SY1010: ( nat > nat ) > set_nat > ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(tp_sK77_SY1010,type,
sK77_SY1010: ( nat > nat ) > set_nat > ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(tp_sK78_SY1010,type,
sK78_SY1010: ( nat > nat ) > set_nat > ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(tp_sK79_SY1010,type,
sK79_SY1010: ( nat > nat ) > set_nat > ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(tp_sK7_SY944,type,
sK7_SY944: ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(tp_sK80_SY1010,type,
sK80_SY1010: ( nat > nat ) > set_nat > ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(tp_sK81_SY1010,type,
sK81_SY1010: ( nat > nat ) > set_nat > ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(tp_sK82_SY1010,type,
sK82_SY1010: ( nat > nat ) > set_nat > ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(tp_sK83_SY1010,type,
sK83_SY1010: ( nat > nat ) > set_nat > ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(tp_sK84_SY1010,type,
sK84_SY1010: ( nat > nat ) > set_nat > ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(tp_sK85_SY1010,type,
sK85_SY1010: ( nat > nat ) > set_nat > ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(tp_sK86_SY1010,type,
sK86_SY1010: ( nat > nat ) > set_nat > ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(tp_sK87_SY1010,type,
sK87_SY1010: ( nat > nat ) > set_nat > ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(tp_sK88_SY1010,type,
sK88_SY1010: ( nat > nat ) > set_nat > ( nat > nat ) > ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(tp_sK89_SY1002,type,
sK89_SY1002: nat > ( nat > nat ) > ( nat > nat ) > set_nat > ( nat > nat ) > set_nat > nat ).
thf(tp_sK8_SY1011,type,
sK8_SY1011: ( nat > nat > $o ) > nat > nat > nat ).
thf(tp_sK90_SY1002,type,
sK90_SY1002: nat > ( nat > nat ) > ( nat > nat ) > set_nat > ( nat > nat ) > set_nat > nat ).
thf(tp_sK9_SY1012,type,
sK9_SY1012: ( nat > nat ) > nat > nat > nat ).
thf(tp_set_or1086813439et_nat,type,
set_or1086813439et_nat: set_nat > set_set_nat ).
thf(tp_set_ord_atMost_nat,type,
set_ord_atMost_nat: nat > set_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,
! [A2: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ A2 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_order_Ostrict__trans1) ).
thf(3,axiom,
! [A2: nat,B: nat,C: nat] :
( ( ord_less_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_nat @ A2 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_order_Ostrict__trans2) ).
thf(5,axiom,
( ord_less_eq_nat
= ( ^ [A4: nat,B4: nat] :
( ( ord_less_nat @ A4 @ B4 )
| ( A4 = B4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_order_Oorder__iff__strict) ).
thf(7,axiom,
( ord_less_nat
= ( ^ [A4: nat,B4: nat] :
( ( ord_less_eq_nat @ A4 @ B4 )
& ( A4 != B4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_order_Ostrict__iff__order) ).
thf(9,axiom,
! [B: nat,A2: nat,C: nat] :
( ( ord_less_eq_nat @ B @ A2 )
=> ( ( ord_less_nat @ C @ B )
=> ( ord_less_nat @ C @ A2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_dual__order_Ostrict__trans1) ).
thf(11,axiom,
! [B: nat,A2: nat,C: nat] :
( ( ord_less_nat @ B @ A2 )
=> ( ( ord_less_eq_nat @ C @ B )
=> ( ord_less_nat @ C @ A2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_dual__order_Ostrict__trans2) ).
thf(13,axiom,
! [A2: nat,B: nat] :
( ( ord_less_nat @ A2 @ B )
=> ( ord_less_eq_nat @ A2 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_order_Ostrict__implies__order) ).
thf(15,axiom,
( ord_less_eq_nat
= ( ^ [B4: nat,A4: nat] :
( ( ord_less_nat @ B4 @ A4 )
| ( A4 = B4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_dual__order_Oorder__iff__strict) ).
thf(17,axiom,
( ord_less_nat
= ( ^ [B4: nat,A4: nat] :
( ( ord_less_eq_nat @ B4 @ A4 )
& ( A4 != B4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_dual__order_Ostrict__iff__order) ).
thf(19,axiom,
! [B: nat,A2: nat] :
( ( ord_less_nat @ B @ A2 )
=> ( ord_less_eq_nat @ B @ A2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_dual__order_Ostrict__implies__order) ).
thf(21,axiom,
! [A2: nat,B: nat] :
( ( A2 != B )
=> ( ( ord_less_eq_nat @ A2 @ B )
=> ( ord_less_nat @ A2 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_order_Onot__eq__order__implies__strict) ).
thf(23,axiom,
~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_less__numeral__extra_I3_J) ).
thf(24,axiom,
~ ( ord_less_nat @ one_one_nat @ one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_less__numeral__extra_I4_J) ).
thf(32,axiom,
! [A2: nat] :
~ ( ord_less_nat @ A2 @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_bot__nat__0_Oextremum__strict) ).
thf(33,axiom,
! [P3: nat > $o,N: nat] :
( ( P3 @ zero_zero_nat )
=> ( ! [N3: nat] :
( ( ord_less_nat @ zero_zero_nat @ N3 )
=> ( ~ ( P3 @ N3 )
=> ? [M5: nat] :
( ( ord_less_nat @ M5 @ N3 )
& ~ ( P3 @ M5 ) ) ) )
=> ( P3 @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_infinite__descent0) ).
thf(34,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_gr__implies__not0) ).
thf(35,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_less__zeroE) ).
thf(36,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_not__less0) ).
thf(37,axiom,
! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_not__gr0) ).
thf(38,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_gr0I) ).
thf(39,axiom,
! [F: nat > nat,I4: nat,J: nat] :
( ! [I3: nat,J3: nat] :
( ( ord_less_nat @ I3 @ J3 )
=> ( ord_less_nat @ ( F @ I3 ) @ ( F @ J3 ) ) )
=> ( ( ord_less_eq_nat @ I4 @ J )
=> ( ord_less_eq_nat @ ( F @ I4 ) @ ( F @ J ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_less__mono__imp__le__mono) ).
thf(40,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( M != N )
=> ( ord_less_nat @ M @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_le__neq__implies__less) ).
thf(41,axiom,
! [M: nat,N: nat] :
( ( ( ord_less_nat @ M @ N )
| ( M = N ) )
=> ( ord_less_eq_nat @ M @ N ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_less__or__eq__imp__le) ).
thf(42,axiom,
( ord_less_eq_nat
= ( ^ [M4: nat,N2: nat] :
( ( ord_less_nat @ M4 @ N2 )
| ( M4 = N2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_le__eq__less__or__eq) ).
thf(43,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_eq_nat @ M @ N ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_less__imp__le__nat) ).
thf(44,axiom,
( ord_less_nat
= ( ^ [M4: nat,N2: nat] :
( ( ord_less_eq_nat @ M4 @ N2 )
& ( M4 != N2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_nat__less__le) ).
thf(45,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( N != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_zero__less__iff__neq__zero) ).
thf(46,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_gr__implies__not__zero) ).
thf(47,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_not__less__zero) ).
thf(48,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_gr__zeroI) ).
thf(82,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/sandbox2/benchmark/theBenchmark.p',fact_179_nat__mult__le__cancel__disj) ).
thf(83,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/sandbox2/benchmark/theBenchmark.p',fact_178_mult__le__cancel2) ).
thf(84,axiom,
! [N: nat] :
( ( ord_less_nat @ N @ one_one_nat )
= ( N = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_less__one) ).
thf(85,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/sandbox2/benchmark/theBenchmark.p',fact_176_nat__mult__less__cancel__disj) ).
thf(86,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/sandbox2/benchmark/theBenchmark.p',fact_175_mult__less__cancel2) ).
thf(87,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/sandbox2/benchmark/theBenchmark.p',fact_174_nat__0__less__mult__iff) ).
thf(88,axiom,
! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_not__gr__zero) ).
thf(90,axiom,
! [A2: nat] :
( ( A2 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_bot__nat__0_Onot__eq__extremum) ).
thf(91,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_less__nat__zero__code) ).
thf(92,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ N ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_neq0__conv) ).
thf(99,axiom,
ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_le__numeral__extra_I3_J) ).
thf(100,axiom,
ord_less_eq_nat @ one_one_nat @ one_one_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_le__numeral__extra_I4_J) ).
thf(101,axiom,
! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_zero__le) ).
thf(116,axiom,
! [X: nat] :
( ( one_one_nat = X )
= ( X = one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_one__reorient) ).
thf(117,axiom,
! [B: nat,A2: nat,C: nat] :
( ( times_times_nat @ B @ ( times_times_nat @ A2 @ C ) )
= ( times_times_nat @ A2 @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_mult_Oleft__commute) ).
thf(118,axiom,
( times_times_nat
= ( ^ [A4: nat,B4: nat] : ( times_times_nat @ B4 @ A4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_mult_Ocommute) ).
thf(119,axiom,
! [A2: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A2 @ B ) @ C )
= ( times_times_nat @ A2 @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_mult_Oassoc) ).
thf(120,axiom,
! [A2: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A2 @ B ) @ C )
= ( times_times_nat @ A2 @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(121,axiom,
! [X: nat] :
( ( zero_zero_nat = X )
= ( X = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_zero__reorient) ).
thf(122,axiom,
! [B: nat,A2: nat] :
( ( ord_less_eq_nat @ B @ A2 )
=> ( ( ord_less_eq_nat @ A2 @ B )
=> ( A2 = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_dual__order_Oantisym) ).
thf(124,axiom,
( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
= ( ^ [A4: nat,B4: nat] :
( ( ord_less_eq_nat @ B4 @ A4 )
& ( ord_less_eq_nat @ A4 @ B4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_dual__order_Oeq__iff) ).
thf(126,axiom,
! [B: nat,A2: nat,C: nat] :
( ( ord_less_eq_nat @ B @ A2 )
=> ( ( ord_less_eq_nat @ C @ B )
=> ( ord_less_eq_nat @ C @ A2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_dual__order_Otrans) ).
thf(128,axiom,
! [P3: nat > nat > $o,A2: nat,B: nat] :
( ! [A3: nat,B2: nat] :
( ( ord_less_eq_nat @ A3 @ B2 )
=> ( P3 @ A3 @ B2 ) )
=> ( ! [A3: nat,B2: nat] :
( ( P3 @ B2 @ A3 )
=> ( P3 @ A3 @ B2 ) )
=> ( P3 @ A2 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_linorder__wlog) ).
thf(129,axiom,
! [A2: nat] : ( ord_less_eq_nat @ A2 @ A2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_dual__order_Orefl) ).
thf(131,axiom,
! [X: nat,Y: nat,Z2: nat] :
( ( ord_less_eq_nat @ X @ Y )
=> ( ( ord_less_eq_nat @ Y @ Z2 )
=> ( ord_less_eq_nat @ X @ Z2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_order__trans) ).
thf(133,axiom,
! [A2: nat,B: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ B @ A2 )
=> ( A2 = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_order__class_Oorder_Oantisym) ).
thf(135,axiom,
! [A2: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( B = C )
=> ( ord_less_eq_nat @ A2 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_ord__le__eq__trans) ).
thf(137,axiom,
! [A2: nat,B: nat,C: nat] :
( ( A2 = B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A2 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_ord__eq__le__trans) ).
thf(139,axiom,
( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
= ( ^ [A4: nat,B4: nat] :
( ( ord_less_eq_nat @ A4 @ B4 )
& ( ord_less_eq_nat @ B4 @ A4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_order__class_Oorder_Oeq__iff) ).
thf(141,axiom,
! [Y: nat,X: nat] :
( ( ord_less_eq_nat @ Y @ X )
=> ( ( ord_less_eq_nat @ X @ Y )
= ( X = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_antisym__conv) ).
thf(143,axiom,
! [X: nat,Y: nat,Z2: nat] :
( ( ( ord_less_eq_nat @ X @ Y )
=> ~ ( ord_less_eq_nat @ Y @ Z2 ) )
=> ( ( ( ord_less_eq_nat @ Y @ X )
=> ~ ( ord_less_eq_nat @ X @ Z2 ) )
=> ( ( ( ord_less_eq_nat @ X @ Z2 )
=> ~ ( ord_less_eq_nat @ Z2 @ Y ) )
=> ( ( ( ord_less_eq_nat @ Z2 @ Y )
=> ~ ( ord_less_eq_nat @ Y @ X ) )
=> ( ( ( ord_less_eq_nat @ Y @ Z2 )
=> ~ ( ord_less_eq_nat @ Z2 @ X ) )
=> ~ ( ( ord_less_eq_nat @ Z2 @ X )
=> ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_le__cases3) ).
thf(144,axiom,
! [A2: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A2 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_order_Otrans) ).
thf(146,axiom,
! [X: nat,Y: nat] :
( ~ ( ord_less_eq_nat @ X @ Y )
=> ( ord_less_eq_nat @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_le__cases) ).
thf(147,axiom,
! [X: nat,Y: nat] :
( ( X = Y )
=> ( ord_less_eq_nat @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_eq__refl) ).
thf(149,axiom,
! [X: nat,Y: nat] :
( ( ord_less_eq_nat @ X @ Y )
| ( ord_less_eq_nat @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_linear) ).
thf(150,axiom,
! [X: nat,Y: nat] :
( ( ord_less_eq_nat @ X @ Y )
=> ( ( ord_less_eq_nat @ Y @ X )
=> ( X = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_antisym) ).
thf(152,axiom,
( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
= ( ^ [X4: nat,Y5: nat] :
( ( ord_less_eq_nat @ X4 @ Y5 )
& ( ord_less_eq_nat @ Y5 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_eq__iff) ).
thf(154,axiom,
! [A2: nat,B: nat,F: nat > nat,C: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ( F @ B )
= C )
=> ( ! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_ord__le__eq__subst) ).
thf(156,axiom,
! [A2: set_nat,B: set_nat,F: set_nat > nat,C: nat] :
( ( ord_less_eq_set_nat @ A2 @ B )
=> ( ( ( F @ B )
= C )
=> ( ! [X2: set_nat,Y2: set_nat] :
( ( ord_less_eq_set_nat @ X2 @ Y2 )
=> ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_ord__le__eq__subst) ).
thf(157,axiom,
! [A2: nat,B: nat,F: nat > set_nat,C: set_nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ( F @ B )
= C )
=> ( ! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ord_less_eq_set_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_set_nat @ ( F @ A2 ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_ord__le__eq__subst) ).
thf(158,axiom,
! [A2: nat,F: nat > nat,B: nat,C: nat] :
( ( A2
= ( F @ B ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_ord__eq__le__subst) ).
thf(160,axiom,
! [A2: nat,F: set_nat > nat,B: set_nat,C: set_nat] :
( ( A2
= ( F @ B ) )
=> ( ( ord_less_eq_set_nat @ B @ C )
=> ( ! [X2: set_nat,Y2: set_nat] :
( ( ord_less_eq_set_nat @ X2 @ Y2 )
=> ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_ord__eq__le__subst) ).
thf(161,axiom,
! [A2: set_nat,F: nat > set_nat,B: nat,C: nat] :
( ( A2
= ( F @ B ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ord_less_eq_set_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_set_nat @ A2 @ ( F @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_ord__eq__le__subst) ).
thf(162,axiom,
! [A2: nat,B: nat,F: nat > nat,C: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ ( F @ B ) @ C )
=> ( ! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_order__subst2) ).
thf(164,axiom,
! [A2: set_nat,B: set_nat,F: set_nat > nat,C: nat] :
( ( ord_less_eq_set_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ ( F @ B ) @ C )
=> ( ! [X2: set_nat,Y2: set_nat] :
( ( ord_less_eq_set_nat @ X2 @ Y2 )
=> ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_order__subst2) ).
thf(165,axiom,
! [A2: nat,B: nat,F: nat > set_nat,C: set_nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_set_nat @ ( F @ B ) @ C )
=> ( ! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ord_less_eq_set_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_set_nat @ ( F @ A2 ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_order__subst2) ).
thf(166,axiom,
! [A2: nat,F: nat > nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_order__subst1) ).
thf(168,axiom,
! [A2: set_nat,F: nat > set_nat,B: nat,C: nat] :
( ( ord_less_eq_set_nat @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ord_less_eq_set_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_set_nat @ A2 @ ( F @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_order__subst1) ).
thf(169,axiom,
! [A2: nat,F: set_nat > nat,B: set_nat,C: set_nat] :
( ( ord_less_eq_nat @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_set_nat @ B @ C )
=> ( ! [X2: set_nat,Y2: set_nat] :
( ( ord_less_eq_set_nat @ X2 @ Y2 )
=> ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_order__subst1) ).
thf(170,axiom,
! [A2: nat] :
( ( times_times_nat @ one_one_nat @ A2 )
= A2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_comm__monoid__mult__class_Omult__1) ).
thf(171,axiom,
! [A2: nat] :
( ( times_times_nat @ A2 @ one_one_nat )
= A2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_mult_Ocomm__neutral) ).
thf(172,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/sandbox2/benchmark/theBenchmark.p',fact_89_nat__mult__eq__cancel__disj) ).
thf(173,axiom,
! [X: nat] : ( ord_less_eq_nat @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_order__refl) ).
thf(177,axiom,
! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_le__zero__eq) ).
thf(178,axiom,
! [A2: nat] :
( ( times_times_nat @ one_one_nat @ A2 )
= A2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_mult_Oleft__neutral) ).
thf(179,axiom,
! [A2: nat] :
( ( times_times_nat @ A2 @ one_one_nat )
= A2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_mult_Oright__neutral) ).
thf(180,axiom,
! [A2: nat,B: nat] :
( ( ord_less_eq_nat @ A2 @ one_one_nat )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_eq_nat @ B @ one_one_nat )
=> ( ord_less_eq_nat @ ( times_times_nat @ A2 @ B ) @ one_one_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_mult__le__one) ).
thf(181,axiom,
! [C: nat,A2: nat] :
( ( ord_less_eq_nat @ C @ one_one_nat )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
=> ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C ) @ A2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_mult__left__le) ).
thf(182,axiom,
! [M: nat,N: nat] :
( ( M
= ( times_times_nat @ M @ N ) )
=> ( ( N = one_one_nat )
| ( M = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_mult__eq__self__implies__10) ).
thf(183,axiom,
! [A: set_nat,F: nat > nat] :
( ! [X2: nat] :
( ( member_nat @ X2 @ A )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X2 ) ) )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( groups1842438620at_nat @ F @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_sum__nonneg) ).
thf(184,axiom,
! [A: set_nat,F: nat > nat] :
( ! [X2: nat] :
( ( member_nat @ X2 @ A )
=> ( ord_less_eq_nat @ ( F @ X2 ) @ zero_zero_nat ) )
=> ( ord_less_eq_nat @ ( groups1842438620at_nat @ F @ A ) @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_sum__nonpos) ).
thf(185,axiom,
ord_less_eq_nat @ zero_zero_nat @ one_one_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_zero__le__one) ).
thf(186,axiom,
~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_not__one__le__zero) ).
thf(187,axiom,
! [A2: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_mult__mono) ).
thf(188,axiom,
! [A2: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_mult__mono_H) ).
thf(189,axiom,
! [A2: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ C @ A2 ) @ ( times_times_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_mult__left__mono) ).
thf(190,axiom,
! [A2: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_mult__right__mono) ).
thf(191,axiom,
! [A2: nat,B: nat] :
( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
& ( ord_less_eq_nat @ B @ zero_zero_nat ) )
| ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
& ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
=> ( ord_less_eq_nat @ ( times_times_nat @ A2 @ B ) @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_split__mult__neg__le) ).
thf(192,axiom,
! [A2: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A2 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_mult__nonneg__nonneg) ).
thf(193,axiom,
! [A2: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
=> ( ( ord_less_eq_nat @ B @ zero_zero_nat )
=> ( ord_less_eq_nat @ ( times_times_nat @ A2 @ B ) @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_mult__nonneg__nonpos) ).
thf(194,axiom,
! [A2: nat,B: nat] :
( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ ( times_times_nat @ A2 @ B ) @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_mult__nonpos__nonneg) ).
thf(195,axiom,
! [A2: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
=> ( ( ord_less_eq_nat @ B @ zero_zero_nat )
=> ( ord_less_eq_nat @ ( times_times_nat @ B @ A2 ) @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_mult__nonneg__nonpos2) ).
thf(196,axiom,
! [A2: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ C @ A2 ) @ ( times_times_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_ordered__comm__semiring__class_Ocomm__mult__left__mono) ).
thf(197,axiom,
( set_ord_atMost_nat
= ( ^ [U: nat] :
( collect_nat
@ ^ [X4: nat] : ( ord_less_eq_nat @ X4 @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_atMost__def) ).
thf(199,axiom,
! [F: nat > nat,A: set_nat,G: nat > nat,B3: set_nat] :
( ( times_times_nat @ ( groups1842438620at_nat @ F @ A ) @ ( groups1842438620at_nat @ G @ B3 ) )
= ( groups1842438620at_nat
@ ^ [I2: nat] :
( groups1842438620at_nat
@ ^ [J2: nat] : ( times_times_nat @ ( F @ I2 ) @ ( G @ J2 ) )
@ B3 )
@ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_sum__product) ).
thf(200,axiom,
! [R: nat,F: nat > nat,A: set_nat] :
( ( times_times_nat @ R @ ( groups1842438620at_nat @ F @ A ) )
= ( groups1842438620at_nat
@ ^ [N2: nat] : ( times_times_nat @ R @ ( F @ N2 ) )
@ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_sum__distrib__left) ).
thf(201,axiom,
! [F: nat > nat,A: set_nat,R: nat] :
( ( times_times_nat @ ( groups1842438620at_nat @ F @ A ) @ R )
= ( groups1842438620at_nat
@ ^ [N2: nat] : ( times_times_nat @ ( F @ N2 ) @ R )
@ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_sum__distrib__right) ).
thf(202,axiom,
! [K2: set_nat,F: nat > nat,G: nat > nat] :
( ! [I3: nat] :
( ( member_nat @ I3 @ K2 )
=> ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
=> ( ord_less_eq_nat @ ( groups1842438620at_nat @ F @ K2 ) @ ( groups1842438620at_nat @ G @ K2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_sum__mono) ).
thf(203,axiom,
( ( ^ [X4: nat] : X4 )
= ( times_times_nat @ one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_lambda__one) ).
thf(204,axiom,
( ( ^ [H2: nat] : zero_zero_nat )
= ( times_times_nat @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_lambda__zero) ).
thf(205,axiom,
! [N: nat] :
( ( times_times_nat @ one_one_nat @ N )
= N ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_nat__mult__1) ).
thf(206,axiom,
! [N: nat] :
( ( times_times_nat @ N @ one_one_nat )
= N ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_nat__mult__1__right) ).
thf(207,axiom,
! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_le__cube) ).
thf(208,axiom,
! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_le__square) ).
thf(209,axiom,
! [I4: nat,J: nat,K: nat,L: nat] :
( ( ord_less_eq_nat @ I4 @ J )
=> ( ( ord_less_eq_nat @ K @ L )
=> ( ord_less_eq_nat @ ( times_times_nat @ I4 @ K ) @ ( times_times_nat @ J @ L ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_mult__le__mono) ).
thf(210,axiom,
! [I4: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I4 @ J )
=> ( ord_less_eq_nat @ ( times_times_nat @ I4 @ K ) @ ( times_times_nat @ J @ K ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_mult__le__mono1) ).
thf(211,axiom,
! [I4: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I4 @ J )
=> ( ord_less_eq_nat @ ( times_times_nat @ K @ I4 ) @ ( times_times_nat @ K @ J ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_mult__le__mono2) ).
thf(212,axiom,
! [N: nat] :
( ( times_times_nat @ zero_zero_nat @ N )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_mult__0) ).
thf(213,axiom,
! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_less__eq__nat_Osimps_I1_J) ).
thf(214,axiom,
! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_le__0__eq) ).
thf(215,axiom,
! [A2: nat] :
( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
= ( A2 = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_bot__nat__0_Oextremum__unique) ).
thf(216,axiom,
! [A2: nat] :
( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
=> ( A2 = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_bot__nat__0_Oextremum__uniqueI) ).
thf(220,axiom,
! [A: set_nat,G: nat > nat] :
( ! [X2: nat] :
( ( member_nat @ X2 @ A )
=> ( ( G @ X2 )
= zero_zero_nat ) )
=> ( ( groups1842438620at_nat @ G @ A )
= zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_sum_Oneutral) ).
thf(221,axiom,
! [G: nat > nat,A: set_nat] :
( ( ( groups1842438620at_nat @ G @ A )
!= zero_zero_nat )
=> ~ ! [A3: nat] :
( ( member_nat @ A3 @ A )
=> ( ( G @ A3 )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_sum_Onot__neutral__contains__not__neutral) ).
thf(222,axiom,
zero_zero_nat != one_one_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_zero__neq__one) ).
thf(223,axiom,
! [A2: nat,B: nat] :
( ( ( times_times_nat @ A2 @ B )
!= zero_zero_nat )
=> ( ( A2 != zero_zero_nat )
& ( B != zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_mult__not__zero) ).
thf(224,axiom,
! [A2: nat,B: nat] :
( ( ( times_times_nat @ A2 @ B )
= zero_zero_nat )
=> ( ( A2 = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_divisors__zero) ).
thf(225,axiom,
! [A2: nat,B: nat] :
( ( A2 != zero_zero_nat )
=> ( ( B != zero_zero_nat )
=> ( ( times_times_nat @ A2 @ B )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_no__zero__divisors) ).
thf(226,axiom,
! [C: nat,A2: nat,B: nat] :
( ( C != zero_zero_nat )
=> ( ( ( times_times_nat @ C @ A2 )
= ( times_times_nat @ C @ B ) )
= ( A2 = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_mult__left__cancel) ).
thf(227,axiom,
! [C: nat,A2: nat,B: nat] :
( ( C != zero_zero_nat )
=> ( ( ( times_times_nat @ A2 @ C )
= ( times_times_nat @ B @ C ) )
= ( A2 = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_mult__right__cancel) ).
thf(228,axiom,
! [G: nat > nat > nat,B3: set_nat,A: set_nat] :
( ( groups1842438620at_nat
@ ^ [I2: nat] : ( groups1842438620at_nat @ ( G @ I2 ) @ B3 )
@ A )
= ( groups1842438620at_nat
@ ^ [J2: nat] :
( groups1842438620at_nat
@ ^ [I2: nat] : ( G @ I2 @ J2 )
@ A )
@ B3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_sum_Oswap) ).
thf(229,axiom,
! [A: set_nat,B3: set_nat,G: nat > nat,H: nat > nat] :
( ( A = B3 )
=> ( ! [X2: nat] :
( ( member_nat @ X2 @ B3 )
=> ( ( G @ X2 )
= ( H @ X2 ) ) )
=> ( ( groups1842438620at_nat @ G @ A )
= ( groups1842438620at_nat @ H @ B3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_sum_Ocong) ).
thf(230,axiom,
! [B3: set_nat,A: set_nat,H: nat > nat,Gamma: nat > nat,Phi: nat > nat] :
( ! [Y2: nat] :
( ( member_nat @ Y2 @ B3 )
=> ? [X3: nat] :
( ( member_nat @ X3 @ A )
& ( ( H @ X3 )
= Y2 )
& ! [Ya: nat] :
( ( ( member_nat @ Ya @ A )
& ( ( H @ Ya )
= Y2 ) )
=> ( Ya = X3 ) ) ) )
=> ( ! [X2: nat] :
( ( member_nat @ X2 @ A )
=> ( ( member_nat @ ( H @ X2 ) @ B3 )
& ( ( Gamma @ ( H @ X2 ) )
= ( Phi @ X2 ) ) ) )
=> ( ( groups1842438620at_nat @ Phi @ A )
= ( groups1842438620at_nat @ Gamma @ B3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_sum_Oeq__general) ).
thf(231,axiom,
! [B3: set_nat,K: nat > nat,A: set_nat,H: nat > nat,Gamma: nat > nat,Phi: nat > nat] :
( ! [Y2: nat] :
( ( member_nat @ Y2 @ B3 )
=> ( ( member_nat @ ( K @ Y2 ) @ A )
& ( ( H @ ( K @ Y2 ) )
= Y2 ) ) )
=> ( ! [X2: nat] :
( ( member_nat @ X2 @ A )
=> ( ( member_nat @ ( H @ X2 ) @ B3 )
& ( ( K @ ( H @ X2 ) )
= X2 )
& ( ( Gamma @ ( H @ X2 ) )
= ( Phi @ X2 ) ) ) )
=> ( ( groups1842438620at_nat @ Phi @ A )
= ( groups1842438620at_nat @ Gamma @ B3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_sum_Oeq__general__inverses) ).
thf(232,axiom,
! [S: set_nat,I4: nat > nat,J: nat > nat,T: set_nat,H: nat > nat,G: nat > nat] :
( ! [A3: nat] :
( ( member_nat @ A3 @ S )
=> ( ( I4 @ ( J @ A3 ) )
= A3 ) )
=> ( ! [A3: nat] :
( ( member_nat @ A3 @ S )
=> ( member_nat @ ( J @ A3 ) @ T ) )
=> ( ! [B2: nat] :
( ( member_nat @ B2 @ T )
=> ( ( J @ ( I4 @ B2 ) )
= B2 ) )
=> ( ! [B2: nat] :
( ( member_nat @ B2 @ T )
=> ( member_nat @ ( I4 @ B2 ) @ S ) )
=> ( ! [A3: nat] :
( ( member_nat @ A3 @ S )
=> ( ( H @ ( J @ A3 ) )
= ( G @ A3 ) ) )
=> ( ( groups1842438620at_nat @ G @ S )
= ( groups1842438620at_nat @ H @ T ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_sum_Oreindex__bij__witness) ).
thf(233,axiom,
! [N: nat] : ( ord_less_eq_nat @ N @ N ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_le__refl) ).
thf(234,axiom,
! [I4: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I4 @ J )
=> ( ( ord_less_eq_nat @ J @ K )
=> ( ord_less_eq_nat @ I4 @ K ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_le__trans) ).
thf(235,axiom,
! [M: nat,N: nat] :
( ( M = N )
=> ( ord_less_eq_nat @ M @ N ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_eq__imp__le) ).
thf(236,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( ord_less_eq_nat @ N @ M )
=> ( M = N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_le__antisym) ).
thf(237,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
| ( ord_less_eq_nat @ N @ M ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_nat__le__linear) ).
thf(238,axiom,
! [P3: nat > $o,K: nat,B: nat] :
( ( P3 @ K )
=> ( ! [Y2: nat] :
( ( P3 @ Y2 )
=> ( ord_less_eq_nat @ Y2 @ B ) )
=> ? [X2: nat] :
( ( P3 @ X2 )
& ! [Y3: nat] :
( ( P3 @ Y3 )
=> ( ord_less_eq_nat @ Y3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_Nat_Oex__has__greatest__nat) ).
thf(239,axiom,
! [P3: nat > $o,X: nat,M2: nat] :
( ( P3 @ X )
=> ( ! [X2: nat] :
( ( P3 @ X2 )
=> ( ord_less_eq_nat @ X2 @ M2 ) )
=> ~ ! [M3: nat] :
( ( P3 @ M3 )
=> ~ ! [X3: nat] :
( ( P3 @ X3 )
=> ( ord_less_eq_nat @ X3 @ M3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_bounded__Max__nat) ).
thf(240,axiom,
! [M: nat,N: nat] :
( ( ( times_times_nat @ M @ N )
= zero_zero_nat )
= ( ( M = zero_zero_nat )
| ( N = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_mult__is__0) ).
thf(241,axiom,
! [M: nat] :
( ( times_times_nat @ M @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_mult__0__right) ).
thf(242,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/sandbox2/benchmark/theBenchmark.p',fact_19_mult__cancel1) ).
thf(243,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/sandbox2/benchmark/theBenchmark.p',fact_18_mult__cancel2) ).
thf(244,axiom,
! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_le0) ).
thf(245,axiom,
! [A2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_bot__nat__0_Oextremum) ).
thf(246,axiom,
! [A2: nat] :
( ( times_times_nat @ zero_zero_nat @ A2 )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_mult__zero__left) ).
thf(247,axiom,
! [A2: nat] :
( ( times_times_nat @ A2 @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_mult__zero__right) ).
thf(248,axiom,
! [A2: nat,B: nat] :
( ( ( times_times_nat @ A2 @ B )
= zero_zero_nat )
= ( ( A2 = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_mult__eq__0__iff) ).
thf(249,axiom,
! [C: nat,A2: nat,B: nat] :
( ( ( times_times_nat @ C @ A2 )
= ( times_times_nat @ C @ B ) )
= ( ( C = zero_zero_nat )
| ( A2 = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_mult__cancel__left) ).
thf(250,axiom,
! [A2: nat,C: nat,B: nat] :
( ( ( times_times_nat @ A2 @ C )
= ( times_times_nat @ B @ C ) )
= ( ( C = zero_zero_nat )
| ( A2 = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_mult__cancel__right) ).
thf(251,axiom,
! [X: nat,Y: nat] :
( ( ( set_ord_atMost_nat @ X )
= ( set_ord_atMost_nat @ Y ) )
= ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_atMost__eq__iff) ).
thf(252,axiom,
! [I4: nat,K: nat] :
( ( member_nat @ I4 @ ( set_ord_atMost_nat @ K ) )
= ( ord_less_eq_nat @ I4 @ K ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_atMost__iff) ).
thf(254,axiom,
! [X: nat,Y: nat] :
( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ X ) @ ( set_ord_atMost_nat @ Y ) )
= ( ord_less_eq_nat @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_atMost__subset__iff) ).
thf(256,axiom,
! [M: nat,N: nat] :
( ( ( times_times_nat @ M @ N )
= one_one_nat )
= ( ( M = one_one_nat )
& ( N = one_one_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_nat__mult__eq__1__iff) ).
thf(257,axiom,
! [M: nat,N: nat] :
( ( one_one_nat
= ( times_times_nat @ M @ N ) )
= ( ( M = one_one_nat )
& ( N = one_one_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_nat__1__eq__mult__iff) ).
thf(258,axiom,
( number1551313001itions
= ( ^ [P2: nat > nat,N2: nat] :
( ! [I2: nat] :
( ( ( P2 @ I2 )
!= zero_zero_nat )
=> ( ( ord_less_eq_nat @ one_one_nat @ I2 )
& ( ord_less_eq_nat @ I2 @ N2 ) ) )
& ( ( groups1842438620at_nat
@ ^ [I2: nat] : ( times_times_nat @ ( P2 @ I2 ) @ I2 )
@ ( set_ord_atMost_nat @ N2 ) )
= N2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_partitions__def) ).
thf(259,axiom,
! [P: nat > nat,N: nat] :
( ! [I3: nat] :
( ( ( P @ I3 )
!= zero_zero_nat )
=> ( ( ord_less_eq_nat @ one_one_nat @ I3 )
& ( ord_less_eq_nat @ I3 @ N ) ) )
=> ( ( ( groups1842438620at_nat
@ ^ [I2: nat] : ( times_times_nat @ ( P @ I2 ) @ I2 )
@ ( set_ord_atMost_nat @ N ) )
= N )
=> ( number1551313001itions @ P @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_partitionsI) ).
thf(260,axiom,
! [P: nat > nat,N: nat] :
( ( number1551313001itions @ P @ N )
=> ~ ( ! [I: nat] :
( ( ( P @ I )
!= zero_zero_nat )
=> ( ( ord_less_eq_nat @ one_one_nat @ I )
& ( ord_less_eq_nat @ I @ N ) ) )
=> ( ( groups1842438620at_nat
@ ^ [I2: nat] : ( times_times_nat @ ( P @ I2 ) @ I2 )
@ ( set_ord_atMost_nat @ N ) )
!= N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_partitionsE) ).
thf(261,axiom,
! [A: set_nat] :
( ( groups1842438620at_nat
@ ^ [Uu: nat] : zero_zero_nat
@ A )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_sum_Oneutral__const) ).
thf(262,conjecture,
( ( ! [I2: nat] :
( ( ( p @ I2 )
!= zero_zero_nat )
=> ( ( ord_less_eq_nat @ one_one_nat @ I2 )
& ( ord_less_eq_nat @ I2 @ zero_zero_nat ) ) )
& ( ( groups1842438620at_nat
@ ^ [I2: nat] : ( times_times_nat @ ( p @ I2 ) @ I2 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
= zero_zero_nat ) )
= ( p
= ( ^ [I2: nat] : zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(263,negated_conjecture,
( ( ( ! [I2: nat] :
( ( ( p @ I2 )
!= zero_zero_nat )
=> ( ( ord_less_eq_nat @ one_one_nat @ I2 )
& ( ord_less_eq_nat @ I2 @ zero_zero_nat ) ) )
& ( ( groups1842438620at_nat
@ ^ [I2: nat] : ( times_times_nat @ ( p @ I2 ) @ I2 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
= zero_zero_nat ) )
= ( p
= ( ^ [I2: nat] : zero_zero_nat ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[262]) ).
thf(264,plain,
( ( ( ! [I2: nat] :
( ( ( p @ I2 )
!= zero_zero_nat )
=> ( ( ord_less_eq_nat @ one_one_nat @ I2 )
& ( ord_less_eq_nat @ I2 @ zero_zero_nat ) ) )
& ( ( groups1842438620at_nat
@ ^ [I2: nat] : ( times_times_nat @ ( p @ I2 ) @ I2 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
= zero_zero_nat ) )
= ( p
= ( ^ [I2: nat] : zero_zero_nat ) ) )
= $false ),
inference(unfold_def,[status(thm)],[263]) ).
thf(265,plain,
( ( ! [A2: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ A2 @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(266,plain,
( ( ! [A2: nat,B: nat,C: nat] :
( ( ord_less_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_nat @ A2 @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(267,plain,
( ( ord_less_eq_nat
= ( ^ [A4: nat,B4: nat] :
( ( ord_less_nat @ A4 @ B4 )
| ( A4 = B4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(268,plain,
( ( ord_less_nat
= ( ^ [A4: nat,B4: nat] :
( ( ord_less_eq_nat @ A4 @ B4 )
& ( A4 != B4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(269,plain,
( ( ! [B: nat,A2: nat,C: nat] :
( ( ord_less_eq_nat @ B @ A2 )
=> ( ( ord_less_nat @ C @ B )
=> ( ord_less_nat @ C @ A2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(270,plain,
( ( ! [B: nat,A2: nat,C: nat] :
( ( ord_less_nat @ B @ A2 )
=> ( ( ord_less_eq_nat @ C @ B )
=> ( ord_less_nat @ C @ A2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(271,plain,
( ( ! [A2: nat,B: nat] :
( ( ord_less_nat @ A2 @ B )
=> ( ord_less_eq_nat @ A2 @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(272,plain,
( ( ord_less_eq_nat
= ( ^ [B4: nat,A4: nat] :
( ( ord_less_nat @ B4 @ A4 )
| ( A4 = B4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(273,plain,
( ( ord_less_nat
= ( ^ [B4: nat,A4: nat] :
( ( ord_less_eq_nat @ B4 @ A4 )
& ( A4 != B4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(274,plain,
( ( ! [B: nat,A2: nat] :
( ( ord_less_nat @ B @ A2 )
=> ( ord_less_eq_nat @ B @ A2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(275,plain,
( ( ! [A2: nat,B: nat] :
( ( A2 != B )
=> ( ( ord_less_eq_nat @ A2 @ B )
=> ( ord_less_nat @ A2 @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(276,plain,
( ( ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(277,plain,
( ( ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(278,plain,
( ( ! [A2: nat] :
~ ( ord_less_nat @ A2 @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(279,plain,
( ( ! [P3: nat > $o,N: nat] :
( ( P3 @ zero_zero_nat )
=> ( ! [N3: nat] :
( ( ord_less_nat @ zero_zero_nat @ N3 )
=> ( ~ ( P3 @ N3 )
=> ? [M5: nat] :
( ( ord_less_nat @ M5 @ N3 )
& ~ ( P3 @ M5 ) ) ) )
=> ( P3 @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(280,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(281,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(282,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(283,plain,
( ( ! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(284,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(285,plain,
( ( ! [F: nat > nat,I4: nat,J: nat] :
( ! [I3: nat,J3: nat] :
( ( ord_less_nat @ I3 @ J3 )
=> ( ord_less_nat @ ( F @ I3 ) @ ( F @ J3 ) ) )
=> ( ( ord_less_eq_nat @ I4 @ J )
=> ( ord_less_eq_nat @ ( F @ I4 ) @ ( F @ J ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(286,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( M != N )
=> ( ord_less_nat @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(287,plain,
( ( ! [M: nat,N: nat] :
( ( ( ord_less_nat @ M @ N )
| ( M = N ) )
=> ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(288,plain,
( ( ord_less_eq_nat
= ( ^ [M4: nat,N2: nat] :
( ( ord_less_nat @ M4 @ N2 )
| ( M4 = N2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(289,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(290,plain,
( ( ord_less_nat
= ( ^ [M4: nat,N2: nat] :
( ( ord_less_eq_nat @ M4 @ N2 )
& ( M4 != N2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(291,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( N != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(292,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(293,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(294,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(295,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)],[82]) ).
thf(296,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)],[83]) ).
thf(297,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ N @ one_one_nat )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(298,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)],[85]) ).
thf(299,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)],[86]) ).
thf(300,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)],[87]) ).
thf(301,plain,
( ( ! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(302,plain,
( ( ! [A2: nat] :
( ( A2 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(303,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(304,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(305,plain,
( ( ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(306,plain,
( ( ord_less_eq_nat @ one_one_nat @ one_one_nat )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(307,plain,
( ( ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(308,plain,
( ( ! [X: nat] :
( ( one_one_nat = X )
= ( X = one_one_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(309,plain,
( ( ! [B: nat,A2: nat,C: nat] :
( ( times_times_nat @ B @ ( times_times_nat @ A2 @ C ) )
= ( times_times_nat @ A2 @ ( times_times_nat @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(310,plain,
( ( times_times_nat
= ( ^ [A4: nat,B4: nat] : ( times_times_nat @ B4 @ A4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(311,plain,
( ( ! [A2: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A2 @ B ) @ C )
= ( times_times_nat @ A2 @ ( times_times_nat @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(312,plain,
( ( ! [A2: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A2 @ B ) @ C )
= ( times_times_nat @ A2 @ ( times_times_nat @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(313,plain,
( ( ! [X: nat] :
( ( zero_zero_nat = X )
= ( X = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(314,plain,
( ( ! [B: nat,A2: nat] :
( ( ord_less_eq_nat @ B @ A2 )
=> ( ( ord_less_eq_nat @ A2 @ B )
=> ( A2 = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(315,plain,
( ( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
= ( ^ [A4: nat,B4: nat] :
( ( ord_less_eq_nat @ B4 @ A4 )
& ( ord_less_eq_nat @ A4 @ B4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(316,plain,
( ( ! [B: nat,A2: nat,C: nat] :
( ( ord_less_eq_nat @ B @ A2 )
=> ( ( ord_less_eq_nat @ C @ B )
=> ( ord_less_eq_nat @ C @ A2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(317,plain,
( ( ! [P3: nat > nat > $o,A2: nat,B: nat] :
( ! [A3: nat,B2: nat] :
( ( ord_less_eq_nat @ A3 @ B2 )
=> ( P3 @ A3 @ B2 ) )
=> ( ! [A3: nat,B2: nat] :
( ( P3 @ B2 @ A3 )
=> ( P3 @ A3 @ B2 ) )
=> ( P3 @ A2 @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(318,plain,
( ( ! [A2: nat] : ( ord_less_eq_nat @ A2 @ A2 ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(319,plain,
( ( ! [X: nat,Y: nat,Z2: nat] :
( ( ord_less_eq_nat @ X @ Y )
=> ( ( ord_less_eq_nat @ Y @ Z2 )
=> ( ord_less_eq_nat @ X @ Z2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(320,plain,
( ( ! [A2: nat,B: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ B @ A2 )
=> ( A2 = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(321,plain,
( ( ! [A2: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( B = C )
=> ( ord_less_eq_nat @ A2 @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(322,plain,
( ( ! [A2: nat,B: nat,C: nat] :
( ( A2 = B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A2 @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(323,plain,
( ( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
= ( ^ [A4: nat,B4: nat] :
( ( ord_less_eq_nat @ A4 @ B4 )
& ( ord_less_eq_nat @ B4 @ A4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(324,plain,
( ( ! [Y: nat,X: nat] :
( ( ord_less_eq_nat @ Y @ X )
=> ( ( ord_less_eq_nat @ X @ Y )
= ( X = Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(325,plain,
( ( ! [X: nat,Y: nat,Z2: nat] :
( ( ( ord_less_eq_nat @ X @ Y )
=> ~ ( ord_less_eq_nat @ Y @ Z2 ) )
=> ( ( ( ord_less_eq_nat @ Y @ X )
=> ~ ( ord_less_eq_nat @ X @ Z2 ) )
=> ( ( ( ord_less_eq_nat @ X @ Z2 )
=> ~ ( ord_less_eq_nat @ Z2 @ Y ) )
=> ( ( ( ord_less_eq_nat @ Z2 @ Y )
=> ~ ( ord_less_eq_nat @ Y @ X ) )
=> ( ( ( ord_less_eq_nat @ Y @ Z2 )
=> ~ ( ord_less_eq_nat @ Z2 @ X ) )
=> ~ ( ( ord_less_eq_nat @ Z2 @ X )
=> ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(326,plain,
( ( ! [A2: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A2 @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(327,plain,
( ( ! [X: nat,Y: nat] :
( ~ ( ord_less_eq_nat @ X @ Y )
=> ( ord_less_eq_nat @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(328,plain,
( ( ! [X: nat,Y: nat] :
( ( X = Y )
=> ( ord_less_eq_nat @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(329,plain,
( ( ! [X: nat,Y: nat] :
( ( ord_less_eq_nat @ X @ Y )
| ( ord_less_eq_nat @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(330,plain,
( ( ! [X: nat,Y: nat] :
( ( ord_less_eq_nat @ X @ Y )
=> ( ( ord_less_eq_nat @ Y @ X )
=> ( X = Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(331,plain,
( ( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
= ( ^ [X4: nat,Y5: nat] :
( ( ord_less_eq_nat @ X4 @ Y5 )
& ( ord_less_eq_nat @ Y5 @ X4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(332,plain,
( ( ! [A2: nat,B: nat,F: nat > nat,C: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ( F @ B )
= C )
=> ( ! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(333,plain,
( ( ! [A2: set_nat,B: set_nat,F: set_nat > nat,C: nat] :
( ( ord_less_eq_set_nat @ A2 @ B )
=> ( ( ( F @ B )
= C )
=> ( ! [X2: set_nat,Y2: set_nat] :
( ( ord_less_eq_set_nat @ X2 @ Y2 )
=> ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(334,plain,
( ( ! [A2: nat,B: nat,F: nat > set_nat,C: set_nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ( F @ B )
= C )
=> ( ! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ord_less_eq_set_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_set_nat @ ( F @ A2 ) @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(335,plain,
( ( ! [A2: nat,F: nat > nat,B: nat,C: nat] :
( ( A2
= ( F @ B ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(336,plain,
( ( ! [A2: nat,F: set_nat > nat,B: set_nat,C: set_nat] :
( ( A2
= ( F @ B ) )
=> ( ( ord_less_eq_set_nat @ B @ C )
=> ( ! [X2: set_nat,Y2: set_nat] :
( ( ord_less_eq_set_nat @ X2 @ Y2 )
=> ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(337,plain,
( ( ! [A2: set_nat,F: nat > set_nat,B: nat,C: nat] :
( ( A2
= ( F @ B ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ord_less_eq_set_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_set_nat @ A2 @ ( F @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(338,plain,
( ( ! [A2: nat,B: nat,F: nat > nat,C: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ ( F @ B ) @ C )
=> ( ! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(339,plain,
( ( ! [A2: set_nat,B: set_nat,F: set_nat > nat,C: nat] :
( ( ord_less_eq_set_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ ( F @ B ) @ C )
=> ( ! [X2: set_nat,Y2: set_nat] :
( ( ord_less_eq_set_nat @ X2 @ Y2 )
=> ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(340,plain,
( ( ! [A2: nat,B: nat,F: nat > set_nat,C: set_nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_set_nat @ ( F @ B ) @ C )
=> ( ! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ord_less_eq_set_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_set_nat @ ( F @ A2 ) @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(341,plain,
( ( ! [A2: nat,F: nat > nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(342,plain,
( ( ! [A2: set_nat,F: nat > set_nat,B: nat,C: nat] :
( ( ord_less_eq_set_nat @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ord_less_eq_set_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_set_nat @ A2 @ ( F @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(343,plain,
( ( ! [A2: nat,F: set_nat > nat,B: set_nat,C: set_nat] :
( ( ord_less_eq_nat @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_set_nat @ B @ C )
=> ( ! [X2: set_nat,Y2: set_nat] :
( ( ord_less_eq_set_nat @ X2 @ Y2 )
=> ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(344,plain,
( ( ! [A2: nat] :
( ( times_times_nat @ one_one_nat @ A2 )
= A2 ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(345,plain,
( ( ! [A2: nat] :
( ( times_times_nat @ A2 @ one_one_nat )
= A2 ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(346,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)],[172]) ).
thf(347,plain,
( ( ! [X: nat] : ( ord_less_eq_nat @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(348,plain,
( ( ! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(349,plain,
( ( ! [A2: nat] :
( ( times_times_nat @ one_one_nat @ A2 )
= A2 ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(350,plain,
( ( ! [A2: nat] :
( ( times_times_nat @ A2 @ one_one_nat )
= A2 ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(351,plain,
( ( ! [A2: nat,B: nat] :
( ( ord_less_eq_nat @ A2 @ one_one_nat )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_eq_nat @ B @ one_one_nat )
=> ( ord_less_eq_nat @ ( times_times_nat @ A2 @ B ) @ one_one_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(352,plain,
( ( ! [C: nat,A2: nat] :
( ( ord_less_eq_nat @ C @ one_one_nat )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
=> ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C ) @ A2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(353,plain,
( ( ! [M: nat,N: nat] :
( ( M
= ( times_times_nat @ M @ N ) )
=> ( ( N = one_one_nat )
| ( M = zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(354,plain,
( ( ! [A: set_nat,F: nat > nat] :
( ! [X2: nat] :
( ( member_nat @ X2 @ A )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X2 ) ) )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( groups1842438620at_nat @ F @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(355,plain,
( ( ! [A: set_nat,F: nat > nat] :
( ! [X2: nat] :
( ( member_nat @ X2 @ A )
=> ( ord_less_eq_nat @ ( F @ X2 ) @ zero_zero_nat ) )
=> ( ord_less_eq_nat @ ( groups1842438620at_nat @ F @ A ) @ zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(356,plain,
( ( ord_less_eq_nat @ zero_zero_nat @ one_one_nat )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(357,plain,
( ( ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(358,plain,
( ( ! [A2: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(359,plain,
( ( ! [A2: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(360,plain,
( ( ! [A2: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ C @ A2 ) @ ( times_times_nat @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(361,plain,
( ( ! [A2: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(362,plain,
( ( ! [A2: nat,B: nat] :
( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
& ( ord_less_eq_nat @ B @ zero_zero_nat ) )
| ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
& ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
=> ( ord_less_eq_nat @ ( times_times_nat @ A2 @ B ) @ zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(363,plain,
( ( ! [A2: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A2 @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(364,plain,
( ( ! [A2: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
=> ( ( ord_less_eq_nat @ B @ zero_zero_nat )
=> ( ord_less_eq_nat @ ( times_times_nat @ A2 @ B ) @ zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(365,plain,
( ( ! [A2: nat,B: nat] :
( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ ( times_times_nat @ A2 @ B ) @ zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(366,plain,
( ( ! [A2: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
=> ( ( ord_less_eq_nat @ B @ zero_zero_nat )
=> ( ord_less_eq_nat @ ( times_times_nat @ B @ A2 ) @ zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(367,plain,
( ( ! [A2: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ C @ A2 ) @ ( times_times_nat @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(368,plain,
( ( set_ord_atMost_nat
= ( ^ [U: nat] :
( collect_nat
@ ^ [X4: nat] : ( ord_less_eq_nat @ X4 @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(369,plain,
( ( ! [F: nat > nat,A: set_nat,G: nat > nat,B3: set_nat] :
( ( times_times_nat @ ( groups1842438620at_nat @ F @ A ) @ ( groups1842438620at_nat @ G @ B3 ) )
= ( groups1842438620at_nat
@ ^ [I2: nat] :
( groups1842438620at_nat
@ ^ [J2: nat] : ( times_times_nat @ ( F @ I2 ) @ ( G @ J2 ) )
@ B3 )
@ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(370,plain,
( ( ! [R: nat,F: nat > nat,A: set_nat] :
( ( times_times_nat @ R @ ( groups1842438620at_nat @ F @ A ) )
= ( groups1842438620at_nat
@ ^ [N2: nat] : ( times_times_nat @ R @ ( F @ N2 ) )
@ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(371,plain,
( ( ! [F: nat > nat,A: set_nat,R: nat] :
( ( times_times_nat @ ( groups1842438620at_nat @ F @ A ) @ R )
= ( groups1842438620at_nat
@ ^ [N2: nat] : ( times_times_nat @ ( F @ N2 ) @ R )
@ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(372,plain,
( ( ! [K2: set_nat,F: nat > nat,G: nat > nat] :
( ! [I3: nat] :
( ( member_nat @ I3 @ K2 )
=> ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
=> ( ord_less_eq_nat @ ( groups1842438620at_nat @ F @ K2 ) @ ( groups1842438620at_nat @ G @ K2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(373,plain,
( ( ( ^ [X4: nat] : X4 )
= ( times_times_nat @ one_one_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(374,plain,
( ( ( ^ [H2: nat] : zero_zero_nat )
= ( times_times_nat @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(375,plain,
( ( ! [N: nat] :
( ( times_times_nat @ one_one_nat @ N )
= N ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(376,plain,
( ( ! [N: nat] :
( ( times_times_nat @ N @ one_one_nat )
= N ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(377,plain,
( ( ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(378,plain,
( ( ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(379,plain,
( ( ! [I4: nat,J: nat,K: nat,L: nat] :
( ( ord_less_eq_nat @ I4 @ J )
=> ( ( ord_less_eq_nat @ K @ L )
=> ( ord_less_eq_nat @ ( times_times_nat @ I4 @ K ) @ ( times_times_nat @ J @ L ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(380,plain,
( ( ! [I4: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I4 @ J )
=> ( ord_less_eq_nat @ ( times_times_nat @ I4 @ K ) @ ( times_times_nat @ J @ K ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(381,plain,
( ( ! [I4: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I4 @ J )
=> ( ord_less_eq_nat @ ( times_times_nat @ K @ I4 ) @ ( times_times_nat @ K @ J ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(382,plain,
( ( ! [N: nat] :
( ( times_times_nat @ zero_zero_nat @ N )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(383,plain,
( ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(384,plain,
( ( ! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(385,plain,
( ( ! [A2: nat] :
( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
= ( A2 = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(386,plain,
( ( ! [A2: nat] :
( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
=> ( A2 = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(387,plain,
( ( ! [A: set_nat,G: nat > nat] :
( ! [X2: nat] :
( ( member_nat @ X2 @ A )
=> ( ( G @ X2 )
= zero_zero_nat ) )
=> ( ( groups1842438620at_nat @ G @ A )
= zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(388,plain,
( ( ! [G: nat > nat,A: set_nat] :
( ( ( groups1842438620at_nat @ G @ A )
!= zero_zero_nat )
=> ~ ! [A3: nat] :
( ( member_nat @ A3 @ A )
=> ( ( G @ A3 )
= zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(389,plain,
( ( zero_zero_nat != one_one_nat )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(390,plain,
( ( ! [A2: nat,B: nat] :
( ( ( times_times_nat @ A2 @ B )
!= zero_zero_nat )
=> ( ( A2 != zero_zero_nat )
& ( B != zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(391,plain,
( ( ! [A2: nat,B: nat] :
( ( ( times_times_nat @ A2 @ B )
= zero_zero_nat )
=> ( ( A2 = zero_zero_nat )
| ( B = zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(392,plain,
( ( ! [A2: nat,B: nat] :
( ( A2 != zero_zero_nat )
=> ( ( B != zero_zero_nat )
=> ( ( times_times_nat @ A2 @ B )
!= zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(393,plain,
( ( ! [C: nat,A2: nat,B: nat] :
( ( C != zero_zero_nat )
=> ( ( ( times_times_nat @ C @ A2 )
= ( times_times_nat @ C @ B ) )
= ( A2 = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(394,plain,
( ( ! [C: nat,A2: nat,B: nat] :
( ( C != zero_zero_nat )
=> ( ( ( times_times_nat @ A2 @ C )
= ( times_times_nat @ B @ C ) )
= ( A2 = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(395,plain,
( ( ! [G: nat > nat > nat,B3: set_nat,A: set_nat] :
( ( groups1842438620at_nat
@ ^ [I2: nat] : ( groups1842438620at_nat @ ( G @ I2 ) @ B3 )
@ A )
= ( groups1842438620at_nat
@ ^ [J2: nat] :
( groups1842438620at_nat
@ ^ [I2: nat] : ( G @ I2 @ J2 )
@ A )
@ B3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(396,plain,
( ( ! [A: set_nat,B3: set_nat,G: nat > nat,H: nat > nat] :
( ( A = B3 )
=> ( ! [X2: nat] :
( ( member_nat @ X2 @ B3 )
=> ( ( G @ X2 )
= ( H @ X2 ) ) )
=> ( ( groups1842438620at_nat @ G @ A )
= ( groups1842438620at_nat @ H @ B3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(397,plain,
( ( ! [B3: set_nat,A: set_nat,H: nat > nat,Gamma: nat > nat,Phi: nat > nat] :
( ! [Y2: nat] :
( ( member_nat @ Y2 @ B3 )
=> ? [X3: nat] :
( ( member_nat @ X3 @ A )
& ( ( H @ X3 )
= Y2 )
& ! [Ya: nat] :
( ( ( member_nat @ Ya @ A )
& ( ( H @ Ya )
= Y2 ) )
=> ( Ya = X3 ) ) ) )
=> ( ! [X2: nat] :
( ( member_nat @ X2 @ A )
=> ( ( member_nat @ ( H @ X2 ) @ B3 )
& ( ( Gamma @ ( H @ X2 ) )
= ( Phi @ X2 ) ) ) )
=> ( ( groups1842438620at_nat @ Phi @ A )
= ( groups1842438620at_nat @ Gamma @ B3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(398,plain,
( ( ! [B3: set_nat,K: nat > nat,A: set_nat,H: nat > nat,Gamma: nat > nat,Phi: nat > nat] :
( ! [Y2: nat] :
( ( member_nat @ Y2 @ B3 )
=> ( ( member_nat @ ( K @ Y2 ) @ A )
& ( ( H @ ( K @ Y2 ) )
= Y2 ) ) )
=> ( ! [X2: nat] :
( ( member_nat @ X2 @ A )
=> ( ( member_nat @ ( H @ X2 ) @ B3 )
& ( ( K @ ( H @ X2 ) )
= X2 )
& ( ( Gamma @ ( H @ X2 ) )
= ( Phi @ X2 ) ) ) )
=> ( ( groups1842438620at_nat @ Phi @ A )
= ( groups1842438620at_nat @ Gamma @ B3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(399,plain,
( ( ! [S: set_nat,I4: nat > nat,J: nat > nat,T: set_nat,H: nat > nat,G: nat > nat] :
( ! [A3: nat] :
( ( member_nat @ A3 @ S )
=> ( ( I4 @ ( J @ A3 ) )
= A3 ) )
=> ( ! [A3: nat] :
( ( member_nat @ A3 @ S )
=> ( member_nat @ ( J @ A3 ) @ T ) )
=> ( ! [B2: nat] :
( ( member_nat @ B2 @ T )
=> ( ( J @ ( I4 @ B2 ) )
= B2 ) )
=> ( ! [B2: nat] :
( ( member_nat @ B2 @ T )
=> ( member_nat @ ( I4 @ B2 ) @ S ) )
=> ( ! [A3: nat] :
( ( member_nat @ A3 @ S )
=> ( ( H @ ( J @ A3 ) )
= ( G @ A3 ) ) )
=> ( ( groups1842438620at_nat @ G @ S )
= ( groups1842438620at_nat @ H @ T ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(400,plain,
( ( ! [N: nat] : ( ord_less_eq_nat @ N @ N ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(401,plain,
( ( ! [I4: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I4 @ J )
=> ( ( ord_less_eq_nat @ J @ K )
=> ( ord_less_eq_nat @ I4 @ K ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(402,plain,
( ( ! [M: nat,N: nat] :
( ( M = N )
=> ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(403,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)],[236]) ).
thf(404,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
| ( ord_less_eq_nat @ N @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(405,plain,
( ( ! [P3: nat > $o,K: nat,B: nat] :
( ( P3 @ K )
=> ( ! [Y2: nat] :
( ( P3 @ Y2 )
=> ( ord_less_eq_nat @ Y2 @ B ) )
=> ? [X2: nat] :
( ( P3 @ X2 )
& ! [Y3: nat] :
( ( P3 @ Y3 )
=> ( ord_less_eq_nat @ Y3 @ X2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(406,plain,
( ( ! [P3: nat > $o,X: nat,M2: nat] :
( ( P3 @ X )
=> ( ! [X2: nat] :
( ( P3 @ X2 )
=> ( ord_less_eq_nat @ X2 @ M2 ) )
=> ~ ! [M3: nat] :
( ( P3 @ M3 )
=> ~ ! [X3: nat] :
( ( P3 @ X3 )
=> ( ord_less_eq_nat @ X3 @ M3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(407,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)],[240]) ).
thf(408,plain,
( ( ! [M: nat] :
( ( times_times_nat @ M @ zero_zero_nat )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(409,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)],[242]) ).
thf(410,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)],[243]) ).
thf(411,plain,
( ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(412,plain,
( ( ! [A2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A2 ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(413,plain,
( ( ! [A2: nat] :
( ( times_times_nat @ zero_zero_nat @ A2 )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(414,plain,
( ( ! [A2: nat] :
( ( times_times_nat @ A2 @ zero_zero_nat )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(415,plain,
( ( ! [A2: nat,B: nat] :
( ( ( times_times_nat @ A2 @ B )
= zero_zero_nat )
= ( ( A2 = zero_zero_nat )
| ( B = zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(416,plain,
( ( ! [C: nat,A2: nat,B: nat] :
( ( ( times_times_nat @ C @ A2 )
= ( times_times_nat @ C @ B ) )
= ( ( C = zero_zero_nat )
| ( A2 = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(417,plain,
( ( ! [A2: nat,C: nat,B: nat] :
( ( ( times_times_nat @ A2 @ C )
= ( times_times_nat @ B @ C ) )
= ( ( C = zero_zero_nat )
| ( A2 = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(418,plain,
( ( ! [X: nat,Y: nat] :
( ( ( set_ord_atMost_nat @ X )
= ( set_ord_atMost_nat @ Y ) )
= ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(419,plain,
( ( ! [I4: nat,K: nat] :
( ( member_nat @ I4 @ ( set_ord_atMost_nat @ K ) )
= ( ord_less_eq_nat @ I4 @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(420,plain,
( ( ! [X: nat,Y: nat] :
( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ X ) @ ( set_ord_atMost_nat @ Y ) )
= ( ord_less_eq_nat @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(421,plain,
( ( ! [M: nat,N: nat] :
( ( ( times_times_nat @ M @ N )
= one_one_nat )
= ( ( M = one_one_nat )
& ( N = one_one_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(422,plain,
( ( ! [M: nat,N: nat] :
( ( one_one_nat
= ( times_times_nat @ M @ N ) )
= ( ( M = one_one_nat )
& ( N = one_one_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(423,plain,
( ( number1551313001itions
= ( ^ [P2: nat > nat,N2: nat] :
( ! [I2: nat] :
( ( ( P2 @ I2 )
!= zero_zero_nat )
=> ( ( ord_less_eq_nat @ one_one_nat @ I2 )
& ( ord_less_eq_nat @ I2 @ N2 ) ) )
& ( ( groups1842438620at_nat
@ ^ [I2: nat] : ( times_times_nat @ ( P2 @ I2 ) @ I2 )
@ ( set_ord_atMost_nat @ N2 ) )
= N2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(424,plain,
( ( ! [P: nat > nat,N: nat] :
( ! [I3: nat] :
( ( ( P @ I3 )
!= zero_zero_nat )
=> ( ( ord_less_eq_nat @ one_one_nat @ I3 )
& ( ord_less_eq_nat @ I3 @ N ) ) )
=> ( ( ( groups1842438620at_nat
@ ^ [I2: nat] : ( times_times_nat @ ( P @ I2 ) @ I2 )
@ ( set_ord_atMost_nat @ N ) )
= N )
=> ( number1551313001itions @ P @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(425,plain,
( ( ! [P: nat > nat,N: nat] :
( ( number1551313001itions @ P @ N )
=> ~ ( ! [I: nat] :
( ( ( P @ I )
!= zero_zero_nat )
=> ( ( ord_less_eq_nat @ one_one_nat @ I )
& ( ord_less_eq_nat @ I @ N ) ) )
=> ( ( groups1842438620at_nat
@ ^ [I2: nat] : ( times_times_nat @ ( P @ I2 ) @ I2 )
@ ( set_ord_atMost_nat @ N ) )
!= N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(426,plain,
( ( ! [A: set_nat] :
( ( groups1842438620at_nat
@ ^ [Uu: nat] : zero_zero_nat
@ A )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(427,plain,
( ( ( ! [I2: nat] :
( ( ( p @ I2 )
!= zero_zero_nat )
=> ( ( ord_less_eq_nat @ one_one_nat @ I2 )
& ( ord_less_eq_nat @ I2 @ zero_zero_nat ) ) )
& ( ( groups1842438620at_nat
@ ^ [I2: nat] : ( times_times_nat @ ( p @ I2 ) @ I2 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
= zero_zero_nat ) )
!= ( p
= ( ^ [I2: nat] : zero_zero_nat ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[264]) ).
thf(428,plain,
( ( ! [A: set_nat] :
( ( groups1842438620at_nat
@ ^ [Uu: nat] : zero_zero_nat
@ A )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(429,plain,
( ( ! [P: nat > nat,N: nat] :
( ( number1551313001itions @ P @ N )
=> ~ ( ! [I: nat] :
( ( ( P @ I )
!= zero_zero_nat )
=> ( ( ord_less_eq_nat @ one_one_nat @ I )
& ( ord_less_eq_nat @ I @ N ) ) )
=> ( ( groups1842438620at_nat
@ ^ [I2: nat] : ( times_times_nat @ ( P @ I2 ) @ I2 )
@ ( set_ord_atMost_nat @ N ) )
!= N ) ) ) )
= $true ),
inference(copy,[status(thm)],[425]) ).
thf(430,plain,
( ( ! [P: nat > nat,N: nat] :
( ! [I3: nat] :
( ( ( P @ I3 )
!= zero_zero_nat )
=> ( ( ord_less_eq_nat @ one_one_nat @ I3 )
& ( ord_less_eq_nat @ I3 @ N ) ) )
=> ( ( ( groups1842438620at_nat
@ ^ [I2: nat] : ( times_times_nat @ ( P @ I2 ) @ I2 )
@ ( set_ord_atMost_nat @ N ) )
= N )
=> ( number1551313001itions @ P @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(431,plain,
( ( number1551313001itions
= ( ^ [P2: nat > nat,N2: nat] :
( ! [I2: nat] :
( ( ( P2 @ I2 )
!= zero_zero_nat )
=> ( ( ord_less_eq_nat @ one_one_nat @ I2 )
& ( ord_less_eq_nat @ I2 @ N2 ) ) )
& ( ( groups1842438620at_nat
@ ^ [I2: nat] : ( times_times_nat @ ( P2 @ I2 ) @ I2 )
@ ( set_ord_atMost_nat @ N2 ) )
= N2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(432,plain,
( ( ! [M: nat,N: nat] :
( ( one_one_nat
= ( times_times_nat @ M @ N ) )
= ( ( M = one_one_nat )
& ( N = one_one_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(433,plain,
( ( ! [M: nat,N: nat] :
( ( ( times_times_nat @ M @ N )
= one_one_nat )
= ( ( M = one_one_nat )
& ( N = one_one_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(434,plain,
( ( ! [X: nat,Y: nat] :
( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ X ) @ ( set_ord_atMost_nat @ Y ) )
= ( ord_less_eq_nat @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(435,plain,
( ( ! [I4: nat,K: nat] :
( ( member_nat @ I4 @ ( set_ord_atMost_nat @ K ) )
= ( ord_less_eq_nat @ I4 @ K ) ) )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(436,plain,
( ( ! [X: nat,Y: nat] :
( ( ( set_ord_atMost_nat @ X )
= ( set_ord_atMost_nat @ Y ) )
= ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(437,plain,
( ( ! [A2: nat,C: nat,B: nat] :
( ( ( times_times_nat @ A2 @ C )
= ( times_times_nat @ B @ C ) )
= ( ( C = zero_zero_nat )
| ( A2 = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(438,plain,
( ( ! [C: nat,A2: nat,B: nat] :
( ( ( times_times_nat @ C @ A2 )
= ( times_times_nat @ C @ B ) )
= ( ( C = zero_zero_nat )
| ( A2 = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(439,plain,
( ( ! [A2: nat,B: nat] :
( ( ( times_times_nat @ A2 @ B )
= zero_zero_nat )
= ( ( A2 = zero_zero_nat )
| ( B = zero_zero_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(440,plain,
( ( ! [A2: nat] :
( ( times_times_nat @ A2 @ zero_zero_nat )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(441,plain,
( ( ! [A2: nat] :
( ( times_times_nat @ zero_zero_nat @ A2 )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(442,plain,
( ( ! [A2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A2 ) )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(443,plain,
( ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(444,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)],[410]) ).
thf(445,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)],[409]) ).
thf(446,plain,
( ( ! [M: nat] :
( ( times_times_nat @ M @ zero_zero_nat )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(447,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)],[407]) ).
thf(448,plain,
( ( ! [P3: nat > $o,X: nat,M2: nat] :
( ( P3 @ X )
=> ( ! [X2: nat] :
( ( P3 @ X2 )
=> ( ord_less_eq_nat @ X2 @ M2 ) )
=> ~ ! [M3: nat] :
( ( P3 @ M3 )
=> ~ ! [X3: nat] :
( ( P3 @ X3 )
=> ( ord_less_eq_nat @ X3 @ M3 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(449,plain,
( ( ! [P3: nat > $o,K: nat,B: nat] :
( ( P3 @ K )
=> ( ! [Y2: nat] :
( ( P3 @ Y2 )
=> ( ord_less_eq_nat @ Y2 @ B ) )
=> ? [X2: nat] :
( ( P3 @ X2 )
& ! [Y3: nat] :
( ( P3 @ Y3 )
=> ( ord_less_eq_nat @ Y3 @ X2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(450,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
| ( ord_less_eq_nat @ N @ M ) ) )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(451,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( ord_less_eq_nat @ N @ M )
=> ( M = N ) ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(452,plain,
( ( ! [M: nat,N: nat] :
( ( M = N )
=> ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(453,plain,
( ( ! [I4: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I4 @ J )
=> ( ( ord_less_eq_nat @ J @ K )
=> ( ord_less_eq_nat @ I4 @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(454,plain,
( ( ! [N: nat] : ( ord_less_eq_nat @ N @ N ) )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(455,plain,
( ( ! [S: set_nat,I4: nat > nat,J: nat > nat,T: set_nat,H: nat > nat,G: nat > nat] :
( ! [A3: nat] :
( ( member_nat @ A3 @ S )
=> ( ( I4 @ ( J @ A3 ) )
= A3 ) )
=> ( ! [A3: nat] :
( ( member_nat @ A3 @ S )
=> ( member_nat @ ( J @ A3 ) @ T ) )
=> ( ! [B2: nat] :
( ( member_nat @ B2 @ T )
=> ( ( J @ ( I4 @ B2 ) )
= B2 ) )
=> ( ! [B2: nat] :
( ( member_nat @ B2 @ T )
=> ( member_nat @ ( I4 @ B2 ) @ S ) )
=> ( ! [A3: nat] :
( ( member_nat @ A3 @ S )
=> ( ( H @ ( J @ A3 ) )
= ( G @ A3 ) ) )
=> ( ( groups1842438620at_nat @ G @ S )
= ( groups1842438620at_nat @ H @ T ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(456,plain,
( ( ! [B3: set_nat,K: nat > nat,A: set_nat,H: nat > nat,Gamma: nat > nat,Phi: nat > nat] :
( ! [Y2: nat] :
( ( member_nat @ Y2 @ B3 )
=> ( ( member_nat @ ( K @ Y2 ) @ A )
& ( ( H @ ( K @ Y2 ) )
= Y2 ) ) )
=> ( ! [X2: nat] :
( ( member_nat @ X2 @ A )
=> ( ( member_nat @ ( H @ X2 ) @ B3 )
& ( ( K @ ( H @ X2 ) )
= X2 )
& ( ( Gamma @ ( H @ X2 ) )
= ( Phi @ X2 ) ) ) )
=> ( ( groups1842438620at_nat @ Phi @ A )
= ( groups1842438620at_nat @ Gamma @ B3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(457,plain,
( ( ! [B3: set_nat,A: set_nat,H: nat > nat,Gamma: nat > nat,Phi: nat > nat] :
( ! [Y2: nat] :
( ( member_nat @ Y2 @ B3 )
=> ? [X3: nat] :
( ( member_nat @ X3 @ A )
& ( ( H @ X3 )
= Y2 )
& ! [Ya: nat] :
( ( ( member_nat @ Ya @ A )
& ( ( H @ Ya )
= Y2 ) )
=> ( Ya = X3 ) ) ) )
=> ( ! [X2: nat] :
( ( member_nat @ X2 @ A )
=> ( ( member_nat @ ( H @ X2 ) @ B3 )
& ( ( Gamma @ ( H @ X2 ) )
= ( Phi @ X2 ) ) ) )
=> ( ( groups1842438620at_nat @ Phi @ A )
= ( groups1842438620at_nat @ Gamma @ B3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(458,plain,
( ( ! [A: set_nat,B3: set_nat,G: nat > nat,H: nat > nat] :
( ( A = B3 )
=> ( ! [X2: nat] :
( ( member_nat @ X2 @ B3 )
=> ( ( G @ X2 )
= ( H @ X2 ) ) )
=> ( ( groups1842438620at_nat @ G @ A )
= ( groups1842438620at_nat @ H @ B3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(459,plain,
( ( ! [G: nat > nat > nat,B3: set_nat,A: set_nat] :
( ( groups1842438620at_nat
@ ^ [I2: nat] : ( groups1842438620at_nat @ ( G @ I2 ) @ B3 )
@ A )
= ( groups1842438620at_nat
@ ^ [J2: nat] :
( groups1842438620at_nat
@ ^ [I2: nat] : ( G @ I2 @ J2 )
@ A )
@ B3 ) ) )
= $true ),
inference(copy,[status(thm)],[395]) ).
thf(460,plain,
( ( ! [C: nat,A2: nat,B: nat] :
( ( C != zero_zero_nat )
=> ( ( ( times_times_nat @ A2 @ C )
= ( times_times_nat @ B @ C ) )
= ( A2 = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[394]) ).
thf(461,plain,
( ( ! [C: nat,A2: nat,B: nat] :
( ( C != zero_zero_nat )
=> ( ( ( times_times_nat @ C @ A2 )
= ( times_times_nat @ C @ B ) )
= ( A2 = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(462,plain,
( ( ! [A2: nat,B: nat] :
( ( A2 != zero_zero_nat )
=> ( ( B != zero_zero_nat )
=> ( ( times_times_nat @ A2 @ B )
!= zero_zero_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(463,plain,
( ( ! [A2: nat,B: nat] :
( ( ( times_times_nat @ A2 @ B )
= zero_zero_nat )
=> ( ( A2 = zero_zero_nat )
| ( B = zero_zero_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(464,plain,
( ( ! [A2: nat,B: nat] :
( ( ( times_times_nat @ A2 @ B )
!= zero_zero_nat )
=> ( ( A2 != zero_zero_nat )
& ( B != zero_zero_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(465,plain,
( ( zero_zero_nat != one_one_nat )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(466,plain,
( ( ! [G: nat > nat,A: set_nat] :
( ( ( groups1842438620at_nat @ G @ A )
!= zero_zero_nat )
=> ~ ! [A3: nat] :
( ( member_nat @ A3 @ A )
=> ( ( G @ A3 )
= zero_zero_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[388]) ).
thf(467,plain,
( ( ! [A: set_nat,G: nat > nat] :
( ! [X2: nat] :
( ( member_nat @ X2 @ A )
=> ( ( G @ X2 )
= zero_zero_nat ) )
=> ( ( groups1842438620at_nat @ G @ A )
= zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[387]) ).
thf(468,plain,
( ( ! [A2: nat] :
( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
=> ( A2 = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(469,plain,
( ( ! [A2: nat] :
( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
= ( A2 = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[385]) ).
thf(470,plain,
( ( ! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(471,plain,
( ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(472,plain,
( ( ! [N: nat] :
( ( times_times_nat @ zero_zero_nat @ N )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(473,plain,
( ( ! [I4: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I4 @ J )
=> ( ord_less_eq_nat @ ( times_times_nat @ K @ I4 ) @ ( times_times_nat @ K @ J ) ) ) )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(474,plain,
( ( ! [I4: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I4 @ J )
=> ( ord_less_eq_nat @ ( times_times_nat @ I4 @ K ) @ ( times_times_nat @ J @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[380]) ).
thf(475,plain,
( ( ! [I4: nat,J: nat,K: nat,L: nat] :
( ( ord_less_eq_nat @ I4 @ J )
=> ( ( ord_less_eq_nat @ K @ L )
=> ( ord_less_eq_nat @ ( times_times_nat @ I4 @ K ) @ ( times_times_nat @ J @ L ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(476,plain,
( ( ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) )
= $true ),
inference(copy,[status(thm)],[378]) ).
thf(477,plain,
( ( ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(478,plain,
( ( ! [N: nat] :
( ( times_times_nat @ N @ one_one_nat )
= N ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(479,plain,
( ( ! [N: nat] :
( ( times_times_nat @ one_one_nat @ N )
= N ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(480,plain,
( ( ( ^ [H2: nat] : zero_zero_nat )
= ( times_times_nat @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(481,plain,
( ( ( ^ [X4: nat] : X4 )
= ( times_times_nat @ one_one_nat ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(482,plain,
( ( ! [K2: set_nat,F: nat > nat,G: nat > nat] :
( ! [I3: nat] :
( ( member_nat @ I3 @ K2 )
=> ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
=> ( ord_less_eq_nat @ ( groups1842438620at_nat @ F @ K2 ) @ ( groups1842438620at_nat @ G @ K2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(483,plain,
( ( ! [F: nat > nat,A: set_nat,R: nat] :
( ( times_times_nat @ ( groups1842438620at_nat @ F @ A ) @ R )
= ( groups1842438620at_nat
@ ^ [N2: nat] : ( times_times_nat @ ( F @ N2 ) @ R )
@ A ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(484,plain,
( ( ! [R: nat,F: nat > nat,A: set_nat] :
( ( times_times_nat @ R @ ( groups1842438620at_nat @ F @ A ) )
= ( groups1842438620at_nat
@ ^ [N2: nat] : ( times_times_nat @ R @ ( F @ N2 ) )
@ A ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(485,plain,
( ( ! [F: nat > nat,A: set_nat,G: nat > nat,B3: set_nat] :
( ( times_times_nat @ ( groups1842438620at_nat @ F @ A ) @ ( groups1842438620at_nat @ G @ B3 ) )
= ( groups1842438620at_nat
@ ^ [I2: nat] :
( groups1842438620at_nat
@ ^ [J2: nat] : ( times_times_nat @ ( F @ I2 ) @ ( G @ J2 ) )
@ B3 )
@ A ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(486,plain,
( ( set_ord_atMost_nat
= ( ^ [U: nat] :
( collect_nat
@ ^ [X4: nat] : ( ord_less_eq_nat @ X4 @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(487,plain,
( ( ! [A2: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ C @ A2 ) @ ( times_times_nat @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(488,plain,
( ( ! [A2: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
=> ( ( ord_less_eq_nat @ B @ zero_zero_nat )
=> ( ord_less_eq_nat @ ( times_times_nat @ B @ A2 ) @ zero_zero_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(489,plain,
( ( ! [A2: nat,B: nat] :
( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ ( times_times_nat @ A2 @ B ) @ zero_zero_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(490,plain,
( ( ! [A2: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
=> ( ( ord_less_eq_nat @ B @ zero_zero_nat )
=> ( ord_less_eq_nat @ ( times_times_nat @ A2 @ B ) @ zero_zero_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(491,plain,
( ( ! [A2: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A2 @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(492,plain,
( ( ! [A2: nat,B: nat] :
( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
& ( ord_less_eq_nat @ B @ zero_zero_nat ) )
| ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
& ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
=> ( ord_less_eq_nat @ ( times_times_nat @ A2 @ B ) @ zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(493,plain,
( ( ! [A2: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(494,plain,
( ( ! [A2: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ C @ A2 ) @ ( times_times_nat @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(495,plain,
( ( ! [A2: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(496,plain,
( ( ! [A2: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(497,plain,
( ( ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[357]) ).
thf(498,plain,
( ( ord_less_eq_nat @ zero_zero_nat @ one_one_nat )
= $true ),
inference(copy,[status(thm)],[356]) ).
thf(499,plain,
( ( ! [A: set_nat,F: nat > nat] :
( ! [X2: nat] :
( ( member_nat @ X2 @ A )
=> ( ord_less_eq_nat @ ( F @ X2 ) @ zero_zero_nat ) )
=> ( ord_less_eq_nat @ ( groups1842438620at_nat @ F @ A ) @ zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[355]) ).
thf(500,plain,
( ( ! [A: set_nat,F: nat > nat] :
( ! [X2: nat] :
( ( member_nat @ X2 @ A )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X2 ) ) )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( groups1842438620at_nat @ F @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[354]) ).
thf(501,plain,
( ( ! [M: nat,N: nat] :
( ( M
= ( times_times_nat @ M @ N ) )
=> ( ( N = one_one_nat )
| ( M = zero_zero_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[353]) ).
thf(502,plain,
( ( ! [C: nat,A2: nat] :
( ( ord_less_eq_nat @ C @ one_one_nat )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
=> ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C ) @ A2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[352]) ).
thf(503,plain,
( ( ! [A2: nat,B: nat] :
( ( ord_less_eq_nat @ A2 @ one_one_nat )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_eq_nat @ B @ one_one_nat )
=> ( ord_less_eq_nat @ ( times_times_nat @ A2 @ B ) @ one_one_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[351]) ).
thf(504,plain,
( ( ! [A2: nat] :
( ( times_times_nat @ A2 @ one_one_nat )
= A2 ) )
= $true ),
inference(copy,[status(thm)],[350]) ).
thf(505,plain,
( ( ! [A2: nat] :
( ( times_times_nat @ one_one_nat @ A2 )
= A2 ) )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(506,plain,
( ( ! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[348]) ).
thf(507,plain,
( ( ! [X: nat] : ( ord_less_eq_nat @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[347]) ).
thf(508,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)],[346]) ).
thf(509,plain,
( ( ! [A2: nat] :
( ( times_times_nat @ A2 @ one_one_nat )
= A2 ) )
= $true ),
inference(copy,[status(thm)],[345]) ).
thf(510,plain,
( ( ! [A2: nat] :
( ( times_times_nat @ one_one_nat @ A2 )
= A2 ) )
= $true ),
inference(copy,[status(thm)],[344]) ).
thf(511,plain,
( ( ! [A2: nat,F: set_nat > nat,B: set_nat,C: set_nat] :
( ( ord_less_eq_nat @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_set_nat @ B @ C )
=> ( ! [X2: set_nat,Y2: set_nat] :
( ( ord_less_eq_set_nat @ X2 @ Y2 )
=> ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[343]) ).
thf(512,plain,
( ( ! [A2: set_nat,F: nat > set_nat,B: nat,C: nat] :
( ( ord_less_eq_set_nat @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ord_less_eq_set_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_set_nat @ A2 @ ( F @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[342]) ).
thf(513,plain,
( ( ! [A2: nat,F: nat > nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[341]) ).
thf(514,plain,
( ( ! [A2: nat,B: nat,F: nat > set_nat,C: set_nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_set_nat @ ( F @ B ) @ C )
=> ( ! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ord_less_eq_set_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_set_nat @ ( F @ A2 ) @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[340]) ).
thf(515,plain,
( ( ! [A2: set_nat,B: set_nat,F: set_nat > nat,C: nat] :
( ( ord_less_eq_set_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ ( F @ B ) @ C )
=> ( ! [X2: set_nat,Y2: set_nat] :
( ( ord_less_eq_set_nat @ X2 @ Y2 )
=> ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[339]) ).
thf(516,plain,
( ( ! [A2: nat,B: nat,F: nat > nat,C: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ ( F @ B ) @ C )
=> ( ! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[338]) ).
thf(517,plain,
( ( ! [A2: set_nat,F: nat > set_nat,B: nat,C: nat] :
( ( A2
= ( F @ B ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ord_less_eq_set_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_set_nat @ A2 @ ( F @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[337]) ).
thf(518,plain,
( ( ! [A2: nat,F: set_nat > nat,B: set_nat,C: set_nat] :
( ( A2
= ( F @ B ) )
=> ( ( ord_less_eq_set_nat @ B @ C )
=> ( ! [X2: set_nat,Y2: set_nat] :
( ( ord_less_eq_set_nat @ X2 @ Y2 )
=> ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[336]) ).
thf(519,plain,
( ( ! [A2: nat,F: nat > nat,B: nat,C: nat] :
( ( A2
= ( F @ B ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[335]) ).
thf(520,plain,
( ( ! [A2: nat,B: nat,F: nat > set_nat,C: set_nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ( F @ B )
= C )
=> ( ! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ord_less_eq_set_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_set_nat @ ( F @ A2 ) @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[334]) ).
thf(521,plain,
( ( ! [A2: set_nat,B: set_nat,F: set_nat > nat,C: nat] :
( ( ord_less_eq_set_nat @ A2 @ B )
=> ( ( ( F @ B )
= C )
=> ( ! [X2: set_nat,Y2: set_nat] :
( ( ord_less_eq_set_nat @ X2 @ Y2 )
=> ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[333]) ).
thf(522,plain,
( ( ! [A2: nat,B: nat,F: nat > nat,C: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ( F @ B )
= C )
=> ( ! [X2: nat,Y2: nat] :
( ( ord_less_eq_nat @ X2 @ Y2 )
=> ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[332]) ).
thf(523,plain,
( ( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
= ( ^ [X4: nat,Y5: nat] :
( ( ord_less_eq_nat @ X4 @ Y5 )
& ( ord_less_eq_nat @ Y5 @ X4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[331]) ).
thf(524,plain,
( ( ! [X: nat,Y: nat] :
( ( ord_less_eq_nat @ X @ Y )
=> ( ( ord_less_eq_nat @ Y @ X )
=> ( X = Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[330]) ).
thf(525,plain,
( ( ! [X: nat,Y: nat] :
( ( ord_less_eq_nat @ X @ Y )
| ( ord_less_eq_nat @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[329]) ).
thf(526,plain,
( ( ! [X: nat,Y: nat] :
( ( X = Y )
=> ( ord_less_eq_nat @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[328]) ).
thf(527,plain,
( ( ! [X: nat,Y: nat] :
( ~ ( ord_less_eq_nat @ X @ Y )
=> ( ord_less_eq_nat @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[327]) ).
thf(528,plain,
( ( ! [A2: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A2 @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[326]) ).
thf(529,plain,
( ( ! [X: nat,Y: nat,Z2: nat] :
( ( ( ord_less_eq_nat @ X @ Y )
=> ~ ( ord_less_eq_nat @ Y @ Z2 ) )
=> ( ( ( ord_less_eq_nat @ Y @ X )
=> ~ ( ord_less_eq_nat @ X @ Z2 ) )
=> ( ( ( ord_less_eq_nat @ X @ Z2 )
=> ~ ( ord_less_eq_nat @ Z2 @ Y ) )
=> ( ( ( ord_less_eq_nat @ Z2 @ Y )
=> ~ ( ord_less_eq_nat @ Y @ X ) )
=> ( ( ( ord_less_eq_nat @ Y @ Z2 )
=> ~ ( ord_less_eq_nat @ Z2 @ X ) )
=> ~ ( ( ord_less_eq_nat @ Z2 @ X )
=> ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[325]) ).
thf(530,plain,
( ( ! [Y: nat,X: nat] :
( ( ord_less_eq_nat @ Y @ X )
=> ( ( ord_less_eq_nat @ X @ Y )
= ( X = Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[324]) ).
thf(531,plain,
( ( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
= ( ^ [A4: nat,B4: nat] :
( ( ord_less_eq_nat @ A4 @ B4 )
& ( ord_less_eq_nat @ B4 @ A4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[323]) ).
thf(532,plain,
( ( ! [A2: nat,B: nat,C: nat] :
( ( A2 = B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A2 @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[322]) ).
thf(533,plain,
( ( ! [A2: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( B = C )
=> ( ord_less_eq_nat @ A2 @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[321]) ).
thf(534,plain,
( ( ! [A2: nat,B: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ B @ A2 )
=> ( A2 = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[320]) ).
thf(535,plain,
( ( ! [X: nat,Y: nat,Z2: nat] :
( ( ord_less_eq_nat @ X @ Y )
=> ( ( ord_less_eq_nat @ Y @ Z2 )
=> ( ord_less_eq_nat @ X @ Z2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[319]) ).
thf(536,plain,
( ( ! [A2: nat] : ( ord_less_eq_nat @ A2 @ A2 ) )
= $true ),
inference(copy,[status(thm)],[318]) ).
thf(537,plain,
( ( ! [P3: nat > nat > $o,A2: nat,B: nat] :
( ! [A3: nat,B2: nat] :
( ( ord_less_eq_nat @ A3 @ B2 )
=> ( P3 @ A3 @ B2 ) )
=> ( ! [A3: nat,B2: nat] :
( ( P3 @ B2 @ A3 )
=> ( P3 @ A3 @ B2 ) )
=> ( P3 @ A2 @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[317]) ).
thf(538,plain,
( ( ! [B: nat,A2: nat,C: nat] :
( ( ord_less_eq_nat @ B @ A2 )
=> ( ( ord_less_eq_nat @ C @ B )
=> ( ord_less_eq_nat @ C @ A2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[316]) ).
thf(539,plain,
( ( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
= ( ^ [A4: nat,B4: nat] :
( ( ord_less_eq_nat @ B4 @ A4 )
& ( ord_less_eq_nat @ A4 @ B4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[315]) ).
thf(540,plain,
( ( ! [B: nat,A2: nat] :
( ( ord_less_eq_nat @ B @ A2 )
=> ( ( ord_less_eq_nat @ A2 @ B )
=> ( A2 = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[314]) ).
thf(541,plain,
( ( ! [X: nat] :
( ( zero_zero_nat = X )
= ( X = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[313]) ).
thf(542,plain,
( ( ! [A2: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A2 @ B ) @ C )
= ( times_times_nat @ A2 @ ( times_times_nat @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[312]) ).
thf(543,plain,
( ( ! [A2: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A2 @ B ) @ C )
= ( times_times_nat @ A2 @ ( times_times_nat @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[311]) ).
thf(544,plain,
( ( times_times_nat
= ( ^ [A4: nat,B4: nat] : ( times_times_nat @ B4 @ A4 ) ) )
= $true ),
inference(copy,[status(thm)],[310]) ).
thf(545,plain,
( ( ! [B: nat,A2: nat,C: nat] :
( ( times_times_nat @ B @ ( times_times_nat @ A2 @ C ) )
= ( times_times_nat @ A2 @ ( times_times_nat @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[309]) ).
thf(546,plain,
( ( ! [X: nat] :
( ( one_one_nat = X )
= ( X = one_one_nat ) ) )
= $true ),
inference(copy,[status(thm)],[308]) ).
thf(547,plain,
( ( ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) )
= $true ),
inference(copy,[status(thm)],[307]) ).
thf(548,plain,
( ( ord_less_eq_nat @ one_one_nat @ one_one_nat )
= $true ),
inference(copy,[status(thm)],[306]) ).
thf(549,plain,
( ( ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat )
= $true ),
inference(copy,[status(thm)],[305]) ).
thf(550,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(copy,[status(thm)],[304]) ).
thf(551,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[303]) ).
thf(552,plain,
( ( ! [A2: nat] :
( ( A2 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A2 ) ) )
= $true ),
inference(copy,[status(thm)],[302]) ).
thf(553,plain,
( ( ! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[301]) ).
thf(554,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)],[300]) ).
thf(555,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)],[299]) ).
thf(556,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)],[298]) ).
thf(557,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ N @ one_one_nat )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[297]) ).
thf(558,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)],[296]) ).
thf(559,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)],[295]) ).
thf(560,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(copy,[status(thm)],[294]) ).
thf(561,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[293]) ).
thf(562,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[292]) ).
thf(563,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( N != zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[291]) ).
thf(564,plain,
( ( ord_less_nat
= ( ^ [M4: nat,N2: nat] :
( ( ord_less_eq_nat @ M4 @ N2 )
& ( M4 != N2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[290]) ).
thf(565,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[289]) ).
thf(566,plain,
( ( ord_less_eq_nat
= ( ^ [M4: nat,N2: nat] :
( ( ord_less_nat @ M4 @ N2 )
| ( M4 = N2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[288]) ).
thf(567,plain,
( ( ! [M: nat,N: nat] :
( ( ( ord_less_nat @ M @ N )
| ( M = N ) )
=> ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[287]) ).
thf(568,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( M != N )
=> ( ord_less_nat @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[286]) ).
thf(569,plain,
( ( ! [F: nat > nat,I4: nat,J: nat] :
( ! [I3: nat,J3: nat] :
( ( ord_less_nat @ I3 @ J3 )
=> ( ord_less_nat @ ( F @ I3 ) @ ( F @ J3 ) ) )
=> ( ( ord_less_eq_nat @ I4 @ J )
=> ( ord_less_eq_nat @ ( F @ I4 ) @ ( F @ J ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[285]) ).
thf(570,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(copy,[status(thm)],[284]) ).
thf(571,plain,
( ( ! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[283]) ).
thf(572,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[282]) ).
thf(573,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[281]) ).
thf(574,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[280]) ).
thf(575,plain,
( ( ! [P3: nat > $o,N: nat] :
( ( P3 @ zero_zero_nat )
=> ( ! [N3: nat] :
( ( ord_less_nat @ zero_zero_nat @ N3 )
=> ( ~ ( P3 @ N3 )
=> ? [M5: nat] :
( ( ord_less_nat @ M5 @ N3 )
& ~ ( P3 @ M5 ) ) ) )
=> ( P3 @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[279]) ).
thf(576,plain,
( ( ! [A2: nat] :
~ ( ord_less_nat @ A2 @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[278]) ).
thf(577,plain,
( ( ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) )
= $true ),
inference(copy,[status(thm)],[277]) ).
thf(578,plain,
( ( ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[276]) ).
thf(579,plain,
( ( ! [A2: nat,B: nat] :
( ( A2 != B )
=> ( ( ord_less_eq_nat @ A2 @ B )
=> ( ord_less_nat @ A2 @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[275]) ).
thf(580,plain,
( ( ! [B: nat,A2: nat] :
( ( ord_less_nat @ B @ A2 )
=> ( ord_less_eq_nat @ B @ A2 ) ) )
= $true ),
inference(copy,[status(thm)],[274]) ).
thf(581,plain,
( ( ord_less_nat
= ( ^ [B4: nat,A4: nat] :
( ( ord_less_eq_nat @ B4 @ A4 )
& ( A4 != B4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[273]) ).
thf(582,plain,
( ( ord_less_eq_nat
= ( ^ [B4: nat,A4: nat] :
( ( ord_less_nat @ B4 @ A4 )
| ( A4 = B4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[272]) ).
thf(583,plain,
( ( ! [A2: nat,B: nat] :
( ( ord_less_nat @ A2 @ B )
=> ( ord_less_eq_nat @ A2 @ B ) ) )
= $true ),
inference(copy,[status(thm)],[271]) ).
thf(584,plain,
( ( ! [B: nat,A2: nat,C: nat] :
( ( ord_less_nat @ B @ A2 )
=> ( ( ord_less_eq_nat @ C @ B )
=> ( ord_less_nat @ C @ A2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[270]) ).
thf(585,plain,
( ( ! [B: nat,A2: nat,C: nat] :
( ( ord_less_eq_nat @ B @ A2 )
=> ( ( ord_less_nat @ C @ B )
=> ( ord_less_nat @ C @ A2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[269]) ).
thf(586,plain,
( ( ord_less_nat
= ( ^ [A4: nat,B4: nat] :
( ( ord_less_eq_nat @ A4 @ B4 )
& ( A4 != B4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[268]) ).
thf(587,plain,
( ( ord_less_eq_nat
= ( ^ [A4: nat,B4: nat] :
( ( ord_less_nat @ A4 @ B4 )
| ( A4 = B4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[267]) ).
thf(588,plain,
( ( ! [A2: nat,B: nat,C: nat] :
( ( ord_less_nat @ A2 @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_nat @ A2 @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[266]) ).
thf(589,plain,
( ( ! [A2: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A2 @ B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ A2 @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[265]) ).
thf(590,plain,
( ( ( ! [I2: nat] :
( ( ( p @ I2 )
!= zero_zero_nat )
=> ( ( ord_less_eq_nat @ one_one_nat @ I2 )
& ( ord_less_eq_nat @ I2 @ zero_zero_nat ) ) )
& ( ( groups1842438620at_nat
@ ^ [I2: nat] : ( times_times_nat @ ( p @ I2 ) @ I2 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
= zero_zero_nat ) )
!= ( p
= ( ^ [I2: nat] : zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(591,plain,
( ( ! [SX0: set_nat,SX1: nat > nat,SX2: nat > nat,SX3: set_nat,SX4: nat > nat,SX5: nat > nat] :
( ~ ! [SX6: nat] :
( ~ ( member_nat @ SX6 @ SX0 )
| ( ( SX1 @ ( SX2 @ SX6 ) )
= SX6 ) )
| ~ ! [SX6: nat] :
( ~ ( member_nat @ SX6 @ SX0 )
| ( member_nat @ ( SX2 @ SX6 ) @ SX3 ) )
| ~ ! [SX6: nat] :
( ~ ( member_nat @ SX6 @ SX3 )
| ( ( SX2 @ ( SX1 @ SX6 ) )
= SX6 ) )
| ~ ! [SX6: nat] :
( ~ ( member_nat @ SX6 @ SX3 )
| ( member_nat @ ( SX1 @ SX6 ) @ SX0 ) )
| ~ ! [SX6: nat] :
( ~ ( member_nat @ SX6 @ SX0 )
| ( ( SX4 @ ( SX2 @ SX6 ) )
= ( SX5 @ SX6 ) ) )
| ( ( groups1842438620at_nat @ SX5 @ SX0 )
= ( groups1842438620at_nat @ SX4 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[455]) ).
thf(592,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)],[524]) ).
thf(593,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ( SX0 != zero_zero_nat ) )
| ~ ( ( SX1 != zero_zero_nat ) )
| ( ( times_times_nat @ SX0 @ SX1 )
!= zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[462]) ).
thf(594,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SX2 )
| ( ord_less_eq_nat @ ( times_times_nat @ SX2 @ SX0 ) @ ( times_times_nat @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[494]) ).
thf(595,plain,
( ( ( ^ [SX0: nat,SX1: nat] : ( SX0 = SX1 ) )
= ( ^ [SX0: nat,SX1: nat] :
~ ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[531]) ).
thf(596,plain,
( ( ! [SX0: set_nat,SX1: nat > nat] :
( ~ ! [SX2: nat] :
( ~ ( member_nat @ SX2 @ SX0 )
| ( ( SX1 @ SX2 )
= zero_zero_nat ) )
| ( ( groups1842438620at_nat @ SX1 @ SX0 )
= zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[467]) ).
thf(597,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ord_less_eq_nat @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[527]) ).
thf(598,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ord_less_eq_nat @ ( times_times_nat @ SX2 @ SX0 ) @ ( times_times_nat @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473]) ).
thf(599,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( SX0
!= ( times_times_nat @ SX0 @ SX1 ) )
| ( SX1 = one_one_nat )
| ( SX0 = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[501]) ).
thf(600,plain,
( ( ! [SX0: set_nat,SX1: set_nat,SX2: set_nat > nat,SX3: nat] :
( ~ ( ord_less_eq_set_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ ( SX2 @ SX1 ) @ SX3 )
| ~ ! [SX4: set_nat,SX5: set_nat] :
( ~ ( ord_less_eq_set_nat @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SX2 @ SX4 ) @ ( SX2 @ SX5 ) ) )
| ( ord_less_eq_nat @ ( SX2 @ SX0 ) @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[515]) ).
thf(601,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)],[448]) ).
thf(602,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 @ ( times_times_nat @ SX0 @ SX2 ) @ ( times_times_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[475]) ).
thf(603,plain,
( ( number1551313001itions
= ( ^ [SX0: nat > nat,SX1: nat] :
~ ( ~ ! [SX2: nat] :
( ~ ( ( ( SX0 @ SX2 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SX2 )
| ~ ( ord_less_eq_nat @ SX2 @ SX1 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SX2: nat] : ( times_times_nat @ ( SX0 @ SX2 ) @ SX2 )
@ ( set_ord_atMost_nat @ SX1 ) )
!= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431]) ).
thf(604,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ zero_zero_nat )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SX1 )
| ( ord_less_eq_nat @ ( times_times_nat @ SX0 @ SX1 ) @ zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[489]) ).
thf(605,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat > set_nat,SX3: set_nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( SX2 @ SX1 )
!= SX3 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_set_nat @ ( SX2 @ SX4 ) @ ( SX2 @ SX5 ) ) )
| ( ord_less_eq_set_nat @ ( SX2 @ SX0 ) @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[520]) ).
thf(606,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)],[528]) ).
thf(607,plain,
( ( ! [SX0: nat > nat > $o,SX1: nat,SX2: nat] :
( ~ ! [SX3: nat,SX4: nat] :
( ~ ( ord_less_eq_nat @ SX3 @ SX4 )
| ( SX0 @ SX3 @ SX4 ) )
| ~ ! [SX3: nat,SX4: nat] :
( ~ ( SX0 @ SX4 @ SX3 )
| ( SX0 @ SX3 @ SX4 ) )
| ( SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[537]) ).
thf(608,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ( SX0 != SX1 )
| ~ ( ord_less_eq_nat @ SX1 @ SX2 )
| ( ord_less_eq_nat @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[532]) ).
thf(609,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( SX0 != SX1 )
| ( ord_less_eq_nat @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[452]) ).
thf(610,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_nat @ SX1 @ SX2 )
| ( ord_less_nat @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[589]) ).
thf(611,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ( ( times_times_nat @ SX0 @ SX1 )
!= zero_zero_nat ) )
| ~ ( ~ ( ( SX0 != zero_zero_nat ) )
| ~ ( ( SX1 != zero_zero_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[464]) ).
thf(612,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( SX1 != SX2 )
| ( ord_less_eq_nat @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[533]) ).
thf(613,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX2 @ SX0 )
| ( ord_less_eq_nat @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[538]) ).
thf(614,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 @ zero_zero_nat @ SX0 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SX2 )
| ( ord_less_eq_nat @ ( times_times_nat @ SX0 @ SX2 ) @ ( times_times_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495]) ).
thf(615,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( ord_less_eq_nat @ SX1 @ SX0 )
= ( SX1 = SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[530]) ).
thf(616,plain,
( ( ! [SX0: set_nat,SX1: set_nat,SX2: nat > nat,SX3: nat > nat,SX4: nat > nat] :
( ~ ! [SX5: nat] :
( ~ ( member_nat @ SX5 @ SX0 )
| ~ ! [SX6: nat] :
~ ~ ( ~ ~ ( ~ ( member_nat @ SX6 @ SX1 )
| ( ( SX2 @ SX6 )
!= SX5 ) )
| ~ ! [SX7: nat] :
( ~ ~ ( ~ ( member_nat @ SX7 @ SX1 )
| ( ( SX2 @ SX7 )
!= SX5 ) )
| ( SX7 = SX6 ) ) ) )
| ~ ! [SX5: nat] :
( ~ ( member_nat @ SX5 @ SX1 )
| ~ ( ~ ( member_nat @ ( SX2 @ SX5 ) @ SX0 )
| ( ( SX3 @ ( SX2 @ SX5 ) )
!= ( SX4 @ SX5 ) ) ) )
| ( ( groups1842438620at_nat @ SX4 @ SX1 )
= ( groups1842438620at_nat @ SX3 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(617,plain,
( ( ! [SX0: set_nat,SX1: nat > set_nat,SX2: nat,SX3: nat] :
( ( SX0
!= ( SX1 @ SX2 ) )
| ~ ( ord_less_eq_nat @ SX2 @ SX3 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_set_nat @ ( SX1 @ SX4 ) @ ( SX1 @ SX5 ) ) )
| ( ord_less_eq_set_nat @ SX0 @ ( SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[517]) ).
thf(618,plain,
( ( ! [SX0: nat,SX1: set_nat > nat,SX2: set_nat,SX3: set_nat] :
( ( SX0
!= ( SX1 @ SX2 ) )
| ~ ( ord_less_eq_set_nat @ SX2 @ SX3 )
| ~ ! [SX4: set_nat,SX5: set_nat] :
( ~ ( ord_less_eq_set_nat @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SX1 @ SX4 ) @ ( SX1 @ SX5 ) ) )
| ( ord_less_eq_nat @ SX0 @ ( SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[518]) ).
thf(619,plain,
( ( ! [SX0: nat] :
( ( SX0 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[552]) ).
thf(620,plain,
( ( ( ~ ( ~ ! [SX0: nat] :
( ~ ( ( ( p @ SX0 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SX0 )
| ~ ( ord_less_eq_nat @ SX0 @ zero_zero_nat ) ) )
| ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
!= zero_zero_nat ) ) )
!= ( p
= ( ^ [SX0: nat] : zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[590]) ).
thf(621,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ zero_zero_nat @ SX0 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SX1 )
| ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491]) ).
thf(622,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_eq_nat @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[583]) ).
thf(623,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX1 @ SX0 )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[540]) ).
thf(624,plain,
( ( ( ^ [SX0: nat,SX1: nat] : ( SX0 = SX1 ) )
= ( ^ [SX0: nat,SX1: nat] :
~ ( ~ ( ord_less_eq_nat @ SX1 @ SX0 )
| ~ ( ord_less_eq_nat @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[539]) ).
thf(625,plain,
( ( ! [SX0: set_nat,SX1: set_nat,SX2: nat > nat,SX3: nat > nat] :
( ( SX0 != SX1 )
| ~ ! [SX4: nat] :
( ~ ( member_nat @ SX4 @ SX1 )
| ( ( SX2 @ SX4 )
= ( SX3 @ SX4 ) ) )
| ( ( groups1842438620at_nat @ SX2 @ SX0 )
= ( groups1842438620at_nat @ SX3 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458]) ).
thf(626,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ zero_zero_nat @ SX0 )
| ~ ( ord_less_eq_nat @ SX1 @ zero_zero_nat )
| ( ord_less_eq_nat @ ( times_times_nat @ SX0 @ SX1 ) @ zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[490]) ).
thf(627,plain,
( ( ! [SX0: nat,SX1: set_nat > nat,SX2: set_nat,SX3: set_nat] :
( ~ ( ord_less_eq_nat @ SX0 @ ( SX1 @ SX2 ) )
| ~ ( ord_less_eq_set_nat @ SX2 @ SX3 )
| ~ ! [SX4: set_nat,SX5: set_nat] :
( ~ ( ord_less_eq_set_nat @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SX1 @ SX4 ) @ ( SX1 @ SX5 ) ) )
| ( ord_less_eq_nat @ SX0 @ ( SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[511]) ).
thf(628,plain,
( ( ! [SX0: set_nat,SX1: nat > nat] :
( ~ ! [SX2: nat] :
( ~ ( member_nat @ SX2 @ SX0 )
| ( ord_less_eq_nat @ ( SX1 @ SX2 ) @ zero_zero_nat ) )
| ( ord_less_eq_nat @ ( groups1842438620at_nat @ SX1 @ SX0 ) @ zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[499]) ).
thf(629,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)],[569]) ).
thf(630,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)],[555]) ).
thf(631,plain,
( ( ! [SX0: nat,SX1: nat > nat,SX2: nat,SX3: nat] :
( ( SX0
!= ( SX1 @ SX2 ) )
| ~ ( ord_less_eq_nat @ SX2 @ SX3 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SX1 @ SX4 ) @ ( SX1 @ SX5 ) ) )
| ( ord_less_eq_nat @ SX0 @ ( SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[519]) ).
thf(632,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)],[449]) ).
thf(633,plain,
( ( ord_less_nat
= ( ^ [SX0: nat,SX1: nat] :
~ ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ( SX1 != SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[581]) ).
thf(634,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ( SX0 != SX1 ) )
| ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ord_less_nat @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[579]) ).
thf(635,plain,
( ( ! [SX0: nat > nat,SX1: nat] :
( ~ ( number1551313001itions @ SX0 @ SX1 )
| ~ ( ~ ! [SX2: nat] :
( ~ ( ( ( SX0 @ SX2 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SX2 )
| ~ ( ord_less_eq_nat @ SX2 @ SX1 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SX2: nat] : ( times_times_nat @ ( SX0 @ SX2 ) @ SX2 )
@ ( set_ord_atMost_nat @ SX1 ) )
!= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[429]) ).
thf(636,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)],[451]) ).
thf(637,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ( ord_less_nat @ SX0 @ SX1 )
| ( SX0 = SX1 ) )
| ( ord_less_eq_nat @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[567]) ).
thf(638,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat > nat,SX3: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ ( SX2 @ SX1 ) @ SX3 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SX2 @ SX4 ) @ ( SX2 @ SX5 ) ) )
| ( ord_less_eq_nat @ ( SX2 @ SX0 ) @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[516]) ).
thf(639,plain,
( ( ord_less_nat
= ( ^ [SX0: nat,SX1: nat] :
~ ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[586]) ).
thf(640,plain,
( ( ! [SX0: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ zero_zero_nat )
| ( SX0 = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[468]) ).
thf(641,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX2 @ SX0 )
| ( ord_less_nat @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[584]) ).
thf(642,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)],[575]) ).
thf(643,plain,
( ( ! [SX0: nat > nat,SX1: set_nat] :
( ~ ( ( ( groups1842438620at_nat @ SX0 @ SX1 )
!= zero_zero_nat ) )
| ~ ! [SX2: nat] :
( ~ ( member_nat @ SX2 @ SX1 )
| ( ( SX0 @ SX2 )
= zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[466]) ).
thf(644,plain,
( ( ! [SX0: set_nat,SX1: nat > nat] :
( ~ ! [SX2: nat] :
( ~ ( member_nat @ SX2 @ SX0 )
| ( ord_less_eq_nat @ zero_zero_nat @ ( SX1 @ SX2 ) ) )
| ( ord_less_eq_nat @ zero_zero_nat @ ( groups1842438620at_nat @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[500]) ).
thf(645,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( SX0 != SX1 )
| ( ord_less_eq_nat @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[526]) ).
thf(646,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( SX1 != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[574]) ).
thf(647,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SX2 )
| ( ord_less_eq_nat @ ( times_times_nat @ SX0 @ SX2 ) @ ( times_times_nat @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(648,plain,
( ( ! [SX0: set_nat,SX1: nat > nat,SX2: set_nat,SX3: nat > nat,SX4: nat > nat,SX5: nat > nat] :
( ~ ! [SX6: nat] :
( ~ ( member_nat @ SX6 @ SX0 )
| ~ ( ~ ( member_nat @ ( SX1 @ SX6 ) @ SX2 )
| ( ( SX3 @ ( SX1 @ SX6 ) )
!= SX6 ) ) )
| ~ ! [SX6: nat] :
( ~ ( member_nat @ SX6 @ SX2 )
| ~ ( ~ ~ ( ~ ( member_nat @ ( SX3 @ SX6 ) @ SX0 )
| ( ( SX1 @ ( SX3 @ SX6 ) )
!= SX6 ) )
| ( ( SX4 @ ( SX3 @ SX6 ) )
!= ( SX5 @ SX6 ) ) ) )
| ( ( groups1842438620at_nat @ SX5 @ SX2 )
= ( groups1842438620at_nat @ SX4 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(649,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat > set_nat,SX3: set_nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_nat @ ( SX2 @ SX1 ) @ SX3 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_set_nat @ ( SX2 @ SX4 ) @ ( SX2 @ SX5 ) ) )
| ( ord_less_eq_set_nat @ ( SX2 @ SX0 ) @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[514]) ).
thf(650,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ one_one_nat )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SX1 )
| ~ ( ord_less_eq_nat @ SX1 @ one_one_nat )
| ( ord_less_eq_nat @ ( times_times_nat @ SX0 @ SX1 ) @ one_one_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[503]) ).
thf(651,plain,
( ( ! [SX0: nat,SX1: nat > nat,SX2: nat,SX3: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ ( SX1 @ SX2 ) )
| ~ ( ord_less_eq_nat @ SX2 @ SX3 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SX1 @ SX4 ) @ ( SX1 @ SX5 ) ) )
| ( ord_less_eq_nat @ SX0 @ ( SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[513]) ).
thf(652,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( ( times_times_nat @ SX0 @ SX1 )
!= zero_zero_nat )
| ( SX0 = zero_zero_nat )
| ( SX1 = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(653,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ord_less_eq_nat @ ( times_times_nat @ SX0 @ SX2 ) @ ( times_times_nat @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[474]) ).
thf(654,plain,
( ( ! [SX0: nat] :
( ~ ( ( SX0 != zero_zero_nat ) )
| ( ord_less_nat @ zero_zero_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[560]) ).
thf(655,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ one_one_nat )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SX1 )
| ( ord_less_eq_nat @ ( times_times_nat @ SX1 @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[502]) ).
thf(656,plain,
( ( ( ^ [SX0: nat,SX1: nat] : ( SX0 = SX1 ) )
= ( ^ [SX0: nat,SX1: nat] :
~ ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[523]) ).
thf(657,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)],[453]) ).
thf(658,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) )
| ( ord_less_nat @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[568]) ).
thf(659,plain,
( ( ! [SX0: set_nat,SX1: nat > set_nat,SX2: nat,SX3: nat] :
( ~ ( ord_less_eq_set_nat @ SX0 @ ( SX1 @ SX2 ) )
| ~ ( ord_less_eq_nat @ SX2 @ SX3 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_set_nat @ ( SX1 @ SX4 ) @ ( SX1 @ SX5 ) ) )
| ( ord_less_eq_set_nat @ SX0 @ ( SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[512]) ).
thf(660,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 @ zero_zero_nat @ SX1 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SX2 )
| ( ord_less_eq_nat @ ( times_times_nat @ SX0 @ SX2 ) @ ( times_times_nat @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[496]) ).
thf(661,plain,
( ( ! [SX0: nat] :
( ~ ( ( SX0 != zero_zero_nat ) )
| ( ord_less_nat @ zero_zero_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[570]) ).
thf(662,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ( SX0 != zero_zero_nat ) )
| ( ( ( times_times_nat @ SX0 @ SX1 )
= ( times_times_nat @ SX0 @ SX2 ) )
= ( SX1 = SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[461]) ).
thf(663,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)],[558]) ).
thf(664,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat > nat,SX3: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( SX2 @ SX1 )
!= SX3 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SX2 @ SX4 ) @ ( SX2 @ SX5 ) ) )
| ( ord_less_eq_nat @ ( SX2 @ SX0 ) @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[522]) ).
thf(665,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)],[535]) ).
thf(666,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX1 @ SX2 ) )
| ~ ( ~ ( ord_less_eq_nat @ SX1 @ SX0 )
| ~ ( ord_less_eq_nat @ SX0 @ SX2 ) )
| ~ ( ~ ( ord_less_eq_nat @ SX0 @ SX2 )
| ~ ( ord_less_eq_nat @ SX2 @ SX1 ) )
| ~ ( ~ ( ord_less_eq_nat @ SX2 @ SX1 )
| ~ ( ord_less_eq_nat @ SX1 @ SX0 ) )
| ~ ( ~ ( ord_less_eq_nat @ SX1 @ SX2 )
| ~ ( ord_less_eq_nat @ SX2 @ SX0 ) )
| ~ ( ~ ( ord_less_eq_nat @ SX2 @ SX0 )
| ~ ( ord_less_eq_nat @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[529]) ).
thf(667,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)],[556]) ).
thf(668,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)],[554]) ).
thf(669,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)],[534]) ).
thf(670,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SX2 )
| ( ord_less_eq_nat @ ( times_times_nat @ SX2 @ SX0 ) @ ( times_times_nat @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[487]) ).
thf(671,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_eq_nat @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[565]) ).
thf(672,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ~ ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SX0 )
| ~ ( ord_less_eq_nat @ SX1 @ zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ SX0 @ zero_zero_nat )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SX1 ) ) )
| ( ord_less_eq_nat @ ( times_times_nat @ SX0 @ SX1 ) @ zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(673,plain,
( ( ord_less_nat
= ( ^ [SX0: nat,SX1: nat] :
~ ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[564]) ).
thf(674,plain,
( ( ! [SX0: set_nat,SX1: nat > nat,SX2: nat > nat] :
( ~ ! [SX3: nat] :
( ~ ( member_nat @ SX3 @ SX0 )
| ( ord_less_eq_nat @ ( SX1 @ SX3 ) @ ( SX2 @ SX3 ) ) )
| ( ord_less_eq_nat @ ( groups1842438620at_nat @ SX1 @ SX0 ) @ ( groups1842438620at_nat @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[482]) ).
thf(675,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( ord_less_eq_nat @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[580]) ).
thf(676,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( SX1 != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[562]) ).
thf(677,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( one_one_nat
= ( times_times_nat @ SX0 @ SX1 ) )
= ( ~ ( ( SX0 != one_one_nat )
| ( SX1 != one_one_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[432]) ).
thf(678,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ( SX0 != zero_zero_nat ) )
| ( ( ( times_times_nat @ SX1 @ SX0 )
= ( times_times_nat @ SX2 @ SX0 ) )
= ( SX1 = SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[460]) ).
thf(679,plain,
( ( ! [SX0: nat] :
( ( SX0 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[550]) ).
thf(680,plain,
( ( ! [SX0: nat > nat,SX1: nat] :
( ~ ! [SX2: nat] :
( ~ ( ( ( SX0 @ SX2 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SX2 )
| ~ ( ord_less_eq_nat @ SX2 @ SX1 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SX2: nat] : ( times_times_nat @ ( SX0 @ SX2 ) @ SX2 )
@ ( set_ord_atMost_nat @ SX1 ) )
!= SX1 )
| ( number1551313001itions @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[430]) ).
thf(681,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( ( times_times_nat @ SX0 @ SX1 )
= one_one_nat )
= ( ~ ( ( SX0 != one_one_nat )
| ( SX1 != one_one_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[433]) ).
thf(682,plain,
( ( ! [SX0: nat] :
( ( ord_less_nat @ zero_zero_nat @ SX0 )
= ( SX0 != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[563]) ).
thf(683,plain,
( ( ! [SX0: set_nat,SX1: set_nat,SX2: set_nat > nat,SX3: nat] :
( ~ ( ord_less_eq_set_nat @ SX0 @ SX1 )
| ( ( SX2 @ SX1 )
!= SX3 )
| ~ ! [SX4: set_nat,SX5: set_nat] :
( ~ ( ord_less_eq_set_nat @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SX2 @ SX4 ) @ ( SX2 @ SX5 ) ) )
| ( ord_less_eq_nat @ ( SX2 @ SX0 ) @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[521]) ).
thf(684,plain,
( ( zero_zero_nat != one_one_nat )
= $true ),
inference(unfold_def,[status(thm)],[465]) ).
thf(685,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_nat @ SX2 @ SX0 )
| ( ord_less_nat @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[585]) ).
thf(686,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)],[559]) ).
thf(687,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ zero_zero_nat @ SX0 )
| ~ ( ord_less_eq_nat @ SX1 @ zero_zero_nat )
| ( ord_less_eq_nat @ ( times_times_nat @ SX1 @ SX0 ) @ zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[488]) ).
thf(688,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX1 @ SX2 )
| ( ord_less_nat @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[588]) ).
thf(689,plain,
! [SV1: set_nat] :
( ( ( groups1842438620at_nat
@ ^ [Uu: nat] : zero_zero_nat
@ SV1 )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(690,plain,
! [SV2: nat] :
( ( ! [SY431: nat] :
( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ SV2 ) @ ( set_ord_atMost_nat @ SY431 ) )
= ( ord_less_eq_nat @ SV2 @ SY431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(691,plain,
! [SV3: nat] :
( ( ! [SY432: nat] :
( ( member_nat @ SV3 @ ( set_ord_atMost_nat @ SY432 ) )
= ( ord_less_eq_nat @ SV3 @ SY432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(692,plain,
! [SV4: nat] :
( ( ! [SY433: nat] :
( ( ( set_ord_atMost_nat @ SV4 )
= ( set_ord_atMost_nat @ SY433 ) )
= ( SV4 = SY433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(693,plain,
! [SV5: nat] :
( ( ! [SY434: nat,SY435: nat] :
( ( ( times_times_nat @ SV5 @ SY434 )
= ( times_times_nat @ SY435 @ SY434 ) )
= ( ( SY434 = zero_zero_nat )
| ( SV5 = SY435 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(694,plain,
! [SV6: nat] :
( ( ! [SY436: nat,SY437: nat] :
( ( ( times_times_nat @ SV6 @ SY436 )
= ( times_times_nat @ SV6 @ SY437 ) )
= ( ( SV6 = zero_zero_nat )
| ( SY436 = SY437 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(695,plain,
! [SV7: nat] :
( ( ! [SY438: nat] :
( ( ( times_times_nat @ SV7 @ SY438 )
= zero_zero_nat )
= ( ( SV7 = zero_zero_nat )
| ( SY438 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(696,plain,
! [SV8: nat] :
( ( ( times_times_nat @ SV8 @ zero_zero_nat )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(697,plain,
! [SV9: nat] :
( ( ( times_times_nat @ zero_zero_nat @ SV9 )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(698,plain,
! [SV10: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(699,plain,
! [SV11: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(700,plain,
! [SV12: nat] :
( ( ! [SY439: nat,SY440: nat] :
( ( ( times_times_nat @ SV12 @ SY439 )
= ( times_times_nat @ SY440 @ SY439 ) )
= ( ( SV12 = SY440 )
| ( SY439 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(701,plain,
! [SV13: nat] :
( ( ! [SY441: nat,SY442: nat] :
( ( ( times_times_nat @ SV13 @ SY441 )
= ( times_times_nat @ SV13 @ SY442 ) )
= ( ( SY441 = SY442 )
| ( SV13 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(702,plain,
! [SV14: nat] :
( ( ( times_times_nat @ SV14 @ zero_zero_nat )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(703,plain,
! [SV15: nat] :
( ( ! [SY443: nat] :
( ( ( times_times_nat @ SV15 @ SY443 )
= zero_zero_nat )
= ( ( SV15 = zero_zero_nat )
| ( SY443 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(704,plain,
! [SV16: nat] :
( ( ! [SY444: nat] :
( ( ord_less_eq_nat @ SV16 @ SY444 )
| ( ord_less_eq_nat @ SY444 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(705,plain,
! [SV17: nat] :
( ( ord_less_eq_nat @ SV17 @ SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(706,plain,
! [SV18: nat > nat > nat] :
( ( ! [SY445: set_nat,SY446: set_nat] :
( ( groups1842438620at_nat
@ ^ [SY447: nat] : ( groups1842438620at_nat @ ( SV18 @ SY447 ) @ SY445 )
@ SY446 )
= ( groups1842438620at_nat
@ ^ [SY448: nat] :
( groups1842438620at_nat
@ ^ [SY449: nat] : ( SV18 @ SY449 @ SY448 )
@ SY446 )
@ SY445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(707,plain,
! [SV19: nat] :
( ( ( ord_less_eq_nat @ SV19 @ zero_zero_nat )
= ( SV19 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(708,plain,
! [SV20: nat] :
( ( ( ord_less_eq_nat @ SV20 @ zero_zero_nat )
= ( SV20 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(709,plain,
! [SV21: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ SV21 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(710,plain,
! [SV22: nat] :
( ( ( times_times_nat @ zero_zero_nat @ SV22 )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(711,plain,
! [SV23: nat] :
( ( ord_less_eq_nat @ SV23 @ ( times_times_nat @ SV23 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(712,plain,
! [SV24: nat] :
( ( ord_less_eq_nat @ SV24 @ ( times_times_nat @ SV24 @ ( times_times_nat @ SV24 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(713,plain,
! [SV25: nat] :
( ( ( times_times_nat @ SV25 @ one_one_nat )
= SV25 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(714,plain,
! [SV26: nat] :
( ( ( times_times_nat @ one_one_nat @ SV26 )
= SV26 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(715,plain,
( ( ! [SV27: nat] :
( zero_zero_nat
= ( times_times_nat @ zero_zero_nat @ SV27 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[480]) ).
thf(716,plain,
( ( ( ^ [H2: nat] : zero_zero_nat )
= ( times_times_nat @ zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[480]) ).
thf(717,plain,
( ( ! [SV28: nat] :
( SV28
= ( times_times_nat @ one_one_nat @ SV28 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[481]) ).
thf(718,plain,
( ( ( ^ [X4: nat] : X4 )
= ( times_times_nat @ one_one_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[481]) ).
thf(719,plain,
! [SV29: nat > nat] :
( ( ! [SY450: set_nat,SY451: nat] :
( ( times_times_nat @ ( groups1842438620at_nat @ SV29 @ SY450 ) @ SY451 )
= ( groups1842438620at_nat
@ ^ [SY452: nat] : ( times_times_nat @ ( SV29 @ SY452 ) @ SY451 )
@ SY450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(720,plain,
! [SV30: nat] :
( ( ! [SY453: nat > nat,SY454: set_nat] :
( ( times_times_nat @ SV30 @ ( groups1842438620at_nat @ SY453 @ SY454 ) )
= ( groups1842438620at_nat
@ ^ [SY455: nat] : ( times_times_nat @ SV30 @ ( SY453 @ SY455 ) )
@ SY454 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(721,plain,
! [SV31: nat > nat] :
( ( ! [SY456: set_nat,SY457: nat > nat,SY458: set_nat] :
( ( times_times_nat @ ( groups1842438620at_nat @ SV31 @ SY456 ) @ ( groups1842438620at_nat @ SY457 @ SY458 ) )
= ( groups1842438620at_nat
@ ^ [SY459: nat] :
( groups1842438620at_nat
@ ^ [SY460: nat] : ( times_times_nat @ ( SV31 @ SY459 ) @ ( SY457 @ SY460 ) )
@ SY458 )
@ SY456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(722,plain,
( ( ! [SV32: nat] :
( ( set_ord_atMost_nat @ SV32 )
= ( collect_nat
@ ^ [SY461: nat] : ( ord_less_eq_nat @ SY461 @ SV32 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[486]) ).
thf(723,plain,
( ( set_ord_atMost_nat
= ( ^ [U: nat] :
( collect_nat
@ ^ [X4: nat] : ( ord_less_eq_nat @ X4 @ U ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[486]) ).
thf(724,plain,
( ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(725,plain,
! [SV33: nat] :
( ( ( times_times_nat @ SV33 @ one_one_nat )
= SV33 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(726,plain,
! [SV34: nat] :
( ( ( times_times_nat @ one_one_nat @ SV34 )
= SV34 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(727,plain,
! [SV35: nat] :
( ( ( ord_less_eq_nat @ SV35 @ zero_zero_nat )
= ( SV35 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(728,plain,
! [SV36: nat] :
( ( ord_less_eq_nat @ SV36 @ SV36 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(729,plain,
! [SV37: nat] :
( ( ! [SY462: nat,SY463: nat] :
( ( ( times_times_nat @ SV37 @ SY462 )
= ( times_times_nat @ SV37 @ SY463 ) )
= ( ( SV37 = zero_zero_nat )
| ( SY462 = SY463 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(730,plain,
! [SV38: nat] :
( ( ( times_times_nat @ SV38 @ one_one_nat )
= SV38 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(731,plain,
! [SV39: nat] :
( ( ( times_times_nat @ one_one_nat @ SV39 )
= SV39 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(732,plain,
! [SV40: nat] :
( ( ! [SY464: nat] :
( ( ord_less_eq_nat @ SV40 @ SY464 )
| ( ord_less_eq_nat @ SY464 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(733,plain,
! [SV41: nat] :
( ( ord_less_eq_nat @ SV41 @ SV41 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(734,plain,
! [SV42: nat] :
( ( ( zero_zero_nat = SV42 )
= ( SV42 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(735,plain,
! [SV43: nat] :
( ( ! [SY465: nat,SY466: nat] :
( ( times_times_nat @ ( times_times_nat @ SV43 @ SY465 ) @ SY466 )
= ( times_times_nat @ SV43 @ ( times_times_nat @ SY465 @ SY466 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(736,plain,
! [SV44: nat] :
( ( ! [SY467: nat,SY468: nat] :
( ( times_times_nat @ ( times_times_nat @ SV44 @ SY467 ) @ SY468 )
= ( times_times_nat @ SV44 @ ( times_times_nat @ SY467 @ SY468 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(737,plain,
( ( ! [SV45: nat] :
( ( times_times_nat @ SV45 )
= ( ^ [SY469: nat] : ( times_times_nat @ SY469 @ SV45 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[544]) ).
thf(738,plain,
( ( times_times_nat
= ( ^ [A4: nat,B4: nat] : ( times_times_nat @ B4 @ A4 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[544]) ).
thf(739,plain,
! [SV46: nat] :
( ( ! [SY470: nat,SY471: nat] :
( ( times_times_nat @ SV46 @ ( times_times_nat @ SY470 @ SY471 ) )
= ( times_times_nat @ SY470 @ ( times_times_nat @ SV46 @ SY471 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(740,plain,
! [SV47: nat] :
( ( ( one_one_nat = SV47 )
= ( SV47 = one_one_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(741,plain,
! [SV48: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ SV48 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(742,plain,
! [SV49: nat] :
( ( ~ ( ord_less_nat @ SV49 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(743,plain,
! [SV50: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV50 ) )
= ( SV50 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(744,plain,
! [SV51: nat] :
( ( ( ord_less_nat @ SV51 @ one_one_nat )
= ( SV51 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(745,plain,
! [SV52: nat] :
( ( ~ ( ord_less_nat @ SV52 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(746,plain,
( ( ! [SV53: nat] :
( ( ord_less_eq_nat @ SV53 )
= ( ^ [SY472: nat] :
( ( ord_less_nat @ SV53 @ SY472 )
| ( SV53 = SY472 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[566]) ).
thf(747,plain,
( ( ord_less_eq_nat
= ( ^ [M4: nat,N2: nat] :
( ( ord_less_nat @ M4 @ N2 )
| ( M4 = N2 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[566]) ).
thf(748,plain,
! [SV54: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV54 ) )
= ( SV54 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(749,plain,
! [SV55: nat] :
( ( ~ ( ord_less_nat @ SV55 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(750,plain,
! [SV56: nat] :
( ( ~ ( ord_less_nat @ SV56 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(751,plain,
! [SV57: nat] :
( ( ~ ( ord_less_nat @ SV57 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(752,plain,
( ( ord_less_nat @ one_one_nat @ one_one_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(753,plain,
( ( ord_less_nat @ zero_zero_nat @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(754,plain,
( ( ! [SV58: nat] :
( ( ord_less_eq_nat @ SV58 )
= ( ^ [SY473: nat] :
( ( ord_less_nat @ SV58 @ SY473 )
| ( SY473 = SV58 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[582]) ).
thf(755,plain,
( ( ord_less_eq_nat
= ( ^ [B4: nat,A4: nat] :
( ( ord_less_nat @ B4 @ A4 )
| ( A4 = B4 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[582]) ).
thf(756,plain,
( ( ! [SV59: nat] :
( ( ord_less_eq_nat @ SV59 )
= ( ^ [SY474: nat] :
( ( ord_less_nat @ SV59 @ SY474 )
| ( SV59 = SY474 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[587]) ).
thf(757,plain,
( ( ord_less_eq_nat
= ( ^ [A4: nat,B4: nat] :
( ( ord_less_nat @ A4 @ B4 )
| ( A4 = B4 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[587]) ).
thf(758,plain,
! [SV60: set_nat] :
( ( ! [SY475: nat > nat,SY476: nat > nat,SY477: set_nat,SY478: nat > nat,SY479: nat > nat] :
( ~ ! [SY480: nat] :
( ~ ( member_nat @ SY480 @ SV60 )
| ( ( SY475 @ ( SY476 @ SY480 ) )
= SY480 ) )
| ~ ! [SY481: nat] :
( ~ ( member_nat @ SY481 @ SV60 )
| ( member_nat @ ( SY476 @ SY481 ) @ SY477 ) )
| ~ ! [SX6: nat] :
( ~ ( member_nat @ SX6 @ SY477 )
| ( ( SY476 @ ( SY475 @ SX6 ) )
= SX6 ) )
| ~ ! [SY483: nat] :
( ~ ( member_nat @ SY483 @ SY477 )
| ( member_nat @ ( SY475 @ SY483 ) @ SV60 ) )
| ~ ! [SY484: nat] :
( ~ ( member_nat @ SY484 @ SV60 )
| ( ( SY478 @ ( SY476 @ SY484 ) )
= ( SY479 @ SY484 ) ) )
| ( ( groups1842438620at_nat @ SY479 @ SV60 )
= ( groups1842438620at_nat @ SY478 @ SY477 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(759,plain,
! [SV61: nat] :
( ( ! [SY485: nat] :
( ~ ( ord_less_eq_nat @ SV61 @ SY485 )
| ~ ( ord_less_eq_nat @ SY485 @ SV61 )
| ( SV61 = SY485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(760,plain,
! [SV62: nat] :
( ( ! [SY486: nat] :
( ~ ( ( SV62 != zero_zero_nat ) )
| ~ ( ( SY486 != zero_zero_nat ) )
| ( ( times_times_nat @ SV62 @ SY486 )
!= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(761,plain,
! [SV63: nat] :
( ( ! [SY487: nat,SY488: nat] :
( ~ ( ord_less_eq_nat @ SV63 @ SY487 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY488 )
| ( ord_less_eq_nat @ ( times_times_nat @ SY488 @ SV63 ) @ ( times_times_nat @ SY488 @ SY487 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(762,plain,
( ( ! [SV64: nat] :
( ( ^ [SY489: nat] : ( SV64 = SY489 ) )
= ( ^ [SY490: nat] :
~ ( ~ ( ord_less_eq_nat @ SV64 @ SY490 )
| ~ ( ord_less_eq_nat @ SY490 @ SV64 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[595]) ).
thf(763,plain,
( ( ( ^ [SX0: nat,SX1: nat] : ( SX0 = SX1 ) )
= ( ^ [SX0: nat,SX1: nat] :
~ ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[595]) ).
thf(764,plain,
! [SV65: set_nat] :
( ( ! [SY491: nat > nat] :
( ~ ! [SY492: nat] :
( ~ ( member_nat @ SY492 @ SV65 )
| ( ( SY491 @ SY492 )
= zero_zero_nat ) )
| ( ( groups1842438620at_nat @ SY491 @ SV65 )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(765,plain,
! [SV66: nat] :
( ( ! [SY493: nat] :
( ~ ~ ( ord_less_eq_nat @ SV66 @ SY493 )
| ( ord_less_eq_nat @ SY493 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(766,plain,
! [SV67: nat] :
( ( ! [SY494: nat,SY495: nat] :
( ~ ( ord_less_eq_nat @ SV67 @ SY494 )
| ( ord_less_eq_nat @ ( times_times_nat @ SY495 @ SV67 ) @ ( times_times_nat @ SY495 @ SY494 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(767,plain,
! [SV68: nat] :
( ( ! [SY496: nat] :
( ( SV68
!= ( times_times_nat @ SV68 @ SY496 ) )
| ( SY496 = one_one_nat )
| ( SV68 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(768,plain,
! [SV69: set_nat] :
( ( ! [SY497: set_nat,SY498: set_nat > nat,SY499: nat] :
( ~ ( ord_less_eq_set_nat @ SV69 @ SY497 )
| ~ ( ord_less_eq_nat @ ( SY498 @ SY497 ) @ SY499 )
| ~ ! [SX4: set_nat,SX5: set_nat] :
( ~ ( ord_less_eq_set_nat @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SY498 @ SX4 ) @ ( SY498 @ SX5 ) ) )
| ( ord_less_eq_nat @ ( SY498 @ SV69 ) @ SY499 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(769,plain,
! [SV70: nat > $o] :
( ( ! [SY502: nat,SY503: nat] :
( ~ ( SV70 @ SY502 )
| ~ ! [SY504: nat] :
( ~ ( SV70 @ SY504 )
| ( ord_less_eq_nat @ SY504 @ SY503 ) )
| ~ ! [SY505: nat] :
( ~ ( SV70 @ SY505 )
| ~ ! [SY506: nat] :
( ~ ( SV70 @ SY506 )
| ( ord_less_eq_nat @ SY506 @ SY505 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(770,plain,
! [SV71: nat] :
( ( ! [SY507: nat,SY508: nat,SY509: nat] :
( ~ ( ord_less_eq_nat @ SV71 @ SY507 )
| ~ ( ord_less_eq_nat @ SY508 @ SY509 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV71 @ SY508 ) @ ( times_times_nat @ SY507 @ SY509 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(771,plain,
( ( ! [SV72: nat > nat] :
( ( number1551313001itions @ SV72 )
= ( ^ [SY510: nat] :
~ ( ~ ! [SY511: nat] :
( ~ ( ( ( SV72 @ SY511 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY511 )
| ~ ( ord_less_eq_nat @ SY511 @ SY510 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY512: nat] : ( times_times_nat @ ( SV72 @ SY512 ) @ SY512 )
@ ( set_ord_atMost_nat @ SY510 ) )
!= SY510 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[603]) ).
thf(772,plain,
( ( number1551313001itions
= ( ^ [SX0: nat > nat,SX1: nat] :
~ ( ~ ! [SX2: nat] :
( ~ ( ( ( SX0 @ SX2 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SX2 )
| ~ ( ord_less_eq_nat @ SX2 @ SX1 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SX2: nat] : ( times_times_nat @ ( SX0 @ SX2 ) @ SX2 )
@ ( set_ord_atMost_nat @ SX1 ) )
!= SX1 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[603]) ).
thf(773,plain,
! [SV73: nat] :
( ( ! [SY513: nat] :
( ~ ( ord_less_eq_nat @ SV73 @ zero_zero_nat )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY513 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV73 @ SY513 ) @ zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(774,plain,
! [SV74: nat] :
( ( ! [SY514: nat,SY515: nat > set_nat,SY516: set_nat] :
( ~ ( ord_less_eq_nat @ SV74 @ SY514 )
| ( ( SY515 @ SY514 )
!= SY516 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_set_nat @ ( SY515 @ SX4 ) @ ( SY515 @ SX5 ) ) )
| ( ord_less_eq_set_nat @ ( SY515 @ SV74 ) @ SY516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(775,plain,
! [SV75: nat] :
( ( ! [SY519: nat,SY520: nat] :
( ~ ( ord_less_eq_nat @ SV75 @ SY519 )
| ~ ( ord_less_eq_nat @ SY519 @ SY520 )
| ( ord_less_eq_nat @ SV75 @ SY520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(776,plain,
! [SV76: nat > nat > $o] :
( ( ! [SY521: nat,SY522: nat] :
( ~ ! [SY523: nat,SY524: nat] :
( ~ ( ord_less_eq_nat @ SY523 @ SY524 )
| ( SV76 @ SY523 @ SY524 ) )
| ~ ! [SY525: nat,SY526: nat] :
( ~ ( SV76 @ SY526 @ SY525 )
| ( SV76 @ SY525 @ SY526 ) )
| ( SV76 @ SY521 @ SY522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(777,plain,
! [SV77: nat] :
( ( ! [SY527: nat,SY528: nat] :
( ( SV77 != SY527 )
| ~ ( ord_less_eq_nat @ SY527 @ SY528 )
| ( ord_less_eq_nat @ SV77 @ SY528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(778,plain,
! [SV78: nat] :
( ( ! [SY529: nat] :
( ( SV78 != SY529 )
| ( ord_less_eq_nat @ SV78 @ SY529 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(779,plain,
! [SV79: nat] :
( ( ! [SY530: nat,SY531: nat] :
( ~ ( ord_less_eq_nat @ SV79 @ SY530 )
| ~ ( ord_less_nat @ SY530 @ SY531 )
| ( ord_less_nat @ SV79 @ SY531 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(780,plain,
! [SV80: nat] :
( ( ! [SY532: nat] :
( ~ ( ( ( times_times_nat @ SV80 @ SY532 )
!= zero_zero_nat ) )
| ~ ( ~ ( ( SV80 != zero_zero_nat ) )
| ~ ( ( SY532 != zero_zero_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(781,plain,
! [SV81: nat] :
( ( ! [SY533: nat,SY534: nat] :
( ~ ( ord_less_eq_nat @ SV81 @ SY533 )
| ( SY533 != SY534 )
| ( ord_less_eq_nat @ SV81 @ SY534 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(782,plain,
! [SV82: nat] :
( ( ! [SY535: nat,SY536: nat] :
( ~ ( ord_less_eq_nat @ SV82 @ SY535 )
| ~ ( ord_less_eq_nat @ SY536 @ SV82 )
| ( ord_less_eq_nat @ SY536 @ SY535 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(783,plain,
! [SV83: nat] :
( ( ! [SY537: nat,SY538: nat,SY539: nat] :
( ~ ( ord_less_eq_nat @ SV83 @ SY537 )
| ~ ( ord_less_eq_nat @ SY538 @ SY539 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV83 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY538 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV83 @ SY538 ) @ ( times_times_nat @ SY537 @ SY539 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(784,plain,
! [SV84: nat] :
( ( ! [SY540: nat] :
( ~ ( ord_less_eq_nat @ SV84 @ SY540 )
| ( ( ord_less_eq_nat @ SY540 @ SV84 )
= ( SY540 = SV84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(785,plain,
! [SV85: set_nat] :
( ( ! [SY541: set_nat,SY542: nat > nat,SY543: nat > nat,SY544: nat > nat] :
( ~ ! [SY545: nat] :
( ~ ( member_nat @ SY545 @ SV85 )
| ~ ! [SX6: nat] :
~ ~ ( ~ ~ ( ~ ( member_nat @ SX6 @ SY541 )
| ( ( SY542 @ SX6 )
!= SY545 ) )
| ~ ! [SX7: nat] :
( ~ ~ ( ~ ( member_nat @ SX7 @ SY541 )
| ( ( SY542 @ SX7 )
!= SY545 ) )
| ( SX7 = SX6 ) ) ) )
| ~ ! [SY548: nat] :
( ~ ( member_nat @ SY548 @ SY541 )
| ~ ( ~ ( member_nat @ ( SY542 @ SY548 ) @ SV85 )
| ( ( SY543 @ ( SY542 @ SY548 ) )
!= ( SY544 @ SY548 ) ) ) )
| ( ( groups1842438620at_nat @ SY544 @ SY541 )
= ( groups1842438620at_nat @ SY543 @ SV85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(786,plain,
! [SV86: set_nat] :
( ( ! [SY549: nat > set_nat,SY550: nat,SY551: nat] :
( ( SV86
!= ( SY549 @ SY550 ) )
| ~ ( ord_less_eq_nat @ SY550 @ SY551 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_set_nat @ ( SY549 @ SX4 ) @ ( SY549 @ SX5 ) ) )
| ( ord_less_eq_set_nat @ SV86 @ ( SY549 @ SY551 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(787,plain,
! [SV87: nat] :
( ( ! [SY554: set_nat > nat,SY555: set_nat,SY556: set_nat] :
( ( SV87
!= ( SY554 @ SY555 ) )
| ~ ( ord_less_eq_set_nat @ SY555 @ SY556 )
| ~ ! [SX4: set_nat,SX5: set_nat] :
( ~ ( ord_less_eq_set_nat @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SY554 @ SX4 ) @ ( SY554 @ SX5 ) ) )
| ( ord_less_eq_nat @ SV87 @ ( SY554 @ SY556 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(788,plain,
! [SV88: nat] :
( ( ( SV88 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(789,plain,
( ( ( ~ ( ~ ! [SX0: nat] :
( ~ ( ( ( p @ SX0 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SX0 )
| ~ ( ord_less_eq_nat @ SX0 @ zero_zero_nat ) ) )
| ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
!= zero_zero_nat ) ) )
= ( p
= ( ^ [SX0: nat] : zero_zero_nat ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[620]) ).
thf(790,plain,
! [SV89: nat] :
( ( ! [SY559: nat] :
( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV89 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY559 )
| ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ SV89 @ SY559 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(791,plain,
! [SV90: nat] :
( ( ! [SY560: nat] :
( ~ ( ord_less_nat @ SV90 @ SY560 )
| ( ord_less_eq_nat @ SV90 @ SY560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(792,plain,
! [SV91: nat] :
( ( ! [SY561: nat] :
( ~ ( ord_less_eq_nat @ SV91 @ SY561 )
| ~ ( ord_less_eq_nat @ SY561 @ SV91 )
| ( SY561 = SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(793,plain,
( ( ! [SV92: nat] :
( ( ^ [SY562: nat] : ( SV92 = SY562 ) )
= ( ^ [SY563: nat] :
~ ( ~ ( ord_less_eq_nat @ SY563 @ SV92 )
| ~ ( ord_less_eq_nat @ SV92 @ SY563 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[624]) ).
thf(794,plain,
( ( ( ^ [SX0: nat,SX1: nat] : ( SX0 = SX1 ) )
= ( ^ [SX0: nat,SX1: nat] :
~ ( ~ ( ord_less_eq_nat @ SX1 @ SX0 )
| ~ ( ord_less_eq_nat @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[624]) ).
thf(795,plain,
! [SV93: set_nat] :
( ( ! [SY564: set_nat,SY565: nat > nat,SY566: nat > nat] :
( ( SV93 != SY564 )
| ~ ! [SX4: nat] :
( ~ ( member_nat @ SX4 @ SY564 )
| ( ( SY565 @ SX4 )
= ( SY566 @ SX4 ) ) )
| ( ( groups1842438620at_nat @ SY565 @ SV93 )
= ( groups1842438620at_nat @ SY566 @ SY564 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(796,plain,
! [SV94: nat] :
( ( ! [SY568: nat] :
( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
| ~ ( ord_less_eq_nat @ SY568 @ zero_zero_nat )
| ( ord_less_eq_nat @ ( times_times_nat @ SV94 @ SY568 ) @ zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(797,plain,
! [SV95: nat] :
( ( ! [SY569: set_nat > nat,SY570: set_nat,SY571: set_nat] :
( ~ ( ord_less_eq_nat @ SV95 @ ( SY569 @ SY570 ) )
| ~ ( ord_less_eq_set_nat @ SY570 @ SY571 )
| ~ ! [SX4: set_nat,SX5: set_nat] :
( ~ ( ord_less_eq_set_nat @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SY569 @ SX4 ) @ ( SY569 @ SX5 ) ) )
| ( ord_less_eq_nat @ SV95 @ ( SY569 @ SY571 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(798,plain,
! [SV96: set_nat] :
( ( ! [SY574: nat > nat] :
( ~ ! [SY575: nat] :
( ~ ( member_nat @ SY575 @ SV96 )
| ( ord_less_eq_nat @ ( SY574 @ SY575 ) @ zero_zero_nat ) )
| ( ord_less_eq_nat @ ( groups1842438620at_nat @ SY574 @ SV96 ) @ zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(799,plain,
! [SV97: nat > nat] :
( ( ! [SY576: nat,SY577: nat] :
( ~ ! [SY578: nat,SY579: nat] :
( ~ ( ord_less_nat @ SY578 @ SY579 )
| ( ord_less_nat @ ( SV97 @ SY578 ) @ ( SV97 @ SY579 ) ) )
| ~ ( ord_less_eq_nat @ SY576 @ SY577 )
| ( ord_less_eq_nat @ ( SV97 @ SY576 ) @ ( SV97 @ SY577 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(800,plain,
! [SV98: nat] :
( ( ! [SY580: nat,SY581: nat] :
( ( ord_less_nat @ ( times_times_nat @ SV98 @ SY580 ) @ ( times_times_nat @ SY581 @ SY580 ) )
= ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SY580 )
| ~ ( ord_less_nat @ SV98 @ SY581 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(801,plain,
! [SV99: nat] :
( ( ! [SY582: nat > nat,SY583: nat,SY584: nat] :
( ( SV99
!= ( SY582 @ SY583 ) )
| ~ ( ord_less_eq_nat @ SY583 @ SY584 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SY582 @ SX4 ) @ ( SY582 @ SX5 ) ) )
| ( ord_less_eq_nat @ SV99 @ ( SY582 @ SY584 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(802,plain,
! [SV100: nat > $o] :
( ( ! [SY587: nat,SY588: nat] :
( ~ ( SV100 @ SY587 )
| ~ ! [SY589: nat] :
( ~ ( SV100 @ SY589 )
| ( ord_less_eq_nat @ SY589 @ SY588 ) )
| ~ ! [SY590: nat] :
~ ~ ( ~ ( SV100 @ SY590 )
| ~ ! [SY591: nat] :
( ~ ( SV100 @ SY591 )
| ( ord_less_eq_nat @ SY591 @ SY590 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(803,plain,
( ( ! [SV101: nat] :
( ( ord_less_nat @ SV101 )
= ( ^ [SY592: nat] :
~ ( ~ ( ord_less_eq_nat @ SV101 @ SY592 )
| ~ ( ( SY592 != SV101 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[633]) ).
thf(804,plain,
( ( ord_less_nat
= ( ^ [SX0: nat,SX1: nat] :
~ ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ( SX1 != SX0 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[633]) ).
thf(805,plain,
! [SV102: nat] :
( ( ! [SY593: nat] :
( ~ ( ( SV102 != SY593 ) )
| ~ ( ord_less_eq_nat @ SV102 @ SY593 )
| ( ord_less_nat @ SV102 @ SY593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(806,plain,
! [SV103: nat > nat] :
( ( ! [SY594: nat] :
( ~ ( number1551313001itions @ SV103 @ SY594 )
| ~ ( ~ ! [SY595: nat] :
( ~ ( ( ( SV103 @ SY595 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY595 )
| ~ ( ord_less_eq_nat @ SY595 @ SY594 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY596: nat] : ( times_times_nat @ ( SV103 @ SY596 ) @ SY596 )
@ ( set_ord_atMost_nat @ SY594 ) )
!= SY594 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(807,plain,
! [SV104: nat] :
( ( ! [SY597: nat] :
( ~ ( ord_less_eq_nat @ SV104 @ SY597 )
| ~ ( ord_less_eq_nat @ SY597 @ SV104 )
| ( SV104 = SY597 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(808,plain,
! [SV105: nat] :
( ( ! [SY598: nat] :
( ~ ( ( ord_less_nat @ SV105 @ SY598 )
| ( SV105 = SY598 ) )
| ( ord_less_eq_nat @ SV105 @ SY598 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(809,plain,
! [SV106: nat] :
( ( ! [SY599: nat,SY600: nat > nat,SY601: nat] :
( ~ ( ord_less_eq_nat @ SV106 @ SY599 )
| ~ ( ord_less_eq_nat @ ( SY600 @ SY599 ) @ SY601 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SY600 @ SX4 ) @ ( SY600 @ SX5 ) ) )
| ( ord_less_eq_nat @ ( SY600 @ SV106 ) @ SY601 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(810,plain,
( ( ! [SV107: nat] :
( ( ord_less_nat @ SV107 )
= ( ^ [SY604: nat] :
~ ( ~ ( ord_less_eq_nat @ SV107 @ SY604 )
| ~ ( ( SV107 != SY604 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[639]) ).
thf(811,plain,
( ( ord_less_nat
= ( ^ [SX0: nat,SX1: nat] :
~ ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[639]) ).
thf(812,plain,
! [SV108: nat] :
( ( ~ ( ord_less_eq_nat @ SV108 @ zero_zero_nat )
| ( SV108 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(813,plain,
! [SV109: nat] :
( ( ! [SY605: nat,SY606: nat] :
( ~ ( ord_less_nat @ SV109 @ SY605 )
| ~ ( ord_less_eq_nat @ SY606 @ SV109 )
| ( ord_less_nat @ SY606 @ SY605 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(814,plain,
! [SV110: nat > $o] :
( ( ! [SY607: nat] :
( ~ ( SV110 @ zero_zero_nat )
| ~ ! [SY608: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY608 )
| ~ ~ ( SV110 @ SY608 )
| ~ ! [SY609: nat] :
~ ~ ( ~ ( ord_less_nat @ SY609 @ SY608 )
| ~ ~ ( SV110 @ SY609 ) ) )
| ( SV110 @ SY607 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(815,plain,
! [SV111: nat > nat] :
( ( ! [SY610: set_nat] :
( ~ ( ( ( groups1842438620at_nat @ SV111 @ SY610 )
!= zero_zero_nat ) )
| ~ ! [SY611: nat] :
( ~ ( member_nat @ SY611 @ SY610 )
| ( ( SV111 @ SY611 )
= zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(816,plain,
! [SV112: set_nat] :
( ( ! [SY612: nat > nat] :
( ~ ! [SY613: nat] :
( ~ ( member_nat @ SY613 @ SV112 )
| ( ord_less_eq_nat @ zero_zero_nat @ ( SY612 @ SY613 ) ) )
| ( ord_less_eq_nat @ zero_zero_nat @ ( groups1842438620at_nat @ SY612 @ SV112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(817,plain,
! [SV113: nat] :
( ( ! [SY614: nat] :
( ( SV113 != SY614 )
| ( ord_less_eq_nat @ SV113 @ SY614 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(818,plain,
! [SV114: nat] :
( ( ! [SY615: nat] :
( ~ ( ord_less_nat @ SV114 @ SY615 )
| ( SY615 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(819,plain,
! [SV115: nat] :
( ( ! [SY616: nat,SY617: nat] :
( ~ ( ord_less_eq_nat @ SV115 @ SY616 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY617 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV115 @ SY617 ) @ ( times_times_nat @ SY616 @ SY617 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(820,plain,
! [SV116: set_nat] :
( ( ! [SY618: nat > nat,SY619: set_nat,SY620: nat > nat,SY621: nat > nat,SY622: nat > nat] :
( ~ ! [SY623: nat] :
( ~ ( member_nat @ SY623 @ SV116 )
| ~ ( ~ ( member_nat @ ( SY618 @ SY623 ) @ SY619 )
| ( ( SY620 @ ( SY618 @ SY623 ) )
!= SY623 ) ) )
| ~ ! [SY624: nat] :
( ~ ( member_nat @ SY624 @ SY619 )
| ~ ( ~ ~ ( ~ ( member_nat @ ( SY620 @ SY624 ) @ SV116 )
| ( ( SY618 @ ( SY620 @ SY624 ) )
!= SY624 ) )
| ( ( SY621 @ ( SY620 @ SY624 ) )
!= ( SY622 @ SY624 ) ) ) )
| ( ( groups1842438620at_nat @ SY622 @ SY619 )
= ( groups1842438620at_nat @ SY621 @ SV116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(821,plain,
! [SV117: nat] :
( ( ! [SY625: nat,SY626: nat > set_nat,SY627: set_nat] :
( ~ ( ord_less_eq_nat @ SV117 @ SY625 )
| ~ ( ord_less_eq_set_nat @ ( SY626 @ SY625 ) @ SY627 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_set_nat @ ( SY626 @ SX4 ) @ ( SY626 @ SX5 ) ) )
| ( ord_less_eq_set_nat @ ( SY626 @ SV117 ) @ SY627 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(822,plain,
! [SV118: nat] :
( ( ! [SY630: nat] :
( ~ ( ord_less_eq_nat @ SV118 @ one_one_nat )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY630 )
| ~ ( ord_less_eq_nat @ SY630 @ one_one_nat )
| ( ord_less_eq_nat @ ( times_times_nat @ SV118 @ SY630 ) @ one_one_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(823,plain,
! [SV119: nat] :
( ( ! [SY631: nat > nat,SY632: nat,SY633: nat] :
( ~ ( ord_less_eq_nat @ SV119 @ ( SY631 @ SY632 ) )
| ~ ( ord_less_eq_nat @ SY632 @ SY633 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SY631 @ SX4 ) @ ( SY631 @ SX5 ) ) )
| ( ord_less_eq_nat @ SV119 @ ( SY631 @ SY633 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(824,plain,
! [SV120: nat] :
( ( ! [SY636: nat] :
( ( ( times_times_nat @ SV120 @ SY636 )
!= zero_zero_nat )
| ( SV120 = zero_zero_nat )
| ( SY636 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(825,plain,
! [SV121: nat] :
( ( ! [SY637: nat,SY638: nat] :
( ~ ( ord_less_eq_nat @ SV121 @ SY637 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV121 @ SY638 ) @ ( times_times_nat @ SY637 @ SY638 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(826,plain,
! [SV122: nat] :
( ( ~ ( ( SV122 != zero_zero_nat ) )
| ( ord_less_nat @ zero_zero_nat @ SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(827,plain,
! [SV123: nat] :
( ( ! [SY639: nat] :
( ~ ( ord_less_eq_nat @ SV123 @ one_one_nat )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY639 )
| ( ord_less_eq_nat @ ( times_times_nat @ SY639 @ SV123 ) @ SY639 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(828,plain,
( ( ! [SV124: nat] :
( ( ^ [SY640: nat] : ( SV124 = SY640 ) )
= ( ^ [SY641: nat] :
~ ( ~ ( ord_less_eq_nat @ SV124 @ SY641 )
| ~ ( ord_less_eq_nat @ SY641 @ SV124 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[656]) ).
thf(829,plain,
( ( ( ^ [SX0: nat,SX1: nat] : ( SX0 = SX1 ) )
= ( ^ [SX0: nat,SX1: nat] :
~ ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[656]) ).
thf(830,plain,
! [SV125: nat] :
( ( ! [SY642: nat,SY643: nat] :
( ~ ( ord_less_eq_nat @ SV125 @ SY642 )
| ~ ( ord_less_eq_nat @ SY642 @ SY643 )
| ( ord_less_eq_nat @ SV125 @ SY643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(831,plain,
! [SV126: nat] :
( ( ! [SY644: nat] :
( ~ ( ord_less_eq_nat @ SV126 @ SY644 )
| ~ ( ( SV126 != SY644 ) )
| ( ord_less_nat @ SV126 @ SY644 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(832,plain,
! [SV127: set_nat] :
( ( ! [SY645: nat > set_nat,SY646: nat,SY647: nat] :
( ~ ( ord_less_eq_set_nat @ SV127 @ ( SY645 @ SY646 ) )
| ~ ( ord_less_eq_nat @ SY646 @ SY647 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_set_nat @ ( SY645 @ SX4 ) @ ( SY645 @ SX5 ) ) )
| ( ord_less_eq_set_nat @ SV127 @ ( SY645 @ SY647 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(833,plain,
! [SV128: nat] :
( ( ! [SY650: nat,SY651: nat,SY652: nat] :
( ~ ( ord_less_eq_nat @ SV128 @ SY650 )
| ~ ( ord_less_eq_nat @ SY651 @ SY652 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY650 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY651 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV128 @ SY651 ) @ ( times_times_nat @ SY650 @ SY652 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(834,plain,
! [SV129: nat] :
( ( ~ ( ( SV129 != zero_zero_nat ) )
| ( ord_less_nat @ zero_zero_nat @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(835,plain,
! [SV130: nat] :
( ( ! [SY653: nat,SY654: nat] :
( ~ ( ( SV130 != zero_zero_nat ) )
| ( ( ( times_times_nat @ SV130 @ SY653 )
= ( times_times_nat @ SV130 @ SY654 ) )
= ( SY653 = SY654 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(836,plain,
! [SV131: nat] :
( ( ! [SY655: nat,SY656: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SY655 ) @ ( times_times_nat @ SY656 @ SY655 ) )
= ( ~ ( ord_less_nat @ zero_zero_nat @ SY655 )
| ( ord_less_eq_nat @ SV131 @ SY656 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(837,plain,
! [SV132: nat] :
( ( ! [SY657: nat,SY658: nat > nat,SY659: nat] :
( ~ ( ord_less_eq_nat @ SV132 @ SY657 )
| ( ( SY658 @ SY657 )
!= SY659 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SY658 @ SX4 ) @ ( SY658 @ SX5 ) ) )
| ( ord_less_eq_nat @ ( SY658 @ SV132 ) @ SY659 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(838,plain,
! [SV133: nat] :
( ( ! [SY662: nat,SY663: nat] :
( ~ ( ord_less_eq_nat @ SV133 @ SY662 )
| ~ ( ord_less_eq_nat @ SY662 @ SY663 )
| ( ord_less_eq_nat @ SV133 @ SY663 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(839,plain,
! [SV134: nat] :
( ( ! [SY664: nat,SY665: nat] :
( ~ ( ~ ( ord_less_eq_nat @ SV134 @ SY664 )
| ~ ( ord_less_eq_nat @ SY664 @ SY665 ) )
| ~ ( ~ ( ord_less_eq_nat @ SY664 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SY665 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV134 @ SY665 )
| ~ ( ord_less_eq_nat @ SY665 @ SY664 ) )
| ~ ( ~ ( ord_less_eq_nat @ SY665 @ SY664 )
| ~ ( ord_less_eq_nat @ SY664 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SY664 @ SY665 )
| ~ ( ord_less_eq_nat @ SY665 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SY665 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SY664 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(840,plain,
! [SV135: nat] :
( ( ! [SY666: nat,SY667: nat] :
( ( ord_less_nat @ ( times_times_nat @ SV135 @ SY666 ) @ ( times_times_nat @ SV135 @ SY667 ) )
= ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 )
| ~ ( ord_less_nat @ SY666 @ SY667 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(841,plain,
! [SV136: nat] :
( ( ! [SY668: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SY668 ) )
= ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV136 )
| ~ ( ord_less_nat @ zero_zero_nat @ SY668 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(842,plain,
! [SV137: nat] :
( ( ! [SY669: nat] :
( ~ ( ord_less_eq_nat @ SV137 @ SY669 )
| ~ ( ord_less_eq_nat @ SY669 @ SV137 )
| ( SV137 = SY669 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(843,plain,
! [SV138: nat] :
( ( ! [SY670: nat,SY671: nat] :
( ~ ( ord_less_eq_nat @ SV138 @ SY670 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY671 )
| ( ord_less_eq_nat @ ( times_times_nat @ SY671 @ SV138 ) @ ( times_times_nat @ SY671 @ SY670 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(844,plain,
! [SV139: nat] :
( ( ! [SY672: nat] :
( ~ ( ord_less_nat @ SV139 @ SY672 )
| ( ord_less_eq_nat @ SV139 @ SY672 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(845,plain,
! [SV140: nat] :
( ( ! [SY673: nat] :
( ~ ( ~ ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV140 )
| ~ ( ord_less_eq_nat @ SY673 @ zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ SV140 @ zero_zero_nat )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY673 ) ) )
| ( ord_less_eq_nat @ ( times_times_nat @ SV140 @ SY673 ) @ zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(846,plain,
( ( ! [SV141: nat] :
( ( ord_less_nat @ SV141 )
= ( ^ [SY674: nat] :
~ ( ~ ( ord_less_eq_nat @ SV141 @ SY674 )
| ~ ( ( SV141 != SY674 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[673]) ).
thf(847,plain,
( ( ord_less_nat
= ( ^ [SX0: nat,SX1: nat] :
~ ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[673]) ).
thf(848,plain,
! [SV142: set_nat] :
( ( ! [SY675: nat > nat,SY676: nat > nat] :
( ~ ! [SY677: nat] :
( ~ ( member_nat @ SY677 @ SV142 )
| ( ord_less_eq_nat @ ( SY675 @ SY677 ) @ ( SY676 @ SY677 ) ) )
| ( ord_less_eq_nat @ ( groups1842438620at_nat @ SY675 @ SV142 ) @ ( groups1842438620at_nat @ SY676 @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(849,plain,
! [SV143: nat] :
( ( ! [SY678: nat] :
( ~ ( ord_less_nat @ SV143 @ SY678 )
| ( ord_less_eq_nat @ SV143 @ SY678 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(850,plain,
! [SV144: nat] :
( ( ! [SY679: nat] :
( ~ ( ord_less_nat @ SV144 @ SY679 )
| ( SY679 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(851,plain,
! [SV145: nat] :
( ( ! [SY680: nat] :
( ( one_one_nat
= ( times_times_nat @ SV145 @ SY680 ) )
= ( ~ ( ( SV145 != one_one_nat )
| ( SY680 != one_one_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(852,plain,
! [SV146: nat] :
( ( ! [SY681: nat,SY682: nat] :
( ~ ( ( SV146 != zero_zero_nat ) )
| ( ( ( times_times_nat @ SY681 @ SV146 )
= ( times_times_nat @ SY682 @ SV146 ) )
= ( SY681 = SY682 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(853,plain,
! [SV147: nat] :
( ( ( SV147 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SV147 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(854,plain,
! [SV148: nat > nat] :
( ( ! [SY683: nat] :
( ~ ! [SY684: nat] :
( ~ ( ( ( SV148 @ SY684 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY684 )
| ~ ( ord_less_eq_nat @ SY684 @ SY683 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY685: nat] : ( times_times_nat @ ( SV148 @ SY685 ) @ SY685 )
@ ( set_ord_atMost_nat @ SY683 ) )
!= SY683 )
| ( number1551313001itions @ SV148 @ SY683 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(855,plain,
! [SV149: nat] :
( ( ! [SY686: nat] :
( ( ( times_times_nat @ SV149 @ SY686 )
= one_one_nat )
= ( ~ ( ( SV149 != one_one_nat )
| ( SY686 != one_one_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(856,plain,
! [SV150: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV150 )
= ( SV150 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(857,plain,
! [SV151: set_nat] :
( ( ! [SY687: set_nat,SY688: set_nat > nat,SY689: nat] :
( ~ ( ord_less_eq_set_nat @ SV151 @ SY687 )
| ( ( SY688 @ SY687 )
!= SY689 )
| ~ ! [SX4: set_nat,SX5: set_nat] :
( ~ ( ord_less_eq_set_nat @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SY688 @ SX4 ) @ ( SY688 @ SX5 ) ) )
| ( ord_less_eq_nat @ ( SY688 @ SV151 ) @ SY689 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(858,plain,
( ( zero_zero_nat = one_one_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(859,plain,
! [SV152: nat] :
( ( ! [SY692: nat,SY693: nat] :
( ~ ( ord_less_eq_nat @ SV152 @ SY692 )
| ~ ( ord_less_nat @ SY693 @ SV152 )
| ( ord_less_nat @ SY693 @ SY692 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(860,plain,
! [SV153: nat] :
( ( ! [SY694: nat,SY695: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SY694 ) @ ( times_times_nat @ SV153 @ SY695 ) )
= ( ~ ( ord_less_nat @ zero_zero_nat @ SV153 )
| ( ord_less_eq_nat @ SY694 @ SY695 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(861,plain,
! [SV154: nat] :
( ( ! [SY696: nat] :
( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV154 )
| ~ ( ord_less_eq_nat @ SY696 @ zero_zero_nat )
| ( ord_less_eq_nat @ ( times_times_nat @ SY696 @ SV154 ) @ zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(862,plain,
! [SV155: nat] :
( ( ! [SY697: nat,SY698: nat] :
( ~ ( ord_less_nat @ SV155 @ SY697 )
| ~ ( ord_less_eq_nat @ SY697 @ SY698 )
| ( ord_less_nat @ SV155 @ SY698 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(863,plain,
! [SV156: nat,SV2: nat] :
( ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ SV2 ) @ ( set_ord_atMost_nat @ SV156 ) )
= ( ord_less_eq_nat @ SV2 @ SV156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(864,plain,
! [SV157: nat,SV3: nat] :
( ( ( member_nat @ SV3 @ ( set_ord_atMost_nat @ SV157 ) )
= ( ord_less_eq_nat @ SV3 @ SV157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(865,plain,
! [SV158: nat,SV4: nat] :
( ( ( ( set_ord_atMost_nat @ SV4 )
= ( set_ord_atMost_nat @ SV158 ) )
= ( SV4 = SV158 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(866,plain,
! [SV159: nat,SV5: nat] :
( ( ! [SY699: nat] :
( ( ( times_times_nat @ SV5 @ SV159 )
= ( times_times_nat @ SY699 @ SV159 ) )
= ( ( SV159 = zero_zero_nat )
| ( SV5 = SY699 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(867,plain,
! [SV160: nat,SV6: nat] :
( ( ! [SY700: nat] :
( ( ( times_times_nat @ SV6 @ SV160 )
= ( times_times_nat @ SV6 @ SY700 ) )
= ( ( SV6 = zero_zero_nat )
| ( SV160 = SY700 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(868,plain,
! [SV161: nat,SV7: nat] :
( ( ( ( times_times_nat @ SV7 @ SV161 )
= zero_zero_nat )
= ( ( SV7 = zero_zero_nat )
| ( SV161 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(869,plain,
! [SV162: nat,SV12: nat] :
( ( ! [SY701: nat] :
( ( ( times_times_nat @ SV12 @ SV162 )
= ( times_times_nat @ SY701 @ SV162 ) )
= ( ( SV12 = SY701 )
| ( SV162 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(870,plain,
! [SV163: nat,SV13: nat] :
( ( ! [SY702: nat] :
( ( ( times_times_nat @ SV13 @ SV163 )
= ( times_times_nat @ SV13 @ SY702 ) )
= ( ( SV163 = SY702 )
| ( SV13 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(871,plain,
! [SV164: nat,SV15: nat] :
( ( ( ( times_times_nat @ SV15 @ SV164 )
= zero_zero_nat )
= ( ( SV15 = zero_zero_nat )
| ( SV164 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(872,plain,
! [SV165: nat,SV16: nat] :
( ( ( ord_less_eq_nat @ SV16 @ SV165 )
| ( ord_less_eq_nat @ SV165 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(873,plain,
! [SV166: set_nat,SV18: nat > nat > nat] :
( ( ! [SY703: set_nat] :
( ( groups1842438620at_nat
@ ^ [SY704: nat] : ( groups1842438620at_nat @ ( SV18 @ SY704 ) @ SV166 )
@ SY703 )
= ( groups1842438620at_nat
@ ^ [SY448: nat] :
( groups1842438620at_nat
@ ^ [SY449: nat] : ( SV18 @ SY449 @ SY448 )
@ SY703 )
@ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(874,plain,
! [SV19: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV19 @ zero_zero_nat )
| ( SV19 = zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ SV19 @ zero_zero_nat )
| ( SV19 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[707]) ).
thf(875,plain,
! [SV19: nat] :
( ( ( ord_less_eq_nat @ SV19 @ zero_zero_nat )
= ( SV19 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[707]) ).
thf(876,plain,
! [SV20: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV20 @ zero_zero_nat )
| ( SV20 = zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ SV20 @ zero_zero_nat )
| ( SV20 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[708]) ).
thf(877,plain,
! [SV20: nat] :
( ( ( ord_less_eq_nat @ SV20 @ zero_zero_nat )
= ( SV20 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[708]) ).
thf(878,plain,
! [SV167: nat] :
( ( zero_zero_nat
= ( times_times_nat @ zero_zero_nat @ SV167 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(879,plain,
! [SV168: nat] :
( ( SV168
= ( times_times_nat @ one_one_nat @ SV168 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(880,plain,
! [SV169: set_nat,SV29: nat > nat] :
( ( ! [SY707: nat] :
( ( times_times_nat @ ( groups1842438620at_nat @ SV29 @ SV169 ) @ SY707 )
= ( groups1842438620at_nat
@ ^ [SY452: nat] : ( times_times_nat @ ( SV29 @ SY452 ) @ SY707 )
@ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(881,plain,
! [SV170: nat > nat,SV30: nat] :
( ( ! [SY709: set_nat] :
( ( times_times_nat @ SV30 @ ( groups1842438620at_nat @ SV170 @ SY709 ) )
= ( groups1842438620at_nat
@ ^ [SY710: nat] : ( times_times_nat @ SV30 @ ( SV170 @ SY710 ) )
@ SY709 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(882,plain,
! [SV171: set_nat,SV31: nat > nat] :
( ( ! [SY711: nat > nat,SY712: set_nat] :
( ( times_times_nat @ ( groups1842438620at_nat @ SV31 @ SV171 ) @ ( groups1842438620at_nat @ SY711 @ SY712 ) )
= ( groups1842438620at_nat
@ ^ [SY459: nat] :
( groups1842438620at_nat
@ ^ [SY460: nat] : ( times_times_nat @ ( SV31 @ SY459 ) @ ( SY711 @ SY460 ) )
@ SY712 )
@ SV171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(883,plain,
! [SV172: nat] :
( ( ( set_ord_atMost_nat @ SV172 )
= ( collect_nat
@ ^ [SY715: nat] : ( ord_less_eq_nat @ SY715 @ SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(884,plain,
! [SV35: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV35 @ zero_zero_nat )
| ( SV35 = zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ SV35 @ zero_zero_nat )
| ( SV35 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[727]) ).
thf(885,plain,
! [SV35: nat] :
( ( ( ord_less_eq_nat @ SV35 @ zero_zero_nat )
= ( SV35 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[727]) ).
thf(886,plain,
! [SV173: nat,SV37: nat] :
( ( ! [SY716: nat] :
( ( ( times_times_nat @ SV37 @ SV173 )
= ( times_times_nat @ SV37 @ SY716 ) )
= ( ( SV37 = zero_zero_nat )
| ( SV173 = SY716 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(887,plain,
! [SV174: nat,SV40: nat] :
( ( ( ord_less_eq_nat @ SV40 @ SV174 )
| ( ord_less_eq_nat @ SV174 @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(888,plain,
! [SV42: nat] :
( ( ~ ( ( zero_zero_nat = SV42 )
| ( SV42 = zero_zero_nat ) )
| ~ ( ( zero_zero_nat != SV42 )
| ( SV42 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[734]) ).
thf(889,plain,
! [SV42: nat] :
( ( ( zero_zero_nat = SV42 )
= ( SV42 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[734]) ).
thf(890,plain,
! [SV175: nat,SV43: nat] :
( ( ! [SY717: nat] :
( ( times_times_nat @ ( times_times_nat @ SV43 @ SV175 ) @ SY717 )
= ( times_times_nat @ SV43 @ ( times_times_nat @ SV175 @ SY717 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(891,plain,
! [SV176: nat,SV44: nat] :
( ( ! [SY718: nat] :
( ( times_times_nat @ ( times_times_nat @ SV44 @ SV176 ) @ SY718 )
= ( times_times_nat @ SV44 @ ( times_times_nat @ SV176 @ SY718 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(892,plain,
! [SV177: nat] :
( ( ( times_times_nat @ SV177 )
= ( ^ [SY719: nat] : ( times_times_nat @ SY719 @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(893,plain,
! [SV178: nat,SV46: nat] :
( ( ! [SY720: nat] :
( ( times_times_nat @ SV46 @ ( times_times_nat @ SV178 @ SY720 ) )
= ( times_times_nat @ SV178 @ ( times_times_nat @ SV46 @ SY720 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(894,plain,
! [SV47: nat] :
( ( ~ ( ( one_one_nat = SV47 )
| ( SV47 = one_one_nat ) )
| ~ ( ( one_one_nat != SV47 )
| ( SV47 != one_one_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[740]) ).
thf(895,plain,
! [SV47: nat] :
( ( ( one_one_nat = SV47 )
= ( SV47 = one_one_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[740]) ).
thf(896,plain,
! [SV49: nat] :
( ( ord_less_nat @ SV49 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[742]) ).
thf(897,plain,
! [SV50: nat] :
( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV50 )
| ( SV50 = zero_zero_nat ) )
| ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV50 )
| ( SV50 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[743]) ).
thf(898,plain,
! [SV50: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV50 ) )
= ( SV50 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[743]) ).
thf(899,plain,
! [SV51: nat] :
( ( ~ ( ( ord_less_nat @ SV51 @ one_one_nat )
| ( SV51 = zero_zero_nat ) )
| ~ ( ~ ( ord_less_nat @ SV51 @ one_one_nat )
| ( SV51 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[744]) ).
thf(900,plain,
! [SV51: nat] :
( ( ( ord_less_nat @ SV51 @ one_one_nat )
= ( SV51 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[744]) ).
thf(901,plain,
! [SV52: nat] :
( ( ord_less_nat @ SV52 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[745]) ).
thf(902,plain,
! [SV179: nat] :
( ( ( ord_less_eq_nat @ SV179 )
= ( ^ [SY721: nat] :
( ( ord_less_nat @ SV179 @ SY721 )
| ( SV179 = SY721 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(903,plain,
! [SV54: nat] :
( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV54 )
| ( SV54 = zero_zero_nat ) )
| ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV54 )
| ( SV54 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[748]) ).
thf(904,plain,
! [SV54: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV54 ) )
= ( SV54 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[748]) ).
thf(905,plain,
! [SV55: nat] :
( ( ord_less_nat @ SV55 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(906,plain,
! [SV56: nat] :
( ( ord_less_nat @ SV56 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[750]) ).
thf(907,plain,
! [SV57: nat] :
( ( ord_less_nat @ SV57 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[751]) ).
thf(908,plain,
! [SV180: nat] :
( ( ( ord_less_eq_nat @ SV180 )
= ( ^ [SY722: nat] :
( ( ord_less_nat @ SV180 @ SY722 )
| ( SY722 = SV180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(909,plain,
! [SV181: nat] :
( ( ( ord_less_eq_nat @ SV181 )
= ( ^ [SY723: nat] :
( ( ord_less_nat @ SV181 @ SY723 )
| ( SV181 = SY723 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(910,plain,
! [SV182: nat > nat,SV60: set_nat] :
( ( ! [SY724: nat > nat,SY725: set_nat,SY726: nat > nat,SY727: nat > nat] :
( ~ ! [SY728: nat] :
( ~ ( member_nat @ SY728 @ SV60 )
| ( ( SV182 @ ( SY724 @ SY728 ) )
= SY728 ) )
| ~ ! [SY481: nat] :
( ~ ( member_nat @ SY481 @ SV60 )
| ( member_nat @ ( SY724 @ SY481 ) @ SY725 ) )
| ~ ! [SY730: nat] :
( ~ ( member_nat @ SY730 @ SY725 )
| ( ( SY724 @ ( SV182 @ SY730 ) )
= SY730 ) )
| ~ ! [SY731: nat] :
( ~ ( member_nat @ SY731 @ SY725 )
| ( member_nat @ ( SV182 @ SY731 ) @ SV60 ) )
| ~ ! [SY484: nat] :
( ~ ( member_nat @ SY484 @ SV60 )
| ( ( SY726 @ ( SY724 @ SY484 ) )
= ( SY727 @ SY484 ) ) )
| ( ( groups1842438620at_nat @ SY727 @ SV60 )
= ( groups1842438620at_nat @ SY726 @ SY725 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(911,plain,
! [SV183: nat,SV61: nat] :
( ( ~ ( ord_less_eq_nat @ SV61 @ SV183 )
| ~ ( ord_less_eq_nat @ SV183 @ SV61 )
| ( SV61 = SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(912,plain,
! [SV184: nat,SV62: nat] :
( ( ~ ( ( SV62 != zero_zero_nat ) )
| ~ ( ( SV184 != zero_zero_nat ) )
| ( ( times_times_nat @ SV62 @ SV184 )
!= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(913,plain,
! [SV185: nat,SV63: nat] :
( ( ! [SY733: nat] :
( ~ ( ord_less_eq_nat @ SV63 @ SV185 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY733 )
| ( ord_less_eq_nat @ ( times_times_nat @ SY733 @ SV63 ) @ ( times_times_nat @ SY733 @ SV185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(914,plain,
! [SV186: nat] :
( ( ( ^ [SY734: nat] : ( SV186 = SY734 ) )
= ( ^ [SY735: nat] :
~ ( ~ ( ord_less_eq_nat @ SV186 @ SY735 )
| ~ ( ord_less_eq_nat @ SY735 @ SV186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(915,plain,
! [SV187: nat > nat,SV65: set_nat] :
( ( ~ ! [SY736: nat] :
( ~ ( member_nat @ SY736 @ SV65 )
| ( ( SV187 @ SY736 )
= zero_zero_nat ) )
| ( ( groups1842438620at_nat @ SV187 @ SV65 )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(916,plain,
! [SV188: nat,SV66: nat] :
( ( ~ ~ ( ord_less_eq_nat @ SV66 @ SV188 )
| ( ord_less_eq_nat @ SV188 @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(917,plain,
! [SV189: nat,SV67: nat] :
( ( ! [SY737: nat] :
( ~ ( ord_less_eq_nat @ SV67 @ SV189 )
| ( ord_less_eq_nat @ ( times_times_nat @ SY737 @ SV67 ) @ ( times_times_nat @ SY737 @ SV189 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(918,plain,
! [SV190: nat,SV68: nat] :
( ( ( SV68
!= ( times_times_nat @ SV68 @ SV190 ) )
| ( SV190 = one_one_nat )
| ( SV68 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(919,plain,
! [SV191: set_nat,SV69: set_nat] :
( ( ! [SY738: set_nat > nat,SY739: nat] :
( ~ ( ord_less_eq_set_nat @ SV69 @ SV191 )
| ~ ( ord_less_eq_nat @ ( SY738 @ SV191 ) @ SY739 )
| ~ ! [SX4: set_nat,SX5: set_nat] :
( ~ ( ord_less_eq_set_nat @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SY738 @ SX4 ) @ ( SY738 @ SX5 ) ) )
| ( ord_less_eq_nat @ ( SY738 @ SV69 ) @ SY739 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(920,plain,
! [SV192: nat,SV70: nat > $o] :
( ( ! [SY742: nat] :
( ~ ( SV70 @ SV192 )
| ~ ! [SY504: nat] :
( ~ ( SV70 @ SY504 )
| ( ord_less_eq_nat @ SY504 @ SY742 ) )
| ~ ! [SY505: nat] :
( ~ ( SV70 @ SY505 )
| ~ ! [SY506: nat] :
( ~ ( SV70 @ SY506 )
| ( ord_less_eq_nat @ SY506 @ SY505 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(921,plain,
! [SV193: nat,SV71: nat] :
( ( ! [SY746: nat,SY747: nat] :
( ~ ( ord_less_eq_nat @ SV71 @ SV193 )
| ~ ( ord_less_eq_nat @ SY746 @ SY747 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV71 @ SY746 ) @ ( times_times_nat @ SV193 @ SY747 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(922,plain,
! [SV194: nat > nat] :
( ( ( number1551313001itions @ SV194 )
= ( ^ [SY748: nat] :
~ ( ~ ! [SY749: nat] :
( ~ ( ( ( SV194 @ SY749 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY749 )
| ~ ( ord_less_eq_nat @ SY749 @ SY748 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SY748 ) )
!= SY748 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(923,plain,
! [SV195: nat,SV73: nat] :
( ( ~ ( ord_less_eq_nat @ SV73 @ zero_zero_nat )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV195 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV73 @ SV195 ) @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(924,plain,
! [SV196: nat,SV74: nat] :
( ( ! [SY751: nat > set_nat,SY752: set_nat] :
( ~ ( ord_less_eq_nat @ SV74 @ SV196 )
| ( ( SY751 @ SV196 )
!= SY752 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_set_nat @ ( SY751 @ SX4 ) @ ( SY751 @ SX5 ) ) )
| ( ord_less_eq_set_nat @ ( SY751 @ SV74 ) @ SY752 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(925,plain,
! [SV197: nat,SV75: nat] :
( ( ! [SY755: nat] :
( ~ ( ord_less_eq_nat @ SV75 @ SV197 )
| ~ ( ord_less_eq_nat @ SV197 @ SY755 )
| ( ord_less_eq_nat @ SV75 @ SY755 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(926,plain,
! [SV198: nat,SV76: nat > nat > $o] :
( ( ! [SY756: nat] :
( ~ ! [SY523: nat,SY524: nat] :
( ~ ( ord_less_eq_nat @ SY523 @ SY524 )
| ( SV76 @ SY523 @ SY524 ) )
| ~ ! [SY525: nat,SY526: nat] :
( ~ ( SV76 @ SY526 @ SY525 )
| ( SV76 @ SY525 @ SY526 ) )
| ( SV76 @ SV198 @ SY756 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(927,plain,
! [SV199: nat,SV77: nat] :
( ( ! [SY761: nat] :
( ( SV77 != SV199 )
| ~ ( ord_less_eq_nat @ SV199 @ SY761 )
| ( ord_less_eq_nat @ SV77 @ SY761 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(928,plain,
! [SV200: nat,SV78: nat] :
( ( ( SV78 != SV200 )
| ( ord_less_eq_nat @ SV78 @ SV200 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(929,plain,
! [SV201: nat,SV79: nat] :
( ( ! [SY762: nat] :
( ~ ( ord_less_eq_nat @ SV79 @ SV201 )
| ~ ( ord_less_nat @ SV201 @ SY762 )
| ( ord_less_nat @ SV79 @ SY762 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(930,plain,
! [SV202: nat,SV80: nat] :
( ( ~ ( ( ( times_times_nat @ SV80 @ SV202 )
!= zero_zero_nat ) )
| ~ ( ~ ( ( SV80 != zero_zero_nat ) )
| ~ ( ( SV202 != zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(931,plain,
! [SV203: nat,SV81: nat] :
( ( ! [SY763: nat] :
( ~ ( ord_less_eq_nat @ SV81 @ SV203 )
| ( SV203 != SY763 )
| ( ord_less_eq_nat @ SV81 @ SY763 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(932,plain,
! [SV204: nat,SV82: nat] :
( ( ! [SY764: nat] :
( ~ ( ord_less_eq_nat @ SV82 @ SV204 )
| ~ ( ord_less_eq_nat @ SY764 @ SV82 )
| ( ord_less_eq_nat @ SY764 @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(933,plain,
! [SV205: nat,SV83: nat] :
( ( ! [SY765: nat,SY766: nat] :
( ~ ( ord_less_eq_nat @ SV83 @ SV205 )
| ~ ( ord_less_eq_nat @ SY765 @ SY766 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV83 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY765 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV83 @ SY765 ) @ ( times_times_nat @ SV205 @ SY766 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(934,plain,
! [SV206: nat,SV84: nat] :
( ( ~ ( ord_less_eq_nat @ SV84 @ SV206 )
| ( ( ord_less_eq_nat @ SV206 @ SV84 )
= ( SV206 = SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(935,plain,
! [SV207: set_nat,SV85: set_nat] :
( ( ! [SY767: nat > nat,SY768: nat > nat,SY769: nat > nat] :
( ~ ! [SY770: nat] :
( ~ ( member_nat @ SY770 @ SV85 )
| ~ ! [SY771: nat] :
~ ~ ( ~ ~ ( ~ ( member_nat @ SY771 @ SV207 )
| ( ( SY767 @ SY771 )
!= SY770 ) )
| ~ ! [SY772: nat] :
( ~ ~ ( ~ ( member_nat @ SY772 @ SV207 )
| ( ( SY767 @ SY772 )
!= SY770 ) )
| ( SY772 = SY771 ) ) ) )
| ~ ! [SY773: nat] :
( ~ ( member_nat @ SY773 @ SV207 )
| ~ ( ~ ( member_nat @ ( SY767 @ SY773 ) @ SV85 )
| ( ( SY768 @ ( SY767 @ SY773 ) )
!= ( SY769 @ SY773 ) ) ) )
| ( ( groups1842438620at_nat @ SY769 @ SV207 )
= ( groups1842438620at_nat @ SY768 @ SV85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(936,plain,
! [SV208: nat > set_nat,SV86: set_nat] :
( ( ! [SY774: nat,SY775: nat] :
( ( SV86
!= ( SV208 @ SY774 ) )
| ~ ( ord_less_eq_nat @ SY774 @ SY775 )
| ~ ! [SY776: nat,SY777: nat] :
( ~ ( ord_less_eq_nat @ SY776 @ SY777 )
| ( ord_less_eq_set_nat @ ( SV208 @ SY776 ) @ ( SV208 @ SY777 ) ) )
| ( ord_less_eq_set_nat @ SV86 @ ( SV208 @ SY775 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(937,plain,
! [SV209: set_nat > nat,SV87: nat] :
( ( ! [SY778: set_nat,SY779: set_nat] :
( ( SV87
!= ( SV209 @ SY778 ) )
| ~ ( ord_less_eq_set_nat @ SY778 @ SY779 )
| ~ ! [SY780: set_nat,SY781: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY780 @ SY781 )
| ( ord_less_eq_nat @ ( SV209 @ SY780 ) @ ( SV209 @ SY781 ) ) )
| ( ord_less_eq_nat @ SV87 @ ( SV209 @ SY779 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(938,plain,
! [SV88: nat] :
( ( ~ ( ( SV88 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV88 ) )
| ~ ( ~ ( ( SV88 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV88 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[788]) ).
thf(939,plain,
! [SV88: nat] :
( ( ( SV88 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SV88 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[788]) ).
thf(940,plain,
( ( ~ ( ~ ( ~ ! [SX0: nat] :
( ~ ( ( ( p @ SX0 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SX0 )
| ~ ( ord_less_eq_nat @ SX0 @ zero_zero_nat ) ) )
| ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
!= zero_zero_nat ) )
| ( p
= ( ^ [SX0: nat] : zero_zero_nat ) ) )
| ~ ( ~ ~ ( ~ ! [SX0: nat] :
( ~ ( ( ( p @ SX0 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SX0 )
| ~ ( ord_less_eq_nat @ SX0 @ zero_zero_nat ) ) )
| ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
!= zero_zero_nat ) )
| ( p
!= ( ^ [SX0: nat] : zero_zero_nat ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[789]) ).
thf(941,plain,
( ( ( ~ ( ~ ! [SX0: nat] :
( ~ ( ( ( p @ SX0 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SX0 )
| ~ ( ord_less_eq_nat @ SX0 @ zero_zero_nat ) ) )
| ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
!= zero_zero_nat ) ) )
= ( p
= ( ^ [SX0: nat] : zero_zero_nat ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[789]) ).
thf(942,plain,
! [SV210: nat,SV89: nat] :
( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV89 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV210 )
| ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ SV89 @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(943,plain,
! [SV211: nat,SV90: nat] :
( ( ~ ( ord_less_nat @ SV90 @ SV211 )
| ( ord_less_eq_nat @ SV90 @ SV211 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(944,plain,
! [SV212: nat,SV91: nat] :
( ( ~ ( ord_less_eq_nat @ SV91 @ SV212 )
| ~ ( ord_less_eq_nat @ SV212 @ SV91 )
| ( SV212 = SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(945,plain,
! [SV213: nat] :
( ( ( ^ [SY782: nat] : ( SV213 = SY782 ) )
= ( ^ [SY783: nat] :
~ ( ~ ( ord_less_eq_nat @ SY783 @ SV213 )
| ~ ( ord_less_eq_nat @ SV213 @ SY783 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(946,plain,
! [SV214: set_nat,SV93: set_nat] :
( ( ! [SY784: nat > nat,SY785: nat > nat] :
( ( SV93 != SV214 )
| ~ ! [SY786: nat] :
( ~ ( member_nat @ SY786 @ SV214 )
| ( ( SY784 @ SY786 )
= ( SY785 @ SY786 ) ) )
| ( ( groups1842438620at_nat @ SY784 @ SV93 )
= ( groups1842438620at_nat @ SY785 @ SV214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(947,plain,
! [SV215: nat,SV94: nat] :
( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
| ~ ( ord_less_eq_nat @ SV215 @ zero_zero_nat )
| ( ord_less_eq_nat @ ( times_times_nat @ SV94 @ SV215 ) @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(948,plain,
! [SV216: set_nat > nat,SV95: nat] :
( ( ! [SY787: set_nat,SY788: set_nat] :
( ~ ( ord_less_eq_nat @ SV95 @ ( SV216 @ SY787 ) )
| ~ ( ord_less_eq_set_nat @ SY787 @ SY788 )
| ~ ! [SY789: set_nat,SY790: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY789 @ SY790 )
| ( ord_less_eq_nat @ ( SV216 @ SY789 ) @ ( SV216 @ SY790 ) ) )
| ( ord_less_eq_nat @ SV95 @ ( SV216 @ SY788 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(949,plain,
! [SV217: nat > nat,SV96: set_nat] :
( ( ~ ! [SY791: nat] :
( ~ ( member_nat @ SY791 @ SV96 )
| ( ord_less_eq_nat @ ( SV217 @ SY791 ) @ zero_zero_nat ) )
| ( ord_less_eq_nat @ ( groups1842438620at_nat @ SV217 @ SV96 ) @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(950,plain,
! [SV218: nat,SV97: nat > nat] :
( ( ! [SY792: nat] :
( ~ ! [SY578: nat,SY579: nat] :
( ~ ( ord_less_nat @ SY578 @ SY579 )
| ( ord_less_nat @ ( SV97 @ SY578 ) @ ( SV97 @ SY579 ) ) )
| ~ ( ord_less_eq_nat @ SV218 @ SY792 )
| ( ord_less_eq_nat @ ( SV97 @ SV218 ) @ ( SV97 @ SY792 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(951,plain,
! [SV219: nat,SV98: nat] :
( ( ! [SY795: nat] :
( ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SY795 @ SV219 ) )
= ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV219 )
| ~ ( ord_less_nat @ SV98 @ SY795 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(952,plain,
! [SV220: nat > nat,SV99: nat] :
( ( ! [SY796: nat,SY797: nat] :
( ( SV99
!= ( SV220 @ SY796 ) )
| ~ ( ord_less_eq_nat @ SY796 @ SY797 )
| ~ ! [SY798: nat,SY799: nat] :
( ~ ( ord_less_eq_nat @ SY798 @ SY799 )
| ( ord_less_eq_nat @ ( SV220 @ SY798 ) @ ( SV220 @ SY799 ) ) )
| ( ord_less_eq_nat @ SV99 @ ( SV220 @ SY797 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(953,plain,
! [SV221: nat,SV100: nat > $o] :
( ( ! [SY800: nat] :
( ~ ( SV100 @ SV221 )
| ~ ! [SY589: nat] :
( ~ ( SV100 @ SY589 )
| ( ord_less_eq_nat @ SY589 @ SY800 ) )
| ~ ! [SY590: nat] :
~ ~ ( ~ ( SV100 @ SY590 )
| ~ ! [SY591: nat] :
( ~ ( SV100 @ SY591 )
| ( ord_less_eq_nat @ SY591 @ SY590 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(954,plain,
! [SV222: nat] :
( ( ( ord_less_nat @ SV222 )
= ( ^ [SY804: nat] :
~ ( ~ ( ord_less_eq_nat @ SV222 @ SY804 )
| ~ ( ( SY804 != SV222 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(955,plain,
! [SV223: nat,SV102: nat] :
( ( ~ ( ( SV102 != SV223 ) )
| ~ ( ord_less_eq_nat @ SV102 @ SV223 )
| ( ord_less_nat @ SV102 @ SV223 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(956,plain,
! [SV224: nat,SV103: nat > nat] :
( ( ~ ( number1551313001itions @ SV103 @ SV224 )
| ~ ( ~ ! [SY805: nat] :
( ~ ( ( ( SV103 @ SY805 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY805 )
| ~ ( ord_less_eq_nat @ SY805 @ SV224 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY596: nat] : ( times_times_nat @ ( SV103 @ SY596 ) @ SY596 )
@ ( set_ord_atMost_nat @ SV224 ) )
!= SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(957,plain,
! [SV225: nat,SV104: nat] :
( ( ~ ( ord_less_eq_nat @ SV104 @ SV225 )
| ~ ( ord_less_eq_nat @ SV225 @ SV104 )
| ( SV104 = SV225 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(958,plain,
! [SV226: nat,SV105: nat] :
( ( ~ ( ( ord_less_nat @ SV105 @ SV226 )
| ( SV105 = SV226 ) )
| ( ord_less_eq_nat @ SV105 @ SV226 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(959,plain,
! [SV227: nat,SV106: nat] :
( ( ! [SY807: nat > nat,SY808: nat] :
( ~ ( ord_less_eq_nat @ SV106 @ SV227 )
| ~ ( ord_less_eq_nat @ ( SY807 @ SV227 ) @ SY808 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SY807 @ SX4 ) @ ( SY807 @ SX5 ) ) )
| ( ord_less_eq_nat @ ( SY807 @ SV106 ) @ SY808 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(960,plain,
! [SV228: nat] :
( ( ( ord_less_nat @ SV228 )
= ( ^ [SY811: nat] :
~ ( ~ ( ord_less_eq_nat @ SV228 @ SY811 )
| ~ ( ( SV228 != SY811 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(961,plain,
! [SV108: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV108 @ zero_zero_nat ) )
= $true )
| ( ( SV108 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[812]) ).
thf(962,plain,
! [SV229: nat,SV109: nat] :
( ( ! [SY812: nat] :
( ~ ( ord_less_nat @ SV109 @ SV229 )
| ~ ( ord_less_eq_nat @ SY812 @ SV109 )
| ( ord_less_nat @ SY812 @ SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(963,plain,
! [SV230: nat,SV110: nat > $o] :
( ( ~ ( SV110 @ zero_zero_nat )
| ~ ! [SY608: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY608 )
| ~ ~ ( SV110 @ SY608 )
| ~ ! [SY609: nat] :
~ ~ ( ~ ( ord_less_nat @ SY609 @ SY608 )
| ~ ~ ( SV110 @ SY609 ) ) )
| ( SV110 @ SV230 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(964,plain,
! [SV231: set_nat,SV111: nat > nat] :
( ( ~ ( ( ( groups1842438620at_nat @ SV111 @ SV231 )
!= zero_zero_nat ) )
| ~ ! [SY815: nat] :
( ~ ( member_nat @ SY815 @ SV231 )
| ( ( SV111 @ SY815 )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(965,plain,
! [SV232: nat > nat,SV112: set_nat] :
( ( ~ ! [SY816: nat] :
( ~ ( member_nat @ SY816 @ SV112 )
| ( ord_less_eq_nat @ zero_zero_nat @ ( SV232 @ SY816 ) ) )
| ( ord_less_eq_nat @ zero_zero_nat @ ( groups1842438620at_nat @ SV232 @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(966,plain,
! [SV233: nat,SV113: nat] :
( ( ( SV113 != SV233 )
| ( ord_less_eq_nat @ SV113 @ SV233 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(967,plain,
! [SV234: nat,SV114: nat] :
( ( ~ ( ord_less_nat @ SV114 @ SV234 )
| ( SV234 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(968,plain,
! [SV235: nat,SV115: nat] :
( ( ! [SY817: nat] :
( ~ ( ord_less_eq_nat @ SV115 @ SV235 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY817 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV115 @ SY817 ) @ ( times_times_nat @ SV235 @ SY817 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(969,plain,
! [SV236: nat > nat,SV116: set_nat] :
( ( ! [SY818: set_nat,SY819: nat > nat,SY820: nat > nat,SY821: nat > nat] :
( ~ ! [SY822: nat] :
( ~ ( member_nat @ SY822 @ SV116 )
| ~ ( ~ ( member_nat @ ( SV236 @ SY822 ) @ SY818 )
| ( ( SY819 @ ( SV236 @ SY822 ) )
!= SY822 ) ) )
| ~ ! [SY823: nat] :
( ~ ( member_nat @ SY823 @ SY818 )
| ~ ( ~ ~ ( ~ ( member_nat @ ( SY819 @ SY823 ) @ SV116 )
| ( ( SV236 @ ( SY819 @ SY823 ) )
!= SY823 ) )
| ( ( SY820 @ ( SY819 @ SY823 ) )
!= ( SY821 @ SY823 ) ) ) )
| ( ( groups1842438620at_nat @ SY821 @ SY818 )
= ( groups1842438620at_nat @ SY820 @ SV116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(970,plain,
! [SV237: nat,SV117: nat] :
( ( ! [SY824: nat > set_nat,SY825: set_nat] :
( ~ ( ord_less_eq_nat @ SV117 @ SV237 )
| ~ ( ord_less_eq_set_nat @ ( SY824 @ SV237 ) @ SY825 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_set_nat @ ( SY824 @ SX4 ) @ ( SY824 @ SX5 ) ) )
| ( ord_less_eq_set_nat @ ( SY824 @ SV117 ) @ SY825 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(971,plain,
! [SV238: nat,SV118: nat] :
( ( ~ ( ord_less_eq_nat @ SV118 @ one_one_nat )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV238 )
| ~ ( ord_less_eq_nat @ SV238 @ one_one_nat )
| ( ord_less_eq_nat @ ( times_times_nat @ SV118 @ SV238 ) @ one_one_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(972,plain,
! [SV239: nat > nat,SV119: nat] :
( ( ! [SY828: nat,SY829: nat] :
( ~ ( ord_less_eq_nat @ SV119 @ ( SV239 @ SY828 ) )
| ~ ( ord_less_eq_nat @ SY828 @ SY829 )
| ~ ! [SY830: nat,SY831: nat] :
( ~ ( ord_less_eq_nat @ SY830 @ SY831 )
| ( ord_less_eq_nat @ ( SV239 @ SY830 ) @ ( SV239 @ SY831 ) ) )
| ( ord_less_eq_nat @ SV119 @ ( SV239 @ SY829 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(973,plain,
! [SV240: nat,SV120: nat] :
( ( ( ( times_times_nat @ SV120 @ SV240 )
!= zero_zero_nat )
| ( SV120 = zero_zero_nat )
| ( SV240 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(974,plain,
! [SV241: nat,SV121: nat] :
( ( ! [SY832: nat] :
( ~ ( ord_less_eq_nat @ SV121 @ SV241 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV121 @ SY832 ) @ ( times_times_nat @ SV241 @ SY832 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(975,plain,
! [SV122: nat] :
( ( ( ~ ( ( SV122 != zero_zero_nat ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV122 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[826]) ).
thf(976,plain,
! [SV242: nat,SV123: nat] :
( ( ~ ( ord_less_eq_nat @ SV123 @ one_one_nat )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV242 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV242 @ SV123 ) @ SV242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(977,plain,
! [SV243: nat] :
( ( ( ^ [SY833: nat] : ( SV243 = SY833 ) )
= ( ^ [SY834: nat] :
~ ( ~ ( ord_less_eq_nat @ SV243 @ SY834 )
| ~ ( ord_less_eq_nat @ SY834 @ SV243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(978,plain,
! [SV244: nat,SV125: nat] :
( ( ! [SY835: nat] :
( ~ ( ord_less_eq_nat @ SV125 @ SV244 )
| ~ ( ord_less_eq_nat @ SV244 @ SY835 )
| ( ord_less_eq_nat @ SV125 @ SY835 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(979,plain,
! [SV245: nat,SV126: nat] :
( ( ~ ( ord_less_eq_nat @ SV126 @ SV245 )
| ~ ( ( SV126 != SV245 ) )
| ( ord_less_nat @ SV126 @ SV245 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(980,plain,
! [SV246: nat > set_nat,SV127: set_nat] :
( ( ! [SY836: nat,SY837: nat] :
( ~ ( ord_less_eq_set_nat @ SV127 @ ( SV246 @ SY836 ) )
| ~ ( ord_less_eq_nat @ SY836 @ SY837 )
| ~ ! [SY838: nat,SY839: nat] :
( ~ ( ord_less_eq_nat @ SY838 @ SY839 )
| ( ord_less_eq_set_nat @ ( SV246 @ SY838 ) @ ( SV246 @ SY839 ) ) )
| ( ord_less_eq_set_nat @ SV127 @ ( SV246 @ SY837 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(981,plain,
! [SV247: nat,SV128: nat] :
( ( ! [SY840: nat,SY841: nat] :
( ~ ( ord_less_eq_nat @ SV128 @ SV247 )
| ~ ( ord_less_eq_nat @ SY840 @ SY841 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV247 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY840 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV128 @ SY840 ) @ ( times_times_nat @ SV247 @ SY841 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(982,plain,
! [SV129: nat] :
( ( ( ~ ( ( SV129 != zero_zero_nat ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV129 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[834]) ).
thf(983,plain,
! [SV248: nat,SV130: nat] :
( ( ! [SY842: nat] :
( ~ ( ( SV130 != zero_zero_nat ) )
| ( ( ( times_times_nat @ SV130 @ SV248 )
= ( times_times_nat @ SV130 @ SY842 ) )
= ( SV248 = SY842 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(984,plain,
! [SV249: nat,SV131: nat] :
( ( ! [SY843: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SY843 @ SV249 ) )
= ( ~ ( ord_less_nat @ zero_zero_nat @ SV249 )
| ( ord_less_eq_nat @ SV131 @ SY843 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(985,plain,
! [SV250: nat,SV132: nat] :
( ( ! [SY844: nat > nat,SY845: nat] :
( ~ ( ord_less_eq_nat @ SV132 @ SV250 )
| ( ( SY844 @ SV250 )
!= SY845 )
| ~ ! [SX4: nat,SX5: nat] :
( ~ ( ord_less_eq_nat @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SY844 @ SX4 ) @ ( SY844 @ SX5 ) ) )
| ( ord_less_eq_nat @ ( SY844 @ SV132 ) @ SY845 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(986,plain,
! [SV251: nat,SV133: nat] :
( ( ! [SY848: nat] :
( ~ ( ord_less_eq_nat @ SV133 @ SV251 )
| ~ ( ord_less_eq_nat @ SV251 @ SY848 )
| ( ord_less_eq_nat @ SV133 @ SY848 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(987,plain,
! [SV252: nat,SV134: nat] :
( ( ! [SY849: nat] :
( ~ ( ~ ( ord_less_eq_nat @ SV134 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SY849 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SY849 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV134 @ SY849 )
| ~ ( ord_less_eq_nat @ SY849 @ SV252 ) )
| ~ ( ~ ( ord_less_eq_nat @ SY849 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SY849 )
| ~ ( ord_less_eq_nat @ SY849 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SY849 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(988,plain,
! [SV253: nat,SV135: nat] :
( ( ! [SY850: nat] :
( ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SY850 ) )
= ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 )
| ~ ( ord_less_nat @ SV253 @ SY850 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(989,plain,
! [SV254: nat,SV136: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
= ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV136 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV254 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(990,plain,
! [SV255: nat,SV137: nat] :
( ( ~ ( ord_less_eq_nat @ SV137 @ SV255 )
| ~ ( ord_less_eq_nat @ SV255 @ SV137 )
| ( SV137 = SV255 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(991,plain,
! [SV256: nat,SV138: nat] :
( ( ! [SY851: nat] :
( ~ ( ord_less_eq_nat @ SV138 @ SV256 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY851 )
| ( ord_less_eq_nat @ ( times_times_nat @ SY851 @ SV138 ) @ ( times_times_nat @ SY851 @ SV256 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(992,plain,
! [SV257: nat,SV139: nat] :
( ( ~ ( ord_less_nat @ SV139 @ SV257 )
| ( ord_less_eq_nat @ SV139 @ SV257 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(993,plain,
! [SV258: nat,SV140: nat] :
( ( ~ ( ~ ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV140 )
| ~ ( ord_less_eq_nat @ SV258 @ zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ SV140 @ zero_zero_nat )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV258 ) ) )
| ( ord_less_eq_nat @ ( times_times_nat @ SV140 @ SV258 ) @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(994,plain,
! [SV259: nat] :
( ( ( ord_less_nat @ SV259 )
= ( ^ [SY852: nat] :
~ ( ~ ( ord_less_eq_nat @ SV259 @ SY852 )
| ~ ( ( SV259 != SY852 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(995,plain,
! [SV260: nat > nat,SV142: set_nat] :
( ( ! [SY853: nat > nat] :
( ~ ! [SY854: nat] :
( ~ ( member_nat @ SY854 @ SV142 )
| ( ord_less_eq_nat @ ( SV260 @ SY854 ) @ ( SY853 @ SY854 ) ) )
| ( ord_less_eq_nat @ ( groups1842438620at_nat @ SV260 @ SV142 ) @ ( groups1842438620at_nat @ SY853 @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(996,plain,
! [SV261: nat,SV143: nat] :
( ( ~ ( ord_less_nat @ SV143 @ SV261 )
| ( ord_less_eq_nat @ SV143 @ SV261 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(997,plain,
! [SV262: nat,SV144: nat] :
( ( ~ ( ord_less_nat @ SV144 @ SV262 )
| ( SV262 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(998,plain,
! [SV263: nat,SV145: nat] :
( ( ( one_one_nat
= ( times_times_nat @ SV145 @ SV263 ) )
= ( ~ ( ( SV145 != one_one_nat )
| ( SV263 != one_one_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(999,plain,
! [SV264: nat,SV146: nat] :
( ( ! [SY855: nat] :
( ~ ( ( SV146 != zero_zero_nat ) )
| ( ( ( times_times_nat @ SV264 @ SV146 )
= ( times_times_nat @ SY855 @ SV146 ) )
= ( SV264 = SY855 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(1000,plain,
! [SV147: nat] :
( ( ~ ( ( SV147 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV147 ) )
| ~ ( ~ ( ( SV147 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV147 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[853]) ).
thf(1001,plain,
! [SV147: nat] :
( ( ( SV147 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SV147 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[853]) ).
thf(1002,plain,
! [SV265: nat,SV148: nat > nat] :
( ( ~ ! [SY856: nat] :
( ~ ( ( ( SV148 @ SY856 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY856 )
| ~ ( ord_less_eq_nat @ SY856 @ SV265 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY685: nat] : ( times_times_nat @ ( SV148 @ SY685 ) @ SY685 )
@ ( set_ord_atMost_nat @ SV265 ) )
!= SV265 )
| ( number1551313001itions @ SV148 @ SV265 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(1003,plain,
! [SV266: nat,SV149: nat] :
( ( ( ( times_times_nat @ SV149 @ SV266 )
= one_one_nat )
= ( ~ ( ( SV149 != one_one_nat )
| ( SV266 != one_one_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(1004,plain,
! [SV150: nat] :
( ( ~ ( ( ord_less_nat @ zero_zero_nat @ SV150 )
| ( SV150 != zero_zero_nat ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV150 )
| ~ ( ( SV150 != zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[856]) ).
thf(1005,plain,
! [SV150: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV150 )
= ( SV150 != zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[856]) ).
thf(1006,plain,
! [SV267: set_nat,SV151: set_nat] :
( ( ! [SY858: set_nat > nat,SY859: nat] :
( ~ ( ord_less_eq_set_nat @ SV151 @ SV267 )
| ( ( SY858 @ SV267 )
!= SY859 )
| ~ ! [SX4: set_nat,SX5: set_nat] :
( ~ ( ord_less_eq_set_nat @ SX4 @ SX5 )
| ( ord_less_eq_nat @ ( SY858 @ SX4 ) @ ( SY858 @ SX5 ) ) )
| ( ord_less_eq_nat @ ( SY858 @ SV151 ) @ SY859 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1007,plain,
! [SV268: nat,SV152: nat] :
( ( ! [SY862: nat] :
( ~ ( ord_less_eq_nat @ SV152 @ SV268 )
| ~ ( ord_less_nat @ SY862 @ SV152 )
| ( ord_less_nat @ SY862 @ SV268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1008,plain,
! [SV269: nat,SV153: nat] :
( ( ! [SY863: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SY863 ) )
= ( ~ ( ord_less_nat @ zero_zero_nat @ SV153 )
| ( ord_less_eq_nat @ SV269 @ SY863 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(1009,plain,
! [SV270: nat,SV154: nat] :
( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV154 )
| ~ ( ord_less_eq_nat @ SV270 @ zero_zero_nat )
| ( ord_less_eq_nat @ ( times_times_nat @ SV270 @ SV154 ) @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1010,plain,
! [SV271: nat,SV155: nat] :
( ( ! [SY864: nat] :
( ~ ( ord_less_nat @ SV155 @ SV271 )
| ~ ( ord_less_eq_nat @ SV271 @ SY864 )
| ( ord_less_nat @ SV155 @ SY864 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1011,plain,
! [SV156: nat,SV2: nat] :
( ( ~ ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ SV2 ) @ ( set_ord_atMost_nat @ SV156 ) )
| ( ord_less_eq_nat @ SV2 @ SV156 ) )
| ~ ( ~ ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ SV2 ) @ ( set_ord_atMost_nat @ SV156 ) )
| ~ ( ord_less_eq_nat @ SV2 @ SV156 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[863]) ).
thf(1012,plain,
! [SV156: nat,SV2: nat] :
( ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ SV2 ) @ ( set_ord_atMost_nat @ SV156 ) )
= ( ord_less_eq_nat @ SV2 @ SV156 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[863]) ).
thf(1013,plain,
! [SV157: nat,SV3: nat] :
( ( ~ ( ( member_nat @ SV3 @ ( set_ord_atMost_nat @ SV157 ) )
| ( ord_less_eq_nat @ SV3 @ SV157 ) )
| ~ ( ~ ( member_nat @ SV3 @ ( set_ord_atMost_nat @ SV157 ) )
| ~ ( ord_less_eq_nat @ SV3 @ SV157 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[864]) ).
thf(1014,plain,
! [SV157: nat,SV3: nat] :
( ( ( member_nat @ SV3 @ ( set_ord_atMost_nat @ SV157 ) )
= ( ord_less_eq_nat @ SV3 @ SV157 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[864]) ).
thf(1015,plain,
! [SV158: nat,SV4: nat] :
( ( ~ ( ( ( set_ord_atMost_nat @ SV4 )
= ( set_ord_atMost_nat @ SV158 ) )
| ( SV4 = SV158 ) )
| ~ ( ( ( set_ord_atMost_nat @ SV4 )
!= ( set_ord_atMost_nat @ SV158 ) )
| ( SV4 != SV158 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[865]) ).
thf(1016,plain,
! [SV158: nat,SV4: nat] :
( ( ( ( set_ord_atMost_nat @ SV4 )
= ( set_ord_atMost_nat @ SV158 ) )
= ( SV4 = SV158 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[865]) ).
thf(1017,plain,
! [SV272: nat,SV159: nat,SV5: nat] :
( ( ( ( times_times_nat @ SV5 @ SV159 )
= ( times_times_nat @ SV272 @ SV159 ) )
= ( ( SV159 = zero_zero_nat )
| ( SV5 = SV272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(1018,plain,
! [SV273: nat,SV160: nat,SV6: nat] :
( ( ( ( times_times_nat @ SV6 @ SV160 )
= ( times_times_nat @ SV6 @ SV273 ) )
= ( ( SV6 = zero_zero_nat )
| ( SV160 = SV273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(1019,plain,
! [SV161: nat,SV7: nat] :
( ( ~ ( ( ( times_times_nat @ SV7 @ SV161 )
= zero_zero_nat )
| ( SV7 = zero_zero_nat )
| ( SV161 = zero_zero_nat ) )
| ~ ( ( ( times_times_nat @ SV7 @ SV161 )
!= zero_zero_nat )
| ~ ( ( SV7 = zero_zero_nat )
| ( SV161 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[868]) ).
thf(1020,plain,
! [SV161: nat,SV7: nat] :
( ( ( ( times_times_nat @ SV7 @ SV161 )
= zero_zero_nat )
= ( ( SV7 = zero_zero_nat )
| ( SV161 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[868]) ).
thf(1021,plain,
! [SV274: nat,SV162: nat,SV12: nat] :
( ( ( ( times_times_nat @ SV12 @ SV162 )
= ( times_times_nat @ SV274 @ SV162 ) )
= ( ( SV12 = SV274 )
| ( SV162 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(1022,plain,
! [SV275: nat,SV163: nat,SV13: nat] :
( ( ( ( times_times_nat @ SV13 @ SV163 )
= ( times_times_nat @ SV13 @ SV275 ) )
= ( ( SV163 = SV275 )
| ( SV13 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(1023,plain,
! [SV164: nat,SV15: nat] :
( ( ~ ( ( ( times_times_nat @ SV15 @ SV164 )
= zero_zero_nat )
| ( SV15 = zero_zero_nat )
| ( SV164 = zero_zero_nat ) )
| ~ ( ( ( times_times_nat @ SV15 @ SV164 )
!= zero_zero_nat )
| ~ ( ( SV15 = zero_zero_nat )
| ( SV164 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[871]) ).
thf(1024,plain,
! [SV164: nat,SV15: nat] :
( ( ( ( times_times_nat @ SV15 @ SV164 )
= zero_zero_nat )
= ( ( SV15 = zero_zero_nat )
| ( SV164 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[871]) ).
thf(1025,plain,
! [SV165: nat,SV16: nat] :
( ( ( ord_less_eq_nat @ SV16 @ SV165 )
= $true )
| ( ( ord_less_eq_nat @ SV165 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[872]) ).
thf(1026,plain,
! [SV276: set_nat,SV166: set_nat,SV18: nat > nat > nat] :
( ( ( groups1842438620at_nat
@ ^ [SY704: nat] : ( groups1842438620at_nat @ ( SV18 @ SY704 ) @ SV166 )
@ SV276 )
= ( groups1842438620at_nat
@ ^ [SY866: nat] :
( groups1842438620at_nat
@ ^ [SY449: nat] : ( SV18 @ SY449 @ SY866 )
@ SV276 )
@ SV166 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(1027,plain,
! [SV19: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV19 @ zero_zero_nat )
| ( SV19 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV19 @ zero_zero_nat )
| ( SV19 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[874]) ).
thf(1028,plain,
! [SV20: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV20 @ zero_zero_nat )
| ( SV20 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV20 @ zero_zero_nat )
| ( SV20 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[876]) ).
thf(1029,plain,
! [SV277: nat,SV169: set_nat,SV29: nat > nat] :
( ( ( times_times_nat @ ( groups1842438620at_nat @ SV29 @ SV169 ) @ SV277 )
= ( groups1842438620at_nat
@ ^ [SY868: nat] : ( times_times_nat @ ( SV29 @ SY868 ) @ SV277 )
@ SV169 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(1030,plain,
! [SV278: set_nat,SV170: nat > nat,SV30: nat] :
( ( ( times_times_nat @ SV30 @ ( groups1842438620at_nat @ SV170 @ SV278 ) )
= ( groups1842438620at_nat
@ ^ [SY710: nat] : ( times_times_nat @ SV30 @ ( SV170 @ SY710 ) )
@ SV278 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(1031,plain,
! [SV279: nat > nat,SV171: set_nat,SV31: nat > nat] :
( ( ! [SY870: set_nat] :
( ( times_times_nat @ ( groups1842438620at_nat @ SV31 @ SV171 ) @ ( groups1842438620at_nat @ SV279 @ SY870 ) )
= ( groups1842438620at_nat
@ ^ [SY871: nat] :
( groups1842438620at_nat
@ ^ [SY872: nat] : ( times_times_nat @ ( SV31 @ SY871 ) @ ( SV279 @ SY872 ) )
@ SY870 )
@ SV171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(1032,plain,
! [SV35: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV35 @ zero_zero_nat )
| ( SV35 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV35 @ zero_zero_nat )
| ( SV35 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[884]) ).
thf(1033,plain,
! [SV280: nat,SV173: nat,SV37: nat] :
( ( ( ( times_times_nat @ SV37 @ SV173 )
= ( times_times_nat @ SV37 @ SV280 ) )
= ( ( SV37 = zero_zero_nat )
| ( SV173 = SV280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(1034,plain,
! [SV174: nat,SV40: nat] :
( ( ( ord_less_eq_nat @ SV40 @ SV174 )
= $true )
| ( ( ord_less_eq_nat @ SV174 @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[887]) ).
thf(1035,plain,
! [SV42: nat] :
( ( ( ~ ( ( zero_zero_nat = SV42 )
| ( SV42 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( zero_zero_nat != SV42 )
| ( SV42 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[888]) ).
thf(1036,plain,
! [SV281: nat,SV175: nat,SV43: nat] :
( ( ( times_times_nat @ ( times_times_nat @ SV43 @ SV175 ) @ SV281 )
= ( times_times_nat @ SV43 @ ( times_times_nat @ SV175 @ SV281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(1037,plain,
! [SV282: nat,SV176: nat,SV44: nat] :
( ( ( times_times_nat @ ( times_times_nat @ SV44 @ SV176 ) @ SV282 )
= ( times_times_nat @ SV44 @ ( times_times_nat @ SV176 @ SV282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1038,plain,
! [SV177: nat] :
( ( ! [SV283: nat] :
( ( times_times_nat @ SV177 @ SV283 )
= ( times_times_nat @ SV283 @ SV177 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[892]) ).
thf(1039,plain,
! [SV177: nat] :
( ( ( times_times_nat @ SV177 )
= ( ^ [SY719: nat] : ( times_times_nat @ SY719 @ SV177 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[892]) ).
thf(1040,plain,
! [SV284: nat,SV178: nat,SV46: nat] :
( ( ( times_times_nat @ SV46 @ ( times_times_nat @ SV178 @ SV284 ) )
= ( times_times_nat @ SV178 @ ( times_times_nat @ SV46 @ SV284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1041,plain,
! [SV47: nat] :
( ( ( ~ ( ( one_one_nat = SV47 )
| ( SV47 = one_one_nat ) ) )
= $true )
| ( ( ~ ( ( one_one_nat != SV47 )
| ( SV47 != one_one_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[894]) ).
thf(1042,plain,
! [SV50: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV50 )
| ( SV50 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV50 )
| ( SV50 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[897]) ).
thf(1043,plain,
! [SV51: nat] :
( ( ( ~ ( ( ord_less_nat @ SV51 @ one_one_nat )
| ( SV51 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV51 @ one_one_nat )
| ( SV51 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[899]) ).
thf(1044,plain,
! [SV179: nat] :
( ( ! [SV285: nat] :
( ( ord_less_eq_nat @ SV179 @ SV285 )
= ( ( ord_less_nat @ SV179 @ SV285 )
| ( SV179 = SV285 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[902]) ).
thf(1045,plain,
! [SV179: nat] :
( ( ( ord_less_eq_nat @ SV179 )
= ( ^ [SY721: nat] :
( ( ord_less_nat @ SV179 @ SY721 )
| ( SV179 = SY721 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[902]) ).
thf(1046,plain,
! [SV54: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV54 )
| ( SV54 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV54 )
| ( SV54 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[903]) ).
thf(1047,plain,
! [SV180: nat] :
( ( ! [SV286: nat] :
( ( ord_less_eq_nat @ SV180 @ SV286 )
= ( ( ord_less_nat @ SV180 @ SV286 )
| ( SV286 = SV180 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[908]) ).
thf(1048,plain,
! [SV180: nat] :
( ( ( ord_less_eq_nat @ SV180 )
= ( ^ [SY722: nat] :
( ( ord_less_nat @ SV180 @ SY722 )
| ( SY722 = SV180 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[908]) ).
thf(1049,plain,
! [SV181: nat] :
( ( ! [SV287: nat] :
( ( ord_less_eq_nat @ SV181 @ SV287 )
= ( ( ord_less_nat @ SV181 @ SV287 )
| ( SV181 = SV287 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[909]) ).
thf(1050,plain,
! [SV181: nat] :
( ( ( ord_less_eq_nat @ SV181 )
= ( ^ [SY723: nat] :
( ( ord_less_nat @ SV181 @ SY723 )
| ( SV181 = SY723 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[909]) ).
thf(1051,plain,
! [SV288: nat > nat,SV182: nat > nat,SV60: set_nat] :
( ( ! [SY873: set_nat,SY874: nat > nat,SY875: nat > nat] :
( ~ ! [SY876: nat] :
( ~ ( member_nat @ SY876 @ SV60 )
| ( ( SV182 @ ( SV288 @ SY876 ) )
= SY876 ) )
| ~ ! [SY877: nat] :
( ~ ( member_nat @ SY877 @ SV60 )
| ( member_nat @ ( SV288 @ SY877 ) @ SY873 ) )
| ~ ! [SY878: nat] :
( ~ ( member_nat @ SY878 @ SY873 )
| ( ( SV288 @ ( SV182 @ SY878 ) )
= SY878 ) )
| ~ ! [SY731: nat] :
( ~ ( member_nat @ SY731 @ SY873 )
| ( member_nat @ ( SV182 @ SY731 ) @ SV60 ) )
| ~ ! [SY880: nat] :
( ~ ( member_nat @ SY880 @ SV60 )
| ( ( SY874 @ ( SV288 @ SY880 ) )
= ( SY875 @ SY880 ) ) )
| ( ( groups1842438620at_nat @ SY875 @ SV60 )
= ( groups1842438620at_nat @ SY874 @ SY873 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1052,plain,
! [SV183: nat,SV61: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV61 @ SV183 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV183 @ SV61 )
| ( SV61 = SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[911]) ).
thf(1053,plain,
! [SV184: nat,SV62: nat] :
( ( ( ~ ( ( SV62 != zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( SV184 != zero_zero_nat ) )
| ( ( times_times_nat @ SV62 @ SV184 )
!= zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(1054,plain,
! [SV289: nat,SV185: nat,SV63: nat] :
( ( ~ ( ord_less_eq_nat @ SV63 @ SV185 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV289 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV289 @ SV63 ) @ ( times_times_nat @ SV289 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1055,plain,
! [SV186: nat] :
( ( ! [SV290: nat] :
( ( SV186 = SV290 )
= ( ~ ( ~ ( ord_less_eq_nat @ SV186 @ SV290 )
| ~ ( ord_less_eq_nat @ SV290 @ SV186 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[914]) ).
thf(1056,plain,
! [SV186: nat] :
( ( ( ^ [SY734: nat] : ( SV186 = SY734 ) )
= ( ^ [SY735: nat] :
~ ( ~ ( ord_less_eq_nat @ SV186 @ SY735 )
| ~ ( ord_less_eq_nat @ SY735 @ SV186 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[914]) ).
thf(1057,plain,
! [SV187: nat > nat,SV65: set_nat] :
( ( ( ~ ! [SY736: nat] :
( ~ ( member_nat @ SY736 @ SV65 )
| ( ( SV187 @ SY736 )
= zero_zero_nat ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV187 @ SV65 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[915]) ).
thf(1058,plain,
! [SV188: nat,SV66: nat] :
( ( ( ~ ~ ( ord_less_eq_nat @ SV66 @ SV188 ) )
= $true )
| ( ( ord_less_eq_nat @ SV188 @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[916]) ).
thf(1059,plain,
! [SV291: nat,SV189: nat,SV67: nat] :
( ( ~ ( ord_less_eq_nat @ SV67 @ SV189 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV291 @ SV67 ) @ ( times_times_nat @ SV291 @ SV189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1060,plain,
! [SV190: nat,SV68: nat] :
( ( ( SV68
!= ( times_times_nat @ SV68 @ SV190 ) )
= $true )
| ( ( ( SV190 = one_one_nat )
| ( SV68 = zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[918]) ).
thf(1061,plain,
! [SV292: set_nat > nat,SV191: set_nat,SV69: set_nat] :
( ( ! [SY881: nat] :
( ~ ( ord_less_eq_set_nat @ SV69 @ SV191 )
| ~ ( ord_less_eq_nat @ ( SV292 @ SV191 ) @ SY881 )
| ~ ! [SY882: set_nat,SY883: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY882 @ SY883 )
| ( ord_less_eq_nat @ ( SV292 @ SY882 ) @ ( SV292 @ SY883 ) ) )
| ( ord_less_eq_nat @ ( SV292 @ SV69 ) @ SY881 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1062,plain,
! [SV293: nat,SV192: nat,SV70: nat > $o] :
( ( ~ ( SV70 @ SV192 )
| ~ ! [SY884: nat] :
( ~ ( SV70 @ SY884 )
| ( ord_less_eq_nat @ SY884 @ SV293 ) )
| ~ ! [SY505: nat] :
( ~ ( SV70 @ SY505 )
| ~ ! [SY506: nat] :
( ~ ( SV70 @ SY506 )
| ( ord_less_eq_nat @ SY506 @ SY505 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1063,plain,
! [SV294: nat,SV193: nat,SV71: nat] :
( ( ! [SY887: nat] :
( ~ ( ord_less_eq_nat @ SV71 @ SV193 )
| ~ ( ord_less_eq_nat @ SV294 @ SY887 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV71 @ SV294 ) @ ( times_times_nat @ SV193 @ SY887 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1064,plain,
! [SV194: nat > nat] :
( ( ! [SV295: nat] :
( ( number1551313001itions @ SV194 @ SV295 )
= ( ~ ( ~ ! [SY888: nat] :
( ~ ( ( ( SV194 @ SY888 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY888 )
| ~ ( ord_less_eq_nat @ SY888 @ SV295 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV295 ) )
!= SV295 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[922]) ).
thf(1065,plain,
! [SV194: nat > nat] :
( ( ( number1551313001itions @ SV194 )
= ( ^ [SY748: nat] :
~ ( ~ ! [SY749: nat] :
( ~ ( ( ( SV194 @ SY749 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY749 )
| ~ ( ord_less_eq_nat @ SY749 @ SY748 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SY748 ) )
!= SY748 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[922]) ).
thf(1066,plain,
! [SV195: nat,SV73: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV73 @ zero_zero_nat ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV195 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV73 @ SV195 ) @ zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[923]) ).
thf(1067,plain,
! [SV296: nat > set_nat,SV196: nat,SV74: nat] :
( ( ! [SY890: set_nat] :
( ~ ( ord_less_eq_nat @ SV74 @ SV196 )
| ( ( SV296 @ SV196 )
!= SY890 )
| ~ ! [SY891: nat,SY892: nat] :
( ~ ( ord_less_eq_nat @ SY891 @ SY892 )
| ( ord_less_eq_set_nat @ ( SV296 @ SY891 ) @ ( SV296 @ SY892 ) ) )
| ( ord_less_eq_set_nat @ ( SV296 @ SV74 ) @ SY890 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1068,plain,
! [SV297: nat,SV197: nat,SV75: nat] :
( ( ~ ( ord_less_eq_nat @ SV75 @ SV197 )
| ~ ( ord_less_eq_nat @ SV197 @ SV297 )
| ( ord_less_eq_nat @ SV75 @ SV297 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1069,plain,
! [SV298: nat,SV198: nat,SV76: nat > nat > $o] :
( ( ~ ! [SY523: nat,SY524: nat] :
( ~ ( ord_less_eq_nat @ SY523 @ SY524 )
| ( SV76 @ SY523 @ SY524 ) )
| ~ ! [SY525: nat,SY526: nat] :
( ~ ( SV76 @ SY526 @ SY525 )
| ( SV76 @ SY525 @ SY526 ) )
| ( SV76 @ SV198 @ SV298 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1070,plain,
! [SV299: nat,SV199: nat,SV77: nat] :
( ( ( SV77 != SV199 )
| ~ ( ord_less_eq_nat @ SV199 @ SV299 )
| ( ord_less_eq_nat @ SV77 @ SV299 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1071,plain,
! [SV200: nat,SV78: nat] :
( ( ( SV78 != SV200 )
= $true )
| ( ( ord_less_eq_nat @ SV78 @ SV200 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[928]) ).
thf(1072,plain,
! [SV300: nat,SV201: nat,SV79: nat] :
( ( ~ ( ord_less_eq_nat @ SV79 @ SV201 )
| ~ ( ord_less_nat @ SV201 @ SV300 )
| ( ord_less_nat @ SV79 @ SV300 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1073,plain,
! [SV202: nat,SV80: nat] :
( ( ( ~ ( ( ( times_times_nat @ SV80 @ SV202 )
!= zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV80 != zero_zero_nat ) )
| ~ ( ( SV202 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[930]) ).
thf(1074,plain,
! [SV301: nat,SV203: nat,SV81: nat] :
( ( ~ ( ord_less_eq_nat @ SV81 @ SV203 )
| ( SV203 != SV301 )
| ( ord_less_eq_nat @ SV81 @ SV301 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1075,plain,
! [SV302: nat,SV204: nat,SV82: nat] :
( ( ~ ( ord_less_eq_nat @ SV82 @ SV204 )
| ~ ( ord_less_eq_nat @ SV302 @ SV82 )
| ( ord_less_eq_nat @ SV302 @ SV204 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1076,plain,
! [SV303: nat,SV205: nat,SV83: nat] :
( ( ! [SY897: nat] :
( ~ ( ord_less_eq_nat @ SV83 @ SV205 )
| ~ ( ord_less_eq_nat @ SV303 @ SY897 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV83 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV303 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV83 @ SV303 ) @ ( times_times_nat @ SV205 @ SY897 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1077,plain,
! [SV206: nat,SV84: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV84 @ SV206 ) )
= $true )
| ( ( ( ord_less_eq_nat @ SV206 @ SV84 )
= ( SV206 = SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[934]) ).
thf(1078,plain,
! [SV304: nat > nat,SV207: set_nat,SV85: set_nat] :
( ( ! [SY898: nat > nat,SY899: nat > nat] :
( ~ ! [SY900: nat] :
( ~ ( member_nat @ SY900 @ SV85 )
| ~ ! [SY901: nat] :
~ ~ ( ~ ~ ( ~ ( member_nat @ SY901 @ SV207 )
| ( ( SV304 @ SY901 )
!= SY900 ) )
| ~ ! [SY902: nat] :
( ~ ~ ( ~ ( member_nat @ SY902 @ SV207 )
| ( ( SV304 @ SY902 )
!= SY900 ) )
| ( SY902 = SY901 ) ) ) )
| ~ ! [SY903: nat] :
( ~ ( member_nat @ SY903 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY903 ) @ SV85 )
| ( ( SY898 @ ( SV304 @ SY903 ) )
!= ( SY899 @ SY903 ) ) ) )
| ( ( groups1842438620at_nat @ SY899 @ SV207 )
= ( groups1842438620at_nat @ SY898 @ SV85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1079,plain,
! [SV305: nat,SV208: nat > set_nat,SV86: set_nat] :
( ( ! [SY904: nat] :
( ( SV86
!= ( SV208 @ SV305 ) )
| ~ ( ord_less_eq_nat @ SV305 @ SY904 )
| ~ ! [SY776: nat,SY777: nat] :
( ~ ( ord_less_eq_nat @ SY776 @ SY777 )
| ( ord_less_eq_set_nat @ ( SV208 @ SY776 ) @ ( SV208 @ SY777 ) ) )
| ( ord_less_eq_set_nat @ SV86 @ ( SV208 @ SY904 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1080,plain,
! [SV306: set_nat,SV209: set_nat > nat,SV87: nat] :
( ( ! [SY907: set_nat] :
( ( SV87
!= ( SV209 @ SV306 ) )
| ~ ( ord_less_eq_set_nat @ SV306 @ SY907 )
| ~ ! [SY780: set_nat,SY781: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY780 @ SY781 )
| ( ord_less_eq_nat @ ( SV209 @ SY780 ) @ ( SV209 @ SY781 ) ) )
| ( ord_less_eq_nat @ SV87 @ ( SV209 @ SY907 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1081,plain,
! [SV88: nat] :
( ( ( ~ ( ( SV88 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV88 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV88 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV88 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[938]) ).
thf(1082,plain,
( ( ~ ( ~ ( ~ ! [SX0: nat] :
( ~ ( ( ( p @ SX0 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SX0 )
| ~ ( ord_less_eq_nat @ SX0 @ zero_zero_nat ) ) )
| ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
!= zero_zero_nat ) )
| ( p
= ( ^ [SX0: nat] : zero_zero_nat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[940]) ).
thf(1083,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: nat] :
( ~ ( ( ( p @ SX0 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SX0 )
| ~ ( ord_less_eq_nat @ SX0 @ zero_zero_nat ) ) )
| ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
!= zero_zero_nat ) )
| ( p
!= ( ^ [SX0: nat] : zero_zero_nat ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[940]) ).
thf(1084,plain,
! [SV210: nat,SV89: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV89 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV210 )
| ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ SV89 @ SV210 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[942]) ).
thf(1085,plain,
! [SV211: nat,SV90: nat] :
( ( ( ~ ( ord_less_nat @ SV90 @ SV211 ) )
= $true )
| ( ( ord_less_eq_nat @ SV90 @ SV211 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[943]) ).
thf(1086,plain,
! [SV212: nat,SV91: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV91 @ SV212 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV212 @ SV91 )
| ( SV212 = SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[944]) ).
thf(1087,plain,
! [SV213: nat] :
( ( ! [SV307: nat] :
( ( SV213 = SV307 )
= ( ~ ( ~ ( ord_less_eq_nat @ SV307 @ SV213 )
| ~ ( ord_less_eq_nat @ SV213 @ SV307 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[945]) ).
thf(1088,plain,
! [SV213: nat] :
( ( ( ^ [SY782: nat] : ( SV213 = SY782 ) )
= ( ^ [SY783: nat] :
~ ( ~ ( ord_less_eq_nat @ SY783 @ SV213 )
| ~ ( ord_less_eq_nat @ SV213 @ SY783 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[945]) ).
thf(1089,plain,
! [SV308: nat > nat,SV214: set_nat,SV93: set_nat] :
( ( ! [SY910: nat > nat] :
( ( SV93 != SV214 )
| ~ ! [SY911: nat] :
( ~ ( member_nat @ SY911 @ SV214 )
| ( ( SV308 @ SY911 )
= ( SY910 @ SY911 ) ) )
| ( ( groups1842438620at_nat @ SV308 @ SV93 )
= ( groups1842438620at_nat @ SY910 @ SV214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1090,plain,
! [SV215: nat,SV94: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV94 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV215 @ zero_zero_nat )
| ( ord_less_eq_nat @ ( times_times_nat @ SV94 @ SV215 ) @ zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[947]) ).
thf(1091,plain,
! [SV309: set_nat,SV216: set_nat > nat,SV95: nat] :
( ( ! [SY912: set_nat] :
( ~ ( ord_less_eq_nat @ SV95 @ ( SV216 @ SV309 ) )
| ~ ( ord_less_eq_set_nat @ SV309 @ SY912 )
| ~ ! [SY789: set_nat,SY790: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY789 @ SY790 )
| ( ord_less_eq_nat @ ( SV216 @ SY789 ) @ ( SV216 @ SY790 ) ) )
| ( ord_less_eq_nat @ SV95 @ ( SV216 @ SY912 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1092,plain,
! [SV217: nat > nat,SV96: set_nat] :
( ( ( ~ ! [SY791: nat] :
( ~ ( member_nat @ SY791 @ SV96 )
| ( ord_less_eq_nat @ ( SV217 @ SY791 ) @ zero_zero_nat ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( groups1842438620at_nat @ SV217 @ SV96 ) @ zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[949]) ).
thf(1093,plain,
! [SV310: nat,SV218: nat,SV97: nat > nat] :
( ( ~ ! [SY578: nat,SY579: nat] :
( ~ ( ord_less_nat @ SY578 @ SY579 )
| ( ord_less_nat @ ( SV97 @ SY578 ) @ ( SV97 @ SY579 ) ) )
| ~ ( ord_less_eq_nat @ SV218 @ SV310 )
| ( ord_less_eq_nat @ ( SV97 @ SV218 ) @ ( SV97 @ SV310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1094,plain,
! [SV311: nat,SV219: nat,SV98: nat] :
( ( ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
= ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV219 )
| ~ ( ord_less_nat @ SV98 @ SV311 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1095,plain,
! [SV312: nat,SV220: nat > nat,SV99: nat] :
( ( ! [SY917: nat] :
( ( SV99
!= ( SV220 @ SV312 ) )
| ~ ( ord_less_eq_nat @ SV312 @ SY917 )
| ~ ! [SY798: nat,SY799: nat] :
( ~ ( ord_less_eq_nat @ SY798 @ SY799 )
| ( ord_less_eq_nat @ ( SV220 @ SY798 ) @ ( SV220 @ SY799 ) ) )
| ( ord_less_eq_nat @ SV99 @ ( SV220 @ SY917 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1096,plain,
! [SV313: nat,SV221: nat,SV100: nat > $o] :
( ( ~ ( SV100 @ SV221 )
| ~ ! [SY920: nat] :
( ~ ( SV100 @ SY920 )
| ( ord_less_eq_nat @ SY920 @ SV313 ) )
| ~ ! [SY590: nat] :
~ ~ ( ~ ( SV100 @ SY590 )
| ~ ! [SY591: nat] :
( ~ ( SV100 @ SY591 )
| ( ord_less_eq_nat @ SY591 @ SY590 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1097,plain,
! [SV222: nat] :
( ( ! [SV314: nat] :
( ( ord_less_nat @ SV222 @ SV314 )
= ( ~ ( ~ ( ord_less_eq_nat @ SV222 @ SV314 )
| ~ ( ( SV314 != SV222 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[954]) ).
thf(1098,plain,
! [SV222: nat] :
( ( ( ord_less_nat @ SV222 )
= ( ^ [SY804: nat] :
~ ( ~ ( ord_less_eq_nat @ SV222 @ SY804 )
| ~ ( ( SY804 != SV222 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[954]) ).
thf(1099,plain,
! [SV223: nat,SV102: nat] :
( ( ( ~ ( ( SV102 != SV223 ) ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV102 @ SV223 )
| ( ord_less_nat @ SV102 @ SV223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[955]) ).
thf(1100,plain,
! [SV224: nat,SV103: nat > nat] :
( ( ( ~ ( number1551313001itions @ SV103 @ SV224 ) )
= $true )
| ( ( ~ ( ~ ! [SY805: nat] :
( ~ ( ( ( SV103 @ SY805 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY805 )
| ~ ( ord_less_eq_nat @ SY805 @ SV224 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY596: nat] : ( times_times_nat @ ( SV103 @ SY596 ) @ SY596 )
@ ( set_ord_atMost_nat @ SV224 ) )
!= SV224 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[956]) ).
thf(1101,plain,
! [SV225: nat,SV104: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV104 @ SV225 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV225 @ SV104 )
| ( SV104 = SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[957]) ).
thf(1102,plain,
! [SV226: nat,SV105: nat] :
( ( ( ~ ( ( ord_less_nat @ SV105 @ SV226 )
| ( SV105 = SV226 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV105 @ SV226 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[958]) ).
thf(1103,plain,
! [SV315: nat > nat,SV227: nat,SV106: nat] :
( ( ! [SY923: nat] :
( ~ ( ord_less_eq_nat @ SV106 @ SV227 )
| ~ ( ord_less_eq_nat @ ( SV315 @ SV227 ) @ SY923 )
| ~ ! [SY924: nat,SY925: nat] :
( ~ ( ord_less_eq_nat @ SY924 @ SY925 )
| ( ord_less_eq_nat @ ( SV315 @ SY924 ) @ ( SV315 @ SY925 ) ) )
| ( ord_less_eq_nat @ ( SV315 @ SV106 ) @ SY923 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1104,plain,
! [SV228: nat] :
( ( ! [SV316: nat] :
( ( ord_less_nat @ SV228 @ SV316 )
= ( ~ ( ~ ( ord_less_eq_nat @ SV228 @ SV316 )
| ~ ( ( SV228 != SV316 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[960]) ).
thf(1105,plain,
! [SV228: nat] :
( ( ( ord_less_nat @ SV228 )
= ( ^ [SY811: nat] :
~ ( ~ ( ord_less_eq_nat @ SV228 @ SY811 )
| ~ ( ( SV228 != SY811 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[960]) ).
thf(1106,plain,
! [SV108: nat] :
( ( ( ord_less_eq_nat @ SV108 @ zero_zero_nat )
= $false )
| ( ( SV108 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[961]) ).
thf(1107,plain,
! [SV317: nat,SV229: nat,SV109: nat] :
( ( ~ ( ord_less_nat @ SV109 @ SV229 )
| ~ ( ord_less_eq_nat @ SV317 @ SV109 )
| ( ord_less_nat @ SV317 @ SV229 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1108,plain,
! [SV230: nat,SV110: nat > $o] :
( ( ( ~ ( SV110 @ zero_zero_nat ) )
= $true )
| ( ( ~ ! [SY608: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY608 )
| ~ ~ ( SV110 @ SY608 )
| ~ ! [SY609: nat] :
~ ~ ( ~ ( ord_less_nat @ SY609 @ SY608 )
| ~ ~ ( SV110 @ SY609 ) ) )
| ( SV110 @ SV230 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[963]) ).
thf(1109,plain,
! [SV231: set_nat,SV111: nat > nat] :
( ( ( ~ ( ( ( groups1842438620at_nat @ SV111 @ SV231 )
!= zero_zero_nat ) ) )
= $true )
| ( ( ~ ! [SY815: nat] :
( ~ ( member_nat @ SY815 @ SV231 )
| ( ( SV111 @ SY815 )
= zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[964]) ).
thf(1110,plain,
! [SV232: nat > nat,SV112: set_nat] :
( ( ( ~ ! [SY816: nat] :
( ~ ( member_nat @ SY816 @ SV112 )
| ( ord_less_eq_nat @ zero_zero_nat @ ( SV232 @ SY816 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ ( groups1842438620at_nat @ SV232 @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[965]) ).
thf(1111,plain,
! [SV233: nat,SV113: nat] :
( ( ( SV113 != SV233 )
= $true )
| ( ( ord_less_eq_nat @ SV113 @ SV233 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[966]) ).
thf(1112,plain,
! [SV234: nat,SV114: nat] :
( ( ( ~ ( ord_less_nat @ SV114 @ SV234 ) )
= $true )
| ( ( SV234 != zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[967]) ).
thf(1113,plain,
! [SV318: nat,SV235: nat,SV115: nat] :
( ( ~ ( ord_less_eq_nat @ SV115 @ SV235 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV318 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV115 @ SV318 ) @ ( times_times_nat @ SV235 @ SV318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1114,plain,
! [SV319: set_nat,SV236: nat > nat,SV116: set_nat] :
( ( ! [SY926: nat > nat,SY927: nat > nat,SY928: nat > nat] :
( ~ ! [SY929: nat] :
( ~ ( member_nat @ SY929 @ SV116 )
| ~ ( ~ ( member_nat @ ( SV236 @ SY929 ) @ SV319 )
| ( ( SY926 @ ( SV236 @ SY929 ) )
!= SY929 ) ) )
| ~ ! [SY930: nat] :
( ~ ( member_nat @ SY930 @ SV319 )
| ~ ( ~ ~ ( ~ ( member_nat @ ( SY926 @ SY930 ) @ SV116 )
| ( ( SV236 @ ( SY926 @ SY930 ) )
!= SY930 ) )
| ( ( SY927 @ ( SY926 @ SY930 ) )
!= ( SY928 @ SY930 ) ) ) )
| ( ( groups1842438620at_nat @ SY928 @ SV319 )
= ( groups1842438620at_nat @ SY927 @ SV116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1115,plain,
! [SV320: nat > set_nat,SV237: nat,SV117: nat] :
( ( ! [SY931: set_nat] :
( ~ ( ord_less_eq_nat @ SV117 @ SV237 )
| ~ ( ord_less_eq_set_nat @ ( SV320 @ SV237 ) @ SY931 )
| ~ ! [SY932: nat,SY933: nat] :
( ~ ( ord_less_eq_nat @ SY932 @ SY933 )
| ( ord_less_eq_set_nat @ ( SV320 @ SY932 ) @ ( SV320 @ SY933 ) ) )
| ( ord_less_eq_set_nat @ ( SV320 @ SV117 ) @ SY931 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1116,plain,
! [SV238: nat,SV118: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV118 @ one_one_nat ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV238 )
| ~ ( ord_less_eq_nat @ SV238 @ one_one_nat )
| ( ord_less_eq_nat @ ( times_times_nat @ SV118 @ SV238 ) @ one_one_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[971]) ).
thf(1117,plain,
! [SV321: nat,SV239: nat > nat,SV119: nat] :
( ( ! [SY934: nat] :
( ~ ( ord_less_eq_nat @ SV119 @ ( SV239 @ SV321 ) )
| ~ ( ord_less_eq_nat @ SV321 @ SY934 )
| ~ ! [SY830: nat,SY831: nat] :
( ~ ( ord_less_eq_nat @ SY830 @ SY831 )
| ( ord_less_eq_nat @ ( SV239 @ SY830 ) @ ( SV239 @ SY831 ) ) )
| ( ord_less_eq_nat @ SV119 @ ( SV239 @ SY934 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1118,plain,
! [SV240: nat,SV120: nat] :
( ( ( ( times_times_nat @ SV120 @ SV240 )
!= zero_zero_nat )
= $true )
| ( ( ( SV120 = zero_zero_nat )
| ( SV240 = zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[973]) ).
thf(1119,plain,
! [SV322: nat,SV241: nat,SV121: nat] :
( ( ~ ( ord_less_eq_nat @ SV121 @ SV241 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV121 @ SV322 ) @ ( times_times_nat @ SV241 @ SV322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1120,plain,
! [SV122: nat] :
( ( ( SV122 != zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV122 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[975]) ).
thf(1121,plain,
! [SV242: nat,SV123: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV123 @ one_one_nat ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV242 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV242 @ SV123 ) @ SV242 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[976]) ).
thf(1122,plain,
! [SV243: nat] :
( ( ! [SV323: nat] :
( ( SV243 = SV323 )
= ( ~ ( ~ ( ord_less_eq_nat @ SV243 @ SV323 )
| ~ ( ord_less_eq_nat @ SV323 @ SV243 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[977]) ).
thf(1123,plain,
! [SV243: nat] :
( ( ( ^ [SY833: nat] : ( SV243 = SY833 ) )
= ( ^ [SY834: nat] :
~ ( ~ ( ord_less_eq_nat @ SV243 @ SY834 )
| ~ ( ord_less_eq_nat @ SY834 @ SV243 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[977]) ).
thf(1124,plain,
! [SV324: nat,SV244: nat,SV125: nat] :
( ( ~ ( ord_less_eq_nat @ SV125 @ SV244 )
| ~ ( ord_less_eq_nat @ SV244 @ SV324 )
| ( ord_less_eq_nat @ SV125 @ SV324 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1125,plain,
! [SV245: nat,SV126: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV126 @ SV245 ) )
= $true )
| ( ( ~ ( ( SV126 != SV245 ) )
| ( ord_less_nat @ SV126 @ SV245 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[979]) ).
thf(1126,plain,
! [SV325: nat,SV246: nat > set_nat,SV127: set_nat] :
( ( ! [SY937: nat] :
( ~ ( ord_less_eq_set_nat @ SV127 @ ( SV246 @ SV325 ) )
| ~ ( ord_less_eq_nat @ SV325 @ SY937 )
| ~ ! [SY838: nat,SY839: nat] :
( ~ ( ord_less_eq_nat @ SY838 @ SY839 )
| ( ord_less_eq_set_nat @ ( SV246 @ SY838 ) @ ( SV246 @ SY839 ) ) )
| ( ord_less_eq_set_nat @ SV127 @ ( SV246 @ SY937 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1127,plain,
! [SV326: nat,SV247: nat,SV128: nat] :
( ( ! [SY940: nat] :
( ~ ( ord_less_eq_nat @ SV128 @ SV247 )
| ~ ( ord_less_eq_nat @ SV326 @ SY940 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV247 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV326 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV128 @ SV326 ) @ ( times_times_nat @ SV247 @ SY940 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1128,plain,
! [SV129: nat] :
( ( ( SV129 != zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV129 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1129,plain,
! [SV327: nat,SV248: nat,SV130: nat] :
( ( ~ ( ( SV130 != zero_zero_nat ) )
| ( ( ( times_times_nat @ SV130 @ SV248 )
= ( times_times_nat @ SV130 @ SV327 ) )
= ( SV248 = SV327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1130,plain,
! [SV328: nat,SV249: nat,SV131: nat] :
( ( ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) )
= ( ~ ( ord_less_nat @ zero_zero_nat @ SV249 )
| ( ord_less_eq_nat @ SV131 @ SV328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1131,plain,
! [SV329: nat > nat,SV250: nat,SV132: nat] :
( ( ! [SY941: nat] :
( ~ ( ord_less_eq_nat @ SV132 @ SV250 )
| ( ( SV329 @ SV250 )
!= SY941 )
| ~ ! [SY942: nat,SY943: nat] :
( ~ ( ord_less_eq_nat @ SY942 @ SY943 )
| ( ord_less_eq_nat @ ( SV329 @ SY942 ) @ ( SV329 @ SY943 ) ) )
| ( ord_less_eq_nat @ ( SV329 @ SV132 ) @ SY941 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1132,plain,
! [SV330: nat,SV251: nat,SV133: nat] :
( ( ~ ( ord_less_eq_nat @ SV133 @ SV251 )
| ~ ( ord_less_eq_nat @ SV251 @ SV330 )
| ( ord_less_eq_nat @ SV133 @ SV330 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1133,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ~ ( ~ ( ord_less_eq_nat @ SV134 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV331 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV331 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV134 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1134,plain,
! [SV332: nat,SV253: nat,SV135: nat] :
( ( ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
= ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 )
| ~ ( ord_less_nat @ SV253 @ SV332 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1135,plain,
! [SV254: nat,SV136: nat] :
( ( ~ ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV136 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV254 ) ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV136 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV254 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[989]) ).
thf(1136,plain,
! [SV254: nat,SV136: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
= ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV136 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV254 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[989]) ).
thf(1137,plain,
! [SV255: nat,SV137: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV137 @ SV255 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV255 @ SV137 )
| ( SV137 = SV255 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[990]) ).
thf(1138,plain,
! [SV333: nat,SV256: nat,SV138: nat] :
( ( ~ ( ord_less_eq_nat @ SV138 @ SV256 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV333 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV333 @ SV138 ) @ ( times_times_nat @ SV333 @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1139,plain,
! [SV257: nat,SV139: nat] :
( ( ( ~ ( ord_less_nat @ SV139 @ SV257 ) )
= $true )
| ( ( ord_less_eq_nat @ SV139 @ SV257 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[992]) ).
thf(1140,plain,
! [SV258: nat,SV140: nat] :
( ( ( ~ ( ~ ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV140 )
| ~ ( ord_less_eq_nat @ SV258 @ zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ SV140 @ zero_zero_nat )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV258 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV140 @ SV258 ) @ zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[993]) ).
thf(1141,plain,
! [SV259: nat] :
( ( ! [SV334: nat] :
( ( ord_less_nat @ SV259 @ SV334 )
= ( ~ ( ~ ( ord_less_eq_nat @ SV259 @ SV334 )
| ~ ( ( SV259 != SV334 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[994]) ).
thf(1142,plain,
! [SV259: nat] :
( ( ( ord_less_nat @ SV259 )
= ( ^ [SY852: nat] :
~ ( ~ ( ord_less_eq_nat @ SV259 @ SY852 )
| ~ ( ( SV259 != SY852 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[994]) ).
thf(1143,plain,
! [SV335: nat > nat,SV260: nat > nat,SV142: set_nat] :
( ( ~ ! [SY944: nat] :
( ~ ( member_nat @ SY944 @ SV142 )
| ( ord_less_eq_nat @ ( SV260 @ SY944 ) @ ( SV335 @ SY944 ) ) )
| ( ord_less_eq_nat @ ( groups1842438620at_nat @ SV260 @ SV142 ) @ ( groups1842438620at_nat @ SV335 @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1144,plain,
! [SV261: nat,SV143: nat] :
( ( ( ~ ( ord_less_nat @ SV143 @ SV261 ) )
= $true )
| ( ( ord_less_eq_nat @ SV143 @ SV261 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[996]) ).
thf(1145,plain,
! [SV262: nat,SV144: nat] :
( ( ( ~ ( ord_less_nat @ SV144 @ SV262 ) )
= $true )
| ( ( SV262 != zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[997]) ).
thf(1146,plain,
! [SV263: nat,SV145: nat] :
( ( ~ ( ( one_one_nat
= ( times_times_nat @ SV145 @ SV263 ) )
| ~ ( ( SV145 != one_one_nat )
| ( SV263 != one_one_nat ) ) )
| ~ ( ( one_one_nat
!= ( times_times_nat @ SV145 @ SV263 ) )
| ~ ~ ( ( SV145 != one_one_nat )
| ( SV263 != one_one_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[998]) ).
thf(1147,plain,
! [SV263: nat,SV145: nat] :
( ( ( one_one_nat
= ( times_times_nat @ SV145 @ SV263 ) )
= ( ~ ( ( SV145 != one_one_nat )
| ( SV263 != one_one_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[998]) ).
thf(1148,plain,
! [SV336: nat,SV264: nat,SV146: nat] :
( ( ~ ( ( SV146 != zero_zero_nat ) )
| ( ( ( times_times_nat @ SV264 @ SV146 )
= ( times_times_nat @ SV336 @ SV146 ) )
= ( SV264 = SV336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1149,plain,
! [SV147: nat] :
( ( ( ~ ( ( SV147 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV147 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV147 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV147 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1000]) ).
thf(1150,plain,
! [SV265: nat,SV148: nat > nat] :
( ( ( ~ ! [SY856: nat] :
( ~ ( ( ( SV148 @ SY856 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY856 )
| ~ ( ord_less_eq_nat @ SY856 @ SV265 ) ) ) )
= $true )
| ( ( ( ( groups1842438620at_nat
@ ^ [SY685: nat] : ( times_times_nat @ ( SV148 @ SY685 ) @ SY685 )
@ ( set_ord_atMost_nat @ SV265 ) )
!= SV265 )
| ( number1551313001itions @ SV148 @ SV265 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1002]) ).
thf(1151,plain,
! [SV266: nat,SV149: nat] :
( ( ~ ( ( ( times_times_nat @ SV149 @ SV266 )
= one_one_nat )
| ~ ( ( SV149 != one_one_nat )
| ( SV266 != one_one_nat ) ) )
| ~ ( ( ( times_times_nat @ SV149 @ SV266 )
!= one_one_nat )
| ~ ~ ( ( SV149 != one_one_nat )
| ( SV266 != one_one_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1003]) ).
thf(1152,plain,
! [SV266: nat,SV149: nat] :
( ( ( ( times_times_nat @ SV149 @ SV266 )
= one_one_nat )
= ( ~ ( ( SV149 != one_one_nat )
| ( SV266 != one_one_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1003]) ).
thf(1153,plain,
! [SV150: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ SV150 )
| ( SV150 != zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV150 )
| ~ ( ( SV150 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1004]) ).
thf(1154,plain,
! [SV337: set_nat > nat,SV267: set_nat,SV151: set_nat] :
( ( ! [SY945: nat] :
( ~ ( ord_less_eq_set_nat @ SV151 @ SV267 )
| ( ( SV337 @ SV267 )
!= SY945 )
| ~ ! [SY946: set_nat,SY947: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY946 @ SY947 )
| ( ord_less_eq_nat @ ( SV337 @ SY946 ) @ ( SV337 @ SY947 ) ) )
| ( ord_less_eq_nat @ ( SV337 @ SV151 ) @ SY945 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1155,plain,
! [SV338: nat,SV268: nat,SV152: nat] :
( ( ~ ( ord_less_eq_nat @ SV152 @ SV268 )
| ~ ( ord_less_nat @ SV338 @ SV152 )
| ( ord_less_nat @ SV338 @ SV268 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1156,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) )
= ( ~ ( ord_less_nat @ zero_zero_nat @ SV153 )
| ( ord_less_eq_nat @ SV269 @ SV339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1157,plain,
! [SV270: nat,SV154: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV154 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV270 @ zero_zero_nat )
| ( ord_less_eq_nat @ ( times_times_nat @ SV270 @ SV154 ) @ zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1009]) ).
thf(1158,plain,
! [SV340: nat,SV271: nat,SV155: nat] :
( ( ~ ( ord_less_nat @ SV155 @ SV271 )
| ~ ( ord_less_eq_nat @ SV271 @ SV340 )
| ( ord_less_nat @ SV155 @ SV340 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1159,plain,
! [SV156: nat,SV2: nat] :
( ( ( ~ ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ SV2 ) @ ( set_ord_atMost_nat @ SV156 ) )
| ( ord_less_eq_nat @ SV2 @ SV156 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ SV2 ) @ ( set_ord_atMost_nat @ SV156 ) )
| ~ ( ord_less_eq_nat @ SV2 @ SV156 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1011]) ).
thf(1160,plain,
! [SV157: nat,SV3: nat] :
( ( ( ~ ( ( member_nat @ SV3 @ ( set_ord_atMost_nat @ SV157 ) )
| ( ord_less_eq_nat @ SV3 @ SV157 ) ) )
= $true )
| ( ( ~ ( ~ ( member_nat @ SV3 @ ( set_ord_atMost_nat @ SV157 ) )
| ~ ( ord_less_eq_nat @ SV3 @ SV157 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1013]) ).
thf(1161,plain,
! [SV158: nat,SV4: nat] :
( ( ( ~ ( ( ( set_ord_atMost_nat @ SV4 )
= ( set_ord_atMost_nat @ SV158 ) )
| ( SV4 = SV158 ) ) )
= $true )
| ( ( ~ ( ( ( set_ord_atMost_nat @ SV4 )
!= ( set_ord_atMost_nat @ SV158 ) )
| ( SV4 != SV158 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1015]) ).
thf(1162,plain,
! [SV272: nat,SV159: nat,SV5: nat] :
( ( ~ ( ( ( times_times_nat @ SV5 @ SV159 )
= ( times_times_nat @ SV272 @ SV159 ) )
| ( SV159 = zero_zero_nat )
| ( SV5 = SV272 ) )
| ~ ( ( ( times_times_nat @ SV5 @ SV159 )
!= ( times_times_nat @ SV272 @ SV159 ) )
| ~ ( ( SV159 = zero_zero_nat )
| ( SV5 = SV272 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1017]) ).
thf(1163,plain,
! [SV272: nat,SV159: nat,SV5: nat] :
( ( ( ( times_times_nat @ SV5 @ SV159 )
= ( times_times_nat @ SV272 @ SV159 ) )
= ( ( SV159 = zero_zero_nat )
| ( SV5 = SV272 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1017]) ).
thf(1164,plain,
! [SV273: nat,SV160: nat,SV6: nat] :
( ( ~ ( ( ( times_times_nat @ SV6 @ SV160 )
= ( times_times_nat @ SV6 @ SV273 ) )
| ( SV6 = zero_zero_nat )
| ( SV160 = SV273 ) )
| ~ ( ( ( times_times_nat @ SV6 @ SV160 )
!= ( times_times_nat @ SV6 @ SV273 ) )
| ~ ( ( SV6 = zero_zero_nat )
| ( SV160 = SV273 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1018]) ).
thf(1165,plain,
! [SV273: nat,SV160: nat,SV6: nat] :
( ( ( ( times_times_nat @ SV6 @ SV160 )
= ( times_times_nat @ SV6 @ SV273 ) )
= ( ( SV6 = zero_zero_nat )
| ( SV160 = SV273 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1018]) ).
thf(1166,plain,
! [SV161: nat,SV7: nat] :
( ( ( ~ ( ( ( times_times_nat @ SV7 @ SV161 )
= zero_zero_nat )
| ( SV7 = zero_zero_nat )
| ( SV161 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( ( times_times_nat @ SV7 @ SV161 )
!= zero_zero_nat )
| ~ ( ( SV7 = zero_zero_nat )
| ( SV161 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1019]) ).
thf(1167,plain,
! [SV274: nat,SV162: nat,SV12: nat] :
( ( ~ ( ( ( times_times_nat @ SV12 @ SV162 )
= ( times_times_nat @ SV274 @ SV162 ) )
| ( SV12 = SV274 )
| ( SV162 = zero_zero_nat ) )
| ~ ( ( ( times_times_nat @ SV12 @ SV162 )
!= ( times_times_nat @ SV274 @ SV162 ) )
| ~ ( ( SV12 = SV274 )
| ( SV162 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1021]) ).
thf(1168,plain,
! [SV274: nat,SV162: nat,SV12: nat] :
( ( ( ( times_times_nat @ SV12 @ SV162 )
= ( times_times_nat @ SV274 @ SV162 ) )
= ( ( SV12 = SV274 )
| ( SV162 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1021]) ).
thf(1169,plain,
! [SV275: nat,SV163: nat,SV13: nat] :
( ( ~ ( ( ( times_times_nat @ SV13 @ SV163 )
= ( times_times_nat @ SV13 @ SV275 ) )
| ( SV163 = SV275 )
| ( SV13 = zero_zero_nat ) )
| ~ ( ( ( times_times_nat @ SV13 @ SV163 )
!= ( times_times_nat @ SV13 @ SV275 ) )
| ~ ( ( SV163 = SV275 )
| ( SV13 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1022]) ).
thf(1170,plain,
! [SV275: nat,SV163: nat,SV13: nat] :
( ( ( ( times_times_nat @ SV13 @ SV163 )
= ( times_times_nat @ SV13 @ SV275 ) )
= ( ( SV163 = SV275 )
| ( SV13 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1022]) ).
thf(1171,plain,
! [SV164: nat,SV15: nat] :
( ( ( ~ ( ( ( times_times_nat @ SV15 @ SV164 )
= zero_zero_nat )
| ( SV15 = zero_zero_nat )
| ( SV164 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( ( times_times_nat @ SV15 @ SV164 )
!= zero_zero_nat )
| ~ ( ( SV15 = zero_zero_nat )
| ( SV164 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1023]) ).
thf(1172,plain,
! [SV19: nat] :
( ( ( ( ord_less_eq_nat @ SV19 @ zero_zero_nat )
| ( SV19 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV19 @ zero_zero_nat )
| ( SV19 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1027]) ).
thf(1173,plain,
! [SV20: nat] :
( ( ( ( ord_less_eq_nat @ SV20 @ zero_zero_nat )
| ( SV20 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV20 @ zero_zero_nat )
| ( SV20 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1028]) ).
thf(1174,plain,
! [SV341: set_nat,SV279: nat > nat,SV171: set_nat,SV31: nat > nat] :
( ( ( times_times_nat @ ( groups1842438620at_nat @ SV31 @ SV171 ) @ ( groups1842438620at_nat @ SV279 @ SV341 ) )
= ( groups1842438620at_nat
@ ^ [SY948: nat] :
( groups1842438620at_nat
@ ^ [SY872: nat] : ( times_times_nat @ ( SV31 @ SY948 ) @ ( SV279 @ SY872 ) )
@ SV341 )
@ SV171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1175,plain,
! [SV35: nat] :
( ( ( ( ord_less_eq_nat @ SV35 @ zero_zero_nat )
| ( SV35 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV35 @ zero_zero_nat )
| ( SV35 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1032]) ).
thf(1176,plain,
! [SV280: nat,SV173: nat,SV37: nat] :
( ( ~ ( ( ( times_times_nat @ SV37 @ SV173 )
= ( times_times_nat @ SV37 @ SV280 ) )
| ( SV37 = zero_zero_nat )
| ( SV173 = SV280 ) )
| ~ ( ( ( times_times_nat @ SV37 @ SV173 )
!= ( times_times_nat @ SV37 @ SV280 ) )
| ~ ( ( SV37 = zero_zero_nat )
| ( SV173 = SV280 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1033]) ).
thf(1177,plain,
! [SV280: nat,SV173: nat,SV37: nat] :
( ( ( ( times_times_nat @ SV37 @ SV173 )
= ( times_times_nat @ SV37 @ SV280 ) )
= ( ( SV37 = zero_zero_nat )
| ( SV173 = SV280 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1033]) ).
thf(1178,plain,
! [SV42: nat] :
( ( ( ( zero_zero_nat = SV42 )
| ( SV42 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( zero_zero_nat != SV42 )
| ( SV42 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1035]) ).
thf(1179,plain,
! [SV342: nat,SV177: nat] :
( ( ( times_times_nat @ SV177 @ SV342 )
= ( times_times_nat @ SV342 @ SV177 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1180,plain,
! [SV47: nat] :
( ( ( ( one_one_nat = SV47 )
| ( SV47 = one_one_nat ) )
= $false )
| ( ( ~ ( ( one_one_nat != SV47 )
| ( SV47 != one_one_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1041]) ).
thf(1181,plain,
! [SV50: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV50 )
| ( SV50 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV50 )
| ( SV50 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1042]) ).
thf(1182,plain,
! [SV51: nat] :
( ( ( ( ord_less_nat @ SV51 @ one_one_nat )
| ( SV51 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV51 @ one_one_nat )
| ( SV51 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1043]) ).
thf(1183,plain,
! [SV343: nat,SV179: nat] :
( ( ( ord_less_eq_nat @ SV179 @ SV343 )
= ( ( ord_less_nat @ SV179 @ SV343 )
| ( SV179 = SV343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1184,plain,
! [SV54: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV54 )
| ( SV54 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV54 )
| ( SV54 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1046]) ).
thf(1185,plain,
! [SV344: nat,SV180: nat] :
( ( ( ord_less_eq_nat @ SV180 @ SV344 )
= ( ( ord_less_nat @ SV180 @ SV344 )
| ( SV344 = SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1186,plain,
! [SV345: nat,SV181: nat] :
( ( ( ord_less_eq_nat @ SV181 @ SV345 )
= ( ( ord_less_nat @ SV181 @ SV345 )
| ( SV181 = SV345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1187,plain,
! [SV346: set_nat,SV288: nat > nat,SV182: nat > nat,SV60: set_nat] :
( ( ! [SY950: nat > nat,SY951: nat > nat] :
( ~ ! [SY876: nat] :
( ~ ( member_nat @ SY876 @ SV60 )
| ( ( SV182 @ ( SV288 @ SY876 ) )
= SY876 ) )
| ~ ! [SY953: nat] :
( ~ ( member_nat @ SY953 @ SV60 )
| ( member_nat @ ( SV288 @ SY953 ) @ SV346 ) )
| ~ ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) )
| ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY880: nat] :
( ~ ( member_nat @ SY880 @ SV60 )
| ( ( SY950 @ ( SV288 @ SY880 ) )
= ( SY951 @ SY880 ) ) )
| ( ( groups1842438620at_nat @ SY951 @ SV60 )
= ( groups1842438620at_nat @ SY950 @ SV346 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1188,plain,
! [SV183: nat,SV61: nat] :
( ( ( ord_less_eq_nat @ SV61 @ SV183 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV183 @ SV61 )
| ( SV61 = SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1052]) ).
thf(1189,plain,
! [SV184: nat,SV62: nat] :
( ( ( SV62 != zero_zero_nat )
= $false )
| ( ( ~ ( ( SV184 != zero_zero_nat ) )
| ( ( times_times_nat @ SV62 @ SV184 )
!= zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1053]) ).
thf(1190,plain,
! [SV289: nat,SV185: nat,SV63: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV63 @ SV185 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV289 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV289 @ SV63 ) @ ( times_times_nat @ SV289 @ SV185 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1054]) ).
thf(1191,plain,
! [SV347: nat,SV186: nat] :
( ( ( SV186 = SV347 )
= ( ~ ( ~ ( ord_less_eq_nat @ SV186 @ SV347 )
| ~ ( ord_less_eq_nat @ SV347 @ SV186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1192,plain,
! [SV187: nat > nat,SV65: set_nat] :
( ( ( ! [SY736: nat] :
( ~ ( member_nat @ SY736 @ SV65 )
| ( ( SV187 @ SY736 )
= zero_zero_nat ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV187 @ SV65 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1057]) ).
thf(1193,plain,
! [SV188: nat,SV66: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV66 @ SV188 ) )
= $false )
| ( ( ord_less_eq_nat @ SV188 @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1194,plain,
! [SV291: nat,SV189: nat,SV67: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV67 @ SV189 ) )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV291 @ SV67 ) @ ( times_times_nat @ SV291 @ SV189 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1059]) ).
thf(1195,plain,
! [SV190: nat,SV68: nat] :
( ( ( SV68
= ( times_times_nat @ SV68 @ SV190 ) )
= $false )
| ( ( ( SV190 = one_one_nat )
| ( SV68 = zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1060]) ).
thf(1196,plain,
! [SV348: nat,SV292: set_nat > nat,SV191: set_nat,SV69: set_nat] :
( ( ~ ( ord_less_eq_set_nat @ SV69 @ SV191 )
| ~ ( ord_less_eq_nat @ ( SV292 @ SV191 ) @ SV348 )
| ~ ! [SY882: set_nat,SY883: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY882 @ SY883 )
| ( ord_less_eq_nat @ ( SV292 @ SY882 ) @ ( SV292 @ SY883 ) ) )
| ( ord_less_eq_nat @ ( SV292 @ SV69 ) @ SV348 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1197,plain,
! [SV293: nat,SV192: nat,SV70: nat > $o] :
( ( ( ~ ( SV70 @ SV192 ) )
= $true )
| ( ( ~ ! [SY884: nat] :
( ~ ( SV70 @ SY884 )
| ( ord_less_eq_nat @ SY884 @ SV293 ) )
| ~ ! [SY505: nat] :
( ~ ( SV70 @ SY505 )
| ~ ! [SY506: nat] :
( ~ ( SV70 @ SY506 )
| ( ord_less_eq_nat @ SY506 @ SY505 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1062]) ).
thf(1198,plain,
! [SV349: nat,SV294: nat,SV193: nat,SV71: nat] :
( ( ~ ( ord_less_eq_nat @ SV71 @ SV193 )
| ~ ( ord_less_eq_nat @ SV294 @ SV349 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV71 @ SV294 ) @ ( times_times_nat @ SV193 @ SV349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1199,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( number1551313001itions @ SV194 @ SV350 )
= ( ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1200,plain,
! [SV195: nat,SV73: nat] :
( ( ( ord_less_eq_nat @ SV73 @ zero_zero_nat )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV195 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV73 @ SV195 ) @ zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1066]) ).
thf(1201,plain,
! [SV351: set_nat,SV296: nat > set_nat,SV196: nat,SV74: nat] :
( ( ~ ( ord_less_eq_nat @ SV74 @ SV196 )
| ( ( SV296 @ SV196 )
!= SV351 )
| ~ ! [SY891: nat,SY892: nat] :
( ~ ( ord_less_eq_nat @ SY891 @ SY892 )
| ( ord_less_eq_set_nat @ ( SV296 @ SY891 ) @ ( SV296 @ SY892 ) ) )
| ( ord_less_eq_set_nat @ ( SV296 @ SV74 ) @ SV351 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1202,plain,
! [SV297: nat,SV197: nat,SV75: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV75 @ SV197 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV197 @ SV297 )
| ( ord_less_eq_nat @ SV75 @ SV297 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1068]) ).
thf(1203,plain,
! [SV298: nat,SV198: nat,SV76: nat > nat > $o] :
( ( ( ~ ! [SY523: nat,SY524: nat] :
( ~ ( ord_less_eq_nat @ SY523 @ SY524 )
| ( SV76 @ SY523 @ SY524 ) ) )
= $true )
| ( ( ~ ! [SY525: nat,SY526: nat] :
( ~ ( SV76 @ SY526 @ SY525 )
| ( SV76 @ SY525 @ SY526 ) )
| ( SV76 @ SV198 @ SV298 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1069]) ).
thf(1204,plain,
! [SV299: nat,SV199: nat,SV77: nat] :
( ( ( SV77 != SV199 )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV199 @ SV299 )
| ( ord_less_eq_nat @ SV77 @ SV299 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1070]) ).
thf(1205,plain,
! [SV200: nat,SV78: nat] :
( ( ( SV78 = SV200 )
= $false )
| ( ( ord_less_eq_nat @ SV78 @ SV200 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1071]) ).
thf(1206,plain,
! [SV300: nat,SV201: nat,SV79: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV79 @ SV201 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV201 @ SV300 )
| ( ord_less_nat @ SV79 @ SV300 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1072]) ).
thf(1207,plain,
! [SV202: nat,SV80: nat] :
( ( ( ( times_times_nat @ SV80 @ SV202 )
!= zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ( SV80 != zero_zero_nat ) )
| ~ ( ( SV202 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1073]) ).
thf(1208,plain,
! [SV301: nat,SV203: nat,SV81: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV81 @ SV203 ) )
= $true )
| ( ( ( SV203 != SV301 )
| ( ord_less_eq_nat @ SV81 @ SV301 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1074]) ).
thf(1209,plain,
! [SV302: nat,SV204: nat,SV82: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV82 @ SV204 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV302 @ SV82 )
| ( ord_less_eq_nat @ SV302 @ SV204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1075]) ).
thf(1210,plain,
! [SV352: nat,SV303: nat,SV205: nat,SV83: nat] :
( ( ~ ( ord_less_eq_nat @ SV83 @ SV205 )
| ~ ( ord_less_eq_nat @ SV303 @ SV352 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV83 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV303 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV83 @ SV303 ) @ ( times_times_nat @ SV205 @ SV352 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1211,plain,
! [SV206: nat,SV84: nat] :
( ( ( ord_less_eq_nat @ SV84 @ SV206 )
= $false )
| ( ( ( ord_less_eq_nat @ SV206 @ SV84 )
= ( SV206 = SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1077]) ).
thf(1212,plain,
! [SV353: nat > nat,SV304: nat > nat,SV207: set_nat,SV85: set_nat] :
( ( ! [SY963: nat > nat] :
( ~ ! [SY900: nat] :
( ~ ( member_nat @ SY900 @ SV85 )
| ~ ! [SY901: nat] :
~ ~ ( ~ ~ ( ~ ( member_nat @ SY901 @ SV207 )
| ( ( SV304 @ SY901 )
!= SY900 ) )
| ~ ! [SY902: nat] :
( ~ ~ ( ~ ( member_nat @ SY902 @ SV207 )
| ( ( SV304 @ SY902 )
!= SY900 ) )
| ( SY902 = SY901 ) ) ) )
| ~ ! [SY967: nat] :
( ~ ( member_nat @ SY967 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY967 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY967 ) )
!= ( SY963 @ SY967 ) ) ) )
| ( ( groups1842438620at_nat @ SY963 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1213,plain,
! [SV354: nat,SV305: nat,SV208: nat > set_nat,SV86: set_nat] :
( ( ( SV86
!= ( SV208 @ SV305 ) )
| ~ ( ord_less_eq_nat @ SV305 @ SV354 )
| ~ ! [SY776: nat,SY777: nat] :
( ~ ( ord_less_eq_nat @ SY776 @ SY777 )
| ( ord_less_eq_set_nat @ ( SV208 @ SY776 ) @ ( SV208 @ SY777 ) ) )
| ( ord_less_eq_set_nat @ SV86 @ ( SV208 @ SV354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1214,plain,
! [SV355: set_nat,SV306: set_nat,SV209: set_nat > nat,SV87: nat] :
( ( ( SV87
!= ( SV209 @ SV306 ) )
| ~ ( ord_less_eq_set_nat @ SV306 @ SV355 )
| ~ ! [SY780: set_nat,SY781: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY780 @ SY781 )
| ( ord_less_eq_nat @ ( SV209 @ SY780 ) @ ( SV209 @ SY781 ) ) )
| ( ord_less_eq_nat @ SV87 @ ( SV209 @ SV355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1215,plain,
! [SV88: nat] :
( ( ( ( SV88 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV88 ) )
= $false )
| ( ( ~ ( ~ ( ( SV88 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV88 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1081]) ).
thf(1216,plain,
( ( ~ ( ~ ! [SX0: nat] :
( ~ ( ( ( p @ SX0 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SX0 )
| ~ ( ord_less_eq_nat @ SX0 @ zero_zero_nat ) ) )
| ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
!= zero_zero_nat ) )
| ( p
= ( ^ [SX0: nat] : zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1082]) ).
thf(1217,plain,
( ( ~ ~ ( ~ ! [SX0: nat] :
( ~ ( ( ( p @ SX0 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SX0 )
| ~ ( ord_less_eq_nat @ SX0 @ zero_zero_nat ) ) )
| ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
!= zero_zero_nat ) )
| ( p
!= ( ^ [SX0: nat] : zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1083]) ).
thf(1218,plain,
! [SV210: nat,SV89: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV89 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV210 )
| ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ SV89 @ SV210 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1084]) ).
thf(1219,plain,
! [SV211: nat,SV90: nat] :
( ( ( ord_less_nat @ SV90 @ SV211 )
= $false )
| ( ( ord_less_eq_nat @ SV90 @ SV211 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1220,plain,
! [SV212: nat,SV91: nat] :
( ( ( ord_less_eq_nat @ SV91 @ SV212 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV212 @ SV91 )
| ( SV212 = SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1086]) ).
thf(1221,plain,
! [SV356: nat,SV213: nat] :
( ( ( SV213 = SV356 )
= ( ~ ( ~ ( ord_less_eq_nat @ SV356 @ SV213 )
| ~ ( ord_less_eq_nat @ SV213 @ SV356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1222,plain,
! [SV357: nat > nat,SV308: nat > nat,SV214: set_nat,SV93: set_nat] :
( ( ( SV93 != SV214 )
| ~ ! [SY972: nat] :
( ~ ( member_nat @ SY972 @ SV214 )
| ( ( SV308 @ SY972 )
= ( SV357 @ SY972 ) ) )
| ( ( groups1842438620at_nat @ SV308 @ SV93 )
= ( groups1842438620at_nat @ SV357 @ SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1223,plain,
! [SV215: nat,SV94: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV215 @ zero_zero_nat )
| ( ord_less_eq_nat @ ( times_times_nat @ SV94 @ SV215 ) @ zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1090]) ).
thf(1224,plain,
! [SV358: set_nat,SV309: set_nat,SV216: set_nat > nat,SV95: nat] :
( ( ~ ( ord_less_eq_nat @ SV95 @ ( SV216 @ SV309 ) )
| ~ ( ord_less_eq_set_nat @ SV309 @ SV358 )
| ~ ! [SY789: set_nat,SY790: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY789 @ SY790 )
| ( ord_less_eq_nat @ ( SV216 @ SY789 ) @ ( SV216 @ SY790 ) ) )
| ( ord_less_eq_nat @ SV95 @ ( SV216 @ SV358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1225,plain,
! [SV217: nat > nat,SV96: set_nat] :
( ( ( ! [SY791: nat] :
( ~ ( member_nat @ SY791 @ SV96 )
| ( ord_less_eq_nat @ ( SV217 @ SY791 ) @ zero_zero_nat ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( groups1842438620at_nat @ SV217 @ SV96 ) @ zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1092]) ).
thf(1226,plain,
! [SV310: nat,SV218: nat,SV97: nat > nat] :
( ( ( ~ ! [SY578: nat,SY579: nat] :
( ~ ( ord_less_nat @ SY578 @ SY579 )
| ( ord_less_nat @ ( SV97 @ SY578 ) @ ( SV97 @ SY579 ) ) ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV218 @ SV310 )
| ( ord_less_eq_nat @ ( SV97 @ SV218 ) @ ( SV97 @ SV310 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1093]) ).
thf(1227,plain,
! [SV311: nat,SV219: nat,SV98: nat] :
( ( ~ ( ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV219 )
| ~ ( ord_less_nat @ SV98 @ SV311 ) ) )
| ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV219 )
| ~ ( ord_less_nat @ SV98 @ SV311 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1094]) ).
thf(1228,plain,
! [SV311: nat,SV219: nat,SV98: nat] :
( ( ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
= ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV219 )
| ~ ( ord_less_nat @ SV98 @ SV311 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1094]) ).
thf(1229,plain,
! [SV359: nat,SV312: nat,SV220: nat > nat,SV99: nat] :
( ( ( SV99
!= ( SV220 @ SV312 ) )
| ~ ( ord_less_eq_nat @ SV312 @ SV359 )
| ~ ! [SY798: nat,SY799: nat] :
( ~ ( ord_less_eq_nat @ SY798 @ SY799 )
| ( ord_less_eq_nat @ ( SV220 @ SY798 ) @ ( SV220 @ SY799 ) ) )
| ( ord_less_eq_nat @ SV99 @ ( SV220 @ SV359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1230,plain,
! [SV313: nat,SV221: nat,SV100: nat > $o] :
( ( ( ~ ( SV100 @ SV221 ) )
= $true )
| ( ( ~ ! [SY920: nat] :
( ~ ( SV100 @ SY920 )
| ( ord_less_eq_nat @ SY920 @ SV313 ) )
| ~ ! [SY590: nat] :
~ ~ ( ~ ( SV100 @ SY590 )
| ~ ! [SY591: nat] :
( ~ ( SV100 @ SY591 )
| ( ord_less_eq_nat @ SY591 @ SY590 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1096]) ).
thf(1231,plain,
! [SV360: nat,SV222: nat] :
( ( ( ord_less_nat @ SV222 @ SV360 )
= ( ~ ( ~ ( ord_less_eq_nat @ SV222 @ SV360 )
| ~ ( ( SV360 != SV222 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1232,plain,
! [SV223: nat,SV102: nat] :
( ( ( SV102 != SV223 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV102 @ SV223 )
| ( ord_less_nat @ SV102 @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1099]) ).
thf(1233,plain,
! [SV224: nat,SV103: nat > nat] :
( ( ( number1551313001itions @ SV103 @ SV224 )
= $false )
| ( ( ~ ( ~ ! [SY805: nat] :
( ~ ( ( ( SV103 @ SY805 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY805 )
| ~ ( ord_less_eq_nat @ SY805 @ SV224 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY596: nat] : ( times_times_nat @ ( SV103 @ SY596 ) @ SY596 )
@ ( set_ord_atMost_nat @ SV224 ) )
!= SV224 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1100]) ).
thf(1234,plain,
! [SV225: nat,SV104: nat] :
( ( ( ord_less_eq_nat @ SV104 @ SV225 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV225 @ SV104 )
| ( SV104 = SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1101]) ).
thf(1235,plain,
! [SV226: nat,SV105: nat] :
( ( ( ( ord_less_nat @ SV105 @ SV226 )
| ( SV105 = SV226 ) )
= $false )
| ( ( ord_less_eq_nat @ SV105 @ SV226 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1102]) ).
thf(1236,plain,
! [SV361: nat,SV315: nat > nat,SV227: nat,SV106: nat] :
( ( ~ ( ord_less_eq_nat @ SV106 @ SV227 )
| ~ ( ord_less_eq_nat @ ( SV315 @ SV227 ) @ SV361 )
| ~ ! [SY924: nat,SY925: nat] :
( ~ ( ord_less_eq_nat @ SY924 @ SY925 )
| ( ord_less_eq_nat @ ( SV315 @ SY924 ) @ ( SV315 @ SY925 ) ) )
| ( ord_less_eq_nat @ ( SV315 @ SV106 ) @ SV361 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1237,plain,
! [SV362: nat,SV228: nat] :
( ( ( ord_less_nat @ SV228 @ SV362 )
= ( ~ ( ~ ( ord_less_eq_nat @ SV228 @ SV362 )
| ~ ( ( SV228 != SV362 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1238,plain,
! [SV317: nat,SV229: nat,SV109: nat] :
( ( ( ~ ( ord_less_nat @ SV109 @ SV229 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV317 @ SV109 )
| ( ord_less_nat @ SV317 @ SV229 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1107]) ).
thf(1239,plain,
! [SV230: nat,SV110: nat > $o] :
( ( ( SV110 @ zero_zero_nat )
= $false )
| ( ( ~ ! [SY608: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY608 )
| ~ ~ ( SV110 @ SY608 )
| ~ ! [SY609: nat] :
~ ~ ( ~ ( ord_less_nat @ SY609 @ SY608 )
| ~ ~ ( SV110 @ SY609 ) ) )
| ( SV110 @ SV230 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1108]) ).
thf(1240,plain,
! [SV231: set_nat,SV111: nat > nat] :
( ( ( ( groups1842438620at_nat @ SV111 @ SV231 )
!= zero_zero_nat )
= $false )
| ( ( ~ ! [SY815: nat] :
( ~ ( member_nat @ SY815 @ SV231 )
| ( ( SV111 @ SY815 )
= zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1109]) ).
thf(1241,plain,
! [SV232: nat > nat,SV112: set_nat] :
( ( ( ! [SY816: nat] :
( ~ ( member_nat @ SY816 @ SV112 )
| ( ord_less_eq_nat @ zero_zero_nat @ ( SV232 @ SY816 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ ( groups1842438620at_nat @ SV232 @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1242,plain,
! [SV233: nat,SV113: nat] :
( ( ( SV113 = SV233 )
= $false )
| ( ( ord_less_eq_nat @ SV113 @ SV233 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1111]) ).
thf(1243,plain,
! [SV234: nat,SV114: nat] :
( ( ( ord_less_nat @ SV114 @ SV234 )
= $false )
| ( ( SV234 != zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1112]) ).
thf(1244,plain,
! [SV318: nat,SV235: nat,SV115: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV115 @ SV235 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV318 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV115 @ SV318 ) @ ( times_times_nat @ SV235 @ SV318 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1113]) ).
thf(1245,plain,
! [SV363: nat > nat,SV319: set_nat,SV236: nat > nat,SV116: set_nat] :
( ( ! [SY979: nat > nat,SY980: nat > nat] :
( ~ ! [SY981: nat] :
( ~ ( member_nat @ SY981 @ SV116 )
| ~ ( ~ ( member_nat @ ( SV236 @ SY981 ) @ SV319 )
| ( ( SV363 @ ( SV236 @ SY981 ) )
!= SY981 ) ) )
| ~ ! [SY982: nat] :
( ~ ( member_nat @ SY982 @ SV319 )
| ~ ( ~ ~ ( ~ ( member_nat @ ( SV363 @ SY982 ) @ SV116 )
| ( ( SV236 @ ( SV363 @ SY982 ) )
!= SY982 ) )
| ( ( SY979 @ ( SV363 @ SY982 ) )
!= ( SY980 @ SY982 ) ) ) )
| ( ( groups1842438620at_nat @ SY980 @ SV319 )
= ( groups1842438620at_nat @ SY979 @ SV116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1246,plain,
! [SV364: set_nat,SV320: nat > set_nat,SV237: nat,SV117: nat] :
( ( ~ ( ord_less_eq_nat @ SV117 @ SV237 )
| ~ ( ord_less_eq_set_nat @ ( SV320 @ SV237 ) @ SV364 )
| ~ ! [SY932: nat,SY933: nat] :
( ~ ( ord_less_eq_nat @ SY932 @ SY933 )
| ( ord_less_eq_set_nat @ ( SV320 @ SY932 ) @ ( SV320 @ SY933 ) ) )
| ( ord_less_eq_set_nat @ ( SV320 @ SV117 ) @ SV364 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1247,plain,
! [SV238: nat,SV118: nat] :
( ( ( ord_less_eq_nat @ SV118 @ one_one_nat )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV238 )
| ~ ( ord_less_eq_nat @ SV238 @ one_one_nat )
| ( ord_less_eq_nat @ ( times_times_nat @ SV118 @ SV238 ) @ one_one_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1116]) ).
thf(1248,plain,
! [SV365: nat,SV321: nat,SV239: nat > nat,SV119: nat] :
( ( ~ ( ord_less_eq_nat @ SV119 @ ( SV239 @ SV321 ) )
| ~ ( ord_less_eq_nat @ SV321 @ SV365 )
| ~ ! [SY830: nat,SY831: nat] :
( ~ ( ord_less_eq_nat @ SY830 @ SY831 )
| ( ord_less_eq_nat @ ( SV239 @ SY830 ) @ ( SV239 @ SY831 ) ) )
| ( ord_less_eq_nat @ SV119 @ ( SV239 @ SV365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1249,plain,
! [SV240: nat,SV120: nat] :
( ( ( ( times_times_nat @ SV120 @ SV240 )
= zero_zero_nat )
= $false )
| ( ( ( SV120 = zero_zero_nat )
| ( SV240 = zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1118]) ).
thf(1250,plain,
! [SV322: nat,SV241: nat,SV121: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV121 @ SV241 ) )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV121 @ SV322 ) @ ( times_times_nat @ SV241 @ SV322 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1119]) ).
thf(1251,plain,
! [SV122: nat] :
( ( ( SV122 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV122 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1120]) ).
thf(1252,plain,
! [SV242: nat,SV123: nat] :
( ( ( ord_less_eq_nat @ SV123 @ one_one_nat )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV242 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV242 @ SV123 ) @ SV242 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1121]) ).
thf(1253,plain,
! [SV366: nat,SV243: nat] :
( ( ( SV243 = SV366 )
= ( ~ ( ~ ( ord_less_eq_nat @ SV243 @ SV366 )
| ~ ( ord_less_eq_nat @ SV366 @ SV243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1254,plain,
! [SV324: nat,SV244: nat,SV125: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV125 @ SV244 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV244 @ SV324 )
| ( ord_less_eq_nat @ SV125 @ SV324 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1124]) ).
thf(1255,plain,
! [SV245: nat,SV126: nat] :
( ( ( ord_less_eq_nat @ SV126 @ SV245 )
= $false )
| ( ( ~ ( ( SV126 != SV245 ) )
| ( ord_less_nat @ SV126 @ SV245 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1125]) ).
thf(1256,plain,
! [SV367: nat,SV325: nat,SV246: nat > set_nat,SV127: set_nat] :
( ( ~ ( ord_less_eq_set_nat @ SV127 @ ( SV246 @ SV325 ) )
| ~ ( ord_less_eq_nat @ SV325 @ SV367 )
| ~ ! [SY838: nat,SY839: nat] :
( ~ ( ord_less_eq_nat @ SY838 @ SY839 )
| ( ord_less_eq_set_nat @ ( SV246 @ SY838 ) @ ( SV246 @ SY839 ) ) )
| ( ord_less_eq_set_nat @ SV127 @ ( SV246 @ SV367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1257,plain,
! [SV368: nat,SV326: nat,SV247: nat,SV128: nat] :
( ( ~ ( ord_less_eq_nat @ SV128 @ SV247 )
| ~ ( ord_less_eq_nat @ SV326 @ SV368 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV247 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV326 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV128 @ SV326 ) @ ( times_times_nat @ SV247 @ SV368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1258,plain,
! [SV129: nat] :
( ( ( SV129 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV129 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1128]) ).
thf(1259,plain,
! [SV327: nat,SV248: nat,SV130: nat] :
( ( ( ~ ( ( SV130 != zero_zero_nat ) ) )
= $true )
| ( ( ( ( times_times_nat @ SV130 @ SV248 )
= ( times_times_nat @ SV130 @ SV327 ) )
= ( SV248 = SV327 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1129]) ).
thf(1260,plain,
! [SV328: nat,SV249: nat,SV131: nat] :
( ( ~ ( ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV249 )
| ( ord_less_eq_nat @ SV131 @ SV328 ) )
| ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV249 )
| ( ord_less_eq_nat @ SV131 @ SV328 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1130]) ).
thf(1261,plain,
! [SV328: nat,SV249: nat,SV131: nat] :
( ( ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) )
= ( ~ ( ord_less_nat @ zero_zero_nat @ SV249 )
| ( ord_less_eq_nat @ SV131 @ SV328 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1130]) ).
thf(1262,plain,
! [SV369: nat,SV329: nat > nat,SV250: nat,SV132: nat] :
( ( ~ ( ord_less_eq_nat @ SV132 @ SV250 )
| ( ( SV329 @ SV250 )
!= SV369 )
| ~ ! [SY942: nat,SY943: nat] :
( ~ ( ord_less_eq_nat @ SY942 @ SY943 )
| ( ord_less_eq_nat @ ( SV329 @ SY942 ) @ ( SV329 @ SY943 ) ) )
| ( ord_less_eq_nat @ ( SV329 @ SV132 ) @ SV369 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1263,plain,
! [SV330: nat,SV251: nat,SV133: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV133 @ SV251 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV251 @ SV330 )
| ( ord_less_eq_nat @ SV133 @ SV330 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1132]) ).
thf(1264,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV134 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV331 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV331 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV134 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1133]) ).
thf(1265,plain,
! [SV332: nat,SV253: nat,SV135: nat] :
( ( ~ ( ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 )
| ~ ( ord_less_nat @ SV253 @ SV332 ) ) )
| ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 )
| ~ ( ord_less_nat @ SV253 @ SV332 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1134]) ).
thf(1266,plain,
! [SV332: nat,SV253: nat,SV135: nat] :
( ( ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
= ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 )
| ~ ( ord_less_nat @ SV253 @ SV332 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1134]) ).
thf(1267,plain,
! [SV254: nat,SV136: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV136 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV254 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV136 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV254 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1135]) ).
thf(1268,plain,
! [SV255: nat,SV137: nat] :
( ( ( ord_less_eq_nat @ SV137 @ SV255 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV255 @ SV137 )
| ( SV137 = SV255 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1137]) ).
thf(1269,plain,
! [SV333: nat,SV256: nat,SV138: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV138 @ SV256 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV333 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV333 @ SV138 ) @ ( times_times_nat @ SV333 @ SV256 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1138]) ).
thf(1270,plain,
! [SV257: nat,SV139: nat] :
( ( ( ord_less_nat @ SV139 @ SV257 )
= $false )
| ( ( ord_less_eq_nat @ SV139 @ SV257 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1139]) ).
thf(1271,plain,
! [SV258: nat,SV140: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV140 )
| ~ ( ord_less_eq_nat @ SV258 @ zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ SV140 @ zero_zero_nat )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV258 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV140 @ SV258 ) @ zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1140]) ).
thf(1272,plain,
! [SV370: nat,SV259: nat] :
( ( ( ord_less_nat @ SV259 @ SV370 )
= ( ~ ( ~ ( ord_less_eq_nat @ SV259 @ SV370 )
| ~ ( ( SV259 != SV370 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1273,plain,
! [SV335: nat > nat,SV260: nat > nat,SV142: set_nat] :
( ( ( ~ ! [SY944: nat] :
( ~ ( member_nat @ SY944 @ SV142 )
| ( ord_less_eq_nat @ ( SV260 @ SY944 ) @ ( SV335 @ SY944 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( groups1842438620at_nat @ SV260 @ SV142 ) @ ( groups1842438620at_nat @ SV335 @ SV142 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1143]) ).
thf(1274,plain,
! [SV261: nat,SV143: nat] :
( ( ( ord_less_nat @ SV143 @ SV261 )
= $false )
| ( ( ord_less_eq_nat @ SV143 @ SV261 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1144]) ).
thf(1275,plain,
! [SV262: nat,SV144: nat] :
( ( ( ord_less_nat @ SV144 @ SV262 )
= $false )
| ( ( SV262 != zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1276,plain,
! [SV263: nat,SV145: nat] :
( ( ( ~ ( ( one_one_nat
= ( times_times_nat @ SV145 @ SV263 ) )
| ~ ( ( SV145 != one_one_nat )
| ( SV263 != one_one_nat ) ) ) )
= $true )
| ( ( ~ ( ( one_one_nat
!= ( times_times_nat @ SV145 @ SV263 ) )
| ~ ~ ( ( SV145 != one_one_nat )
| ( SV263 != one_one_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1146]) ).
thf(1277,plain,
! [SV336: nat,SV264: nat,SV146: nat] :
( ( ( ~ ( ( SV146 != zero_zero_nat ) ) )
= $true )
| ( ( ( ( times_times_nat @ SV264 @ SV146 )
= ( times_times_nat @ SV336 @ SV146 ) )
= ( SV264 = SV336 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1148]) ).
thf(1278,plain,
! [SV147: nat] :
( ( ( ( SV147 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV147 ) )
= $false )
| ( ( ~ ( ~ ( ( SV147 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV147 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1279,plain,
! [SV265: nat,SV148: nat > nat] :
( ( ( ! [SY856: nat] :
( ~ ( ( ( SV148 @ SY856 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY856 )
| ~ ( ord_less_eq_nat @ SY856 @ SV265 ) ) ) )
= $false )
| ( ( ( ( groups1842438620at_nat
@ ^ [SY685: nat] : ( times_times_nat @ ( SV148 @ SY685 ) @ SY685 )
@ ( set_ord_atMost_nat @ SV265 ) )
!= SV265 )
| ( number1551313001itions @ SV148 @ SV265 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1150]) ).
thf(1280,plain,
! [SV266: nat,SV149: nat] :
( ( ( ~ ( ( ( times_times_nat @ SV149 @ SV266 )
= one_one_nat )
| ~ ( ( SV149 != one_one_nat )
| ( SV266 != one_one_nat ) ) ) )
= $true )
| ( ( ~ ( ( ( times_times_nat @ SV149 @ SV266 )
!= one_one_nat )
| ~ ~ ( ( SV149 != one_one_nat )
| ( SV266 != one_one_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1151]) ).
thf(1281,plain,
! [SV150: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ SV150 )
| ( SV150 != zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV150 )
| ~ ( ( SV150 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1153]) ).
thf(1282,plain,
! [SV371: nat,SV337: set_nat > nat,SV267: set_nat,SV151: set_nat] :
( ( ~ ( ord_less_eq_set_nat @ SV151 @ SV267 )
| ( ( SV337 @ SV267 )
!= SV371 )
| ~ ! [SY946: set_nat,SY947: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY946 @ SY947 )
| ( ord_less_eq_nat @ ( SV337 @ SY946 ) @ ( SV337 @ SY947 ) ) )
| ( ord_less_eq_nat @ ( SV337 @ SV151 ) @ SV371 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1283,plain,
! [SV338: nat,SV268: nat,SV152: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV152 @ SV268 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV338 @ SV152 )
| ( ord_less_nat @ SV338 @ SV268 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1155]) ).
thf(1284,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ~ ( ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV153 )
| ( ord_less_eq_nat @ SV269 @ SV339 ) )
| ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV153 )
| ( ord_less_eq_nat @ SV269 @ SV339 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1156]) ).
thf(1285,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) )
= ( ~ ( ord_less_nat @ zero_zero_nat @ SV153 )
| ( ord_less_eq_nat @ SV269 @ SV339 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1156]) ).
thf(1286,plain,
! [SV270: nat,SV154: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV154 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV270 @ zero_zero_nat )
| ( ord_less_eq_nat @ ( times_times_nat @ SV270 @ SV154 ) @ zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1157]) ).
thf(1287,plain,
! [SV340: nat,SV271: nat,SV155: nat] :
( ( ( ~ ( ord_less_nat @ SV155 @ SV271 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV271 @ SV340 )
| ( ord_less_nat @ SV155 @ SV340 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1158]) ).
thf(1288,plain,
! [SV156: nat,SV2: nat] :
( ( ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ SV2 ) @ ( set_ord_atMost_nat @ SV156 ) )
| ( ord_less_eq_nat @ SV2 @ SV156 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ SV2 ) @ ( set_ord_atMost_nat @ SV156 ) )
| ~ ( ord_less_eq_nat @ SV2 @ SV156 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1159]) ).
thf(1289,plain,
! [SV157: nat,SV3: nat] :
( ( ( ( member_nat @ SV3 @ ( set_ord_atMost_nat @ SV157 ) )
| ( ord_less_eq_nat @ SV3 @ SV157 ) )
= $false )
| ( ( ~ ( ~ ( member_nat @ SV3 @ ( set_ord_atMost_nat @ SV157 ) )
| ~ ( ord_less_eq_nat @ SV3 @ SV157 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1160]) ).
thf(1290,plain,
! [SV158: nat,SV4: nat] :
( ( ( ( ( set_ord_atMost_nat @ SV4 )
= ( set_ord_atMost_nat @ SV158 ) )
| ( SV4 = SV158 ) )
= $false )
| ( ( ~ ( ( ( set_ord_atMost_nat @ SV4 )
!= ( set_ord_atMost_nat @ SV158 ) )
| ( SV4 != SV158 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1161]) ).
thf(1291,plain,
! [SV272: nat,SV159: nat,SV5: nat] :
( ( ( ~ ( ( ( times_times_nat @ SV5 @ SV159 )
= ( times_times_nat @ SV272 @ SV159 ) )
| ( SV159 = zero_zero_nat )
| ( SV5 = SV272 ) ) )
= $true )
| ( ( ~ ( ( ( times_times_nat @ SV5 @ SV159 )
!= ( times_times_nat @ SV272 @ SV159 ) )
| ~ ( ( SV159 = zero_zero_nat )
| ( SV5 = SV272 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1162]) ).
thf(1292,plain,
! [SV273: nat,SV160: nat,SV6: nat] :
( ( ( ~ ( ( ( times_times_nat @ SV6 @ SV160 )
= ( times_times_nat @ SV6 @ SV273 ) )
| ( SV6 = zero_zero_nat )
| ( SV160 = SV273 ) ) )
= $true )
| ( ( ~ ( ( ( times_times_nat @ SV6 @ SV160 )
!= ( times_times_nat @ SV6 @ SV273 ) )
| ~ ( ( SV6 = zero_zero_nat )
| ( SV160 = SV273 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1164]) ).
thf(1293,plain,
! [SV161: nat,SV7: nat] :
( ( ( ( ( times_times_nat @ SV7 @ SV161 )
= zero_zero_nat )
| ( SV7 = zero_zero_nat )
| ( SV161 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV7 @ SV161 )
!= zero_zero_nat )
| ~ ( ( SV7 = zero_zero_nat )
| ( SV161 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1166]) ).
thf(1294,plain,
! [SV274: nat,SV162: nat,SV12: nat] :
( ( ( ~ ( ( ( times_times_nat @ SV12 @ SV162 )
= ( times_times_nat @ SV274 @ SV162 ) )
| ( SV12 = SV274 )
| ( SV162 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( ( times_times_nat @ SV12 @ SV162 )
!= ( times_times_nat @ SV274 @ SV162 ) )
| ~ ( ( SV12 = SV274 )
| ( SV162 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1167]) ).
thf(1295,plain,
! [SV275: nat,SV163: nat,SV13: nat] :
( ( ( ~ ( ( ( times_times_nat @ SV13 @ SV163 )
= ( times_times_nat @ SV13 @ SV275 ) )
| ( SV163 = SV275 )
| ( SV13 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( ( times_times_nat @ SV13 @ SV163 )
!= ( times_times_nat @ SV13 @ SV275 ) )
| ~ ( ( SV163 = SV275 )
| ( SV13 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1169]) ).
thf(1296,plain,
! [SV164: nat,SV15: nat] :
( ( ( ( ( times_times_nat @ SV15 @ SV164 )
= zero_zero_nat )
| ( SV15 = zero_zero_nat )
| ( SV164 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV15 @ SV164 )
!= zero_zero_nat )
| ~ ( ( SV15 = zero_zero_nat )
| ( SV164 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1171]) ).
thf(1297,plain,
! [SV19: nat] :
( ( ( ord_less_eq_nat @ SV19 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV19 @ zero_zero_nat )
| ( SV19 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1172]) ).
thf(1298,plain,
! [SV19: nat] :
( ( ( SV19 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV19 @ zero_zero_nat )
| ( SV19 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1172]) ).
thf(1299,plain,
! [SV20: nat] :
( ( ( ord_less_eq_nat @ SV20 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV20 @ zero_zero_nat )
| ( SV20 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1173]) ).
thf(1300,plain,
! [SV20: nat] :
( ( ( SV20 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV20 @ zero_zero_nat )
| ( SV20 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1173]) ).
thf(1301,plain,
! [SV35: nat] :
( ( ( ord_less_eq_nat @ SV35 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV35 @ zero_zero_nat )
| ( SV35 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1175]) ).
thf(1302,plain,
! [SV35: nat] :
( ( ( SV35 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV35 @ zero_zero_nat )
| ( SV35 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1175]) ).
thf(1303,plain,
! [SV280: nat,SV173: nat,SV37: nat] :
( ( ( ~ ( ( ( times_times_nat @ SV37 @ SV173 )
= ( times_times_nat @ SV37 @ SV280 ) )
| ( SV37 = zero_zero_nat )
| ( SV173 = SV280 ) ) )
= $true )
| ( ( ~ ( ( ( times_times_nat @ SV37 @ SV173 )
!= ( times_times_nat @ SV37 @ SV280 ) )
| ~ ( ( SV37 = zero_zero_nat )
| ( SV173 = SV280 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1176]) ).
thf(1304,plain,
! [SV42: nat] :
( ( ( zero_zero_nat = SV42 )
= $false )
| ( ( ~ ( ( zero_zero_nat != SV42 )
| ( SV42 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1178]) ).
thf(1305,plain,
! [SV42: nat] :
( ( ( SV42 = zero_zero_nat )
= $false )
| ( ( ~ ( ( zero_zero_nat != SV42 )
| ( SV42 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1178]) ).
thf(1306,plain,
! [SV47: nat] :
( ( ( one_one_nat = SV47 )
= $false )
| ( ( ~ ( ( one_one_nat != SV47 )
| ( SV47 != one_one_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1180]) ).
thf(1307,plain,
! [SV47: nat] :
( ( ( SV47 = one_one_nat )
= $false )
| ( ( ~ ( ( one_one_nat != SV47 )
| ( SV47 != one_one_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1180]) ).
thf(1308,plain,
! [SV50: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV50 ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV50 )
| ( SV50 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1181]) ).
thf(1309,plain,
! [SV50: nat] :
( ( ( SV50 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV50 )
| ( SV50 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1181]) ).
thf(1310,plain,
! [SV51: nat] :
( ( ( ord_less_nat @ SV51 @ one_one_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV51 @ one_one_nat )
| ( SV51 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1182]) ).
thf(1311,plain,
! [SV51: nat] :
( ( ( SV51 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV51 @ one_one_nat )
| ( SV51 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1182]) ).
thf(1312,plain,
! [SV343: nat,SV179: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV179 @ SV343 )
| ( ord_less_nat @ SV179 @ SV343 )
| ( SV179 = SV343 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV179 @ SV343 )
| ~ ( ( ord_less_nat @ SV179 @ SV343 )
| ( SV179 = SV343 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1183]) ).
thf(1313,plain,
! [SV343: nat,SV179: nat] :
( ( ( ord_less_eq_nat @ SV179 @ SV343 )
= ( ( ord_less_nat @ SV179 @ SV343 )
| ( SV179 = SV343 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1183]) ).
thf(1314,plain,
! [SV54: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV54 ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV54 )
| ( SV54 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1184]) ).
thf(1315,plain,
! [SV54: nat] :
( ( ( SV54 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV54 )
| ( SV54 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1184]) ).
thf(1316,plain,
! [SV344: nat,SV180: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV180 @ SV344 )
| ( ord_less_nat @ SV180 @ SV344 )
| ( SV344 = SV180 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV180 @ SV344 )
| ~ ( ( ord_less_nat @ SV180 @ SV344 )
| ( SV344 = SV180 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1185]) ).
thf(1317,plain,
! [SV344: nat,SV180: nat] :
( ( ( ord_less_eq_nat @ SV180 @ SV344 )
= ( ( ord_less_nat @ SV180 @ SV344 )
| ( SV344 = SV180 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1185]) ).
thf(1318,plain,
! [SV345: nat,SV181: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV181 @ SV345 )
| ( ord_less_nat @ SV181 @ SV345 )
| ( SV181 = SV345 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV181 @ SV345 )
| ~ ( ( ord_less_nat @ SV181 @ SV345 )
| ( SV181 = SV345 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1186]) ).
thf(1319,plain,
! [SV345: nat,SV181: nat] :
( ( ( ord_less_eq_nat @ SV181 @ SV345 )
= ( ( ord_less_nat @ SV181 @ SV345 )
| ( SV181 = SV345 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1186]) ).
thf(1320,plain,
! [SV372: nat > nat,SV346: set_nat,SV288: nat > nat,SV182: nat > nat,SV60: set_nat] :
( ( ! [SY993: nat > nat] :
( ~ ! [SY876: nat] :
( ~ ( member_nat @ SY876 @ SV60 )
| ( ( SV182 @ ( SV288 @ SY876 ) )
= SY876 ) )
| ~ ! [SY953: nat] :
( ~ ( member_nat @ SY953 @ SV60 )
| ( member_nat @ ( SV288 @ SY953 ) @ SV346 ) )
| ~ ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) )
| ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY998: nat] :
( ~ ( member_nat @ SY998 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY998 ) )
= ( SY993 @ SY998 ) ) )
| ( ( groups1842438620at_nat @ SY993 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1321,plain,
! [SV61: nat,SV183: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV183 @ SV61 ) )
= $true )
| ( ( SV61 = SV183 )
= $true )
| ( ( ord_less_eq_nat @ SV61 @ SV183 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1188]) ).
thf(1322,plain,
! [SV184: nat,SV62: nat] :
( ( ( SV62 = zero_zero_nat )
= $true )
| ( ( ~ ( ( SV184 != zero_zero_nat ) )
| ( ( times_times_nat @ SV62 @ SV184 )
!= zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1189]) ).
thf(1323,plain,
! [SV289: nat,SV185: nat,SV63: nat] :
( ( ( ord_less_eq_nat @ SV63 @ SV185 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV289 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV289 @ SV63 ) @ ( times_times_nat @ SV289 @ SV185 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1190]) ).
thf(1324,plain,
! [SV347: nat,SV186: nat] :
( ( ~ ( ( SV186 = SV347 )
| ~ ( ~ ( ord_less_eq_nat @ SV186 @ SV347 )
| ~ ( ord_less_eq_nat @ SV347 @ SV186 ) ) )
| ~ ( ( SV186 != SV347 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV186 @ SV347 )
| ~ ( ord_less_eq_nat @ SV347 @ SV186 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1191]) ).
thf(1325,plain,
! [SV347: nat,SV186: nat] :
( ( ( SV186 = SV347 )
= ( ~ ( ~ ( ord_less_eq_nat @ SV186 @ SV347 )
| ~ ( ord_less_eq_nat @ SV347 @ SV186 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1191]) ).
thf(1326,plain,
! [SV65: set_nat,SV187: nat > nat] :
( ( ( ~ ( member_nat @ ( sK1_SY736 @ SV187 @ SV65 ) @ SV65 )
| ( ( SV187 @ ( sK1_SY736 @ SV187 @ SV65 ) )
= zero_zero_nat ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV187 @ SV65 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1192]) ).
thf(1327,plain,
! [SV188: nat,SV66: nat] :
( ( ( ord_less_eq_nat @ SV66 @ SV188 )
= $true )
| ( ( ord_less_eq_nat @ SV188 @ SV66 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1193]) ).
thf(1328,plain,
! [SV291: nat,SV189: nat,SV67: nat] :
( ( ( ord_less_eq_nat @ SV67 @ SV189 )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV291 @ SV67 ) @ ( times_times_nat @ SV291 @ SV189 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1194]) ).
thf(1329,plain,
! [SV68: nat,SV190: nat] :
( ( ( SV190 = one_one_nat )
= $true )
| ( ( SV68 = zero_zero_nat )
= $true )
| ( ( SV68
= ( times_times_nat @ SV68 @ SV190 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1195]) ).
thf(1330,plain,
! [SV348: nat,SV292: set_nat > nat,SV191: set_nat,SV69: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ SV69 @ SV191 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ ( SV292 @ SV191 ) @ SV348 )
| ~ ! [SY882: set_nat,SY883: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY882 @ SY883 )
| ( ord_less_eq_nat @ ( SV292 @ SY882 ) @ ( SV292 @ SY883 ) ) )
| ( ord_less_eq_nat @ ( SV292 @ SV69 ) @ SV348 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1196]) ).
thf(1331,plain,
! [SV293: nat,SV192: nat,SV70: nat > $o] :
( ( ( SV70 @ SV192 )
= $false )
| ( ( ~ ! [SY884: nat] :
( ~ ( SV70 @ SY884 )
| ( ord_less_eq_nat @ SY884 @ SV293 ) )
| ~ ! [SY505: nat] :
( ~ ( SV70 @ SY505 )
| ~ ! [SY506: nat] :
( ~ ( SV70 @ SY506 )
| ( ord_less_eq_nat @ SY506 @ SY505 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1197]) ).
thf(1332,plain,
! [SV349: nat,SV294: nat,SV193: nat,SV71: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV71 @ SV193 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV294 @ SV349 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV71 @ SV294 ) @ ( times_times_nat @ SV193 @ SV349 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1198]) ).
thf(1333,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ~ ( ( number1551313001itions @ SV194 @ SV350 )
| ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) )
| ~ ( ~ ( number1551313001itions @ SV194 @ SV350 )
| ~ ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1199]) ).
thf(1334,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( number1551313001itions @ SV194 @ SV350 )
= ( ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1199]) ).
thf(1335,plain,
! [SV73: nat,SV195: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV195 ) )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV73 @ SV195 ) @ zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV73 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1200]) ).
thf(1336,plain,
! [SV351: set_nat,SV296: nat > set_nat,SV196: nat,SV74: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV74 @ SV196 ) )
= $true )
| ( ( ( ( SV296 @ SV196 )
!= SV351 )
| ~ ! [SY891: nat,SY892: nat] :
( ~ ( ord_less_eq_nat @ SY891 @ SY892 )
| ( ord_less_eq_set_nat @ ( SV296 @ SY891 ) @ ( SV296 @ SY892 ) ) )
| ( ord_less_eq_set_nat @ ( SV296 @ SV74 ) @ SV351 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1201]) ).
thf(1337,plain,
! [SV297: nat,SV197: nat,SV75: nat] :
( ( ( ord_less_eq_nat @ SV75 @ SV197 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV197 @ SV297 )
| ( ord_less_eq_nat @ SV75 @ SV297 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1338,plain,
! [SV298: nat,SV198: nat,SV76: nat > nat > $o] :
( ( ( ! [SY523: nat,SY524: nat] :
( ~ ( ord_less_eq_nat @ SY523 @ SY524 )
| ( SV76 @ SY523 @ SY524 ) ) )
= $false )
| ( ( ~ ! [SY525: nat,SY526: nat] :
( ~ ( SV76 @ SY526 @ SY525 )
| ( SV76 @ SY525 @ SY526 ) )
| ( SV76 @ SV198 @ SV298 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1203]) ).
thf(1339,plain,
! [SV299: nat,SV199: nat,SV77: nat] :
( ( ( SV77 = SV199 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV199 @ SV299 )
| ( ord_less_eq_nat @ SV77 @ SV299 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1204]) ).
thf(1340,plain,
! [SV300: nat,SV201: nat,SV79: nat] :
( ( ( ord_less_eq_nat @ SV79 @ SV201 )
= $false )
| ( ( ~ ( ord_less_nat @ SV201 @ SV300 )
| ( ord_less_nat @ SV79 @ SV300 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1341,plain,
! [SV202: nat,SV80: nat] :
( ( ( ( times_times_nat @ SV80 @ SV202 )
= zero_zero_nat )
= $true )
| ( ( ~ ( ~ ( ( SV80 != zero_zero_nat ) )
| ~ ( ( SV202 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1207]) ).
thf(1342,plain,
! [SV301: nat,SV203: nat,SV81: nat] :
( ( ( ord_less_eq_nat @ SV81 @ SV203 )
= $false )
| ( ( ( SV203 != SV301 )
| ( ord_less_eq_nat @ SV81 @ SV301 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1208]) ).
thf(1343,plain,
! [SV302: nat,SV204: nat,SV82: nat] :
( ( ( ord_less_eq_nat @ SV82 @ SV204 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV302 @ SV82 )
| ( ord_less_eq_nat @ SV302 @ SV204 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1209]) ).
thf(1344,plain,
! [SV352: nat,SV303: nat,SV205: nat,SV83: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV83 @ SV205 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV303 @ SV352 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV83 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV303 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV83 @ SV303 ) @ ( times_times_nat @ SV205 @ SV352 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1210]) ).
thf(1345,plain,
! [SV84: nat,SV206: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV206 @ SV84 )
| ( SV206 = SV84 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV206 @ SV84 )
| ( SV206 != SV84 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV84 @ SV206 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1211]) ).
thf(1346,plain,
! [SV84: nat,SV206: nat] :
( ( ( ( ord_less_eq_nat @ SV206 @ SV84 )
= ( SV206 = SV84 ) )
= $true )
| ( ( ord_less_eq_nat @ SV84 @ SV206 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1211]) ).
thf(1347,plain,
! [SV373: nat > nat,SV353: nat > nat,SV304: nat > nat,SV207: set_nat,SV85: set_nat] :
( ( ~ ! [SY900: nat] :
( ~ ( member_nat @ SY900 @ SV85 )
| ~ ! [SY901: nat] :
~ ~ ( ~ ~ ( ~ ( member_nat @ SY901 @ SV207 )
| ( ( SV304 @ SY901 )
!= SY900 ) )
| ~ ! [SY902: nat] :
( ~ ~ ( ~ ( member_nat @ SY902 @ SV207 )
| ( ( SV304 @ SY902 )
!= SY900 ) )
| ( SY902 = SY901 ) ) ) )
| ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) )
| ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1348,plain,
! [SV354: nat,SV305: nat,SV208: nat > set_nat,SV86: set_nat] :
( ( ( SV86
!= ( SV208 @ SV305 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV305 @ SV354 )
| ~ ! [SY776: nat,SY777: nat] :
( ~ ( ord_less_eq_nat @ SY776 @ SY777 )
| ( ord_less_eq_set_nat @ ( SV208 @ SY776 ) @ ( SV208 @ SY777 ) ) )
| ( ord_less_eq_set_nat @ SV86 @ ( SV208 @ SV354 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1213]) ).
thf(1349,plain,
! [SV355: set_nat,SV306: set_nat,SV209: set_nat > nat,SV87: nat] :
( ( ( SV87
!= ( SV209 @ SV306 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_nat @ SV306 @ SV355 )
| ~ ! [SY780: set_nat,SY781: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY780 @ SY781 )
| ( ord_less_eq_nat @ ( SV209 @ SY780 ) @ ( SV209 @ SY781 ) ) )
| ( ord_less_eq_nat @ SV87 @ ( SV209 @ SV355 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1214]) ).
thf(1350,plain,
! [SV88: nat] :
( ( ( SV88 != zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ( SV88 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV88 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1215]) ).
thf(1351,plain,
! [SV88: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV88 )
= $false )
| ( ( ~ ( ~ ( ( SV88 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV88 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1215]) ).
thf(1352,plain,
( ( ( ~ ( ~ ! [SX0: nat] :
( ~ ( ( ( p @ SX0 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SX0 )
| ~ ( ord_less_eq_nat @ SX0 @ zero_zero_nat ) ) )
| ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
!= zero_zero_nat ) ) )
= $true )
| ( ( p
= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1216]) ).
thf(1353,plain,
( ( ( ~ ~ ( ~ ! [SX0: nat] :
( ~ ( ( ( p @ SX0 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SX0 )
| ~ ( ord_less_eq_nat @ SX0 @ zero_zero_nat ) ) )
| ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
!= zero_zero_nat ) ) )
= $true )
| ( ( p
!= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1217]) ).
thf(1354,plain,
! [SV89: nat,SV210: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV210 ) )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ SV89 @ SV210 ) )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1218]) ).
thf(1355,plain,
! [SV91: nat,SV212: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV212 @ SV91 ) )
= $true )
| ( ( SV212 = SV91 )
= $true )
| ( ( ord_less_eq_nat @ SV91 @ SV212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1220]) ).
thf(1356,plain,
! [SV356: nat,SV213: nat] :
( ( ~ ( ( SV213 = SV356 )
| ~ ( ~ ( ord_less_eq_nat @ SV356 @ SV213 )
| ~ ( ord_less_eq_nat @ SV213 @ SV356 ) ) )
| ~ ( ( SV213 != SV356 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV356 @ SV213 )
| ~ ( ord_less_eq_nat @ SV213 @ SV356 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1221]) ).
thf(1357,plain,
! [SV356: nat,SV213: nat] :
( ( ( SV213 = SV356 )
= ( ~ ( ~ ( ord_less_eq_nat @ SV356 @ SV213 )
| ~ ( ord_less_eq_nat @ SV213 @ SV356 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1221]) ).
thf(1358,plain,
! [SV357: nat > nat,SV308: nat > nat,SV214: set_nat,SV93: set_nat] :
( ( ( SV93 != SV214 )
= $true )
| ( ( ~ ! [SY972: nat] :
( ~ ( member_nat @ SY972 @ SV214 )
| ( ( SV308 @ SY972 )
= ( SV357 @ SY972 ) ) )
| ( ( groups1842438620at_nat @ SV308 @ SV93 )
= ( groups1842438620at_nat @ SV357 @ SV214 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1222]) ).
thf(1359,plain,
! [SV94: nat,SV215: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV215 @ zero_zero_nat ) )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV94 @ SV215 ) @ zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1223]) ).
thf(1360,plain,
! [SV358: set_nat,SV309: set_nat,SV216: set_nat > nat,SV95: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV95 @ ( SV216 @ SV309 ) ) )
= $true )
| ( ( ~ ( ord_less_eq_set_nat @ SV309 @ SV358 )
| ~ ! [SY789: set_nat,SY790: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY789 @ SY790 )
| ( ord_less_eq_nat @ ( SV216 @ SY789 ) @ ( SV216 @ SY790 ) ) )
| ( ord_less_eq_nat @ SV95 @ ( SV216 @ SV358 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1224]) ).
thf(1361,plain,
! [SV96: set_nat,SV217: nat > nat] :
( ( ( ~ ( member_nat @ ( sK2_SY791 @ SV217 @ SV96 ) @ SV96 )
| ( ord_less_eq_nat @ ( SV217 @ ( sK2_SY791 @ SV217 @ SV96 ) ) @ zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ ( groups1842438620at_nat @ SV217 @ SV96 ) @ zero_zero_nat )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1225]) ).
thf(1362,plain,
! [SV310: nat,SV218: nat,SV97: nat > nat] :
( ( ( ! [SY578: nat,SY579: nat] :
( ~ ( ord_less_nat @ SY578 @ SY579 )
| ( ord_less_nat @ ( SV97 @ SY578 ) @ ( SV97 @ SY579 ) ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV218 @ SV310 )
| ( ord_less_eq_nat @ ( SV97 @ SV218 ) @ ( SV97 @ SV310 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1226]) ).
thf(1363,plain,
! [SV311: nat,SV219: nat,SV98: nat] :
( ( ( ~ ( ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV219 )
| ~ ( ord_less_nat @ SV98 @ SV311 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV219 )
| ~ ( ord_less_nat @ SV98 @ SV311 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1227]) ).
thf(1364,plain,
! [SV359: nat,SV312: nat,SV220: nat > nat,SV99: nat] :
( ( ( SV99
!= ( SV220 @ SV312 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV312 @ SV359 )
| ~ ! [SY798: nat,SY799: nat] :
( ~ ( ord_less_eq_nat @ SY798 @ SY799 )
| ( ord_less_eq_nat @ ( SV220 @ SY798 ) @ ( SV220 @ SY799 ) ) )
| ( ord_less_eq_nat @ SV99 @ ( SV220 @ SV359 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1229]) ).
thf(1365,plain,
! [SV313: nat,SV221: nat,SV100: nat > $o] :
( ( ( SV100 @ SV221 )
= $false )
| ( ( ~ ! [SY920: nat] :
( ~ ( SV100 @ SY920 )
| ( ord_less_eq_nat @ SY920 @ SV313 ) )
| ~ ! [SY590: nat] :
~ ~ ( ~ ( SV100 @ SY590 )
| ~ ! [SY591: nat] :
( ~ ( SV100 @ SY591 )
| ( ord_less_eq_nat @ SY591 @ SY590 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1230]) ).
thf(1366,plain,
! [SV360: nat,SV222: nat] :
( ( ~ ( ( ord_less_nat @ SV222 @ SV360 )
| ~ ( ~ ( ord_less_eq_nat @ SV222 @ SV360 )
| ~ ( ( SV360 != SV222 ) ) ) )
| ~ ( ~ ( ord_less_nat @ SV222 @ SV360 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV222 @ SV360 )
| ~ ( ( SV360 != SV222 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1231]) ).
thf(1367,plain,
! [SV360: nat,SV222: nat] :
( ( ( ord_less_nat @ SV222 @ SV360 )
= ( ~ ( ~ ( ord_less_eq_nat @ SV222 @ SV360 )
| ~ ( ( SV360 != SV222 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1231]) ).
thf(1368,plain,
! [SV223: nat,SV102: nat] :
( ( ( SV102 = SV223 )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV102 @ SV223 )
| ( ord_less_nat @ SV102 @ SV223 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1232]) ).
thf(1369,plain,
! [SV224: nat,SV103: nat > nat] :
( ( ( ~ ! [SY805: nat] :
( ~ ( ( ( SV103 @ SY805 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY805 )
| ~ ( ord_less_eq_nat @ SY805 @ SV224 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY596: nat] : ( times_times_nat @ ( SV103 @ SY596 ) @ SY596 )
@ ( set_ord_atMost_nat @ SV224 ) )
!= SV224 ) )
= $false )
| ( ( number1551313001itions @ SV103 @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1233]) ).
thf(1370,plain,
! [SV104: nat,SV225: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV225 @ SV104 ) )
= $true )
| ( ( SV104 = SV225 )
= $true )
| ( ( ord_less_eq_nat @ SV104 @ SV225 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1234]) ).
thf(1371,plain,
! [SV226: nat,SV105: nat] :
( ( ( ord_less_nat @ SV105 @ SV226 )
= $false )
| ( ( ord_less_eq_nat @ SV105 @ SV226 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1235]) ).
thf(1372,plain,
! [SV226: nat,SV105: nat] :
( ( ( SV105 = SV226 )
= $false )
| ( ( ord_less_eq_nat @ SV105 @ SV226 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1235]) ).
thf(1373,plain,
! [SV361: nat,SV315: nat > nat,SV227: nat,SV106: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV106 @ SV227 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ ( SV315 @ SV227 ) @ SV361 )
| ~ ! [SY924: nat,SY925: nat] :
( ~ ( ord_less_eq_nat @ SY924 @ SY925 )
| ( ord_less_eq_nat @ ( SV315 @ SY924 ) @ ( SV315 @ SY925 ) ) )
| ( ord_less_eq_nat @ ( SV315 @ SV106 ) @ SV361 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1236]) ).
thf(1374,plain,
! [SV362: nat,SV228: nat] :
( ( ~ ( ( ord_less_nat @ SV228 @ SV362 )
| ~ ( ~ ( ord_less_eq_nat @ SV228 @ SV362 )
| ~ ( ( SV228 != SV362 ) ) ) )
| ~ ( ~ ( ord_less_nat @ SV228 @ SV362 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV228 @ SV362 )
| ~ ( ( SV228 != SV362 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1237]) ).
thf(1375,plain,
! [SV362: nat,SV228: nat] :
( ( ( ord_less_nat @ SV228 @ SV362 )
= ( ~ ( ~ ( ord_less_eq_nat @ SV228 @ SV362 )
| ~ ( ( SV228 != SV362 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1237]) ).
thf(1376,plain,
! [SV317: nat,SV229: nat,SV109: nat] :
( ( ( ord_less_nat @ SV109 @ SV229 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV317 @ SV109 )
| ( ord_less_nat @ SV317 @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1238]) ).
thf(1377,plain,
! [SV230: nat,SV110: nat > $o] :
( ( ( ~ ! [SY608: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY608 )
| ~ ~ ( SV110 @ SY608 )
| ~ ! [SY609: nat] :
~ ~ ( ~ ( ord_less_nat @ SY609 @ SY608 )
| ~ ~ ( SV110 @ SY609 ) ) ) )
= $true )
| ( ( SV110 @ SV230 )
= $true )
| ( ( SV110 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1378,plain,
! [SV231: set_nat,SV111: nat > nat] :
( ( ( ( groups1842438620at_nat @ SV111 @ SV231 )
= zero_zero_nat )
= $true )
| ( ( ~ ! [SY815: nat] :
( ~ ( member_nat @ SY815 @ SV231 )
| ( ( SV111 @ SY815 )
= zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1240]) ).
thf(1379,plain,
! [SV112: set_nat,SV232: nat > nat] :
( ( ( ~ ( member_nat @ ( sK3_SY816 @ SV232 @ SV112 ) @ SV112 )
| ( ord_less_eq_nat @ zero_zero_nat @ ( SV232 @ ( sK3_SY816 @ SV232 @ SV112 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ ( groups1842438620at_nat @ SV232 @ SV112 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1241]) ).
thf(1380,plain,
! [SV114: nat,SV234: nat] :
( ( ( SV234 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ SV114 @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1243]) ).
thf(1381,plain,
! [SV318: nat,SV235: nat,SV115: nat] :
( ( ( ord_less_eq_nat @ SV115 @ SV235 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV318 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV115 @ SV318 ) @ ( times_times_nat @ SV235 @ SV318 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1244]) ).
thf(1382,plain,
! [SV374: nat > nat,SV363: nat > nat,SV319: set_nat,SV236: nat > nat,SV116: set_nat] :
( ( ! [SY1003: nat > nat] :
( ~ ! [SY981: nat] :
( ~ ( member_nat @ SY981 @ SV116 )
| ~ ( ~ ( member_nat @ ( SV236 @ SY981 ) @ SV319 )
| ( ( SV363 @ ( SV236 @ SY981 ) )
!= SY981 ) ) )
| ~ ! [SY1005: nat] :
( ~ ( member_nat @ SY1005 @ SV319 )
| ~ ( ~ ~ ( ~ ( member_nat @ ( SV363 @ SY1005 ) @ SV116 )
| ( ( SV236 @ ( SV363 @ SY1005 ) )
!= SY1005 ) )
| ( ( SV374 @ ( SV363 @ SY1005 ) )
!= ( SY1003 @ SY1005 ) ) ) )
| ( ( groups1842438620at_nat @ SY1003 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1383,plain,
! [SV364: set_nat,SV320: nat > set_nat,SV237: nat,SV117: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV117 @ SV237 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_nat @ ( SV320 @ SV237 ) @ SV364 )
| ~ ! [SY932: nat,SY933: nat] :
( ~ ( ord_less_eq_nat @ SY932 @ SY933 )
| ( ord_less_eq_set_nat @ ( SV320 @ SY932 ) @ ( SV320 @ SY933 ) ) )
| ( ord_less_eq_set_nat @ ( SV320 @ SV117 ) @ SV364 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1246]) ).
thf(1384,plain,
! [SV118: nat,SV238: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV238 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV238 @ one_one_nat )
| ( ord_less_eq_nat @ ( times_times_nat @ SV118 @ SV238 ) @ one_one_nat ) )
= $true )
| ( ( ord_less_eq_nat @ SV118 @ one_one_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1247]) ).
thf(1385,plain,
! [SV365: nat,SV321: nat,SV239: nat > nat,SV119: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV119 @ ( SV239 @ SV321 ) ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV321 @ SV365 )
| ~ ! [SY830: nat,SY831: nat] :
( ~ ( ord_less_eq_nat @ SY830 @ SY831 )
| ( ord_less_eq_nat @ ( SV239 @ SY830 ) @ ( SV239 @ SY831 ) ) )
| ( ord_less_eq_nat @ SV119 @ ( SV239 @ SV365 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1248]) ).
thf(1386,plain,
! [SV240: nat,SV120: nat] :
( ( ( SV120 = zero_zero_nat )
= $true )
| ( ( SV240 = zero_zero_nat )
= $true )
| ( ( ( times_times_nat @ SV120 @ SV240 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1249]) ).
thf(1387,plain,
! [SV322: nat,SV241: nat,SV121: nat] :
( ( ( ord_less_eq_nat @ SV121 @ SV241 )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV121 @ SV322 ) @ ( times_times_nat @ SV241 @ SV322 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1250]) ).
thf(1388,plain,
! [SV123: nat,SV242: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV242 ) )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV242 @ SV123 ) @ SV242 )
= $true )
| ( ( ord_less_eq_nat @ SV123 @ one_one_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1252]) ).
thf(1389,plain,
! [SV366: nat,SV243: nat] :
( ( ~ ( ( SV243 = SV366 )
| ~ ( ~ ( ord_less_eq_nat @ SV243 @ SV366 )
| ~ ( ord_less_eq_nat @ SV366 @ SV243 ) ) )
| ~ ( ( SV243 != SV366 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV243 @ SV366 )
| ~ ( ord_less_eq_nat @ SV366 @ SV243 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1253]) ).
thf(1390,plain,
! [SV366: nat,SV243: nat] :
( ( ( SV243 = SV366 )
= ( ~ ( ~ ( ord_less_eq_nat @ SV243 @ SV366 )
| ~ ( ord_less_eq_nat @ SV366 @ SV243 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1253]) ).
thf(1391,plain,
! [SV324: nat,SV244: nat,SV125: nat] :
( ( ( ord_less_eq_nat @ SV125 @ SV244 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV244 @ SV324 )
| ( ord_less_eq_nat @ SV125 @ SV324 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1254]) ).
thf(1392,plain,
! [SV245: nat,SV126: nat] :
( ( ( ~ ( ( SV126 != SV245 ) ) )
= $true )
| ( ( ord_less_nat @ SV126 @ SV245 )
= $true )
| ( ( ord_less_eq_nat @ SV126 @ SV245 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1255]) ).
thf(1393,plain,
! [SV367: nat,SV325: nat,SV246: nat > set_nat,SV127: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ SV127 @ ( SV246 @ SV325 ) ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV325 @ SV367 )
| ~ ! [SY838: nat,SY839: nat] :
( ~ ( ord_less_eq_nat @ SY838 @ SY839 )
| ( ord_less_eq_set_nat @ ( SV246 @ SY838 ) @ ( SV246 @ SY839 ) ) )
| ( ord_less_eq_set_nat @ SV127 @ ( SV246 @ SV367 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1256]) ).
thf(1394,plain,
! [SV368: nat,SV326: nat,SV247: nat,SV128: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV128 @ SV247 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV326 @ SV368 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV247 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV326 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV128 @ SV326 ) @ ( times_times_nat @ SV247 @ SV368 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1257]) ).
thf(1395,plain,
! [SV327: nat,SV248: nat,SV130: nat] :
( ( ( SV130 != zero_zero_nat )
= $false )
| ( ( ( ( times_times_nat @ SV130 @ SV248 )
= ( times_times_nat @ SV130 @ SV327 ) )
= ( SV248 = SV327 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1259]) ).
thf(1396,plain,
! [SV328: nat,SV249: nat,SV131: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV249 )
| ( ord_less_eq_nat @ SV131 @ SV328 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV249 )
| ( ord_less_eq_nat @ SV131 @ SV328 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1260]) ).
thf(1397,plain,
! [SV369: nat,SV329: nat > nat,SV250: nat,SV132: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV132 @ SV250 ) )
= $true )
| ( ( ( ( SV329 @ SV250 )
!= SV369 )
| ~ ! [SY942: nat,SY943: nat] :
( ~ ( ord_less_eq_nat @ SY942 @ SY943 )
| ( ord_less_eq_nat @ ( SV329 @ SY942 ) @ ( SV329 @ SY943 ) ) )
| ( ord_less_eq_nat @ ( SV329 @ SV132 ) @ SV369 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1262]) ).
thf(1398,plain,
! [SV330: nat,SV251: nat,SV133: nat] :
( ( ( ord_less_eq_nat @ SV133 @ SV251 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV251 @ SV330 )
| ( ord_less_eq_nat @ SV133 @ SV330 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1263]) ).
thf(1399,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV331 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV331 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV134 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1264]) ).
thf(1400,plain,
! [SV332: nat,SV253: nat,SV135: nat] :
( ( ( ~ ( ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 )
| ~ ( ord_less_nat @ SV253 @ SV332 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 )
| ~ ( ord_less_nat @ SV253 @ SV332 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1265]) ).
thf(1401,plain,
! [SV254: nat,SV136: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV136 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV254 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV136 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV254 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1267]) ).
thf(1402,plain,
! [SV137: nat,SV255: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV255 @ SV137 ) )
= $true )
| ( ( SV137 = SV255 )
= $true )
| ( ( ord_less_eq_nat @ SV137 @ SV255 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1268]) ).
thf(1403,plain,
! [SV333: nat,SV256: nat,SV138: nat] :
( ( ( ord_less_eq_nat @ SV138 @ SV256 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV333 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV333 @ SV138 ) @ ( times_times_nat @ SV333 @ SV256 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1404,plain,
! [SV258: nat,SV140: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV140 )
| ~ ( ord_less_eq_nat @ SV258 @ zero_zero_nat ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV140 @ SV258 ) @ zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1271]) ).
thf(1405,plain,
! [SV258: nat,SV140: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV140 @ zero_zero_nat )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV258 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV140 @ SV258 ) @ zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1271]) ).
thf(1406,plain,
! [SV370: nat,SV259: nat] :
( ( ~ ( ( ord_less_nat @ SV259 @ SV370 )
| ~ ( ~ ( ord_less_eq_nat @ SV259 @ SV370 )
| ~ ( ( SV259 != SV370 ) ) ) )
| ~ ( ~ ( ord_less_nat @ SV259 @ SV370 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV259 @ SV370 )
| ~ ( ( SV259 != SV370 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1272]) ).
thf(1407,plain,
! [SV370: nat,SV259: nat] :
( ( ( ord_less_nat @ SV259 @ SV370 )
= ( ~ ( ~ ( ord_less_eq_nat @ SV259 @ SV370 )
| ~ ( ( SV259 != SV370 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1272]) ).
thf(1408,plain,
! [SV335: nat > nat,SV260: nat > nat,SV142: set_nat] :
( ( ( ! [SY944: nat] :
( ~ ( member_nat @ SY944 @ SV142 )
| ( ord_less_eq_nat @ ( SV260 @ SY944 ) @ ( SV335 @ SY944 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( groups1842438620at_nat @ SV260 @ SV142 ) @ ( groups1842438620at_nat @ SV335 @ SV142 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1273]) ).
thf(1409,plain,
! [SV144: nat,SV262: nat] :
( ( ( SV262 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ SV144 @ SV262 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1275]) ).
thf(1410,plain,
! [SV263: nat,SV145: nat] :
( ( ( ( one_one_nat
= ( times_times_nat @ SV145 @ SV263 ) )
| ~ ( ( SV145 != one_one_nat )
| ( SV263 != one_one_nat ) ) )
= $false )
| ( ( ~ ( ( one_one_nat
!= ( times_times_nat @ SV145 @ SV263 ) )
| ~ ~ ( ( SV145 != one_one_nat )
| ( SV263 != one_one_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1276]) ).
thf(1411,plain,
! [SV336: nat,SV264: nat,SV146: nat] :
( ( ( SV146 != zero_zero_nat )
= $false )
| ( ( ( ( times_times_nat @ SV264 @ SV146 )
= ( times_times_nat @ SV336 @ SV146 ) )
= ( SV264 = SV336 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1277]) ).
thf(1412,plain,
! [SV147: nat] :
( ( ( SV147 != zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ( SV147 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV147 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1278]) ).
thf(1413,plain,
! [SV147: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV147 )
= $false )
| ( ( ~ ( ~ ( ( SV147 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV147 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1278]) ).
thf(1414,plain,
! [SV265: nat,SV148: nat > nat] :
( ( ( ~ ( ( ( SV148 @ ( sK4_SY856 @ SV265 @ SV148 ) )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ ( sK4_SY856 @ SV265 @ SV148 ) )
| ~ ( ord_less_eq_nat @ ( sK4_SY856 @ SV265 @ SV148 ) @ SV265 ) ) )
= $false )
| ( ( ( ( groups1842438620at_nat
@ ^ [SY685: nat] : ( times_times_nat @ ( SV148 @ SY685 ) @ SY685 )
@ ( set_ord_atMost_nat @ SV265 ) )
!= SV265 )
| ( number1551313001itions @ SV148 @ SV265 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1279]) ).
thf(1415,plain,
! [SV266: nat,SV149: nat] :
( ( ( ( ( times_times_nat @ SV149 @ SV266 )
= one_one_nat )
| ~ ( ( SV149 != one_one_nat )
| ( SV266 != one_one_nat ) ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV149 @ SV266 )
!= one_one_nat )
| ~ ~ ( ( SV149 != one_one_nat )
| ( SV266 != one_one_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1416,plain,
! [SV150: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV150 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV150 )
| ~ ( ( SV150 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1281]) ).
thf(1417,plain,
! [SV150: nat] :
( ( ( SV150 != zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV150 )
| ~ ( ( SV150 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1281]) ).
thf(1418,plain,
! [SV371: nat,SV337: set_nat > nat,SV267: set_nat,SV151: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ SV151 @ SV267 ) )
= $true )
| ( ( ( ( SV337 @ SV267 )
!= SV371 )
| ~ ! [SY946: set_nat,SY947: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY946 @ SY947 )
| ( ord_less_eq_nat @ ( SV337 @ SY946 ) @ ( SV337 @ SY947 ) ) )
| ( ord_less_eq_nat @ ( SV337 @ SV151 ) @ SV371 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1282]) ).
thf(1419,plain,
! [SV338: nat,SV268: nat,SV152: nat] :
( ( ( ord_less_eq_nat @ SV152 @ SV268 )
= $false )
| ( ( ~ ( ord_less_nat @ SV338 @ SV152 )
| ( ord_less_nat @ SV338 @ SV268 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1283]) ).
thf(1420,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV153 )
| ( ord_less_eq_nat @ SV269 @ SV339 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV153 )
| ( ord_less_eq_nat @ SV269 @ SV339 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1284]) ).
thf(1421,plain,
! [SV154: nat,SV270: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV270 @ zero_zero_nat ) )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV270 @ SV154 ) @ zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1286]) ).
thf(1422,plain,
! [SV340: nat,SV271: nat,SV155: nat] :
( ( ( ord_less_nat @ SV155 @ SV271 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV271 @ SV340 )
| ( ord_less_nat @ SV155 @ SV340 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1287]) ).
thf(1423,plain,
! [SV156: nat,SV2: nat] :
( ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ SV2 ) @ ( set_ord_atMost_nat @ SV156 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ SV2 ) @ ( set_ord_atMost_nat @ SV156 ) )
| ~ ( ord_less_eq_nat @ SV2 @ SV156 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1288]) ).
thf(1424,plain,
! [SV156: nat,SV2: nat] :
( ( ( ord_less_eq_nat @ SV2 @ SV156 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ SV2 ) @ ( set_ord_atMost_nat @ SV156 ) )
| ~ ( ord_less_eq_nat @ SV2 @ SV156 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1288]) ).
thf(1425,plain,
! [SV157: nat,SV3: nat] :
( ( ( member_nat @ SV3 @ ( set_ord_atMost_nat @ SV157 ) )
= $false )
| ( ( ~ ( ~ ( member_nat @ SV3 @ ( set_ord_atMost_nat @ SV157 ) )
| ~ ( ord_less_eq_nat @ SV3 @ SV157 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1289]) ).
thf(1426,plain,
! [SV157: nat,SV3: nat] :
( ( ( ord_less_eq_nat @ SV3 @ SV157 )
= $false )
| ( ( ~ ( ~ ( member_nat @ SV3 @ ( set_ord_atMost_nat @ SV157 ) )
| ~ ( ord_less_eq_nat @ SV3 @ SV157 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1289]) ).
thf(1427,plain,
! [SV158: nat,SV4: nat] :
( ( ( ( set_ord_atMost_nat @ SV4 )
= ( set_ord_atMost_nat @ SV158 ) )
= $false )
| ( ( ~ ( ( ( set_ord_atMost_nat @ SV4 )
!= ( set_ord_atMost_nat @ SV158 ) )
| ( SV4 != SV158 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1290]) ).
thf(1428,plain,
! [SV158: nat,SV4: nat] :
( ( ( SV4 = SV158 )
= $false )
| ( ( ~ ( ( ( set_ord_atMost_nat @ SV4 )
!= ( set_ord_atMost_nat @ SV158 ) )
| ( SV4 != SV158 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1290]) ).
thf(1429,plain,
! [SV272: nat,SV159: nat,SV5: nat] :
( ( ( ( ( times_times_nat @ SV5 @ SV159 )
= ( times_times_nat @ SV272 @ SV159 ) )
| ( SV159 = zero_zero_nat )
| ( SV5 = SV272 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV5 @ SV159 )
!= ( times_times_nat @ SV272 @ SV159 ) )
| ~ ( ( SV159 = zero_zero_nat )
| ( SV5 = SV272 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1291]) ).
thf(1430,plain,
! [SV273: nat,SV160: nat,SV6: nat] :
( ( ( ( ( times_times_nat @ SV6 @ SV160 )
= ( times_times_nat @ SV6 @ SV273 ) )
| ( SV6 = zero_zero_nat )
| ( SV160 = SV273 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV6 @ SV160 )
!= ( times_times_nat @ SV6 @ SV273 ) )
| ~ ( ( SV6 = zero_zero_nat )
| ( SV160 = SV273 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1292]) ).
thf(1431,plain,
! [SV161: nat,SV7: nat] :
( ( ( ( times_times_nat @ SV7 @ SV161 )
= zero_zero_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV7 @ SV161 )
!= zero_zero_nat )
| ~ ( ( SV7 = zero_zero_nat )
| ( SV161 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1293]) ).
thf(1432,plain,
! [SV161: nat,SV7: nat] :
( ( ( ( SV7 = zero_zero_nat )
| ( SV161 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV7 @ SV161 )
!= zero_zero_nat )
| ~ ( ( SV7 = zero_zero_nat )
| ( SV161 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1293]) ).
thf(1433,plain,
! [SV274: nat,SV162: nat,SV12: nat] :
( ( ( ( ( times_times_nat @ SV12 @ SV162 )
= ( times_times_nat @ SV274 @ SV162 ) )
| ( SV12 = SV274 )
| ( SV162 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV12 @ SV162 )
!= ( times_times_nat @ SV274 @ SV162 ) )
| ~ ( ( SV12 = SV274 )
| ( SV162 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1294]) ).
thf(1434,plain,
! [SV275: nat,SV163: nat,SV13: nat] :
( ( ( ( ( times_times_nat @ SV13 @ SV163 )
= ( times_times_nat @ SV13 @ SV275 ) )
| ( SV163 = SV275 )
| ( SV13 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV13 @ SV163 )
!= ( times_times_nat @ SV13 @ SV275 ) )
| ~ ( ( SV163 = SV275 )
| ( SV13 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1435,plain,
! [SV164: nat,SV15: nat] :
( ( ( ( times_times_nat @ SV15 @ SV164 )
= zero_zero_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV15 @ SV164 )
!= zero_zero_nat )
| ~ ( ( SV15 = zero_zero_nat )
| ( SV164 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1296]) ).
thf(1436,plain,
! [SV164: nat,SV15: nat] :
( ( ( ( SV15 = zero_zero_nat )
| ( SV164 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV15 @ SV164 )
!= zero_zero_nat )
| ~ ( ( SV15 = zero_zero_nat )
| ( SV164 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1296]) ).
thf(1437,plain,
! [SV19: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV19 @ zero_zero_nat )
| ( SV19 != zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV19 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1297]) ).
thf(1438,plain,
! [SV19: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV19 @ zero_zero_nat )
| ( SV19 != zero_zero_nat ) )
= $false )
| ( ( SV19 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1298]) ).
thf(1439,plain,
! [SV20: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV20 @ zero_zero_nat )
| ( SV20 != zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV20 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1299]) ).
thf(1440,plain,
! [SV20: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV20 @ zero_zero_nat )
| ( SV20 != zero_zero_nat ) )
= $false )
| ( ( SV20 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1300]) ).
thf(1441,plain,
! [SV35: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV35 @ zero_zero_nat )
| ( SV35 != zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV35 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1301]) ).
thf(1442,plain,
! [SV35: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV35 @ zero_zero_nat )
| ( SV35 != zero_zero_nat ) )
= $false )
| ( ( SV35 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1302]) ).
thf(1443,plain,
! [SV280: nat,SV173: nat,SV37: nat] :
( ( ( ( ( times_times_nat @ SV37 @ SV173 )
= ( times_times_nat @ SV37 @ SV280 ) )
| ( SV37 = zero_zero_nat )
| ( SV173 = SV280 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV37 @ SV173 )
!= ( times_times_nat @ SV37 @ SV280 ) )
| ~ ( ( SV37 = zero_zero_nat )
| ( SV173 = SV280 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1303]) ).
thf(1444,plain,
! [SV42: nat] :
( ( ( ( zero_zero_nat != SV42 )
| ( SV42 != zero_zero_nat ) )
= $false )
| ( ( zero_zero_nat = SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1304]) ).
thf(1445,plain,
! [SV42: nat] :
( ( ( ( zero_zero_nat != SV42 )
| ( SV42 != zero_zero_nat ) )
= $false )
| ( ( SV42 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1305]) ).
thf(1446,plain,
! [SV47: nat] :
( ( ( ( one_one_nat != SV47 )
| ( SV47 != one_one_nat ) )
= $false )
| ( ( one_one_nat = SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1306]) ).
thf(1447,plain,
! [SV47: nat] :
( ( ( ( one_one_nat != SV47 )
| ( SV47 != one_one_nat ) )
= $false )
| ( ( SV47 = one_one_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1307]) ).
thf(1448,plain,
! [SV50: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV50 )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV50 )
| ( SV50 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1308]) ).
thf(1449,plain,
! [SV50: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV50 )
| ( SV50 != zero_zero_nat ) )
= $false )
| ( ( SV50 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1309]) ).
thf(1450,plain,
! [SV51: nat] :
( ( ( ~ ( ord_less_nat @ SV51 @ one_one_nat )
| ( SV51 != zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ SV51 @ one_one_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1310]) ).
thf(1451,plain,
! [SV51: nat] :
( ( ( ~ ( ord_less_nat @ SV51 @ one_one_nat )
| ( SV51 != zero_zero_nat ) )
= $false )
| ( ( SV51 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1311]) ).
thf(1452,plain,
! [SV343: nat,SV179: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV179 @ SV343 )
| ( ord_less_nat @ SV179 @ SV343 )
| ( SV179 = SV343 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV179 @ SV343 )
| ~ ( ( ord_less_nat @ SV179 @ SV343 )
| ( SV179 = SV343 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1312]) ).
thf(1453,plain,
! [SV54: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV54 )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV54 )
| ( SV54 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1314]) ).
thf(1454,plain,
! [SV54: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV54 )
| ( SV54 != zero_zero_nat ) )
= $false )
| ( ( SV54 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1315]) ).
thf(1455,plain,
! [SV344: nat,SV180: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV180 @ SV344 )
| ( ord_less_nat @ SV180 @ SV344 )
| ( SV344 = SV180 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV180 @ SV344 )
| ~ ( ( ord_less_nat @ SV180 @ SV344 )
| ( SV344 = SV180 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1316]) ).
thf(1456,plain,
! [SV345: nat,SV181: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV181 @ SV345 )
| ( ord_less_nat @ SV181 @ SV345 )
| ( SV181 = SV345 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV181 @ SV345 )
| ~ ( ( ord_less_nat @ SV181 @ SV345 )
| ( SV181 = SV345 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1318]) ).
thf(1457,plain,
! [SV375: nat > nat,SV372: nat > nat,SV346: set_nat,SV288: nat > nat,SV182: nat > nat,SV60: set_nat] :
( ( ~ ! [SY876: nat] :
( ~ ( member_nat @ SY876 @ SV60 )
| ( ( SV182 @ ( SV288 @ SY876 ) )
= SY876 ) )
| ~ ! [SY953: nat] :
( ~ ( member_nat @ SY953 @ SV60 )
| ( member_nat @ ( SV288 @ SY953 ) @ SV346 ) )
| ~ ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) )
| ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1320]) ).
thf(1458,plain,
! [SV61: nat,SV183: nat] :
( ( ( ord_less_eq_nat @ SV183 @ SV61 )
= $false )
| ( ( SV61 = SV183 )
= $true )
| ( ( ord_less_eq_nat @ SV61 @ SV183 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1321]) ).
thf(1459,plain,
! [SV62: nat,SV184: nat] :
( ( ( ~ ( ( SV184 != zero_zero_nat ) ) )
= $true )
| ( ( ( times_times_nat @ SV62 @ SV184 )
!= zero_zero_nat )
= $true )
| ( ( SV62 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1322]) ).
thf(1460,plain,
! [SV185: nat,SV63: nat,SV289: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV289 ) )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV289 @ SV63 ) @ ( times_times_nat @ SV289 @ SV185 ) )
= $true )
| ( ( ord_less_eq_nat @ SV63 @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1323]) ).
thf(1461,plain,
! [SV347: nat,SV186: nat] :
( ( ( ~ ( ( SV186 = SV347 )
| ~ ( ~ ( ord_less_eq_nat @ SV186 @ SV347 )
| ~ ( ord_less_eq_nat @ SV347 @ SV186 ) ) ) )
= $true )
| ( ( ~ ( ( SV186 != SV347 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV186 @ SV347 )
| ~ ( ord_less_eq_nat @ SV347 @ SV186 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1324]) ).
thf(1462,plain,
! [SV65: set_nat,SV187: nat > nat] :
( ( ( ~ ( member_nat @ ( sK1_SY736 @ SV187 @ SV65 ) @ SV65 ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV187 @ SV65 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1326]) ).
thf(1463,plain,
! [SV65: set_nat,SV187: nat > nat] :
( ( ( ( SV187 @ ( sK1_SY736 @ SV187 @ SV65 ) )
= zero_zero_nat )
= $false )
| ( ( ( groups1842438620at_nat @ SV187 @ SV65 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1326]) ).
thf(1464,plain,
! [SV348: nat,SV292: set_nat > nat,SV191: set_nat,SV69: set_nat] :
( ( ( ord_less_eq_set_nat @ SV69 @ SV191 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ ( SV292 @ SV191 ) @ SV348 )
| ~ ! [SY882: set_nat,SY883: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY882 @ SY883 )
| ( ord_less_eq_nat @ ( SV292 @ SY882 ) @ ( SV292 @ SY883 ) ) )
| ( ord_less_eq_nat @ ( SV292 @ SV69 ) @ SV348 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1330]) ).
thf(1465,plain,
! [SV192: nat,SV293: nat,SV70: nat > $o] :
( ( ( ~ ! [SY884: nat] :
( ~ ( SV70 @ SY884 )
| ( ord_less_eq_nat @ SY884 @ SV293 ) ) )
= $true )
| ( ( ~ ! [SY505: nat] :
( ~ ( SV70 @ SY505 )
| ~ ! [SY506: nat] :
( ~ ( SV70 @ SY506 )
| ( ord_less_eq_nat @ SY506 @ SY505 ) ) ) )
= $true )
| ( ( SV70 @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1331]) ).
thf(1466,plain,
! [SV349: nat,SV294: nat,SV193: nat,SV71: nat] :
( ( ( ord_less_eq_nat @ SV71 @ SV193 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV294 @ SV349 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV71 @ SV294 ) @ ( times_times_nat @ SV193 @ SV349 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1332]) ).
thf(1467,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ~ ( ( number1551313001itions @ SV194 @ SV350 )
| ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) ) )
= $true )
| ( ( ~ ( ~ ( number1551313001itions @ SV194 @ SV350 )
| ~ ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1333]) ).
thf(1468,plain,
! [SV73: nat,SV195: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV195 )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV73 @ SV195 ) @ zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV73 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1335]) ).
thf(1469,plain,
! [SV351: set_nat,SV296: nat > set_nat,SV196: nat,SV74: nat] :
( ( ( ord_less_eq_nat @ SV74 @ SV196 )
= $false )
| ( ( ( ( SV296 @ SV196 )
!= SV351 )
| ~ ! [SY891: nat,SY892: nat] :
( ~ ( ord_less_eq_nat @ SY891 @ SY892 )
| ( ord_less_eq_set_nat @ ( SV296 @ SY891 ) @ ( SV296 @ SY892 ) ) )
| ( ord_less_eq_set_nat @ ( SV296 @ SV74 ) @ SV351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1336]) ).
thf(1470,plain,
! [SV75: nat,SV297: nat,SV197: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV197 @ SV297 ) )
= $true )
| ( ( ord_less_eq_nat @ SV75 @ SV297 )
= $true )
| ( ( ord_less_eq_nat @ SV75 @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1337]) ).
thf(1471,plain,
! [SV76: nat > nat > $o,SV198: nat,SV298: nat] :
( ( ( ! [SY1011: nat] :
( ~ ( ord_less_eq_nat @ ( sK5_SY523 @ SV298 @ SV198 @ SV76 ) @ SY1011 )
| ( SV76 @ ( sK5_SY523 @ SV298 @ SV198 @ SV76 ) @ SY1011 ) ) )
= $false )
| ( ( ~ ! [SY525: nat,SY526: nat] :
( ~ ( SV76 @ SY526 @ SY525 )
| ( SV76 @ SY525 @ SY526 ) )
| ( SV76 @ SV198 @ SV298 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1338]) ).
thf(1472,plain,
! [SV77: nat,SV299: nat,SV199: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV199 @ SV299 ) )
= $true )
| ( ( ord_less_eq_nat @ SV77 @ SV299 )
= $true )
| ( ( SV77 = SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1339]) ).
thf(1473,plain,
! [SV79: nat,SV300: nat,SV201: nat] :
( ( ( ~ ( ord_less_nat @ SV201 @ SV300 ) )
= $true )
| ( ( ord_less_nat @ SV79 @ SV300 )
= $true )
| ( ( ord_less_eq_nat @ SV79 @ SV201 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1340]) ).
thf(1474,plain,
! [SV202: nat,SV80: nat] :
( ( ( ~ ( ( SV80 != zero_zero_nat ) )
| ~ ( ( SV202 != zero_zero_nat ) ) )
= $false )
| ( ( ( times_times_nat @ SV80 @ SV202 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1341]) ).
thf(1475,plain,
! [SV81: nat,SV301: nat,SV203: nat] :
( ( ( SV203 != SV301 )
= $true )
| ( ( ord_less_eq_nat @ SV81 @ SV301 )
= $true )
| ( ( ord_less_eq_nat @ SV81 @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1342]) ).
thf(1476,plain,
! [SV204: nat,SV82: nat,SV302: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV302 @ SV82 ) )
= $true )
| ( ( ord_less_eq_nat @ SV302 @ SV204 )
= $true )
| ( ( ord_less_eq_nat @ SV82 @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1343]) ).
thf(1477,plain,
! [SV352: nat,SV303: nat,SV205: nat,SV83: nat] :
( ( ( ord_less_eq_nat @ SV83 @ SV205 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV303 @ SV352 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV83 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV303 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV83 @ SV303 ) @ ( times_times_nat @ SV205 @ SV352 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1344]) ).
thf(1478,plain,
! [SV84: nat,SV206: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV206 @ SV84 )
| ( SV206 = SV84 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV206 @ SV84 )
| ( SV206 != SV84 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV84 @ SV206 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1345]) ).
thf(1479,plain,
! [SV373: nat > nat,SV353: nat > nat,SV304: nat > nat,SV207: set_nat,SV85: set_nat] :
( ( ( ~ ! [SY900: nat] :
( ~ ( member_nat @ SY900 @ SV85 )
| ~ ! [SY901: nat] :
~ ~ ( ~ ~ ( ~ ( member_nat @ SY901 @ SV207 )
| ( ( SV304 @ SY901 )
!= SY900 ) )
| ~ ! [SY902: nat] :
( ~ ~ ( ~ ( member_nat @ SY902 @ SV207 )
| ( ( SV304 @ SY902 )
!= SY900 ) )
| ( SY902 = SY901 ) ) ) ) )
= $true )
| ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) )
| ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1347]) ).
thf(1480,plain,
! [SV354: nat,SV305: nat,SV208: nat > set_nat,SV86: set_nat] :
( ( ( SV86
= ( SV208 @ SV305 ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV305 @ SV354 )
| ~ ! [SY776: nat,SY777: nat] :
( ~ ( ord_less_eq_nat @ SY776 @ SY777 )
| ( ord_less_eq_set_nat @ ( SV208 @ SY776 ) @ ( SV208 @ SY777 ) ) )
| ( ord_less_eq_set_nat @ SV86 @ ( SV208 @ SV354 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1348]) ).
thf(1481,plain,
! [SV355: set_nat,SV306: set_nat,SV209: set_nat > nat,SV87: nat] :
( ( ( SV87
= ( SV209 @ SV306 ) )
= $false )
| ( ( ~ ( ord_less_eq_set_nat @ SV306 @ SV355 )
| ~ ! [SY780: set_nat,SY781: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY780 @ SY781 )
| ( ord_less_eq_nat @ ( SV209 @ SY780 ) @ ( SV209 @ SY781 ) ) )
| ( ord_less_eq_nat @ SV87 @ ( SV209 @ SV355 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1349]) ).
thf(1482,plain,
! [SV88: nat] :
( ( ( SV88 = zero_zero_nat )
= $true )
| ( ( ~ ( ~ ( ( SV88 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV88 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1350]) ).
thf(1483,plain,
! [SV88: nat] :
( ( ( ~ ( ( SV88 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV88 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1351]) ).
thf(1484,plain,
( ( ( ~ ! [SX0: nat] :
( ~ ( ( ( p @ SX0 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SX0 )
| ~ ( ord_less_eq_nat @ SX0 @ zero_zero_nat ) ) )
| ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
!= zero_zero_nat ) )
= $false )
| ( ( p
= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1352]) ).
thf(1485,plain,
( ( ( ~ ( ~ ! [SX0: nat] :
( ~ ( ( ( p @ SX0 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SX0 )
| ~ ( ord_less_eq_nat @ SX0 @ zero_zero_nat ) ) )
| ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
!= zero_zero_nat ) ) )
= $false )
| ( ( p
!= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1353]) ).
thf(1486,plain,
! [SV89: nat,SV210: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV210 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ SV89 @ SV210 ) )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1354]) ).
thf(1487,plain,
! [SV91: nat,SV212: nat] :
( ( ( ord_less_eq_nat @ SV212 @ SV91 )
= $false )
| ( ( SV212 = SV91 )
= $true )
| ( ( ord_less_eq_nat @ SV91 @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1355]) ).
thf(1488,plain,
! [SV356: nat,SV213: nat] :
( ( ( ~ ( ( SV213 = SV356 )
| ~ ( ~ ( ord_less_eq_nat @ SV356 @ SV213 )
| ~ ( ord_less_eq_nat @ SV213 @ SV356 ) ) ) )
= $true )
| ( ( ~ ( ( SV213 != SV356 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV356 @ SV213 )
| ~ ( ord_less_eq_nat @ SV213 @ SV356 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1356]) ).
thf(1489,plain,
! [SV357: nat > nat,SV308: nat > nat,SV214: set_nat,SV93: set_nat] :
( ( ( SV93 = SV214 )
= $false )
| ( ( ~ ! [SY972: nat] :
( ~ ( member_nat @ SY972 @ SV214 )
| ( ( SV308 @ SY972 )
= ( SV357 @ SY972 ) ) )
| ( ( groups1842438620at_nat @ SV308 @ SV93 )
= ( groups1842438620at_nat @ SV357 @ SV214 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1358]) ).
thf(1490,plain,
! [SV94: nat,SV215: nat] :
( ( ( ord_less_eq_nat @ SV215 @ zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV94 @ SV215 ) @ zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1359]) ).
thf(1491,plain,
! [SV358: set_nat,SV309: set_nat,SV216: set_nat > nat,SV95: nat] :
( ( ( ord_less_eq_nat @ SV95 @ ( SV216 @ SV309 ) )
= $false )
| ( ( ~ ( ord_less_eq_set_nat @ SV309 @ SV358 )
| ~ ! [SY789: set_nat,SY790: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY789 @ SY790 )
| ( ord_less_eq_nat @ ( SV216 @ SY789 ) @ ( SV216 @ SY790 ) ) )
| ( ord_less_eq_nat @ SV95 @ ( SV216 @ SV358 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1360]) ).
thf(1492,plain,
! [SV96: set_nat,SV217: nat > nat] :
( ( ( ~ ( member_nat @ ( sK2_SY791 @ SV217 @ SV96 ) @ SV96 ) )
= $false )
| ( ( ord_less_eq_nat @ ( groups1842438620at_nat @ SV217 @ SV96 ) @ zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1361]) ).
thf(1493,plain,
! [SV96: set_nat,SV217: nat > nat] :
( ( ( ord_less_eq_nat @ ( SV217 @ ( sK2_SY791 @ SV217 @ SV96 ) ) @ zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ ( groups1842438620at_nat @ SV217 @ SV96 ) @ zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1361]) ).
thf(1494,plain,
! [SV97: nat > nat,SV218: nat,SV310: nat] :
( ( ( ! [SY1012: nat] :
( ~ ( ord_less_nat @ ( sK6_SY578 @ SV310 @ SV218 @ SV97 ) @ SY1012 )
| ( ord_less_nat @ ( SV97 @ ( sK6_SY578 @ SV310 @ SV218 @ SV97 ) ) @ ( SV97 @ SY1012 ) ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV218 @ SV310 )
| ( ord_less_eq_nat @ ( SV97 @ SV218 ) @ ( SV97 @ SV310 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1362]) ).
thf(1495,plain,
! [SV311: nat,SV219: nat,SV98: nat] :
( ( ( ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV219 )
| ~ ( ord_less_nat @ SV98 @ SV311 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV219 )
| ~ ( ord_less_nat @ SV98 @ SV311 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1496,plain,
! [SV359: nat,SV312: nat,SV220: nat > nat,SV99: nat] :
( ( ( SV99
= ( SV220 @ SV312 ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV312 @ SV359 )
| ~ ! [SY798: nat,SY799: nat] :
( ~ ( ord_less_eq_nat @ SY798 @ SY799 )
| ( ord_less_eq_nat @ ( SV220 @ SY798 ) @ ( SV220 @ SY799 ) ) )
| ( ord_less_eq_nat @ SV99 @ ( SV220 @ SV359 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1364]) ).
thf(1497,plain,
! [SV221: nat,SV313: nat,SV100: nat > $o] :
( ( ( ~ ! [SY920: nat] :
( ~ ( SV100 @ SY920 )
| ( ord_less_eq_nat @ SY920 @ SV313 ) ) )
= $true )
| ( ( ~ ! [SY590: nat] :
~ ~ ( ~ ( SV100 @ SY590 )
| ~ ! [SY591: nat] :
( ~ ( SV100 @ SY591 )
| ( ord_less_eq_nat @ SY591 @ SY590 ) ) ) )
= $true )
| ( ( SV100 @ SV221 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1365]) ).
thf(1498,plain,
! [SV360: nat,SV222: nat] :
( ( ( ~ ( ( ord_less_nat @ SV222 @ SV360 )
| ~ ( ~ ( ord_less_eq_nat @ SV222 @ SV360 )
| ~ ( ( SV360 != SV222 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV222 @ SV360 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV222 @ SV360 )
| ~ ( ( SV360 != SV222 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1366]) ).
thf(1499,plain,
! [SV223: nat,SV102: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV102 @ SV223 ) )
= $true )
| ( ( ord_less_nat @ SV102 @ SV223 )
= $true )
| ( ( SV102 = SV223 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1368]) ).
thf(1500,plain,
! [SV224: nat,SV103: nat > nat] :
( ( ( ~ ! [SY805: nat] :
( ~ ( ( ( SV103 @ SY805 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY805 )
| ~ ( ord_less_eq_nat @ SY805 @ SV224 ) ) ) )
= $false )
| ( ( number1551313001itions @ SV103 @ SV224 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1369]) ).
thf(1501,plain,
! [SV224: nat,SV103: nat > nat] :
( ( ( ( groups1842438620at_nat
@ ^ [SY596: nat] : ( times_times_nat @ ( SV103 @ SY596 ) @ SY596 )
@ ( set_ord_atMost_nat @ SV224 ) )
!= SV224 )
= $false )
| ( ( number1551313001itions @ SV103 @ SV224 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1369]) ).
thf(1502,plain,
! [SV104: nat,SV225: nat] :
( ( ( ord_less_eq_nat @ SV225 @ SV104 )
= $false )
| ( ( SV104 = SV225 )
= $true )
| ( ( ord_less_eq_nat @ SV104 @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1370]) ).
thf(1503,plain,
! [SV361: nat,SV315: nat > nat,SV227: nat,SV106: nat] :
( ( ( ord_less_eq_nat @ SV106 @ SV227 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ ( SV315 @ SV227 ) @ SV361 )
| ~ ! [SY924: nat,SY925: nat] :
( ~ ( ord_less_eq_nat @ SY924 @ SY925 )
| ( ord_less_eq_nat @ ( SV315 @ SY924 ) @ ( SV315 @ SY925 ) ) )
| ( ord_less_eq_nat @ ( SV315 @ SV106 ) @ SV361 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1504,plain,
! [SV362: nat,SV228: nat] :
( ( ( ~ ( ( ord_less_nat @ SV228 @ SV362 )
| ~ ( ~ ( ord_less_eq_nat @ SV228 @ SV362 )
| ~ ( ( SV228 != SV362 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV228 @ SV362 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV228 @ SV362 )
| ~ ( ( SV228 != SV362 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1374]) ).
thf(1505,plain,
! [SV229: nat,SV109: nat,SV317: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV317 @ SV109 ) )
= $true )
| ( ( ord_less_nat @ SV317 @ SV229 )
= $true )
| ( ( ord_less_nat @ SV109 @ SV229 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1376]) ).
thf(1506,plain,
! [SV230: nat,SV110: nat > $o] :
( ( ( ! [SY608: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY608 )
| ~ ~ ( SV110 @ SY608 )
| ~ ! [SY609: nat] :
~ ~ ( ~ ( ord_less_nat @ SY609 @ SY608 )
| ~ ~ ( SV110 @ SY609 ) ) ) )
= $false )
| ( ( SV110 @ SV230 )
= $true )
| ( ( SV110 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1377]) ).
thf(1507,plain,
! [SV111: nat > nat,SV231: set_nat] :
( ( ( ! [SY815: nat] :
( ~ ( member_nat @ SY815 @ SV231 )
| ( ( SV111 @ SY815 )
= zero_zero_nat ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV111 @ SV231 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1378]) ).
thf(1508,plain,
! [SV112: set_nat,SV232: nat > nat] :
( ( ( ~ ( member_nat @ ( sK3_SY816 @ SV232 @ SV112 ) @ SV112 ) )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ ( groups1842438620at_nat @ SV232 @ SV112 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1379]) ).
thf(1509,plain,
! [SV112: set_nat,SV232: nat > nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ ( SV232 @ ( sK3_SY816 @ SV232 @ SV112 ) ) )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ ( groups1842438620at_nat @ SV232 @ SV112 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1379]) ).
thf(1510,plain,
! [SV235: nat,SV115: nat,SV318: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV318 ) )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV115 @ SV318 ) @ ( times_times_nat @ SV235 @ SV318 ) )
= $true )
| ( ( ord_less_eq_nat @ SV115 @ SV235 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1381]) ).
thf(1511,plain,
! [SV376: nat > nat,SV374: nat > nat,SV363: nat > nat,SV319: set_nat,SV236: nat > nat,SV116: set_nat] :
( ( ~ ! [SY981: nat] :
( ~ ( member_nat @ SY981 @ SV116 )
| ~ ( ~ ( member_nat @ ( SV236 @ SY981 ) @ SV319 )
| ( ( SV363 @ ( SV236 @ SY981 ) )
!= SY981 ) ) )
| ~ ! [SY1014: nat] :
( ~ ( member_nat @ SY1014 @ SV319 )
| ~ ( ~ ~ ( ~ ( member_nat @ ( SV363 @ SY1014 ) @ SV116 )
| ( ( SV236 @ ( SV363 @ SY1014 ) )
!= SY1014 ) )
| ( ( SV374 @ ( SV363 @ SY1014 ) )
!= ( SV376 @ SY1014 ) ) ) )
| ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1382]) ).
thf(1512,plain,
! [SV364: set_nat,SV320: nat > set_nat,SV237: nat,SV117: nat] :
( ( ( ord_less_eq_nat @ SV117 @ SV237 )
= $false )
| ( ( ~ ( ord_less_eq_set_nat @ ( SV320 @ SV237 ) @ SV364 )
| ~ ! [SY932: nat,SY933: nat] :
( ~ ( ord_less_eq_nat @ SY932 @ SY933 )
| ( ord_less_eq_set_nat @ ( SV320 @ SY932 ) @ ( SV320 @ SY933 ) ) )
| ( ord_less_eq_set_nat @ ( SV320 @ SV117 ) @ SV364 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1383]) ).
thf(1513,plain,
! [SV118: nat,SV238: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV238 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV238 @ one_one_nat )
| ( ord_less_eq_nat @ ( times_times_nat @ SV118 @ SV238 ) @ one_one_nat ) )
= $true )
| ( ( ord_less_eq_nat @ SV118 @ one_one_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1384]) ).
thf(1514,plain,
! [SV365: nat,SV321: nat,SV239: nat > nat,SV119: nat] :
( ( ( ord_less_eq_nat @ SV119 @ ( SV239 @ SV321 ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV321 @ SV365 )
| ~ ! [SY830: nat,SY831: nat] :
( ~ ( ord_less_eq_nat @ SY830 @ SY831 )
| ( ord_less_eq_nat @ ( SV239 @ SY830 ) @ ( SV239 @ SY831 ) ) )
| ( ord_less_eq_nat @ SV119 @ ( SV239 @ SV365 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1385]) ).
thf(1515,plain,
! [SV123: nat,SV242: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV242 )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV242 @ SV123 ) @ SV242 )
= $true )
| ( ( ord_less_eq_nat @ SV123 @ one_one_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1388]) ).
thf(1516,plain,
! [SV366: nat,SV243: nat] :
( ( ( ~ ( ( SV243 = SV366 )
| ~ ( ~ ( ord_less_eq_nat @ SV243 @ SV366 )
| ~ ( ord_less_eq_nat @ SV366 @ SV243 ) ) ) )
= $true )
| ( ( ~ ( ( SV243 != SV366 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV243 @ SV366 )
| ~ ( ord_less_eq_nat @ SV366 @ SV243 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1389]) ).
thf(1517,plain,
! [SV125: nat,SV324: nat,SV244: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV244 @ SV324 ) )
= $true )
| ( ( ord_less_eq_nat @ SV125 @ SV324 )
= $true )
| ( ( ord_less_eq_nat @ SV125 @ SV244 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1391]) ).
thf(1518,plain,
! [SV245: nat,SV126: nat] :
( ( ( SV126 != SV245 )
= $false )
| ( ( ord_less_nat @ SV126 @ SV245 )
= $true )
| ( ( ord_less_eq_nat @ SV126 @ SV245 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1392]) ).
thf(1519,plain,
! [SV367: nat,SV325: nat,SV246: nat > set_nat,SV127: set_nat] :
( ( ( ord_less_eq_set_nat @ SV127 @ ( SV246 @ SV325 ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV325 @ SV367 )
| ~ ! [SY838: nat,SY839: nat] :
( ~ ( ord_less_eq_nat @ SY838 @ SY839 )
| ( ord_less_eq_set_nat @ ( SV246 @ SY838 ) @ ( SV246 @ SY839 ) ) )
| ( ord_less_eq_set_nat @ SV127 @ ( SV246 @ SV367 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1393]) ).
thf(1520,plain,
! [SV368: nat,SV326: nat,SV247: nat,SV128: nat] :
( ( ( ord_less_eq_nat @ SV128 @ SV247 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV326 @ SV368 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV247 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV326 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV128 @ SV326 ) @ ( times_times_nat @ SV247 @ SV368 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1394]) ).
thf(1521,plain,
! [SV327: nat,SV248: nat,SV130: nat] :
( ( ( SV130 = zero_zero_nat )
= $true )
| ( ( ( ( times_times_nat @ SV130 @ SV248 )
= ( times_times_nat @ SV130 @ SV327 ) )
= ( SV248 = SV327 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1395]) ).
thf(1522,plain,
! [SV328: nat,SV249: nat,SV131: nat] :
( ( ( ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV249 )
| ( ord_less_eq_nat @ SV131 @ SV328 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV249 )
| ( ord_less_eq_nat @ SV131 @ SV328 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1396]) ).
thf(1523,plain,
! [SV369: nat,SV329: nat > nat,SV250: nat,SV132: nat] :
( ( ( ord_less_eq_nat @ SV132 @ SV250 )
= $false )
| ( ( ( ( SV329 @ SV250 )
!= SV369 )
| ~ ! [SY942: nat,SY943: nat] :
( ~ ( ord_less_eq_nat @ SY942 @ SY943 )
| ( ord_less_eq_nat @ ( SV329 @ SY942 ) @ ( SV329 @ SY943 ) ) )
| ( ord_less_eq_nat @ ( SV329 @ SV132 ) @ SV369 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1397]) ).
thf(1524,plain,
! [SV133: nat,SV330: nat,SV251: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV251 @ SV330 ) )
= $true )
| ( ( ord_less_eq_nat @ SV133 @ SV330 )
= $true )
| ( ( ord_less_eq_nat @ SV133 @ SV251 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1398]) ).
thf(1525,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV331 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV134 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1399]) ).
thf(1526,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV331 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV134 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1399]) ).
thf(1527,plain,
! [SV332: nat,SV253: nat,SV135: nat] :
( ( ( ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 )
| ~ ( ord_less_nat @ SV253 @ SV332 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 )
| ~ ( ord_less_nat @ SV253 @ SV332 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1400]) ).
thf(1528,plain,
! [SV254: nat,SV136: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV136 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV254 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1401]) ).
thf(1529,plain,
! [SV254: nat,SV136: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV136 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV254 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV136 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV254 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1401]) ).
thf(1530,plain,
! [SV137: nat,SV255: nat] :
( ( ( ord_less_eq_nat @ SV255 @ SV137 )
= $false )
| ( ( SV137 = SV255 )
= $true )
| ( ( ord_less_eq_nat @ SV137 @ SV255 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1402]) ).
thf(1531,plain,
! [SV256: nat,SV138: nat,SV333: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV333 ) )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV333 @ SV138 ) @ ( times_times_nat @ SV333 @ SV256 ) )
= $true )
| ( ( ord_less_eq_nat @ SV138 @ SV256 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1403]) ).
thf(1532,plain,
! [SV258: nat,SV140: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV140 )
| ~ ( ord_less_eq_nat @ SV258 @ zero_zero_nat ) )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV140 @ SV258 ) @ zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1404]) ).
thf(1533,plain,
! [SV258: nat,SV140: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV140 @ zero_zero_nat )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV258 ) )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV140 @ SV258 ) @ zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1405]) ).
thf(1534,plain,
! [SV370: nat,SV259: nat] :
( ( ( ~ ( ( ord_less_nat @ SV259 @ SV370 )
| ~ ( ~ ( ord_less_eq_nat @ SV259 @ SV370 )
| ~ ( ( SV259 != SV370 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV259 @ SV370 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV259 @ SV370 )
| ~ ( ( SV259 != SV370 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1406]) ).
thf(1535,plain,
! [SV142: set_nat,SV260: nat > nat,SV335: nat > nat] :
( ( ( ~ ( member_nat @ ( sK7_SY944 @ SV335 @ SV260 @ SV142 ) @ SV142 )
| ( ord_less_eq_nat @ ( SV260 @ ( sK7_SY944 @ SV335 @ SV260 @ SV142 ) ) @ ( SV335 @ ( sK7_SY944 @ SV335 @ SV260 @ SV142 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( groups1842438620at_nat @ SV260 @ SV142 ) @ ( groups1842438620at_nat @ SV335 @ SV142 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1408]) ).
thf(1536,plain,
! [SV263: nat,SV145: nat] :
( ( ( one_one_nat
= ( times_times_nat @ SV145 @ SV263 ) )
= $false )
| ( ( ~ ( ( one_one_nat
!= ( times_times_nat @ SV145 @ SV263 ) )
| ~ ~ ( ( SV145 != one_one_nat )
| ( SV263 != one_one_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1410]) ).
thf(1537,plain,
! [SV263: nat,SV145: nat] :
( ( ( ~ ( ( SV145 != one_one_nat )
| ( SV263 != one_one_nat ) ) )
= $false )
| ( ( ~ ( ( one_one_nat
!= ( times_times_nat @ SV145 @ SV263 ) )
| ~ ~ ( ( SV145 != one_one_nat )
| ( SV263 != one_one_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1410]) ).
thf(1538,plain,
! [SV336: nat,SV264: nat,SV146: nat] :
( ( ( SV146 = zero_zero_nat )
= $true )
| ( ( ( ( times_times_nat @ SV264 @ SV146 )
= ( times_times_nat @ SV336 @ SV146 ) )
= ( SV264 = SV336 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1411]) ).
thf(1539,plain,
! [SV147: nat] :
( ( ( SV147 = zero_zero_nat )
= $true )
| ( ( ~ ( ~ ( ( SV147 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV147 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1412]) ).
thf(1540,plain,
! [SV147: nat] :
( ( ( ~ ( ( SV147 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV147 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1413]) ).
thf(1541,plain,
! [SV265: nat,SV148: nat > nat] :
( ( ( ~ ( ( ( SV148 @ ( sK4_SY856 @ SV265 @ SV148 ) )
!= zero_zero_nat ) ) )
= $false )
| ( ( ( ( groups1842438620at_nat
@ ^ [SY685: nat] : ( times_times_nat @ ( SV148 @ SY685 ) @ SY685 )
@ ( set_ord_atMost_nat @ SV265 ) )
!= SV265 )
| ( number1551313001itions @ SV148 @ SV265 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1414]) ).
thf(1542,plain,
! [SV148: nat > nat,SV265: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ ( sK4_SY856 @ SV265 @ SV148 ) )
| ~ ( ord_less_eq_nat @ ( sK4_SY856 @ SV265 @ SV148 ) @ SV265 ) ) )
= $false )
| ( ( ( ( groups1842438620at_nat
@ ^ [SY685: nat] : ( times_times_nat @ ( SV148 @ SY685 ) @ SY685 )
@ ( set_ord_atMost_nat @ SV265 ) )
!= SV265 )
| ( number1551313001itions @ SV148 @ SV265 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1414]) ).
thf(1543,plain,
! [SV266: nat,SV149: nat] :
( ( ( ( times_times_nat @ SV149 @ SV266 )
= one_one_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV149 @ SV266 )
!= one_one_nat )
| ~ ~ ( ( SV149 != one_one_nat )
| ( SV266 != one_one_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1415]) ).
thf(1544,plain,
! [SV266: nat,SV149: nat] :
( ( ( ~ ( ( SV149 != one_one_nat )
| ( SV266 != one_one_nat ) ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV149 @ SV266 )
!= one_one_nat )
| ~ ~ ( ( SV149 != one_one_nat )
| ( SV266 != one_one_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1415]) ).
thf(1545,plain,
! [SV150: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV150 )
| ~ ( ( SV150 != zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV150 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1416]) ).
thf(1546,plain,
! [SV150: nat] :
( ( ( SV150 = zero_zero_nat )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV150 )
| ~ ( ( SV150 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1417]) ).
thf(1547,plain,
! [SV371: nat,SV337: set_nat > nat,SV267: set_nat,SV151: set_nat] :
( ( ( ord_less_eq_set_nat @ SV151 @ SV267 )
= $false )
| ( ( ( ( SV337 @ SV267 )
!= SV371 )
| ~ ! [SY946: set_nat,SY947: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY946 @ SY947 )
| ( ord_less_eq_nat @ ( SV337 @ SY946 ) @ ( SV337 @ SY947 ) ) )
| ( ord_less_eq_nat @ ( SV337 @ SV151 ) @ SV371 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1418]) ).
thf(1548,plain,
! [SV268: nat,SV152: nat,SV338: nat] :
( ( ( ~ ( ord_less_nat @ SV338 @ SV152 ) )
= $true )
| ( ( ord_less_nat @ SV338 @ SV268 )
= $true )
| ( ( ord_less_eq_nat @ SV152 @ SV268 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1419]) ).
thf(1549,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV153 )
| ( ord_less_eq_nat @ SV269 @ SV339 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV153 )
| ( ord_less_eq_nat @ SV269 @ SV339 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1420]) ).
thf(1550,plain,
! [SV154: nat,SV270: nat] :
( ( ( ord_less_eq_nat @ SV270 @ zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV270 @ SV154 ) @ zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1421]) ).
thf(1551,plain,
! [SV155: nat,SV340: nat,SV271: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV271 @ SV340 ) )
= $true )
| ( ( ord_less_nat @ SV155 @ SV340 )
= $true )
| ( ( ord_less_nat @ SV155 @ SV271 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1422]) ).
thf(1552,plain,
! [SV156: nat,SV2: nat] :
( ( ( ~ ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ SV2 ) @ ( set_ord_atMost_nat @ SV156 ) )
| ~ ( ord_less_eq_nat @ SV2 @ SV156 ) )
= $false )
| ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ SV2 ) @ ( set_ord_atMost_nat @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1423]) ).
thf(1553,plain,
! [SV156: nat,SV2: nat] :
( ( ( ~ ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ SV2 ) @ ( set_ord_atMost_nat @ SV156 ) )
| ~ ( ord_less_eq_nat @ SV2 @ SV156 ) )
= $false )
| ( ( ord_less_eq_nat @ SV2 @ SV156 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1424]) ).
thf(1554,plain,
! [SV157: nat,SV3: nat] :
( ( ( ~ ( member_nat @ SV3 @ ( set_ord_atMost_nat @ SV157 ) )
| ~ ( ord_less_eq_nat @ SV3 @ SV157 ) )
= $false )
| ( ( member_nat @ SV3 @ ( set_ord_atMost_nat @ SV157 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1425]) ).
thf(1555,plain,
! [SV157: nat,SV3: nat] :
( ( ( ~ ( member_nat @ SV3 @ ( set_ord_atMost_nat @ SV157 ) )
| ~ ( ord_less_eq_nat @ SV3 @ SV157 ) )
= $false )
| ( ( ord_less_eq_nat @ SV3 @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1426]) ).
thf(1556,plain,
! [SV158: nat,SV4: nat] :
( ( ( ( ( set_ord_atMost_nat @ SV4 )
!= ( set_ord_atMost_nat @ SV158 ) )
| ( SV4 != SV158 ) )
= $false )
| ( ( ( set_ord_atMost_nat @ SV4 )
= ( set_ord_atMost_nat @ SV158 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1427]) ).
thf(1557,plain,
! [SV158: nat,SV4: nat] :
( ( ( ( ( set_ord_atMost_nat @ SV4 )
!= ( set_ord_atMost_nat @ SV158 ) )
| ( SV4 != SV158 ) )
= $false )
| ( ( SV4 = SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1428]) ).
thf(1558,plain,
! [SV272: nat,SV159: nat,SV5: nat] :
( ( ( ( times_times_nat @ SV5 @ SV159 )
= ( times_times_nat @ SV272 @ SV159 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV5 @ SV159 )
!= ( times_times_nat @ SV272 @ SV159 ) )
| ~ ( ( SV159 = zero_zero_nat )
| ( SV5 = SV272 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1429]) ).
thf(1559,plain,
! [SV272: nat,SV5: nat,SV159: nat] :
( ( ( ( SV159 = zero_zero_nat )
| ( SV5 = SV272 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV5 @ SV159 )
!= ( times_times_nat @ SV272 @ SV159 ) )
| ~ ( ( SV159 = zero_zero_nat )
| ( SV5 = SV272 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1429]) ).
thf(1560,plain,
! [SV273: nat,SV160: nat,SV6: nat] :
( ( ( ( times_times_nat @ SV6 @ SV160 )
= ( times_times_nat @ SV6 @ SV273 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV6 @ SV160 )
!= ( times_times_nat @ SV6 @ SV273 ) )
| ~ ( ( SV6 = zero_zero_nat )
| ( SV160 = SV273 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1430]) ).
thf(1561,plain,
! [SV273: nat,SV160: nat,SV6: nat] :
( ( ( ( SV6 = zero_zero_nat )
| ( SV160 = SV273 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV6 @ SV160 )
!= ( times_times_nat @ SV6 @ SV273 ) )
| ~ ( ( SV6 = zero_zero_nat )
| ( SV160 = SV273 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1430]) ).
thf(1562,plain,
! [SV161: nat,SV7: nat] :
( ( ( ( ( times_times_nat @ SV7 @ SV161 )
!= zero_zero_nat )
| ~ ( ( SV7 = zero_zero_nat )
| ( SV161 = zero_zero_nat ) ) )
= $false )
| ( ( ( times_times_nat @ SV7 @ SV161 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1431]) ).
thf(1563,plain,
! [SV161: nat,SV7: nat] :
( ( ( SV7 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV7 @ SV161 )
!= zero_zero_nat )
| ~ ( ( SV7 = zero_zero_nat )
| ( SV161 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1432]) ).
thf(1564,plain,
! [SV7: nat,SV161: nat] :
( ( ( SV161 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV7 @ SV161 )
!= zero_zero_nat )
| ~ ( ( SV7 = zero_zero_nat )
| ( SV161 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1432]) ).
thf(1565,plain,
! [SV274: nat,SV162: nat,SV12: nat] :
( ( ( ( times_times_nat @ SV12 @ SV162 )
= ( times_times_nat @ SV274 @ SV162 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV12 @ SV162 )
!= ( times_times_nat @ SV274 @ SV162 ) )
| ~ ( ( SV12 = SV274 )
| ( SV162 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1433]) ).
thf(1566,plain,
! [SV162: nat,SV274: nat,SV12: nat] :
( ( ( ( SV12 = SV274 )
| ( SV162 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV12 @ SV162 )
!= ( times_times_nat @ SV274 @ SV162 ) )
| ~ ( ( SV12 = SV274 )
| ( SV162 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1433]) ).
thf(1567,plain,
! [SV275: nat,SV163: nat,SV13: nat] :
( ( ( ( times_times_nat @ SV13 @ SV163 )
= ( times_times_nat @ SV13 @ SV275 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV13 @ SV163 )
!= ( times_times_nat @ SV13 @ SV275 ) )
| ~ ( ( SV163 = SV275 )
| ( SV13 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1434]) ).
thf(1568,plain,
! [SV13: nat,SV275: nat,SV163: nat] :
( ( ( ( SV163 = SV275 )
| ( SV13 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV13 @ SV163 )
!= ( times_times_nat @ SV13 @ SV275 ) )
| ~ ( ( SV163 = SV275 )
| ( SV13 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1434]) ).
thf(1569,plain,
! [SV164: nat,SV15: nat] :
( ( ( ( ( times_times_nat @ SV15 @ SV164 )
!= zero_zero_nat )
| ~ ( ( SV15 = zero_zero_nat )
| ( SV164 = zero_zero_nat ) ) )
= $false )
| ( ( ( times_times_nat @ SV15 @ SV164 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1435]) ).
thf(1570,plain,
! [SV164: nat,SV15: nat] :
( ( ( SV15 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV15 @ SV164 )
!= zero_zero_nat )
| ~ ( ( SV15 = zero_zero_nat )
| ( SV164 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1436]) ).
thf(1571,plain,
! [SV15: nat,SV164: nat] :
( ( ( SV164 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV15 @ SV164 )
!= zero_zero_nat )
| ~ ( ( SV15 = zero_zero_nat )
| ( SV164 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1436]) ).
thf(1572,plain,
! [SV19: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV19 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV19 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1437]) ).
thf(1573,plain,
! [SV19: nat] :
( ( ( SV19 != zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ SV19 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1437]) ).
thf(1574,plain,
! [SV19: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV19 @ zero_zero_nat ) )
= $false )
| ( ( SV19 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1438]) ).
thf(1575,plain,
! [SV19: nat] :
( ( ( SV19 != zero_zero_nat )
= $false )
| ( ( SV19 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1438]) ).
thf(1576,plain,
! [SV20: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV20 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV20 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1439]) ).
thf(1577,plain,
! [SV20: nat] :
( ( ( SV20 != zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ SV20 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1439]) ).
thf(1578,plain,
! [SV20: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV20 @ zero_zero_nat ) )
= $false )
| ( ( SV20 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1440]) ).
thf(1579,plain,
! [SV20: nat] :
( ( ( SV20 != zero_zero_nat )
= $false )
| ( ( SV20 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1440]) ).
thf(1580,plain,
! [SV35: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV35 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV35 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1441]) ).
thf(1581,plain,
! [SV35: nat] :
( ( ( SV35 != zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ SV35 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1441]) ).
thf(1582,plain,
! [SV35: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV35 @ zero_zero_nat ) )
= $false )
| ( ( SV35 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1442]) ).
thf(1583,plain,
! [SV35: nat] :
( ( ( SV35 != zero_zero_nat )
= $false )
| ( ( SV35 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1442]) ).
thf(1584,plain,
! [SV280: nat,SV173: nat,SV37: nat] :
( ( ( ( times_times_nat @ SV37 @ SV173 )
= ( times_times_nat @ SV37 @ SV280 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV37 @ SV173 )
!= ( times_times_nat @ SV37 @ SV280 ) )
| ~ ( ( SV37 = zero_zero_nat )
| ( SV173 = SV280 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1443]) ).
thf(1585,plain,
! [SV280: nat,SV173: nat,SV37: nat] :
( ( ( ( SV37 = zero_zero_nat )
| ( SV173 = SV280 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV37 @ SV173 )
!= ( times_times_nat @ SV37 @ SV280 ) )
| ~ ( ( SV37 = zero_zero_nat )
| ( SV173 = SV280 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1443]) ).
thf(1586,plain,
! [SV42: nat] :
( ( ( zero_zero_nat != SV42 )
= $false )
| ( ( zero_zero_nat = SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1444]) ).
thf(1587,plain,
! [SV42: nat] :
( ( ( SV42 != zero_zero_nat )
= $false )
| ( ( zero_zero_nat = SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1444]) ).
thf(1588,plain,
! [SV42: nat] :
( ( ( zero_zero_nat != SV42 )
= $false )
| ( ( SV42 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1445]) ).
thf(1589,plain,
! [SV42: nat] :
( ( ( SV42 != zero_zero_nat )
= $false )
| ( ( SV42 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1445]) ).
thf(1590,plain,
! [SV47: nat] :
( ( ( one_one_nat != SV47 )
= $false )
| ( ( one_one_nat = SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1446]) ).
thf(1591,plain,
! [SV47: nat] :
( ( ( SV47 != one_one_nat )
= $false )
| ( ( one_one_nat = SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1446]) ).
thf(1592,plain,
! [SV47: nat] :
( ( ( one_one_nat != SV47 )
= $false )
| ( ( SV47 = one_one_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1447]) ).
thf(1593,plain,
! [SV47: nat] :
( ( ( SV47 != one_one_nat )
= $false )
| ( ( SV47 = one_one_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1447]) ).
thf(1594,plain,
! [SV50: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV50 )
| ( SV50 != zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1448]) ).
thf(1595,plain,
! [SV50: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV50 ) )
= $false )
| ( ( SV50 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1449]) ).
thf(1596,plain,
! [SV50: nat] :
( ( ( SV50 != zero_zero_nat )
= $false )
| ( ( SV50 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1449]) ).
thf(1597,plain,
! [SV51: nat] :
( ( ( ~ ( ord_less_nat @ SV51 @ one_one_nat ) )
= $false )
| ( ( ord_less_nat @ SV51 @ one_one_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1450]) ).
thf(1598,plain,
! [SV51: nat] :
( ( ( SV51 != zero_zero_nat )
= $false )
| ( ( ord_less_nat @ SV51 @ one_one_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1450]) ).
thf(1599,plain,
! [SV51: nat] :
( ( ( ~ ( ord_less_nat @ SV51 @ one_one_nat ) )
= $false )
| ( ( SV51 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1451]) ).
thf(1600,plain,
! [SV51: nat] :
( ( ( SV51 != zero_zero_nat )
= $false )
| ( ( SV51 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1451]) ).
thf(1601,plain,
! [SV343: nat,SV179: nat] :
( ( ( ( ord_less_eq_nat @ SV179 @ SV343 )
| ( ord_less_nat @ SV179 @ SV343 )
| ( SV179 = SV343 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV179 @ SV343 )
| ~ ( ( ord_less_nat @ SV179 @ SV343 )
| ( SV179 = SV343 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1452]) ).
thf(1602,plain,
! [SV54: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV54 )
| ( SV54 != zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1453]) ).
thf(1603,plain,
! [SV54: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV54 ) )
= $false )
| ( ( SV54 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1454]) ).
thf(1604,plain,
! [SV54: nat] :
( ( ( SV54 != zero_zero_nat )
= $false )
| ( ( SV54 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1454]) ).
thf(1605,plain,
! [SV344: nat,SV180: nat] :
( ( ( ( ord_less_eq_nat @ SV180 @ SV344 )
| ( ord_less_nat @ SV180 @ SV344 )
| ( SV344 = SV180 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV180 @ SV344 )
| ~ ( ( ord_less_nat @ SV180 @ SV344 )
| ( SV344 = SV180 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1455]) ).
thf(1606,plain,
! [SV345: nat,SV181: nat] :
( ( ( ( ord_less_eq_nat @ SV181 @ SV345 )
| ( ord_less_nat @ SV181 @ SV345 )
| ( SV181 = SV345 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV181 @ SV345 )
| ~ ( ( ord_less_nat @ SV181 @ SV345 )
| ( SV181 = SV345 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1456]) ).
thf(1607,plain,
! [SV375: nat > nat,SV372: nat > nat,SV346: set_nat,SV288: nat > nat,SV182: nat > nat,SV60: set_nat] :
( ( ( ~ ! [SY876: nat] :
( ~ ( member_nat @ SY876 @ SV60 )
| ( ( SV182 @ ( SV288 @ SY876 ) )
= SY876 ) ) )
= $true )
| ( ( ~ ! [SY953: nat] :
( ~ ( member_nat @ SY953 @ SV60 )
| ( member_nat @ ( SV288 @ SY953 ) @ SV346 ) )
| ~ ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) )
| ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1457]) ).
thf(1608,plain,
! [SV62: nat,SV184: nat] :
( ( ( SV184 != zero_zero_nat )
= $false )
| ( ( ( times_times_nat @ SV62 @ SV184 )
!= zero_zero_nat )
= $true )
| ( ( SV62 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1459]) ).
thf(1609,plain,
! [SV185: nat,SV63: nat,SV289: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV289 )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV289 @ SV63 ) @ ( times_times_nat @ SV289 @ SV185 ) )
= $true )
| ( ( ord_less_eq_nat @ SV63 @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1460]) ).
thf(1610,plain,
! [SV347: nat,SV186: nat] :
( ( ( ( SV186 = SV347 )
| ~ ( ~ ( ord_less_eq_nat @ SV186 @ SV347 )
| ~ ( ord_less_eq_nat @ SV347 @ SV186 ) ) )
= $false )
| ( ( ~ ( ( SV186 != SV347 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV186 @ SV347 )
| ~ ( ord_less_eq_nat @ SV347 @ SV186 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1461]) ).
thf(1611,plain,
! [SV65: set_nat,SV187: nat > nat] :
( ( ( member_nat @ ( sK1_SY736 @ SV187 @ SV65 ) @ SV65 )
= $true )
| ( ( ( groups1842438620at_nat @ SV187 @ SV65 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1462]) ).
thf(1612,plain,
! [SV69: set_nat,SV348: nat,SV191: set_nat,SV292: set_nat > nat] :
( ( ( ~ ( ord_less_eq_nat @ ( SV292 @ SV191 ) @ SV348 ) )
= $true )
| ( ( ~ ! [SY882: set_nat,SY883: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY882 @ SY883 )
| ( ord_less_eq_nat @ ( SV292 @ SY882 ) @ ( SV292 @ SY883 ) ) )
| ( ord_less_eq_nat @ ( SV292 @ SV69 ) @ SV348 ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV69 @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1464]) ).
thf(1613,plain,
! [SV192: nat,SV293: nat,SV70: nat > $o] :
( ( ( ! [SY884: nat] :
( ~ ( SV70 @ SY884 )
| ( ord_less_eq_nat @ SY884 @ SV293 ) ) )
= $false )
| ( ( ~ ! [SY505: nat] :
( ~ ( SV70 @ SY505 )
| ~ ! [SY506: nat] :
( ~ ( SV70 @ SY506 )
| ( ord_less_eq_nat @ SY506 @ SY505 ) ) ) )
= $true )
| ( ( SV70 @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1465]) ).
thf(1614,plain,
! [SV193: nat,SV71: nat,SV349: nat,SV294: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV294 @ SV349 ) )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV71 @ SV294 ) @ ( times_times_nat @ SV193 @ SV349 ) )
= $true )
| ( ( ord_less_eq_nat @ SV71 @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1466]) ).
thf(1615,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ( number1551313001itions @ SV194 @ SV350 )
| ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) )
= $false )
| ( ( ~ ( ~ ( number1551313001itions @ SV194 @ SV350 )
| ~ ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1467]) ).
thf(1616,plain,
! [SV74: nat,SV351: set_nat,SV196: nat,SV296: nat > set_nat] :
( ( ( ( SV296 @ SV196 )
!= SV351 )
= $true )
| ( ( ~ ! [SY891: nat,SY892: nat] :
( ~ ( ord_less_eq_nat @ SY891 @ SY892 )
| ( ord_less_eq_set_nat @ ( SV296 @ SY891 ) @ ( SV296 @ SY892 ) ) )
| ( ord_less_eq_set_nat @ ( SV296 @ SV74 ) @ SV351 ) )
= $true )
| ( ( ord_less_eq_nat @ SV74 @ SV196 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1469]) ).
thf(1617,plain,
! [SV75: nat,SV297: nat,SV197: nat] :
( ( ( ord_less_eq_nat @ SV197 @ SV297 )
= $false )
| ( ( ord_less_eq_nat @ SV75 @ SV297 )
= $true )
| ( ( ord_less_eq_nat @ SV75 @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1470]) ).
thf(1618,plain,
! [SV76: nat > nat > $o,SV198: nat,SV298: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK5_SY523 @ SV298 @ SV198 @ SV76 ) @ ( sK8_SY1011 @ SV76 @ SV198 @ SV298 ) )
| ( SV76 @ ( sK5_SY523 @ SV298 @ SV198 @ SV76 ) @ ( sK8_SY1011 @ SV76 @ SV198 @ SV298 ) ) )
= $false )
| ( ( ~ ! [SY525: nat,SY526: nat] :
( ~ ( SV76 @ SY526 @ SY525 )
| ( SV76 @ SY525 @ SY526 ) )
| ( SV76 @ SV198 @ SV298 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1471]) ).
thf(1619,plain,
! [SV77: nat,SV299: nat,SV199: nat] :
( ( ( ord_less_eq_nat @ SV199 @ SV299 )
= $false )
| ( ( ord_less_eq_nat @ SV77 @ SV299 )
= $true )
| ( ( SV77 = SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1472]) ).
thf(1620,plain,
! [SV79: nat,SV300: nat,SV201: nat] :
( ( ( ord_less_nat @ SV201 @ SV300 )
= $false )
| ( ( ord_less_nat @ SV79 @ SV300 )
= $true )
| ( ( ord_less_eq_nat @ SV79 @ SV201 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1473]) ).
thf(1621,plain,
! [SV202: nat,SV80: nat] :
( ( ( ~ ( ( SV80 != zero_zero_nat ) ) )
= $false )
| ( ( ( times_times_nat @ SV80 @ SV202 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1474]) ).
thf(1622,plain,
! [SV80: nat,SV202: nat] :
( ( ( ~ ( ( SV202 != zero_zero_nat ) ) )
= $false )
| ( ( ( times_times_nat @ SV80 @ SV202 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1474]) ).
thf(1623,plain,
! [SV81: nat,SV301: nat,SV203: nat] :
( ( ( SV203 = SV301 )
= $false )
| ( ( ord_less_eq_nat @ SV81 @ SV301 )
= $true )
| ( ( ord_less_eq_nat @ SV81 @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1475]) ).
thf(1624,plain,
! [SV204: nat,SV82: nat,SV302: nat] :
( ( ( ord_less_eq_nat @ SV302 @ SV82 )
= $false )
| ( ( ord_less_eq_nat @ SV302 @ SV204 )
= $true )
| ( ( ord_less_eq_nat @ SV82 @ SV204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1476]) ).
thf(1625,plain,
! [SV205: nat,SV83: nat,SV352: nat,SV303: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV303 @ SV352 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV83 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV303 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV83 @ SV303 ) @ ( times_times_nat @ SV205 @ SV352 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV83 @ SV205 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1477]) ).
thf(1626,plain,
! [SV84: nat,SV206: nat] :
( ( ( ( ord_less_eq_nat @ SV206 @ SV84 )
| ( SV206 = SV84 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV206 @ SV84 )
| ( SV206 != SV84 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV84 @ SV206 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1478]) ).
thf(1627,plain,
! [SV373: nat > nat,SV353: nat > nat,SV304: nat > nat,SV207: set_nat,SV85: set_nat] :
( ( ( ! [SY900: nat] :
( ~ ( member_nat @ SY900 @ SV85 )
| ~ ! [SY901: nat] :
~ ~ ( ~ ~ ( ~ ( member_nat @ SY901 @ SV207 )
| ( ( SV304 @ SY901 )
!= SY900 ) )
| ~ ! [SY902: nat] :
( ~ ~ ( ~ ( member_nat @ SY902 @ SV207 )
| ( ( SV304 @ SY902 )
!= SY900 ) )
| ( SY902 = SY901 ) ) ) ) )
= $false )
| ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) )
| ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1479]) ).
thf(1628,plain,
! [SV86: set_nat,SV208: nat > set_nat,SV354: nat,SV305: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV305 @ SV354 ) )
= $true )
| ( ( ~ ! [SY776: nat,SY777: nat] :
( ~ ( ord_less_eq_nat @ SY776 @ SY777 )
| ( ord_less_eq_set_nat @ ( SV208 @ SY776 ) @ ( SV208 @ SY777 ) ) )
| ( ord_less_eq_set_nat @ SV86 @ ( SV208 @ SV354 ) ) )
= $true )
| ( ( SV86
= ( SV208 @ SV305 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1480]) ).
thf(1629,plain,
! [SV87: nat,SV209: set_nat > nat,SV355: set_nat,SV306: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ SV306 @ SV355 ) )
= $true )
| ( ( ~ ! [SY780: set_nat,SY781: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY780 @ SY781 )
| ( ord_less_eq_nat @ ( SV209 @ SY780 ) @ ( SV209 @ SY781 ) ) )
| ( ord_less_eq_nat @ SV87 @ ( SV209 @ SV355 ) ) )
= $true )
| ( ( SV87
= ( SV209 @ SV306 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1481]) ).
thf(1630,plain,
! [SV88: nat] :
( ( ( ~ ( ( SV88 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV88 ) )
= $false )
| ( ( SV88 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1482]) ).
thf(1631,plain,
! [SV88: nat] :
( ( ( ~ ( ( SV88 != zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1483]) ).
thf(1632,plain,
! [SV88: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV88 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1483]) ).
thf(1633,plain,
( ( ( ~ ! [SX0: nat] :
( ~ ( ( ( p @ SX0 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SX0 )
| ~ ( ord_less_eq_nat @ SX0 @ zero_zero_nat ) ) ) )
= $false )
| ( ( p
= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1484]) ).
thf(1634,plain,
( ( ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
!= zero_zero_nat )
= $false )
| ( ( p
= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1484]) ).
thf(1635,plain,
( ( ( ~ ! [SX0: nat] :
( ~ ( ( ( p @ SX0 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SX0 )
| ~ ( ord_less_eq_nat @ SX0 @ zero_zero_nat ) ) )
| ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
!= zero_zero_nat ) )
= $true )
| ( ( p
!= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1485]) ).
thf(1636,plain,
! [SV356: nat,SV213: nat] :
( ( ( ( SV213 = SV356 )
| ~ ( ~ ( ord_less_eq_nat @ SV356 @ SV213 )
| ~ ( ord_less_eq_nat @ SV213 @ SV356 ) ) )
= $false )
| ( ( ~ ( ( SV213 != SV356 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV356 @ SV213 )
| ~ ( ord_less_eq_nat @ SV213 @ SV356 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1488]) ).
thf(1637,plain,
! [SV93: set_nat,SV357: nat > nat,SV308: nat > nat,SV214: set_nat] :
( ( ( ~ ! [SY972: nat] :
( ~ ( member_nat @ SY972 @ SV214 )
| ( ( SV308 @ SY972 )
= ( SV357 @ SY972 ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV308 @ SV93 )
= ( groups1842438620at_nat @ SV357 @ SV214 ) )
= $true )
| ( ( SV93 = SV214 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1489]) ).
thf(1638,plain,
! [SV95: nat,SV216: set_nat > nat,SV358: set_nat,SV309: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ SV309 @ SV358 ) )
= $true )
| ( ( ~ ! [SY789: set_nat,SY790: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY789 @ SY790 )
| ( ord_less_eq_nat @ ( SV216 @ SY789 ) @ ( SV216 @ SY790 ) ) )
| ( ord_less_eq_nat @ SV95 @ ( SV216 @ SV358 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV95 @ ( SV216 @ SV309 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1491]) ).
thf(1639,plain,
! [SV96: set_nat,SV217: nat > nat] :
( ( ( member_nat @ ( sK2_SY791 @ SV217 @ SV96 ) @ SV96 )
= $true )
| ( ( ord_less_eq_nat @ ( groups1842438620at_nat @ SV217 @ SV96 ) @ zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1492]) ).
thf(1640,plain,
! [SV97: nat > nat,SV218: nat,SV310: nat] :
( ( ( ~ ( ord_less_nat @ ( sK6_SY578 @ SV310 @ SV218 @ SV97 ) @ ( sK9_SY1012 @ SV97 @ SV218 @ SV310 ) )
| ( ord_less_nat @ ( SV97 @ ( sK6_SY578 @ SV310 @ SV218 @ SV97 ) ) @ ( SV97 @ ( sK9_SY1012 @ SV97 @ SV218 @ SV310 ) ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV218 @ SV310 )
| ( ord_less_eq_nat @ ( SV97 @ SV218 ) @ ( SV97 @ SV310 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1494]) ).
thf(1641,plain,
! [SV311: nat,SV219: nat,SV98: nat] :
( ( ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV219 )
| ~ ( ord_less_nat @ SV98 @ SV311 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1495]) ).
thf(1642,plain,
! [SV311: nat,SV98: nat,SV219: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV219 )
| ~ ( ord_less_nat @ SV98 @ SV311 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV219 )
| ~ ( ord_less_nat @ SV98 @ SV311 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1495]) ).
thf(1643,plain,
! [SV99: nat,SV220: nat > nat,SV359: nat,SV312: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV312 @ SV359 ) )
= $true )
| ( ( ~ ! [SY798: nat,SY799: nat] :
( ~ ( ord_less_eq_nat @ SY798 @ SY799 )
| ( ord_less_eq_nat @ ( SV220 @ SY798 ) @ ( SV220 @ SY799 ) ) )
| ( ord_less_eq_nat @ SV99 @ ( SV220 @ SV359 ) ) )
= $true )
| ( ( SV99
= ( SV220 @ SV312 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1496]) ).
thf(1644,plain,
! [SV221: nat,SV313: nat,SV100: nat > $o] :
( ( ( ! [SY920: nat] :
( ~ ( SV100 @ SY920 )
| ( ord_less_eq_nat @ SY920 @ SV313 ) ) )
= $false )
| ( ( ~ ! [SY590: nat] :
~ ~ ( ~ ( SV100 @ SY590 )
| ~ ! [SY591: nat] :
( ~ ( SV100 @ SY591 )
| ( ord_less_eq_nat @ SY591 @ SY590 ) ) ) )
= $true )
| ( ( SV100 @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1497]) ).
thf(1645,plain,
! [SV360: nat,SV222: nat] :
( ( ( ( ord_less_nat @ SV222 @ SV360 )
| ~ ( ~ ( ord_less_eq_nat @ SV222 @ SV360 )
| ~ ( ( SV360 != SV222 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV222 @ SV360 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV222 @ SV360 )
| ~ ( ( SV360 != SV222 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1498]) ).
thf(1646,plain,
! [SV223: nat,SV102: nat] :
( ( ( ord_less_eq_nat @ SV102 @ SV223 )
= $false )
| ( ( ord_less_nat @ SV102 @ SV223 )
= $true )
| ( ( SV102 = SV223 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1499]) ).
thf(1647,plain,
! [SV224: nat,SV103: nat > nat] :
( ( ( ! [SY805: nat] :
( ~ ( ( ( SV103 @ SY805 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY805 )
| ~ ( ord_less_eq_nat @ SY805 @ SV224 ) ) ) )
= $true )
| ( ( number1551313001itions @ SV103 @ SV224 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1500]) ).
thf(1648,plain,
! [SV224: nat,SV103: nat > nat] :
( ( ( ( groups1842438620at_nat
@ ^ [SY596: nat] : ( times_times_nat @ ( SV103 @ SY596 ) @ SY596 )
@ ( set_ord_atMost_nat @ SV224 ) )
= SV224 )
= $true )
| ( ( number1551313001itions @ SV103 @ SV224 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1501]) ).
thf(1649,plain,
! [SV106: nat,SV361: nat,SV227: nat,SV315: nat > nat] :
( ( ( ~ ( ord_less_eq_nat @ ( SV315 @ SV227 ) @ SV361 ) )
= $true )
| ( ( ~ ! [SY924: nat,SY925: nat] :
( ~ ( ord_less_eq_nat @ SY924 @ SY925 )
| ( ord_less_eq_nat @ ( SV315 @ SY924 ) @ ( SV315 @ SY925 ) ) )
| ( ord_less_eq_nat @ ( SV315 @ SV106 ) @ SV361 ) )
= $true )
| ( ( ord_less_eq_nat @ SV106 @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1503]) ).
thf(1650,plain,
! [SV362: nat,SV228: nat] :
( ( ( ( ord_less_nat @ SV228 @ SV362 )
| ~ ( ~ ( ord_less_eq_nat @ SV228 @ SV362 )
| ~ ( ( SV228 != SV362 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV228 @ SV362 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV228 @ SV362 )
| ~ ( ( SV228 != SV362 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1504]) ).
thf(1651,plain,
! [SV229: nat,SV109: nat,SV317: nat] :
( ( ( ord_less_eq_nat @ SV317 @ SV109 )
= $false )
| ( ( ord_less_nat @ SV317 @ SV229 )
= $true )
| ( ( ord_less_nat @ SV109 @ SV229 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1505]) ).
thf(1652,plain,
! [SV110: nat > $o,SV230: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( sK10_SY608 @ SV230 @ SV110 ) )
| ~ ~ ( SV110 @ ( sK10_SY608 @ SV230 @ SV110 ) )
| ~ ! [SY1015: nat] :
~ ~ ( ~ ( ord_less_nat @ SY1015 @ ( sK10_SY608 @ SV230 @ SV110 ) )
| ~ ~ ( SV110 @ SY1015 ) ) )
= $false )
| ( ( SV110 @ SV230 )
= $true )
| ( ( SV110 @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1506]) ).
thf(1653,plain,
! [SV231: set_nat,SV111: nat > nat] :
( ( ( ~ ( member_nat @ ( sK11_SY815 @ SV111 @ SV231 ) @ SV231 )
| ( ( SV111 @ ( sK11_SY815 @ SV111 @ SV231 ) )
= zero_zero_nat ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV111 @ SV231 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1507]) ).
thf(1654,plain,
! [SV112: set_nat,SV232: nat > nat] :
( ( ( member_nat @ ( sK3_SY816 @ SV232 @ SV112 ) @ SV112 )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ ( groups1842438620at_nat @ SV232 @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1508]) ).
thf(1655,plain,
! [SV235: nat,SV115: nat,SV318: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV318 )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV115 @ SV318 ) @ ( times_times_nat @ SV235 @ SV318 ) )
= $true )
| ( ( ord_less_eq_nat @ SV115 @ SV235 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1510]) ).
thf(1656,plain,
! [SV376: nat > nat,SV374: nat > nat,SV363: nat > nat,SV319: set_nat,SV236: nat > nat,SV116: set_nat] :
( ( ( ~ ! [SY981: nat] :
( ~ ( member_nat @ SY981 @ SV116 )
| ~ ( ~ ( member_nat @ ( SV236 @ SY981 ) @ SV319 )
| ( ( SV363 @ ( SV236 @ SY981 ) )
!= SY981 ) ) ) )
= $true )
| ( ( ~ ! [SY1014: nat] :
( ~ ( member_nat @ SY1014 @ SV319 )
| ~ ( ~ ~ ( ~ ( member_nat @ ( SV363 @ SY1014 ) @ SV116 )
| ( ( SV236 @ ( SV363 @ SY1014 ) )
!= SY1014 ) )
| ( ( SV374 @ ( SV363 @ SY1014 ) )
!= ( SV376 @ SY1014 ) ) ) )
| ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1511]) ).
thf(1657,plain,
! [SV117: nat,SV364: set_nat,SV237: nat,SV320: nat > set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ ( SV320 @ SV237 ) @ SV364 ) )
= $true )
| ( ( ~ ! [SY932: nat,SY933: nat] :
( ~ ( ord_less_eq_nat @ SY932 @ SY933 )
| ( ord_less_eq_set_nat @ ( SV320 @ SY932 ) @ ( SV320 @ SY933 ) ) )
| ( ord_less_eq_set_nat @ ( SV320 @ SV117 ) @ SV364 ) )
= $true )
| ( ( ord_less_eq_nat @ SV117 @ SV237 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1512]) ).
thf(1658,plain,
! [SV118: nat,SV238: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV238 @ one_one_nat ) )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV118 @ SV238 ) @ one_one_nat )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV238 )
= $false )
| ( ( ord_less_eq_nat @ SV118 @ one_one_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1513]) ).
thf(1659,plain,
! [SV119: nat,SV239: nat > nat,SV365: nat,SV321: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV321 @ SV365 ) )
= $true )
| ( ( ~ ! [SY830: nat,SY831: nat] :
( ~ ( ord_less_eq_nat @ SY830 @ SY831 )
| ( ord_less_eq_nat @ ( SV239 @ SY830 ) @ ( SV239 @ SY831 ) ) )
| ( ord_less_eq_nat @ SV119 @ ( SV239 @ SV365 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV119 @ ( SV239 @ SV321 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1514]) ).
thf(1660,plain,
! [SV366: nat,SV243: nat] :
( ( ( ( SV243 = SV366 )
| ~ ( ~ ( ord_less_eq_nat @ SV243 @ SV366 )
| ~ ( ord_less_eq_nat @ SV366 @ SV243 ) ) )
= $false )
| ( ( ~ ( ( SV243 != SV366 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV243 @ SV366 )
| ~ ( ord_less_eq_nat @ SV366 @ SV243 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1516]) ).
thf(1661,plain,
! [SV125: nat,SV324: nat,SV244: nat] :
( ( ( ord_less_eq_nat @ SV244 @ SV324 )
= $false )
| ( ( ord_less_eq_nat @ SV125 @ SV324 )
= $true )
| ( ( ord_less_eq_nat @ SV125 @ SV244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1517]) ).
thf(1662,plain,
! [SV245: nat,SV126: nat] :
( ( ( SV126 = SV245 )
= $true )
| ( ( ord_less_nat @ SV126 @ SV245 )
= $true )
| ( ( ord_less_eq_nat @ SV126 @ SV245 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1518]) ).
thf(1663,plain,
! [SV127: set_nat,SV246: nat > set_nat,SV367: nat,SV325: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV325 @ SV367 ) )
= $true )
| ( ( ~ ! [SY838: nat,SY839: nat] :
( ~ ( ord_less_eq_nat @ SY838 @ SY839 )
| ( ord_less_eq_set_nat @ ( SV246 @ SY838 ) @ ( SV246 @ SY839 ) ) )
| ( ord_less_eq_set_nat @ SV127 @ ( SV246 @ SV367 ) ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV127 @ ( SV246 @ SV325 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1519]) ).
thf(1664,plain,
! [SV128: nat,SV247: nat,SV368: nat,SV326: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV326 @ SV368 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV247 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV326 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV128 @ SV326 ) @ ( times_times_nat @ SV247 @ SV368 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV128 @ SV247 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1520]) ).
thf(1665,plain,
! [SV327: nat,SV248: nat,SV130: nat] :
( ( ( ~ ( ( ( times_times_nat @ SV130 @ SV248 )
= ( times_times_nat @ SV130 @ SV327 ) )
| ( SV248 = SV327 ) )
| ~ ( ( ( times_times_nat @ SV130 @ SV248 )
!= ( times_times_nat @ SV130 @ SV327 ) )
| ( SV248 != SV327 ) ) )
= $true )
| ( ( SV130 = zero_zero_nat )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1521]) ).
thf(1666,plain,
! [SV327: nat,SV248: nat,SV130: nat] :
( ( ( ( ( times_times_nat @ SV130 @ SV248 )
= ( times_times_nat @ SV130 @ SV327 ) )
= ( SV248 = SV327 ) )
= $true )
| ( ( SV130 = zero_zero_nat )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1521]) ).
thf(1667,plain,
! [SV328: nat,SV249: nat,SV131: nat] :
( ( ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV249 )
| ( ord_less_eq_nat @ SV131 @ SV328 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1522]) ).
thf(1668,plain,
! [SV328: nat,SV131: nat,SV249: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV249 )
| ( ord_less_eq_nat @ SV131 @ SV328 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV249 )
| ( ord_less_eq_nat @ SV131 @ SV328 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1522]) ).
thf(1669,plain,
! [SV132: nat,SV369: nat,SV250: nat,SV329: nat > nat] :
( ( ( ( SV329 @ SV250 )
!= SV369 )
= $true )
| ( ( ~ ! [SY942: nat,SY943: nat] :
( ~ ( ord_less_eq_nat @ SY942 @ SY943 )
| ( ord_less_eq_nat @ ( SV329 @ SY942 ) @ ( SV329 @ SY943 ) ) )
| ( ord_less_eq_nat @ ( SV329 @ SV132 ) @ SV369 ) )
= $true )
| ( ( ord_less_eq_nat @ SV132 @ SV250 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1523]) ).
thf(1670,plain,
! [SV133: nat,SV330: nat,SV251: nat] :
( ( ( ord_less_eq_nat @ SV251 @ SV330 )
= $false )
| ( ( ord_less_eq_nat @ SV133 @ SV330 )
= $true )
| ( ( ord_less_eq_nat @ SV133 @ SV251 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1524]) ).
thf(1671,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV331 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV134 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1525]) ).
thf(1672,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV331 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV134 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1526]) ).
thf(1673,plain,
! [SV332: nat,SV253: nat,SV135: nat] :
( ( ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 )
| ~ ( ord_less_nat @ SV253 @ SV332 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1527]) ).
thf(1674,plain,
! [SV332: nat,SV253: nat,SV135: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 )
| ~ ( ord_less_nat @ SV253 @ SV332 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 )
| ~ ( ord_less_nat @ SV253 @ SV332 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1527]) ).
thf(1675,plain,
! [SV254: nat,SV136: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV136 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV254 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1528]) ).
thf(1676,plain,
! [SV254: nat,SV136: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV136 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV254 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV136 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV254 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1529]) ).
thf(1677,plain,
! [SV256: nat,SV138: nat,SV333: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV333 )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV333 @ SV138 ) @ ( times_times_nat @ SV333 @ SV256 ) )
= $true )
| ( ( ord_less_eq_nat @ SV138 @ SV256 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1531]) ).
thf(1678,plain,
! [SV258: nat,SV140: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV140 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV258 @ zero_zero_nat ) )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV140 @ SV258 ) @ zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1532]) ).
thf(1679,plain,
! [SV258: nat,SV140: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV140 @ zero_zero_nat ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV258 ) )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV140 @ SV258 ) @ zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1533]) ).
thf(1680,plain,
! [SV370: nat,SV259: nat] :
( ( ( ( ord_less_nat @ SV259 @ SV370 )
| ~ ( ~ ( ord_less_eq_nat @ SV259 @ SV370 )
| ~ ( ( SV259 != SV370 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV259 @ SV370 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV259 @ SV370 )
| ~ ( ( SV259 != SV370 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1534]) ).
thf(1681,plain,
! [SV142: set_nat,SV260: nat > nat,SV335: nat > nat] :
( ( ( ~ ( member_nat @ ( sK7_SY944 @ SV335 @ SV260 @ SV142 ) @ SV142 ) )
= $false )
| ( ( ord_less_eq_nat @ ( groups1842438620at_nat @ SV260 @ SV142 ) @ ( groups1842438620at_nat @ SV335 @ SV142 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1535]) ).
thf(1682,plain,
! [SV142: set_nat,SV335: nat > nat,SV260: nat > nat] :
( ( ( ord_less_eq_nat @ ( SV260 @ ( sK7_SY944 @ SV335 @ SV260 @ SV142 ) ) @ ( SV335 @ ( sK7_SY944 @ SV335 @ SV260 @ SV142 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( groups1842438620at_nat @ SV260 @ SV142 ) @ ( groups1842438620at_nat @ SV335 @ SV142 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1535]) ).
thf(1683,plain,
! [SV263: nat,SV145: nat] :
( ( ( ( one_one_nat
!= ( times_times_nat @ SV145 @ SV263 ) )
| ~ ~ ( ( SV145 != one_one_nat )
| ( SV263 != one_one_nat ) ) )
= $false )
| ( ( one_one_nat
= ( times_times_nat @ SV145 @ SV263 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1536]) ).
thf(1684,plain,
! [SV263: nat,SV145: nat] :
( ( ( ( SV145 != one_one_nat )
| ( SV263 != one_one_nat ) )
= $true )
| ( ( ~ ( ( one_one_nat
!= ( times_times_nat @ SV145 @ SV263 ) )
| ~ ~ ( ( SV145 != one_one_nat )
| ( SV263 != one_one_nat ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1537]) ).
thf(1685,plain,
! [SV336: nat,SV146: nat,SV264: nat] :
( ( ( ~ ( ( ( times_times_nat @ SV264 @ SV146 )
= ( times_times_nat @ SV336 @ SV146 ) )
| ( SV264 = SV336 ) )
| ~ ( ( ( times_times_nat @ SV264 @ SV146 )
!= ( times_times_nat @ SV336 @ SV146 ) )
| ( SV264 != SV336 ) ) )
= $true )
| ( ( SV146 = zero_zero_nat )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1538]) ).
thf(1686,plain,
! [SV336: nat,SV146: nat,SV264: nat] :
( ( ( ( ( times_times_nat @ SV264 @ SV146 )
= ( times_times_nat @ SV336 @ SV146 ) )
= ( SV264 = SV336 ) )
= $true )
| ( ( SV146 = zero_zero_nat )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1538]) ).
thf(1687,plain,
! [SV147: nat] :
( ( ( ~ ( ( SV147 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV147 ) )
= $false )
| ( ( SV147 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1539]) ).
thf(1688,plain,
! [SV147: nat] :
( ( ( ~ ( ( SV147 != zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV147 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1540]) ).
thf(1689,plain,
! [SV147: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV147 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV147 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1540]) ).
thf(1690,plain,
! [SV265: nat,SV148: nat > nat] :
( ( ( ( SV148 @ ( sK4_SY856 @ SV265 @ SV148 ) )
!= zero_zero_nat )
= $true )
| ( ( ( ( groups1842438620at_nat
@ ^ [SY685: nat] : ( times_times_nat @ ( SV148 @ SY685 ) @ SY685 )
@ ( set_ord_atMost_nat @ SV265 ) )
!= SV265 )
| ( number1551313001itions @ SV148 @ SV265 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1541]) ).
thf(1691,plain,
! [SV148: nat > nat,SV265: nat] :
( ( ( ~ ( ord_less_eq_nat @ one_one_nat @ ( sK4_SY856 @ SV265 @ SV148 ) )
| ~ ( ord_less_eq_nat @ ( sK4_SY856 @ SV265 @ SV148 ) @ SV265 ) )
= $true )
| ( ( ( ( groups1842438620at_nat
@ ^ [SY685: nat] : ( times_times_nat @ ( SV148 @ SY685 ) @ SY685 )
@ ( set_ord_atMost_nat @ SV265 ) )
!= SV265 )
| ( number1551313001itions @ SV148 @ SV265 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1542]) ).
thf(1692,plain,
! [SV266: nat,SV149: nat] :
( ( ( ( ( times_times_nat @ SV149 @ SV266 )
!= one_one_nat )
| ~ ~ ( ( SV149 != one_one_nat )
| ( SV266 != one_one_nat ) ) )
= $false )
| ( ( ( times_times_nat @ SV149 @ SV266 )
= one_one_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1543]) ).
thf(1693,plain,
! [SV266: nat,SV149: nat] :
( ( ( ( SV149 != one_one_nat )
| ( SV266 != one_one_nat ) )
= $true )
| ( ( ~ ( ( ( times_times_nat @ SV149 @ SV266 )
!= one_one_nat )
| ~ ~ ( ( SV149 != one_one_nat )
| ( SV266 != one_one_nat ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1544]) ).
thf(1694,plain,
! [SV150: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV150 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV150 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1545]) ).
thf(1695,plain,
! [SV150: nat] :
( ( ( ~ ( ( SV150 != zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV150 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1545]) ).
thf(1696,plain,
! [SV150: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV150 )
| ~ ( ( SV150 != zero_zero_nat ) ) )
= $false )
| ( ( SV150 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1546]) ).
thf(1697,plain,
! [SV151: set_nat,SV371: nat,SV267: set_nat,SV337: set_nat > nat] :
( ( ( ( SV337 @ SV267 )
!= SV371 )
= $true )
| ( ( ~ ! [SY946: set_nat,SY947: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY946 @ SY947 )
| ( ord_less_eq_nat @ ( SV337 @ SY946 ) @ ( SV337 @ SY947 ) ) )
| ( ord_less_eq_nat @ ( SV337 @ SV151 ) @ SV371 ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV151 @ SV267 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1547]) ).
thf(1698,plain,
! [SV268: nat,SV152: nat,SV338: nat] :
( ( ( ord_less_nat @ SV338 @ SV152 )
= $false )
| ( ( ord_less_nat @ SV338 @ SV268 )
= $true )
| ( ( ord_less_eq_nat @ SV152 @ SV268 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1548]) ).
thf(1699,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV153 )
| ( ord_less_eq_nat @ SV269 @ SV339 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1549]) ).
thf(1700,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV153 )
| ( ord_less_eq_nat @ SV269 @ SV339 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV153 )
| ( ord_less_eq_nat @ SV269 @ SV339 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1549]) ).
thf(1701,plain,
! [SV155: nat,SV340: nat,SV271: nat] :
( ( ( ord_less_eq_nat @ SV271 @ SV340 )
= $false )
| ( ( ord_less_nat @ SV155 @ SV340 )
= $true )
| ( ( ord_less_nat @ SV155 @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1551]) ).
thf(1702,plain,
! [SV156: nat,SV2: nat] :
( ( ( ~ ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ SV2 ) @ ( set_ord_atMost_nat @ SV156 ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ SV2 ) @ ( set_ord_atMost_nat @ SV156 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1552]) ).
thf(1703,plain,
! [SV156: nat,SV2: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV2 @ SV156 ) )
= $false )
| ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ SV2 ) @ ( set_ord_atMost_nat @ SV156 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1552]) ).
thf(1704,plain,
! [SV156: nat,SV2: nat] :
( ( ( ~ ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ SV2 ) @ ( set_ord_atMost_nat @ SV156 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV2 @ SV156 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1553]) ).
thf(1705,plain,
! [SV156: nat,SV2: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV2 @ SV156 ) )
= $false )
| ( ( ord_less_eq_nat @ SV2 @ SV156 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1553]) ).
thf(1706,plain,
! [SV157: nat,SV3: nat] :
( ( ( ~ ( member_nat @ SV3 @ ( set_ord_atMost_nat @ SV157 ) ) )
= $false )
| ( ( member_nat @ SV3 @ ( set_ord_atMost_nat @ SV157 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1554]) ).
thf(1707,plain,
! [SV157: nat,SV3: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV3 @ SV157 ) )
= $false )
| ( ( member_nat @ SV3 @ ( set_ord_atMost_nat @ SV157 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1554]) ).
thf(1708,plain,
! [SV157: nat,SV3: nat] :
( ( ( ~ ( member_nat @ SV3 @ ( set_ord_atMost_nat @ SV157 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV3 @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1555]) ).
thf(1709,plain,
! [SV157: nat,SV3: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV3 @ SV157 ) )
= $false )
| ( ( ord_less_eq_nat @ SV3 @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1555]) ).
thf(1710,plain,
! [SV158: nat,SV4: nat] :
( ( ( ( set_ord_atMost_nat @ SV4 )
!= ( set_ord_atMost_nat @ SV158 ) )
= $false )
| ( ( ( set_ord_atMost_nat @ SV4 )
= ( set_ord_atMost_nat @ SV158 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1556]) ).
thf(1711,plain,
! [SV158: nat,SV4: nat] :
( ( ( SV4 != SV158 )
= $false )
| ( ( ( set_ord_atMost_nat @ SV4 )
= ( set_ord_atMost_nat @ SV158 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1556]) ).
thf(1712,plain,
! [SV158: nat,SV4: nat] :
( ( ( ( set_ord_atMost_nat @ SV4 )
!= ( set_ord_atMost_nat @ SV158 ) )
= $false )
| ( ( SV4 = SV158 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1557]) ).
thf(1713,plain,
! [SV158: nat,SV4: nat] :
( ( ( SV4 != SV158 )
= $false )
| ( ( SV4 = SV158 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1557]) ).
thf(1714,plain,
! [SV272: nat,SV159: nat,SV5: nat] :
( ( ( ( ( times_times_nat @ SV5 @ SV159 )
!= ( times_times_nat @ SV272 @ SV159 ) )
| ~ ( ( SV159 = zero_zero_nat )
| ( SV5 = SV272 ) ) )
= $false )
| ( ( ( times_times_nat @ SV5 @ SV159 )
= ( times_times_nat @ SV272 @ SV159 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1558]) ).
thf(1715,plain,
! [SV272: nat,SV5: nat,SV159: nat] :
( ( ( SV159 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV5 @ SV159 )
!= ( times_times_nat @ SV272 @ SV159 ) )
| ~ ( ( SV159 = zero_zero_nat )
| ( SV5 = SV272 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1559]) ).
thf(1716,plain,
! [SV159: nat,SV272: nat,SV5: nat] :
( ( ( SV5 = SV272 )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV5 @ SV159 )
!= ( times_times_nat @ SV272 @ SV159 ) )
| ~ ( ( SV159 = zero_zero_nat )
| ( SV5 = SV272 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1559]) ).
thf(1717,plain,
! [SV273: nat,SV160: nat,SV6: nat] :
( ( ( ( ( times_times_nat @ SV6 @ SV160 )
!= ( times_times_nat @ SV6 @ SV273 ) )
| ~ ( ( SV6 = zero_zero_nat )
| ( SV160 = SV273 ) ) )
= $false )
| ( ( ( times_times_nat @ SV6 @ SV160 )
= ( times_times_nat @ SV6 @ SV273 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1560]) ).
thf(1718,plain,
! [SV273: nat,SV160: nat,SV6: nat] :
( ( ( SV6 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV6 @ SV160 )
!= ( times_times_nat @ SV6 @ SV273 ) )
| ~ ( ( SV6 = zero_zero_nat )
| ( SV160 = SV273 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1561]) ).
thf(1719,plain,
! [SV6: nat,SV273: nat,SV160: nat] :
( ( ( SV160 = SV273 )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV6 @ SV160 )
!= ( times_times_nat @ SV6 @ SV273 ) )
| ~ ( ( SV6 = zero_zero_nat )
| ( SV160 = SV273 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1561]) ).
thf(1720,plain,
! [SV161: nat,SV7: nat] :
( ( ( ( times_times_nat @ SV7 @ SV161 )
!= zero_zero_nat )
= $false )
| ( ( ( times_times_nat @ SV7 @ SV161 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1562]) ).
thf(1721,plain,
! [SV161: nat,SV7: nat] :
( ( ( ~ ( ( SV7 = zero_zero_nat )
| ( SV161 = zero_zero_nat ) ) )
= $false )
| ( ( ( times_times_nat @ SV7 @ SV161 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1562]) ).
thf(1722,plain,
! [SV161: nat,SV7: nat] :
( ( ( ( ( times_times_nat @ SV7 @ SV161 )
!= zero_zero_nat )
| ~ ( ( SV7 = zero_zero_nat )
| ( SV161 = zero_zero_nat ) ) )
= $false )
| ( ( SV7 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1563]) ).
thf(1723,plain,
! [SV161: nat,SV7: nat] :
( ( ( ( ( times_times_nat @ SV7 @ SV161 )
!= zero_zero_nat )
| ~ ( ( SV7 = zero_zero_nat )
| ( SV161 = zero_zero_nat ) ) )
= $false )
| ( ( SV161 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1564]) ).
thf(1724,plain,
! [SV274: nat,SV162: nat,SV12: nat] :
( ( ( ( ( times_times_nat @ SV12 @ SV162 )
!= ( times_times_nat @ SV274 @ SV162 ) )
| ~ ( ( SV12 = SV274 )
| ( SV162 = zero_zero_nat ) ) )
= $false )
| ( ( ( times_times_nat @ SV12 @ SV162 )
= ( times_times_nat @ SV274 @ SV162 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1565]) ).
thf(1725,plain,
! [SV162: nat,SV274: nat,SV12: nat] :
( ( ( SV12 = SV274 )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV12 @ SV162 )
!= ( times_times_nat @ SV274 @ SV162 ) )
| ~ ( ( SV12 = SV274 )
| ( SV162 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1566]) ).
thf(1726,plain,
! [SV274: nat,SV12: nat,SV162: nat] :
( ( ( SV162 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV12 @ SV162 )
!= ( times_times_nat @ SV274 @ SV162 ) )
| ~ ( ( SV12 = SV274 )
| ( SV162 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1566]) ).
thf(1727,plain,
! [SV275: nat,SV163: nat,SV13: nat] :
( ( ( ( ( times_times_nat @ SV13 @ SV163 )
!= ( times_times_nat @ SV13 @ SV275 ) )
| ~ ( ( SV163 = SV275 )
| ( SV13 = zero_zero_nat ) ) )
= $false )
| ( ( ( times_times_nat @ SV13 @ SV163 )
= ( times_times_nat @ SV13 @ SV275 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1567]) ).
thf(1728,plain,
! [SV13: nat,SV275: nat,SV163: nat] :
( ( ( SV163 = SV275 )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV13 @ SV163 )
!= ( times_times_nat @ SV13 @ SV275 ) )
| ~ ( ( SV163 = SV275 )
| ( SV13 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1568]) ).
thf(1729,plain,
! [SV275: nat,SV163: nat,SV13: nat] :
( ( ( SV13 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV13 @ SV163 )
!= ( times_times_nat @ SV13 @ SV275 ) )
| ~ ( ( SV163 = SV275 )
| ( SV13 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1568]) ).
thf(1730,plain,
! [SV164: nat,SV15: nat] :
( ( ( ( times_times_nat @ SV15 @ SV164 )
!= zero_zero_nat )
= $false )
| ( ( ( times_times_nat @ SV15 @ SV164 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1569]) ).
thf(1731,plain,
! [SV164: nat,SV15: nat] :
( ( ( ~ ( ( SV15 = zero_zero_nat )
| ( SV164 = zero_zero_nat ) ) )
= $false )
| ( ( ( times_times_nat @ SV15 @ SV164 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1569]) ).
thf(1732,plain,
! [SV164: nat,SV15: nat] :
( ( ( ( ( times_times_nat @ SV15 @ SV164 )
!= zero_zero_nat )
| ~ ( ( SV15 = zero_zero_nat )
| ( SV164 = zero_zero_nat ) ) )
= $false )
| ( ( SV15 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1570]) ).
thf(1733,plain,
! [SV164: nat,SV15: nat] :
( ( ( ( ( times_times_nat @ SV15 @ SV164 )
!= zero_zero_nat )
| ~ ( ( SV15 = zero_zero_nat )
| ( SV164 = zero_zero_nat ) ) )
= $false )
| ( ( SV164 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1571]) ).
thf(1734,plain,
! [SV19: nat] :
( ( ( ord_less_eq_nat @ SV19 @ zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV19 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1572]) ).
thf(1735,plain,
! [SV19: nat] :
( ( ( SV19 = zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV19 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1573]) ).
thf(1736,plain,
! [SV19: nat] :
( ( ( ord_less_eq_nat @ SV19 @ zero_zero_nat )
= $true )
| ( ( SV19 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1574]) ).
thf(1737,plain,
! [SV19: nat] :
( ( ( SV19 = zero_zero_nat )
= $true )
| ( ( SV19 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1575]) ).
thf(1738,plain,
! [SV20: nat] :
( ( ( ord_less_eq_nat @ SV20 @ zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV20 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1576]) ).
thf(1739,plain,
! [SV20: nat] :
( ( ( SV20 = zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV20 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1577]) ).
thf(1740,plain,
! [SV20: nat] :
( ( ( ord_less_eq_nat @ SV20 @ zero_zero_nat )
= $true )
| ( ( SV20 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1578]) ).
thf(1741,plain,
! [SV20: nat] :
( ( ( SV20 = zero_zero_nat )
= $true )
| ( ( SV20 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1579]) ).
thf(1742,plain,
! [SV35: nat] :
( ( ( ord_less_eq_nat @ SV35 @ zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV35 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1580]) ).
thf(1743,plain,
! [SV35: nat] :
( ( ( SV35 = zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV35 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1581]) ).
thf(1744,plain,
! [SV35: nat] :
( ( ( ord_less_eq_nat @ SV35 @ zero_zero_nat )
= $true )
| ( ( SV35 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1582]) ).
thf(1745,plain,
! [SV35: nat] :
( ( ( SV35 = zero_zero_nat )
= $true )
| ( ( SV35 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1583]) ).
thf(1746,plain,
! [SV280: nat,SV173: nat,SV37: nat] :
( ( ( ( ( times_times_nat @ SV37 @ SV173 )
!= ( times_times_nat @ SV37 @ SV280 ) )
| ~ ( ( SV37 = zero_zero_nat )
| ( SV173 = SV280 ) ) )
= $false )
| ( ( ( times_times_nat @ SV37 @ SV173 )
= ( times_times_nat @ SV37 @ SV280 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1584]) ).
thf(1747,plain,
! [SV280: nat,SV173: nat,SV37: nat] :
( ( ( SV37 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV37 @ SV173 )
!= ( times_times_nat @ SV37 @ SV280 ) )
| ~ ( ( SV37 = zero_zero_nat )
| ( SV173 = SV280 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1585]) ).
thf(1748,plain,
! [SV37: nat,SV280: nat,SV173: nat] :
( ( ( SV173 = SV280 )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV37 @ SV173 )
!= ( times_times_nat @ SV37 @ SV280 ) )
| ~ ( ( SV37 = zero_zero_nat )
| ( SV173 = SV280 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1585]) ).
thf(1749,plain,
! [SV42: nat] :
( ( ( zero_zero_nat = SV42 )
= $true )
| ( ( zero_zero_nat = SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1586]) ).
thf(1750,plain,
! [SV42: nat] :
( ( ( SV42 = zero_zero_nat )
= $true )
| ( ( zero_zero_nat = SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1587]) ).
thf(1751,plain,
! [SV42: nat] :
( ( ( zero_zero_nat = SV42 )
= $true )
| ( ( SV42 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1588]) ).
thf(1752,plain,
! [SV42: nat] :
( ( ( SV42 = zero_zero_nat )
= $true )
| ( ( SV42 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1589]) ).
thf(1753,plain,
! [SV47: nat] :
( ( ( one_one_nat = SV47 )
= $true )
| ( ( one_one_nat = SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1590]) ).
thf(1754,plain,
! [SV47: nat] :
( ( ( SV47 = one_one_nat )
= $true )
| ( ( one_one_nat = SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1591]) ).
thf(1755,plain,
! [SV47: nat] :
( ( ( one_one_nat = SV47 )
= $true )
| ( ( SV47 = one_one_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1592]) ).
thf(1756,plain,
! [SV47: nat] :
( ( ( SV47 = one_one_nat )
= $true )
| ( ( SV47 = one_one_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1593]) ).
thf(1757,plain,
! [SV50: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV50 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV50 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1594]) ).
thf(1758,plain,
! [SV50: nat] :
( ( ( SV50 != zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV50 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1594]) ).
thf(1759,plain,
! [SV50: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV50 ) )
= $true )
| ( ( SV50 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1595]) ).
thf(1760,plain,
! [SV50: nat] :
( ( ( SV50 = zero_zero_nat )
= $true )
| ( ( SV50 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1596]) ).
thf(1761,plain,
! [SV51: nat] :
( ( ( ord_less_nat @ SV51 @ one_one_nat )
= $true )
| ( ( ord_less_nat @ SV51 @ one_one_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1597]) ).
thf(1762,plain,
! [SV51: nat] :
( ( ( SV51 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV51 @ one_one_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1598]) ).
thf(1763,plain,
! [SV51: nat] :
( ( ( ord_less_nat @ SV51 @ one_one_nat )
= $true )
| ( ( SV51 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1599]) ).
thf(1764,plain,
! [SV51: nat] :
( ( ( SV51 = zero_zero_nat )
= $true )
| ( ( SV51 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1600]) ).
thf(1765,plain,
! [SV343: nat,SV179: nat] :
( ( ( ord_less_eq_nat @ SV179 @ SV343 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV179 @ SV343 )
| ~ ( ( ord_less_nat @ SV179 @ SV343 )
| ( SV179 = SV343 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1601]) ).
thf(1766,plain,
! [SV343: nat,SV179: nat] :
( ( ( ( ord_less_nat @ SV179 @ SV343 )
| ( SV179 = SV343 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV179 @ SV343 )
| ~ ( ( ord_less_nat @ SV179 @ SV343 )
| ( SV179 = SV343 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1601]) ).
thf(1767,plain,
! [SV54: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV54 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV54 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1602]) ).
thf(1768,plain,
! [SV54: nat] :
( ( ( SV54 != zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV54 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1602]) ).
thf(1769,plain,
! [SV54: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV54 ) )
= $true )
| ( ( SV54 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1603]) ).
thf(1770,plain,
! [SV54: nat] :
( ( ( SV54 = zero_zero_nat )
= $true )
| ( ( SV54 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1604]) ).
thf(1771,plain,
! [SV344: nat,SV180: nat] :
( ( ( ord_less_eq_nat @ SV180 @ SV344 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV180 @ SV344 )
| ~ ( ( ord_less_nat @ SV180 @ SV344 )
| ( SV344 = SV180 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1605]) ).
thf(1772,plain,
! [SV344: nat,SV180: nat] :
( ( ( ( ord_less_nat @ SV180 @ SV344 )
| ( SV344 = SV180 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV180 @ SV344 )
| ~ ( ( ord_less_nat @ SV180 @ SV344 )
| ( SV344 = SV180 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1605]) ).
thf(1773,plain,
! [SV345: nat,SV181: nat] :
( ( ( ord_less_eq_nat @ SV181 @ SV345 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV181 @ SV345 )
| ~ ( ( ord_less_nat @ SV181 @ SV345 )
| ( SV181 = SV345 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1606]) ).
thf(1774,plain,
! [SV345: nat,SV181: nat] :
( ( ( ( ord_less_nat @ SV181 @ SV345 )
| ( SV181 = SV345 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV181 @ SV345 )
| ~ ( ( ord_less_nat @ SV181 @ SV345 )
| ( SV181 = SV345 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1606]) ).
thf(1775,plain,
! [SV375: nat > nat,SV372: nat > nat,SV346: set_nat,SV288: nat > nat,SV182: nat > nat,SV60: set_nat] :
( ( ( ! [SY876: nat] :
( ~ ( member_nat @ SY876 @ SV60 )
| ( ( SV182 @ ( SV288 @ SY876 ) )
= SY876 ) ) )
= $false )
| ( ( ~ ! [SY953: nat] :
( ~ ( member_nat @ SY953 @ SV60 )
| ( member_nat @ ( SV288 @ SY953 ) @ SV346 ) )
| ~ ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) )
| ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1607]) ).
thf(1776,plain,
! [SV62: nat,SV184: nat] :
( ( ( SV184 = zero_zero_nat )
= $true )
| ( ( ( times_times_nat @ SV62 @ SV184 )
!= zero_zero_nat )
= $true )
| ( ( SV62 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1608]) ).
thf(1777,plain,
! [SV347: nat,SV186: nat] :
( ( ( SV186 = SV347 )
= $false )
| ( ( ~ ( ( SV186 != SV347 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV186 @ SV347 )
| ~ ( ord_less_eq_nat @ SV347 @ SV186 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1610]) ).
thf(1778,plain,
! [SV347: nat,SV186: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV186 @ SV347 )
| ~ ( ord_less_eq_nat @ SV347 @ SV186 ) ) )
= $false )
| ( ( ~ ( ( SV186 != SV347 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV186 @ SV347 )
| ~ ( ord_less_eq_nat @ SV347 @ SV186 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1610]) ).
thf(1779,plain,
! [SV69: set_nat,SV348: nat,SV191: set_nat,SV292: set_nat > nat] :
( ( ( ord_less_eq_nat @ ( SV292 @ SV191 ) @ SV348 )
= $false )
| ( ( ~ ! [SY882: set_nat,SY883: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY882 @ SY883 )
| ( ord_less_eq_nat @ ( SV292 @ SY882 ) @ ( SV292 @ SY883 ) ) )
| ( ord_less_eq_nat @ ( SV292 @ SV69 ) @ SV348 ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV69 @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1612]) ).
thf(1780,plain,
! [SV293: nat,SV192: nat,SV70: nat > $o] :
( ( ( ~ ( SV70 @ ( sK12_SY884 @ SV192 @ SV293 @ SV70 ) )
| ( ord_less_eq_nat @ ( sK12_SY884 @ SV192 @ SV293 @ SV70 ) @ SV293 ) )
= $false )
| ( ( ~ ! [SY505: nat] :
( ~ ( SV70 @ SY505 )
| ~ ! [SY506: nat] :
( ~ ( SV70 @ SY506 )
| ( ord_less_eq_nat @ SY506 @ SY505 ) ) ) )
= $true )
| ( ( SV70 @ SV192 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1613]) ).
thf(1781,plain,
! [SV193: nat,SV71: nat,SV349: nat,SV294: nat] :
( ( ( ord_less_eq_nat @ SV294 @ SV349 )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV71 @ SV294 ) @ ( times_times_nat @ SV193 @ SV349 ) )
= $true )
| ( ( ord_less_eq_nat @ SV71 @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1614]) ).
thf(1782,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( number1551313001itions @ SV194 @ SV350 )
= $false )
| ( ( ~ ( ~ ( number1551313001itions @ SV194 @ SV350 )
| ~ ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1615]) ).
thf(1783,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) )
= $false )
| ( ( ~ ( ~ ( number1551313001itions @ SV194 @ SV350 )
| ~ ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1615]) ).
thf(1784,plain,
! [SV74: nat,SV351: set_nat,SV196: nat,SV296: nat > set_nat] :
( ( ( ( SV296 @ SV196 )
= SV351 )
= $false )
| ( ( ~ ! [SY891: nat,SY892: nat] :
( ~ ( ord_less_eq_nat @ SY891 @ SY892 )
| ( ord_less_eq_set_nat @ ( SV296 @ SY891 ) @ ( SV296 @ SY892 ) ) )
| ( ord_less_eq_set_nat @ ( SV296 @ SV74 ) @ SV351 ) )
= $true )
| ( ( ord_less_eq_nat @ SV74 @ SV196 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1616]) ).
thf(1785,plain,
! [SV76: nat > nat > $o,SV198: nat,SV298: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK5_SY523 @ SV298 @ SV198 @ SV76 ) @ ( sK8_SY1011 @ SV76 @ SV198 @ SV298 ) ) )
= $false )
| ( ( ~ ! [SY525: nat,SY526: nat] :
( ~ ( SV76 @ SY526 @ SY525 )
| ( SV76 @ SY525 @ SY526 ) )
| ( SV76 @ SV198 @ SV298 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1618]) ).
thf(1786,plain,
! [SV198: nat,SV298: nat,SV76: nat > nat > $o] :
( ( ( SV76 @ ( sK5_SY523 @ SV298 @ SV198 @ SV76 ) @ ( sK8_SY1011 @ SV76 @ SV198 @ SV298 ) )
= $false )
| ( ( ~ ! [SY525: nat,SY526: nat] :
( ~ ( SV76 @ SY526 @ SY525 )
| ( SV76 @ SY525 @ SY526 ) )
| ( SV76 @ SV198 @ SV298 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1618]) ).
thf(1787,plain,
! [SV202: nat,SV80: nat] :
( ( ( SV80 != zero_zero_nat )
= $true )
| ( ( ( times_times_nat @ SV80 @ SV202 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1621]) ).
thf(1788,plain,
! [SV80: nat,SV202: nat] :
( ( ( SV202 != zero_zero_nat )
= $true )
| ( ( ( times_times_nat @ SV80 @ SV202 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1622]) ).
thf(1789,plain,
! [SV205: nat,SV83: nat,SV352: nat,SV303: nat] :
( ( ( ord_less_eq_nat @ SV303 @ SV352 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV83 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV303 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV83 @ SV303 ) @ ( times_times_nat @ SV205 @ SV352 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV83 @ SV205 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1625]) ).
thf(1790,plain,
! [SV84: nat,SV206: nat] :
( ( ( ord_less_eq_nat @ SV206 @ SV84 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV206 @ SV84 )
| ( SV206 != SV84 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV84 @ SV206 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1626]) ).
thf(1791,plain,
! [SV84: nat,SV206: nat] :
( ( ( SV206 = SV84 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV206 @ SV84 )
| ( SV206 != SV84 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV84 @ SV206 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1626]) ).
thf(1792,plain,
! [SV85: set_nat,SV207: set_nat,SV304: nat > nat,SV353: nat > nat,SV373: nat > nat] :
( ( ( ~ ( member_nat @ ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) @ SV85 )
| ~ ! [SY1016: nat] :
~ ~ ( ~ ~ ( ~ ( member_nat @ SY1016 @ SV207 )
| ( ( SV304 @ SY1016 )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) ) )
| ~ ! [SY1017: nat] :
( ~ ~ ( ~ ( member_nat @ SY1017 @ SV207 )
| ( ( SV304 @ SY1017 )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) ) )
| ( SY1017 = SY1016 ) ) ) )
= $false )
| ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) )
| ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1627]) ).
thf(1793,plain,
! [SV86: set_nat,SV208: nat > set_nat,SV354: nat,SV305: nat] :
( ( ( ord_less_eq_nat @ SV305 @ SV354 )
= $false )
| ( ( ~ ! [SY776: nat,SY777: nat] :
( ~ ( ord_less_eq_nat @ SY776 @ SY777 )
| ( ord_less_eq_set_nat @ ( SV208 @ SY776 ) @ ( SV208 @ SY777 ) ) )
| ( ord_less_eq_set_nat @ SV86 @ ( SV208 @ SV354 ) ) )
= $true )
| ( ( SV86
= ( SV208 @ SV305 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1628]) ).
thf(1794,plain,
! [SV87: nat,SV209: set_nat > nat,SV355: set_nat,SV306: set_nat] :
( ( ( ord_less_eq_set_nat @ SV306 @ SV355 )
= $false )
| ( ( ~ ! [SY780: set_nat,SY781: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY780 @ SY781 )
| ( ord_less_eq_nat @ ( SV209 @ SY780 ) @ ( SV209 @ SY781 ) ) )
| ( ord_less_eq_nat @ SV87 @ ( SV209 @ SV355 ) ) )
= $true )
| ( ( SV87
= ( SV209 @ SV306 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1629]) ).
thf(1795,plain,
! [SV88: nat] :
( ( ( ~ ( ( SV88 != zero_zero_nat ) ) )
= $false )
| ( ( SV88 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1630]) ).
thf(1796,plain,
! [SV88: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV88 ) )
= $false )
| ( ( SV88 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1630]) ).
thf(1797,plain,
! [SV88: nat] :
( ( ( SV88 != zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1631]) ).
thf(1798,plain,
! [SV88: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV88 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1632]) ).
thf(1799,plain,
( ( ( ! [SX0: nat] :
( ~ ( ( ( p @ SX0 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SX0 )
| ~ ( ord_less_eq_nat @ SX0 @ zero_zero_nat ) ) ) )
= $true )
| ( ( p
= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1633]) ).
thf(1800,plain,
( ( ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
= zero_zero_nat )
= $true )
| ( ( p
= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1634]) ).
thf(1801,plain,
( ( ( ~ ! [SX0: nat] :
( ~ ( ( ( p @ SX0 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SX0 )
| ~ ( ord_less_eq_nat @ SX0 @ zero_zero_nat ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
!= zero_zero_nat )
= $true )
| ( ( p
!= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1635]) ).
thf(1802,plain,
! [SV356: nat,SV213: nat] :
( ( ( SV213 = SV356 )
= $false )
| ( ( ~ ( ( SV213 != SV356 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV356 @ SV213 )
| ~ ( ord_less_eq_nat @ SV213 @ SV356 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1636]) ).
thf(1803,plain,
! [SV213: nat,SV356: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV356 @ SV213 )
| ~ ( ord_less_eq_nat @ SV213 @ SV356 ) ) )
= $false )
| ( ( ~ ( ( SV213 != SV356 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV356 @ SV213 )
| ~ ( ord_less_eq_nat @ SV213 @ SV356 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1636]) ).
thf(1804,plain,
! [SV93: set_nat,SV357: nat > nat,SV308: nat > nat,SV214: set_nat] :
( ( ( ! [SY972: nat] :
( ~ ( member_nat @ SY972 @ SV214 )
| ( ( SV308 @ SY972 )
= ( SV357 @ SY972 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV308 @ SV93 )
= ( groups1842438620at_nat @ SV357 @ SV214 ) )
= $true )
| ( ( SV93 = SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1637]) ).
thf(1805,plain,
! [SV95: nat,SV216: set_nat > nat,SV358: set_nat,SV309: set_nat] :
( ( ( ord_less_eq_set_nat @ SV309 @ SV358 )
= $false )
| ( ( ~ ! [SY789: set_nat,SY790: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY789 @ SY790 )
| ( ord_less_eq_nat @ ( SV216 @ SY789 ) @ ( SV216 @ SY790 ) ) )
| ( ord_less_eq_nat @ SV95 @ ( SV216 @ SV358 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV95 @ ( SV216 @ SV309 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1638]) ).
thf(1806,plain,
! [SV97: nat > nat,SV218: nat,SV310: nat] :
( ( ( ~ ( ord_less_nat @ ( sK6_SY578 @ SV310 @ SV218 @ SV97 ) @ ( sK9_SY1012 @ SV97 @ SV218 @ SV310 ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV218 @ SV310 )
| ( ord_less_eq_nat @ ( SV97 @ SV218 ) @ ( SV97 @ SV310 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1640]) ).
thf(1807,plain,
! [SV218: nat,SV310: nat,SV97: nat > nat] :
( ( ( ord_less_nat @ ( SV97 @ ( sK6_SY578 @ SV310 @ SV218 @ SV97 ) ) @ ( SV97 @ ( sK9_SY1012 @ SV97 @ SV218 @ SV310 ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV218 @ SV310 )
| ( ord_less_eq_nat @ ( SV97 @ SV218 ) @ ( SV97 @ SV310 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1640]) ).
thf(1808,plain,
! [SV311: nat,SV219: nat,SV98: nat] :
( ( ( ~ ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV219 )
| ~ ( ord_less_nat @ SV98 @ SV311 ) ) )
= $false )
| ( ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1641]) ).
thf(1809,plain,
! [SV311: nat,SV98: nat,SV219: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV219 )
| ~ ( ord_less_nat @ SV98 @ SV311 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV219 )
| ~ ( ord_less_nat @ SV98 @ SV311 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1642]) ).
thf(1810,plain,
! [SV99: nat,SV220: nat > nat,SV359: nat,SV312: nat] :
( ( ( ord_less_eq_nat @ SV312 @ SV359 )
= $false )
| ( ( ~ ! [SY798: nat,SY799: nat] :
( ~ ( ord_less_eq_nat @ SY798 @ SY799 )
| ( ord_less_eq_nat @ ( SV220 @ SY798 ) @ ( SV220 @ SY799 ) ) )
| ( ord_less_eq_nat @ SV99 @ ( SV220 @ SV359 ) ) )
= $true )
| ( ( SV99
= ( SV220 @ SV312 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1643]) ).
thf(1811,plain,
! [SV313: nat,SV221: nat,SV100: nat > $o] :
( ( ( ~ ( SV100 @ ( sK14_SY920 @ SV221 @ SV313 @ SV100 ) )
| ( ord_less_eq_nat @ ( sK14_SY920 @ SV221 @ SV313 @ SV100 ) @ SV313 ) )
= $false )
| ( ( ~ ! [SY590: nat] :
~ ~ ( ~ ( SV100 @ SY590 )
| ~ ! [SY591: nat] :
( ~ ( SV100 @ SY591 )
| ( ord_less_eq_nat @ SY591 @ SY590 ) ) ) )
= $true )
| ( ( SV100 @ SV221 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1644]) ).
thf(1812,plain,
! [SV360: nat,SV222: nat] :
( ( ( ord_less_nat @ SV222 @ SV360 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV222 @ SV360 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV222 @ SV360 )
| ~ ( ( SV360 != SV222 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1645]) ).
thf(1813,plain,
! [SV360: nat,SV222: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV222 @ SV360 )
| ~ ( ( SV360 != SV222 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV222 @ SV360 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV222 @ SV360 )
| ~ ( ( SV360 != SV222 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1645]) ).
thf(1814,plain,
! [SV224: nat,SV377: nat,SV103: nat > nat] :
( ( ( ~ ( ( ( SV103 @ SV377 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SV377 )
| ~ ( ord_less_eq_nat @ SV377 @ SV224 ) ) )
= $true )
| ( ( number1551313001itions @ SV103 @ SV224 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(1815,plain,
! [SV106: nat,SV361: nat,SV227: nat,SV315: nat > nat] :
( ( ( ord_less_eq_nat @ ( SV315 @ SV227 ) @ SV361 )
= $false )
| ( ( ~ ! [SY924: nat,SY925: nat] :
( ~ ( ord_less_eq_nat @ SY924 @ SY925 )
| ( ord_less_eq_nat @ ( SV315 @ SY924 ) @ ( SV315 @ SY925 ) ) )
| ( ord_less_eq_nat @ ( SV315 @ SV106 ) @ SV361 ) )
= $true )
| ( ( ord_less_eq_nat @ SV106 @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1649]) ).
thf(1816,plain,
! [SV362: nat,SV228: nat] :
( ( ( ord_less_nat @ SV228 @ SV362 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV228 @ SV362 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV228 @ SV362 )
| ~ ( ( SV228 != SV362 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1650]) ).
thf(1817,plain,
! [SV362: nat,SV228: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV228 @ SV362 )
| ~ ( ( SV228 != SV362 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV228 @ SV362 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV228 @ SV362 )
| ~ ( ( SV228 != SV362 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1650]) ).
thf(1818,plain,
! [SV110: nat > $o,SV230: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( sK10_SY608 @ SV230 @ SV110 ) ) )
= $false )
| ( ( SV110 @ SV230 )
= $true )
| ( ( SV110 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1652]) ).
thf(1819,plain,
! [SV230: nat,SV110: nat > $o] :
( ( ( ~ ~ ( SV110 @ ( sK10_SY608 @ SV230 @ SV110 ) )
| ~ ! [SY1015: nat] :
~ ~ ( ~ ( ord_less_nat @ SY1015 @ ( sK10_SY608 @ SV230 @ SV110 ) )
| ~ ~ ( SV110 @ SY1015 ) ) )
= $false )
| ( ( SV110 @ SV230 )
= $true )
| ( ( SV110 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1652]) ).
thf(1820,plain,
! [SV231: set_nat,SV111: nat > nat] :
( ( ( ~ ( member_nat @ ( sK11_SY815 @ SV111 @ SV231 ) @ SV231 ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV111 @ SV231 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1653]) ).
thf(1821,plain,
! [SV231: set_nat,SV111: nat > nat] :
( ( ( ( SV111 @ ( sK11_SY815 @ SV111 @ SV231 ) )
= zero_zero_nat )
= $false )
| ( ( ( groups1842438620at_nat @ SV111 @ SV231 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1653]) ).
thf(1822,plain,
! [SV376: nat > nat,SV374: nat > nat,SV363: nat > nat,SV319: set_nat,SV236: nat > nat,SV116: set_nat] :
( ( ( ! [SY981: nat] :
( ~ ( member_nat @ SY981 @ SV116 )
| ~ ( ~ ( member_nat @ ( SV236 @ SY981 ) @ SV319 )
| ( ( SV363 @ ( SV236 @ SY981 ) )
!= SY981 ) ) ) )
= $false )
| ( ( ~ ! [SY1014: nat] :
( ~ ( member_nat @ SY1014 @ SV319 )
| ~ ( ~ ~ ( ~ ( member_nat @ ( SV363 @ SY1014 ) @ SV116 )
| ( ( SV236 @ ( SV363 @ SY1014 ) )
!= SY1014 ) )
| ( ( SV374 @ ( SV363 @ SY1014 ) )
!= ( SV376 @ SY1014 ) ) ) )
| ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1656]) ).
thf(1823,plain,
! [SV117: nat,SV364: set_nat,SV237: nat,SV320: nat > set_nat] :
( ( ( ord_less_eq_set_nat @ ( SV320 @ SV237 ) @ SV364 )
= $false )
| ( ( ~ ! [SY932: nat,SY933: nat] :
( ~ ( ord_less_eq_nat @ SY932 @ SY933 )
| ( ord_less_eq_set_nat @ ( SV320 @ SY932 ) @ ( SV320 @ SY933 ) ) )
| ( ord_less_eq_set_nat @ ( SV320 @ SV117 ) @ SV364 ) )
= $true )
| ( ( ord_less_eq_nat @ SV117 @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1657]) ).
thf(1824,plain,
! [SV118: nat,SV238: nat] :
( ( ( ord_less_eq_nat @ SV238 @ one_one_nat )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV118 @ SV238 ) @ one_one_nat )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV238 )
= $false )
| ( ( ord_less_eq_nat @ SV118 @ one_one_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1658]) ).
thf(1825,plain,
! [SV119: nat,SV239: nat > nat,SV365: nat,SV321: nat] :
( ( ( ord_less_eq_nat @ SV321 @ SV365 )
= $false )
| ( ( ~ ! [SY830: nat,SY831: nat] :
( ~ ( ord_less_eq_nat @ SY830 @ SY831 )
| ( ord_less_eq_nat @ ( SV239 @ SY830 ) @ ( SV239 @ SY831 ) ) )
| ( ord_less_eq_nat @ SV119 @ ( SV239 @ SV365 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV119 @ ( SV239 @ SV321 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1659]) ).
thf(1826,plain,
! [SV366: nat,SV243: nat] :
( ( ( SV243 = SV366 )
= $false )
| ( ( ~ ( ( SV243 != SV366 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV243 @ SV366 )
| ~ ( ord_less_eq_nat @ SV366 @ SV243 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1660]) ).
thf(1827,plain,
! [SV366: nat,SV243: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV243 @ SV366 )
| ~ ( ord_less_eq_nat @ SV366 @ SV243 ) ) )
= $false )
| ( ( ~ ( ( SV243 != SV366 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV243 @ SV366 )
| ~ ( ord_less_eq_nat @ SV366 @ SV243 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1660]) ).
thf(1828,plain,
! [SV127: set_nat,SV246: nat > set_nat,SV367: nat,SV325: nat] :
( ( ( ord_less_eq_nat @ SV325 @ SV367 )
= $false )
| ( ( ~ ! [SY838: nat,SY839: nat] :
( ~ ( ord_less_eq_nat @ SY838 @ SY839 )
| ( ord_less_eq_set_nat @ ( SV246 @ SY838 ) @ ( SV246 @ SY839 ) ) )
| ( ord_less_eq_set_nat @ SV127 @ ( SV246 @ SV367 ) ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV127 @ ( SV246 @ SV325 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1663]) ).
thf(1829,plain,
! [SV128: nat,SV247: nat,SV368: nat,SV326: nat] :
( ( ( ord_less_eq_nat @ SV326 @ SV368 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV247 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV326 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV128 @ SV326 ) @ ( times_times_nat @ SV247 @ SV368 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV128 @ SV247 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1664]) ).
thf(1830,plain,
! [SV327: nat,SV248: nat,SV130: nat] :
( ( ( ~ ( ( ( times_times_nat @ SV130 @ SV248 )
= ( times_times_nat @ SV130 @ SV327 ) )
| ( SV248 = SV327 ) ) )
= $true )
| ( ( ~ ( ( ( times_times_nat @ SV130 @ SV248 )
!= ( times_times_nat @ SV130 @ SV327 ) )
| ( SV248 != SV327 ) ) )
= $true )
| ( ( SV130 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1665]) ).
thf(1831,plain,
! [SV328: nat,SV249: nat,SV131: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV249 )
| ( ord_less_eq_nat @ SV131 @ SV328 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1667]) ).
thf(1832,plain,
! [SV328: nat,SV131: nat,SV249: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV249 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV249 )
| ( ord_less_eq_nat @ SV131 @ SV328 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1668]) ).
thf(1833,plain,
! [SV249: nat,SV328: nat,SV131: nat] :
( ( ( ord_less_eq_nat @ SV131 @ SV328 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV249 )
| ( ord_less_eq_nat @ SV131 @ SV328 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1668]) ).
thf(1834,plain,
! [SV132: nat,SV369: nat,SV250: nat,SV329: nat > nat] :
( ( ( ( SV329 @ SV250 )
= SV369 )
= $false )
| ( ( ~ ! [SY942: nat,SY943: nat] :
( ~ ( ord_less_eq_nat @ SY942 @ SY943 )
| ( ord_less_eq_nat @ ( SV329 @ SY942 ) @ ( SV329 @ SY943 ) ) )
| ( ord_less_eq_nat @ ( SV329 @ SV132 ) @ SV369 ) )
= $true )
| ( ( ord_less_eq_nat @ SV132 @ SV250 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1669]) ).
thf(1835,plain,
! [SV331: nat,SV134: nat,SV252: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV331 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV134 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1671]) ).
thf(1836,plain,
! [SV331: nat,SV134: nat,SV252: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV331 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV134 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1672]) ).
thf(1837,plain,
! [SV332: nat,SV253: nat,SV135: nat] :
( ( ( ~ ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 )
| ~ ( ord_less_nat @ SV253 @ SV332 ) ) )
= $false )
| ( ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1673]) ).
thf(1838,plain,
! [SV332: nat,SV253: nat,SV135: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 )
| ~ ( ord_less_nat @ SV253 @ SV332 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 )
| ~ ( ord_less_nat @ SV253 @ SV332 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1674]) ).
thf(1839,plain,
! [SV254: nat,SV136: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1675]) ).
thf(1840,plain,
! [SV254: nat,SV136: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV136 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV254 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1675]) ).
thf(1841,plain,
! [SV254: nat,SV136: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV136 ) )
= $true )
| ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV254 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV136 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV254 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1676]) ).
thf(1842,plain,
! [SV258: nat,SV140: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV140 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV258 @ zero_zero_nat ) )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV140 @ SV258 ) @ zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1678]) ).
thf(1843,plain,
! [SV258: nat,SV140: nat] :
( ( ( ord_less_eq_nat @ SV140 @ zero_zero_nat )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV258 ) )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV140 @ SV258 ) @ zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1679]) ).
thf(1844,plain,
! [SV370: nat,SV259: nat] :
( ( ( ord_less_nat @ SV259 @ SV370 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV259 @ SV370 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV259 @ SV370 )
| ~ ( ( SV259 != SV370 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1680]) ).
thf(1845,plain,
! [SV370: nat,SV259: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV259 @ SV370 )
| ~ ( ( SV259 != SV370 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV259 @ SV370 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV259 @ SV370 )
| ~ ( ( SV259 != SV370 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1680]) ).
thf(1846,plain,
! [SV142: set_nat,SV260: nat > nat,SV335: nat > nat] :
( ( ( member_nat @ ( sK7_SY944 @ SV335 @ SV260 @ SV142 ) @ SV142 )
= $true )
| ( ( ord_less_eq_nat @ ( groups1842438620at_nat @ SV260 @ SV142 ) @ ( groups1842438620at_nat @ SV335 @ SV142 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1681]) ).
thf(1847,plain,
! [SV263: nat,SV145: nat] :
( ( ( one_one_nat
!= ( times_times_nat @ SV145 @ SV263 ) )
= $false )
| ( ( one_one_nat
= ( times_times_nat @ SV145 @ SV263 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1683]) ).
thf(1848,plain,
! [SV263: nat,SV145: nat] :
( ( ( ~ ~ ( ( SV145 != one_one_nat )
| ( SV263 != one_one_nat ) ) )
= $false )
| ( ( one_one_nat
= ( times_times_nat @ SV145 @ SV263 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1683]) ).
thf(1849,plain,
! [SV263: nat,SV145: nat] :
( ( ( SV145 != one_one_nat )
= $true )
| ( ( SV263 != one_one_nat )
= $true )
| ( ( ~ ( ( one_one_nat
!= ( times_times_nat @ SV145 @ SV263 ) )
| ~ ~ ( ( SV145 != one_one_nat )
| ( SV263 != one_one_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1684]) ).
thf(1850,plain,
! [SV336: nat,SV146: nat,SV264: nat] :
( ( ( ~ ( ( ( times_times_nat @ SV264 @ SV146 )
= ( times_times_nat @ SV336 @ SV146 ) )
| ( SV264 = SV336 ) ) )
= $true )
| ( ( ~ ( ( ( times_times_nat @ SV264 @ SV146 )
!= ( times_times_nat @ SV336 @ SV146 ) )
| ( SV264 != SV336 ) ) )
= $true )
| ( ( SV146 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1685]) ).
thf(1851,plain,
! [SV147: nat] :
( ( ( ~ ( ( SV147 != zero_zero_nat ) ) )
= $false )
| ( ( SV147 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1687]) ).
thf(1852,plain,
! [SV147: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV147 ) )
= $false )
| ( ( SV147 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1687]) ).
thf(1853,plain,
! [SV147: nat] :
( ( ( SV147 != zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV147 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1688]) ).
thf(1854,plain,
! [SV147: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV147 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV147 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1689]) ).
thf(1855,plain,
! [SV265: nat,SV148: nat > nat] :
( ( ( ( SV148 @ ( sK4_SY856 @ SV265 @ SV148 ) )
= zero_zero_nat )
= $false )
| ( ( ( ( groups1842438620at_nat
@ ^ [SY685: nat] : ( times_times_nat @ ( SV148 @ SY685 ) @ SY685 )
@ ( set_ord_atMost_nat @ SV265 ) )
!= SV265 )
| ( number1551313001itions @ SV148 @ SV265 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1690]) ).
thf(1856,plain,
! [SV148: nat > nat,SV265: nat] :
( ( ( ~ ( ord_less_eq_nat @ one_one_nat @ ( sK4_SY856 @ SV265 @ SV148 ) ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ ( sK4_SY856 @ SV265 @ SV148 ) @ SV265 ) )
= $true )
| ( ( ( ( groups1842438620at_nat
@ ^ [SY685: nat] : ( times_times_nat @ ( SV148 @ SY685 ) @ SY685 )
@ ( set_ord_atMost_nat @ SV265 ) )
!= SV265 )
| ( number1551313001itions @ SV148 @ SV265 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1691]) ).
thf(1857,plain,
! [SV266: nat,SV149: nat] :
( ( ( ( times_times_nat @ SV149 @ SV266 )
!= one_one_nat )
= $false )
| ( ( ( times_times_nat @ SV149 @ SV266 )
= one_one_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1692]) ).
thf(1858,plain,
! [SV266: nat,SV149: nat] :
( ( ( ~ ~ ( ( SV149 != one_one_nat )
| ( SV266 != one_one_nat ) ) )
= $false )
| ( ( ( times_times_nat @ SV149 @ SV266 )
= one_one_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1692]) ).
thf(1859,plain,
! [SV266: nat,SV149: nat] :
( ( ( SV149 != one_one_nat )
= $true )
| ( ( SV266 != one_one_nat )
= $true )
| ( ( ~ ( ( ( times_times_nat @ SV149 @ SV266 )
!= one_one_nat )
| ~ ~ ( ( SV149 != one_one_nat )
| ( SV266 != one_one_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1693]) ).
thf(1860,plain,
! [SV150: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV150 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV150 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1694]) ).
thf(1861,plain,
! [SV150: nat] :
( ( ( SV150 != zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV150 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1695]) ).
thf(1862,plain,
! [SV150: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV150 ) )
= $false )
| ( ( SV150 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1696]) ).
thf(1863,plain,
! [SV150: nat] :
( ( ( ~ ( ( SV150 != zero_zero_nat ) ) )
= $false )
| ( ( SV150 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1696]) ).
thf(1864,plain,
! [SV151: set_nat,SV371: nat,SV267: set_nat,SV337: set_nat > nat] :
( ( ( ( SV337 @ SV267 )
= SV371 )
= $false )
| ( ( ~ ! [SY946: set_nat,SY947: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY946 @ SY947 )
| ( ord_less_eq_nat @ ( SV337 @ SY946 ) @ ( SV337 @ SY947 ) ) )
| ( ord_less_eq_nat @ ( SV337 @ SV151 ) @ SV371 ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV151 @ SV267 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1697]) ).
thf(1865,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV153 )
| ( ord_less_eq_nat @ SV269 @ SV339 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1699]) ).
thf(1866,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV153 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV153 )
| ( ord_less_eq_nat @ SV269 @ SV339 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1700]) ).
thf(1867,plain,
! [SV153: nat,SV339: nat,SV269: nat] :
( ( ( ord_less_eq_nat @ SV269 @ SV339 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV153 )
| ( ord_less_eq_nat @ SV269 @ SV339 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1700]) ).
thf(1868,plain,
! [SV156: nat,SV2: nat] :
( ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ SV2 ) @ ( set_ord_atMost_nat @ SV156 ) )
= $true )
| ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ SV2 ) @ ( set_ord_atMost_nat @ SV156 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1702]) ).
thf(1869,plain,
! [SV156: nat,SV2: nat] :
( ( ( ord_less_eq_nat @ SV2 @ SV156 )
= $true )
| ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ SV2 ) @ ( set_ord_atMost_nat @ SV156 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1703]) ).
thf(1870,plain,
! [SV156: nat,SV2: nat] :
( ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ SV2 ) @ ( set_ord_atMost_nat @ SV156 ) )
= $true )
| ( ( ord_less_eq_nat @ SV2 @ SV156 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1704]) ).
thf(1871,plain,
! [SV156: nat,SV2: nat] :
( ( ( ord_less_eq_nat @ SV2 @ SV156 )
= $true )
| ( ( ord_less_eq_nat @ SV2 @ SV156 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1705]) ).
thf(1872,plain,
! [SV157: nat,SV3: nat] :
( ( ( member_nat @ SV3 @ ( set_ord_atMost_nat @ SV157 ) )
= $true )
| ( ( member_nat @ SV3 @ ( set_ord_atMost_nat @ SV157 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1706]) ).
thf(1873,plain,
! [SV157: nat,SV3: nat] :
( ( ( ord_less_eq_nat @ SV3 @ SV157 )
= $true )
| ( ( member_nat @ SV3 @ ( set_ord_atMost_nat @ SV157 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1707]) ).
thf(1874,plain,
! [SV157: nat,SV3: nat] :
( ( ( member_nat @ SV3 @ ( set_ord_atMost_nat @ SV157 ) )
= $true )
| ( ( ord_less_eq_nat @ SV3 @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1708]) ).
thf(1875,plain,
! [SV157: nat,SV3: nat] :
( ( ( ord_less_eq_nat @ SV3 @ SV157 )
= $true )
| ( ( ord_less_eq_nat @ SV3 @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1709]) ).
thf(1876,plain,
! [SV158: nat,SV4: nat] :
( ( ( ( set_ord_atMost_nat @ SV4 )
= ( set_ord_atMost_nat @ SV158 ) )
= $true )
| ( ( ( set_ord_atMost_nat @ SV4 )
= ( set_ord_atMost_nat @ SV158 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1710]) ).
thf(1877,plain,
! [SV158: nat,SV4: nat] :
( ( ( SV4 = SV158 )
= $true )
| ( ( ( set_ord_atMost_nat @ SV4 )
= ( set_ord_atMost_nat @ SV158 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1711]) ).
thf(1878,plain,
! [SV158: nat,SV4: nat] :
( ( ( ( set_ord_atMost_nat @ SV4 )
= ( set_ord_atMost_nat @ SV158 ) )
= $true )
| ( ( SV4 = SV158 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1712]) ).
thf(1879,plain,
! [SV158: nat,SV4: nat] :
( ( ( SV4 = SV158 )
= $true )
| ( ( SV4 = SV158 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1713]) ).
thf(1880,plain,
! [SV272: nat,SV159: nat,SV5: nat] :
( ( ( ( times_times_nat @ SV5 @ SV159 )
!= ( times_times_nat @ SV272 @ SV159 ) )
= $false )
| ( ( ( times_times_nat @ SV5 @ SV159 )
= ( times_times_nat @ SV272 @ SV159 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1714]) ).
thf(1881,plain,
! [SV272: nat,SV5: nat,SV159: nat] :
( ( ( ~ ( ( SV159 = zero_zero_nat )
| ( SV5 = SV272 ) ) )
= $false )
| ( ( ( times_times_nat @ SV5 @ SV159 )
= ( times_times_nat @ SV272 @ SV159 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1714]) ).
thf(1882,plain,
! [SV272: nat,SV159: nat,SV5: nat] :
( ( ( ( ( times_times_nat @ SV5 @ SV159 )
!= ( times_times_nat @ SV272 @ SV159 ) )
| ~ ( ( SV159 = zero_zero_nat )
| ( SV5 = SV272 ) ) )
= $false )
| ( ( SV159 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1715]) ).
thf(1883,plain,
! [SV272: nat,SV159: nat,SV5: nat] :
( ( ( ( ( times_times_nat @ SV5 @ SV159 )
!= ( times_times_nat @ SV272 @ SV159 ) )
| ~ ( ( SV159 = zero_zero_nat )
| ( SV5 = SV272 ) ) )
= $false )
| ( ( SV5 = SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1716]) ).
thf(1884,plain,
! [SV273: nat,SV160: nat,SV6: nat] :
( ( ( ( times_times_nat @ SV6 @ SV160 )
!= ( times_times_nat @ SV6 @ SV273 ) )
= $false )
| ( ( ( times_times_nat @ SV6 @ SV160 )
= ( times_times_nat @ SV6 @ SV273 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1717]) ).
thf(1885,plain,
! [SV273: nat,SV160: nat,SV6: nat] :
( ( ( ~ ( ( SV6 = zero_zero_nat )
| ( SV160 = SV273 ) ) )
= $false )
| ( ( ( times_times_nat @ SV6 @ SV160 )
= ( times_times_nat @ SV6 @ SV273 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1717]) ).
thf(1886,plain,
! [SV273: nat,SV160: nat,SV6: nat] :
( ( ( ( ( times_times_nat @ SV6 @ SV160 )
!= ( times_times_nat @ SV6 @ SV273 ) )
| ~ ( ( SV6 = zero_zero_nat )
| ( SV160 = SV273 ) ) )
= $false )
| ( ( SV6 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1718]) ).
thf(1887,plain,
! [SV273: nat,SV160: nat,SV6: nat] :
( ( ( ( ( times_times_nat @ SV6 @ SV160 )
!= ( times_times_nat @ SV6 @ SV273 ) )
| ~ ( ( SV6 = zero_zero_nat )
| ( SV160 = SV273 ) ) )
= $false )
| ( ( SV160 = SV273 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1719]) ).
thf(1888,plain,
! [SV161: nat,SV7: nat] :
( ( ( ( times_times_nat @ SV7 @ SV161 )
= zero_zero_nat )
= $true )
| ( ( ( times_times_nat @ SV7 @ SV161 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1720]) ).
thf(1889,plain,
! [SV161: nat,SV7: nat] :
( ( ( ( SV7 = zero_zero_nat )
| ( SV161 = zero_zero_nat ) )
= $true )
| ( ( ( times_times_nat @ SV7 @ SV161 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1721]) ).
thf(1890,plain,
! [SV161: nat,SV7: nat] :
( ( ( ( times_times_nat @ SV7 @ SV161 )
!= zero_zero_nat )
= $false )
| ( ( SV7 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1722]) ).
thf(1891,plain,
! [SV161: nat,SV7: nat] :
( ( ( ~ ( ( SV7 = zero_zero_nat )
| ( SV161 = zero_zero_nat ) ) )
= $false )
| ( ( SV7 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1722]) ).
thf(1892,plain,
! [SV161: nat,SV7: nat] :
( ( ( ( times_times_nat @ SV7 @ SV161 )
!= zero_zero_nat )
= $false )
| ( ( SV161 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1723]) ).
thf(1893,plain,
! [SV161: nat,SV7: nat] :
( ( ( ~ ( ( SV7 = zero_zero_nat )
| ( SV161 = zero_zero_nat ) ) )
= $false )
| ( ( SV161 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1723]) ).
thf(1894,plain,
! [SV274: nat,SV162: nat,SV12: nat] :
( ( ( ( times_times_nat @ SV12 @ SV162 )
!= ( times_times_nat @ SV274 @ SV162 ) )
= $false )
| ( ( ( times_times_nat @ SV12 @ SV162 )
= ( times_times_nat @ SV274 @ SV162 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1724]) ).
thf(1895,plain,
! [SV162: nat,SV274: nat,SV12: nat] :
( ( ( ~ ( ( SV12 = SV274 )
| ( SV162 = zero_zero_nat ) ) )
= $false )
| ( ( ( times_times_nat @ SV12 @ SV162 )
= ( times_times_nat @ SV274 @ SV162 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1724]) ).
thf(1896,plain,
! [SV274: nat,SV162: nat,SV12: nat] :
( ( ( ( ( times_times_nat @ SV12 @ SV162 )
!= ( times_times_nat @ SV274 @ SV162 ) )
| ~ ( ( SV12 = SV274 )
| ( SV162 = zero_zero_nat ) ) )
= $false )
| ( ( SV12 = SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1725]) ).
thf(1897,plain,
! [SV274: nat,SV162: nat,SV12: nat] :
( ( ( ( ( times_times_nat @ SV12 @ SV162 )
!= ( times_times_nat @ SV274 @ SV162 ) )
| ~ ( ( SV12 = SV274 )
| ( SV162 = zero_zero_nat ) ) )
= $false )
| ( ( SV162 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1726]) ).
thf(1898,plain,
! [SV275: nat,SV163: nat,SV13: nat] :
( ( ( ( times_times_nat @ SV13 @ SV163 )
!= ( times_times_nat @ SV13 @ SV275 ) )
= $false )
| ( ( ( times_times_nat @ SV13 @ SV163 )
= ( times_times_nat @ SV13 @ SV275 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1727]) ).
thf(1899,plain,
! [SV13: nat,SV275: nat,SV163: nat] :
( ( ( ~ ( ( SV163 = SV275 )
| ( SV13 = zero_zero_nat ) ) )
= $false )
| ( ( ( times_times_nat @ SV13 @ SV163 )
= ( times_times_nat @ SV13 @ SV275 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1727]) ).
thf(1900,plain,
! [SV275: nat,SV163: nat,SV13: nat] :
( ( ( ( ( times_times_nat @ SV13 @ SV163 )
!= ( times_times_nat @ SV13 @ SV275 ) )
| ~ ( ( SV163 = SV275 )
| ( SV13 = zero_zero_nat ) ) )
= $false )
| ( ( SV163 = SV275 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1728]) ).
thf(1901,plain,
! [SV275: nat,SV163: nat,SV13: nat] :
( ( ( ( ( times_times_nat @ SV13 @ SV163 )
!= ( times_times_nat @ SV13 @ SV275 ) )
| ~ ( ( SV163 = SV275 )
| ( SV13 = zero_zero_nat ) ) )
= $false )
| ( ( SV13 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1729]) ).
thf(1902,plain,
! [SV164: nat,SV15: nat] :
( ( ( ( times_times_nat @ SV15 @ SV164 )
= zero_zero_nat )
= $true )
| ( ( ( times_times_nat @ SV15 @ SV164 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1730]) ).
thf(1903,plain,
! [SV164: nat,SV15: nat] :
( ( ( ( SV15 = zero_zero_nat )
| ( SV164 = zero_zero_nat ) )
= $true )
| ( ( ( times_times_nat @ SV15 @ SV164 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1731]) ).
thf(1904,plain,
! [SV164: nat,SV15: nat] :
( ( ( ( times_times_nat @ SV15 @ SV164 )
!= zero_zero_nat )
= $false )
| ( ( SV15 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1732]) ).
thf(1905,plain,
! [SV164: nat,SV15: nat] :
( ( ( ~ ( ( SV15 = zero_zero_nat )
| ( SV164 = zero_zero_nat ) ) )
= $false )
| ( ( SV15 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1732]) ).
thf(1906,plain,
! [SV164: nat,SV15: nat] :
( ( ( ( times_times_nat @ SV15 @ SV164 )
!= zero_zero_nat )
= $false )
| ( ( SV164 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1733]) ).
thf(1907,plain,
! [SV164: nat,SV15: nat] :
( ( ( ~ ( ( SV15 = zero_zero_nat )
| ( SV164 = zero_zero_nat ) ) )
= $false )
| ( ( SV164 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1733]) ).
thf(1908,plain,
! [SV280: nat,SV173: nat,SV37: nat] :
( ( ( ( times_times_nat @ SV37 @ SV173 )
!= ( times_times_nat @ SV37 @ SV280 ) )
= $false )
| ( ( ( times_times_nat @ SV37 @ SV173 )
= ( times_times_nat @ SV37 @ SV280 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1746]) ).
thf(1909,plain,
! [SV280: nat,SV173: nat,SV37: nat] :
( ( ( ~ ( ( SV37 = zero_zero_nat )
| ( SV173 = SV280 ) ) )
= $false )
| ( ( ( times_times_nat @ SV37 @ SV173 )
= ( times_times_nat @ SV37 @ SV280 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1746]) ).
thf(1910,plain,
! [SV280: nat,SV173: nat,SV37: nat] :
( ( ( ( ( times_times_nat @ SV37 @ SV173 )
!= ( times_times_nat @ SV37 @ SV280 ) )
| ~ ( ( SV37 = zero_zero_nat )
| ( SV173 = SV280 ) ) )
= $false )
| ( ( SV37 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1747]) ).
thf(1911,plain,
! [SV280: nat,SV173: nat,SV37: nat] :
( ( ( ( ( times_times_nat @ SV37 @ SV173 )
!= ( times_times_nat @ SV37 @ SV280 ) )
| ~ ( ( SV37 = zero_zero_nat )
| ( SV173 = SV280 ) ) )
= $false )
| ( ( SV173 = SV280 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1748]) ).
thf(1912,plain,
! [SV50: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV50 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV50 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1757]) ).
thf(1913,plain,
! [SV50: nat] :
( ( ( SV50 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV50 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1758]) ).
thf(1914,plain,
! [SV50: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV50 )
= $false )
| ( ( SV50 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1759]) ).
thf(1915,plain,
! [SV343: nat,SV179: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV179 @ SV343 )
| ~ ( ( ord_less_nat @ SV179 @ SV343 )
| ( SV179 = SV343 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV179 @ SV343 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1765]) ).
thf(1916,plain,
! [SV343: nat,SV179: nat] :
( ( ( ord_less_nat @ SV179 @ SV343 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV179 @ SV343 )
| ~ ( ( ord_less_nat @ SV179 @ SV343 )
| ( SV179 = SV343 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1766]) ).
thf(1917,plain,
! [SV343: nat,SV179: nat] :
( ( ( SV179 = SV343 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV179 @ SV343 )
| ~ ( ( ord_less_nat @ SV179 @ SV343 )
| ( SV179 = SV343 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1766]) ).
thf(1918,plain,
! [SV54: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV54 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV54 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1767]) ).
thf(1919,plain,
! [SV54: nat] :
( ( ( SV54 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV54 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1768]) ).
thf(1920,plain,
! [SV54: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV54 )
= $false )
| ( ( SV54 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1769]) ).
thf(1921,plain,
! [SV344: nat,SV180: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV180 @ SV344 )
| ~ ( ( ord_less_nat @ SV180 @ SV344 )
| ( SV344 = SV180 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV180 @ SV344 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1771]) ).
thf(1922,plain,
! [SV344: nat,SV180: nat] :
( ( ( ord_less_nat @ SV180 @ SV344 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV180 @ SV344 )
| ~ ( ( ord_less_nat @ SV180 @ SV344 )
| ( SV344 = SV180 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1772]) ).
thf(1923,plain,
! [SV180: nat,SV344: nat] :
( ( ( SV344 = SV180 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV180 @ SV344 )
| ~ ( ( ord_less_nat @ SV180 @ SV344 )
| ( SV344 = SV180 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1772]) ).
thf(1924,plain,
! [SV345: nat,SV181: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV181 @ SV345 )
| ~ ( ( ord_less_nat @ SV181 @ SV345 )
| ( SV181 = SV345 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV181 @ SV345 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1773]) ).
thf(1925,plain,
! [SV345: nat,SV181: nat] :
( ( ( ord_less_nat @ SV181 @ SV345 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV181 @ SV345 )
| ~ ( ( ord_less_nat @ SV181 @ SV345 )
| ( SV181 = SV345 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1774]) ).
thf(1926,plain,
! [SV345: nat,SV181: nat] :
( ( ( SV181 = SV345 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV181 @ SV345 )
| ~ ( ( ord_less_nat @ SV181 @ SV345 )
| ( SV181 = SV345 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1774]) ).
thf(1927,plain,
! [SV60: set_nat,SV182: nat > nat,SV288: nat > nat,SV346: set_nat,SV372: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
| ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= $false )
| ( ( ~ ! [SY953: nat] :
( ~ ( member_nat @ SY953 @ SV60 )
| ( member_nat @ ( SV288 @ SY953 ) @ SV346 ) )
| ~ ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) )
| ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1775]) ).
thf(1928,plain,
! [SV184: nat,SV62: nat] :
( ( ( ( times_times_nat @ SV62 @ SV184 )
= zero_zero_nat )
= $false )
| ( ( SV184 = zero_zero_nat )
= $true )
| ( ( SV62 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1776]) ).
thf(1929,plain,
! [SV347: nat,SV186: nat] :
( ( ( ( SV186 != SV347 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV186 @ SV347 )
| ~ ( ord_less_eq_nat @ SV347 @ SV186 ) ) )
= $false )
| ( ( SV186 = SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1777]) ).
thf(1930,plain,
! [SV347: nat,SV186: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV186 @ SV347 )
| ~ ( ord_less_eq_nat @ SV347 @ SV186 ) )
= $true )
| ( ( ~ ( ( SV186 != SV347 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV186 @ SV347 )
| ~ ( ord_less_eq_nat @ SV347 @ SV186 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1778]) ).
thf(1931,plain,
! [SV191: set_nat,SV348: nat,SV69: set_nat,SV292: set_nat > nat] :
( ( ( ~ ! [SY882: set_nat,SY883: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY882 @ SY883 )
| ( ord_less_eq_nat @ ( SV292 @ SY882 ) @ ( SV292 @ SY883 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( SV292 @ SV69 ) @ SV348 )
= $true )
| ( ( ord_less_eq_nat @ ( SV292 @ SV191 ) @ SV348 )
= $false )
| ( ( ord_less_eq_set_nat @ SV69 @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1779]) ).
thf(1932,plain,
! [SV293: nat,SV192: nat,SV70: nat > $o] :
( ( ( ~ ( SV70 @ ( sK12_SY884 @ SV192 @ SV293 @ SV70 ) ) )
= $false )
| ( ( ~ ! [SY505: nat] :
( ~ ( SV70 @ SY505 )
| ~ ! [SY506: nat] :
( ~ ( SV70 @ SY506 )
| ( ord_less_eq_nat @ SY506 @ SY505 ) ) ) )
= $true )
| ( ( SV70 @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1780]) ).
thf(1933,plain,
! [SV70: nat > $o,SV293: nat,SV192: nat] :
( ( ( ord_less_eq_nat @ ( sK12_SY884 @ SV192 @ SV293 @ SV70 ) @ SV293 )
= $false )
| ( ( ~ ! [SY505: nat] :
( ~ ( SV70 @ SY505 )
| ~ ! [SY506: nat] :
( ~ ( SV70 @ SY506 )
| ( ord_less_eq_nat @ SY506 @ SY505 ) ) ) )
= $true )
| ( ( SV70 @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1780]) ).
thf(1934,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ~ ( number1551313001itions @ SV194 @ SV350 )
| ~ ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) )
= $false )
| ( ( number1551313001itions @ SV194 @ SV350 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1782]) ).
thf(1935,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) )
= $true )
| ( ( ~ ( ~ ( number1551313001itions @ SV194 @ SV350 )
| ~ ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1783]) ).
thf(1936,plain,
! [SV196: nat,SV351: set_nat,SV74: nat,SV296: nat > set_nat] :
( ( ( ~ ! [SY891: nat,SY892: nat] :
( ~ ( ord_less_eq_nat @ SY891 @ SY892 )
| ( ord_less_eq_set_nat @ ( SV296 @ SY891 ) @ ( SV296 @ SY892 ) ) ) )
= $true )
| ( ( ord_less_eq_set_nat @ ( SV296 @ SV74 ) @ SV351 )
= $true )
| ( ( ( SV296 @ SV196 )
= SV351 )
= $false )
| ( ( ord_less_eq_nat @ SV74 @ SV196 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1784]) ).
thf(1937,plain,
! [SV76: nat > nat > $o,SV198: nat,SV298: nat] :
( ( ( ord_less_eq_nat @ ( sK5_SY523 @ SV298 @ SV198 @ SV76 ) @ ( sK8_SY1011 @ SV76 @ SV198 @ SV298 ) )
= $true )
| ( ( ~ ! [SY525: nat,SY526: nat] :
( ~ ( SV76 @ SY526 @ SY525 )
| ( SV76 @ SY525 @ SY526 ) )
| ( SV76 @ SV198 @ SV298 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1785]) ).
thf(1938,plain,
! [SV298: nat,SV198: nat,SV76: nat > nat > $o] :
( ( ( ~ ! [SY525: nat,SY526: nat] :
( ~ ( SV76 @ SY526 @ SY525 )
| ( SV76 @ SY525 @ SY526 ) ) )
= $true )
| ( ( SV76 @ SV198 @ SV298 )
= $true )
| ( ( SV76 @ ( sK5_SY523 @ SV298 @ SV198 @ SV76 ) @ ( sK8_SY1011 @ SV76 @ SV198 @ SV298 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1786]) ).
thf(1939,plain,
! [SV202: nat,SV80: nat] :
( ( ( SV80 = zero_zero_nat )
= $false )
| ( ( ( times_times_nat @ SV80 @ SV202 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1787]) ).
thf(1940,plain,
! [SV80: nat,SV202: nat] :
( ( ( SV202 = zero_zero_nat )
= $false )
| ( ( ( times_times_nat @ SV80 @ SV202 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1788]) ).
thf(1941,plain,
! [SV352: nat,SV205: nat,SV303: nat,SV83: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV83 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV303 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV83 @ SV303 ) @ ( times_times_nat @ SV205 @ SV352 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV303 @ SV352 )
= $false )
| ( ( ord_less_eq_nat @ SV83 @ SV205 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1789]) ).
thf(1942,plain,
! [SV84: nat,SV206: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV206 @ SV84 )
| ( SV206 != SV84 ) )
= $false )
| ( ( ord_less_eq_nat @ SV206 @ SV84 )
= $false )
| ( ( ord_less_eq_nat @ SV84 @ SV206 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1790]) ).
thf(1943,plain,
! [SV84: nat,SV206: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV206 @ SV84 )
| ( SV206 != SV84 ) )
= $false )
| ( ( SV206 = SV84 )
= $false )
| ( ( ord_less_eq_nat @ SV84 @ SV206 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1791]) ).
thf(1944,plain,
! [SV85: set_nat,SV207: set_nat,SV304: nat > nat,SV353: nat > nat,SV373: nat > nat] :
( ( ( ~ ( member_nat @ ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) @ SV85 ) )
= $false )
| ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) )
| ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1792]) ).
thf(1945,plain,
! [SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV304: nat > nat,SV207: set_nat] :
( ( ( ~ ! [SY1016: nat] :
~ ~ ( ~ ~ ( ~ ( member_nat @ SY1016 @ SV207 )
| ( ( SV304 @ SY1016 )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) ) )
| ~ ! [SY1017: nat] :
( ~ ~ ( ~ ( member_nat @ SY1017 @ SV207 )
| ( ( SV304 @ SY1017 )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) ) )
| ( SY1017 = SY1016 ) ) ) )
= $false )
| ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) )
| ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1792]) ).
thf(1946,plain,
! [SV305: nat,SV354: nat,SV86: set_nat,SV208: nat > set_nat] :
( ( ( ~ ! [SY776: nat,SY777: nat] :
( ~ ( ord_less_eq_nat @ SY776 @ SY777 )
| ( ord_less_eq_set_nat @ ( SV208 @ SY776 ) @ ( SV208 @ SY777 ) ) ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV86 @ ( SV208 @ SV354 ) )
= $true )
| ( ( ord_less_eq_nat @ SV305 @ SV354 )
= $false )
| ( ( SV86
= ( SV208 @ SV305 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1793]) ).
thf(1947,plain,
! [SV306: set_nat,SV355: set_nat,SV87: nat,SV209: set_nat > nat] :
( ( ( ~ ! [SY780: set_nat,SY781: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY780 @ SY781 )
| ( ord_less_eq_nat @ ( SV209 @ SY780 ) @ ( SV209 @ SY781 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV87 @ ( SV209 @ SV355 ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV306 @ SV355 )
= $false )
| ( ( SV87
= ( SV209 @ SV306 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1794]) ).
thf(1948,plain,
! [SV88: nat] :
( ( ( SV88 != zero_zero_nat )
= $true )
| ( ( SV88 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1795]) ).
thf(1949,plain,
! [SV88: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV88 )
= $true )
| ( ( SV88 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1796]) ).
thf(1950,plain,
! [SV88: nat] :
( ( ( SV88 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1797]) ).
thf(1951,plain,
! [SV378: nat] :
( ( ( ~ ( ( ( p @ SV378 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SV378 )
| ~ ( ord_less_eq_nat @ SV378 @ zero_zero_nat ) ) )
= $true )
| ( ( p
= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1799]) ).
thf(1952,plain,
( ( ( ! [SV379: nat] :
( ( p @ SV379 )
= zero_zero_nat ) )
= $true )
| ( ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
= zero_zero_nat )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1800]) ).
thf(1953,plain,
( ( ( p
= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true )
| ( ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
= zero_zero_nat )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1800]) ).
thf(1954,plain,
( ( ( ! [SX0: nat] :
( ~ ( ( ( p @ SX0 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SX0 )
| ~ ( ord_less_eq_nat @ SX0 @ zero_zero_nat ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
!= zero_zero_nat )
= $true )
| ( ( p
!= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1801]) ).
thf(1955,plain,
! [SV356: nat,SV213: nat] :
( ( ( ( SV213 != SV356 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV356 @ SV213 )
| ~ ( ord_less_eq_nat @ SV213 @ SV356 ) ) )
= $false )
| ( ( SV213 = SV356 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1802]) ).
thf(1956,plain,
! [SV213: nat,SV356: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV356 @ SV213 )
| ~ ( ord_less_eq_nat @ SV213 @ SV356 ) )
= $true )
| ( ( ~ ( ( SV213 != SV356 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV356 @ SV213 )
| ~ ( ord_less_eq_nat @ SV213 @ SV356 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1803]) ).
thf(1957,plain,
! [SV214: set_nat,SV308: nat > nat,SV357: nat > nat,SV93: set_nat] :
( ( ( ~ ( member_nat @ ( sK16_SY972 @ SV93 @ SV357 @ SV308 @ SV214 ) @ SV214 )
| ( ( SV308 @ ( sK16_SY972 @ SV93 @ SV357 @ SV308 @ SV214 ) )
= ( SV357 @ ( sK16_SY972 @ SV93 @ SV357 @ SV308 @ SV214 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV308 @ SV93 )
= ( groups1842438620at_nat @ SV357 @ SV214 ) )
= $true )
| ( ( SV93 = SV214 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1804]) ).
thf(1958,plain,
! [SV309: set_nat,SV358: set_nat,SV95: nat,SV216: set_nat > nat] :
( ( ( ~ ! [SY789: set_nat,SY790: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY789 @ SY790 )
| ( ord_less_eq_nat @ ( SV216 @ SY789 ) @ ( SV216 @ SY790 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV95 @ ( SV216 @ SV358 ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV309 @ SV358 )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ ( SV216 @ SV309 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1805]) ).
thf(1959,plain,
! [SV97: nat > nat,SV218: nat,SV310: nat] :
( ( ( ord_less_nat @ ( sK6_SY578 @ SV310 @ SV218 @ SV97 ) @ ( sK9_SY1012 @ SV97 @ SV218 @ SV310 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV218 @ SV310 )
| ( ord_less_eq_nat @ ( SV97 @ SV218 ) @ ( SV97 @ SV310 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1806]) ).
thf(1960,plain,
! [SV97: nat > nat,SV310: nat,SV218: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV218 @ SV310 ) )
= $true )
| ( ( ord_less_eq_nat @ ( SV97 @ SV218 ) @ ( SV97 @ SV310 ) )
= $true )
| ( ( ord_less_nat @ ( SV97 @ ( sK6_SY578 @ SV310 @ SV218 @ SV97 ) ) @ ( SV97 @ ( sK9_SY1012 @ SV97 @ SV218 @ SV310 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1807]) ).
thf(1961,plain,
! [SV311: nat,SV219: nat,SV98: nat] :
( ( ( ~ ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) ) )
= $false )
| ( ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1808]) ).
thf(1962,plain,
! [SV311: nat,SV98: nat,SV219: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV219 )
| ~ ( ord_less_nat @ SV98 @ SV311 ) ) )
= $false )
| ( ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1808]) ).
thf(1963,plain,
! [SV311: nat,SV98: nat,SV219: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV219 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV98 @ SV311 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV219 )
| ~ ( ord_less_nat @ SV98 @ SV311 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1809]) ).
thf(1964,plain,
! [SV312: nat,SV359: nat,SV99: nat,SV220: nat > nat] :
( ( ( ~ ! [SY798: nat,SY799: nat] :
( ~ ( ord_less_eq_nat @ SY798 @ SY799 )
| ( ord_less_eq_nat @ ( SV220 @ SY798 ) @ ( SV220 @ SY799 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV99 @ ( SV220 @ SV359 ) )
= $true )
| ( ( ord_less_eq_nat @ SV312 @ SV359 )
= $false )
| ( ( SV99
= ( SV220 @ SV312 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1810]) ).
thf(1965,plain,
! [SV313: nat,SV221: nat,SV100: nat > $o] :
( ( ( ~ ( SV100 @ ( sK14_SY920 @ SV221 @ SV313 @ SV100 ) ) )
= $false )
| ( ( ~ ! [SY590: nat] :
~ ~ ( ~ ( SV100 @ SY590 )
| ~ ! [SY591: nat] :
( ~ ( SV100 @ SY591 )
| ( ord_less_eq_nat @ SY591 @ SY590 ) ) ) )
= $true )
| ( ( SV100 @ SV221 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1811]) ).
thf(1966,plain,
! [SV100: nat > $o,SV313: nat,SV221: nat] :
( ( ( ord_less_eq_nat @ ( sK14_SY920 @ SV221 @ SV313 @ SV100 ) @ SV313 )
= $false )
| ( ( ~ ! [SY590: nat] :
~ ~ ( ~ ( SV100 @ SY590 )
| ~ ! [SY591: nat] :
( ~ ( SV100 @ SY591 )
| ( ord_less_eq_nat @ SY591 @ SY590 ) ) ) )
= $true )
| ( ( SV100 @ SV221 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1811]) ).
thf(1967,plain,
! [SV360: nat,SV222: nat] :
( ( ( ~ ( ord_less_nat @ SV222 @ SV360 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV222 @ SV360 )
| ~ ( ( SV360 != SV222 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV222 @ SV360 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1812]) ).
thf(1968,plain,
! [SV360: nat,SV222: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV222 @ SV360 )
| ~ ( ( SV360 != SV222 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV222 @ SV360 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV222 @ SV360 )
| ~ ( ( SV360 != SV222 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1813]) ).
thf(1969,plain,
! [SV224: nat,SV377: nat,SV103: nat > nat] :
( ( ( ~ ( ( ( SV103 @ SV377 )
!= zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SV377 )
| ~ ( ord_less_eq_nat @ SV377 @ SV224 ) ) )
= $true )
| ( ( number1551313001itions @ SV103 @ SV224 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1814]) ).
thf(1970,plain,
! [SV227: nat,SV361: nat,SV106: nat,SV315: nat > nat] :
( ( ( ~ ! [SY924: nat,SY925: nat] :
( ~ ( ord_less_eq_nat @ SY924 @ SY925 )
| ( ord_less_eq_nat @ ( SV315 @ SY924 ) @ ( SV315 @ SY925 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( SV315 @ SV106 ) @ SV361 )
= $true )
| ( ( ord_less_eq_nat @ ( SV315 @ SV227 ) @ SV361 )
= $false )
| ( ( ord_less_eq_nat @ SV106 @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1815]) ).
thf(1971,plain,
! [SV362: nat,SV228: nat] :
( ( ( ~ ( ord_less_nat @ SV228 @ SV362 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV228 @ SV362 )
| ~ ( ( SV228 != SV362 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV228 @ SV362 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1816]) ).
thf(1972,plain,
! [SV362: nat,SV228: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV228 @ SV362 )
| ~ ( ( SV228 != SV362 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV228 @ SV362 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV228 @ SV362 )
| ~ ( ( SV228 != SV362 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1817]) ).
thf(1973,plain,
! [SV110: nat > $o,SV230: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( sK10_SY608 @ SV230 @ SV110 ) )
= $true )
| ( ( SV110 @ SV230 )
= $true )
| ( ( SV110 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1818]) ).
thf(1974,plain,
! [SV230: nat,SV110: nat > $o] :
( ( ( ~ ~ ( SV110 @ ( sK10_SY608 @ SV230 @ SV110 ) ) )
= $false )
| ( ( SV110 @ SV230 )
= $true )
| ( ( SV110 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1819]) ).
thf(1975,plain,
! [SV110: nat > $o,SV230: nat] :
( ( ( ~ ! [SY1015: nat] :
~ ~ ( ~ ( ord_less_nat @ SY1015 @ ( sK10_SY608 @ SV230 @ SV110 ) )
| ~ ~ ( SV110 @ SY1015 ) ) )
= $false )
| ( ( SV110 @ SV230 )
= $true )
| ( ( SV110 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1819]) ).
thf(1976,plain,
! [SV231: set_nat,SV111: nat > nat] :
( ( ( member_nat @ ( sK11_SY815 @ SV111 @ SV231 ) @ SV231 )
= $true )
| ( ( ( groups1842438620at_nat @ SV111 @ SV231 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1820]) ).
thf(1977,plain,
! [SV116: set_nat,SV236: nat > nat,SV319: set_nat,SV363: nat > nat,SV374: nat > nat,SV376: nat > nat] :
( ( ( ~ ( member_nat @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) @ SV116 )
| ~ ( ~ ( member_nat @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) @ SV319 )
| ( ( SV363 @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) )
!= ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) ) )
= $false )
| ( ( ~ ! [SY1014: nat] :
( ~ ( member_nat @ SY1014 @ SV319 )
| ~ ( ~ ~ ( ~ ( member_nat @ ( SV363 @ SY1014 ) @ SV116 )
| ( ( SV236 @ ( SV363 @ SY1014 ) )
!= SY1014 ) )
| ( ( SV374 @ ( SV363 @ SY1014 ) )
!= ( SV376 @ SY1014 ) ) ) )
| ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1822]) ).
thf(1978,plain,
! [SV237: nat,SV364: set_nat,SV117: nat,SV320: nat > set_nat] :
( ( ( ~ ! [SY932: nat,SY933: nat] :
( ~ ( ord_less_eq_nat @ SY932 @ SY933 )
| ( ord_less_eq_set_nat @ ( SV320 @ SY932 ) @ ( SV320 @ SY933 ) ) ) )
= $true )
| ( ( ord_less_eq_set_nat @ ( SV320 @ SV117 ) @ SV364 )
= $true )
| ( ( ord_less_eq_set_nat @ ( SV320 @ SV237 ) @ SV364 )
= $false )
| ( ( ord_less_eq_nat @ SV117 @ SV237 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1823]) ).
thf(1979,plain,
! [SV321: nat,SV365: nat,SV119: nat,SV239: nat > nat] :
( ( ( ~ ! [SY830: nat,SY831: nat] :
( ~ ( ord_less_eq_nat @ SY830 @ SY831 )
| ( ord_less_eq_nat @ ( SV239 @ SY830 ) @ ( SV239 @ SY831 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV119 @ ( SV239 @ SV365 ) )
= $true )
| ( ( ord_less_eq_nat @ SV321 @ SV365 )
= $false )
| ( ( ord_less_eq_nat @ SV119 @ ( SV239 @ SV321 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1825]) ).
thf(1980,plain,
! [SV366: nat,SV243: nat] :
( ( ( ( SV243 != SV366 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV243 @ SV366 )
| ~ ( ord_less_eq_nat @ SV366 @ SV243 ) ) )
= $false )
| ( ( SV243 = SV366 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1826]) ).
thf(1981,plain,
! [SV366: nat,SV243: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV243 @ SV366 )
| ~ ( ord_less_eq_nat @ SV366 @ SV243 ) )
= $true )
| ( ( ~ ( ( SV243 != SV366 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV243 @ SV366 )
| ~ ( ord_less_eq_nat @ SV366 @ SV243 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1827]) ).
thf(1982,plain,
! [SV325: nat,SV367: nat,SV127: set_nat,SV246: nat > set_nat] :
( ( ( ~ ! [SY838: nat,SY839: nat] :
( ~ ( ord_less_eq_nat @ SY838 @ SY839 )
| ( ord_less_eq_set_nat @ ( SV246 @ SY838 ) @ ( SV246 @ SY839 ) ) ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV127 @ ( SV246 @ SV367 ) )
= $true )
| ( ( ord_less_eq_nat @ SV325 @ SV367 )
= $false )
| ( ( ord_less_eq_set_nat @ SV127 @ ( SV246 @ SV325 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1828]) ).
thf(1983,plain,
! [SV368: nat,SV128: nat,SV326: nat,SV247: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV247 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV326 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV128 @ SV326 ) @ ( times_times_nat @ SV247 @ SV368 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV326 @ SV368 )
= $false )
| ( ( ord_less_eq_nat @ SV128 @ SV247 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1829]) ).
thf(1984,plain,
! [SV327: nat,SV248: nat,SV130: nat] :
( ( ( ( ( times_times_nat @ SV130 @ SV248 )
= ( times_times_nat @ SV130 @ SV327 ) )
| ( SV248 = SV327 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV130 @ SV248 )
!= ( times_times_nat @ SV130 @ SV327 ) )
| ( SV248 != SV327 ) ) )
= $true )
| ( ( SV130 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1830]) ).
thf(1985,plain,
! [SV328: nat,SV249: nat,SV131: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1831]) ).
thf(1986,plain,
! [SV328: nat,SV131: nat,SV249: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV249 )
| ( ord_less_eq_nat @ SV131 @ SV328 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1831]) ).
thf(1987,plain,
! [SV328: nat,SV131: nat,SV249: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV249 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV249 )
| ( ord_less_eq_nat @ SV131 @ SV328 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1832]) ).
thf(1988,plain,
! [SV328: nat,SV249: nat,SV131: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV249 )
| ( ord_less_eq_nat @ SV131 @ SV328 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV131 @ SV328 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1833]) ).
thf(1989,plain,
! [SV250: nat,SV369: nat,SV132: nat,SV329: nat > nat] :
( ( ( ~ ! [SY942: nat,SY943: nat] :
( ~ ( ord_less_eq_nat @ SY942 @ SY943 )
| ( ord_less_eq_nat @ ( SV329 @ SY942 ) @ ( SV329 @ SY943 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( SV329 @ SV132 ) @ SV369 )
= $true )
| ( ( ( SV329 @ SV250 )
= SV369 )
= $false )
| ( ( ord_less_eq_nat @ SV132 @ SV250 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1834]) ).
thf(1990,plain,
! [SV331: nat,SV134: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV331 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV134 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1835]) ).
thf(1991,plain,
! [SV331: nat,SV134: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV331 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV134 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1836]) ).
thf(1992,plain,
! [SV332: nat,SV253: nat,SV135: nat] :
( ( ( ~ ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) ) )
= $false )
| ( ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1837]) ).
thf(1993,plain,
! [SV332: nat,SV253: nat,SV135: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 )
| ~ ( ord_less_nat @ SV253 @ SV332 ) ) )
= $false )
| ( ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1837]) ).
thf(1994,plain,
! [SV332: nat,SV253: nat,SV135: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV253 @ SV332 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 )
| ~ ( ord_less_nat @ SV253 @ SV332 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1838]) ).
thf(1995,plain,
! [SV254: nat,SV136: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1839]) ).
thf(1996,plain,
! [SV254: nat,SV136: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV136 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV254 ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1840]) ).
thf(1997,plain,
! [SV254: nat,SV136: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV136 )
= $false )
| ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV254 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV136 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV254 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1841]) ).
thf(1998,plain,
! [SV140: nat,SV258: nat] :
( ( ( ord_less_eq_nat @ SV258 @ zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV140 )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV140 @ SV258 ) @ zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1842]) ).
thf(1999,plain,
! [SV140: nat,SV258: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV258 )
= $false )
| ( ( ord_less_eq_nat @ SV140 @ zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV140 @ SV258 ) @ zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1843]) ).
thf(2000,plain,
! [SV370: nat,SV259: nat] :
( ( ( ~ ( ord_less_nat @ SV259 @ SV370 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV259 @ SV370 )
| ~ ( ( SV259 != SV370 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV259 @ SV370 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1844]) ).
thf(2001,plain,
! [SV370: nat,SV259: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV259 @ SV370 )
| ~ ( ( SV259 != SV370 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV259 @ SV370 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV259 @ SV370 )
| ~ ( ( SV259 != SV370 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1845]) ).
thf(2002,plain,
! [SV263: nat,SV145: nat] :
( ( ( one_one_nat
= ( times_times_nat @ SV145 @ SV263 ) )
= $true )
| ( ( one_one_nat
= ( times_times_nat @ SV145 @ SV263 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1847]) ).
thf(2003,plain,
! [SV263: nat,SV145: nat] :
( ( ( ~ ( ( SV145 != one_one_nat )
| ( SV263 != one_one_nat ) ) )
= $true )
| ( ( one_one_nat
= ( times_times_nat @ SV145 @ SV263 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1848]) ).
thf(2004,plain,
! [SV263: nat,SV145: nat] :
( ( ( SV145 = one_one_nat )
= $false )
| ( ( SV263 != one_one_nat )
= $true )
| ( ( ~ ( ( one_one_nat
!= ( times_times_nat @ SV145 @ SV263 ) )
| ~ ~ ( ( SV145 != one_one_nat )
| ( SV263 != one_one_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1849]) ).
thf(2005,plain,
! [SV336: nat,SV146: nat,SV264: nat] :
( ( ( ( ( times_times_nat @ SV264 @ SV146 )
= ( times_times_nat @ SV336 @ SV146 ) )
| ( SV264 = SV336 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV264 @ SV146 )
!= ( times_times_nat @ SV336 @ SV146 ) )
| ( SV264 != SV336 ) ) )
= $true )
| ( ( SV146 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1850]) ).
thf(2006,plain,
! [SV147: nat] :
( ( ( SV147 != zero_zero_nat )
= $true )
| ( ( SV147 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1851]) ).
thf(2007,plain,
! [SV147: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV147 )
= $true )
| ( ( SV147 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1852]) ).
thf(2008,plain,
! [SV147: nat] :
( ( ( SV147 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1853]) ).
thf(2009,plain,
! [SV265: nat,SV148: nat > nat] :
( ( ( ( groups1842438620at_nat
@ ^ [SY685: nat] : ( times_times_nat @ ( SV148 @ SY685 ) @ SY685 )
@ ( set_ord_atMost_nat @ SV265 ) )
!= SV265 )
= $true )
| ( ( number1551313001itions @ SV148 @ SV265 )
= $true )
| ( ( ( SV148 @ ( sK4_SY856 @ SV265 @ SV148 ) )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1855]) ).
thf(2010,plain,
! [SV148: nat > nat,SV265: nat] :
( ( ( ord_less_eq_nat @ one_one_nat @ ( sK4_SY856 @ SV265 @ SV148 ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ ( sK4_SY856 @ SV265 @ SV148 ) @ SV265 ) )
= $true )
| ( ( ( ( groups1842438620at_nat
@ ^ [SY685: nat] : ( times_times_nat @ ( SV148 @ SY685 ) @ SY685 )
@ ( set_ord_atMost_nat @ SV265 ) )
!= SV265 )
| ( number1551313001itions @ SV148 @ SV265 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1856]) ).
thf(2011,plain,
! [SV266: nat,SV149: nat] :
( ( ( ( times_times_nat @ SV149 @ SV266 )
= one_one_nat )
= $true )
| ( ( ( times_times_nat @ SV149 @ SV266 )
= one_one_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1857]) ).
thf(2012,plain,
! [SV266: nat,SV149: nat] :
( ( ( ~ ( ( SV149 != one_one_nat )
| ( SV266 != one_one_nat ) ) )
= $true )
| ( ( ( times_times_nat @ SV149 @ SV266 )
= one_one_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1858]) ).
thf(2013,plain,
! [SV266: nat,SV149: nat] :
( ( ( SV149 = one_one_nat )
= $false )
| ( ( SV266 != one_one_nat )
= $true )
| ( ( ~ ( ( ( times_times_nat @ SV149 @ SV266 )
!= one_one_nat )
| ~ ~ ( ( SV149 != one_one_nat )
| ( SV266 != one_one_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1859]) ).
thf(2014,plain,
! [SV150: nat] :
( ( ( SV150 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV150 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1861]) ).
thf(2015,plain,
! [SV150: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV150 )
= $true )
| ( ( SV150 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1862]) ).
thf(2016,plain,
! [SV150: nat] :
( ( ( SV150 != zero_zero_nat )
= $true )
| ( ( SV150 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1863]) ).
thf(2017,plain,
! [SV267: set_nat,SV371: nat,SV151: set_nat,SV337: set_nat > nat] :
( ( ( ~ ! [SY946: set_nat,SY947: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY946 @ SY947 )
| ( ord_less_eq_nat @ ( SV337 @ SY946 ) @ ( SV337 @ SY947 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( SV337 @ SV151 ) @ SV371 )
= $true )
| ( ( ( SV337 @ SV267 )
= SV371 )
= $false )
| ( ( ord_less_eq_set_nat @ SV151 @ SV267 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1864]) ).
thf(2018,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1865]) ).
thf(2019,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV153 )
| ( ord_less_eq_nat @ SV269 @ SV339 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1865]) ).
thf(2020,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV153 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV153 )
| ( ord_less_eq_nat @ SV269 @ SV339 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1866]) ).
thf(2021,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV153 )
| ( ord_less_eq_nat @ SV269 @ SV339 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV269 @ SV339 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1867]) ).
thf(2022,plain,
! [SV272: nat,SV159: nat,SV5: nat] :
( ( ( ( times_times_nat @ SV5 @ SV159 )
= ( times_times_nat @ SV272 @ SV159 ) )
= $true )
| ( ( ( times_times_nat @ SV5 @ SV159 )
= ( times_times_nat @ SV272 @ SV159 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1880]) ).
thf(2023,plain,
! [SV272: nat,SV5: nat,SV159: nat] :
( ( ( ( SV159 = zero_zero_nat )
| ( SV5 = SV272 ) )
= $true )
| ( ( ( times_times_nat @ SV5 @ SV159 )
= ( times_times_nat @ SV272 @ SV159 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1881]) ).
thf(2024,plain,
! [SV272: nat,SV159: nat,SV5: nat] :
( ( ( ( times_times_nat @ SV5 @ SV159 )
!= ( times_times_nat @ SV272 @ SV159 ) )
= $false )
| ( ( SV159 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1882]) ).
thf(2025,plain,
! [SV272: nat,SV5: nat,SV159: nat] :
( ( ( ~ ( ( SV159 = zero_zero_nat )
| ( SV5 = SV272 ) ) )
= $false )
| ( ( SV159 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1882]) ).
thf(2026,plain,
! [SV272: nat,SV159: nat,SV5: nat] :
( ( ( ( times_times_nat @ SV5 @ SV159 )
!= ( times_times_nat @ SV272 @ SV159 ) )
= $false )
| ( ( SV5 = SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1883]) ).
thf(2027,plain,
! [SV272: nat,SV5: nat,SV159: nat] :
( ( ( ~ ( ( SV159 = zero_zero_nat )
| ( SV5 = SV272 ) ) )
= $false )
| ( ( SV5 = SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1883]) ).
thf(2028,plain,
! [SV273: nat,SV160: nat,SV6: nat] :
( ( ( ( times_times_nat @ SV6 @ SV160 )
= ( times_times_nat @ SV6 @ SV273 ) )
= $true )
| ( ( ( times_times_nat @ SV6 @ SV160 )
= ( times_times_nat @ SV6 @ SV273 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1884]) ).
thf(2029,plain,
! [SV273: nat,SV160: nat,SV6: nat] :
( ( ( ( SV6 = zero_zero_nat )
| ( SV160 = SV273 ) )
= $true )
| ( ( ( times_times_nat @ SV6 @ SV160 )
= ( times_times_nat @ SV6 @ SV273 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1885]) ).
thf(2030,plain,
! [SV273: nat,SV160: nat,SV6: nat] :
( ( ( ( times_times_nat @ SV6 @ SV160 )
!= ( times_times_nat @ SV6 @ SV273 ) )
= $false )
| ( ( SV6 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1886]) ).
thf(2031,plain,
! [SV273: nat,SV160: nat,SV6: nat] :
( ( ( ~ ( ( SV6 = zero_zero_nat )
| ( SV160 = SV273 ) ) )
= $false )
| ( ( SV6 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1886]) ).
thf(2032,plain,
! [SV273: nat,SV160: nat,SV6: nat] :
( ( ( ( times_times_nat @ SV6 @ SV160 )
!= ( times_times_nat @ SV6 @ SV273 ) )
= $false )
| ( ( SV160 = SV273 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1887]) ).
thf(2033,plain,
! [SV273: nat,SV160: nat,SV6: nat] :
( ( ( ~ ( ( SV6 = zero_zero_nat )
| ( SV160 = SV273 ) ) )
= $false )
| ( ( SV160 = SV273 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1887]) ).
thf(2034,plain,
! [SV161: nat,SV7: nat] :
( ( ( SV7 = zero_zero_nat )
= $true )
| ( ( SV161 = zero_zero_nat )
= $true )
| ( ( ( times_times_nat @ SV7 @ SV161 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1889]) ).
thf(2035,plain,
! [SV161: nat,SV7: nat] :
( ( ( ( times_times_nat @ SV7 @ SV161 )
= zero_zero_nat )
= $true )
| ( ( SV7 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1890]) ).
thf(2036,plain,
! [SV161: nat,SV7: nat] :
( ( ( ( SV7 = zero_zero_nat )
| ( SV161 = zero_zero_nat ) )
= $true )
| ( ( SV7 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1891]) ).
thf(2037,plain,
! [SV161: nat,SV7: nat] :
( ( ( ( times_times_nat @ SV7 @ SV161 )
= zero_zero_nat )
= $true )
| ( ( SV161 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1892]) ).
thf(2038,plain,
! [SV161: nat,SV7: nat] :
( ( ( ( SV7 = zero_zero_nat )
| ( SV161 = zero_zero_nat ) )
= $true )
| ( ( SV161 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1893]) ).
thf(2039,plain,
! [SV274: nat,SV162: nat,SV12: nat] :
( ( ( ( times_times_nat @ SV12 @ SV162 )
= ( times_times_nat @ SV274 @ SV162 ) )
= $true )
| ( ( ( times_times_nat @ SV12 @ SV162 )
= ( times_times_nat @ SV274 @ SV162 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1894]) ).
thf(2040,plain,
! [SV162: nat,SV274: nat,SV12: nat] :
( ( ( ( SV12 = SV274 )
| ( SV162 = zero_zero_nat ) )
= $true )
| ( ( ( times_times_nat @ SV12 @ SV162 )
= ( times_times_nat @ SV274 @ SV162 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1895]) ).
thf(2041,plain,
! [SV274: nat,SV162: nat,SV12: nat] :
( ( ( ( times_times_nat @ SV12 @ SV162 )
!= ( times_times_nat @ SV274 @ SV162 ) )
= $false )
| ( ( SV12 = SV274 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1896]) ).
thf(2042,plain,
! [SV162: nat,SV274: nat,SV12: nat] :
( ( ( ~ ( ( SV12 = SV274 )
| ( SV162 = zero_zero_nat ) ) )
= $false )
| ( ( SV12 = SV274 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1896]) ).
thf(2043,plain,
! [SV274: nat,SV162: nat,SV12: nat] :
( ( ( ( times_times_nat @ SV12 @ SV162 )
!= ( times_times_nat @ SV274 @ SV162 ) )
= $false )
| ( ( SV162 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1897]) ).
thf(2044,plain,
! [SV162: nat,SV274: nat,SV12: nat] :
( ( ( ~ ( ( SV12 = SV274 )
| ( SV162 = zero_zero_nat ) ) )
= $false )
| ( ( SV162 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1897]) ).
thf(2045,plain,
! [SV275: nat,SV163: nat,SV13: nat] :
( ( ( ( times_times_nat @ SV13 @ SV163 )
= ( times_times_nat @ SV13 @ SV275 ) )
= $true )
| ( ( ( times_times_nat @ SV13 @ SV163 )
= ( times_times_nat @ SV13 @ SV275 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1898]) ).
thf(2046,plain,
! [SV13: nat,SV275: nat,SV163: nat] :
( ( ( ( SV163 = SV275 )
| ( SV13 = zero_zero_nat ) )
= $true )
| ( ( ( times_times_nat @ SV13 @ SV163 )
= ( times_times_nat @ SV13 @ SV275 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1899]) ).
thf(2047,plain,
! [SV275: nat,SV163: nat,SV13: nat] :
( ( ( ( times_times_nat @ SV13 @ SV163 )
!= ( times_times_nat @ SV13 @ SV275 ) )
= $false )
| ( ( SV163 = SV275 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1900]) ).
thf(2048,plain,
! [SV13: nat,SV275: nat,SV163: nat] :
( ( ( ~ ( ( SV163 = SV275 )
| ( SV13 = zero_zero_nat ) ) )
= $false )
| ( ( SV163 = SV275 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1900]) ).
thf(2049,plain,
! [SV275: nat,SV163: nat,SV13: nat] :
( ( ( ( times_times_nat @ SV13 @ SV163 )
!= ( times_times_nat @ SV13 @ SV275 ) )
= $false )
| ( ( SV13 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1901]) ).
thf(2050,plain,
! [SV13: nat,SV275: nat,SV163: nat] :
( ( ( ~ ( ( SV163 = SV275 )
| ( SV13 = zero_zero_nat ) ) )
= $false )
| ( ( SV13 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1901]) ).
thf(2051,plain,
! [SV164: nat,SV15: nat] :
( ( ( SV15 = zero_zero_nat )
= $true )
| ( ( SV164 = zero_zero_nat )
= $true )
| ( ( ( times_times_nat @ SV15 @ SV164 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1903]) ).
thf(2052,plain,
! [SV164: nat,SV15: nat] :
( ( ( ( times_times_nat @ SV15 @ SV164 )
= zero_zero_nat )
= $true )
| ( ( SV15 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1904]) ).
thf(2053,plain,
! [SV164: nat,SV15: nat] :
( ( ( ( SV15 = zero_zero_nat )
| ( SV164 = zero_zero_nat ) )
= $true )
| ( ( SV15 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1905]) ).
thf(2054,plain,
! [SV164: nat,SV15: nat] :
( ( ( ( times_times_nat @ SV15 @ SV164 )
= zero_zero_nat )
= $true )
| ( ( SV164 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1906]) ).
thf(2055,plain,
! [SV164: nat,SV15: nat] :
( ( ( ( SV15 = zero_zero_nat )
| ( SV164 = zero_zero_nat ) )
= $true )
| ( ( SV164 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1907]) ).
thf(2056,plain,
! [SV280: nat,SV173: nat,SV37: nat] :
( ( ( ( times_times_nat @ SV37 @ SV173 )
= ( times_times_nat @ SV37 @ SV280 ) )
= $true )
| ( ( ( times_times_nat @ SV37 @ SV173 )
= ( times_times_nat @ SV37 @ SV280 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1908]) ).
thf(2057,plain,
! [SV280: nat,SV173: nat,SV37: nat] :
( ( ( ( SV37 = zero_zero_nat )
| ( SV173 = SV280 ) )
= $true )
| ( ( ( times_times_nat @ SV37 @ SV173 )
= ( times_times_nat @ SV37 @ SV280 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1909]) ).
thf(2058,plain,
! [SV280: nat,SV173: nat,SV37: nat] :
( ( ( ( times_times_nat @ SV37 @ SV173 )
!= ( times_times_nat @ SV37 @ SV280 ) )
= $false )
| ( ( SV37 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1910]) ).
thf(2059,plain,
! [SV280: nat,SV173: nat,SV37: nat] :
( ( ( ~ ( ( SV37 = zero_zero_nat )
| ( SV173 = SV280 ) ) )
= $false )
| ( ( SV37 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1910]) ).
thf(2060,plain,
! [SV280: nat,SV173: nat,SV37: nat] :
( ( ( ( times_times_nat @ SV37 @ SV173 )
!= ( times_times_nat @ SV37 @ SV280 ) )
= $false )
| ( ( SV173 = SV280 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1911]) ).
thf(2061,plain,
! [SV280: nat,SV173: nat,SV37: nat] :
( ( ( ~ ( ( SV37 = zero_zero_nat )
| ( SV173 = SV280 ) ) )
= $false )
| ( ( SV173 = SV280 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1911]) ).
thf(2062,plain,
! [SV50: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV50 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1912]) ).
thf(2063,plain,
! [SV343: nat,SV179: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV179 @ SV343 ) )
= $false )
| ( ( ord_less_eq_nat @ SV179 @ SV343 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1915]) ).
thf(2064,plain,
! [SV343: nat,SV179: nat] :
( ( ( ~ ( ( ord_less_nat @ SV179 @ SV343 )
| ( SV179 = SV343 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV179 @ SV343 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1915]) ).
thf(2065,plain,
! [SV343: nat,SV179: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV179 @ SV343 )
| ~ ( ( ord_less_nat @ SV179 @ SV343 )
| ( SV179 = SV343 ) ) )
= $false )
| ( ( ord_less_nat @ SV179 @ SV343 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1916]) ).
thf(2066,plain,
! [SV343: nat,SV179: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV179 @ SV343 )
| ~ ( ( ord_less_nat @ SV179 @ SV343 )
| ( SV179 = SV343 ) ) )
= $false )
| ( ( SV179 = SV343 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1917]) ).
thf(2067,plain,
! [SV54: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV54 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1918]) ).
thf(2068,plain,
! [SV344: nat,SV180: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV180 @ SV344 ) )
= $false )
| ( ( ord_less_eq_nat @ SV180 @ SV344 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1921]) ).
thf(2069,plain,
! [SV344: nat,SV180: nat] :
( ( ( ~ ( ( ord_less_nat @ SV180 @ SV344 )
| ( SV344 = SV180 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV180 @ SV344 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1921]) ).
thf(2070,plain,
! [SV344: nat,SV180: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV180 @ SV344 )
| ~ ( ( ord_less_nat @ SV180 @ SV344 )
| ( SV344 = SV180 ) ) )
= $false )
| ( ( ord_less_nat @ SV180 @ SV344 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1922]) ).
thf(2071,plain,
! [SV344: nat,SV180: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV180 @ SV344 )
| ~ ( ( ord_less_nat @ SV180 @ SV344 )
| ( SV344 = SV180 ) ) )
= $false )
| ( ( SV344 = SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1923]) ).
thf(2072,plain,
! [SV345: nat,SV181: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV181 @ SV345 ) )
= $false )
| ( ( ord_less_eq_nat @ SV181 @ SV345 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1924]) ).
thf(2073,plain,
! [SV345: nat,SV181: nat] :
( ( ( ~ ( ( ord_less_nat @ SV181 @ SV345 )
| ( SV181 = SV345 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV181 @ SV345 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1924]) ).
thf(2074,plain,
! [SV345: nat,SV181: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV181 @ SV345 )
| ~ ( ( ord_less_nat @ SV181 @ SV345 )
| ( SV181 = SV345 ) ) )
= $false )
| ( ( ord_less_nat @ SV181 @ SV345 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1925]) ).
thf(2075,plain,
! [SV345: nat,SV181: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV181 @ SV345 )
| ~ ( ( ord_less_nat @ SV181 @ SV345 )
| ( SV181 = SV345 ) ) )
= $false )
| ( ( SV181 = SV345 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1926]) ).
thf(2076,plain,
! [SV60: set_nat,SV182: nat > nat,SV288: nat > nat,SV346: set_nat,SV372: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 ) )
= $false )
| ( ( ~ ! [SY953: nat] :
( ~ ( member_nat @ SY953 @ SV60 )
| ( member_nat @ ( SV288 @ SY953 ) @ SV346 ) )
| ~ ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) )
| ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1927]) ).
thf(2077,plain,
! [SV60: set_nat,SV346: set_nat,SV372: nat > nat,SV375: nat > nat,SV288: nat > nat,SV182: nat > nat] :
( ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false )
| ( ( ~ ! [SY953: nat] :
( ~ ( member_nat @ SY953 @ SV60 )
| ( member_nat @ ( SV288 @ SY953 ) @ SV346 ) )
| ~ ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) )
| ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1927]) ).
thf(2078,plain,
! [SV347: nat,SV186: nat] :
( ( ( SV186 != SV347 )
= $false )
| ( ( SV186 = SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1929]) ).
thf(2079,plain,
! [SV347: nat,SV186: nat] :
( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV186 @ SV347 )
| ~ ( ord_less_eq_nat @ SV347 @ SV186 ) ) )
= $false )
| ( ( SV186 = SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1929]) ).
thf(2080,plain,
! [SV347: nat,SV186: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV186 @ SV347 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV347 @ SV186 ) )
= $true )
| ( ( ~ ( ( SV186 != SV347 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV186 @ SV347 )
| ~ ( ord_less_eq_nat @ SV347 @ SV186 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1930]) ).
thf(2081,plain,
! [SV191: set_nat,SV348: nat,SV69: set_nat,SV292: set_nat > nat] :
( ( ( ! [SY882: set_nat,SY883: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY882 @ SY883 )
| ( ord_less_eq_nat @ ( SV292 @ SY882 ) @ ( SV292 @ SY883 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV292 @ SV69 ) @ SV348 )
= $true )
| ( ( ord_less_eq_nat @ ( SV292 @ SV191 ) @ SV348 )
= $false )
| ( ( ord_less_eq_set_nat @ SV69 @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1931]) ).
thf(2082,plain,
! [SV293: nat,SV192: nat,SV70: nat > $o] :
( ( ( SV70 @ ( sK12_SY884 @ SV192 @ SV293 @ SV70 ) )
= $true )
| ( ( ~ ! [SY505: nat] :
( ~ ( SV70 @ SY505 )
| ~ ! [SY506: nat] :
( ~ ( SV70 @ SY506 )
| ( ord_less_eq_nat @ SY506 @ SY505 ) ) ) )
= $true )
| ( ( SV70 @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1932]) ).
thf(2083,plain,
! [SV293: nat,SV192: nat,SV70: nat > $o] :
( ( ( ! [SY505: nat] :
( ~ ( SV70 @ SY505 )
| ~ ! [SY506: nat] :
( ~ ( SV70 @ SY506 )
| ( ord_less_eq_nat @ SY506 @ SY505 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK12_SY884 @ SV192 @ SV293 @ SV70 ) @ SV293 )
= $false )
| ( ( SV70 @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1933]) ).
thf(2084,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ~ ( number1551313001itions @ SV194 @ SV350 ) )
= $false )
| ( ( number1551313001itions @ SV194 @ SV350 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1934]) ).
thf(2085,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ~ ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) )
= $false )
| ( ( number1551313001itions @ SV194 @ SV350 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1934]) ).
thf(2086,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 )
= $true )
| ( ( ~ ( ~ ( number1551313001itions @ SV194 @ SV350 )
| ~ ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1935]) ).
thf(2087,plain,
! [SV196: nat,SV351: set_nat,SV74: nat,SV296: nat > set_nat] :
( ( ( ! [SY891: nat,SY892: nat] :
( ~ ( ord_less_eq_nat @ SY891 @ SY892 )
| ( ord_less_eq_set_nat @ ( SV296 @ SY891 ) @ ( SV296 @ SY892 ) ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ ( SV296 @ SV74 ) @ SV351 )
= $true )
| ( ( ( SV296 @ SV196 )
= SV351 )
= $false )
| ( ( ord_less_eq_nat @ SV74 @ SV196 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1936]) ).
thf(2088,plain,
! [SV298: nat,SV198: nat,SV76: nat > nat > $o] :
( ( ( ~ ! [SY525: nat,SY526: nat] :
( ~ ( SV76 @ SY526 @ SY525 )
| ( SV76 @ SY525 @ SY526 ) ) )
= $true )
| ( ( SV76 @ SV198 @ SV298 )
= $true )
| ( ( ord_less_eq_nat @ ( sK5_SY523 @ SV298 @ SV198 @ SV76 ) @ ( sK8_SY1011 @ SV76 @ SV198 @ SV298 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1937]) ).
thf(2089,plain,
! [SV298: nat,SV198: nat,SV76: nat > nat > $o] :
( ( ( ! [SY525: nat,SY526: nat] :
( ~ ( SV76 @ SY526 @ SY525 )
| ( SV76 @ SY525 @ SY526 ) ) )
= $false )
| ( ( SV76 @ SV198 @ SV298 )
= $true )
| ( ( SV76 @ ( sK5_SY523 @ SV298 @ SV198 @ SV76 ) @ ( sK8_SY1011 @ SV76 @ SV198 @ SV298 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1938]) ).
thf(2090,plain,
! [SV352: nat,SV205: nat,SV303: nat,SV83: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV83 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV303 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV83 @ SV303 ) @ ( times_times_nat @ SV205 @ SV352 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV303 @ SV352 )
= $false )
| ( ( ord_less_eq_nat @ SV83 @ SV205 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1941]) ).
thf(2091,plain,
! [SV84: nat,SV206: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV206 @ SV84 ) )
= $false )
| ( ( ord_less_eq_nat @ SV206 @ SV84 )
= $false )
| ( ( ord_less_eq_nat @ SV84 @ SV206 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1942]) ).
thf(2092,plain,
! [SV84: nat,SV206: nat] :
( ( ( SV206 != SV84 )
= $false )
| ( ( ord_less_eq_nat @ SV206 @ SV84 )
= $false )
| ( ( ord_less_eq_nat @ SV84 @ SV206 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1942]) ).
thf(2093,plain,
! [SV84: nat,SV206: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV206 @ SV84 ) )
= $false )
| ( ( SV206 = SV84 )
= $false )
| ( ( ord_less_eq_nat @ SV84 @ SV206 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1943]) ).
thf(2094,plain,
! [SV84: nat,SV206: nat] :
( ( ( SV206 != SV84 )
= $false )
| ( ( SV206 = SV84 )
= $false )
| ( ( ord_less_eq_nat @ SV84 @ SV206 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1943]) ).
thf(2095,plain,
! [SV85: set_nat,SV207: set_nat,SV304: nat > nat,SV353: nat > nat,SV373: nat > nat] :
( ( ( member_nat @ ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) @ SV85 )
= $true )
| ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) )
| ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1944]) ).
thf(2096,plain,
! [SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV304: nat > nat,SV207: set_nat] :
( ( ( ! [SY1016: nat] :
~ ~ ( ~ ~ ( ~ ( member_nat @ SY1016 @ SV207 )
| ( ( SV304 @ SY1016 )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) ) )
| ~ ! [SY1017: nat] :
( ~ ~ ( ~ ( member_nat @ SY1017 @ SV207 )
| ( ( SV304 @ SY1017 )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) ) )
| ( SY1017 = SY1016 ) ) ) )
= $true )
| ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) )
| ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1945]) ).
thf(2097,plain,
! [SV305: nat,SV354: nat,SV86: set_nat,SV208: nat > set_nat] :
( ( ( ! [SY776: nat,SY777: nat] :
( ~ ( ord_less_eq_nat @ SY776 @ SY777 )
| ( ord_less_eq_set_nat @ ( SV208 @ SY776 ) @ ( SV208 @ SY777 ) ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ SV86 @ ( SV208 @ SV354 ) )
= $true )
| ( ( ord_less_eq_nat @ SV305 @ SV354 )
= $false )
| ( ( SV86
= ( SV208 @ SV305 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1946]) ).
thf(2098,plain,
! [SV306: set_nat,SV355: set_nat,SV87: nat,SV209: set_nat > nat] :
( ( ( ! [SY780: set_nat,SY781: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY780 @ SY781 )
| ( ord_less_eq_nat @ ( SV209 @ SY780 ) @ ( SV209 @ SY781 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV87 @ ( SV209 @ SV355 ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV306 @ SV355 )
= $false )
| ( ( SV87
= ( SV209 @ SV306 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1947]) ).
thf(2099,plain,
! [SV88: nat] :
( ( ( SV88 = zero_zero_nat )
= $false )
| ( ( SV88 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1948]) ).
thf(2100,plain,
! [SV378: nat] :
( ( ( ~ ( ( ( p @ SV378 )
!= zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SV378 )
| ~ ( ord_less_eq_nat @ SV378 @ zero_zero_nat ) ) )
= $true )
| ( ( p
= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1951]) ).
thf(2101,plain,
! [SV380: nat] :
( ( ( ( p @ SV380 )
= zero_zero_nat )
= $true )
| ( ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
= zero_zero_nat )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1952]) ).
thf(2102,plain,
( ( ( ~ ( ( ( p @ sK18_SX0 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ sK18_SX0 )
| ~ ( ord_less_eq_nat @ sK18_SX0 @ zero_zero_nat ) ) )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
!= zero_zero_nat )
= $true )
| ( ( p
!= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1954]) ).
thf(2103,plain,
! [SV356: nat,SV213: nat] :
( ( ( SV213 != SV356 )
= $false )
| ( ( SV213 = SV356 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1955]) ).
thf(2104,plain,
! [SV213: nat,SV356: nat] :
( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV356 @ SV213 )
| ~ ( ord_less_eq_nat @ SV213 @ SV356 ) ) )
= $false )
| ( ( SV213 = SV356 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1955]) ).
thf(2105,plain,
! [SV213: nat,SV356: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV356 @ SV213 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV213 @ SV356 ) )
= $true )
| ( ( ~ ( ( SV213 != SV356 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV356 @ SV213 )
| ~ ( ord_less_eq_nat @ SV213 @ SV356 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1956]) ).
thf(2106,plain,
! [SV214: set_nat,SV308: nat > nat,SV357: nat > nat,SV93: set_nat] :
( ( ( ~ ( member_nat @ ( sK16_SY972 @ SV93 @ SV357 @ SV308 @ SV214 ) @ SV214 ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV308 @ SV93 )
= ( groups1842438620at_nat @ SV357 @ SV214 ) )
= $true )
| ( ( SV93 = SV214 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1957]) ).
thf(2107,plain,
! [SV214: set_nat,SV357: nat > nat,SV93: set_nat,SV308: nat > nat] :
( ( ( ( SV308 @ ( sK16_SY972 @ SV93 @ SV357 @ SV308 @ SV214 ) )
= ( SV357 @ ( sK16_SY972 @ SV93 @ SV357 @ SV308 @ SV214 ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV308 @ SV93 )
= ( groups1842438620at_nat @ SV357 @ SV214 ) )
= $true )
| ( ( SV93 = SV214 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1957]) ).
thf(2108,plain,
! [SV309: set_nat,SV358: set_nat,SV95: nat,SV216: set_nat > nat] :
( ( ( ! [SY789: set_nat,SY790: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY789 @ SY790 )
| ( ord_less_eq_nat @ ( SV216 @ SY789 ) @ ( SV216 @ SY790 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ ( SV216 @ SV358 ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV309 @ SV358 )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ ( SV216 @ SV309 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1958]) ).
thf(2109,plain,
! [SV97: nat > nat,SV310: nat,SV218: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV218 @ SV310 ) )
= $true )
| ( ( ord_less_eq_nat @ ( SV97 @ SV218 ) @ ( SV97 @ SV310 ) )
= $true )
| ( ( ord_less_nat @ ( sK6_SY578 @ SV310 @ SV218 @ SV97 ) @ ( sK9_SY1012 @ SV97 @ SV218 @ SV310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1959]) ).
thf(2110,plain,
! [SV97: nat > nat,SV310: nat,SV218: nat] :
( ( ( ord_less_eq_nat @ SV218 @ SV310 )
= $false )
| ( ( ord_less_eq_nat @ ( SV97 @ SV218 ) @ ( SV97 @ SV310 ) )
= $true )
| ( ( ord_less_nat @ ( SV97 @ ( sK6_SY578 @ SV310 @ SV218 @ SV97 ) ) @ ( SV97 @ ( sK9_SY1012 @ SV97 @ SV218 @ SV310 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1960]) ).
thf(2111,plain,
! [SV311: nat,SV219: nat,SV98: nat] :
( ( ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
= $true )
| ( ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1961]) ).
thf(2112,plain,
! [SV311: nat,SV98: nat,SV219: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV219 )
| ~ ( ord_less_nat @ SV98 @ SV311 ) ) )
= $true )
| ( ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1962]) ).
thf(2113,plain,
! [SV311: nat,SV98: nat,SV219: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV219 )
= $false )
| ( ( ~ ( ord_less_nat @ SV98 @ SV311 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV219 )
| ~ ( ord_less_nat @ SV98 @ SV311 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1963]) ).
thf(2114,plain,
! [SV312: nat,SV359: nat,SV99: nat,SV220: nat > nat] :
( ( ( ! [SY798: nat,SY799: nat] :
( ~ ( ord_less_eq_nat @ SY798 @ SY799 )
| ( ord_less_eq_nat @ ( SV220 @ SY798 ) @ ( SV220 @ SY799 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV99 @ ( SV220 @ SV359 ) )
= $true )
| ( ( ord_less_eq_nat @ SV312 @ SV359 )
= $false )
| ( ( SV99
= ( SV220 @ SV312 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1964]) ).
thf(2115,plain,
! [SV313: nat,SV221: nat,SV100: nat > $o] :
( ( ( SV100 @ ( sK14_SY920 @ SV221 @ SV313 @ SV100 ) )
= $true )
| ( ( ~ ! [SY590: nat] :
~ ~ ( ~ ( SV100 @ SY590 )
| ~ ! [SY591: nat] :
( ~ ( SV100 @ SY591 )
| ( ord_less_eq_nat @ SY591 @ SY590 ) ) ) )
= $true )
| ( ( SV100 @ SV221 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1965]) ).
thf(2116,plain,
! [SV313: nat,SV221: nat,SV100: nat > $o] :
( ( ( ! [SY590: nat] :
~ ~ ( ~ ( SV100 @ SY590 )
| ~ ! [SY591: nat] :
( ~ ( SV100 @ SY591 )
| ( ord_less_eq_nat @ SY591 @ SY590 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK14_SY920 @ SV221 @ SV313 @ SV100 ) @ SV313 )
= $false )
| ( ( SV100 @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1966]) ).
thf(2117,plain,
! [SV360: nat,SV222: nat] :
( ( ( ~ ( ord_less_nat @ SV222 @ SV360 ) )
= $false )
| ( ( ord_less_nat @ SV222 @ SV360 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1967]) ).
thf(2118,plain,
! [SV360: nat,SV222: nat] :
( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV222 @ SV360 )
| ~ ( ( SV360 != SV222 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV222 @ SV360 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1967]) ).
thf(2119,plain,
! [SV360: nat,SV222: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV222 @ SV360 ) )
= $true )
| ( ( ~ ( ( SV360 != SV222 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV222 @ SV360 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV222 @ SV360 )
| ~ ( ( SV360 != SV222 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1968]) ).
thf(2120,plain,
! [SV224: nat,SV377: nat,SV103: nat > nat] :
( ( ( ( SV103 @ SV377 )
!= zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SV377 )
| ~ ( ord_less_eq_nat @ SV377 @ SV224 ) ) )
= $true )
| ( ( number1551313001itions @ SV103 @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1969]) ).
thf(2121,plain,
! [SV227: nat,SV361: nat,SV106: nat,SV315: nat > nat] :
( ( ( ! [SY924: nat,SY925: nat] :
( ~ ( ord_less_eq_nat @ SY924 @ SY925 )
| ( ord_less_eq_nat @ ( SV315 @ SY924 ) @ ( SV315 @ SY925 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV315 @ SV106 ) @ SV361 )
= $true )
| ( ( ord_less_eq_nat @ ( SV315 @ SV227 ) @ SV361 )
= $false )
| ( ( ord_less_eq_nat @ SV106 @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1970]) ).
thf(2122,plain,
! [SV362: nat,SV228: nat] :
( ( ( ~ ( ord_less_nat @ SV228 @ SV362 ) )
= $false )
| ( ( ord_less_nat @ SV228 @ SV362 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1971]) ).
thf(2123,plain,
! [SV362: nat,SV228: nat] :
( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV228 @ SV362 )
| ~ ( ( SV228 != SV362 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV228 @ SV362 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1971]) ).
thf(2124,plain,
! [SV362: nat,SV228: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV228 @ SV362 ) )
= $true )
| ( ( ~ ( ( SV228 != SV362 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV228 @ SV362 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV228 @ SV362 )
| ~ ( ( SV228 != SV362 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1972]) ).
thf(2125,plain,
! [SV230: nat,SV110: nat > $o] :
( ( ( ~ ( SV110 @ ( sK10_SY608 @ SV230 @ SV110 ) ) )
= $true )
| ( ( SV110 @ SV230 )
= $true )
| ( ( SV110 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1974]) ).
thf(2126,plain,
! [SV110: nat > $o,SV230: nat] :
( ( ( ! [SY1015: nat] :
~ ~ ( ~ ( ord_less_nat @ SY1015 @ ( sK10_SY608 @ SV230 @ SV110 ) )
| ~ ~ ( SV110 @ SY1015 ) ) )
= $true )
| ( ( SV110 @ SV230 )
= $true )
| ( ( SV110 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1975]) ).
thf(2127,plain,
! [SV116: set_nat,SV236: nat > nat,SV319: set_nat,SV363: nat > nat,SV374: nat > nat,SV376: nat > nat] :
( ( ( ~ ( member_nat @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) @ SV116 ) )
= $false )
| ( ( ~ ! [SY1014: nat] :
( ~ ( member_nat @ SY1014 @ SV319 )
| ~ ( ~ ~ ( ~ ( member_nat @ ( SV363 @ SY1014 ) @ SV116 )
| ( ( SV236 @ ( SV363 @ SY1014 ) )
!= SY1014 ) )
| ( ( SV374 @ ( SV363 @ SY1014 ) )
!= ( SV376 @ SY1014 ) ) ) )
| ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1977]) ).
thf(2128,plain,
! [SV116: set_nat,SV319: set_nat,SV363: nat > nat,SV374: nat > nat,SV376: nat > nat,SV236: nat > nat] :
( ( ( ~ ( ~ ( member_nat @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) @ SV319 )
| ( ( SV363 @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) )
!= ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) ) )
= $false )
| ( ( ~ ! [SY1014: nat] :
( ~ ( member_nat @ SY1014 @ SV319 )
| ~ ( ~ ~ ( ~ ( member_nat @ ( SV363 @ SY1014 ) @ SV116 )
| ( ( SV236 @ ( SV363 @ SY1014 ) )
!= SY1014 ) )
| ( ( SV374 @ ( SV363 @ SY1014 ) )
!= ( SV376 @ SY1014 ) ) ) )
| ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1977]) ).
thf(2129,plain,
! [SV237: nat,SV364: set_nat,SV117: nat,SV320: nat > set_nat] :
( ( ( ! [SY932: nat,SY933: nat] :
( ~ ( ord_less_eq_nat @ SY932 @ SY933 )
| ( ord_less_eq_set_nat @ ( SV320 @ SY932 ) @ ( SV320 @ SY933 ) ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ ( SV320 @ SV117 ) @ SV364 )
= $true )
| ( ( ord_less_eq_set_nat @ ( SV320 @ SV237 ) @ SV364 )
= $false )
| ( ( ord_less_eq_nat @ SV117 @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1978]) ).
thf(2130,plain,
! [SV321: nat,SV365: nat,SV119: nat,SV239: nat > nat] :
( ( ( ! [SY830: nat,SY831: nat] :
( ~ ( ord_less_eq_nat @ SY830 @ SY831 )
| ( ord_less_eq_nat @ ( SV239 @ SY830 ) @ ( SV239 @ SY831 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV119 @ ( SV239 @ SV365 ) )
= $true )
| ( ( ord_less_eq_nat @ SV321 @ SV365 )
= $false )
| ( ( ord_less_eq_nat @ SV119 @ ( SV239 @ SV321 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1979]) ).
thf(2131,plain,
! [SV366: nat,SV243: nat] :
( ( ( SV243 != SV366 )
= $false )
| ( ( SV243 = SV366 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1980]) ).
thf(2132,plain,
! [SV366: nat,SV243: nat] :
( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV243 @ SV366 )
| ~ ( ord_less_eq_nat @ SV366 @ SV243 ) ) )
= $false )
| ( ( SV243 = SV366 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1980]) ).
thf(2133,plain,
! [SV366: nat,SV243: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV243 @ SV366 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV366 @ SV243 ) )
= $true )
| ( ( ~ ( ( SV243 != SV366 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV243 @ SV366 )
| ~ ( ord_less_eq_nat @ SV366 @ SV243 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1981]) ).
thf(2134,plain,
! [SV325: nat,SV367: nat,SV127: set_nat,SV246: nat > set_nat] :
( ( ( ! [SY838: nat,SY839: nat] :
( ~ ( ord_less_eq_nat @ SY838 @ SY839 )
| ( ord_less_eq_set_nat @ ( SV246 @ SY838 ) @ ( SV246 @ SY839 ) ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ SV127 @ ( SV246 @ SV367 ) )
= $true )
| ( ( ord_less_eq_nat @ SV325 @ SV367 )
= $false )
| ( ( ord_less_eq_set_nat @ SV127 @ ( SV246 @ SV325 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1982]) ).
thf(2135,plain,
! [SV368: nat,SV128: nat,SV326: nat,SV247: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV247 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV326 )
| ( ord_less_eq_nat @ ( times_times_nat @ SV128 @ SV326 ) @ ( times_times_nat @ SV247 @ SV368 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV326 @ SV368 )
= $false )
| ( ( ord_less_eq_nat @ SV128 @ SV247 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1983]) ).
thf(2136,plain,
! [SV327: nat,SV248: nat,SV130: nat] :
( ( ( ( times_times_nat @ SV130 @ SV248 )
= ( times_times_nat @ SV130 @ SV327 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV130 @ SV248 )
!= ( times_times_nat @ SV130 @ SV327 ) )
| ( SV248 != SV327 ) ) )
= $true )
| ( ( SV130 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1984]) ).
thf(2137,plain,
! [SV130: nat,SV327: nat,SV248: nat] :
( ( ( SV248 = SV327 )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV130 @ SV248 )
!= ( times_times_nat @ SV130 @ SV327 ) )
| ( SV248 != SV327 ) ) )
= $true )
| ( ( SV130 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1984]) ).
thf(2138,plain,
! [SV328: nat,SV249: nat,SV131: nat] :
( ( ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1985]) ).
thf(2139,plain,
! [SV328: nat,SV131: nat,SV249: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV249 )
| ( ord_less_eq_nat @ SV131 @ SV328 ) )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1986]) ).
thf(2140,plain,
! [SV328: nat,SV249: nat,SV131: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV249 )
| ( ord_less_eq_nat @ SV131 @ SV328 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV249 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1987]) ).
thf(2141,plain,
! [SV328: nat,SV249: nat,SV131: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV131 @ SV328 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1988]) ).
thf(2142,plain,
! [SV328: nat,SV131: nat,SV249: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV249 )
| ( ord_less_eq_nat @ SV131 @ SV328 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV131 @ SV328 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1988]) ).
thf(2143,plain,
! [SV250: nat,SV369: nat,SV132: nat,SV329: nat > nat] :
( ( ( ! [SY942: nat,SY943: nat] :
( ~ ( ord_less_eq_nat @ SY942 @ SY943 )
| ( ord_less_eq_nat @ ( SV329 @ SY942 ) @ ( SV329 @ SY943 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV329 @ SV132 ) @ SV369 )
= $true )
| ( ( ( SV329 @ SV250 )
= SV369 )
= $false )
| ( ( ord_less_eq_nat @ SV132 @ SV250 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1989]) ).
thf(2144,plain,
! [SV331: nat,SV134: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV134 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1990]) ).
thf(2145,plain,
! [SV252: nat,SV331: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV331 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV134 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1990]) ).
thf(2146,plain,
! [SV331: nat,SV134: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV134 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1991]) ).
thf(2147,plain,
! [SV252: nat,SV331: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV331 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV134 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1991]) ).
thf(2148,plain,
! [SV332: nat,SV253: nat,SV135: nat] :
( ( ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
= $true )
| ( ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1992]) ).
thf(2149,plain,
! [SV332: nat,SV253: nat,SV135: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 )
| ~ ( ord_less_nat @ SV253 @ SV332 ) ) )
= $true )
| ( ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1993]) ).
thf(2150,plain,
! [SV332: nat,SV253: nat,SV135: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV135 )
= $false )
| ( ( ~ ( ord_less_nat @ SV253 @ SV332 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 )
| ~ ( ord_less_nat @ SV253 @ SV332 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1994]) ).
thf(2151,plain,
! [SV254: nat,SV136: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV136 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV254 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1996]) ).
thf(2152,plain,
! [SV136: nat,SV254: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV254 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV136 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV136 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV254 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1997]) ).
thf(2153,plain,
! [SV370: nat,SV259: nat] :
( ( ( ~ ( ord_less_nat @ SV259 @ SV370 ) )
= $false )
| ( ( ord_less_nat @ SV259 @ SV370 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2000]) ).
thf(2154,plain,
! [SV370: nat,SV259: nat] :
( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV259 @ SV370 )
| ~ ( ( SV259 != SV370 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV259 @ SV370 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2000]) ).
thf(2155,plain,
! [SV370: nat,SV259: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV259 @ SV370 ) )
= $true )
| ( ( ~ ( ( SV259 != SV370 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV259 @ SV370 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV259 @ SV370 )
| ~ ( ( SV259 != SV370 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2001]) ).
thf(2156,plain,
! [SV263: nat,SV145: nat] :
( ( ( ( SV145 != one_one_nat )
| ( SV263 != one_one_nat ) )
= $false )
| ( ( one_one_nat
= ( times_times_nat @ SV145 @ SV263 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2003]) ).
thf(2157,plain,
! [SV145: nat,SV263: nat] :
( ( ( SV263 = one_one_nat )
= $false )
| ( ( SV145 = one_one_nat )
= $false )
| ( ( ~ ( ( one_one_nat
!= ( times_times_nat @ SV145 @ SV263 ) )
| ~ ~ ( ( SV145 != one_one_nat )
| ( SV263 != one_one_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2004]) ).
thf(2158,plain,
! [SV336: nat,SV146: nat,SV264: nat] :
( ( ( ( times_times_nat @ SV264 @ SV146 )
= ( times_times_nat @ SV336 @ SV146 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV264 @ SV146 )
!= ( times_times_nat @ SV336 @ SV146 ) )
| ( SV264 != SV336 ) ) )
= $true )
| ( ( SV146 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2005]) ).
thf(2159,plain,
! [SV146: nat,SV336: nat,SV264: nat] :
( ( ( SV264 = SV336 )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV264 @ SV146 )
!= ( times_times_nat @ SV336 @ SV146 ) )
| ( SV264 != SV336 ) ) )
= $true )
| ( ( SV146 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2005]) ).
thf(2160,plain,
! [SV147: nat] :
( ( ( SV147 = zero_zero_nat )
= $false )
| ( ( SV147 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2006]) ).
thf(2161,plain,
! [SV265: nat,SV148: nat > nat] :
( ( ( ( groups1842438620at_nat
@ ^ [SY685: nat] : ( times_times_nat @ ( SV148 @ SY685 ) @ SY685 )
@ ( set_ord_atMost_nat @ SV265 ) )
= SV265 )
= $false )
| ( ( number1551313001itions @ SV148 @ SV265 )
= $true )
| ( ( ( SV148 @ ( sK4_SY856 @ SV265 @ SV148 ) )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2009]) ).
thf(2162,plain,
! [SV148: nat > nat,SV265: nat] :
( ( ( ord_less_eq_nat @ ( sK4_SY856 @ SV265 @ SV148 ) @ SV265 )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ ( sK4_SY856 @ SV265 @ SV148 ) )
= $false )
| ( ( ( ( groups1842438620at_nat
@ ^ [SY685: nat] : ( times_times_nat @ ( SV148 @ SY685 ) @ SY685 )
@ ( set_ord_atMost_nat @ SV265 ) )
!= SV265 )
| ( number1551313001itions @ SV148 @ SV265 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2010]) ).
thf(2163,plain,
! [SV266: nat,SV149: nat] :
( ( ( ( SV149 != one_one_nat )
| ( SV266 != one_one_nat ) )
= $false )
| ( ( ( times_times_nat @ SV149 @ SV266 )
= one_one_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2012]) ).
thf(2164,plain,
! [SV149: nat,SV266: nat] :
( ( ( SV266 = one_one_nat )
= $false )
| ( ( SV149 = one_one_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV149 @ SV266 )
!= one_one_nat )
| ~ ~ ( ( SV149 != one_one_nat )
| ( SV266 != one_one_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2013]) ).
thf(2165,plain,
! [SV150: nat] :
( ( ( SV150 = zero_zero_nat )
= $false )
| ( ( SV150 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2016]) ).
thf(2166,plain,
! [SV267: set_nat,SV371: nat,SV151: set_nat,SV337: set_nat > nat] :
( ( ( ! [SY946: set_nat,SY947: set_nat] :
( ~ ( ord_less_eq_set_nat @ SY946 @ SY947 )
| ( ord_less_eq_nat @ ( SV337 @ SY946 ) @ ( SV337 @ SY947 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV337 @ SV151 ) @ SV371 )
= $true )
| ( ( ( SV337 @ SV267 )
= SV371 )
= $false )
| ( ( ord_less_eq_set_nat @ SV151 @ SV267 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2017]) ).
thf(2167,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2018]) ).
thf(2168,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV153 )
| ( ord_less_eq_nat @ SV269 @ SV339 ) )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2019]) ).
thf(2169,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV153 )
| ( ord_less_eq_nat @ SV269 @ SV339 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV153 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2020]) ).
thf(2170,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV269 @ SV339 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2021]) ).
thf(2171,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV153 )
| ( ord_less_eq_nat @ SV269 @ SV339 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV269 @ SV339 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2021]) ).
thf(2172,plain,
! [SV272: nat,SV5: nat,SV159: nat] :
( ( ( SV159 = zero_zero_nat )
= $true )
| ( ( SV5 = SV272 )
= $true )
| ( ( ( times_times_nat @ SV5 @ SV159 )
= ( times_times_nat @ SV272 @ SV159 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2023]) ).
thf(2173,plain,
! [SV272: nat,SV159: nat,SV5: nat] :
( ( ( ( times_times_nat @ SV5 @ SV159 )
= ( times_times_nat @ SV272 @ SV159 ) )
= $true )
| ( ( SV159 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2024]) ).
thf(2174,plain,
! [SV272: nat,SV5: nat,SV159: nat] :
( ( ( ( SV159 = zero_zero_nat )
| ( SV5 = SV272 ) )
= $true )
| ( ( SV159 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2025]) ).
thf(2175,plain,
! [SV272: nat,SV159: nat,SV5: nat] :
( ( ( ( times_times_nat @ SV5 @ SV159 )
= ( times_times_nat @ SV272 @ SV159 ) )
= $true )
| ( ( SV5 = SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2026]) ).
thf(2176,plain,
! [SV272: nat,SV5: nat,SV159: nat] :
( ( ( ( SV159 = zero_zero_nat )
| ( SV5 = SV272 ) )
= $true )
| ( ( SV5 = SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2027]) ).
thf(2177,plain,
! [SV273: nat,SV160: nat,SV6: nat] :
( ( ( SV6 = zero_zero_nat )
= $true )
| ( ( SV160 = SV273 )
= $true )
| ( ( ( times_times_nat @ SV6 @ SV160 )
= ( times_times_nat @ SV6 @ SV273 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2029]) ).
thf(2178,plain,
! [SV273: nat,SV160: nat,SV6: nat] :
( ( ( ( times_times_nat @ SV6 @ SV160 )
= ( times_times_nat @ SV6 @ SV273 ) )
= $true )
| ( ( SV6 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2030]) ).
thf(2179,plain,
! [SV273: nat,SV160: nat,SV6: nat] :
( ( ( ( SV6 = zero_zero_nat )
| ( SV160 = SV273 ) )
= $true )
| ( ( SV6 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2031]) ).
thf(2180,plain,
! [SV273: nat,SV160: nat,SV6: nat] :
( ( ( ( times_times_nat @ SV6 @ SV160 )
= ( times_times_nat @ SV6 @ SV273 ) )
= $true )
| ( ( SV160 = SV273 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2032]) ).
thf(2181,plain,
! [SV273: nat,SV160: nat,SV6: nat] :
( ( ( ( SV6 = zero_zero_nat )
| ( SV160 = SV273 ) )
= $true )
| ( ( SV160 = SV273 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2033]) ).
thf(2182,plain,
! [SV161: nat,SV7: nat] :
( ( ( SV7 = zero_zero_nat )
= $true )
| ( ( SV161 = zero_zero_nat )
= $true )
| ( ( SV7 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2036]) ).
thf(2183,plain,
! [SV161: nat,SV7: nat] :
( ( ( SV7 = zero_zero_nat )
= $true )
| ( ( SV161 = zero_zero_nat )
= $true )
| ( ( SV161 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2038]) ).
thf(2184,plain,
! [SV162: nat,SV274: nat,SV12: nat] :
( ( ( SV12 = SV274 )
= $true )
| ( ( SV162 = zero_zero_nat )
= $true )
| ( ( ( times_times_nat @ SV12 @ SV162 )
= ( times_times_nat @ SV274 @ SV162 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2040]) ).
thf(2185,plain,
! [SV274: nat,SV162: nat,SV12: nat] :
( ( ( ( times_times_nat @ SV12 @ SV162 )
= ( times_times_nat @ SV274 @ SV162 ) )
= $true )
| ( ( SV12 = SV274 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2041]) ).
thf(2186,plain,
! [SV162: nat,SV274: nat,SV12: nat] :
( ( ( ( SV12 = SV274 )
| ( SV162 = zero_zero_nat ) )
= $true )
| ( ( SV12 = SV274 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2042]) ).
thf(2187,plain,
! [SV274: nat,SV162: nat,SV12: nat] :
( ( ( ( times_times_nat @ SV12 @ SV162 )
= ( times_times_nat @ SV274 @ SV162 ) )
= $true )
| ( ( SV162 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2043]) ).
thf(2188,plain,
! [SV162: nat,SV274: nat,SV12: nat] :
( ( ( ( SV12 = SV274 )
| ( SV162 = zero_zero_nat ) )
= $true )
| ( ( SV162 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2044]) ).
thf(2189,plain,
! [SV13: nat,SV275: nat,SV163: nat] :
( ( ( SV163 = SV275 )
= $true )
| ( ( SV13 = zero_zero_nat )
= $true )
| ( ( ( times_times_nat @ SV13 @ SV163 )
= ( times_times_nat @ SV13 @ SV275 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2046]) ).
thf(2190,plain,
! [SV275: nat,SV163: nat,SV13: nat] :
( ( ( ( times_times_nat @ SV13 @ SV163 )
= ( times_times_nat @ SV13 @ SV275 ) )
= $true )
| ( ( SV163 = SV275 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2047]) ).
thf(2191,plain,
! [SV13: nat,SV275: nat,SV163: nat] :
( ( ( ( SV163 = SV275 )
| ( SV13 = zero_zero_nat ) )
= $true )
| ( ( SV163 = SV275 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2048]) ).
thf(2192,plain,
! [SV275: nat,SV163: nat,SV13: nat] :
( ( ( ( times_times_nat @ SV13 @ SV163 )
= ( times_times_nat @ SV13 @ SV275 ) )
= $true )
| ( ( SV13 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2049]) ).
thf(2193,plain,
! [SV13: nat,SV275: nat,SV163: nat] :
( ( ( ( SV163 = SV275 )
| ( SV13 = zero_zero_nat ) )
= $true )
| ( ( SV13 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2050]) ).
thf(2194,plain,
! [SV164: nat,SV15: nat] :
( ( ( SV15 = zero_zero_nat )
= $true )
| ( ( SV164 = zero_zero_nat )
= $true )
| ( ( SV15 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2053]) ).
thf(2195,plain,
! [SV164: nat,SV15: nat] :
( ( ( SV15 = zero_zero_nat )
= $true )
| ( ( SV164 = zero_zero_nat )
= $true )
| ( ( SV164 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2055]) ).
thf(2196,plain,
! [SV280: nat,SV173: nat,SV37: nat] :
( ( ( SV37 = zero_zero_nat )
= $true )
| ( ( SV173 = SV280 )
= $true )
| ( ( ( times_times_nat @ SV37 @ SV173 )
= ( times_times_nat @ SV37 @ SV280 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2057]) ).
thf(2197,plain,
! [SV280: nat,SV173: nat,SV37: nat] :
( ( ( ( times_times_nat @ SV37 @ SV173 )
= ( times_times_nat @ SV37 @ SV280 ) )
= $true )
| ( ( SV37 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2058]) ).
thf(2198,plain,
! [SV280: nat,SV173: nat,SV37: nat] :
( ( ( ( SV37 = zero_zero_nat )
| ( SV173 = SV280 ) )
= $true )
| ( ( SV37 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2059]) ).
thf(2199,plain,
! [SV280: nat,SV173: nat,SV37: nat] :
( ( ( ( times_times_nat @ SV37 @ SV173 )
= ( times_times_nat @ SV37 @ SV280 ) )
= $true )
| ( ( SV173 = SV280 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2060]) ).
thf(2200,plain,
! [SV280: nat,SV173: nat,SV37: nat] :
( ( ( ( SV37 = zero_zero_nat )
| ( SV173 = SV280 ) )
= $true )
| ( ( SV173 = SV280 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2061]) ).
thf(2201,plain,
! [SV343: nat,SV179: nat] :
( ( ( ord_less_eq_nat @ SV179 @ SV343 )
= $true )
| ( ( ord_less_eq_nat @ SV179 @ SV343 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2063]) ).
thf(2202,plain,
! [SV343: nat,SV179: nat] :
( ( ( ( ord_less_nat @ SV179 @ SV343 )
| ( SV179 = SV343 ) )
= $true )
| ( ( ord_less_eq_nat @ SV179 @ SV343 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2064]) ).
thf(2203,plain,
! [SV343: nat,SV179: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV179 @ SV343 ) )
= $false )
| ( ( ord_less_nat @ SV179 @ SV343 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2065]) ).
thf(2204,plain,
! [SV343: nat,SV179: nat] :
( ( ( ~ ( ( ord_less_nat @ SV179 @ SV343 )
| ( SV179 = SV343 ) ) )
= $false )
| ( ( ord_less_nat @ SV179 @ SV343 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2065]) ).
thf(2205,plain,
! [SV343: nat,SV179: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV179 @ SV343 ) )
= $false )
| ( ( SV179 = SV343 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2066]) ).
thf(2206,plain,
! [SV343: nat,SV179: nat] :
( ( ( ~ ( ( ord_less_nat @ SV179 @ SV343 )
| ( SV179 = SV343 ) ) )
= $false )
| ( ( SV179 = SV343 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2066]) ).
thf(2207,plain,
! [SV344: nat,SV180: nat] :
( ( ( ord_less_eq_nat @ SV180 @ SV344 )
= $true )
| ( ( ord_less_eq_nat @ SV180 @ SV344 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2068]) ).
thf(2208,plain,
! [SV344: nat,SV180: nat] :
( ( ( ( ord_less_nat @ SV180 @ SV344 )
| ( SV344 = SV180 ) )
= $true )
| ( ( ord_less_eq_nat @ SV180 @ SV344 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2069]) ).
thf(2209,plain,
! [SV344: nat,SV180: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV180 @ SV344 ) )
= $false )
| ( ( ord_less_nat @ SV180 @ SV344 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2070]) ).
thf(2210,plain,
! [SV344: nat,SV180: nat] :
( ( ( ~ ( ( ord_less_nat @ SV180 @ SV344 )
| ( SV344 = SV180 ) ) )
= $false )
| ( ( ord_less_nat @ SV180 @ SV344 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2070]) ).
thf(2211,plain,
! [SV344: nat,SV180: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV180 @ SV344 ) )
= $false )
| ( ( SV344 = SV180 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2071]) ).
thf(2212,plain,
! [SV344: nat,SV180: nat] :
( ( ( ~ ( ( ord_less_nat @ SV180 @ SV344 )
| ( SV344 = SV180 ) ) )
= $false )
| ( ( SV344 = SV180 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2071]) ).
thf(2213,plain,
! [SV345: nat,SV181: nat] :
( ( ( ord_less_eq_nat @ SV181 @ SV345 )
= $true )
| ( ( ord_less_eq_nat @ SV181 @ SV345 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2072]) ).
thf(2214,plain,
! [SV345: nat,SV181: nat] :
( ( ( ( ord_less_nat @ SV181 @ SV345 )
| ( SV181 = SV345 ) )
= $true )
| ( ( ord_less_eq_nat @ SV181 @ SV345 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2073]) ).
thf(2215,plain,
! [SV345: nat,SV181: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV181 @ SV345 ) )
= $false )
| ( ( ord_less_nat @ SV181 @ SV345 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2074]) ).
thf(2216,plain,
! [SV345: nat,SV181: nat] :
( ( ( ~ ( ( ord_less_nat @ SV181 @ SV345 )
| ( SV181 = SV345 ) ) )
= $false )
| ( ( ord_less_nat @ SV181 @ SV345 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2074]) ).
thf(2217,plain,
! [SV345: nat,SV181: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV181 @ SV345 ) )
= $false )
| ( ( SV181 = SV345 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2075]) ).
thf(2218,plain,
! [SV345: nat,SV181: nat] :
( ( ( ~ ( ( ord_less_nat @ SV181 @ SV345 )
| ( SV181 = SV345 ) ) )
= $false )
| ( ( SV181 = SV345 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2075]) ).
thf(2219,plain,
! [SV60: set_nat,SV182: nat > nat,SV288: nat > nat,SV346: set_nat,SV372: nat > nat,SV375: nat > nat] :
( ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true )
| ( ( ~ ! [SY953: nat] :
( ~ ( member_nat @ SY953 @ SV60 )
| ( member_nat @ ( SV288 @ SY953 ) @ SV346 ) )
| ~ ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) )
| ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2076]) ).
thf(2220,plain,
! [SV375: nat > nat,SV372: nat > nat,SV182: nat > nat,SV346: set_nat,SV288: nat > nat,SV60: set_nat] :
( ( ( ~ ! [SY953: nat] :
( ~ ( member_nat @ SY953 @ SV60 )
| ( member_nat @ ( SV288 @ SY953 ) @ SV346 ) ) )
= $true )
| ( ( ~ ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) )
| ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2077]) ).
thf(2221,plain,
! [SV347: nat,SV186: nat] :
( ( ( SV186 = SV347 )
= $true )
| ( ( SV186 = SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2078]) ).
thf(2222,plain,
! [SV347: nat,SV186: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV186 @ SV347 )
| ~ ( ord_less_eq_nat @ SV347 @ SV186 ) ) )
= $true )
| ( ( SV186 = SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2079]) ).
thf(2223,plain,
! [SV347: nat,SV186: nat] :
( ( ( ord_less_eq_nat @ SV186 @ SV347 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV347 @ SV186 ) )
= $true )
| ( ( ~ ( ( SV186 != SV347 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV186 @ SV347 )
| ~ ( ord_less_eq_nat @ SV347 @ SV186 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2080]) ).
thf(2224,plain,
! [SV292: set_nat > nat,SV69: set_nat,SV348: nat,SV191: set_nat] :
( ( ( ! [SY1018: set_nat] :
( ~ ( ord_less_eq_set_nat @ ( sK19_SY882 @ SV191 @ SV348 @ SV69 @ SV292 ) @ SY1018 )
| ( ord_less_eq_nat @ ( SV292 @ ( sK19_SY882 @ SV191 @ SV348 @ SV69 @ SV292 ) ) @ ( SV292 @ SY1018 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV292 @ SV69 ) @ SV348 )
= $true )
| ( ( ord_less_eq_nat @ ( SV292 @ SV191 ) @ SV348 )
= $false )
| ( ( ord_less_eq_set_nat @ SV69 @ SV191 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2081]) ).
thf(2225,plain,
! [SV293: nat,SV192: nat,SV70: nat > $o] :
( ( ( ! [SY505: nat] :
( ~ ( SV70 @ SY505 )
| ~ ! [SY506: nat] :
( ~ ( SV70 @ SY506 )
| ( ord_less_eq_nat @ SY506 @ SY505 ) ) ) )
= $false )
| ( ( SV70 @ ( sK12_SY884 @ SV192 @ SV293 @ SV70 ) )
= $true )
| ( ( SV70 @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2082]) ).
thf(2226,plain,
! [SV192: nat,SV293: nat,SV70: nat > $o] :
( ( ( ~ ( SV70 @ ( sK20_SY505 @ SV293 @ SV192 @ SV70 ) )
| ~ ! [SY1019: nat] :
( ~ ( SV70 @ SY1019 )
| ( ord_less_eq_nat @ SY1019 @ ( sK20_SY505 @ SV293 @ SV192 @ SV70 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK12_SY884 @ SV192 @ SV293 @ SV70 ) @ SV293 )
= $false )
| ( ( SV70 @ SV192 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2083]) ).
thf(2227,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( number1551313001itions @ SV194 @ SV350 )
= $true )
| ( ( number1551313001itions @ SV194 @ SV350 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2084]) ).
thf(2228,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) )
= $true )
| ( ( number1551313001itions @ SV194 @ SV350 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2085]) ).
thf(2229,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 )
= $true )
| ( ( ~ ( ~ ( number1551313001itions @ SV194 @ SV350 )
| ~ ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2086]) ).
thf(2230,plain,
! [SV296: nat > set_nat,SV74: nat,SV351: set_nat,SV196: nat] :
( ( ( ! [SY1020: nat] :
( ~ ( ord_less_eq_nat @ ( sK21_SY891 @ SV196 @ SV351 @ SV74 @ SV296 ) @ SY1020 )
| ( ord_less_eq_set_nat @ ( SV296 @ ( sK21_SY891 @ SV196 @ SV351 @ SV74 @ SV296 ) ) @ ( SV296 @ SY1020 ) ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ ( SV296 @ SV74 ) @ SV351 )
= $true )
| ( ( ( SV296 @ SV196 )
= SV351 )
= $false )
| ( ( ord_less_eq_nat @ SV74 @ SV196 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2087]) ).
thf(2231,plain,
! [SV298: nat,SV198: nat,SV76: nat > nat > $o] :
( ( ( ! [SY525: nat,SY526: nat] :
( ~ ( SV76 @ SY526 @ SY525 )
| ( SV76 @ SY525 @ SY526 ) ) )
= $false )
| ( ( SV76 @ SV198 @ SV298 )
= $true )
| ( ( ord_less_eq_nat @ ( sK5_SY523 @ SV298 @ SV198 @ SV76 ) @ ( sK8_SY1011 @ SV76 @ SV198 @ SV298 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2088]) ).
thf(2232,plain,
! [SV198: nat,SV298: nat,SV76: nat > nat > $o] :
( ( ( ! [SY1021: nat] :
( ~ ( SV76 @ SY1021 @ ( sK22_SY525 @ SV298 @ SV198 @ SV76 ) )
| ( SV76 @ ( sK22_SY525 @ SV298 @ SV198 @ SV76 ) @ SY1021 ) ) )
= $false )
| ( ( SV76 @ SV198 @ SV298 )
= $true )
| ( ( SV76 @ ( sK5_SY523 @ SV298 @ SV198 @ SV76 ) @ ( sK8_SY1011 @ SV76 @ SV198 @ SV298 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2089]) ).
thf(2233,plain,
! [SV352: nat,SV205: nat,SV83: nat,SV303: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV303 ) )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV83 @ SV303 ) @ ( times_times_nat @ SV205 @ SV352 ) )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV83 )
= $false )
| ( ( ord_less_eq_nat @ SV303 @ SV352 )
= $false )
| ( ( ord_less_eq_nat @ SV83 @ SV205 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2090]) ).
thf(2234,plain,
! [SV84: nat,SV206: nat] :
( ( ( ord_less_eq_nat @ SV206 @ SV84 )
= $true )
| ( ( ord_less_eq_nat @ SV206 @ SV84 )
= $false )
| ( ( ord_less_eq_nat @ SV84 @ SV206 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2091]) ).
thf(2235,plain,
! [SV84: nat,SV206: nat] :
( ( ( SV206 = SV84 )
= $true )
| ( ( ord_less_eq_nat @ SV206 @ SV84 )
= $false )
| ( ( ord_less_eq_nat @ SV84 @ SV206 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2092]) ).
thf(2236,plain,
! [SV84: nat,SV206: nat] :
( ( ( ord_less_eq_nat @ SV206 @ SV84 )
= $true )
| ( ( SV206 = SV84 )
= $false )
| ( ( ord_less_eq_nat @ SV84 @ SV206 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2093]) ).
thf(2237,plain,
! [SV84: nat,SV206: nat] :
( ( ( SV206 = SV84 )
= $true )
| ( ( SV206 = SV84 )
= $false )
| ( ( ord_less_eq_nat @ SV84 @ SV206 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2094]) ).
thf(2238,plain,
! [SV373: nat > nat,SV353: nat > nat,SV85: set_nat,SV304: nat > nat,SV207: set_nat] :
( ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( member_nat @ ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) @ SV85 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2095]) ).
thf(2239,plain,
! [SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV304: nat > nat,SV207: set_nat,SV381: nat] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member_nat @ SV381 @ SV207 )
| ( ( SV304 @ SV381 )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) ) )
| ~ ! [SY1022: nat] :
( ~ ~ ( ~ ( member_nat @ SY1022 @ SV207 )
| ( ( SV304 @ SY1022 )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) ) )
| ( SY1022 = SV381 ) ) ) )
= $true )
| ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) )
| ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2096]) ).
thf(2240,plain,
! [SV208: nat > set_nat,SV86: set_nat,SV354: nat,SV305: nat] :
( ( ( ! [SY1023: nat] :
( ~ ( ord_less_eq_nat @ ( sK23_SY776 @ SV305 @ SV354 @ SV86 @ SV208 ) @ SY1023 )
| ( ord_less_eq_set_nat @ ( SV208 @ ( sK23_SY776 @ SV305 @ SV354 @ SV86 @ SV208 ) ) @ ( SV208 @ SY1023 ) ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ SV86 @ ( SV208 @ SV354 ) )
= $true )
| ( ( ord_less_eq_nat @ SV305 @ SV354 )
= $false )
| ( ( SV86
= ( SV208 @ SV305 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2097]) ).
thf(2241,plain,
! [SV209: set_nat > nat,SV87: nat,SV355: set_nat,SV306: set_nat] :
( ( ( ! [SY1024: set_nat] :
( ~ ( ord_less_eq_set_nat @ ( sK24_SY780 @ SV306 @ SV355 @ SV87 @ SV209 ) @ SY1024 )
| ( ord_less_eq_nat @ ( SV209 @ ( sK24_SY780 @ SV306 @ SV355 @ SV87 @ SV209 ) ) @ ( SV209 @ SY1024 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV87 @ ( SV209 @ SV355 ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV306 @ SV355 )
= $false )
| ( ( SV87
= ( SV209 @ SV306 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2098]) ).
thf(2242,plain,
! [SV378: nat] :
( ( ( ( p @ SV378 )
!= zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SV378 )
| ~ ( ord_less_eq_nat @ SV378 @ zero_zero_nat ) ) )
= $true )
| ( ( p
= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2100]) ).
thf(2243,plain,
( ( ( ~ ( ( ( p @ sK18_SX0 )
!= zero_zero_nat ) ) )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
!= zero_zero_nat )
= $true )
| ( ( p
!= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2102]) ).
thf(2244,plain,
( ( ( ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ sK18_SX0 )
| ~ ( ord_less_eq_nat @ sK18_SX0 @ zero_zero_nat ) ) )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
!= zero_zero_nat )
= $true )
| ( ( p
!= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2102]) ).
thf(2245,plain,
! [SV356: nat,SV213: nat] :
( ( ( SV213 = SV356 )
= $true )
| ( ( SV213 = SV356 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2103]) ).
thf(2246,plain,
! [SV213: nat,SV356: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV356 @ SV213 )
| ~ ( ord_less_eq_nat @ SV213 @ SV356 ) ) )
= $true )
| ( ( SV213 = SV356 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2104]) ).
thf(2247,plain,
! [SV213: nat,SV356: nat] :
( ( ( ord_less_eq_nat @ SV356 @ SV213 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV213 @ SV356 ) )
= $true )
| ( ( ~ ( ( SV213 != SV356 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV356 @ SV213 )
| ~ ( ord_less_eq_nat @ SV213 @ SV356 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2105]) ).
thf(2248,plain,
! [SV214: set_nat,SV308: nat > nat,SV357: nat > nat,SV93: set_nat] :
( ( ( member_nat @ ( sK16_SY972 @ SV93 @ SV357 @ SV308 @ SV214 ) @ SV214 )
= $true )
| ( ( ( groups1842438620at_nat @ SV308 @ SV93 )
= ( groups1842438620at_nat @ SV357 @ SV214 ) )
= $true )
| ( ( SV93 = SV214 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2106]) ).
thf(2249,plain,
! [SV216: set_nat > nat,SV95: nat,SV358: set_nat,SV309: set_nat] :
( ( ( ! [SY1025: set_nat] :
( ~ ( ord_less_eq_set_nat @ ( sK25_SY789 @ SV309 @ SV358 @ SV95 @ SV216 ) @ SY1025 )
| ( ord_less_eq_nat @ ( SV216 @ ( sK25_SY789 @ SV309 @ SV358 @ SV95 @ SV216 ) ) @ ( SV216 @ SY1025 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ ( SV216 @ SV358 ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV309 @ SV358 )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ ( SV216 @ SV309 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2108]) ).
thf(2250,plain,
! [SV97: nat > nat,SV310: nat,SV218: nat] :
( ( ( ord_less_eq_nat @ SV218 @ SV310 )
= $false )
| ( ( ord_less_eq_nat @ ( SV97 @ SV218 ) @ ( SV97 @ SV310 ) )
= $true )
| ( ( ord_less_nat @ ( sK6_SY578 @ SV310 @ SV218 @ SV97 ) @ ( sK9_SY1012 @ SV97 @ SV218 @ SV310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2109]) ).
thf(2251,plain,
! [SV311: nat,SV98: nat,SV219: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV219 )
| ~ ( ord_less_nat @ SV98 @ SV311 ) )
= $false )
| ( ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2112]) ).
thf(2252,plain,
! [SV219: nat,SV311: nat,SV98: nat] :
( ( ( ord_less_nat @ SV98 @ SV311 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV219 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV219 )
| ~ ( ord_less_nat @ SV98 @ SV311 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2113]) ).
thf(2253,plain,
! [SV220: nat > nat,SV99: nat,SV359: nat,SV312: nat] :
( ( ( ! [SY1026: nat] :
( ~ ( ord_less_eq_nat @ ( sK26_SY798 @ SV312 @ SV359 @ SV99 @ SV220 ) @ SY1026 )
| ( ord_less_eq_nat @ ( SV220 @ ( sK26_SY798 @ SV312 @ SV359 @ SV99 @ SV220 ) ) @ ( SV220 @ SY1026 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV99 @ ( SV220 @ SV359 ) )
= $true )
| ( ( ord_less_eq_nat @ SV312 @ SV359 )
= $false )
| ( ( SV99
= ( SV220 @ SV312 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2114]) ).
thf(2254,plain,
! [SV313: nat,SV221: nat,SV100: nat > $o] :
( ( ( ! [SY590: nat] :
~ ~ ( ~ ( SV100 @ SY590 )
| ~ ! [SY591: nat] :
( ~ ( SV100 @ SY591 )
| ( ord_less_eq_nat @ SY591 @ SY590 ) ) ) )
= $false )
| ( ( SV100 @ ( sK14_SY920 @ SV221 @ SV313 @ SV100 ) )
= $true )
| ( ( SV100 @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2115]) ).
thf(2255,plain,
! [SV221: nat,SV313: nat,SV100: nat > $o] :
( ( ( ~ ~ ( ~ ( SV100 @ ( sK27_SY590 @ SV313 @ SV221 @ SV100 ) )
| ~ ! [SY1027: nat] :
( ~ ( SV100 @ SY1027 )
| ( ord_less_eq_nat @ SY1027 @ ( sK27_SY590 @ SV313 @ SV221 @ SV100 ) ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK14_SY920 @ SV221 @ SV313 @ SV100 ) @ SV313 )
= $false )
| ( ( SV100 @ SV221 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2116]) ).
thf(2256,plain,
! [SV360: nat,SV222: nat] :
( ( ( ord_less_nat @ SV222 @ SV360 )
= $true )
| ( ( ord_less_nat @ SV222 @ SV360 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2117]) ).
thf(2257,plain,
! [SV360: nat,SV222: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV222 @ SV360 )
| ~ ( ( SV360 != SV222 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV222 @ SV360 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2118]) ).
thf(2258,plain,
! [SV360: nat,SV222: nat] :
( ( ( ord_less_eq_nat @ SV222 @ SV360 )
= $false )
| ( ( ~ ( ( SV360 != SV222 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV222 @ SV360 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV222 @ SV360 )
| ~ ( ( SV360 != SV222 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2119]) ).
thf(2259,plain,
! [SV224: nat,SV377: nat,SV103: nat > nat] :
( ( ( ( SV103 @ SV377 )
= zero_zero_nat )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SV377 )
| ~ ( ord_less_eq_nat @ SV377 @ SV224 ) ) )
= $true )
| ( ( number1551313001itions @ SV103 @ SV224 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2120]) ).
thf(2260,plain,
! [SV315: nat > nat,SV106: nat,SV361: nat,SV227: nat] :
( ( ( ! [SY1028: nat] :
( ~ ( ord_less_eq_nat @ ( sK28_SY924 @ SV227 @ SV361 @ SV106 @ SV315 ) @ SY1028 )
| ( ord_less_eq_nat @ ( SV315 @ ( sK28_SY924 @ SV227 @ SV361 @ SV106 @ SV315 ) ) @ ( SV315 @ SY1028 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV315 @ SV106 ) @ SV361 )
= $true )
| ( ( ord_less_eq_nat @ ( SV315 @ SV227 ) @ SV361 )
= $false )
| ( ( ord_less_eq_nat @ SV106 @ SV227 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2121]) ).
thf(2261,plain,
! [SV362: nat,SV228: nat] :
( ( ( ord_less_nat @ SV228 @ SV362 )
= $true )
| ( ( ord_less_nat @ SV228 @ SV362 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2122]) ).
thf(2262,plain,
! [SV362: nat,SV228: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV228 @ SV362 )
| ~ ( ( SV228 != SV362 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV228 @ SV362 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2123]) ).
thf(2263,plain,
! [SV362: nat,SV228: nat] :
( ( ( ord_less_eq_nat @ SV228 @ SV362 )
= $false )
| ( ( ~ ( ( SV228 != SV362 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV228 @ SV362 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV228 @ SV362 )
| ~ ( ( SV228 != SV362 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2124]) ).
thf(2264,plain,
! [SV230: nat,SV110: nat > $o] :
( ( ( SV110 @ ( sK10_SY608 @ SV230 @ SV110 ) )
= $false )
| ( ( SV110 @ SV230 )
= $true )
| ( ( SV110 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2125]) ).
thf(2265,plain,
! [SV110: nat > $o,SV230: nat,SV382: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ SV382 @ ( sK10_SY608 @ SV230 @ SV110 ) )
| ~ ~ ( SV110 @ SV382 ) ) )
= $true )
| ( ( SV110 @ SV230 )
= $true )
| ( ( SV110 @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2126]) ).
thf(2266,plain,
! [SV116: set_nat,SV236: nat > nat,SV319: set_nat,SV363: nat > nat,SV374: nat > nat,SV376: nat > nat] :
( ( ( member_nat @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) @ SV116 )
= $true )
| ( ( ~ ! [SY1014: nat] :
( ~ ( member_nat @ SY1014 @ SV319 )
| ~ ( ~ ~ ( ~ ( member_nat @ ( SV363 @ SY1014 ) @ SV116 )
| ( ( SV236 @ ( SV363 @ SY1014 ) )
!= SY1014 ) )
| ( ( SV374 @ ( SV363 @ SY1014 ) )
!= ( SV376 @ SY1014 ) ) ) )
| ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2127]) ).
thf(2267,plain,
! [SV116: set_nat,SV319: set_nat,SV363: nat > nat,SV374: nat > nat,SV376: nat > nat,SV236: nat > nat] :
( ( ( ~ ( member_nat @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) @ SV319 )
| ( ( SV363 @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) )
!= ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) )
= $true )
| ( ( ~ ! [SY1014: nat] :
( ~ ( member_nat @ SY1014 @ SV319 )
| ~ ( ~ ~ ( ~ ( member_nat @ ( SV363 @ SY1014 ) @ SV116 )
| ( ( SV236 @ ( SV363 @ SY1014 ) )
!= SY1014 ) )
| ( ( SV374 @ ( SV363 @ SY1014 ) )
!= ( SV376 @ SY1014 ) ) ) )
| ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2128]) ).
thf(2268,plain,
! [SV320: nat > set_nat,SV117: nat,SV364: set_nat,SV237: nat] :
( ( ( ! [SY1029: nat] :
( ~ ( ord_less_eq_nat @ ( sK29_SY932 @ SV237 @ SV364 @ SV117 @ SV320 ) @ SY1029 )
| ( ord_less_eq_set_nat @ ( SV320 @ ( sK29_SY932 @ SV237 @ SV364 @ SV117 @ SV320 ) ) @ ( SV320 @ SY1029 ) ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ ( SV320 @ SV117 ) @ SV364 )
= $true )
| ( ( ord_less_eq_set_nat @ ( SV320 @ SV237 ) @ SV364 )
= $false )
| ( ( ord_less_eq_nat @ SV117 @ SV237 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2129]) ).
thf(2269,plain,
! [SV239: nat > nat,SV119: nat,SV365: nat,SV321: nat] :
( ( ( ! [SY1030: nat] :
( ~ ( ord_less_eq_nat @ ( sK30_SY830 @ SV321 @ SV365 @ SV119 @ SV239 ) @ SY1030 )
| ( ord_less_eq_nat @ ( SV239 @ ( sK30_SY830 @ SV321 @ SV365 @ SV119 @ SV239 ) ) @ ( SV239 @ SY1030 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV119 @ ( SV239 @ SV365 ) )
= $true )
| ( ( ord_less_eq_nat @ SV321 @ SV365 )
= $false )
| ( ( ord_less_eq_nat @ SV119 @ ( SV239 @ SV321 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2130]) ).
thf(2270,plain,
! [SV366: nat,SV243: nat] :
( ( ( SV243 = SV366 )
= $true )
| ( ( SV243 = SV366 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2131]) ).
thf(2271,plain,
! [SV366: nat,SV243: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV243 @ SV366 )
| ~ ( ord_less_eq_nat @ SV366 @ SV243 ) ) )
= $true )
| ( ( SV243 = SV366 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2132]) ).
thf(2272,plain,
! [SV366: nat,SV243: nat] :
( ( ( ord_less_eq_nat @ SV243 @ SV366 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV366 @ SV243 ) )
= $true )
| ( ( ~ ( ( SV243 != SV366 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV243 @ SV366 )
| ~ ( ord_less_eq_nat @ SV366 @ SV243 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2133]) ).
thf(2273,plain,
! [SV246: nat > set_nat,SV127: set_nat,SV367: nat,SV325: nat] :
( ( ( ! [SY1031: nat] :
( ~ ( ord_less_eq_nat @ ( sK31_SY838 @ SV325 @ SV367 @ SV127 @ SV246 ) @ SY1031 )
| ( ord_less_eq_set_nat @ ( SV246 @ ( sK31_SY838 @ SV325 @ SV367 @ SV127 @ SV246 ) ) @ ( SV246 @ SY1031 ) ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ SV127 @ ( SV246 @ SV367 ) )
= $true )
| ( ( ord_less_eq_nat @ SV325 @ SV367 )
= $false )
| ( ( ord_less_eq_set_nat @ SV127 @ ( SV246 @ SV325 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2134]) ).
thf(2274,plain,
! [SV368: nat,SV247: nat,SV128: nat,SV326: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV326 ) )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV128 @ SV326 ) @ ( times_times_nat @ SV247 @ SV368 ) )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV247 )
= $false )
| ( ( ord_less_eq_nat @ SV326 @ SV368 )
= $false )
| ( ( ord_less_eq_nat @ SV128 @ SV247 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2135]) ).
thf(2275,plain,
! [SV327: nat,SV248: nat,SV130: nat] :
( ( ( ( ( times_times_nat @ SV130 @ SV248 )
!= ( times_times_nat @ SV130 @ SV327 ) )
| ( SV248 != SV327 ) )
= $false )
| ( ( ( times_times_nat @ SV130 @ SV248 )
= ( times_times_nat @ SV130 @ SV327 ) )
= $false )
| ( ( SV130 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2136]) ).
thf(2276,plain,
! [SV327: nat,SV248: nat,SV130: nat] :
( ( ( ( ( times_times_nat @ SV130 @ SV248 )
!= ( times_times_nat @ SV130 @ SV327 ) )
| ( SV248 != SV327 ) )
= $false )
| ( ( SV248 = SV327 )
= $false )
| ( ( SV130 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2137]) ).
thf(2277,plain,
! [SV328: nat,SV131: nat,SV249: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV249 ) )
= $true )
| ( ( ord_less_eq_nat @ SV131 @ SV328 )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2139]) ).
thf(2278,plain,
! [SV328: nat,SV249: nat,SV131: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV249 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2140]) ).
thf(2279,plain,
! [SV328: nat,SV131: nat,SV249: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV249 )
| ( ord_less_eq_nat @ SV131 @ SV328 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV249 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2140]) ).
thf(2280,plain,
! [SV328: nat,SV249: nat,SV131: nat] :
( ( ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) )
= $true )
| ( ( ord_less_eq_nat @ SV131 @ SV328 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2141]) ).
thf(2281,plain,
! [SV328: nat,SV131: nat,SV249: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV249 )
| ( ord_less_eq_nat @ SV131 @ SV328 ) )
= $true )
| ( ( ord_less_eq_nat @ SV131 @ SV328 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2142]) ).
thf(2282,plain,
! [SV329: nat > nat,SV132: nat,SV369: nat,SV250: nat] :
( ( ( ! [SY1032: nat] :
( ~ ( ord_less_eq_nat @ ( sK32_SY942 @ SV250 @ SV369 @ SV132 @ SV329 ) @ SY1032 )
| ( ord_less_eq_nat @ ( SV329 @ ( sK32_SY942 @ SV250 @ SV369 @ SV132 @ SV329 ) ) @ ( SV329 @ SY1032 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV329 @ SV132 ) @ SV369 )
= $true )
| ( ( ( SV329 @ SV250 )
= SV369 )
= $false )
| ( ( ord_less_eq_nat @ SV132 @ SV250 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2143]) ).
thf(2283,plain,
! [SV331: nat,SV134: nat,SV252: nat] :
( ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV134 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2144]) ).
thf(2284,plain,
! [SV252: nat,SV331: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV134 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2145]) ).
thf(2285,plain,
! [SV331: nat,SV134: nat,SV252: nat] :
( ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV134 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2146]) ).
thf(2286,plain,
! [SV252: nat,SV331: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV134 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2147]) ).
thf(2287,plain,
! [SV332: nat,SV253: nat,SV135: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 )
| ~ ( ord_less_nat @ SV253 @ SV332 ) )
= $false )
| ( ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2149]) ).
thf(2288,plain,
! [SV135: nat,SV332: nat,SV253: nat] :
( ( ( ord_less_nat @ SV253 @ SV332 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV135 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 )
| ~ ( ord_less_nat @ SV253 @ SV332 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2150]) ).
thf(2289,plain,
! [SV254: nat,SV136: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV136 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2151]) ).
thf(2290,plain,
! [SV136: nat,SV254: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV254 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2151]) ).
thf(2291,plain,
! [SV254: nat,SV136: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV136 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV254 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV136 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV254 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2152]) ).
thf(2292,plain,
! [SV370: nat,SV259: nat] :
( ( ( ord_less_nat @ SV259 @ SV370 )
= $true )
| ( ( ord_less_nat @ SV259 @ SV370 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2153]) ).
thf(2293,plain,
! [SV370: nat,SV259: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV259 @ SV370 )
| ~ ( ( SV259 != SV370 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV259 @ SV370 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2154]) ).
thf(2294,plain,
! [SV370: nat,SV259: nat] :
( ( ( ord_less_eq_nat @ SV259 @ SV370 )
= $false )
| ( ( ~ ( ( SV259 != SV370 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV259 @ SV370 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV259 @ SV370 )
| ~ ( ( SV259 != SV370 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2155]) ).
thf(2295,plain,
! [SV263: nat,SV145: nat] :
( ( ( SV145 != one_one_nat )
= $false )
| ( ( one_one_nat
= ( times_times_nat @ SV145 @ SV263 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2156]) ).
thf(2296,plain,
! [SV145: nat,SV263: nat] :
( ( ( SV263 != one_one_nat )
= $false )
| ( ( one_one_nat
= ( times_times_nat @ SV145 @ SV263 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2156]) ).
thf(2297,plain,
! [SV263: nat,SV145: nat] :
( ( ( ( one_one_nat
!= ( times_times_nat @ SV145 @ SV263 ) )
| ~ ~ ( ( SV145 != one_one_nat )
| ( SV263 != one_one_nat ) ) )
= $false )
| ( ( SV145 = one_one_nat )
= $false )
| ( ( SV263 = one_one_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2157]) ).
thf(2298,plain,
! [SV336: nat,SV146: nat,SV264: nat] :
( ( ( ( ( times_times_nat @ SV264 @ SV146 )
!= ( times_times_nat @ SV336 @ SV146 ) )
| ( SV264 != SV336 ) )
= $false )
| ( ( ( times_times_nat @ SV264 @ SV146 )
= ( times_times_nat @ SV336 @ SV146 ) )
= $false )
| ( ( SV146 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2158]) ).
thf(2299,plain,
! [SV336: nat,SV146: nat,SV264: nat] :
( ( ( ( ( times_times_nat @ SV264 @ SV146 )
!= ( times_times_nat @ SV336 @ SV146 ) )
| ( SV264 != SV336 ) )
= $false )
| ( ( SV264 = SV336 )
= $false )
| ( ( SV146 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2159]) ).
thf(2300,plain,
! [SV265: nat,SV148: nat > nat] :
( ( ( ( groups1842438620at_nat
@ ^ [SY685: nat] : ( times_times_nat @ ( SV148 @ SY685 ) @ SY685 )
@ ( set_ord_atMost_nat @ SV265 ) )
!= SV265 )
= $true )
| ( ( number1551313001itions @ SV148 @ SV265 )
= $true )
| ( ( ord_less_eq_nat @ one_one_nat @ ( sK4_SY856 @ SV265 @ SV148 ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK4_SY856 @ SV265 @ SV148 ) @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2162]) ).
thf(2301,plain,
! [SV266: nat,SV149: nat] :
( ( ( SV149 != one_one_nat )
= $false )
| ( ( ( times_times_nat @ SV149 @ SV266 )
= one_one_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2163]) ).
thf(2302,plain,
! [SV149: nat,SV266: nat] :
( ( ( SV266 != one_one_nat )
= $false )
| ( ( ( times_times_nat @ SV149 @ SV266 )
= one_one_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2163]) ).
thf(2303,plain,
! [SV266: nat,SV149: nat] :
( ( ( ( ( times_times_nat @ SV149 @ SV266 )
!= one_one_nat )
| ~ ~ ( ( SV149 != one_one_nat )
| ( SV266 != one_one_nat ) ) )
= $false )
| ( ( SV149 = one_one_nat )
= $false )
| ( ( SV266 = one_one_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2164]) ).
thf(2304,plain,
! [SV337: set_nat > nat,SV151: set_nat,SV371: nat,SV267: set_nat] :
( ( ( ! [SY1033: set_nat] :
( ~ ( ord_less_eq_set_nat @ ( sK33_SY946 @ SV267 @ SV371 @ SV151 @ SV337 ) @ SY1033 )
| ( ord_less_eq_nat @ ( SV337 @ ( sK33_SY946 @ SV267 @ SV371 @ SV151 @ SV337 ) ) @ ( SV337 @ SY1033 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV337 @ SV151 ) @ SV371 )
= $true )
| ( ( ( SV337 @ SV267 )
= SV371 )
= $false )
| ( ( ord_less_eq_set_nat @ SV151 @ SV267 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2166]) ).
thf(2305,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV153 ) )
= $true )
| ( ( ord_less_eq_nat @ SV269 @ SV339 )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2168]) ).
thf(2306,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV153 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2169]) ).
thf(2307,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV153 )
| ( ord_less_eq_nat @ SV269 @ SV339 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV153 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2169]) ).
thf(2308,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) )
= $true )
| ( ( ord_less_eq_nat @ SV269 @ SV339 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2170]) ).
thf(2309,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV153 )
| ( ord_less_eq_nat @ SV269 @ SV339 ) )
= $true )
| ( ( ord_less_eq_nat @ SV269 @ SV339 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2171]) ).
thf(2310,plain,
! [SV272: nat,SV5: nat,SV159: nat] :
( ( ( SV159 = zero_zero_nat )
= $true )
| ( ( SV5 = SV272 )
= $true )
| ( ( SV159 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2174]) ).
thf(2311,plain,
! [SV272: nat,SV5: nat,SV159: nat] :
( ( ( SV159 = zero_zero_nat )
= $true )
| ( ( SV5 = SV272 )
= $true )
| ( ( SV5 = SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2176]) ).
thf(2312,plain,
! [SV273: nat,SV160: nat,SV6: nat] :
( ( ( SV6 = zero_zero_nat )
= $true )
| ( ( SV160 = SV273 )
= $true )
| ( ( SV6 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2179]) ).
thf(2313,plain,
! [SV273: nat,SV160: nat,SV6: nat] :
( ( ( SV6 = zero_zero_nat )
= $true )
| ( ( SV160 = SV273 )
= $true )
| ( ( SV160 = SV273 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2181]) ).
thf(2314,plain,
! [SV162: nat,SV274: nat,SV12: nat] :
( ( ( SV12 = SV274 )
= $true )
| ( ( SV162 = zero_zero_nat )
= $true )
| ( ( SV12 = SV274 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2186]) ).
thf(2315,plain,
! [SV162: nat,SV274: nat,SV12: nat] :
( ( ( SV12 = SV274 )
= $true )
| ( ( SV162 = zero_zero_nat )
= $true )
| ( ( SV162 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2188]) ).
thf(2316,plain,
! [SV13: nat,SV275: nat,SV163: nat] :
( ( ( SV163 = SV275 )
= $true )
| ( ( SV13 = zero_zero_nat )
= $true )
| ( ( SV163 = SV275 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2191]) ).
thf(2317,plain,
! [SV13: nat,SV275: nat,SV163: nat] :
( ( ( SV163 = SV275 )
= $true )
| ( ( SV13 = zero_zero_nat )
= $true )
| ( ( SV13 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2193]) ).
thf(2318,plain,
! [SV280: nat,SV173: nat,SV37: nat] :
( ( ( SV37 = zero_zero_nat )
= $true )
| ( ( SV173 = SV280 )
= $true )
| ( ( SV37 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2198]) ).
thf(2319,plain,
! [SV280: nat,SV173: nat,SV37: nat] :
( ( ( SV37 = zero_zero_nat )
= $true )
| ( ( SV173 = SV280 )
= $true )
| ( ( SV173 = SV280 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2200]) ).
thf(2320,plain,
! [SV343: nat,SV179: nat] :
( ( ( ord_less_nat @ SV179 @ SV343 )
= $true )
| ( ( SV179 = SV343 )
= $true )
| ( ( ord_less_eq_nat @ SV179 @ SV343 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2202]) ).
thf(2321,plain,
! [SV343: nat,SV179: nat] :
( ( ( ord_less_eq_nat @ SV179 @ SV343 )
= $true )
| ( ( ord_less_nat @ SV179 @ SV343 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2203]) ).
thf(2322,plain,
! [SV343: nat,SV179: nat] :
( ( ( ( ord_less_nat @ SV179 @ SV343 )
| ( SV179 = SV343 ) )
= $true )
| ( ( ord_less_nat @ SV179 @ SV343 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2204]) ).
thf(2323,plain,
! [SV343: nat,SV179: nat] :
( ( ( ord_less_eq_nat @ SV179 @ SV343 )
= $true )
| ( ( SV179 = SV343 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2205]) ).
thf(2324,plain,
! [SV343: nat,SV179: nat] :
( ( ( ( ord_less_nat @ SV179 @ SV343 )
| ( SV179 = SV343 ) )
= $true )
| ( ( SV179 = SV343 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2206]) ).
thf(2325,plain,
! [SV344: nat,SV180: nat] :
( ( ( ord_less_nat @ SV180 @ SV344 )
= $true )
| ( ( SV344 = SV180 )
= $true )
| ( ( ord_less_eq_nat @ SV180 @ SV344 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2208]) ).
thf(2326,plain,
! [SV344: nat,SV180: nat] :
( ( ( ord_less_eq_nat @ SV180 @ SV344 )
= $true )
| ( ( ord_less_nat @ SV180 @ SV344 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2209]) ).
thf(2327,plain,
! [SV344: nat,SV180: nat] :
( ( ( ( ord_less_nat @ SV180 @ SV344 )
| ( SV344 = SV180 ) )
= $true )
| ( ( ord_less_nat @ SV180 @ SV344 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2210]) ).
thf(2328,plain,
! [SV344: nat,SV180: nat] :
( ( ( ord_less_eq_nat @ SV180 @ SV344 )
= $true )
| ( ( SV344 = SV180 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2211]) ).
thf(2329,plain,
! [SV344: nat,SV180: nat] :
( ( ( ( ord_less_nat @ SV180 @ SV344 )
| ( SV344 = SV180 ) )
= $true )
| ( ( SV344 = SV180 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2212]) ).
thf(2330,plain,
! [SV345: nat,SV181: nat] :
( ( ( ord_less_nat @ SV181 @ SV345 )
= $true )
| ( ( SV181 = SV345 )
= $true )
| ( ( ord_less_eq_nat @ SV181 @ SV345 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2214]) ).
thf(2331,plain,
! [SV345: nat,SV181: nat] :
( ( ( ord_less_eq_nat @ SV181 @ SV345 )
= $true )
| ( ( ord_less_nat @ SV181 @ SV345 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2215]) ).
thf(2332,plain,
! [SV345: nat,SV181: nat] :
( ( ( ( ord_less_nat @ SV181 @ SV345 )
| ( SV181 = SV345 ) )
= $true )
| ( ( ord_less_nat @ SV181 @ SV345 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2216]) ).
thf(2333,plain,
! [SV345: nat,SV181: nat] :
( ( ( ord_less_eq_nat @ SV181 @ SV345 )
= $true )
| ( ( SV181 = SV345 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2217]) ).
thf(2334,plain,
! [SV345: nat,SV181: nat] :
( ( ( ( ord_less_nat @ SV181 @ SV345 )
| ( SV181 = SV345 ) )
= $true )
| ( ( SV181 = SV345 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2218]) ).
thf(2335,plain,
! [SV375: nat > nat,SV372: nat > nat,SV182: nat > nat,SV346: set_nat,SV288: nat > nat,SV60: set_nat] :
( ( ( ~ ! [SY953: nat] :
( ~ ( member_nat @ SY953 @ SV60 )
| ( member_nat @ ( SV288 @ SY953 ) @ SV346 ) ) )
= $true )
| ( ( ~ ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) )
| ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2219]) ).
thf(2336,plain,
! [SV375: nat > nat,SV372: nat > nat,SV182: nat > nat,SV346: set_nat,SV288: nat > nat,SV60: set_nat] :
( ( ( ! [SY953: nat] :
( ~ ( member_nat @ SY953 @ SV60 )
| ( member_nat @ ( SV288 @ SY953 ) @ SV346 ) ) )
= $false )
| ( ( ~ ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) )
| ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2220]) ).
thf(2337,plain,
! [SV347: nat,SV186: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV186 @ SV347 )
| ~ ( ord_less_eq_nat @ SV347 @ SV186 ) )
= $false )
| ( ( SV186 = SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2222]) ).
thf(2338,plain,
! [SV186: nat,SV347: nat] :
( ( ( ord_less_eq_nat @ SV347 @ SV186 )
= $false )
| ( ( ord_less_eq_nat @ SV186 @ SV347 )
= $false )
| ( ( ~ ( ( SV186 != SV347 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV186 @ SV347 )
| ~ ( ord_less_eq_nat @ SV347 @ SV186 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2223]) ).
thf(2339,plain,
! [SV292: set_nat > nat,SV69: set_nat,SV348: nat,SV191: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ ( sK19_SY882 @ SV191 @ SV348 @ SV69 @ SV292 ) @ ( sK34_SY1018 @ SV292 @ SV69 @ SV348 @ SV191 ) )
| ( ord_less_eq_nat @ ( SV292 @ ( sK19_SY882 @ SV191 @ SV348 @ SV69 @ SV292 ) ) @ ( SV292 @ ( sK34_SY1018 @ SV292 @ SV69 @ SV348 @ SV191 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV292 @ SV69 ) @ SV348 )
= $true )
| ( ( ord_less_eq_nat @ ( SV292 @ SV191 ) @ SV348 )
= $false )
| ( ( ord_less_eq_set_nat @ SV69 @ SV191 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2224]) ).
thf(2340,plain,
! [SV192: nat,SV293: nat,SV70: nat > $o] :
( ( ( ~ ( SV70 @ ( sK35_SY505 @ SV293 @ SV192 @ SV70 ) )
| ~ ! [SY1034: nat] :
( ~ ( SV70 @ SY1034 )
| ( ord_less_eq_nat @ SY1034 @ ( sK35_SY505 @ SV293 @ SV192 @ SV70 ) ) ) )
= $false )
| ( ( SV70 @ ( sK12_SY884 @ SV192 @ SV293 @ SV70 ) )
= $true )
| ( ( SV70 @ SV192 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2225]) ).
thf(2341,plain,
! [SV192: nat,SV293: nat,SV70: nat > $o] :
( ( ( ~ ( SV70 @ ( sK20_SY505 @ SV293 @ SV192 @ SV70 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK12_SY884 @ SV192 @ SV293 @ SV70 ) @ SV293 )
= $false )
| ( ( SV70 @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2226]) ).
thf(2342,plain,
! [SV192: nat,SV293: nat,SV70: nat > $o] :
( ( ( ~ ! [SY1019: nat] :
( ~ ( SV70 @ SY1019 )
| ( ord_less_eq_nat @ SY1019 @ ( sK20_SY505 @ SV293 @ SV192 @ SV70 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK12_SY884 @ SV192 @ SV293 @ SV70 ) @ SV293 )
= $false )
| ( ( SV70 @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2226]) ).
thf(2343,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) )
= $false )
| ( ( number1551313001itions @ SV194 @ SV350 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2228]) ).
thf(2344,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ~ ( ( ( SV194 @ ( sK36_SY959 @ SV350 @ SV194 ) )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ ( sK36_SY959 @ SV350 @ SV194 ) )
| ~ ( ord_less_eq_nat @ ( sK36_SY959 @ SV350 @ SV194 ) @ SV350 ) ) )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 )
= $true )
| ( ( ~ ( ~ ( number1551313001itions @ SV194 @ SV350 )
| ~ ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2229]) ).
thf(2345,plain,
! [SV296: nat > set_nat,SV74: nat,SV351: set_nat,SV196: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK21_SY891 @ SV196 @ SV351 @ SV74 @ SV296 ) @ ( sK37_SY1020 @ SV296 @ SV74 @ SV351 @ SV196 ) )
| ( ord_less_eq_set_nat @ ( SV296 @ ( sK21_SY891 @ SV196 @ SV351 @ SV74 @ SV296 ) ) @ ( SV296 @ ( sK37_SY1020 @ SV296 @ SV74 @ SV351 @ SV196 ) ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ ( SV296 @ SV74 ) @ SV351 )
= $true )
| ( ( ( SV296 @ SV196 )
= SV351 )
= $false )
| ( ( ord_less_eq_nat @ SV74 @ SV196 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2230]) ).
thf(2346,plain,
! [SV198: nat,SV298: nat,SV76: nat > nat > $o] :
( ( ( ! [SY1035: nat] :
( ~ ( SV76 @ SY1035 @ ( sK38_SY525 @ SV298 @ SV198 @ SV76 ) )
| ( SV76 @ ( sK38_SY525 @ SV298 @ SV198 @ SV76 ) @ SY1035 ) ) )
= $false )
| ( ( SV76 @ SV198 @ SV298 )
= $true )
| ( ( ord_less_eq_nat @ ( sK5_SY523 @ SV298 @ SV198 @ SV76 ) @ ( sK8_SY1011 @ SV76 @ SV198 @ SV298 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2231]) ).
thf(2347,plain,
! [SV298: nat,SV198: nat,SV76: nat > nat > $o] :
( ( ( ~ ( SV76 @ ( sK39_SY1021 @ SV198 @ SV298 @ SV76 ) @ ( sK22_SY525 @ SV298 @ SV198 @ SV76 ) )
| ( SV76 @ ( sK22_SY525 @ SV298 @ SV198 @ SV76 ) @ ( sK39_SY1021 @ SV198 @ SV298 @ SV76 ) ) )
= $false )
| ( ( SV76 @ SV198 @ SV298 )
= $true )
| ( ( SV76 @ ( sK5_SY523 @ SV298 @ SV198 @ SV76 ) @ ( sK8_SY1011 @ SV76 @ SV198 @ SV298 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2232]) ).
thf(2348,plain,
! [SV352: nat,SV205: nat,SV83: nat,SV303: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV303 )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV83 @ SV303 ) @ ( times_times_nat @ SV205 @ SV352 ) )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV83 )
= $false )
| ( ( ord_less_eq_nat @ SV303 @ SV352 )
= $false )
| ( ( ord_less_eq_nat @ SV83 @ SV205 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2233]) ).
thf(2349,plain,
! [SV373: nat > nat,SV353: nat > nat,SV85: set_nat,SV304: nat > nat,SV207: set_nat] :
( ( ( ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( member_nat @ ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) @ SV85 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2238]) ).
thf(2350,plain,
! [SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV304: nat > nat,SV207: set_nat,SV381: nat] :
( ( ( ~ ( ~ ~ ( ~ ( member_nat @ SV381 @ SV207 )
| ( ( SV304 @ SV381 )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) ) )
| ~ ! [SY1022: nat] :
( ~ ~ ( ~ ( member_nat @ SY1022 @ SV207 )
| ( ( SV304 @ SY1022 )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) ) )
| ( SY1022 = SV381 ) ) ) )
= $false )
| ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) )
| ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2239]) ).
thf(2351,plain,
! [SV208: nat > set_nat,SV86: set_nat,SV354: nat,SV305: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK23_SY776 @ SV305 @ SV354 @ SV86 @ SV208 ) @ ( sK40_SY1023 @ SV208 @ SV86 @ SV354 @ SV305 ) )
| ( ord_less_eq_set_nat @ ( SV208 @ ( sK23_SY776 @ SV305 @ SV354 @ SV86 @ SV208 ) ) @ ( SV208 @ ( sK40_SY1023 @ SV208 @ SV86 @ SV354 @ SV305 ) ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ SV86 @ ( SV208 @ SV354 ) )
= $true )
| ( ( ord_less_eq_nat @ SV305 @ SV354 )
= $false )
| ( ( SV86
= ( SV208 @ SV305 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2240]) ).
thf(2352,plain,
! [SV209: set_nat > nat,SV87: nat,SV355: set_nat,SV306: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ ( sK24_SY780 @ SV306 @ SV355 @ SV87 @ SV209 ) @ ( sK41_SY1024 @ SV209 @ SV87 @ SV355 @ SV306 ) )
| ( ord_less_eq_nat @ ( SV209 @ ( sK24_SY780 @ SV306 @ SV355 @ SV87 @ SV209 ) ) @ ( SV209 @ ( sK41_SY1024 @ SV209 @ SV87 @ SV355 @ SV306 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV87 @ ( SV209 @ SV355 ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV306 @ SV355 )
= $false )
| ( ( SV87
= ( SV209 @ SV306 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2241]) ).
thf(2353,plain,
! [SV378: nat] :
( ( ( ( p @ SV378 )
= zero_zero_nat )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SV378 )
| ~ ( ord_less_eq_nat @ SV378 @ zero_zero_nat ) ) )
= $true )
| ( ( p
= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2242]) ).
thf(2354,plain,
( ( ( ( p @ sK18_SX0 )
!= zero_zero_nat )
= $true )
| ( ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
!= zero_zero_nat )
= $true )
| ( ( p
!= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2243]) ).
thf(2355,plain,
( ( ( ~ ( ord_less_eq_nat @ one_one_nat @ sK18_SX0 )
| ~ ( ord_less_eq_nat @ sK18_SX0 @ zero_zero_nat ) )
= $true )
| ( ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
!= zero_zero_nat )
= $true )
| ( ( p
!= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2244]) ).
thf(2356,plain,
! [SV213: nat,SV356: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV356 @ SV213 )
| ~ ( ord_less_eq_nat @ SV213 @ SV356 ) )
= $false )
| ( ( SV213 = SV356 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2246]) ).
thf(2357,plain,
! [SV356: nat,SV213: nat] :
( ( ( ord_less_eq_nat @ SV213 @ SV356 )
= $false )
| ( ( ord_less_eq_nat @ SV356 @ SV213 )
= $false )
| ( ( ~ ( ( SV213 != SV356 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV356 @ SV213 )
| ~ ( ord_less_eq_nat @ SV213 @ SV356 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2247]) ).
thf(2358,plain,
! [SV216: set_nat > nat,SV95: nat,SV358: set_nat,SV309: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ ( sK25_SY789 @ SV309 @ SV358 @ SV95 @ SV216 ) @ ( sK42_SY1025 @ SV216 @ SV95 @ SV358 @ SV309 ) )
| ( ord_less_eq_nat @ ( SV216 @ ( sK25_SY789 @ SV309 @ SV358 @ SV95 @ SV216 ) ) @ ( SV216 @ ( sK42_SY1025 @ SV216 @ SV95 @ SV358 @ SV309 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ ( SV216 @ SV358 ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV309 @ SV358 )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ ( SV216 @ SV309 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2249]) ).
thf(2359,plain,
! [SV311: nat,SV98: nat,SV219: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV219 ) )
= $false )
| ( ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2251]) ).
thf(2360,plain,
! [SV219: nat,SV311: nat,SV98: nat] :
( ( ( ~ ( ord_less_nat @ SV98 @ SV311 ) )
= $false )
| ( ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2251]) ).
thf(2361,plain,
! [SV311: nat,SV219: nat,SV98: nat] :
( ( ( ~ ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV219 )
| ~ ( ord_less_nat @ SV98 @ SV311 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV219 )
= $false )
| ( ( ord_less_nat @ SV98 @ SV311 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2252]) ).
thf(2362,plain,
! [SV220: nat > nat,SV99: nat,SV359: nat,SV312: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK26_SY798 @ SV312 @ SV359 @ SV99 @ SV220 ) @ ( sK43_SY1026 @ SV220 @ SV99 @ SV359 @ SV312 ) )
| ( ord_less_eq_nat @ ( SV220 @ ( sK26_SY798 @ SV312 @ SV359 @ SV99 @ SV220 ) ) @ ( SV220 @ ( sK43_SY1026 @ SV220 @ SV99 @ SV359 @ SV312 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV99 @ ( SV220 @ SV359 ) )
= $true )
| ( ( ord_less_eq_nat @ SV312 @ SV359 )
= $false )
| ( ( SV99
= ( SV220 @ SV312 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2253]) ).
thf(2363,plain,
! [SV221: nat,SV313: nat,SV100: nat > $o] :
( ( ( ~ ~ ( ~ ( SV100 @ ( sK44_SY590 @ SV313 @ SV221 @ SV100 ) )
| ~ ! [SY1036: nat] :
( ~ ( SV100 @ SY1036 )
| ( ord_less_eq_nat @ SY1036 @ ( sK44_SY590 @ SV313 @ SV221 @ SV100 ) ) ) ) )
= $false )
| ( ( SV100 @ ( sK14_SY920 @ SV221 @ SV313 @ SV100 ) )
= $true )
| ( ( SV100 @ SV221 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2254]) ).
thf(2364,plain,
! [SV221: nat,SV313: nat,SV100: nat > $o] :
( ( ( ~ ( ~ ( SV100 @ ( sK27_SY590 @ SV313 @ SV221 @ SV100 ) )
| ~ ! [SY1027: nat] :
( ~ ( SV100 @ SY1027 )
| ( ord_less_eq_nat @ SY1027 @ ( sK27_SY590 @ SV313 @ SV221 @ SV100 ) ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK14_SY920 @ SV221 @ SV313 @ SV100 ) @ SV313 )
= $false )
| ( ( SV100 @ SV221 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2255]) ).
thf(2365,plain,
! [SV360: nat,SV222: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV222 @ SV360 )
| ~ ( ( SV360 != SV222 ) ) )
= $false )
| ( ( ord_less_nat @ SV222 @ SV360 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2257]) ).
thf(2366,plain,
! [SV222: nat,SV360: nat] :
( ( ( SV360 != SV222 )
= $false )
| ( ( ord_less_eq_nat @ SV222 @ SV360 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV222 @ SV360 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV222 @ SV360 )
| ~ ( ( SV360 != SV222 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2258]) ).
thf(2367,plain,
! [SV103: nat > nat,SV224: nat,SV377: nat] :
( ( ( ~ ( ord_less_eq_nat @ one_one_nat @ SV377 )
| ~ ( ord_less_eq_nat @ SV377 @ SV224 ) )
= $false )
| ( ( ( SV103 @ SV377 )
= zero_zero_nat )
= $true )
| ( ( number1551313001itions @ SV103 @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2259]) ).
thf(2368,plain,
! [SV315: nat > nat,SV106: nat,SV361: nat,SV227: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK28_SY924 @ SV227 @ SV361 @ SV106 @ SV315 ) @ ( sK45_SY1028 @ SV315 @ SV106 @ SV361 @ SV227 ) )
| ( ord_less_eq_nat @ ( SV315 @ ( sK28_SY924 @ SV227 @ SV361 @ SV106 @ SV315 ) ) @ ( SV315 @ ( sK45_SY1028 @ SV315 @ SV106 @ SV361 @ SV227 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV315 @ SV106 ) @ SV361 )
= $true )
| ( ( ord_less_eq_nat @ ( SV315 @ SV227 ) @ SV361 )
= $false )
| ( ( ord_less_eq_nat @ SV106 @ SV227 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2260]) ).
thf(2369,plain,
! [SV362: nat,SV228: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV228 @ SV362 )
| ~ ( ( SV228 != SV362 ) ) )
= $false )
| ( ( ord_less_nat @ SV228 @ SV362 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2262]) ).
thf(2370,plain,
! [SV362: nat,SV228: nat] :
( ( ( SV228 != SV362 )
= $false )
| ( ( ord_less_eq_nat @ SV228 @ SV362 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV228 @ SV362 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV228 @ SV362 )
| ~ ( ( SV228 != SV362 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2263]) ).
thf(2371,plain,
! [SV110: nat > $o,SV230: nat,SV382: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV382 @ ( sK10_SY608 @ SV230 @ SV110 ) )
| ~ ~ ( SV110 @ SV382 ) ) )
= $false )
| ( ( SV110 @ SV230 )
= $true )
| ( ( SV110 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2265]) ).
thf(2372,plain,
! [SV376: nat > nat,SV374: nat > nat,SV236: nat > nat,SV116: set_nat,SV363: nat > nat,SV319: set_nat] :
( ( ( ~ ! [SY1014: nat] :
( ~ ( member_nat @ SY1014 @ SV319 )
| ~ ( ~ ~ ( ~ ( member_nat @ ( SV363 @ SY1014 ) @ SV116 )
| ( ( SV236 @ ( SV363 @ SY1014 ) )
!= SY1014 ) )
| ( ( SV374 @ ( SV363 @ SY1014 ) )
!= ( SV376 @ SY1014 ) ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) )
= $true )
| ( ( member_nat @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) @ SV116 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2266]) ).
thf(2373,plain,
! [SV116: set_nat,SV319: set_nat,SV363: nat > nat,SV374: nat > nat,SV376: nat > nat,SV236: nat > nat] :
( ( ( ~ ( member_nat @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) @ SV319 ) )
= $true )
| ( ( ( SV363 @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) )
!= ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) )
= $true )
| ( ( ~ ! [SY1014: nat] :
( ~ ( member_nat @ SY1014 @ SV319 )
| ~ ( ~ ~ ( ~ ( member_nat @ ( SV363 @ SY1014 ) @ SV116 )
| ( ( SV236 @ ( SV363 @ SY1014 ) )
!= SY1014 ) )
| ( ( SV374 @ ( SV363 @ SY1014 ) )
!= ( SV376 @ SY1014 ) ) ) )
| ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2267]) ).
thf(2374,plain,
! [SV320: nat > set_nat,SV117: nat,SV364: set_nat,SV237: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK29_SY932 @ SV237 @ SV364 @ SV117 @ SV320 ) @ ( sK46_SY1029 @ SV320 @ SV117 @ SV364 @ SV237 ) )
| ( ord_less_eq_set_nat @ ( SV320 @ ( sK29_SY932 @ SV237 @ SV364 @ SV117 @ SV320 ) ) @ ( SV320 @ ( sK46_SY1029 @ SV320 @ SV117 @ SV364 @ SV237 ) ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ ( SV320 @ SV117 ) @ SV364 )
= $true )
| ( ( ord_less_eq_set_nat @ ( SV320 @ SV237 ) @ SV364 )
= $false )
| ( ( ord_less_eq_nat @ SV117 @ SV237 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2268]) ).
thf(2375,plain,
! [SV239: nat > nat,SV119: nat,SV365: nat,SV321: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK30_SY830 @ SV321 @ SV365 @ SV119 @ SV239 ) @ ( sK47_SY1030 @ SV239 @ SV119 @ SV365 @ SV321 ) )
| ( ord_less_eq_nat @ ( SV239 @ ( sK30_SY830 @ SV321 @ SV365 @ SV119 @ SV239 ) ) @ ( SV239 @ ( sK47_SY1030 @ SV239 @ SV119 @ SV365 @ SV321 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV119 @ ( SV239 @ SV365 ) )
= $true )
| ( ( ord_less_eq_nat @ SV321 @ SV365 )
= $false )
| ( ( ord_less_eq_nat @ SV119 @ ( SV239 @ SV321 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2269]) ).
thf(2376,plain,
! [SV366: nat,SV243: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV243 @ SV366 )
| ~ ( ord_less_eq_nat @ SV366 @ SV243 ) )
= $false )
| ( ( SV243 = SV366 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2271]) ).
thf(2377,plain,
! [SV243: nat,SV366: nat] :
( ( ( ord_less_eq_nat @ SV366 @ SV243 )
= $false )
| ( ( ord_less_eq_nat @ SV243 @ SV366 )
= $false )
| ( ( ~ ( ( SV243 != SV366 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV243 @ SV366 )
| ~ ( ord_less_eq_nat @ SV366 @ SV243 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2272]) ).
thf(2378,plain,
! [SV246: nat > set_nat,SV127: set_nat,SV367: nat,SV325: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK31_SY838 @ SV325 @ SV367 @ SV127 @ SV246 ) @ ( sK48_SY1031 @ SV246 @ SV127 @ SV367 @ SV325 ) )
| ( ord_less_eq_set_nat @ ( SV246 @ ( sK31_SY838 @ SV325 @ SV367 @ SV127 @ SV246 ) ) @ ( SV246 @ ( sK48_SY1031 @ SV246 @ SV127 @ SV367 @ SV325 ) ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ SV127 @ ( SV246 @ SV367 ) )
= $true )
| ( ( ord_less_eq_nat @ SV325 @ SV367 )
= $false )
| ( ( ord_less_eq_set_nat @ SV127 @ ( SV246 @ SV325 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2273]) ).
thf(2379,plain,
! [SV368: nat,SV247: nat,SV128: nat,SV326: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV326 )
= $false )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV128 @ SV326 ) @ ( times_times_nat @ SV247 @ SV368 ) )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV247 )
= $false )
| ( ( ord_less_eq_nat @ SV326 @ SV368 )
= $false )
| ( ( ord_less_eq_nat @ SV128 @ SV247 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2274]) ).
thf(2380,plain,
! [SV327: nat,SV248: nat,SV130: nat] :
( ( ( ( times_times_nat @ SV130 @ SV248 )
!= ( times_times_nat @ SV130 @ SV327 ) )
= $false )
| ( ( ( times_times_nat @ SV130 @ SV248 )
= ( times_times_nat @ SV130 @ SV327 ) )
= $false )
| ( ( SV130 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2275]) ).
thf(2381,plain,
! [SV130: nat,SV327: nat,SV248: nat] :
( ( ( SV248 != SV327 )
= $false )
| ( ( ( times_times_nat @ SV130 @ SV248 )
= ( times_times_nat @ SV130 @ SV327 ) )
= $false )
| ( ( SV130 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2275]) ).
thf(2382,plain,
! [SV327: nat,SV248: nat,SV130: nat] :
( ( ( ( times_times_nat @ SV130 @ SV248 )
!= ( times_times_nat @ SV130 @ SV327 ) )
= $false )
| ( ( SV248 = SV327 )
= $false )
| ( ( SV130 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2276]) ).
thf(2383,plain,
! [SV130: nat,SV327: nat,SV248: nat] :
( ( ( SV248 != SV327 )
= $false )
| ( ( SV248 = SV327 )
= $false )
| ( ( SV130 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2276]) ).
thf(2384,plain,
! [SV328: nat,SV131: nat,SV249: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV249 )
= $false )
| ( ( ord_less_eq_nat @ SV131 @ SV328 )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2277]) ).
thf(2385,plain,
! [SV328: nat,SV249: nat,SV131: nat] :
( ( ( ord_less_eq_nat @ ( times_times_nat @ SV131 @ SV249 ) @ ( times_times_nat @ SV328 @ SV249 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV249 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2278]) ).
thf(2386,plain,
! [SV328: nat,SV131: nat,SV249: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV249 )
| ( ord_less_eq_nat @ SV131 @ SV328 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV249 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2279]) ).
thf(2387,plain,
! [SV328: nat,SV131: nat,SV249: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV249 ) )
= $true )
| ( ( ord_less_eq_nat @ SV131 @ SV328 )
= $true )
| ( ( ord_less_eq_nat @ SV131 @ SV328 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2281]) ).
thf(2388,plain,
! [SV329: nat > nat,SV132: nat,SV369: nat,SV250: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK32_SY942 @ SV250 @ SV369 @ SV132 @ SV329 ) @ ( sK49_SY1032 @ SV329 @ SV132 @ SV369 @ SV250 ) )
| ( ord_less_eq_nat @ ( SV329 @ ( sK32_SY942 @ SV250 @ SV369 @ SV132 @ SV329 ) ) @ ( SV329 @ ( sK49_SY1032 @ SV329 @ SV132 @ SV369 @ SV250 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV329 @ SV132 ) @ SV369 )
= $true )
| ( ( ( SV329 @ SV250 )
= SV369 )
= $false )
| ( ( ord_less_eq_nat @ SV132 @ SV250 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2282]) ).
thf(2389,plain,
! [SV252: nat,SV331: nat,SV134: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV134 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV252 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2283]) ).
thf(2390,plain,
! [SV252: nat,SV331: nat,SV134: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV134 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV252 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2284]) ).
thf(2391,plain,
! [SV252: nat,SV331: nat,SV134: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV134 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV252 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2285]) ).
thf(2392,plain,
! [SV252: nat,SV331: nat,SV134: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV134 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV252 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2286]) ).
thf(2393,plain,
! [SV332: nat,SV253: nat,SV135: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 ) )
= $false )
| ( ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2287]) ).
thf(2394,plain,
! [SV135: nat,SV332: nat,SV253: nat] :
( ( ( ~ ( ord_less_nat @ SV253 @ SV332 ) )
= $false )
| ( ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2287]) ).
thf(2395,plain,
! [SV332: nat,SV253: nat,SV135: nat] :
( ( ( ~ ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
| ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 )
| ~ ( ord_less_nat @ SV253 @ SV332 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV135 )
= $false )
| ( ( ord_less_nat @ SV253 @ SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2288]) ).
thf(2396,plain,
! [SV254: nat,SV136: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV136 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2289]) ).
thf(2397,plain,
! [SV136: nat,SV254: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV254 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2290]) ).
thf(2398,plain,
! [SV254: nat,SV136: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV136 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV254 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2291]) ).
thf(2399,plain,
! [SV254: nat,SV136: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV136 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV254 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV136 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV254 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2291]) ).
thf(2400,plain,
! [SV370: nat,SV259: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV259 @ SV370 )
| ~ ( ( SV259 != SV370 ) ) )
= $false )
| ( ( ord_less_nat @ SV259 @ SV370 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2293]) ).
thf(2401,plain,
! [SV370: nat,SV259: nat] :
( ( ( SV259 != SV370 )
= $false )
| ( ( ord_less_eq_nat @ SV259 @ SV370 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV259 @ SV370 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV259 @ SV370 )
| ~ ( ( SV259 != SV370 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2294]) ).
thf(2402,plain,
! [SV263: nat,SV145: nat] :
( ( ( SV145 = one_one_nat )
= $true )
| ( ( one_one_nat
= ( times_times_nat @ SV145 @ SV263 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2295]) ).
thf(2403,plain,
! [SV145: nat,SV263: nat] :
( ( ( SV263 = one_one_nat )
= $true )
| ( ( one_one_nat
= ( times_times_nat @ SV145 @ SV263 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2296]) ).
thf(2404,plain,
! [SV263: nat,SV145: nat] :
( ( ( one_one_nat
!= ( times_times_nat @ SV145 @ SV263 ) )
= $false )
| ( ( SV145 = one_one_nat )
= $false )
| ( ( SV263 = one_one_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2297]) ).
thf(2405,plain,
! [SV263: nat,SV145: nat] :
( ( ( ~ ~ ( ( SV145 != one_one_nat )
| ( SV263 != one_one_nat ) ) )
= $false )
| ( ( SV145 = one_one_nat )
= $false )
| ( ( SV263 = one_one_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2297]) ).
thf(2406,plain,
! [SV336: nat,SV146: nat,SV264: nat] :
( ( ( ( times_times_nat @ SV264 @ SV146 )
!= ( times_times_nat @ SV336 @ SV146 ) )
= $false )
| ( ( ( times_times_nat @ SV264 @ SV146 )
= ( times_times_nat @ SV336 @ SV146 ) )
= $false )
| ( ( SV146 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2298]) ).
thf(2407,plain,
! [SV146: nat,SV336: nat,SV264: nat] :
( ( ( SV264 != SV336 )
= $false )
| ( ( ( times_times_nat @ SV264 @ SV146 )
= ( times_times_nat @ SV336 @ SV146 ) )
= $false )
| ( ( SV146 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2298]) ).
thf(2408,plain,
! [SV336: nat,SV146: nat,SV264: nat] :
( ( ( ( times_times_nat @ SV264 @ SV146 )
!= ( times_times_nat @ SV336 @ SV146 ) )
= $false )
| ( ( SV264 = SV336 )
= $false )
| ( ( SV146 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2299]) ).
thf(2409,plain,
! [SV146: nat,SV336: nat,SV264: nat] :
( ( ( SV264 != SV336 )
= $false )
| ( ( SV264 = SV336 )
= $false )
| ( ( SV146 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2299]) ).
thf(2410,plain,
! [SV265: nat,SV148: nat > nat] :
( ( ( ( groups1842438620at_nat
@ ^ [SY685: nat] : ( times_times_nat @ ( SV148 @ SY685 ) @ SY685 )
@ ( set_ord_atMost_nat @ SV265 ) )
= SV265 )
= $false )
| ( ( number1551313001itions @ SV148 @ SV265 )
= $true )
| ( ( ord_less_eq_nat @ one_one_nat @ ( sK4_SY856 @ SV265 @ SV148 ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK4_SY856 @ SV265 @ SV148 ) @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2300]) ).
thf(2411,plain,
! [SV266: nat,SV149: nat] :
( ( ( SV149 = one_one_nat )
= $true )
| ( ( ( times_times_nat @ SV149 @ SV266 )
= one_one_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2301]) ).
thf(2412,plain,
! [SV149: nat,SV266: nat] :
( ( ( SV266 = one_one_nat )
= $true )
| ( ( ( times_times_nat @ SV149 @ SV266 )
= one_one_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2302]) ).
thf(2413,plain,
! [SV266: nat,SV149: nat] :
( ( ( ( times_times_nat @ SV149 @ SV266 )
!= one_one_nat )
= $false )
| ( ( SV149 = one_one_nat )
= $false )
| ( ( SV266 = one_one_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2303]) ).
thf(2414,plain,
! [SV266: nat,SV149: nat] :
( ( ( ~ ~ ( ( SV149 != one_one_nat )
| ( SV266 != one_one_nat ) ) )
= $false )
| ( ( SV149 = one_one_nat )
= $false )
| ( ( SV266 = one_one_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2303]) ).
thf(2415,plain,
! [SV337: set_nat > nat,SV151: set_nat,SV371: nat,SV267: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ ( sK33_SY946 @ SV267 @ SV371 @ SV151 @ SV337 ) @ ( sK50_SY1033 @ SV337 @ SV151 @ SV371 @ SV267 ) )
| ( ord_less_eq_nat @ ( SV337 @ ( sK33_SY946 @ SV267 @ SV371 @ SV151 @ SV337 ) ) @ ( SV337 @ ( sK50_SY1033 @ SV337 @ SV151 @ SV371 @ SV267 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV337 @ SV151 ) @ SV371 )
= $true )
| ( ( ( SV337 @ SV267 )
= SV371 )
= $false )
| ( ( ord_less_eq_set_nat @ SV151 @ SV267 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2304]) ).
thf(2416,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV153 )
= $false )
| ( ( ord_less_eq_nat @ SV269 @ SV339 )
= $true )
| ( ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2305]) ).
thf(2417,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ord_less_eq_nat @ ( times_times_nat @ SV153 @ SV269 ) @ ( times_times_nat @ SV153 @ SV339 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV153 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2306]) ).
thf(2418,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV153 )
| ( ord_less_eq_nat @ SV269 @ SV339 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV153 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2307]) ).
thf(2419,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV153 ) )
= $true )
| ( ( ord_less_eq_nat @ SV269 @ SV339 )
= $true )
| ( ( ord_less_eq_nat @ SV269 @ SV339 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2309]) ).
thf(2420,plain,
! [SV343: nat,SV179: nat] :
( ( ( ord_less_nat @ SV179 @ SV343 )
= $true )
| ( ( SV179 = SV343 )
= $true )
| ( ( ord_less_nat @ SV179 @ SV343 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2322]) ).
thf(2421,plain,
! [SV343: nat,SV179: nat] :
( ( ( ord_less_nat @ SV179 @ SV343 )
= $true )
| ( ( SV179 = SV343 )
= $true )
| ( ( SV179 = SV343 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2324]) ).
thf(2422,plain,
! [SV344: nat,SV180: nat] :
( ( ( ord_less_nat @ SV180 @ SV344 )
= $true )
| ( ( SV344 = SV180 )
= $true )
| ( ( ord_less_nat @ SV180 @ SV344 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2327]) ).
thf(2423,plain,
! [SV344: nat,SV180: nat] :
( ( ( ord_less_nat @ SV180 @ SV344 )
= $true )
| ( ( SV344 = SV180 )
= $true )
| ( ( SV344 = SV180 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2329]) ).
thf(2424,plain,
! [SV345: nat,SV181: nat] :
( ( ( ord_less_nat @ SV181 @ SV345 )
= $true )
| ( ( SV181 = SV345 )
= $true )
| ( ( ord_less_nat @ SV181 @ SV345 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2332]) ).
thf(2425,plain,
! [SV345: nat,SV181: nat] :
( ( ( ord_less_nat @ SV181 @ SV345 )
= $true )
| ( ( SV181 = SV345 )
= $true )
| ( ( SV181 = SV345 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2334]) ).
thf(2426,plain,
! [SV375: nat > nat,SV372: nat > nat,SV182: nat > nat,SV346: set_nat,SV288: nat > nat,SV60: set_nat] :
( ( ( ! [SY953: nat] :
( ~ ( member_nat @ SY953 @ SV60 )
| ( member_nat @ ( SV288 @ SY953 ) @ SV346 ) ) )
= $false )
| ( ( ~ ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) )
| ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2335]) ).
thf(2427,plain,
! [SV60: set_nat,SV288: nat > nat,SV346: set_nat,SV182: nat > nat,SV372: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
| ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 ) )
= $false )
| ( ( ~ ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) )
| ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2336]) ).
thf(2428,plain,
! [SV347: nat,SV186: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV186 @ SV347 ) )
= $false )
| ( ( SV186 = SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2337]) ).
thf(2429,plain,
! [SV186: nat,SV347: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV347 @ SV186 ) )
= $false )
| ( ( SV186 = SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2337]) ).
thf(2430,plain,
! [SV347: nat,SV186: nat] :
( ( ( ( SV186 != SV347 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV186 @ SV347 )
| ~ ( ord_less_eq_nat @ SV347 @ SV186 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV186 @ SV347 )
= $false )
| ( ( ord_less_eq_nat @ SV347 @ SV186 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2338]) ).
thf(2431,plain,
! [SV292: set_nat > nat,SV69: set_nat,SV348: nat,SV191: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ ( sK19_SY882 @ SV191 @ SV348 @ SV69 @ SV292 ) @ ( sK34_SY1018 @ SV292 @ SV69 @ SV348 @ SV191 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV292 @ SV69 ) @ SV348 )
= $true )
| ( ( ord_less_eq_nat @ ( SV292 @ SV191 ) @ SV348 )
= $false )
| ( ( ord_less_eq_set_nat @ SV69 @ SV191 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2339]) ).
thf(2432,plain,
! [SV69: set_nat,SV348: nat,SV191: set_nat,SV292: set_nat > nat] :
( ( ( ord_less_eq_nat @ ( SV292 @ ( sK19_SY882 @ SV191 @ SV348 @ SV69 @ SV292 ) ) @ ( SV292 @ ( sK34_SY1018 @ SV292 @ SV69 @ SV348 @ SV191 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV292 @ SV69 ) @ SV348 )
= $true )
| ( ( ord_less_eq_nat @ ( SV292 @ SV191 ) @ SV348 )
= $false )
| ( ( ord_less_eq_set_nat @ SV69 @ SV191 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2339]) ).
thf(2433,plain,
! [SV192: nat,SV293: nat,SV70: nat > $o] :
( ( ( ~ ( SV70 @ ( sK35_SY505 @ SV293 @ SV192 @ SV70 ) ) )
= $false )
| ( ( SV70 @ ( sK12_SY884 @ SV192 @ SV293 @ SV70 ) )
= $true )
| ( ( SV70 @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2340]) ).
thf(2434,plain,
! [SV192: nat,SV293: nat,SV70: nat > $o] :
( ( ( ~ ! [SY1034: nat] :
( ~ ( SV70 @ SY1034 )
| ( ord_less_eq_nat @ SY1034 @ ( sK35_SY505 @ SV293 @ SV192 @ SV70 ) ) ) )
= $false )
| ( ( SV70 @ ( sK12_SY884 @ SV192 @ SV293 @ SV70 ) )
= $true )
| ( ( SV70 @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2340]) ).
thf(2435,plain,
! [SV192: nat,SV293: nat,SV70: nat > $o] :
( ( ( SV70 @ ( sK20_SY505 @ SV293 @ SV192 @ SV70 ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK12_SY884 @ SV192 @ SV293 @ SV70 ) @ SV293 )
= $false )
| ( ( SV70 @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2341]) ).
thf(2436,plain,
! [SV192: nat,SV293: nat,SV70: nat > $o] :
( ( ( ! [SY1019: nat] :
( ~ ( SV70 @ SY1019 )
| ( ord_less_eq_nat @ SY1019 @ ( sK20_SY505 @ SV293 @ SV192 @ SV70 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK12_SY884 @ SV192 @ SV293 @ SV70 ) @ SV293 )
= $false )
| ( ( SV70 @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2342]) ).
thf(2437,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) ) )
= $false )
| ( ( number1551313001itions @ SV194 @ SV350 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2343]) ).
thf(2438,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 )
= $false )
| ( ( number1551313001itions @ SV194 @ SV350 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2343]) ).
thf(2439,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ~ ( ( ( SV194 @ ( sK36_SY959 @ SV350 @ SV194 ) )
!= zero_zero_nat ) ) )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 )
= $true )
| ( ( ~ ( ~ ( number1551313001itions @ SV194 @ SV350 )
| ~ ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2344]) ).
thf(2440,plain,
! [SV194: nat > nat,SV350: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ ( sK36_SY959 @ SV350 @ SV194 ) )
| ~ ( ord_less_eq_nat @ ( sK36_SY959 @ SV350 @ SV194 ) @ SV350 ) ) )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 )
= $true )
| ( ( ~ ( ~ ( number1551313001itions @ SV194 @ SV350 )
| ~ ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2344]) ).
thf(2441,plain,
! [SV296: nat > set_nat,SV74: nat,SV351: set_nat,SV196: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK21_SY891 @ SV196 @ SV351 @ SV74 @ SV296 ) @ ( sK37_SY1020 @ SV296 @ SV74 @ SV351 @ SV196 ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ ( SV296 @ SV74 ) @ SV351 )
= $true )
| ( ( ( SV296 @ SV196 )
= SV351 )
= $false )
| ( ( ord_less_eq_nat @ SV74 @ SV196 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2345]) ).
thf(2442,plain,
! [SV74: nat,SV351: set_nat,SV196: nat,SV296: nat > set_nat] :
( ( ( ord_less_eq_set_nat @ ( SV296 @ ( sK21_SY891 @ SV196 @ SV351 @ SV74 @ SV296 ) ) @ ( SV296 @ ( sK37_SY1020 @ SV296 @ SV74 @ SV351 @ SV196 ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ ( SV296 @ SV74 ) @ SV351 )
= $true )
| ( ( ( SV296 @ SV196 )
= SV351 )
= $false )
| ( ( ord_less_eq_nat @ SV74 @ SV196 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2345]) ).
thf(2443,plain,
! [SV298: nat,SV198: nat,SV76: nat > nat > $o] :
( ( ( ~ ( SV76 @ ( sK52_SY1035 @ SV198 @ SV298 @ SV76 ) @ ( sK38_SY525 @ SV298 @ SV198 @ SV76 ) )
| ( SV76 @ ( sK38_SY525 @ SV298 @ SV198 @ SV76 ) @ ( sK52_SY1035 @ SV198 @ SV298 @ SV76 ) ) )
= $false )
| ( ( SV76 @ SV198 @ SV298 )
= $true )
| ( ( ord_less_eq_nat @ ( sK5_SY523 @ SV298 @ SV198 @ SV76 ) @ ( sK8_SY1011 @ SV76 @ SV198 @ SV298 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2346]) ).
thf(2444,plain,
! [SV298: nat,SV198: nat,SV76: nat > nat > $o] :
( ( ( ~ ( SV76 @ ( sK39_SY1021 @ SV198 @ SV298 @ SV76 ) @ ( sK22_SY525 @ SV298 @ SV198 @ SV76 ) ) )
= $false )
| ( ( SV76 @ SV198 @ SV298 )
= $true )
| ( ( SV76 @ ( sK5_SY523 @ SV298 @ SV198 @ SV76 ) @ ( sK8_SY1011 @ SV76 @ SV198 @ SV298 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2347]) ).
thf(2445,plain,
! [SV198: nat,SV298: nat,SV76: nat > nat > $o] :
( ( ( SV76 @ ( sK22_SY525 @ SV298 @ SV198 @ SV76 ) @ ( sK39_SY1021 @ SV198 @ SV298 @ SV76 ) )
= $false )
| ( ( SV76 @ SV198 @ SV298 )
= $true )
| ( ( SV76 @ ( sK5_SY523 @ SV298 @ SV198 @ SV76 ) @ ( sK8_SY1011 @ SV76 @ SV198 @ SV298 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2347]) ).
thf(2446,plain,
! [SV207: set_nat,SV304: nat > nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat] :
( ( ( ~ ( member_nat @ ( sK53_SY1002 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ ( sK53_SY1002 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) @ SV85 )
| ( ( SV353 @ ( SV304 @ ( sK53_SY1002 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
!= ( SV373 @ ( sK53_SY1002 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( member_nat @ ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) @ SV85 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2349]) ).
thf(2447,plain,
! [SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV304: nat > nat,SV207: set_nat,SV381: nat] :
( ( ( ~ ~ ( ~ ( member_nat @ SV381 @ SV207 )
| ( ( SV304 @ SV381 )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) ) )
| ~ ! [SY1022: nat] :
( ~ ~ ( ~ ( member_nat @ SY1022 @ SV207 )
| ( ( SV304 @ SY1022 )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) ) )
| ( SY1022 = SV381 ) ) )
= $true )
| ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) )
| ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2350]) ).
thf(2448,plain,
! [SV208: nat > set_nat,SV86: set_nat,SV354: nat,SV305: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK23_SY776 @ SV305 @ SV354 @ SV86 @ SV208 ) @ ( sK40_SY1023 @ SV208 @ SV86 @ SV354 @ SV305 ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ SV86 @ ( SV208 @ SV354 ) )
= $true )
| ( ( ord_less_eq_nat @ SV305 @ SV354 )
= $false )
| ( ( SV86
= ( SV208 @ SV305 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2351]) ).
thf(2449,plain,
! [SV86: set_nat,SV354: nat,SV305: nat,SV208: nat > set_nat] :
( ( ( ord_less_eq_set_nat @ ( SV208 @ ( sK23_SY776 @ SV305 @ SV354 @ SV86 @ SV208 ) ) @ ( SV208 @ ( sK40_SY1023 @ SV208 @ SV86 @ SV354 @ SV305 ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ SV86 @ ( SV208 @ SV354 ) )
= $true )
| ( ( ord_less_eq_nat @ SV305 @ SV354 )
= $false )
| ( ( SV86
= ( SV208 @ SV305 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2351]) ).
thf(2450,plain,
! [SV209: set_nat > nat,SV87: nat,SV355: set_nat,SV306: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ ( sK24_SY780 @ SV306 @ SV355 @ SV87 @ SV209 ) @ ( sK41_SY1024 @ SV209 @ SV87 @ SV355 @ SV306 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV87 @ ( SV209 @ SV355 ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV306 @ SV355 )
= $false )
| ( ( SV87
= ( SV209 @ SV306 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2352]) ).
thf(2451,plain,
! [SV87: nat,SV355: set_nat,SV306: set_nat,SV209: set_nat > nat] :
( ( ( ord_less_eq_nat @ ( SV209 @ ( sK24_SY780 @ SV306 @ SV355 @ SV87 @ SV209 ) ) @ ( SV209 @ ( sK41_SY1024 @ SV209 @ SV87 @ SV355 @ SV306 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV87 @ ( SV209 @ SV355 ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV306 @ SV355 )
= $false )
| ( ( SV87
= ( SV209 @ SV306 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2352]) ).
thf(2452,plain,
! [SV378: nat] :
( ( ( ~ ( ord_less_eq_nat @ one_one_nat @ SV378 )
| ~ ( ord_less_eq_nat @ SV378 @ zero_zero_nat ) )
= $false )
| ( ( ( p @ SV378 )
= zero_zero_nat )
= $true )
| ( ( p
= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2353]) ).
thf(2453,plain,
( ( ( ( p @ sK18_SX0 )
= zero_zero_nat )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
!= zero_zero_nat )
= $true )
| ( ( p
!= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2354]) ).
thf(2454,plain,
( ( ( ~ ( ord_less_eq_nat @ one_one_nat @ sK18_SX0 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ sK18_SX0 @ zero_zero_nat ) )
= $true )
| ( ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
!= zero_zero_nat )
= $true )
| ( ( p
!= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2355]) ).
thf(2455,plain,
! [SV213: nat,SV356: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV356 @ SV213 ) )
= $false )
| ( ( SV213 = SV356 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2356]) ).
thf(2456,plain,
! [SV356: nat,SV213: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV213 @ SV356 ) )
= $false )
| ( ( SV213 = SV356 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2356]) ).
thf(2457,plain,
! [SV356: nat,SV213: nat] :
( ( ( ( SV213 != SV356 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV356 @ SV213 )
| ~ ( ord_less_eq_nat @ SV213 @ SV356 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV356 @ SV213 )
= $false )
| ( ( ord_less_eq_nat @ SV213 @ SV356 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2357]) ).
thf(2458,plain,
! [SV216: set_nat > nat,SV95: nat,SV358: set_nat,SV309: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ ( sK25_SY789 @ SV309 @ SV358 @ SV95 @ SV216 ) @ ( sK42_SY1025 @ SV216 @ SV95 @ SV358 @ SV309 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ ( SV216 @ SV358 ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV309 @ SV358 )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ ( SV216 @ SV309 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2358]) ).
thf(2459,plain,
! [SV95: nat,SV358: set_nat,SV309: set_nat,SV216: set_nat > nat] :
( ( ( ord_less_eq_nat @ ( SV216 @ ( sK25_SY789 @ SV309 @ SV358 @ SV95 @ SV216 ) ) @ ( SV216 @ ( sK42_SY1025 @ SV216 @ SV95 @ SV358 @ SV309 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ ( SV216 @ SV358 ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV309 @ SV358 )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ ( SV216 @ SV309 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2358]) ).
thf(2460,plain,
! [SV311: nat,SV98: nat,SV219: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV219 )
= $true )
| ( ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2359]) ).
thf(2461,plain,
! [SV219: nat,SV311: nat,SV98: nat] :
( ( ( ord_less_nat @ SV98 @ SV311 )
= $true )
| ( ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2360]) ).
thf(2462,plain,
! [SV311: nat,SV219: nat,SV98: nat] :
( ( ( ~ ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV219 )
= $false )
| ( ( ord_less_nat @ SV98 @ SV311 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2361]) ).
thf(2463,plain,
! [SV311: nat,SV98: nat,SV219: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV219 )
| ~ ( ord_less_nat @ SV98 @ SV311 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV219 )
= $false )
| ( ( ord_less_nat @ SV98 @ SV311 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2361]) ).
thf(2464,plain,
! [SV220: nat > nat,SV99: nat,SV359: nat,SV312: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK26_SY798 @ SV312 @ SV359 @ SV99 @ SV220 ) @ ( sK43_SY1026 @ SV220 @ SV99 @ SV359 @ SV312 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV99 @ ( SV220 @ SV359 ) )
= $true )
| ( ( ord_less_eq_nat @ SV312 @ SV359 )
= $false )
| ( ( SV99
= ( SV220 @ SV312 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2362]) ).
thf(2465,plain,
! [SV99: nat,SV359: nat,SV312: nat,SV220: nat > nat] :
( ( ( ord_less_eq_nat @ ( SV220 @ ( sK26_SY798 @ SV312 @ SV359 @ SV99 @ SV220 ) ) @ ( SV220 @ ( sK43_SY1026 @ SV220 @ SV99 @ SV359 @ SV312 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV99 @ ( SV220 @ SV359 ) )
= $true )
| ( ( ord_less_eq_nat @ SV312 @ SV359 )
= $false )
| ( ( SV99
= ( SV220 @ SV312 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2362]) ).
thf(2466,plain,
! [SV221: nat,SV313: nat,SV100: nat > $o] :
( ( ( ~ ( ~ ( SV100 @ ( sK44_SY590 @ SV313 @ SV221 @ SV100 ) )
| ~ ! [SY1036: nat] :
( ~ ( SV100 @ SY1036 )
| ( ord_less_eq_nat @ SY1036 @ ( sK44_SY590 @ SV313 @ SV221 @ SV100 ) ) ) ) )
= $true )
| ( ( SV100 @ ( sK14_SY920 @ SV221 @ SV313 @ SV100 ) )
= $true )
| ( ( SV100 @ SV221 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2363]) ).
thf(2467,plain,
! [SV221: nat,SV313: nat,SV100: nat > $o] :
( ( ( ~ ( SV100 @ ( sK27_SY590 @ SV313 @ SV221 @ SV100 ) )
| ~ ! [SY1027: nat] :
( ~ ( SV100 @ SY1027 )
| ( ord_less_eq_nat @ SY1027 @ ( sK27_SY590 @ SV313 @ SV221 @ SV100 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK14_SY920 @ SV221 @ SV313 @ SV100 ) @ SV313 )
= $false )
| ( ( SV100 @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2364]) ).
thf(2468,plain,
! [SV360: nat,SV222: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV222 @ SV360 ) )
= $false )
| ( ( ord_less_nat @ SV222 @ SV360 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2365]) ).
thf(2469,plain,
! [SV222: nat,SV360: nat] :
( ( ( ~ ( ( SV360 != SV222 ) ) )
= $false )
| ( ( ord_less_nat @ SV222 @ SV360 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2365]) ).
thf(2470,plain,
! [SV222: nat,SV360: nat] :
( ( ( SV360 = SV222 )
= $true )
| ( ( ord_less_eq_nat @ SV222 @ SV360 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV222 @ SV360 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV222 @ SV360 )
| ~ ( ( SV360 != SV222 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2366]) ).
thf(2471,plain,
! [SV224: nat,SV103: nat > nat,SV377: nat] :
( ( ( ~ ( ord_less_eq_nat @ one_one_nat @ SV377 ) )
= $false )
| ( ( ( SV103 @ SV377 )
= zero_zero_nat )
= $true )
| ( ( number1551313001itions @ SV103 @ SV224 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2367]) ).
thf(2472,plain,
! [SV103: nat > nat,SV224: nat,SV377: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV377 @ SV224 ) )
= $false )
| ( ( ( SV103 @ SV377 )
= zero_zero_nat )
= $true )
| ( ( number1551313001itions @ SV103 @ SV224 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2367]) ).
thf(2473,plain,
! [SV315: nat > nat,SV106: nat,SV361: nat,SV227: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK28_SY924 @ SV227 @ SV361 @ SV106 @ SV315 ) @ ( sK45_SY1028 @ SV315 @ SV106 @ SV361 @ SV227 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV315 @ SV106 ) @ SV361 )
= $true )
| ( ( ord_less_eq_nat @ ( SV315 @ SV227 ) @ SV361 )
= $false )
| ( ( ord_less_eq_nat @ SV106 @ SV227 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2368]) ).
thf(2474,plain,
! [SV106: nat,SV361: nat,SV227: nat,SV315: nat > nat] :
( ( ( ord_less_eq_nat @ ( SV315 @ ( sK28_SY924 @ SV227 @ SV361 @ SV106 @ SV315 ) ) @ ( SV315 @ ( sK45_SY1028 @ SV315 @ SV106 @ SV361 @ SV227 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV315 @ SV106 ) @ SV361 )
= $true )
| ( ( ord_less_eq_nat @ ( SV315 @ SV227 ) @ SV361 )
= $false )
| ( ( ord_less_eq_nat @ SV106 @ SV227 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2368]) ).
thf(2475,plain,
! [SV362: nat,SV228: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV228 @ SV362 ) )
= $false )
| ( ( ord_less_nat @ SV228 @ SV362 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2369]) ).
thf(2476,plain,
! [SV362: nat,SV228: nat] :
( ( ( ~ ( ( SV228 != SV362 ) ) )
= $false )
| ( ( ord_less_nat @ SV228 @ SV362 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2369]) ).
thf(2477,plain,
! [SV362: nat,SV228: nat] :
( ( ( SV228 = SV362 )
= $true )
| ( ( ord_less_eq_nat @ SV228 @ SV362 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV228 @ SV362 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV228 @ SV362 )
| ~ ( ( SV228 != SV362 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2370]) ).
thf(2478,plain,
! [SV110: nat > $o,SV230: nat,SV382: nat] :
( ( ( ~ ( ord_less_nat @ SV382 @ ( sK10_SY608 @ SV230 @ SV110 ) )
| ~ ~ ( SV110 @ SV382 ) )
= $true )
| ( ( SV110 @ SV230 )
= $true )
| ( ( SV110 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2371]) ).
thf(2479,plain,
! [SV376: nat > nat,SV374: nat > nat,SV236: nat > nat,SV116: set_nat,SV363: nat > nat,SV319: set_nat] :
( ( ( ! [SY1014: nat] :
( ~ ( member_nat @ SY1014 @ SV319 )
| ~ ( ~ ~ ( ~ ( member_nat @ ( SV363 @ SY1014 ) @ SV116 )
| ( ( SV236 @ ( SV363 @ SY1014 ) )
!= SY1014 ) )
| ( ( SV374 @ ( SV363 @ SY1014 ) )
!= ( SV376 @ SY1014 ) ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) )
= $true )
| ( ( member_nat @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) @ SV116 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2372]) ).
thf(2480,plain,
! [SV116: set_nat,SV319: set_nat,SV363: nat > nat,SV374: nat > nat,SV376: nat > nat,SV236: nat > nat] :
( ( ( member_nat @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) @ SV319 )
= $false )
| ( ( ( SV363 @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) )
!= ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) )
= $true )
| ( ( ~ ! [SY1014: nat] :
( ~ ( member_nat @ SY1014 @ SV319 )
| ~ ( ~ ~ ( ~ ( member_nat @ ( SV363 @ SY1014 ) @ SV116 )
| ( ( SV236 @ ( SV363 @ SY1014 ) )
!= SY1014 ) )
| ( ( SV374 @ ( SV363 @ SY1014 ) )
!= ( SV376 @ SY1014 ) ) ) )
| ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2373]) ).
thf(2481,plain,
! [SV320: nat > set_nat,SV117: nat,SV364: set_nat,SV237: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK29_SY932 @ SV237 @ SV364 @ SV117 @ SV320 ) @ ( sK46_SY1029 @ SV320 @ SV117 @ SV364 @ SV237 ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ ( SV320 @ SV117 ) @ SV364 )
= $true )
| ( ( ord_less_eq_set_nat @ ( SV320 @ SV237 ) @ SV364 )
= $false )
| ( ( ord_less_eq_nat @ SV117 @ SV237 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2374]) ).
thf(2482,plain,
! [SV117: nat,SV364: set_nat,SV237: nat,SV320: nat > set_nat] :
( ( ( ord_less_eq_set_nat @ ( SV320 @ ( sK29_SY932 @ SV237 @ SV364 @ SV117 @ SV320 ) ) @ ( SV320 @ ( sK46_SY1029 @ SV320 @ SV117 @ SV364 @ SV237 ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ ( SV320 @ SV117 ) @ SV364 )
= $true )
| ( ( ord_less_eq_set_nat @ ( SV320 @ SV237 ) @ SV364 )
= $false )
| ( ( ord_less_eq_nat @ SV117 @ SV237 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2374]) ).
thf(2483,plain,
! [SV239: nat > nat,SV119: nat,SV365: nat,SV321: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK30_SY830 @ SV321 @ SV365 @ SV119 @ SV239 ) @ ( sK47_SY1030 @ SV239 @ SV119 @ SV365 @ SV321 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV119 @ ( SV239 @ SV365 ) )
= $true )
| ( ( ord_less_eq_nat @ SV321 @ SV365 )
= $false )
| ( ( ord_less_eq_nat @ SV119 @ ( SV239 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2375]) ).
thf(2484,plain,
! [SV119: nat,SV365: nat,SV321: nat,SV239: nat > nat] :
( ( ( ord_less_eq_nat @ ( SV239 @ ( sK30_SY830 @ SV321 @ SV365 @ SV119 @ SV239 ) ) @ ( SV239 @ ( sK47_SY1030 @ SV239 @ SV119 @ SV365 @ SV321 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV119 @ ( SV239 @ SV365 ) )
= $true )
| ( ( ord_less_eq_nat @ SV321 @ SV365 )
= $false )
| ( ( ord_less_eq_nat @ SV119 @ ( SV239 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2375]) ).
thf(2485,plain,
! [SV366: nat,SV243: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV243 @ SV366 ) )
= $false )
| ( ( SV243 = SV366 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2376]) ).
thf(2486,plain,
! [SV243: nat,SV366: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV366 @ SV243 ) )
= $false )
| ( ( SV243 = SV366 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2376]) ).
thf(2487,plain,
! [SV366: nat,SV243: nat] :
( ( ( ( SV243 != SV366 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV243 @ SV366 )
| ~ ( ord_less_eq_nat @ SV366 @ SV243 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV243 @ SV366 )
= $false )
| ( ( ord_less_eq_nat @ SV366 @ SV243 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2377]) ).
thf(2488,plain,
! [SV246: nat > set_nat,SV127: set_nat,SV367: nat,SV325: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK31_SY838 @ SV325 @ SV367 @ SV127 @ SV246 ) @ ( sK48_SY1031 @ SV246 @ SV127 @ SV367 @ SV325 ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ SV127 @ ( SV246 @ SV367 ) )
= $true )
| ( ( ord_less_eq_nat @ SV325 @ SV367 )
= $false )
| ( ( ord_less_eq_set_nat @ SV127 @ ( SV246 @ SV325 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2378]) ).
thf(2489,plain,
! [SV127: set_nat,SV367: nat,SV325: nat,SV246: nat > set_nat] :
( ( ( ord_less_eq_set_nat @ ( SV246 @ ( sK31_SY838 @ SV325 @ SV367 @ SV127 @ SV246 ) ) @ ( SV246 @ ( sK48_SY1031 @ SV246 @ SV127 @ SV367 @ SV325 ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ SV127 @ ( SV246 @ SV367 ) )
= $true )
| ( ( ord_less_eq_nat @ SV325 @ SV367 )
= $false )
| ( ( ord_less_eq_set_nat @ SV127 @ ( SV246 @ SV325 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2378]) ).
thf(2490,plain,
! [SV327: nat,SV248: nat,SV130: nat] :
( ( ( ( times_times_nat @ SV130 @ SV248 )
= ( times_times_nat @ SV130 @ SV327 ) )
= $true )
| ( ( ( times_times_nat @ SV130 @ SV248 )
= ( times_times_nat @ SV130 @ SV327 ) )
= $false )
| ( ( SV130 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2380]) ).
thf(2491,plain,
! [SV130: nat,SV327: nat,SV248: nat] :
( ( ( SV248 = SV327 )
= $true )
| ( ( ( times_times_nat @ SV130 @ SV248 )
= ( times_times_nat @ SV130 @ SV327 ) )
= $false )
| ( ( SV130 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2381]) ).
thf(2492,plain,
! [SV327: nat,SV248: nat,SV130: nat] :
( ( ( ( times_times_nat @ SV130 @ SV248 )
= ( times_times_nat @ SV130 @ SV327 ) )
= $true )
| ( ( SV248 = SV327 )
= $false )
| ( ( SV130 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2382]) ).
thf(2493,plain,
! [SV130: nat,SV327: nat,SV248: nat] :
( ( ( SV248 = SV327 )
= $true )
| ( ( SV248 = SV327 )
= $false )
| ( ( SV130 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2383]) ).
thf(2494,plain,
! [SV328: nat,SV131: nat,SV249: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV249 ) )
= $true )
| ( ( ord_less_eq_nat @ SV131 @ SV328 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV249 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2386]) ).
thf(2495,plain,
! [SV328: nat,SV131: nat,SV249: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV249 )
= $false )
| ( ( ord_less_eq_nat @ SV131 @ SV328 )
= $true )
| ( ( ord_less_eq_nat @ SV131 @ SV328 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2387]) ).
thf(2496,plain,
! [SV329: nat > nat,SV132: nat,SV369: nat,SV250: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( sK32_SY942 @ SV250 @ SV369 @ SV132 @ SV329 ) @ ( sK49_SY1032 @ SV329 @ SV132 @ SV369 @ SV250 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV329 @ SV132 ) @ SV369 )
= $true )
| ( ( ( SV329 @ SV250 )
= SV369 )
= $false )
| ( ( ord_less_eq_nat @ SV132 @ SV250 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2388]) ).
thf(2497,plain,
! [SV132: nat,SV369: nat,SV250: nat,SV329: nat > nat] :
( ( ( ord_less_eq_nat @ ( SV329 @ ( sK32_SY942 @ SV250 @ SV369 @ SV132 @ SV329 ) ) @ ( SV329 @ ( sK49_SY1032 @ SV329 @ SV132 @ SV369 @ SV250 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV329 @ SV132 ) @ SV369 )
= $true )
| ( ( ( SV329 @ SV250 )
= SV369 )
= $false )
| ( ( ord_less_eq_nat @ SV132 @ SV250 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2388]) ).
thf(2498,plain,
! [SV252: nat,SV331: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2389]) ).
thf(2499,plain,
! [SV252: nat,SV331: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2390]) ).
thf(2500,plain,
! [SV252: nat,SV331: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2391]) ).
thf(2501,plain,
! [SV252: nat,SV331: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2392]) ).
thf(2502,plain,
! [SV332: nat,SV253: nat,SV135: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV135 )
= $true )
| ( ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2393]) ).
thf(2503,plain,
! [SV135: nat,SV332: nat,SV253: nat] :
( ( ( ord_less_nat @ SV253 @ SV332 )
= $true )
| ( ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2394]) ).
thf(2504,plain,
! [SV332: nat,SV253: nat,SV135: nat] :
( ( ( ~ ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV135 )
= $false )
| ( ( ord_less_nat @ SV253 @ SV332 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2395]) ).
thf(2505,plain,
! [SV332: nat,SV253: nat,SV135: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 )
| ~ ( ord_less_nat @ SV253 @ SV332 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV135 )
= $false )
| ( ( ord_less_nat @ SV253 @ SV332 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2395]) ).
thf(2506,plain,
! [SV254: nat,SV136: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ SV136 @ SV254 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV136 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV254 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2398]) ).
thf(2507,plain,
! [SV254: nat,SV136: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV136 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV254 ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV136 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV254 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2399]) ).
thf(2508,plain,
! [SV370: nat,SV259: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV259 @ SV370 ) )
= $false )
| ( ( ord_less_nat @ SV259 @ SV370 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2400]) ).
thf(2509,plain,
! [SV370: nat,SV259: nat] :
( ( ( ~ ( ( SV259 != SV370 ) ) )
= $false )
| ( ( ord_less_nat @ SV259 @ SV370 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2400]) ).
thf(2510,plain,
! [SV370: nat,SV259: nat] :
( ( ( SV259 = SV370 )
= $true )
| ( ( ord_less_eq_nat @ SV259 @ SV370 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV259 @ SV370 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV259 @ SV370 )
| ~ ( ( SV259 != SV370 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2401]) ).
thf(2511,plain,
! [SV263: nat,SV145: nat] :
( ( ( one_one_nat
= ( times_times_nat @ SV145 @ SV263 ) )
= $true )
| ( ( SV145 = one_one_nat )
= $false )
| ( ( SV263 = one_one_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2404]) ).
thf(2512,plain,
! [SV263: nat,SV145: nat] :
( ( ( ~ ( ( SV145 != one_one_nat )
| ( SV263 != one_one_nat ) ) )
= $true )
| ( ( SV145 = one_one_nat )
= $false )
| ( ( SV263 = one_one_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2405]) ).
thf(2513,plain,
! [SV336: nat,SV146: nat,SV264: nat] :
( ( ( ( times_times_nat @ SV264 @ SV146 )
= ( times_times_nat @ SV336 @ SV146 ) )
= $true )
| ( ( ( times_times_nat @ SV264 @ SV146 )
= ( times_times_nat @ SV336 @ SV146 ) )
= $false )
| ( ( SV146 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2406]) ).
thf(2514,plain,
! [SV146: nat,SV336: nat,SV264: nat] :
( ( ( SV264 = SV336 )
= $true )
| ( ( ( times_times_nat @ SV264 @ SV146 )
= ( times_times_nat @ SV336 @ SV146 ) )
= $false )
| ( ( SV146 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2407]) ).
thf(2515,plain,
! [SV336: nat,SV146: nat,SV264: nat] :
( ( ( ( times_times_nat @ SV264 @ SV146 )
= ( times_times_nat @ SV336 @ SV146 ) )
= $true )
| ( ( SV264 = SV336 )
= $false )
| ( ( SV146 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2408]) ).
thf(2516,plain,
! [SV146: nat,SV336: nat,SV264: nat] :
( ( ( SV264 = SV336 )
= $true )
| ( ( SV264 = SV336 )
= $false )
| ( ( SV146 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2409]) ).
thf(2517,plain,
! [SV266: nat,SV149: nat] :
( ( ( ( times_times_nat @ SV149 @ SV266 )
= one_one_nat )
= $true )
| ( ( SV149 = one_one_nat )
= $false )
| ( ( SV266 = one_one_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2413]) ).
thf(2518,plain,
! [SV266: nat,SV149: nat] :
( ( ( ~ ( ( SV149 != one_one_nat )
| ( SV266 != one_one_nat ) ) )
= $true )
| ( ( SV149 = one_one_nat )
= $false )
| ( ( SV266 = one_one_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2414]) ).
thf(2519,plain,
! [SV337: set_nat > nat,SV151: set_nat,SV371: nat,SV267: set_nat] :
( ( ( ~ ( ord_less_eq_set_nat @ ( sK33_SY946 @ SV267 @ SV371 @ SV151 @ SV337 ) @ ( sK50_SY1033 @ SV337 @ SV151 @ SV371 @ SV267 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV337 @ SV151 ) @ SV371 )
= $true )
| ( ( ( SV337 @ SV267 )
= SV371 )
= $false )
| ( ( ord_less_eq_set_nat @ SV151 @ SV267 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2415]) ).
thf(2520,plain,
! [SV151: set_nat,SV371: nat,SV267: set_nat,SV337: set_nat > nat] :
( ( ( ord_less_eq_nat @ ( SV337 @ ( sK33_SY946 @ SV267 @ SV371 @ SV151 @ SV337 ) ) @ ( SV337 @ ( sK50_SY1033 @ SV337 @ SV151 @ SV371 @ SV267 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( SV337 @ SV151 ) @ SV371 )
= $true )
| ( ( ( SV337 @ SV267 )
= SV371 )
= $false )
| ( ( ord_less_eq_set_nat @ SV151 @ SV267 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2415]) ).
thf(2521,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV153 ) )
= $true )
| ( ( ord_less_eq_nat @ SV269 @ SV339 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV153 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2418]) ).
thf(2522,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV153 )
= $false )
| ( ( ord_less_eq_nat @ SV269 @ SV339 )
= $true )
| ( ( ord_less_eq_nat @ SV269 @ SV339 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2419]) ).
thf(2523,plain,
! [SV60: set_nat,SV288: nat > nat,SV346: set_nat,SV182: nat > nat,SV372: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
| ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 ) )
= $false )
| ( ( ~ ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) )
| ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2426]) ).
thf(2524,plain,
! [SV60: set_nat,SV288: nat > nat,SV346: set_nat,SV182: nat > nat,SV372: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 ) )
= $false )
| ( ( ~ ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) )
| ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2427]) ).
thf(2525,plain,
! [SV60: set_nat,SV346: set_nat,SV182: nat > nat,SV372: nat > nat,SV375: nat > nat,SV288: nat > nat] :
( ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ~ ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) )
| ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2427]) ).
thf(2526,plain,
! [SV347: nat,SV186: nat] :
( ( ( ord_less_eq_nat @ SV186 @ SV347 )
= $true )
| ( ( SV186 = SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2428]) ).
thf(2527,plain,
! [SV186: nat,SV347: nat] :
( ( ( ord_less_eq_nat @ SV347 @ SV186 )
= $true )
| ( ( SV186 = SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2429]) ).
thf(2528,plain,
! [SV347: nat,SV186: nat] :
( ( ( SV186 != SV347 )
= $false )
| ( ( ord_less_eq_nat @ SV186 @ SV347 )
= $false )
| ( ( ord_less_eq_nat @ SV347 @ SV186 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2430]) ).
thf(2529,plain,
! [SV347: nat,SV186: nat] :
( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV186 @ SV347 )
| ~ ( ord_less_eq_nat @ SV347 @ SV186 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV186 @ SV347 )
= $false )
| ( ( ord_less_eq_nat @ SV347 @ SV186 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2430]) ).
thf(2530,plain,
! [SV292: set_nat > nat,SV69: set_nat,SV348: nat,SV191: set_nat] :
( ( ( ord_less_eq_set_nat @ ( sK19_SY882 @ SV191 @ SV348 @ SV69 @ SV292 ) @ ( sK34_SY1018 @ SV292 @ SV69 @ SV348 @ SV191 ) )
= $true )
| ( ( ord_less_eq_nat @ ( SV292 @ SV69 ) @ SV348 )
= $true )
| ( ( ord_less_eq_nat @ ( SV292 @ SV191 ) @ SV348 )
= $false )
| ( ( ord_less_eq_set_nat @ SV69 @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2431]) ).
thf(2531,plain,
! [SV192: nat,SV293: nat,SV70: nat > $o] :
( ( ( SV70 @ ( sK35_SY505 @ SV293 @ SV192 @ SV70 ) )
= $true )
| ( ( SV70 @ ( sK12_SY884 @ SV192 @ SV293 @ SV70 ) )
= $true )
| ( ( SV70 @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2433]) ).
thf(2532,plain,
! [SV192: nat,SV293: nat,SV70: nat > $o] :
( ( ( ! [SY1034: nat] :
( ~ ( SV70 @ SY1034 )
| ( ord_less_eq_nat @ SY1034 @ ( sK35_SY505 @ SV293 @ SV192 @ SV70 ) ) ) )
= $true )
| ( ( SV70 @ ( sK12_SY884 @ SV192 @ SV293 @ SV70 ) )
= $true )
| ( ( SV70 @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2434]) ).
thf(2533,plain,
! [SV192: nat,SV293: nat,SV383: nat,SV70: nat > $o] :
( ( ( ~ ( SV70 @ SV383 )
| ( ord_less_eq_nat @ SV383 @ ( sK20_SY505 @ SV293 @ SV192 @ SV70 ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK12_SY884 @ SV192 @ SV293 @ SV70 ) @ SV293 )
= $false )
| ( ( SV70 @ SV192 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2436]) ).
thf(2534,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) ) )
= $true )
| ( ( number1551313001itions @ SV194 @ SV350 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2437]) ).
thf(2535,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $true )
| ( ( number1551313001itions @ SV194 @ SV350 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2438]) ).
thf(2536,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ( SV194 @ ( sK36_SY959 @ SV350 @ SV194 ) )
!= zero_zero_nat )
= $true )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 )
= $true )
| ( ( ~ ( ~ ( number1551313001itions @ SV194 @ SV350 )
| ~ ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2439]) ).
thf(2537,plain,
! [SV194: nat > nat,SV350: nat] :
( ( ( ~ ( ord_less_eq_nat @ one_one_nat @ ( sK36_SY959 @ SV350 @ SV194 ) )
| ~ ( ord_less_eq_nat @ ( sK36_SY959 @ SV350 @ SV194 ) @ SV350 ) )
= $true )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 )
= $true )
| ( ( ~ ( ~ ( number1551313001itions @ SV194 @ SV350 )
| ~ ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2440]) ).
thf(2538,plain,
! [SV296: nat > set_nat,SV74: nat,SV351: set_nat,SV196: nat] :
( ( ( ord_less_eq_nat @ ( sK21_SY891 @ SV196 @ SV351 @ SV74 @ SV296 ) @ ( sK37_SY1020 @ SV296 @ SV74 @ SV351 @ SV196 ) )
= $true )
| ( ( ord_less_eq_set_nat @ ( SV296 @ SV74 ) @ SV351 )
= $true )
| ( ( ( SV296 @ SV196 )
= SV351 )
= $false )
| ( ( ord_less_eq_nat @ SV74 @ SV196 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2441]) ).
thf(2539,plain,
! [SV298: nat,SV198: nat,SV76: nat > nat > $o] :
( ( ( ~ ( SV76 @ ( sK52_SY1035 @ SV198 @ SV298 @ SV76 ) @ ( sK38_SY525 @ SV298 @ SV198 @ SV76 ) ) )
= $false )
| ( ( SV76 @ SV198 @ SV298 )
= $true )
| ( ( ord_less_eq_nat @ ( sK5_SY523 @ SV298 @ SV198 @ SV76 ) @ ( sK8_SY1011 @ SV76 @ SV198 @ SV298 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2443]) ).
thf(2540,plain,
! [SV198: nat,SV298: nat,SV76: nat > nat > $o] :
( ( ( SV76 @ ( sK38_SY525 @ SV298 @ SV198 @ SV76 ) @ ( sK52_SY1035 @ SV198 @ SV298 @ SV76 ) )
= $false )
| ( ( SV76 @ SV198 @ SV298 )
= $true )
| ( ( ord_less_eq_nat @ ( sK5_SY523 @ SV298 @ SV198 @ SV76 ) @ ( sK8_SY1011 @ SV76 @ SV198 @ SV298 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2443]) ).
thf(2541,plain,
! [SV298: nat,SV198: nat,SV76: nat > nat > $o] :
( ( ( SV76 @ ( sK39_SY1021 @ SV198 @ SV298 @ SV76 ) @ ( sK22_SY525 @ SV298 @ SV198 @ SV76 ) )
= $true )
| ( ( SV76 @ SV198 @ SV298 )
= $true )
| ( ( SV76 @ ( sK5_SY523 @ SV298 @ SV198 @ SV76 ) @ ( sK8_SY1011 @ SV76 @ SV198 @ SV298 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2444]) ).
thf(2542,plain,
! [SV207: set_nat,SV304: nat > nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat] :
( ( ( ~ ( member_nat @ ( sK53_SY1002 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) @ SV207 ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( member_nat @ ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) @ SV85 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2446]) ).
thf(2543,plain,
! [SV207: set_nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV304: nat > nat] :
( ( ( ~ ( ~ ( member_nat @ ( SV304 @ ( sK53_SY1002 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) @ SV85 )
| ( ( SV353 @ ( SV304 @ ( sK53_SY1002 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
!= ( SV373 @ ( sK53_SY1002 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( member_nat @ ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) @ SV85 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2446]) ).
thf(2544,plain,
! [SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV304: nat > nat,SV207: set_nat,SV381: nat] :
( ( ( ~ ~ ( ~ ( member_nat @ SV381 @ SV207 )
| ( ( SV304 @ SV381 )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) ) ) )
= $true )
| ( ( ~ ! [SY1022: nat] :
( ~ ~ ( ~ ( member_nat @ SY1022 @ SV207 )
| ( ( SV304 @ SY1022 )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) ) )
| ( SY1022 = SV381 ) ) )
= $true )
| ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) )
| ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2447]) ).
thf(2545,plain,
! [SV208: nat > set_nat,SV86: set_nat,SV354: nat,SV305: nat] :
( ( ( ord_less_eq_nat @ ( sK23_SY776 @ SV305 @ SV354 @ SV86 @ SV208 ) @ ( sK40_SY1023 @ SV208 @ SV86 @ SV354 @ SV305 ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV86 @ ( SV208 @ SV354 ) )
= $true )
| ( ( ord_less_eq_nat @ SV305 @ SV354 )
= $false )
| ( ( SV86
= ( SV208 @ SV305 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2448]) ).
thf(2546,plain,
! [SV209: set_nat > nat,SV87: nat,SV355: set_nat,SV306: set_nat] :
( ( ( ord_less_eq_set_nat @ ( sK24_SY780 @ SV306 @ SV355 @ SV87 @ SV209 ) @ ( sK41_SY1024 @ SV209 @ SV87 @ SV355 @ SV306 ) )
= $true )
| ( ( ord_less_eq_nat @ SV87 @ ( SV209 @ SV355 ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV306 @ SV355 )
= $false )
| ( ( SV87
= ( SV209 @ SV306 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2450]) ).
thf(2547,plain,
! [SV378: nat] :
( ( ( ~ ( ord_less_eq_nat @ one_one_nat @ SV378 ) )
= $false )
| ( ( ( p @ SV378 )
= zero_zero_nat )
= $true )
| ( ( p
= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2452]) ).
thf(2548,plain,
! [SV378: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV378 @ zero_zero_nat ) )
= $false )
| ( ( ( p @ SV378 )
= zero_zero_nat )
= $true )
| ( ( p
= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2452]) ).
thf(2549,plain,
( ( ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
= zero_zero_nat )
= $false )
| ( ( ( p @ sK18_SX0 )
= zero_zero_nat )
= $false )
| ( ( p
!= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2453]) ).
thf(2550,plain,
( ( ( ord_less_eq_nat @ one_one_nat @ sK18_SX0 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ sK18_SX0 @ zero_zero_nat ) )
= $true )
| ( ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
!= zero_zero_nat )
= $true )
| ( ( p
!= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2454]) ).
thf(2551,plain,
! [SV213: nat,SV356: nat] :
( ( ( ord_less_eq_nat @ SV356 @ SV213 )
= $true )
| ( ( SV213 = SV356 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2455]) ).
thf(2552,plain,
! [SV356: nat,SV213: nat] :
( ( ( ord_less_eq_nat @ SV213 @ SV356 )
= $true )
| ( ( SV213 = SV356 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2456]) ).
thf(2553,plain,
! [SV356: nat,SV213: nat] :
( ( ( SV213 != SV356 )
= $false )
| ( ( ord_less_eq_nat @ SV356 @ SV213 )
= $false )
| ( ( ord_less_eq_nat @ SV213 @ SV356 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2457]) ).
thf(2554,plain,
! [SV213: nat,SV356: nat] :
( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV356 @ SV213 )
| ~ ( ord_less_eq_nat @ SV213 @ SV356 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV356 @ SV213 )
= $false )
| ( ( ord_less_eq_nat @ SV213 @ SV356 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2457]) ).
thf(2555,plain,
! [SV216: set_nat > nat,SV95: nat,SV358: set_nat,SV309: set_nat] :
( ( ( ord_less_eq_set_nat @ ( sK25_SY789 @ SV309 @ SV358 @ SV95 @ SV216 ) @ ( sK42_SY1025 @ SV216 @ SV95 @ SV358 @ SV309 ) )
= $true )
| ( ( ord_less_eq_nat @ SV95 @ ( SV216 @ SV358 ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV309 @ SV358 )
= $false )
| ( ( ord_less_eq_nat @ SV95 @ ( SV216 @ SV309 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2458]) ).
thf(2556,plain,
! [SV311: nat,SV219: nat,SV98: nat] :
( ( ( ord_less_nat @ ( times_times_nat @ SV98 @ SV219 ) @ ( times_times_nat @ SV311 @ SV219 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV219 )
= $false )
| ( ( ord_less_nat @ SV98 @ SV311 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2462]) ).
thf(2557,plain,
! [SV311: nat,SV98: nat,SV219: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV219 )
| ~ ( ord_less_nat @ SV98 @ SV311 ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV219 )
= $false )
| ( ( ord_less_nat @ SV98 @ SV311 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2463]) ).
thf(2558,plain,
! [SV220: nat > nat,SV99: nat,SV359: nat,SV312: nat] :
( ( ( ord_less_eq_nat @ ( sK26_SY798 @ SV312 @ SV359 @ SV99 @ SV220 ) @ ( sK43_SY1026 @ SV220 @ SV99 @ SV359 @ SV312 ) )
= $true )
| ( ( ord_less_eq_nat @ SV99 @ ( SV220 @ SV359 ) )
= $true )
| ( ( ord_less_eq_nat @ SV312 @ SV359 )
= $false )
| ( ( SV99
= ( SV220 @ SV312 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2464]) ).
thf(2559,plain,
! [SV221: nat,SV313: nat,SV100: nat > $o] :
( ( ( ~ ( SV100 @ ( sK44_SY590 @ SV313 @ SV221 @ SV100 ) )
| ~ ! [SY1036: nat] :
( ~ ( SV100 @ SY1036 )
| ( ord_less_eq_nat @ SY1036 @ ( sK44_SY590 @ SV313 @ SV221 @ SV100 ) ) ) )
= $false )
| ( ( SV100 @ ( sK14_SY920 @ SV221 @ SV313 @ SV100 ) )
= $true )
| ( ( SV100 @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2466]) ).
thf(2560,plain,
! [SV221: nat,SV313: nat,SV100: nat > $o] :
( ( ( ~ ( SV100 @ ( sK27_SY590 @ SV313 @ SV221 @ SV100 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK14_SY920 @ SV221 @ SV313 @ SV100 ) @ SV313 )
= $false )
| ( ( SV100 @ SV221 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2467]) ).
thf(2561,plain,
! [SV221: nat,SV313: nat,SV100: nat > $o] :
( ( ( ~ ! [SY1027: nat] :
( ~ ( SV100 @ SY1027 )
| ( ord_less_eq_nat @ SY1027 @ ( sK27_SY590 @ SV313 @ SV221 @ SV100 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK14_SY920 @ SV221 @ SV313 @ SV100 ) @ SV313 )
= $false )
| ( ( SV100 @ SV221 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2467]) ).
thf(2562,plain,
! [SV360: nat,SV222: nat] :
( ( ( ord_less_eq_nat @ SV222 @ SV360 )
= $true )
| ( ( ord_less_nat @ SV222 @ SV360 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2468]) ).
thf(2563,plain,
! [SV222: nat,SV360: nat] :
( ( ( SV360 != SV222 )
= $true )
| ( ( ord_less_nat @ SV222 @ SV360 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2469]) ).
thf(2564,plain,
! [SV360: nat,SV222: nat] :
( ( ( ~ ( ord_less_nat @ SV222 @ SV360 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV222 @ SV360 )
| ~ ( ( SV360 != SV222 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV222 @ SV360 )
= $false )
| ( ( SV360 = SV222 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2470]) ).
thf(2565,plain,
! [SV224: nat,SV103: nat > nat,SV377: nat] :
( ( ( ord_less_eq_nat @ one_one_nat @ SV377 )
= $true )
| ( ( ( SV103 @ SV377 )
= zero_zero_nat )
= $true )
| ( ( number1551313001itions @ SV103 @ SV224 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2471]) ).
thf(2566,plain,
! [SV103: nat > nat,SV224: nat,SV377: nat] :
( ( ( ord_less_eq_nat @ SV377 @ SV224 )
= $true )
| ( ( ( SV103 @ SV377 )
= zero_zero_nat )
= $true )
| ( ( number1551313001itions @ SV103 @ SV224 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2472]) ).
thf(2567,plain,
! [SV315: nat > nat,SV106: nat,SV361: nat,SV227: nat] :
( ( ( ord_less_eq_nat @ ( sK28_SY924 @ SV227 @ SV361 @ SV106 @ SV315 ) @ ( sK45_SY1028 @ SV315 @ SV106 @ SV361 @ SV227 ) )
= $true )
| ( ( ord_less_eq_nat @ ( SV315 @ SV106 ) @ SV361 )
= $true )
| ( ( ord_less_eq_nat @ ( SV315 @ SV227 ) @ SV361 )
= $false )
| ( ( ord_less_eq_nat @ SV106 @ SV227 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2473]) ).
thf(2568,plain,
! [SV362: nat,SV228: nat] :
( ( ( ord_less_eq_nat @ SV228 @ SV362 )
= $true )
| ( ( ord_less_nat @ SV228 @ SV362 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2475]) ).
thf(2569,plain,
! [SV362: nat,SV228: nat] :
( ( ( SV228 != SV362 )
= $true )
| ( ( ord_less_nat @ SV228 @ SV362 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2476]) ).
thf(2570,plain,
! [SV362: nat,SV228: nat] :
( ( ( ~ ( ord_less_nat @ SV228 @ SV362 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV228 @ SV362 )
| ~ ( ( SV228 != SV362 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV228 @ SV362 )
= $false )
| ( ( SV228 = SV362 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2477]) ).
thf(2571,plain,
! [SV110: nat > $o,SV230: nat,SV382: nat] :
( ( ( ~ ( ord_less_nat @ SV382 @ ( sK10_SY608 @ SV230 @ SV110 ) ) )
= $true )
| ( ( ~ ~ ( SV110 @ SV382 ) )
= $true )
| ( ( SV110 @ SV230 )
= $true )
| ( ( SV110 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2478]) ).
thf(2572,plain,
! [SV319: set_nat,SV363: nat > nat,SV116: set_nat,SV236: nat > nat,SV374: nat > nat,SV376: nat > nat] :
( ( ( ~ ( member_nat @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) @ SV319 )
| ~ ( ~ ~ ( ~ ( member_nat @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) @ SV116 )
| ( ( SV236 @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
| ( ( SV374 @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( SV376 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) )
= $true )
| ( ( member_nat @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) @ SV116 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2479]) ).
thf(2573,plain,
! [SV116: set_nat,SV319: set_nat,SV374: nat > nat,SV376: nat > nat,SV236: nat > nat,SV363: nat > nat] :
( ( ( ( SV363 @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) )
= ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) )
= $false )
| ( ( member_nat @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) @ SV319 )
= $false )
| ( ( ~ ! [SY1014: nat] :
( ~ ( member_nat @ SY1014 @ SV319 )
| ~ ( ~ ~ ( ~ ( member_nat @ ( SV363 @ SY1014 ) @ SV116 )
| ( ( SV236 @ ( SV363 @ SY1014 ) )
!= SY1014 ) )
| ( ( SV374 @ ( SV363 @ SY1014 ) )
!= ( SV376 @ SY1014 ) ) ) )
| ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2480]) ).
thf(2574,plain,
! [SV320: nat > set_nat,SV117: nat,SV364: set_nat,SV237: nat] :
( ( ( ord_less_eq_nat @ ( sK29_SY932 @ SV237 @ SV364 @ SV117 @ SV320 ) @ ( sK46_SY1029 @ SV320 @ SV117 @ SV364 @ SV237 ) )
= $true )
| ( ( ord_less_eq_set_nat @ ( SV320 @ SV117 ) @ SV364 )
= $true )
| ( ( ord_less_eq_set_nat @ ( SV320 @ SV237 ) @ SV364 )
= $false )
| ( ( ord_less_eq_nat @ SV117 @ SV237 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2481]) ).
thf(2575,plain,
! [SV239: nat > nat,SV119: nat,SV365: nat,SV321: nat] :
( ( ( ord_less_eq_nat @ ( sK30_SY830 @ SV321 @ SV365 @ SV119 @ SV239 ) @ ( sK47_SY1030 @ SV239 @ SV119 @ SV365 @ SV321 ) )
= $true )
| ( ( ord_less_eq_nat @ SV119 @ ( SV239 @ SV365 ) )
= $true )
| ( ( ord_less_eq_nat @ SV321 @ SV365 )
= $false )
| ( ( ord_less_eq_nat @ SV119 @ ( SV239 @ SV321 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2483]) ).
thf(2576,plain,
! [SV366: nat,SV243: nat] :
( ( ( ord_less_eq_nat @ SV243 @ SV366 )
= $true )
| ( ( SV243 = SV366 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2485]) ).
thf(2577,plain,
! [SV243: nat,SV366: nat] :
( ( ( ord_less_eq_nat @ SV366 @ SV243 )
= $true )
| ( ( SV243 = SV366 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2486]) ).
thf(2578,plain,
! [SV366: nat,SV243: nat] :
( ( ( SV243 != SV366 )
= $false )
| ( ( ord_less_eq_nat @ SV243 @ SV366 )
= $false )
| ( ( ord_less_eq_nat @ SV366 @ SV243 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2487]) ).
thf(2579,plain,
! [SV366: nat,SV243: nat] :
( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV243 @ SV366 )
| ~ ( ord_less_eq_nat @ SV366 @ SV243 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV243 @ SV366 )
= $false )
| ( ( ord_less_eq_nat @ SV366 @ SV243 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2487]) ).
thf(2580,plain,
! [SV246: nat > set_nat,SV127: set_nat,SV367: nat,SV325: nat] :
( ( ( ord_less_eq_nat @ ( sK31_SY838 @ SV325 @ SV367 @ SV127 @ SV246 ) @ ( sK48_SY1031 @ SV246 @ SV127 @ SV367 @ SV325 ) )
= $true )
| ( ( ord_less_eq_set_nat @ SV127 @ ( SV246 @ SV367 ) )
= $true )
| ( ( ord_less_eq_nat @ SV325 @ SV367 )
= $false )
| ( ( ord_less_eq_set_nat @ SV127 @ ( SV246 @ SV325 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2488]) ).
thf(2581,plain,
! [SV328: nat,SV131: nat,SV249: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV249 )
= $false )
| ( ( ord_less_eq_nat @ SV131 @ SV328 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV249 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2494]) ).
thf(2582,plain,
! [SV329: nat > nat,SV132: nat,SV369: nat,SV250: nat] :
( ( ( ord_less_eq_nat @ ( sK32_SY942 @ SV250 @ SV369 @ SV132 @ SV329 ) @ ( sK49_SY1032 @ SV329 @ SV132 @ SV369 @ SV250 ) )
= $true )
| ( ( ord_less_eq_nat @ ( SV329 @ SV132 ) @ SV369 )
= $true )
| ( ( ( SV329 @ SV250 )
= SV369 )
= $false )
| ( ( ord_less_eq_nat @ SV132 @ SV250 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2496]) ).
thf(2583,plain,
! [SV252: nat,SV331: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV331 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2498]) ).
thf(2584,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2498]) ).
thf(2585,plain,
! [SV252: nat,SV331: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV331 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2499]) ).
thf(2586,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2499]) ).
thf(2587,plain,
! [SV252: nat,SV331: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV331 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2500]) ).
thf(2588,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2500]) ).
thf(2589,plain,
! [SV252: nat,SV331: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV331 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2501]) ).
thf(2590,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2501]) ).
thf(2591,plain,
! [SV332: nat,SV253: nat,SV135: nat] :
( ( ( ord_less_nat @ ( times_times_nat @ SV135 @ SV253 ) @ ( times_times_nat @ SV135 @ SV332 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV135 )
= $false )
| ( ( ord_less_nat @ SV253 @ SV332 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2504]) ).
thf(2592,plain,
! [SV332: nat,SV253: nat,SV135: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 )
| ~ ( ord_less_nat @ SV253 @ SV332 ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV135 )
= $false )
| ( ( ord_less_nat @ SV253 @ SV332 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2505]) ).
thf(2593,plain,
! [SV254: nat,SV136: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV136 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV254 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV136 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV254 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2507]) ).
thf(2594,plain,
! [SV370: nat,SV259: nat] :
( ( ( ord_less_eq_nat @ SV259 @ SV370 )
= $true )
| ( ( ord_less_nat @ SV259 @ SV370 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2508]) ).
thf(2595,plain,
! [SV370: nat,SV259: nat] :
( ( ( SV259 != SV370 )
= $true )
| ( ( ord_less_nat @ SV259 @ SV370 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2509]) ).
thf(2596,plain,
! [SV370: nat,SV259: nat] :
( ( ( ~ ( ord_less_nat @ SV259 @ SV370 )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV259 @ SV370 )
| ~ ( ( SV259 != SV370 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV259 @ SV370 )
= $false )
| ( ( SV259 = SV370 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2510]) ).
thf(2597,plain,
! [SV263: nat,SV145: nat] :
( ( ( ( SV145 != one_one_nat )
| ( SV263 != one_one_nat ) )
= $false )
| ( ( SV145 = one_one_nat )
= $false )
| ( ( SV263 = one_one_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2512]) ).
thf(2598,plain,
! [SV266: nat,SV149: nat] :
( ( ( ( SV149 != one_one_nat )
| ( SV266 != one_one_nat ) )
= $false )
| ( ( SV149 = one_one_nat )
= $false )
| ( ( SV266 = one_one_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2518]) ).
thf(2599,plain,
! [SV337: set_nat > nat,SV151: set_nat,SV371: nat,SV267: set_nat] :
( ( ( ord_less_eq_set_nat @ ( sK33_SY946 @ SV267 @ SV371 @ SV151 @ SV337 ) @ ( sK50_SY1033 @ SV337 @ SV151 @ SV371 @ SV267 ) )
= $true )
| ( ( ord_less_eq_nat @ ( SV337 @ SV151 ) @ SV371 )
= $true )
| ( ( ( SV337 @ SV267 )
= SV371 )
= $false )
| ( ( ord_less_eq_set_nat @ SV151 @ SV267 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2519]) ).
thf(2600,plain,
! [SV339: nat,SV269: nat,SV153: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV153 )
= $false )
| ( ( ord_less_eq_nat @ SV269 @ SV339 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV153 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2521]) ).
thf(2601,plain,
! [SV60: set_nat,SV288: nat > nat,SV346: set_nat,SV182: nat > nat,SV372: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 ) )
= $false )
| ( ( ~ ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) )
| ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2523]) ).
thf(2602,plain,
! [SV60: set_nat,SV346: set_nat,SV182: nat > nat,SV372: nat > nat,SV375: nat > nat,SV288: nat > nat] :
( ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ~ ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) )
| ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2523]) ).
thf(2603,plain,
! [SV60: set_nat,SV288: nat > nat,SV346: set_nat,SV182: nat > nat,SV372: nat > nat,SV375: nat > nat] :
( ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ~ ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) )
| ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2524]) ).
thf(2604,plain,
! [SV375: nat > nat,SV372: nat > nat,SV60: set_nat,SV182: nat > nat,SV288: nat > nat,SV346: set_nat] :
( ( ( ~ ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) ) )
= $true )
| ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2525]) ).
thf(2605,plain,
! [SV347: nat,SV186: nat] :
( ( ( SV186 = SV347 )
= $true )
| ( ( ord_less_eq_nat @ SV186 @ SV347 )
= $false )
| ( ( ord_less_eq_nat @ SV347 @ SV186 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2528]) ).
thf(2606,plain,
! [SV347: nat,SV186: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV186 @ SV347 )
| ~ ( ord_less_eq_nat @ SV347 @ SV186 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV186 @ SV347 )
= $false )
| ( ( ord_less_eq_nat @ SV347 @ SV186 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2529]) ).
thf(2607,plain,
! [SV192: nat,SV293: nat,SV384: nat,SV70: nat > $o] :
( ( ( ~ ( SV70 @ SV384 )
| ( ord_less_eq_nat @ SV384 @ ( sK35_SY505 @ SV293 @ SV192 @ SV70 ) ) )
= $true )
| ( ( SV70 @ ( sK12_SY884 @ SV192 @ SV293 @ SV70 ) )
= $true )
| ( ( SV70 @ SV192 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2532]) ).
thf(2608,plain,
! [SV192: nat,SV293: nat,SV383: nat,SV70: nat > $o] :
( ( ( ~ ( SV70 @ SV383 ) )
= $true )
| ( ( ord_less_eq_nat @ SV383 @ ( sK20_SY505 @ SV293 @ SV192 @ SV70 ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK12_SY884 @ SV192 @ SV293 @ SV70 ) @ SV293 )
= $false )
| ( ( SV70 @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2533]) ).
thf(2609,plain,
! [SV350: nat,SV385: nat,SV194: nat > nat] :
( ( ( ~ ( ( ( SV194 @ SV385 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SV385 )
| ~ ( ord_less_eq_nat @ SV385 @ SV350 ) ) )
= $true )
| ( ( number1551313001itions @ SV194 @ SV350 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2534]) ).
thf(2610,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ( SV194 @ ( sK36_SY959 @ SV350 @ SV194 ) )
= zero_zero_nat )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 )
= $true )
| ( ( ~ ( ~ ( number1551313001itions @ SV194 @ SV350 )
| ~ ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2536]) ).
thf(2611,plain,
! [SV194: nat > nat,SV350: nat] :
( ( ( ~ ( ord_less_eq_nat @ one_one_nat @ ( sK36_SY959 @ SV350 @ SV194 ) ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ ( sK36_SY959 @ SV350 @ SV194 ) @ SV350 ) )
= $true )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 )
= $true )
| ( ( ~ ( ~ ( number1551313001itions @ SV194 @ SV350 )
| ~ ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2537]) ).
thf(2612,plain,
! [SV298: nat,SV198: nat,SV76: nat > nat > $o] :
( ( ( SV76 @ ( sK52_SY1035 @ SV198 @ SV298 @ SV76 ) @ ( sK38_SY525 @ SV298 @ SV198 @ SV76 ) )
= $true )
| ( ( SV76 @ SV198 @ SV298 )
= $true )
| ( ( ord_less_eq_nat @ ( sK5_SY523 @ SV298 @ SV198 @ SV76 ) @ ( sK8_SY1011 @ SV76 @ SV198 @ SV298 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2539]) ).
thf(2613,plain,
! [SV207: set_nat,SV304: nat > nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat] :
( ( ( member_nat @ ( sK53_SY1002 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) @ SV207 )
= $true )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( member_nat @ ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) @ SV85 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2542]) ).
thf(2614,plain,
! [SV207: set_nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV304: nat > nat] :
( ( ( ~ ( member_nat @ ( SV304 @ ( sK53_SY1002 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) @ SV85 )
| ( ( SV353 @ ( SV304 @ ( sK53_SY1002 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
!= ( SV373 @ ( sK53_SY1002 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( member_nat @ ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) @ SV85 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2543]) ).
thf(2615,plain,
! [SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV304: nat > nat,SV207: set_nat,SV381: nat] :
( ( ( ~ ( ~ ( member_nat @ SV381 @ SV207 )
| ( ( SV304 @ SV381 )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) ) ) )
= $false )
| ( ( ~ ! [SY1022: nat] :
( ~ ~ ( ~ ( member_nat @ SY1022 @ SV207 )
| ( ( SV304 @ SY1022 )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) ) )
| ( SY1022 = SV381 ) ) )
= $true )
| ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) )
| ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2544]) ).
thf(2616,plain,
! [SV378: nat] :
( ( ( ord_less_eq_nat @ one_one_nat @ SV378 )
= $true )
| ( ( ( p @ SV378 )
= zero_zero_nat )
= $true )
| ( ( p
= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2547]) ).
thf(2617,plain,
! [SV378: nat] :
( ( ( ord_less_eq_nat @ SV378 @ zero_zero_nat )
= $true )
| ( ( ( p @ SV378 )
= zero_zero_nat )
= $true )
| ( ( p
= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2548]) ).
thf(2618,plain,
( ( ( p
= ( ^ [SX0: nat] : zero_zero_nat ) )
= $false )
| ( ( ( p @ sK18_SX0 )
= zero_zero_nat )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2549]) ).
thf(2619,plain,
( ( ( ord_less_eq_nat @ sK18_SX0 @ zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ sK18_SX0 )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
!= zero_zero_nat )
= $true )
| ( ( p
!= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2550]) ).
thf(2620,plain,
! [SV356: nat,SV213: nat] :
( ( ( SV213 = SV356 )
= $true )
| ( ( ord_less_eq_nat @ SV356 @ SV213 )
= $false )
| ( ( ord_less_eq_nat @ SV213 @ SV356 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2553]) ).
thf(2621,plain,
! [SV213: nat,SV356: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV356 @ SV213 )
| ~ ( ord_less_eq_nat @ SV213 @ SV356 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV356 @ SV213 )
= $false )
| ( ( ord_less_eq_nat @ SV213 @ SV356 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2554]) ).
thf(2622,plain,
! [SV311: nat,SV98: nat,SV219: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV219 )
| ~ ( ord_less_nat @ SV98 @ SV311 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV219 )
= $false )
| ( ( ord_less_nat @ SV98 @ SV311 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2557]) ).
thf(2623,plain,
! [SV221: nat,SV313: nat,SV100: nat > $o] :
( ( ( ~ ( SV100 @ ( sK44_SY590 @ SV313 @ SV221 @ SV100 ) ) )
= $false )
| ( ( SV100 @ ( sK14_SY920 @ SV221 @ SV313 @ SV100 ) )
= $true )
| ( ( SV100 @ SV221 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2559]) ).
thf(2624,plain,
! [SV221: nat,SV313: nat,SV100: nat > $o] :
( ( ( ~ ! [SY1036: nat] :
( ~ ( SV100 @ SY1036 )
| ( ord_less_eq_nat @ SY1036 @ ( sK44_SY590 @ SV313 @ SV221 @ SV100 ) ) ) )
= $false )
| ( ( SV100 @ ( sK14_SY920 @ SV221 @ SV313 @ SV100 ) )
= $true )
| ( ( SV100 @ SV221 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2559]) ).
thf(2625,plain,
! [SV221: nat,SV313: nat,SV100: nat > $o] :
( ( ( SV100 @ ( sK27_SY590 @ SV313 @ SV221 @ SV100 ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK14_SY920 @ SV221 @ SV313 @ SV100 ) @ SV313 )
= $false )
| ( ( SV100 @ SV221 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2560]) ).
thf(2626,plain,
! [SV221: nat,SV313: nat,SV100: nat > $o] :
( ( ( ! [SY1027: nat] :
( ~ ( SV100 @ SY1027 )
| ( ord_less_eq_nat @ SY1027 @ ( sK27_SY590 @ SV313 @ SV221 @ SV100 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK14_SY920 @ SV221 @ SV313 @ SV100 ) @ SV313 )
= $false )
| ( ( SV100 @ SV221 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2561]) ).
thf(2627,plain,
! [SV222: nat,SV360: nat] :
( ( ( SV360 = SV222 )
= $false )
| ( ( ord_less_nat @ SV222 @ SV360 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2563]) ).
thf(2628,plain,
! [SV360: nat,SV222: nat] :
( ( ( ~ ( ord_less_nat @ SV222 @ SV360 ) )
= $false )
| ( ( ord_less_eq_nat @ SV222 @ SV360 )
= $false )
| ( ( SV360 = SV222 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2564]) ).
thf(2629,plain,
! [SV360: nat,SV222: nat] :
( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV222 @ SV360 )
| ~ ( ( SV360 != SV222 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV222 @ SV360 )
= $false )
| ( ( SV360 = SV222 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2564]) ).
thf(2630,plain,
! [SV362: nat,SV228: nat] :
( ( ( SV228 = SV362 )
= $false )
| ( ( ord_less_nat @ SV228 @ SV362 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2569]) ).
thf(2631,plain,
! [SV362: nat,SV228: nat] :
( ( ( ~ ( ord_less_nat @ SV228 @ SV362 ) )
= $false )
| ( ( ord_less_eq_nat @ SV228 @ SV362 )
= $false )
| ( ( SV228 = SV362 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2570]) ).
thf(2632,plain,
! [SV362: nat,SV228: nat] :
( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV228 @ SV362 )
| ~ ( ( SV228 != SV362 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV228 @ SV362 )
= $false )
| ( ( SV228 = SV362 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2570]) ).
thf(2633,plain,
! [SV110: nat > $o,SV230: nat,SV382: nat] :
( ( ( ord_less_nat @ SV382 @ ( sK10_SY608 @ SV230 @ SV110 ) )
= $false )
| ( ( ~ ~ ( SV110 @ SV382 ) )
= $true )
| ( ( SV110 @ SV230 )
= $true )
| ( ( SV110 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2571]) ).
thf(2634,plain,
! [SV319: set_nat,SV363: nat > nat,SV116: set_nat,SV236: nat > nat,SV374: nat > nat,SV376: nat > nat] :
( ( ( ~ ( member_nat @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) @ SV319 ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) )
= $true )
| ( ( member_nat @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) @ SV116 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2572]) ).
thf(2635,plain,
! [SV319: set_nat,SV116: set_nat,SV236: nat > nat,SV374: nat > nat,SV376: nat > nat,SV363: nat > nat] :
( ( ( ~ ( ~ ~ ( ~ ( member_nat @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) @ SV116 )
| ( ( SV236 @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
| ( ( SV374 @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( SV376 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) )
= $true )
| ( ( member_nat @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) @ SV116 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2572]) ).
thf(2636,plain,
! [SV376: nat > nat,SV374: nat > nat,SV236: nat > nat,SV116: set_nat,SV363: nat > nat,SV319: set_nat] :
( ( ( ~ ! [SY1014: nat] :
( ~ ( member_nat @ SY1014 @ SV319 )
| ~ ( ~ ~ ( ~ ( member_nat @ ( SV363 @ SY1014 ) @ SV116 )
| ( ( SV236 @ ( SV363 @ SY1014 ) )
!= SY1014 ) )
| ( ( SV374 @ ( SV363 @ SY1014 ) )
!= ( SV376 @ SY1014 ) ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) )
= $true )
| ( ( member_nat @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) @ SV319 )
= $false )
| ( ( ( SV363 @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) )
= ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2573]) ).
thf(2637,plain,
! [SV366: nat,SV243: nat] :
( ( ( SV243 = SV366 )
= $true )
| ( ( ord_less_eq_nat @ SV243 @ SV366 )
= $false )
| ( ( ord_less_eq_nat @ SV366 @ SV243 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2578]) ).
thf(2638,plain,
! [SV366: nat,SV243: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV243 @ SV366 )
| ~ ( ord_less_eq_nat @ SV366 @ SV243 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV243 @ SV366 )
= $false )
| ( ( ord_less_eq_nat @ SV366 @ SV243 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2579]) ).
thf(2639,plain,
! [SV252: nat,SV331: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2583]) ).
thf(2640,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2584]) ).
thf(2641,plain,
! [SV252: nat,SV331: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2585]) ).
thf(2642,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2586]) ).
thf(2643,plain,
! [SV252: nat,SV331: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2587]) ).
thf(2644,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2588]) ).
thf(2645,plain,
! [SV252: nat,SV331: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2589]) ).
thf(2646,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2590]) ).
thf(2647,plain,
! [SV332: nat,SV253: nat,SV135: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 )
| ~ ( ord_less_nat @ SV253 @ SV332 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV135 )
= $false )
| ( ( ord_less_nat @ SV253 @ SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2592]) ).
thf(2648,plain,
! [SV254: nat,SV136: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV136 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV136 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV254 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2593]) ).
thf(2649,plain,
! [SV136: nat,SV254: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV254 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV136 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV254 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2593]) ).
thf(2650,plain,
! [SV370: nat,SV259: nat] :
( ( ( SV259 = SV370 )
= $false )
| ( ( ord_less_nat @ SV259 @ SV370 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2595]) ).
thf(2651,plain,
! [SV370: nat,SV259: nat] :
( ( ( ~ ( ord_less_nat @ SV259 @ SV370 ) )
= $false )
| ( ( ord_less_eq_nat @ SV259 @ SV370 )
= $false )
| ( ( SV259 = SV370 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2596]) ).
thf(2652,plain,
! [SV370: nat,SV259: nat] :
( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV259 @ SV370 )
| ~ ( ( SV259 != SV370 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV259 @ SV370 )
= $false )
| ( ( SV259 = SV370 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2596]) ).
thf(2653,plain,
! [SV263: nat,SV145: nat] :
( ( ( SV145 != one_one_nat )
= $false )
| ( ( SV145 = one_one_nat )
= $false )
| ( ( SV263 = one_one_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2597]) ).
thf(2654,plain,
! [SV145: nat,SV263: nat] :
( ( ( SV263 != one_one_nat )
= $false )
| ( ( SV145 = one_one_nat )
= $false )
| ( ( SV263 = one_one_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2597]) ).
thf(2655,plain,
! [SV266: nat,SV149: nat] :
( ( ( SV149 != one_one_nat )
= $false )
| ( ( SV149 = one_one_nat )
= $false )
| ( ( SV266 = one_one_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2598]) ).
thf(2656,plain,
! [SV149: nat,SV266: nat] :
( ( ( SV266 != one_one_nat )
= $false )
| ( ( SV149 = one_one_nat )
= $false )
| ( ( SV266 = one_one_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2598]) ).
thf(2657,plain,
! [SV60: set_nat,SV288: nat > nat,SV346: set_nat,SV182: nat > nat,SV372: nat > nat,SV375: nat > nat] :
( ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ~ ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) )
| ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2601]) ).
thf(2658,plain,
! [SV375: nat > nat,SV372: nat > nat,SV60: set_nat,SV182: nat > nat,SV288: nat > nat,SV346: set_nat] :
( ( ( ~ ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) ) )
= $true )
| ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2602]) ).
thf(2659,plain,
! [SV375: nat > nat,SV372: nat > nat,SV60: set_nat,SV182: nat > nat,SV288: nat > nat,SV346: set_nat] :
( ( ( ~ ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) ) )
= $true )
| ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2603]) ).
thf(2660,plain,
! [SV375: nat > nat,SV372: nat > nat,SV60: set_nat,SV182: nat > nat,SV288: nat > nat,SV346: set_nat] :
( ( ( ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) ) )
= $false )
| ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2604]) ).
thf(2661,plain,
! [SV347: nat,SV186: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV186 @ SV347 )
| ~ ( ord_less_eq_nat @ SV347 @ SV186 ) )
= $false )
| ( ( ord_less_eq_nat @ SV186 @ SV347 )
= $false )
| ( ( ord_less_eq_nat @ SV347 @ SV186 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2606]) ).
thf(2662,plain,
! [SV192: nat,SV293: nat,SV384: nat,SV70: nat > $o] :
( ( ( ~ ( SV70 @ SV384 ) )
= $true )
| ( ( ord_less_eq_nat @ SV384 @ ( sK35_SY505 @ SV293 @ SV192 @ SV70 ) )
= $true )
| ( ( SV70 @ ( sK12_SY884 @ SV192 @ SV293 @ SV70 ) )
= $true )
| ( ( SV70 @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2607]) ).
thf(2663,plain,
! [SV192: nat,SV293: nat,SV383: nat,SV70: nat > $o] :
( ( ( SV70 @ SV383 )
= $false )
| ( ( ord_less_eq_nat @ SV383 @ ( sK20_SY505 @ SV293 @ SV192 @ SV70 ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK12_SY884 @ SV192 @ SV293 @ SV70 ) @ SV293 )
= $false )
| ( ( SV70 @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2608]) ).
thf(2664,plain,
! [SV350: nat,SV385: nat,SV194: nat > nat] :
( ( ( ~ ( ( ( SV194 @ SV385 )
!= zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SV385 )
| ~ ( ord_less_eq_nat @ SV385 @ SV350 ) ) )
= $true )
| ( ( number1551313001itions @ SV194 @ SV350 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2609]) ).
thf(2665,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false )
| ( ( ( SV194 @ ( sK36_SY959 @ SV350 @ SV194 ) )
= zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( number1551313001itions @ SV194 @ SV350 )
| ~ ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2610]) ).
thf(2666,plain,
! [SV194: nat > nat,SV350: nat] :
( ( ( ord_less_eq_nat @ one_one_nat @ ( sK36_SY959 @ SV350 @ SV194 ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ ( sK36_SY959 @ SV350 @ SV194 ) @ SV350 ) )
= $true )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 )
= $true )
| ( ( ~ ( ~ ( number1551313001itions @ SV194 @ SV350 )
| ~ ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2611]) ).
thf(2667,plain,
! [SV207: set_nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV304: nat > nat] :
( ( ( ~ ( member_nat @ ( SV304 @ ( sK53_SY1002 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) @ SV85 ) )
= $true )
| ( ( ( SV353 @ ( SV304 @ ( sK53_SY1002 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
!= ( SV373 @ ( sK53_SY1002 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( member_nat @ ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) @ SV85 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2614]) ).
thf(2668,plain,
! [SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV304: nat > nat,SV207: set_nat,SV381: nat] :
( ( ( ~ ( member_nat @ SV381 @ SV207 )
| ( ( SV304 @ SV381 )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) ) )
= $true )
| ( ( ~ ! [SY1022: nat] :
( ~ ~ ( ~ ( member_nat @ SY1022 @ SV207 )
| ( ( SV304 @ SY1022 )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) ) )
| ( SY1022 = SV381 ) ) )
= $true )
| ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) )
| ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2615]) ).
thf(2669,plain,
! [SV378: nat] :
( ( ( ! [SV386: nat] :
( ( p @ SV386 )
= zero_zero_nat ) )
= $true )
| ( ( ( p @ SV378 )
= zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ one_one_nat @ SV378 )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[2616]) ).
thf(2670,plain,
! [SV378: nat] :
( ( ( p
= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true )
| ( ( ( p @ SV378 )
= zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ one_one_nat @ SV378 )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[2616]) ).
thf(2671,plain,
! [SV378: nat] :
( ( ( ! [SV387: nat] :
( ( p @ SV387 )
= zero_zero_nat ) )
= $true )
| ( ( ( p @ SV378 )
= zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV378 @ zero_zero_nat )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[2617]) ).
thf(2672,plain,
! [SV378: nat] :
( ( ( p
= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true )
| ( ( ( p @ SV378 )
= zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV378 @ zero_zero_nat )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[2617]) ).
thf(2673,plain,
( ( ( ! [SV388: nat] :
( ( p @ SV388 )
= zero_zero_nat ) )
= $false )
| ( ( ( p @ sK18_SX0 )
= zero_zero_nat )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
= zero_zero_nat )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[2618]) ).
thf(2674,plain,
( ( ( p
= ( ^ [SX0: nat] : zero_zero_nat ) )
= $false )
| ( ( ( p @ sK18_SX0 )
= zero_zero_nat )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
= zero_zero_nat )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[2618]) ).
thf(2675,plain,
( ( ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
= zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ sK18_SX0 )
= $false )
| ( ( ord_less_eq_nat @ sK18_SX0 @ zero_zero_nat )
= $false )
| ( ( p
!= ( ^ [SX0: nat] : zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2619]) ).
thf(2676,plain,
! [SV213: nat,SV356: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV356 @ SV213 )
| ~ ( ord_less_eq_nat @ SV213 @ SV356 ) )
= $false )
| ( ( ord_less_eq_nat @ SV356 @ SV213 )
= $false )
| ( ( ord_less_eq_nat @ SV213 @ SV356 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2621]) ).
thf(2677,plain,
! [SV311: nat,SV98: nat,SV219: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV219 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV219 )
= $false )
| ( ( ord_less_nat @ SV98 @ SV311 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2622]) ).
thf(2678,plain,
! [SV219: nat,SV311: nat,SV98: nat] :
( ( ( ~ ( ord_less_nat @ SV98 @ SV311 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV219 )
= $false )
| ( ( ord_less_nat @ SV98 @ SV311 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2622]) ).
thf(2679,plain,
! [SV221: nat,SV313: nat,SV100: nat > $o] :
( ( ( SV100 @ ( sK44_SY590 @ SV313 @ SV221 @ SV100 ) )
= $true )
| ( ( SV100 @ ( sK14_SY920 @ SV221 @ SV313 @ SV100 ) )
= $true )
| ( ( SV100 @ SV221 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2623]) ).
thf(2680,plain,
! [SV221: nat,SV313: nat,SV100: nat > $o] :
( ( ( ! [SY1036: nat] :
( ~ ( SV100 @ SY1036 )
| ( ord_less_eq_nat @ SY1036 @ ( sK44_SY590 @ SV313 @ SV221 @ SV100 ) ) ) )
= $true )
| ( ( SV100 @ ( sK14_SY920 @ SV221 @ SV313 @ SV100 ) )
= $true )
| ( ( SV100 @ SV221 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2624]) ).
thf(2681,plain,
! [SV221: nat,SV313: nat,SV389: nat,SV100: nat > $o] :
( ( ( ~ ( SV100 @ SV389 )
| ( ord_less_eq_nat @ SV389 @ ( sK27_SY590 @ SV313 @ SV221 @ SV100 ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK14_SY920 @ SV221 @ SV313 @ SV100 ) @ SV313 )
= $false )
| ( ( SV100 @ SV221 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2626]) ).
thf(2682,plain,
! [SV360: nat,SV222: nat] :
( ( ( ord_less_nat @ SV222 @ SV360 )
= $true )
| ( ( ord_less_eq_nat @ SV222 @ SV360 )
= $false )
| ( ( SV360 = SV222 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2628]) ).
thf(2683,plain,
! [SV360: nat,SV222: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV222 @ SV360 )
| ~ ( ( SV360 != SV222 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV222 @ SV360 )
= $false )
| ( ( SV360 = SV222 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2629]) ).
thf(2684,plain,
! [SV362: nat,SV228: nat] :
( ( ( ord_less_nat @ SV228 @ SV362 )
= $true )
| ( ( ord_less_eq_nat @ SV228 @ SV362 )
= $false )
| ( ( SV228 = SV362 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2631]) ).
thf(2685,plain,
! [SV362: nat,SV228: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV228 @ SV362 )
| ~ ( ( SV228 != SV362 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV228 @ SV362 )
= $false )
| ( ( SV228 = SV362 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2632]) ).
thf(2686,plain,
! [SV230: nat,SV382: nat,SV110: nat > $o] :
( ( ( ~ ( SV110 @ SV382 ) )
= $false )
| ( ( ord_less_nat @ SV382 @ ( sK10_SY608 @ SV230 @ SV110 ) )
= $false )
| ( ( SV110 @ SV230 )
= $true )
| ( ( SV110 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2633]) ).
thf(2687,plain,
! [SV319: set_nat,SV363: nat > nat,SV116: set_nat,SV236: nat > nat,SV374: nat > nat,SV376: nat > nat] :
( ( ( member_nat @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) @ SV319 )
= $true )
| ( ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) )
= $true )
| ( ( member_nat @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) @ SV116 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2634]) ).
thf(2688,plain,
! [SV319: set_nat,SV116: set_nat,SV236: nat > nat,SV374: nat > nat,SV376: nat > nat,SV363: nat > nat] :
( ( ( ~ ~ ( ~ ( member_nat @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) @ SV116 )
| ( ( SV236 @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
| ( ( SV374 @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( SV376 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) )
= $true )
| ( ( member_nat @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) @ SV116 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2635]) ).
thf(2689,plain,
! [SV376: nat > nat,SV374: nat > nat,SV236: nat > nat,SV116: set_nat,SV363: nat > nat,SV319: set_nat] :
( ( ( ! [SY1014: nat] :
( ~ ( member_nat @ SY1014 @ SV319 )
| ~ ( ~ ~ ( ~ ( member_nat @ ( SV363 @ SY1014 ) @ SV116 )
| ( ( SV236 @ ( SV363 @ SY1014 ) )
!= SY1014 ) )
| ( ( SV374 @ ( SV363 @ SY1014 ) )
!= ( SV376 @ SY1014 ) ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) )
= $true )
| ( ( member_nat @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) @ SV319 )
= $false )
| ( ( ( SV363 @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) )
= ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2636]) ).
thf(2690,plain,
! [SV366: nat,SV243: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV243 @ SV366 )
| ~ ( ord_less_eq_nat @ SV366 @ SV243 ) )
= $false )
| ( ( ord_less_eq_nat @ SV243 @ SV366 )
= $false )
| ( ( ord_less_eq_nat @ SV366 @ SV243 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2638]) ).
thf(2691,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2639]) ).
thf(2692,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2640]) ).
thf(2693,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2641]) ).
thf(2694,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2642]) ).
thf(2695,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2643]) ).
thf(2696,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2644]) ).
thf(2697,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2645]) ).
thf(2698,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2646]) ).
thf(2699,plain,
! [SV332: nat,SV253: nat,SV135: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV135 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV135 )
= $false )
| ( ( ord_less_nat @ SV253 @ SV332 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2647]) ).
thf(2700,plain,
! [SV135: nat,SV332: nat,SV253: nat] :
( ( ( ~ ( ord_less_nat @ SV253 @ SV332 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV135 )
= $false )
| ( ( ord_less_nat @ SV253 @ SV332 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2647]) ).
thf(2701,plain,
! [SV254: nat,SV136: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV136 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV136 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV254 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2648]) ).
thf(2702,plain,
! [SV136: nat,SV254: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV254 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV136 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV254 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2649]) ).
thf(2703,plain,
! [SV370: nat,SV259: nat] :
( ( ( ord_less_nat @ SV259 @ SV370 )
= $true )
| ( ( ord_less_eq_nat @ SV259 @ SV370 )
= $false )
| ( ( SV259 = SV370 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2651]) ).
thf(2704,plain,
! [SV370: nat,SV259: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV259 @ SV370 )
| ~ ( ( SV259 != SV370 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV259 @ SV370 )
= $false )
| ( ( SV259 = SV370 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2652]) ).
thf(2705,plain,
! [SV263: nat,SV145: nat] :
( ( ( SV145 = one_one_nat )
= $true )
| ( ( SV145 = one_one_nat )
= $false )
| ( ( SV263 = one_one_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2653]) ).
thf(2706,plain,
! [SV145: nat,SV263: nat] :
( ( ( SV263 = one_one_nat )
= $true )
| ( ( SV145 = one_one_nat )
= $false )
| ( ( SV263 = one_one_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2654]) ).
thf(2707,plain,
! [SV266: nat,SV149: nat] :
( ( ( SV149 = one_one_nat )
= $true )
| ( ( SV149 = one_one_nat )
= $false )
| ( ( SV266 = one_one_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2655]) ).
thf(2708,plain,
! [SV149: nat,SV266: nat] :
( ( ( SV266 = one_one_nat )
= $true )
| ( ( SV149 = one_one_nat )
= $false )
| ( ( SV266 = one_one_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2656]) ).
thf(2709,plain,
! [SV375: nat > nat,SV372: nat > nat,SV60: set_nat,SV182: nat > nat,SV288: nat > nat,SV346: set_nat] :
( ( ( ~ ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) ) )
= $true )
| ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2657]) ).
thf(2710,plain,
! [SV375: nat > nat,SV372: nat > nat,SV60: set_nat,SV182: nat > nat,SV288: nat > nat,SV346: set_nat] :
( ( ( ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) ) )
= $false )
| ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2658]) ).
thf(2711,plain,
! [SV375: nat > nat,SV372: nat > nat,SV60: set_nat,SV182: nat > nat,SV288: nat > nat,SV346: set_nat] :
( ( ( ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) ) )
= $false )
| ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2659]) ).
thf(2712,plain,
! [SV346: set_nat,SV288: nat > nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
| ( ( SV288 @ ( SV182 @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= $false )
| ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2660]) ).
thf(2713,plain,
! [SV347: nat,SV186: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV186 @ SV347 ) )
= $false )
| ( ( ord_less_eq_nat @ SV186 @ SV347 )
= $false )
| ( ( ord_less_eq_nat @ SV347 @ SV186 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2661]) ).
thf(2714,plain,
! [SV186: nat,SV347: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV347 @ SV186 ) )
= $false )
| ( ( ord_less_eq_nat @ SV186 @ SV347 )
= $false )
| ( ( ord_less_eq_nat @ SV347 @ SV186 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2661]) ).
thf(2715,plain,
! [SV192: nat,SV293: nat,SV384: nat,SV70: nat > $o] :
( ( ( SV70 @ SV384 )
= $false )
| ( ( ord_less_eq_nat @ SV384 @ ( sK35_SY505 @ SV293 @ SV192 @ SV70 ) )
= $true )
| ( ( SV70 @ ( sK12_SY884 @ SV192 @ SV293 @ SV70 ) )
= $true )
| ( ( SV70 @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2662]) ).
thf(2716,plain,
! [SV350: nat,SV385: nat,SV194: nat > nat] :
( ( ( ( SV194 @ SV385 )
!= zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SV385 )
| ~ ( ord_less_eq_nat @ SV385 @ SV350 ) ) )
= $true )
| ( ( number1551313001itions @ SV194 @ SV350 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2664]) ).
thf(2717,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ~ ( number1551313001itions @ SV194 @ SV350 )
| ~ ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) )
= $false )
| ( ( ( SV194 @ ( sK36_SY959 @ SV350 @ SV194 ) )
= zero_zero_nat )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2665]) ).
thf(2718,plain,
! [SV194: nat > nat,SV350: nat] :
( ( ( ord_less_eq_nat @ ( sK36_SY959 @ SV350 @ SV194 ) @ SV350 )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ ( sK36_SY959 @ SV350 @ SV194 ) )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 )
= $true )
| ( ( ~ ( ~ ( number1551313001itions @ SV194 @ SV350 )
| ~ ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2666]) ).
thf(2719,plain,
! [SV207: set_nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV304: nat > nat] :
( ( ( member_nat @ ( SV304 @ ( sK53_SY1002 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) @ SV85 )
= $false )
| ( ( ( SV353 @ ( SV304 @ ( sK53_SY1002 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
!= ( SV373 @ ( sK53_SY1002 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( member_nat @ ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) @ SV85 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2667]) ).
thf(2720,plain,
! [SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV304: nat > nat,SV207: set_nat,SV381: nat] :
( ( ( ~ ( member_nat @ SV381 @ SV207 ) )
= $true )
| ( ( ( SV304 @ SV381 )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $true )
| ( ( ~ ! [SY1022: nat] :
( ~ ~ ( ~ ( member_nat @ SY1022 @ SV207 )
| ( ( SV304 @ SY1022 )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) ) )
| ( SY1022 = SV381 ) ) )
= $true )
| ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) )
| ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2668]) ).
thf(2721,plain,
! [SV378: nat,SV390: nat] :
( ( ( ( p @ SV390 )
= zero_zero_nat )
= $true )
| ( ( ( p @ SV378 )
= zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ one_one_nat @ SV378 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2669]) ).
thf(2722,plain,
! [SV378: nat,SV391: nat] :
( ( ( ( p @ SV391 )
= zero_zero_nat )
= $true )
| ( ( ( p @ SV378 )
= zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV378 @ zero_zero_nat )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2671]) ).
thf(2723,plain,
( ( ( ( p @ sK57_SV388 )
= zero_zero_nat )
= $false )
| ( ( ( p @ sK18_SX0 )
= zero_zero_nat )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
= zero_zero_nat )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2673]) ).
thf(2724,plain,
( ( ( p
= ( ^ [SX0: nat] : zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ sK18_SX0 @ zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ sK18_SX0 )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2675]) ).
thf(2725,plain,
! [SV213: nat,SV356: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV356 @ SV213 ) )
= $false )
| ( ( ord_less_eq_nat @ SV356 @ SV213 )
= $false )
| ( ( ord_less_eq_nat @ SV213 @ SV356 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2676]) ).
thf(2726,plain,
! [SV356: nat,SV213: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV213 @ SV356 ) )
= $false )
| ( ( ord_less_eq_nat @ SV356 @ SV213 )
= $false )
| ( ( ord_less_eq_nat @ SV213 @ SV356 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2676]) ).
thf(2727,plain,
! [SV311: nat,SV98: nat,SV219: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV219 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV219 )
= $false )
| ( ( ord_less_nat @ SV98 @ SV311 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2677]) ).
thf(2728,plain,
! [SV219: nat,SV311: nat,SV98: nat] :
( ( ( ord_less_nat @ SV98 @ SV311 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV219 )
= $false )
| ( ( ord_less_nat @ SV98 @ SV311 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2678]) ).
thf(2729,plain,
! [SV221: nat,SV313: nat,SV392: nat,SV100: nat > $o] :
( ( ( ~ ( SV100 @ SV392 )
| ( ord_less_eq_nat @ SV392 @ ( sK44_SY590 @ SV313 @ SV221 @ SV100 ) ) )
= $true )
| ( ( SV100 @ ( sK14_SY920 @ SV221 @ SV313 @ SV100 ) )
= $true )
| ( ( SV100 @ SV221 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2680]) ).
thf(2730,plain,
! [SV221: nat,SV313: nat,SV389: nat,SV100: nat > $o] :
( ( ( ~ ( SV100 @ SV389 ) )
= $true )
| ( ( ord_less_eq_nat @ SV389 @ ( sK27_SY590 @ SV313 @ SV221 @ SV100 ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK14_SY920 @ SV221 @ SV313 @ SV100 ) @ SV313 )
= $false )
| ( ( SV100 @ SV221 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2681]) ).
thf(2731,plain,
! [SV360: nat,SV222: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV222 @ SV360 )
| ~ ( ( SV360 != SV222 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV222 @ SV360 )
= $false )
| ( ( SV360 = SV222 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2683]) ).
thf(2732,plain,
! [SV362: nat,SV228: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV228 @ SV362 )
| ~ ( ( SV228 != SV362 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV228 @ SV362 )
= $false )
| ( ( SV228 = SV362 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2685]) ).
thf(2733,plain,
! [SV230: nat,SV382: nat,SV110: nat > $o] :
( ( ( SV110 @ SV382 )
= $true )
| ( ( ord_less_nat @ SV382 @ ( sK10_SY608 @ SV230 @ SV110 ) )
= $false )
| ( ( SV110 @ SV230 )
= $true )
| ( ( SV110 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2686]) ).
thf(2734,plain,
! [SV319: set_nat,SV116: set_nat,SV236: nat > nat,SV374: nat > nat,SV376: nat > nat,SV363: nat > nat] :
( ( ( ~ ~ ( ~ ( member_nat @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) @ SV116 )
| ( ( SV236 @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) ) )
= $true )
| ( ( ( SV374 @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( SV376 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) )
= $true )
| ( ( member_nat @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) @ SV116 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2688]) ).
thf(2735,plain,
! [SV319: set_nat,SV363: nat > nat,SV116: set_nat,SV236: nat > nat,SV374: nat > nat,SV376: nat > nat] :
( ( ( ~ ( member_nat @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) @ SV319 )
| ~ ( ~ ~ ( ~ ( member_nat @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) @ SV116 )
| ( ( SV236 @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
| ( ( SV374 @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( SV376 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) )
= $true )
| ( ( member_nat @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) @ SV319 )
= $false )
| ( ( ( SV363 @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) )
= ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2689]) ).
thf(2736,plain,
! [SV366: nat,SV243: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV243 @ SV366 ) )
= $false )
| ( ( ord_less_eq_nat @ SV243 @ SV366 )
= $false )
| ( ( ord_less_eq_nat @ SV366 @ SV243 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2690]) ).
thf(2737,plain,
! [SV243: nat,SV366: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV366 @ SV243 ) )
= $false )
| ( ( ord_less_eq_nat @ SV243 @ SV366 )
= $false )
| ( ( ord_less_eq_nat @ SV366 @ SV243 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2690]) ).
thf(2738,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2691]) ).
thf(2739,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2692]) ).
thf(2740,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2693]) ).
thf(2741,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2694]) ).
thf(2742,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2695]) ).
thf(2743,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2696]) ).
thf(2744,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2697]) ).
thf(2745,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV252 )
| ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2698]) ).
thf(2746,plain,
! [SV332: nat,SV253: nat,SV135: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV135 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV135 )
= $false )
| ( ( ord_less_nat @ SV253 @ SV332 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2699]) ).
thf(2747,plain,
! [SV135: nat,SV332: nat,SV253: nat] :
( ( ( ord_less_nat @ SV253 @ SV332 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV135 )
= $false )
| ( ( ord_less_nat @ SV253 @ SV332 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2700]) ).
thf(2748,plain,
! [SV370: nat,SV259: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV259 @ SV370 )
| ~ ( ( SV259 != SV370 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV259 @ SV370 )
= $false )
| ( ( SV259 = SV370 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2704]) ).
thf(2749,plain,
! [SV375: nat > nat,SV372: nat > nat,SV60: set_nat,SV182: nat > nat,SV288: nat > nat,SV346: set_nat] :
( ( ( ! [SY954: nat] :
( ~ ( member_nat @ SY954 @ SV346 )
| ( ( SV288 @ ( SV182 @ SY954 ) )
= SY954 ) ) )
= $false )
| ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2709]) ).
thf(2750,plain,
! [SV346: set_nat,SV288: nat > nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
| ( ( SV288 @ ( SV182 @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= $false )
| ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2710]) ).
thf(2751,plain,
! [SV346: set_nat,SV288: nat > nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
| ( ( SV288 @ ( SV182 @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= $false )
| ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2711]) ).
thf(2752,plain,
! [SV346: set_nat,SV288: nat > nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 ) )
= $false )
| ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2712]) ).
thf(2753,plain,
! [SV346: set_nat,SV60: set_nat,SV372: nat > nat,SV375: nat > nat,SV182: nat > nat,SV288: nat > nat] :
( ( ( ( SV288 @ ( SV182 @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2712]) ).
thf(2754,plain,
! [SV347: nat,SV186: nat] :
( ( ( ord_less_eq_nat @ SV186 @ SV347 )
= $true )
| ( ( ord_less_eq_nat @ SV186 @ SV347 )
= $false )
| ( ( ord_less_eq_nat @ SV347 @ SV186 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2713]) ).
thf(2755,plain,
! [SV186: nat,SV347: nat] :
( ( ( ord_less_eq_nat @ SV347 @ SV186 )
= $true )
| ( ( ord_less_eq_nat @ SV186 @ SV347 )
= $false )
| ( ( ord_less_eq_nat @ SV347 @ SV186 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2714]) ).
thf(2756,plain,
! [SV350: nat,SV385: nat,SV194: nat > nat] :
( ( ( ( SV194 @ SV385 )
= zero_zero_nat )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SV385 )
| ~ ( ord_less_eq_nat @ SV385 @ SV350 ) ) )
= $true )
| ( ( number1551313001itions @ SV194 @ SV350 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2716]) ).
thf(2757,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ~ ( number1551313001itions @ SV194 @ SV350 ) )
= $false )
| ( ( ( SV194 @ ( sK36_SY959 @ SV350 @ SV194 ) )
= zero_zero_nat )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2717]) ).
thf(2758,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ~ ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) )
= $false )
| ( ( ( SV194 @ ( sK36_SY959 @ SV350 @ SV194 ) )
= zero_zero_nat )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2717]) ).
thf(2759,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ ( sK36_SY959 @ SV350 @ SV194 ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK36_SY959 @ SV350 @ SV194 ) @ SV350 )
= $false )
| ( ( ~ ( ~ ( number1551313001itions @ SV194 @ SV350 )
| ~ ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2718]) ).
thf(2760,plain,
! [SV207: set_nat,SV85: set_nat,SV373: nat > nat,SV304: nat > nat,SV353: nat > nat] :
( ( ( ( SV353 @ ( SV304 @ ( sK53_SY1002 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
= ( SV373 @ ( sK53_SY1002 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
= $false )
| ( ( member_nat @ ( SV304 @ ( sK53_SY1002 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) @ SV85 )
= $false )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( member_nat @ ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) @ SV85 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2719]) ).
thf(2761,plain,
! [SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV304: nat > nat,SV207: set_nat,SV381: nat] :
( ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( SV304 @ SV381 )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $true )
| ( ( ~ ! [SY1022: nat] :
( ~ ~ ( ~ ( member_nat @ SY1022 @ SV207 )
| ( ( SV304 @ SY1022 )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) ) )
| ( SY1022 = SV381 ) ) )
= $true )
| ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) )
| ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2720]) ).
thf(2762,plain,
( ( ( ! [SV393: nat] :
( ( p @ SV393 )
= zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ sK18_SX0 @ zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ sK18_SX0 )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
= zero_zero_nat )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[2724]) ).
thf(2763,plain,
( ( ( p
= ( ^ [SX0: nat] : zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ sK18_SX0 @ zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ sK18_SX0 )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
= zero_zero_nat )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[2724]) ).
thf(2764,plain,
! [SV213: nat,SV356: nat] :
( ( ( ord_less_eq_nat @ SV356 @ SV213 )
= $true )
| ( ( ord_less_eq_nat @ SV356 @ SV213 )
= $false )
| ( ( ord_less_eq_nat @ SV213 @ SV356 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2725]) ).
thf(2765,plain,
! [SV356: nat,SV213: nat] :
( ( ( ord_less_eq_nat @ SV213 @ SV356 )
= $true )
| ( ( ord_less_eq_nat @ SV356 @ SV213 )
= $false )
| ( ( ord_less_eq_nat @ SV213 @ SV356 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2726]) ).
thf(2766,plain,
! [SV221: nat,SV313: nat,SV392: nat,SV100: nat > $o] :
( ( ( ~ ( SV100 @ SV392 ) )
= $true )
| ( ( ord_less_eq_nat @ SV392 @ ( sK44_SY590 @ SV313 @ SV221 @ SV100 ) )
= $true )
| ( ( SV100 @ ( sK14_SY920 @ SV221 @ SV313 @ SV100 ) )
= $true )
| ( ( SV100 @ SV221 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2729]) ).
thf(2767,plain,
! [SV221: nat,SV313: nat,SV389: nat,SV100: nat > $o] :
( ( ( SV100 @ SV389 )
= $false )
| ( ( ord_less_eq_nat @ SV389 @ ( sK27_SY590 @ SV313 @ SV221 @ SV100 ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK14_SY920 @ SV221 @ SV313 @ SV100 ) @ SV313 )
= $false )
| ( ( SV100 @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2730]) ).
thf(2768,plain,
! [SV360: nat,SV222: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV222 @ SV360 ) )
= $false )
| ( ( ord_less_eq_nat @ SV222 @ SV360 )
= $false )
| ( ( SV360 = SV222 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2731]) ).
thf(2769,plain,
! [SV222: nat,SV360: nat] :
( ( ( ~ ( ( SV360 != SV222 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV222 @ SV360 )
= $false )
| ( ( SV360 = SV222 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2731]) ).
thf(2770,plain,
! [SV362: nat,SV228: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV228 @ SV362 ) )
= $false )
| ( ( ord_less_eq_nat @ SV228 @ SV362 )
= $false )
| ( ( SV228 = SV362 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2732]) ).
thf(2771,plain,
! [SV362: nat,SV228: nat] :
( ( ( ~ ( ( SV228 != SV362 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV228 @ SV362 )
= $false )
| ( ( SV228 = SV362 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2732]) ).
thf(2772,plain,
! [SV319: set_nat,SV116: set_nat,SV236: nat > nat,SV374: nat > nat,SV376: nat > nat,SV363: nat > nat] :
( ( ( ~ ( ~ ( member_nat @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) @ SV116 )
| ( ( SV236 @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) ) )
= $false )
| ( ( ( SV374 @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( SV376 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) )
= $true )
| ( ( member_nat @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) @ SV116 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2734]) ).
thf(2773,plain,
! [SV319: set_nat,SV363: nat > nat,SV116: set_nat,SV236: nat > nat,SV374: nat > nat,SV376: nat > nat] :
( ( ( ~ ( member_nat @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) @ SV319 ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) )
= $true )
| ( ( member_nat @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) @ SV319 )
= $false )
| ( ( ( SV363 @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) )
= ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2735]) ).
thf(2774,plain,
! [SV319: set_nat,SV116: set_nat,SV236: nat > nat,SV374: nat > nat,SV376: nat > nat,SV363: nat > nat] :
( ( ( ~ ( ~ ~ ( ~ ( member_nat @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) @ SV116 )
| ( ( SV236 @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
| ( ( SV374 @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( SV376 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) )
= $true )
| ( ( member_nat @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) @ SV319 )
= $false )
| ( ( ( SV363 @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) )
= ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2735]) ).
thf(2775,plain,
! [SV366: nat,SV243: nat] :
( ( ( ord_less_eq_nat @ SV243 @ SV366 )
= $true )
| ( ( ord_less_eq_nat @ SV243 @ SV366 )
= $false )
| ( ( ord_less_eq_nat @ SV366 @ SV243 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2736]) ).
thf(2776,plain,
! [SV243: nat,SV366: nat] :
( ( ( ord_less_eq_nat @ SV366 @ SV243 )
= $true )
| ( ( ord_less_eq_nat @ SV243 @ SV366 )
= $false )
| ( ( ord_less_eq_nat @ SV366 @ SV243 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2737]) ).
thf(2777,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2738]) ).
thf(2778,plain,
! [SV331: nat,SV134: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2738]) ).
thf(2779,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2739]) ).
thf(2780,plain,
! [SV331: nat,SV134: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2739]) ).
thf(2781,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2740]) ).
thf(2782,plain,
! [SV331: nat,SV134: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2740]) ).
thf(2783,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2741]) ).
thf(2784,plain,
! [SV331: nat,SV134: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2741]) ).
thf(2785,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2742]) ).
thf(2786,plain,
! [SV331: nat,SV134: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2742]) ).
thf(2787,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2743]) ).
thf(2788,plain,
! [SV331: nat,SV134: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2743]) ).
thf(2789,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2744]) ).
thf(2790,plain,
! [SV331: nat,SV134: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2744]) ).
thf(2791,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV252 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2745]) ).
thf(2792,plain,
! [SV331: nat,SV134: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2745]) ).
thf(2793,plain,
! [SV370: nat,SV259: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV259 @ SV370 ) )
= $false )
| ( ( ord_less_eq_nat @ SV259 @ SV370 )
= $false )
| ( ( SV259 = SV370 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2748]) ).
thf(2794,plain,
! [SV370: nat,SV259: nat] :
( ( ( ~ ( ( SV259 != SV370 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV259 @ SV370 )
= $false )
| ( ( SV259 = SV370 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2748]) ).
thf(2795,plain,
! [SV346: set_nat,SV288: nat > nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
| ( ( SV288 @ ( SV182 @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= $false )
| ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2749]) ).
thf(2796,plain,
! [SV346: set_nat,SV288: nat > nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 ) )
= $false )
| ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2750]) ).
thf(2797,plain,
! [SV346: set_nat,SV60: set_nat,SV372: nat > nat,SV375: nat > nat,SV182: nat > nat,SV288: nat > nat] :
( ( ( ( SV288 @ ( SV182 @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2750]) ).
thf(2798,plain,
! [SV346: set_nat,SV288: nat > nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 ) )
= $false )
| ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2751]) ).
thf(2799,plain,
! [SV346: set_nat,SV60: set_nat,SV372: nat > nat,SV375: nat > nat,SV182: nat > nat,SV288: nat > nat] :
( ( ( ( SV288 @ ( SV182 @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2751]) ).
thf(2800,plain,
! [SV346: set_nat,SV288: nat > nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV375: nat > nat] :
( ( ( member_nat @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2752]) ).
thf(2801,plain,
! [SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat,SV182: nat > nat,SV346: set_nat] :
( ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) ) )
= $true )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2753]) ).
thf(2802,plain,
! [SV194: nat > nat,SV350: nat,SV385: nat] :
( ( ( ~ ( ord_less_eq_nat @ one_one_nat @ SV385 )
| ~ ( ord_less_eq_nat @ SV385 @ SV350 ) )
= $false )
| ( ( ( SV194 @ SV385 )
= zero_zero_nat )
= $true )
| ( ( number1551313001itions @ SV194 @ SV350 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2756]) ).
thf(2803,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( number1551313001itions @ SV194 @ SV350 )
= $true )
| ( ( ( SV194 @ ( sK36_SY959 @ SV350 @ SV194 ) )
= zero_zero_nat )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2757]) ).
thf(2804,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) )
= $true )
| ( ( ( SV194 @ ( sK36_SY959 @ SV350 @ SV194 ) )
= zero_zero_nat )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2758]) ).
thf(2805,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ~ ( number1551313001itions @ SV194 @ SV350 )
| ~ ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK36_SY959 @ SV350 @ SV194 ) @ SV350 )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ ( sK36_SY959 @ SV350 @ SV194 ) )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2759]) ).
thf(2806,plain,
! [SV85: set_nat,SV207: set_nat,SV353: nat > nat,SV373: nat > nat,SV381: nat,SV304: nat > nat] :
( ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ~ ! [SY1022: nat] :
( ~ ~ ( ~ ( member_nat @ SY1022 @ SV207 )
| ( ( SV304 @ SY1022 )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) ) )
| ( SY1022 = SV381 ) ) )
= $true )
| ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) )
| ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2761]) ).
thf(2807,plain,
( ( ( ( p @ sK62_SV393 )
= zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ sK18_SX0 @ zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ sK18_SX0 )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SX0: nat] : ( times_times_nat @ ( p @ SX0 ) @ SX0 )
@ ( set_ord_atMost_nat @ zero_zero_nat ) )
= zero_zero_nat )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2762]) ).
thf(2808,plain,
! [SV221: nat,SV313: nat,SV392: nat,SV100: nat > $o] :
( ( ( SV100 @ SV392 )
= $false )
| ( ( ord_less_eq_nat @ SV392 @ ( sK44_SY590 @ SV313 @ SV221 @ SV100 ) )
= $true )
| ( ( SV100 @ ( sK14_SY920 @ SV221 @ SV313 @ SV100 ) )
= $true )
| ( ( SV100 @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2766]) ).
thf(2809,plain,
! [SV360: nat,SV222: nat] :
( ( ( ord_less_eq_nat @ SV222 @ SV360 )
= $true )
| ( ( ord_less_eq_nat @ SV222 @ SV360 )
= $false )
| ( ( SV360 = SV222 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2768]) ).
thf(2810,plain,
! [SV222: nat,SV360: nat] :
( ( ( SV360 != SV222 )
= $true )
| ( ( ord_less_eq_nat @ SV222 @ SV360 )
= $false )
| ( ( SV360 = SV222 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2769]) ).
thf(2811,plain,
! [SV362: nat,SV228: nat] :
( ( ( ord_less_eq_nat @ SV228 @ SV362 )
= $true )
| ( ( ord_less_eq_nat @ SV228 @ SV362 )
= $false )
| ( ( SV228 = SV362 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2770]) ).
thf(2812,plain,
! [SV362: nat,SV228: nat] :
( ( ( SV228 != SV362 )
= $true )
| ( ( ord_less_eq_nat @ SV228 @ SV362 )
= $false )
| ( ( SV228 = SV362 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2771]) ).
thf(2813,plain,
! [SV319: set_nat,SV116: set_nat,SV236: nat > nat,SV374: nat > nat,SV376: nat > nat,SV363: nat > nat] :
( ( ( ~ ( member_nat @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) @ SV116 )
| ( ( SV236 @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
= $true )
| ( ( ( SV374 @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( SV376 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) )
= $true )
| ( ( member_nat @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) @ SV116 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2772]) ).
thf(2814,plain,
! [SV319: set_nat,SV363: nat > nat,SV116: set_nat,SV236: nat > nat,SV374: nat > nat,SV376: nat > nat] :
( ( ( member_nat @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) @ SV319 )
= $true )
| ( ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) )
= $true )
| ( ( member_nat @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) @ SV319 )
= $false )
| ( ( ( SV363 @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) )
= ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2773]) ).
thf(2815,plain,
! [SV319: set_nat,SV116: set_nat,SV236: nat > nat,SV374: nat > nat,SV376: nat > nat,SV363: nat > nat] :
( ( ( ~ ~ ( ~ ( member_nat @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) @ SV116 )
| ( ( SV236 @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
| ( ( SV374 @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( SV376 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) )
= $true )
| ( ( member_nat @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) @ SV319 )
= $false )
| ( ( ( SV363 @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) )
= ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2774]) ).
thf(2816,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2777]) ).
thf(2817,plain,
! [SV331: nat,SV134: nat,SV252: nat] :
( ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2778]) ).
thf(2818,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2779]) ).
thf(2819,plain,
! [SV331: nat,SV134: nat,SV252: nat] :
( ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2780]) ).
thf(2820,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2781]) ).
thf(2821,plain,
! [SV331: nat,SV134: nat,SV252: nat] :
( ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2782]) ).
thf(2822,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2783]) ).
thf(2823,plain,
! [SV331: nat,SV134: nat,SV252: nat] :
( ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2784]) ).
thf(2824,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2785]) ).
thf(2825,plain,
! [SV331: nat,SV134: nat,SV252: nat] :
( ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2786]) ).
thf(2826,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2787]) ).
thf(2827,plain,
! [SV331: nat,SV134: nat,SV252: nat] :
( ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2788]) ).
thf(2828,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2789]) ).
thf(2829,plain,
! [SV331: nat,SV134: nat,SV252: nat] :
( ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2790]) ).
thf(2830,plain,
! [SV134: nat,SV252: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2791]) ).
thf(2831,plain,
! [SV331: nat,SV134: nat,SV252: nat] :
( ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2792]) ).
thf(2832,plain,
! [SV370: nat,SV259: nat] :
( ( ( ord_less_eq_nat @ SV259 @ SV370 )
= $true )
| ( ( ord_less_eq_nat @ SV259 @ SV370 )
= $false )
| ( ( SV259 = SV370 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2793]) ).
thf(2833,plain,
! [SV370: nat,SV259: nat] :
( ( ( SV259 != SV370 )
= $true )
| ( ( ord_less_eq_nat @ SV259 @ SV370 )
= $false )
| ( ( SV259 = SV370 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2794]) ).
thf(2834,plain,
! [SV346: set_nat,SV288: nat > nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 ) )
= $false )
| ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2795]) ).
thf(2835,plain,
! [SV346: set_nat,SV60: set_nat,SV372: nat > nat,SV375: nat > nat,SV182: nat > nat,SV288: nat > nat] :
( ( ( ( SV288 @ ( SV182 @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2795]) ).
thf(2836,plain,
! [SV346: set_nat,SV288: nat > nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV375: nat > nat] :
( ( ( member_nat @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2796]) ).
thf(2837,plain,
! [SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat,SV182: nat > nat,SV346: set_nat] :
( ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) ) )
= $true )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2797]) ).
thf(2838,plain,
! [SV346: set_nat,SV288: nat > nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV375: nat > nat] :
( ( ( member_nat @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2798]) ).
thf(2839,plain,
! [SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat,SV182: nat > nat,SV346: set_nat] :
( ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) ) )
= $true )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2799]) ).
thf(2840,plain,
! [SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat,SV182: nat > nat,SV346: set_nat] :
( ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) ) )
= $true )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2800]) ).
thf(2841,plain,
! [SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat,SV182: nat > nat,SV346: set_nat] :
( ( ( ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) ) )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2801]) ).
thf(2842,plain,
! [SV350: nat,SV194: nat > nat,SV385: nat] :
( ( ( ~ ( ord_less_eq_nat @ one_one_nat @ SV385 ) )
= $false )
| ( ( ( SV194 @ SV385 )
= zero_zero_nat )
= $true )
| ( ( number1551313001itions @ SV194 @ SV350 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2802]) ).
thf(2843,plain,
! [SV194: nat > nat,SV350: nat,SV385: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV385 @ SV350 ) )
= $false )
| ( ( ( SV194 @ SV385 )
= zero_zero_nat )
= $true )
| ( ( number1551313001itions @ SV194 @ SV350 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2802]) ).
thf(2844,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) )
= $false )
| ( ( ( SV194 @ ( sK36_SY959 @ SV350 @ SV194 ) )
= zero_zero_nat )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2804]) ).
thf(2845,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ~ ( number1551313001itions @ SV194 @ SV350 ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK36_SY959 @ SV350 @ SV194 ) @ SV350 )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ ( sK36_SY959 @ SV350 @ SV194 ) )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2805]) ).
thf(2846,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ~ ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK36_SY959 @ SV350 @ SV194 ) @ SV350 )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ ( sK36_SY959 @ SV350 @ SV194 ) )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2805]) ).
thf(2847,plain,
! [SV381: nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV304: nat > nat,SV207: set_nat] :
( ( ( ! [SY1022: nat] :
( ~ ~ ( ~ ( member_nat @ SY1022 @ SV207 )
| ( ( SV304 @ SY1022 )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) ) )
| ( SY1022 = SV381 ) ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) )
| ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2806]) ).
thf(2848,plain,
! [SV222: nat,SV360: nat] :
( ( ( SV360 = SV222 )
= $false )
| ( ( ord_less_eq_nat @ SV222 @ SV360 )
= $false )
| ( ( SV360 = SV222 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2810]) ).
thf(2849,plain,
! [SV362: nat,SV228: nat] :
( ( ( SV228 = SV362 )
= $false )
| ( ( ord_less_eq_nat @ SV228 @ SV362 )
= $false )
| ( ( SV228 = SV362 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2812]) ).
thf(2850,plain,
! [SV319: set_nat,SV116: set_nat,SV236: nat > nat,SV374: nat > nat,SV376: nat > nat,SV363: nat > nat] :
( ( ( ~ ( member_nat @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) @ SV116 ) )
= $true )
| ( ( ( SV236 @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) )
= $true )
| ( ( ( SV374 @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( SV376 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) )
= $true )
| ( ( member_nat @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) @ SV116 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2813]) ).
thf(2851,plain,
! [SV319: set_nat,SV116: set_nat,SV236: nat > nat,SV374: nat > nat,SV376: nat > nat,SV363: nat > nat] :
( ( ( ~ ~ ( ~ ( member_nat @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) @ SV116 )
| ( ( SV236 @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) ) )
= $true )
| ( ( ( SV374 @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( SV376 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) )
= $true )
| ( ( member_nat @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) @ SV319 )
= $false )
| ( ( ( SV363 @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) )
= ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2815]) ).
thf(2852,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2816]) ).
thf(2853,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2817]) ).
thf(2854,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2818]) ).
thf(2855,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2819]) ).
thf(2856,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2820]) ).
thf(2857,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2821]) ).
thf(2858,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2822]) ).
thf(2859,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2823]) ).
thf(2860,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2824]) ).
thf(2861,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2825]) ).
thf(2862,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2826]) ).
thf(2863,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2827]) ).
thf(2864,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2828]) ).
thf(2865,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2829]) ).
thf(2866,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2830]) ).
thf(2867,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2831]) ).
thf(2868,plain,
! [SV370: nat,SV259: nat] :
( ( ( SV259 = SV370 )
= $false )
| ( ( ord_less_eq_nat @ SV259 @ SV370 )
= $false )
| ( ( SV259 = SV370 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2833]) ).
thf(2869,plain,
! [SV346: set_nat,SV288: nat > nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV375: nat > nat] :
( ( ( member_nat @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) )
| ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2834]) ).
thf(2870,plain,
! [SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat,SV182: nat > nat,SV346: set_nat] :
( ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) ) )
= $true )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2835]) ).
thf(2871,plain,
! [SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat,SV182: nat > nat,SV346: set_nat] :
( ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) ) )
= $true )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2836]) ).
thf(2872,plain,
! [SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat,SV182: nat > nat,SV346: set_nat] :
( ( ( ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) ) )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2837]) ).
thf(2873,plain,
! [SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat,SV182: nat > nat,SV346: set_nat] :
( ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) ) )
= $true )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2838]) ).
thf(2874,plain,
! [SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat,SV182: nat > nat,SV346: set_nat] :
( ( ( ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) ) )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2839]) ).
thf(2875,plain,
! [SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat,SV182: nat > nat,SV346: set_nat] :
( ( ( ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) ) )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2840]) ).
thf(2876,plain,
! [SV346: set_nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK63_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
| ( member_nat @ ( SV182 @ ( sK63_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 ) )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2841]) ).
thf(2877,plain,
! [SV350: nat,SV194: nat > nat,SV385: nat] :
( ( ( ord_less_eq_nat @ one_one_nat @ SV385 )
= $true )
| ( ( ( SV194 @ SV385 )
= zero_zero_nat )
= $true )
| ( ( number1551313001itions @ SV194 @ SV350 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2842]) ).
thf(2878,plain,
! [SV194: nat > nat,SV350: nat,SV385: nat] :
( ( ( ord_less_eq_nat @ SV385 @ SV350 )
= $true )
| ( ( ( SV194 @ SV385 )
= zero_zero_nat )
= $true )
| ( ( number1551313001itions @ SV194 @ SV350 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2843]) ).
thf(2879,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) ) )
= $false )
| ( ( ( SV194 @ ( sK36_SY959 @ SV350 @ SV194 ) )
= zero_zero_nat )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2844]) ).
thf(2880,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 )
= $false )
| ( ( ( SV194 @ ( sK36_SY959 @ SV350 @ SV194 ) )
= zero_zero_nat )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2844]) ).
thf(2881,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( number1551313001itions @ SV194 @ SV350 )
= $true )
| ( ( ord_less_eq_nat @ ( sK36_SY959 @ SV350 @ SV194 ) @ SV350 )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ ( sK36_SY959 @ SV350 @ SV194 ) )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2845]) ).
thf(2882,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ~ ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK36_SY959 @ SV350 @ SV194 ) @ SV350 )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ ( sK36_SY959 @ SV350 @ SV194 ) )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2846]) ).
thf(2883,plain,
! [SV207: set_nat,SV304: nat > nat,SV373: nat > nat,SV353: nat > nat,SV85: set_nat,SV381: nat] :
( ( ( ~ ~ ( ~ ( member_nat @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) @ SV207 )
| ( ( SV304 @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) ) )
| ( ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 )
= SV381 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) )
| ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2847]) ).
thf(2884,plain,
! [SV319: set_nat,SV116: set_nat,SV236: nat > nat,SV374: nat > nat,SV376: nat > nat,SV363: nat > nat] :
( ( ( member_nat @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) @ SV116 )
= $false )
| ( ( ( SV236 @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) )
= $true )
| ( ( ( SV374 @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( SV376 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) )
= $true )
| ( ( member_nat @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) @ SV116 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2850]) ).
thf(2885,plain,
! [SV319: set_nat,SV116: set_nat,SV236: nat > nat,SV374: nat > nat,SV376: nat > nat,SV363: nat > nat] :
( ( ( ~ ( ~ ( member_nat @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) @ SV116 )
| ( ( SV236 @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) ) )
= $false )
| ( ( ( SV374 @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( SV376 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) )
= $true )
| ( ( member_nat @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) @ SV319 )
= $false )
| ( ( ( SV363 @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) )
= ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2851]) ).
thf(2886,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2852]) ).
thf(2887,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2853]) ).
thf(2888,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2854]) ).
thf(2889,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2855]) ).
thf(2890,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2856]) ).
thf(2891,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2857]) ).
thf(2892,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2858]) ).
thf(2893,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2859]) ).
thf(2894,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2860]) ).
thf(2895,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2861]) ).
thf(2896,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2862]) ).
thf(2897,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2863]) ).
thf(2898,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2864]) ).
thf(2899,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2865]) ).
thf(2900,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2866]) ).
thf(2901,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 )
| ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2867]) ).
thf(2902,plain,
! [SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat,SV182: nat > nat,SV346: set_nat] :
( ( ( ~ ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) ) )
= $true )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2869]) ).
thf(2903,plain,
! [SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat,SV182: nat > nat,SV346: set_nat] :
( ( ( ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) ) )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2870]) ).
thf(2904,plain,
! [SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat,SV182: nat > nat,SV346: set_nat] :
( ( ( ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) ) )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2871]) ).
thf(2905,plain,
! [SV346: set_nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK65_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
| ( member_nat @ ( SV182 @ ( sK65_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 ) )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2872]) ).
thf(2906,plain,
! [SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat,SV182: nat > nat,SV346: set_nat] :
( ( ( ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) ) )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2873]) ).
thf(2907,plain,
! [SV346: set_nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK66_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
| ( member_nat @ ( SV182 @ ( sK66_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 ) )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2874]) ).
thf(2908,plain,
! [SV346: set_nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK67_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
| ( member_nat @ ( SV182 @ ( sK67_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 ) )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2875]) ).
thf(2909,plain,
! [SV346: set_nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK63_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 ) )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2876]) ).
thf(2910,plain,
! [SV346: set_nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV182: nat > nat] :
( ( ( member_nat @ ( SV182 @ ( sK63_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2876]) ).
thf(2911,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) ) )
= $true )
| ( ( ( SV194 @ ( sK36_SY959 @ SV350 @ SV194 ) )
= zero_zero_nat )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2879]) ).
thf(2912,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $true )
| ( ( ( SV194 @ ( sK36_SY959 @ SV350 @ SV194 ) )
= zero_zero_nat )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2880]) ).
thf(2913,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) )
| ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK36_SY959 @ SV350 @ SV194 ) @ SV350 )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ ( sK36_SY959 @ SV350 @ SV194 ) )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2882]) ).
thf(2914,plain,
! [SV207: set_nat,SV304: nat > nat,SV373: nat > nat,SV353: nat > nat,SV85: set_nat,SV381: nat] :
( ( ( ~ ~ ( ~ ( member_nat @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) @ SV207 )
| ( ( SV304 @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) ) ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) )
| ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2883]) ).
thf(2915,plain,
! [SV207: set_nat,SV304: nat > nat,SV373: nat > nat,SV353: nat > nat,SV85: set_nat,SV381: nat] :
( ( ( ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 )
= SV381 )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) )
| ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2883]) ).
thf(2916,plain,
! [SV319: set_nat,SV116: set_nat,SV374: nat > nat,SV376: nat > nat,SV363: nat > nat,SV236: nat > nat] :
( ( ( ( SV236 @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
= ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) )
= $false )
| ( ( member_nat @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) @ SV116 )
= $false )
| ( ( ( SV374 @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( SV376 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) )
= $true )
| ( ( member_nat @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) @ SV116 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2884]) ).
thf(2917,plain,
! [SV319: set_nat,SV116: set_nat,SV236: nat > nat,SV374: nat > nat,SV376: nat > nat,SV363: nat > nat] :
( ( ( ~ ( member_nat @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) @ SV116 )
| ( ( SV236 @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
= $true )
| ( ( ( SV374 @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( SV376 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) )
= $true )
| ( ( member_nat @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) @ SV319 )
= $false )
| ( ( ( SV363 @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) )
= ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2885]) ).
thf(2918,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2886]) ).
thf(2919,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2886]) ).
thf(2920,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2887]) ).
thf(2921,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2887]) ).
thf(2922,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2888]) ).
thf(2923,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2888]) ).
thf(2924,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2889]) ).
thf(2925,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2889]) ).
thf(2926,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2890]) ).
thf(2927,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2890]) ).
thf(2928,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2891]) ).
thf(2929,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2891]) ).
thf(2930,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2892]) ).
thf(2931,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2892]) ).
thf(2932,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2893]) ).
thf(2933,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2893]) ).
thf(2934,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2894]) ).
thf(2935,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2894]) ).
thf(2936,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2895]) ).
thf(2937,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2895]) ).
thf(2938,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2896]) ).
thf(2939,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2896]) ).
thf(2940,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2897]) ).
thf(2941,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2897]) ).
thf(2942,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2898]) ).
thf(2943,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2898]) ).
thf(2944,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2899]) ).
thf(2945,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2899]) ).
thf(2946,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2900]) ).
thf(2947,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2900]) ).
thf(2948,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV252 @ SV331 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2901]) ).
thf(2949,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2901]) ).
thf(2950,plain,
! [SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat,SV182: nat > nat,SV346: set_nat] :
( ( ( ! [SY955: nat] :
( ~ ( member_nat @ SY955 @ SV346 )
| ( member_nat @ ( SV182 @ SY955 ) @ SV60 ) ) )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2902]) ).
thf(2951,plain,
! [SV346: set_nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK68_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
| ( member_nat @ ( SV182 @ ( sK68_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 ) )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2903]) ).
thf(2952,plain,
! [SV346: set_nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK69_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
| ( member_nat @ ( SV182 @ ( sK69_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 ) )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2904]) ).
thf(2953,plain,
! [SV346: set_nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK65_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 ) )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2905]) ).
thf(2954,plain,
! [SV346: set_nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV182: nat > nat] :
( ( ( member_nat @ ( SV182 @ ( sK65_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2905]) ).
thf(2955,plain,
! [SV346: set_nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK70_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
| ( member_nat @ ( SV182 @ ( sK70_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 ) )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2906]) ).
thf(2956,plain,
! [SV346: set_nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK66_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 ) )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2907]) ).
thf(2957,plain,
! [SV346: set_nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV182: nat > nat] :
( ( ( member_nat @ ( SV182 @ ( sK66_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2907]) ).
thf(2958,plain,
! [SV346: set_nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK67_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 ) )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2908]) ).
thf(2959,plain,
! [SV346: set_nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV182: nat > nat] :
( ( ( member_nat @ ( SV182 @ ( sK67_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2908]) ).
thf(2960,plain,
! [SV346: set_nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat] :
( ( ( member_nat @ ( sK63_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2909]) ).
thf(2961,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK63_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ( SV288 @ ( SV182 @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2910]) ).
thf(2962,plain,
! [SV350: nat,SV394: nat,SV194: nat > nat] :
( ( ( ~ ( ( ( SV194 @ SV394 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SV394 )
| ~ ( ord_less_eq_nat @ SV394 @ SV350 ) ) )
= $true )
| ( ( ( SV194 @ ( sK36_SY959 @ SV350 @ SV194 ) )
= zero_zero_nat )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2911]) ).
thf(2963,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ~ ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( sK36_SY959 @ SV350 @ SV194 ) @ SV350 )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ ( sK36_SY959 @ SV350 @ SV194 ) )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2913]) ).
thf(2964,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
!= SV350 )
= $false )
| ( ( ord_less_eq_nat @ ( sK36_SY959 @ SV350 @ SV194 ) @ SV350 )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ ( sK36_SY959 @ SV350 @ SV194 ) )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2913]) ).
thf(2965,plain,
! [SV207: set_nat,SV304: nat > nat,SV373: nat > nat,SV353: nat > nat,SV85: set_nat,SV381: nat] :
( ( ( ~ ( ~ ( member_nat @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) @ SV207 )
| ( ( SV304 @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) ) ) )
= $true )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) )
| ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2914]) ).
thf(2966,plain,
! [SV381: nat,SV373: nat > nat,SV353: nat > nat,SV85: set_nat,SV304: nat > nat,SV207: set_nat] :
( ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 )
= SV381 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2915]) ).
thf(2967,plain,
! [SV319: set_nat,SV116: set_nat,SV236: nat > nat,SV376: nat > nat,SV363: nat > nat,SV374: nat > nat] :
( ( ( ( SV374 @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
= ( SV376 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
= $false )
| ( ( member_nat @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) @ SV116 )
= $false )
| ( ( ( SV236 @ ( SV363 @ ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
= ( sK55_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) )
= $true )
| ( ( member_nat @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) @ SV116 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2916]) ).
thf(2968,plain,
! [SV319: set_nat,SV116: set_nat,SV236: nat > nat,SV374: nat > nat,SV376: nat > nat,SV363: nat > nat] :
( ( ( ~ ( member_nat @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) @ SV116 ) )
= $true )
| ( ( ( SV236 @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) )
= $true )
| ( ( ( SV374 @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( SV376 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) )
= $true )
| ( ( member_nat @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) @ SV319 )
= $false )
| ( ( ( SV363 @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) )
= ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2917]) ).
thf(2969,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2918]) ).
thf(2970,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2919]) ).
thf(2971,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2920]) ).
thf(2972,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2921]) ).
thf(2973,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2922]) ).
thf(2974,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2923]) ).
thf(2975,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2924]) ).
thf(2976,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2925]) ).
thf(2977,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2926]) ).
thf(2978,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2927]) ).
thf(2979,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2928]) ).
thf(2980,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2929]) ).
thf(2981,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2930]) ).
thf(2982,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2931]) ).
thf(2983,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2932]) ).
thf(2984,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2933]) ).
thf(2985,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2934]) ).
thf(2986,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2935]) ).
thf(2987,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2936]) ).
thf(2988,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2937]) ).
thf(2989,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2938]) ).
thf(2990,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2939]) ).
thf(2991,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2940]) ).
thf(2992,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2941]) ).
thf(2993,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2942]) ).
thf(2994,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2943]) ).
thf(2995,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2944]) ).
thf(2996,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2945]) ).
thf(2997,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2946]) ).
thf(2998,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2947]) ).
thf(2999,plain,
! [SV134: nat,SV331: nat,SV252: nat] :
( ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2948]) ).
thf(3000,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2949]) ).
thf(3001,plain,
! [SV346: set_nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK71_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
| ( member_nat @ ( SV182 @ ( sK71_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 ) )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2950]) ).
thf(3002,plain,
! [SV346: set_nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK68_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 ) )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2951]) ).
thf(3003,plain,
! [SV346: set_nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV182: nat > nat] :
( ( ( member_nat @ ( SV182 @ ( sK68_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2951]) ).
thf(3004,plain,
! [SV346: set_nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK69_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 ) )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2952]) ).
thf(3005,plain,
! [SV346: set_nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV182: nat > nat] :
( ( ( member_nat @ ( SV182 @ ( sK69_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2952]) ).
thf(3006,plain,
! [SV346: set_nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat] :
( ( ( member_nat @ ( sK65_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2953]) ).
thf(3007,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK65_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ( SV288 @ ( SV182 @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2954]) ).
thf(3008,plain,
! [SV346: set_nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK70_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 ) )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2955]) ).
thf(3009,plain,
! [SV346: set_nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV182: nat > nat] :
( ( ( member_nat @ ( SV182 @ ( sK70_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2955]) ).
thf(3010,plain,
! [SV346: set_nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat] :
( ( ( member_nat @ ( sK66_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2956]) ).
thf(3011,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK66_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ( SV288 @ ( SV182 @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2957]) ).
thf(3012,plain,
! [SV346: set_nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat] :
( ( ( member_nat @ ( sK67_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2958]) ).
thf(3013,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK67_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( member_nat @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2959]) ).
thf(3014,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK63_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2960]) ).
thf(3015,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK63_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ( SV288 @ ( SV182 @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2961]) ).
thf(3016,plain,
! [SV350: nat,SV394: nat,SV194: nat > nat] :
( ( ( ~ ( ( ( SV194 @ SV394 )
!= zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SV394 )
| ~ ( ord_less_eq_nat @ SV394 @ SV350 ) ) )
= $true )
| ( ( ( SV194 @ ( sK36_SY959 @ SV350 @ SV194 ) )
= zero_zero_nat )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2962]) ).
thf(3017,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ! [SY959: nat] :
( ~ ( ( ( SV194 @ SY959 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SY959 )
| ~ ( ord_less_eq_nat @ SY959 @ SV350 ) ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK36_SY959 @ SV350 @ SV194 ) @ SV350 )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ ( sK36_SY959 @ SV350 @ SV194 ) )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2963]) ).
thf(3018,plain,
! [SV350: nat,SV194: nat > nat] :
( ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $true )
| ( ( ord_less_eq_nat @ ( sK36_SY959 @ SV350 @ SV194 ) @ SV350 )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ ( sK36_SY959 @ SV350 @ SV194 ) )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2964]) ).
thf(3019,plain,
! [SV207: set_nat,SV304: nat > nat,SV373: nat > nat,SV353: nat > nat,SV85: set_nat,SV381: nat] :
( ( ( ~ ( member_nat @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) @ SV207 )
| ( ( SV304 @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) )
| ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2965]) ).
thf(3020,plain,
! [SV381: nat,SV373: nat > nat,SV353: nat > nat,SV85: set_nat,SV304: nat > nat,SV207: set_nat] :
( ( ( ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 )
= SV381 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2966]) ).
thf(3021,plain,
! [SV319: set_nat,SV116: set_nat,SV236: nat > nat,SV374: nat > nat,SV376: nat > nat,SV363: nat > nat] :
( ( ( member_nat @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) @ SV116 )
= $false )
| ( ( ( SV236 @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) )
= $true )
| ( ( ( SV374 @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( SV376 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) )
= $true )
| ( ( member_nat @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) @ SV319 )
= $false )
| ( ( ( SV363 @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) )
= ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2968]) ).
thf(3022,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2969]) ).
thf(3023,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2970]) ).
thf(3024,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2971]) ).
thf(3025,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2972]) ).
thf(3026,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2973]) ).
thf(3027,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2974]) ).
thf(3028,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2975]) ).
thf(3029,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2976]) ).
thf(3030,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2977]) ).
thf(3031,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2978]) ).
thf(3032,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2979]) ).
thf(3033,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2980]) ).
thf(3034,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2981]) ).
thf(3035,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2982]) ).
thf(3036,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2983]) ).
thf(3037,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2984]) ).
thf(3038,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2985]) ).
thf(3039,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2986]) ).
thf(3040,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2987]) ).
thf(3041,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2988]) ).
thf(3042,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2989]) ).
thf(3043,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2990]) ).
thf(3044,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2991]) ).
thf(3045,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2992]) ).
thf(3046,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2993]) ).
thf(3047,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2994]) ).
thf(3048,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2995]) ).
thf(3049,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2996]) ).
thf(3050,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2997]) ).
thf(3051,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2998]) ).
thf(3052,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2999]) ).
thf(3053,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 )
| ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3000]) ).
thf(3054,plain,
! [SV346: set_nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat] :
( ( ( ~ ( member_nat @ ( sK71_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 ) )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3001]) ).
thf(3055,plain,
! [SV346: set_nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV182: nat > nat] :
( ( ( member_nat @ ( SV182 @ ( sK71_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3001]) ).
thf(3056,plain,
! [SV346: set_nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat] :
( ( ( member_nat @ ( sK68_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3002]) ).
thf(3057,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK68_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ( SV288 @ ( SV182 @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3003]) ).
thf(3058,plain,
! [SV346: set_nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat] :
( ( ( member_nat @ ( sK69_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3004]) ).
thf(3059,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK69_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( member_nat @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3005]) ).
thf(3060,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK65_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3006]) ).
thf(3061,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK65_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ( SV288 @ ( SV182 @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3007]) ).
thf(3062,plain,
! [SV346: set_nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat] :
( ( ( member_nat @ ( sK70_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3008]) ).
thf(3063,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK70_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( member_nat @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3009]) ).
thf(3064,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK66_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3010]) ).
thf(3065,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK66_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ( SV288 @ ( SV182 @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3011]) ).
thf(3066,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK67_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3012]) ).
thf(3067,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK67_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( member_nat @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3013]) ).
thf(3068,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK63_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3014]) ).
thf(3069,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK72_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
| ( ( SV372 @ ( SV288 @ ( sK72_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK72_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK63_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ( SV288 @ ( SV182 @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3015]) ).
thf(3070,plain,
! [SV350: nat,SV394: nat,SV194: nat > nat] :
( ( ( ( SV194 @ SV394 )
!= zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SV394 )
| ~ ( ord_less_eq_nat @ SV394 @ SV350 ) ) )
= $true )
| ( ( ( SV194 @ ( sK36_SY959 @ SV350 @ SV194 ) )
= zero_zero_nat )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3016]) ).
thf(3071,plain,
! [SV350: nat,SV395: nat,SV194: nat > nat] :
( ( ( ~ ( ( ( SV194 @ SV395 )
!= zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SV395 )
| ~ ( ord_less_eq_nat @ SV395 @ SV350 ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK36_SY959 @ SV350 @ SV194 ) @ SV350 )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ ( sK36_SY959 @ SV350 @ SV194 ) )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3017]) ).
thf(3072,plain,
! [SV207: set_nat,SV304: nat > nat,SV373: nat > nat,SV353: nat > nat,SV85: set_nat,SV381: nat] :
( ( ( ~ ( member_nat @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) @ SV207 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) )
| ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3019]) ).
thf(3073,plain,
! [SV207: set_nat,SV373: nat > nat,SV353: nat > nat,SV85: set_nat,SV381: nat,SV304: nat > nat] :
( ( ( ( SV304 @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) )
!= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) )
| ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3019]) ).
thf(3074,plain,
! [SV207: set_nat,SV304: nat > nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV381: nat] :
( ( ( ~ ( member_nat @ ( sK73_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ ( sK73_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) @ SV85 )
| ( ( SV353 @ ( SV304 @ ( sK73_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
!= ( SV373 @ ( sK73_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 )
= SV381 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3020]) ).
thf(3075,plain,
! [SV319: set_nat,SV116: set_nat,SV374: nat > nat,SV376: nat > nat,SV363: nat > nat,SV236: nat > nat] :
( ( ( ( SV236 @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
= ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) )
= $false )
| ( ( member_nat @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) @ SV116 )
= $false )
| ( ( ( SV374 @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
!= ( SV376 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) )
= $true )
| ( ( member_nat @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) @ SV319 )
= $false )
| ( ( ( SV363 @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) )
= ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3021]) ).
thf(3076,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3022]) ).
thf(3077,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3022]) ).
thf(3078,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3023]) ).
thf(3079,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3023]) ).
thf(3080,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3024]) ).
thf(3081,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3024]) ).
thf(3082,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3025]) ).
thf(3083,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3025]) ).
thf(3084,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3026]) ).
thf(3085,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3026]) ).
thf(3086,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3027]) ).
thf(3087,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3027]) ).
thf(3088,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3028]) ).
thf(3089,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3028]) ).
thf(3090,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3029]) ).
thf(3091,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3029]) ).
thf(3092,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3030]) ).
thf(3093,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3030]) ).
thf(3094,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3031]) ).
thf(3095,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3031]) ).
thf(3096,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3032]) ).
thf(3097,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3032]) ).
thf(3098,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3033]) ).
thf(3099,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3033]) ).
thf(3100,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3034]) ).
thf(3101,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3034]) ).
thf(3102,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3035]) ).
thf(3103,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3035]) ).
thf(3104,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3036]) ).
thf(3105,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3036]) ).
thf(3106,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3037]) ).
thf(3107,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3037]) ).
thf(3108,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3038]) ).
thf(3109,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3038]) ).
thf(3110,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3039]) ).
thf(3111,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3039]) ).
thf(3112,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3040]) ).
thf(3113,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3040]) ).
thf(3114,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3041]) ).
thf(3115,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3041]) ).
thf(3116,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3042]) ).
thf(3117,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3042]) ).
thf(3118,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3043]) ).
thf(3119,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3043]) ).
thf(3120,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3044]) ).
thf(3121,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3044]) ).
thf(3122,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3045]) ).
thf(3123,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3045]) ).
thf(3124,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3046]) ).
thf(3125,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3046]) ).
thf(3126,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3047]) ).
thf(3127,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3047]) ).
thf(3128,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3048]) ).
thf(3129,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3048]) ).
thf(3130,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3049]) ).
thf(3131,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3049]) ).
thf(3132,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3050]) ).
thf(3133,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3050]) ).
thf(3134,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3051]) ).
thf(3135,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3051]) ).
thf(3136,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3052]) ).
thf(3137,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3052]) ).
thf(3138,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV331 @ SV134 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3053]) ).
thf(3139,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV134 @ SV252 ) )
= $false )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3053]) ).
thf(3140,plain,
! [SV346: set_nat,SV182: nat > nat,SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat] :
( ( ( member_nat @ ( sK71_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) )
| ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) ) )
= $true )
| ( ( member_nat @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3054]) ).
thf(3141,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK71_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( member_nat @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3055]) ).
thf(3142,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK68_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3056]) ).
thf(3143,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK68_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ( SV288 @ ( SV182 @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3057]) ).
thf(3144,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK69_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3058]) ).
thf(3145,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK69_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( member_nat @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3059]) ).
thf(3146,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK65_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3060]) ).
thf(3147,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK74_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
| ( ( SV372 @ ( SV288 @ ( sK74_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK74_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK65_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ( SV288 @ ( SV182 @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3061]) ).
thf(3148,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK70_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3062]) ).
thf(3149,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK70_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( member_nat @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3063]) ).
thf(3150,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK66_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3064]) ).
thf(3151,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK75_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
| ( ( SV372 @ ( SV288 @ ( sK75_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK75_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK66_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ( SV288 @ ( SV182 @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3065]) ).
thf(3152,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK67_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3066]) ).
thf(3153,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK76_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
| ( ( SV372 @ ( SV288 @ ( sK76_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK76_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK67_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( member_nat @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3067]) ).
thf(3154,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK77_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
| ( ( SV372 @ ( SV288 @ ( sK77_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK77_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK63_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3068]) ).
thf(3155,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK72_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK63_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ( SV288 @ ( SV182 @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3069]) ).
thf(3156,plain,
! [SV60: set_nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat,SV288: nat > nat,SV372: nat > nat] :
( ( ( ( SV372 @ ( SV288 @ ( sK72_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK72_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK63_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ( SV288 @ ( SV182 @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3069]) ).
thf(3157,plain,
! [SV350: nat,SV394: nat,SV194: nat > nat] :
( ( ( ( SV194 @ SV394 )
= zero_zero_nat )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SV394 )
| ~ ( ord_less_eq_nat @ SV394 @ SV350 ) ) )
= $true )
| ( ( ( SV194 @ ( sK36_SY959 @ SV350 @ SV194 ) )
= zero_zero_nat )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3070]) ).
thf(3158,plain,
! [SV350: nat,SV395: nat,SV194: nat > nat] :
( ( ( ~ ( ( ( SV194 @ SV395 )
!= zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SV395 )
| ~ ( ord_less_eq_nat @ SV395 @ SV350 ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK36_SY959 @ SV350 @ SV194 ) @ SV350 )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ ( sK36_SY959 @ SV350 @ SV194 ) )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3071]) ).
thf(3159,plain,
! [SV207: set_nat,SV304: nat > nat,SV373: nat > nat,SV353: nat > nat,SV85: set_nat,SV381: nat] :
( ( ( member_nat @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) @ SV207 )
= $true )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) )
| ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3072]) ).
thf(3160,plain,
! [SV207: set_nat,SV373: nat > nat,SV353: nat > nat,SV85: set_nat,SV381: nat,SV304: nat > nat] :
( ( ( ( SV304 @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $true )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) )
| ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3073]) ).
thf(3161,plain,
! [SV207: set_nat,SV304: nat > nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV381: nat] :
( ( ( ~ ( member_nat @ ( sK73_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) @ SV207 ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 )
= SV381 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3074]) ).
thf(3162,plain,
! [SV207: set_nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV381: nat,SV304: nat > nat] :
( ( ( ~ ( ~ ( member_nat @ ( SV304 @ ( sK73_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) @ SV85 )
| ( ( SV353 @ ( SV304 @ ( sK73_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
!= ( SV373 @ ( sK73_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 )
= SV381 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3074]) ).
thf(3163,plain,
! [SV319: set_nat,SV116: set_nat,SV236: nat > nat,SV376: nat > nat,SV363: nat > nat,SV374: nat > nat] :
( ( ( ( SV374 @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
= ( SV376 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
= $false )
| ( ( member_nat @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) @ SV116 )
= $false )
| ( ( ( SV236 @ ( SV363 @ ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) ) )
= ( sK58_SY1014 @ SV376 @ SV374 @ SV236 @ SV116 @ SV363 @ SV319 ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV376 @ SV319 )
= ( groups1842438620at_nat @ SV374 @ SV116 ) )
= $true )
| ( ( member_nat @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) @ SV319 )
= $false )
| ( ( ( SV363 @ ( SV236 @ ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) ) )
= ( sK17_SY981 @ SV376 @ SV374 @ SV363 @ SV319 @ SV236 @ SV116 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3075]) ).
thf(3164,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3076]) ).
thf(3165,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3077]) ).
thf(3166,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3078]) ).
thf(3167,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3079]) ).
thf(3168,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3080]) ).
thf(3169,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3081]) ).
thf(3170,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3082]) ).
thf(3171,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3083]) ).
thf(3172,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3084]) ).
thf(3173,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3085]) ).
thf(3174,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3086]) ).
thf(3175,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3087]) ).
thf(3176,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3088]) ).
thf(3177,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3089]) ).
thf(3178,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3090]) ).
thf(3179,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3091]) ).
thf(3180,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3092]) ).
thf(3181,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3093]) ).
thf(3182,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3094]) ).
thf(3183,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3095]) ).
thf(3184,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3096]) ).
thf(3185,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3097]) ).
thf(3186,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3098]) ).
thf(3187,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3099]) ).
thf(3188,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3100]) ).
thf(3189,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3101]) ).
thf(3190,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3102]) ).
thf(3191,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3103]) ).
thf(3192,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3104]) ).
thf(3193,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3105]) ).
thf(3194,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3106]) ).
thf(3195,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3107]) ).
thf(3196,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3108]) ).
thf(3197,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3109]) ).
thf(3198,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3110]) ).
thf(3199,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3111]) ).
thf(3200,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3112]) ).
thf(3201,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3113]) ).
thf(3202,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3114]) ).
thf(3203,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3115]) ).
thf(3204,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3116]) ).
thf(3205,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3117]) ).
thf(3206,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3118]) ).
thf(3207,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3119]) ).
thf(3208,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3120]) ).
thf(3209,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3121]) ).
thf(3210,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3122]) ).
thf(3211,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3123]) ).
thf(3212,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3124]) ).
thf(3213,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3125]) ).
thf(3214,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3126]) ).
thf(3215,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3127]) ).
thf(3216,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3128]) ).
thf(3217,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3129]) ).
thf(3218,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3130]) ).
thf(3219,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3131]) ).
thf(3220,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3132]) ).
thf(3221,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3133]) ).
thf(3222,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3134]) ).
thf(3223,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3135]) ).
thf(3224,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3136]) ).
thf(3225,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3137]) ).
thf(3226,plain,
! [SV252: nat,SV134: nat,SV331: nat] :
( ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3138]) ).
thf(3227,plain,
! [SV331: nat,SV252: nat,SV134: nat] :
( ( ( ord_less_eq_nat @ SV134 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV134 )
= $true )
| ( ( ord_less_eq_nat @ SV331 @ SV252 )
= $true )
| ( ( ord_less_eq_nat @ SV134 @ SV331 )
= $true )
| ( ( ord_less_eq_nat @ SV252 @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3139]) ).
thf(3228,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ~ ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK71_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3140]) ).
thf(3229,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK71_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( member_nat @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3141]) ).
thf(3230,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK68_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3142]) ).
thf(3231,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK78_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
| ( ( SV372 @ ( SV288 @ ( sK78_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK78_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK68_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ( SV288 @ ( SV182 @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3143]) ).
thf(3232,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK69_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3144]) ).
thf(3233,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK79_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
| ( ( SV372 @ ( SV288 @ ( sK79_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK79_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK69_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( member_nat @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3145]) ).
thf(3234,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK80_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
| ( ( SV372 @ ( SV288 @ ( sK80_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK80_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK65_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3146]) ).
thf(3235,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK74_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK65_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ( SV288 @ ( SV182 @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3147]) ).
thf(3236,plain,
! [SV60: set_nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat,SV288: nat > nat,SV372: nat > nat] :
( ( ( ( SV372 @ ( SV288 @ ( sK74_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK74_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK65_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ( SV288 @ ( SV182 @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3147]) ).
thf(3237,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK70_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3148]) ).
thf(3238,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK81_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
| ( ( SV372 @ ( SV288 @ ( sK81_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK81_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK70_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( member_nat @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3149]) ).
thf(3239,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK82_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
| ( ( SV372 @ ( SV288 @ ( sK82_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK82_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK66_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3150]) ).
thf(3240,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK75_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK66_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ( SV288 @ ( SV182 @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3151]) ).
thf(3241,plain,
! [SV60: set_nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat,SV288: nat > nat,SV372: nat > nat] :
( ( ( ( SV372 @ ( SV288 @ ( sK75_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK75_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK66_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ( SV288 @ ( SV182 @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3151]) ).
thf(3242,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK83_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
| ( ( SV372 @ ( SV288 @ ( sK83_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK83_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK67_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3152]) ).
thf(3243,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK76_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK67_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( member_nat @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3153]) ).
thf(3244,plain,
! [SV60: set_nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat,SV288: nat > nat,SV372: nat > nat] :
( ( ( ( SV372 @ ( SV288 @ ( sK76_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK76_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK67_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( member_nat @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3153]) ).
thf(3245,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK77_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK63_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3154]) ).
thf(3246,plain,
! [SV60: set_nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat,SV288: nat > nat,SV372: nat > nat] :
( ( ( ( SV372 @ ( SV288 @ ( sK77_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK77_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK63_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3154]) ).
thf(3247,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( member_nat @ ( sK72_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK63_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ( SV288 @ ( SV182 @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3155]) ).
thf(3248,plain,
! [SV194: nat > nat,SV350: nat,SV394: nat] :
( ( ( ~ ( ord_less_eq_nat @ one_one_nat @ SV394 )
| ~ ( ord_less_eq_nat @ SV394 @ SV350 ) )
= $false )
| ( ( ( SV194 @ SV394 )
= zero_zero_nat )
= $true )
| ( ( ( SV194 @ ( sK36_SY959 @ SV350 @ SV194 ) )
= zero_zero_nat )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3157]) ).
thf(3249,plain,
! [SV350: nat,SV395: nat,SV194: nat > nat] :
( ( ( ( SV194 @ SV395 )
!= zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SV395 )
| ~ ( ord_less_eq_nat @ SV395 @ SV350 ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK36_SY959 @ SV350 @ SV194 ) @ SV350 )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ ( sK36_SY959 @ SV350 @ SV194 ) )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3158]) ).
thf(3250,plain,
! [SV381: nat,SV373: nat > nat,SV353: nat > nat,SV85: set_nat,SV304: nat > nat,SV207: set_nat] :
( ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( member_nat @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) @ SV207 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3159]) ).
thf(3251,plain,
! [SV381: nat,SV373: nat > nat,SV353: nat > nat,SV85: set_nat,SV304: nat > nat,SV207: set_nat] :
( ( ( ~ ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( SV304 @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3160]) ).
thf(3252,plain,
! [SV207: set_nat,SV304: nat > nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV381: nat] :
( ( ( member_nat @ ( sK73_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) @ SV207 )
= $true )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 )
= SV381 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3161]) ).
thf(3253,plain,
! [SV207: set_nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV381: nat,SV304: nat > nat] :
( ( ( ~ ( member_nat @ ( SV304 @ ( sK73_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) @ SV85 )
| ( ( SV353 @ ( SV304 @ ( sK73_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
!= ( SV373 @ ( sK73_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 )
= SV381 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3162]) ).
thf(3254,plain,
! [SV182: nat > nat,SV346: set_nat,SV375: nat > nat,SV288: nat > nat,SV372: nat > nat,SV60: set_nat] :
( ( ( ! [SY1010: nat] :
( ~ ( member_nat @ SY1010 @ SV60 )
| ( ( SV372 @ ( SV288 @ SY1010 ) )
= ( SV375 @ SY1010 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK71_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3228]) ).
thf(3255,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK84_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
| ( ( SV372 @ ( SV288 @ ( sK84_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK84_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK71_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( member_nat @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3229]) ).
thf(3256,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK85_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
| ( ( SV372 @ ( SV288 @ ( sK85_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK85_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK68_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3230]) ).
thf(3257,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK78_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK68_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ( SV288 @ ( SV182 @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3231]) ).
thf(3258,plain,
! [SV60: set_nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat,SV288: nat > nat,SV372: nat > nat] :
( ( ( ( SV372 @ ( SV288 @ ( sK78_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK78_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK68_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ( SV288 @ ( SV182 @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3231]) ).
thf(3259,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK86_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
| ( ( SV372 @ ( SV288 @ ( sK86_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK86_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK69_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3232]) ).
thf(3260,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK79_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK69_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( member_nat @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3233]) ).
thf(3261,plain,
! [SV60: set_nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat,SV288: nat > nat,SV372: nat > nat] :
( ( ( ( SV372 @ ( SV288 @ ( sK79_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK79_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK69_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( member_nat @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3233]) ).
thf(3262,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK80_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK65_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3234]) ).
thf(3263,plain,
! [SV60: set_nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat,SV288: nat > nat,SV372: nat > nat] :
( ( ( ( SV372 @ ( SV288 @ ( sK80_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK80_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK65_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3234]) ).
thf(3264,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( member_nat @ ( sK74_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK65_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ( SV288 @ ( SV182 @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3235]) ).
thf(3265,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK87_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
| ( ( SV372 @ ( SV288 @ ( sK87_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK87_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK70_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3237]) ).
thf(3266,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK81_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK70_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( member_nat @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3238]) ).
thf(3267,plain,
! [SV60: set_nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat,SV288: nat > nat,SV372: nat > nat] :
( ( ( ( SV372 @ ( SV288 @ ( sK81_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK81_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK70_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( member_nat @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3238]) ).
thf(3268,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK82_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK66_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3239]) ).
thf(3269,plain,
! [SV60: set_nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat,SV288: nat > nat,SV372: nat > nat] :
( ( ( ( SV372 @ ( SV288 @ ( sK82_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK82_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK66_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3239]) ).
thf(3270,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( member_nat @ ( sK75_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK66_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ( SV288 @ ( SV182 @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3240]) ).
thf(3271,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK83_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK67_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3242]) ).
thf(3272,plain,
! [SV60: set_nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat,SV288: nat > nat,SV372: nat > nat] :
( ( ( ( SV372 @ ( SV288 @ ( sK83_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK83_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK67_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3242]) ).
thf(3273,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( member_nat @ ( sK76_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK67_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( member_nat @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3243]) ).
thf(3274,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( member_nat @ ( sK77_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK63_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3245]) ).
thf(3275,plain,
! [SV350: nat,SV194: nat > nat,SV394: nat] :
( ( ( ~ ( ord_less_eq_nat @ one_one_nat @ SV394 ) )
= $false )
| ( ( ( SV194 @ SV394 )
= zero_zero_nat )
= $true )
| ( ( ( SV194 @ ( sK36_SY959 @ SV350 @ SV194 ) )
= zero_zero_nat )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3248]) ).
thf(3276,plain,
! [SV194: nat > nat,SV350: nat,SV394: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV394 @ SV350 ) )
= $false )
| ( ( ( SV194 @ SV394 )
= zero_zero_nat )
= $true )
| ( ( ( SV194 @ ( sK36_SY959 @ SV350 @ SV194 ) )
= zero_zero_nat )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3248]) ).
thf(3277,plain,
! [SV350: nat,SV395: nat,SV194: nat > nat] :
( ( ( ( SV194 @ SV395 )
= zero_zero_nat )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ one_one_nat @ SV395 )
| ~ ( ord_less_eq_nat @ SV395 @ SV350 ) ) )
= $true )
| ( ( ord_less_eq_nat @ ( sK36_SY959 @ SV350 @ SV194 ) @ SV350 )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ ( sK36_SY959 @ SV350 @ SV194 ) )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3249]) ).
thf(3278,plain,
! [SV381: nat,SV373: nat > nat,SV353: nat > nat,SV85: set_nat,SV304: nat > nat,SV207: set_nat] :
( ( ( ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( member_nat @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) @ SV207 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3250]) ).
thf(3279,plain,
! [SV381: nat,SV373: nat > nat,SV353: nat > nat,SV85: set_nat,SV304: nat > nat,SV207: set_nat] :
( ( ( ! [SY1002: nat] :
( ~ ( member_nat @ SY1002 @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ SY1002 ) @ SV85 )
| ( ( SV353 @ ( SV304 @ SY1002 ) )
!= ( SV373 @ SY1002 ) ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( SV304 @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3251]) ).
thf(3280,plain,
! [SV207: set_nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV381: nat,SV304: nat > nat] :
( ( ( ~ ( member_nat @ ( SV304 @ ( sK73_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) @ SV85 ) )
= $true )
| ( ( ( SV353 @ ( SV304 @ ( sK73_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
!= ( SV373 @ ( sK73_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 )
= SV381 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3253]) ).
thf(3281,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK88_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
| ( ( SV372 @ ( SV288 @ ( sK88_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK88_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK71_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3254]) ).
thf(3282,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK84_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK71_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( member_nat @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3255]) ).
thf(3283,plain,
! [SV60: set_nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat,SV288: nat > nat,SV372: nat > nat] :
( ( ( ( SV372 @ ( SV288 @ ( sK84_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK84_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK71_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( member_nat @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3255]) ).
thf(3284,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK85_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK68_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3256]) ).
thf(3285,plain,
! [SV60: set_nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat,SV288: nat > nat,SV372: nat > nat] :
( ( ( ( SV372 @ ( SV288 @ ( sK85_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK85_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK68_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3256]) ).
thf(3286,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( member_nat @ ( sK78_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK68_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( ( SV288 @ ( SV182 @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3257]) ).
thf(3287,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK86_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK69_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3259]) ).
thf(3288,plain,
! [SV60: set_nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat,SV288: nat > nat,SV372: nat > nat] :
( ( ( ( SV372 @ ( SV288 @ ( sK86_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK86_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK69_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3259]) ).
thf(3289,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( member_nat @ ( sK79_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK69_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( member_nat @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3260]) ).
thf(3290,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( member_nat @ ( sK80_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK65_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3262]) ).
thf(3291,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK87_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK70_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3265]) ).
thf(3292,plain,
! [SV60: set_nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat,SV288: nat > nat,SV372: nat > nat] :
( ( ( ( SV372 @ ( SV288 @ ( sK87_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK87_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK70_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3265]) ).
thf(3293,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( member_nat @ ( sK81_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK70_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( member_nat @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3266]) ).
thf(3294,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( member_nat @ ( sK82_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK66_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3268]) ).
thf(3295,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( member_nat @ ( sK83_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK67_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK56_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3271]) ).
thf(3296,plain,
! [SV350: nat,SV194: nat > nat,SV394: nat] :
( ( ( ord_less_eq_nat @ one_one_nat @ SV394 )
= $true )
| ( ( ( SV194 @ SV394 )
= zero_zero_nat )
= $true )
| ( ( ( SV194 @ ( sK36_SY959 @ SV350 @ SV194 ) )
= zero_zero_nat )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3275]) ).
thf(3297,plain,
! [SV194: nat > nat,SV350: nat,SV394: nat] :
( ( ( ord_less_eq_nat @ SV394 @ SV350 )
= $true )
| ( ( ( SV194 @ SV394 )
= zero_zero_nat )
= $true )
| ( ( ( SV194 @ ( sK36_SY959 @ SV350 @ SV194 ) )
= zero_zero_nat )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3276]) ).
thf(3298,plain,
! [SV194: nat > nat,SV350: nat,SV395: nat] :
( ( ( ~ ( ord_less_eq_nat @ one_one_nat @ SV395 )
| ~ ( ord_less_eq_nat @ SV395 @ SV350 ) )
= $false )
| ( ( ( SV194 @ SV395 )
= zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ ( sK36_SY959 @ SV350 @ SV194 ) @ SV350 )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ ( sK36_SY959 @ SV350 @ SV194 ) )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3277]) ).
thf(3299,plain,
! [SV207: set_nat,SV304: nat > nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV381: nat] :
( ( ( ~ ( member_nat @ ( sK89_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ ( sK89_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) @ SV85 )
| ( ( SV353 @ ( SV304 @ ( sK89_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
!= ( SV373 @ ( sK89_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( member_nat @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) @ SV207 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3278]) ).
thf(3300,plain,
! [SV207: set_nat,SV304: nat > nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV381: nat] :
( ( ( ~ ( member_nat @ ( sK90_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) @ SV207 )
| ~ ( ~ ( member_nat @ ( SV304 @ ( sK90_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) @ SV85 )
| ( ( SV353 @ ( SV304 @ ( sK90_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
!= ( SV373 @ ( sK90_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( SV304 @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3279]) ).
thf(3301,plain,
! [SV207: set_nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV381: nat,SV304: nat > nat] :
( ( ( member_nat @ ( SV304 @ ( sK73_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) @ SV85 )
= $false )
| ( ( ( SV353 @ ( SV304 @ ( sK73_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
!= ( SV373 @ ( sK73_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 )
= SV381 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3280]) ).
thf(3302,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( ~ ( member_nat @ ( sK88_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK71_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3281]) ).
thf(3303,plain,
! [SV60: set_nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat,SV288: nat > nat,SV372: nat > nat] :
( ( ( ( SV372 @ ( SV288 @ ( sK88_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= ( SV375 @ ( sK88_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK71_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3281]) ).
thf(3304,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( member_nat @ ( sK84_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( SV182 @ ( sK71_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) ) @ SV60 )
= $false )
| ( ( member_nat @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3282]) ).
thf(3305,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( member_nat @ ( sK85_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK68_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( ( SV288 @ ( SV182 @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) ) )
= ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) )
= $false )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3284]) ).
thf(3306,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( member_nat @ ( sK86_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK69_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK59_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( SV288 @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) ) @ SV346 )
= $false )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3287]) ).
thf(3307,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( member_nat @ ( sK87_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK70_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK60_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK51_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( ( SV182 @ ( SV288 @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) ) )
= ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3291]) ).
thf(3308,plain,
! [SV350: nat,SV194: nat > nat,SV395: nat] :
( ( ( ~ ( ord_less_eq_nat @ one_one_nat @ SV395 ) )
= $false )
| ( ( ( SV194 @ SV395 )
= zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ ( sK36_SY959 @ SV350 @ SV194 ) @ SV350 )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ ( sK36_SY959 @ SV350 @ SV194 ) )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3298]) ).
thf(3309,plain,
! [SV194: nat > nat,SV350: nat,SV395: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV395 @ SV350 ) )
= $false )
| ( ( ( SV194 @ SV395 )
= zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ ( sK36_SY959 @ SV350 @ SV194 ) @ SV350 )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ ( sK36_SY959 @ SV350 @ SV194 ) )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3298]) ).
thf(3310,plain,
! [SV207: set_nat,SV304: nat > nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV381: nat] :
( ( ( ~ ( member_nat @ ( sK89_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) @ SV207 ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( member_nat @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) @ SV207 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3299]) ).
thf(3311,plain,
! [SV207: set_nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV381: nat,SV304: nat > nat] :
( ( ( ~ ( ~ ( member_nat @ ( SV304 @ ( sK89_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) @ SV85 )
| ( ( SV353 @ ( SV304 @ ( sK89_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
!= ( SV373 @ ( sK89_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( member_nat @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) @ SV207 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3299]) ).
thf(3312,plain,
! [SV207: set_nat,SV304: nat > nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV381: nat] :
( ( ( ~ ( member_nat @ ( sK90_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) @ SV207 ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( SV304 @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3300]) ).
thf(3313,plain,
! [SV207: set_nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV381: nat,SV304: nat > nat] :
( ( ( ~ ( ~ ( member_nat @ ( SV304 @ ( sK90_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) @ SV85 )
| ( ( SV353 @ ( SV304 @ ( sK90_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
!= ( SV373 @ ( sK90_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) ) ) )
= $false )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( SV304 @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3300]) ).
thf(3314,plain,
! [SV207: set_nat,SV85: set_nat,SV373: nat > nat,SV381: nat,SV304: nat > nat,SV353: nat > nat] :
( ( ( ( SV353 @ ( SV304 @ ( sK73_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
= ( SV373 @ ( sK73_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
= $false )
| ( ( member_nat @ ( SV304 @ ( sK73_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) @ SV85 )
= $false )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 )
= SV381 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3301]) ).
thf(3315,plain,
! [SV60: set_nat,SV372: nat > nat,SV288: nat > nat,SV375: nat > nat,SV346: set_nat,SV182: nat > nat] :
( ( ( member_nat @ ( sK88_SY1010 @ SV182 @ SV346 @ SV375 @ SV288 @ SV372 @ SV60 ) @ SV60 )
= $true )
| ( ( ( groups1842438620at_nat @ SV375 @ SV60 )
= ( groups1842438620at_nat @ SV372 @ SV346 ) )
= $true )
| ( ( member_nat @ ( sK71_SY955 @ SV375 @ SV288 @ SV372 @ SV60 @ SV182 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK61_SY954 @ SV375 @ SV372 @ SV60 @ SV182 @ SV288 @ SV346 ) @ SV346 )
= $true )
| ( ( member_nat @ ( sK54_SY953 @ SV375 @ SV372 @ SV182 @ SV346 @ SV288 @ SV60 ) @ SV60 )
= $true )
| ( ( member_nat @ ( sK15_SY876 @ SV375 @ SV372 @ SV346 @ SV288 @ SV182 @ SV60 ) @ SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3302]) ).
thf(3316,plain,
! [SV350: nat,SV194: nat > nat,SV395: nat] :
( ( ( ord_less_eq_nat @ one_one_nat @ SV395 )
= $true )
| ( ( ( SV194 @ SV395 )
= zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ ( sK36_SY959 @ SV350 @ SV194 ) @ SV350 )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ ( sK36_SY959 @ SV350 @ SV194 ) )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3308]) ).
thf(3317,plain,
! [SV194: nat > nat,SV350: nat,SV395: nat] :
( ( ( ord_less_eq_nat @ SV395 @ SV350 )
= $true )
| ( ( ( SV194 @ SV395 )
= zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ ( sK36_SY959 @ SV350 @ SV194 ) @ SV350 )
= $false )
| ( ( ord_less_eq_nat @ one_one_nat @ ( sK36_SY959 @ SV350 @ SV194 ) )
= $false )
| ( ( ( groups1842438620at_nat
@ ^ [SY750: nat] : ( times_times_nat @ ( SV194 @ SY750 ) @ SY750 )
@ ( set_ord_atMost_nat @ SV350 ) )
= SV350 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3309]) ).
thf(3318,plain,
! [SV207: set_nat,SV304: nat > nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV381: nat] :
( ( ( member_nat @ ( sK89_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) @ SV207 )
= $true )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( member_nat @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) @ SV207 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3310]) ).
thf(3319,plain,
! [SV207: set_nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV381: nat,SV304: nat > nat] :
( ( ( ~ ( member_nat @ ( SV304 @ ( sK89_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) @ SV85 )
| ( ( SV353 @ ( SV304 @ ( sK89_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
!= ( SV373 @ ( sK89_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( member_nat @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) @ SV207 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3311]) ).
thf(3320,plain,
! [SV207: set_nat,SV304: nat > nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV381: nat] :
( ( ( member_nat @ ( sK90_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) @ SV207 )
= $true )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( SV304 @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3312]) ).
thf(3321,plain,
! [SV207: set_nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV381: nat,SV304: nat > nat] :
( ( ( ~ ( member_nat @ ( SV304 @ ( sK90_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) @ SV85 )
| ( ( SV353 @ ( SV304 @ ( sK90_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
!= ( SV373 @ ( sK90_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( SV304 @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3313]) ).
thf(3322,plain,
! [SV207: set_nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV381: nat,SV304: nat > nat] :
( ( ( ~ ( member_nat @ ( SV304 @ ( sK89_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) @ SV85 ) )
= $true )
| ( ( ( SV353 @ ( SV304 @ ( sK89_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
!= ( SV373 @ ( sK89_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( member_nat @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) @ SV207 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3319]) ).
thf(3323,plain,
! [SV207: set_nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV381: nat,SV304: nat > nat] :
( ( ( ~ ( member_nat @ ( SV304 @ ( sK90_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) @ SV85 ) )
= $true )
| ( ( ( SV353 @ ( SV304 @ ( sK90_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
!= ( SV373 @ ( sK90_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( SV304 @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3321]) ).
thf(3324,plain,
! [SV207: set_nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV381: nat,SV304: nat > nat] :
( ( ( member_nat @ ( SV304 @ ( sK89_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) @ SV85 )
= $false )
| ( ( ( SV353 @ ( SV304 @ ( sK89_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
!= ( SV373 @ ( sK89_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( member_nat @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) @ SV207 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3322]) ).
thf(3325,plain,
! [SV207: set_nat,SV85: set_nat,SV353: nat > nat,SV373: nat > nat,SV381: nat,SV304: nat > nat] :
( ( ( member_nat @ ( SV304 @ ( sK90_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) @ SV85 )
= $false )
| ( ( ( SV353 @ ( SV304 @ ( sK90_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
!= ( SV373 @ ( sK90_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
= $true )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( SV304 @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3323]) ).
thf(3326,plain,
! [SV207: set_nat,SV85: set_nat,SV373: nat > nat,SV381: nat,SV304: nat > nat,SV353: nat > nat] :
( ( ( ( SV353 @ ( SV304 @ ( sK89_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
= ( SV373 @ ( sK89_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
= $false )
| ( ( member_nat @ ( SV304 @ ( sK89_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) @ SV85 )
= $false )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( member_nat @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) @ SV207 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3324]) ).
thf(3327,plain,
! [SV207: set_nat,SV85: set_nat,SV373: nat > nat,SV381: nat,SV304: nat > nat,SV353: nat > nat] :
( ( ( ( SV353 @ ( SV304 @ ( sK90_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
= ( SV373 @ ( sK90_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) )
= $false )
| ( ( member_nat @ ( SV304 @ ( sK90_SY1002 @ SV381 @ SV373 @ SV353 @ SV85 @ SV304 @ SV207 ) ) @ SV85 )
= $false )
| ( ( ( groups1842438620at_nat @ SV373 @ SV207 )
= ( groups1842438620at_nat @ SV353 @ SV85 ) )
= $true )
| ( ( ( SV304 @ SV381 )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $false )
| ( ( member_nat @ SV381 @ SV207 )
= $false )
| ( ( ( SV304 @ ( sK64_SY1022 @ SV381 @ SV85 @ SV353 @ SV373 @ SV304 @ SV207 ) )
= ( sK13_SY900 @ SV373 @ SV353 @ SV304 @ SV207 @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3325]) ).
thf(3328,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[498,3327,3326,3320,3318,3317,3316,3315,3314,3307,3306,3305,3304,3303,3297,3296,3295,3294,3293,3292,3290,3289,3288,3286,3285,3283,3274,3273,3272,3270,3269,3267,3264,3263,3261,3258,3252,3247,3246,3244,3241,3236,3227,3226,3225,3224,3223,3222,3221,3220,3219,3218,3217,3216,3215,3214,3213,3212,3211,3210,3209,3208,3207,3206,3205,3204,3203,3202,3201,3200,3199,3198,3197,3196,3195,3194,3193,3192,3191,3190,3189,3188,3187,3186,3185,3184,3183,3182,3181,3180,3179,3178,3177,3176,3175,3174,3173,3172,3171,3170,3169,3168,3167,3166,3165,3164,3163,3156,3018,2967,2912,2881,2878,2877,2868,2849,2848,2832,2814,2811,2809,2808,2807,2803,2776,2775,2767,2765,2764,2763,2760,2755,2754,2747,2746,2733,2728,2727,2723,2722,2721,2715,2708,2707,2706,2705,2703,2702,2701,2687,2684,2682,2679,2674,2672,2670,2663,2650,2637,2630,2627,2625,2620,2613,2612,2605,2600,2599,2594,2591,2582,2581,2580,2577,2576,2575,2574,2568,2567,2566,2565,2562,2558,2556,2555,2552,2551,2546,2545,2541,2540,2538,2535,2531,2530,2527,2526,2522,2520,2517,2516,2515,2514,2513,2511,2506,2503,2502,2497,2495,2493,2492,2491,2490,2489,2484,2482,2474,2465,2461,2460,2459,2451,2449,2445,2442,2435,2432,2425,2424,2423,2422,2421,2420,2417,2416,2412,2411,2410,2403,2402,2397,2396,2385,2384,2379,2348,2333,2331,2330,2328,2326,2325,2323,2321,2320,2319,2318,2317,2316,2315,2314,2313,2312,2311,2310,2308,2292,2280,2270,2264,2261,2256,2250,2248,2245,2237,2236,2235,2234,2227,2221,2213,2207,2201,2199,2197,2196,2195,2194,2192,2190,2189,2187,2185,2184,2183,2182,2180,2178,2177,2175,2173,2172,2167,2165,2161,2160,2148,2138,2111,2110,2107,2101,2099,2067,2062,2056,2054,2052,2051,2045,2039,2037,2035,2034,2028,2022,2015,2014,2011,2008,2007,2002,1999,1998,1995,1976,1973,1953,1950,1949,1940,1939,1928,1920,1919,1914,1913,1902,1888,1879,1878,1877,1876,1875,1874,1873,1872,1871,1870,1869,1868,1860,1854,1846,1824,1821,1798,1781,1770,1764,1763,1762,1761,1760,1756,1755,1754,1753,1752,1751,1750,1749,1745,1744,1743,1742,1741,1740,1739,1738,1737,1736,1735,1734,1701,1698,1686,1682,1677,1670,1666,1662,1661,1655,1654,1651,1648,1646,1639,1624,1623,1620,1619,1617,1611,1609,1550,1530,1515,1509,1502,1493,1490,1487,1486,1468,1463,1458,1409,1407,1390,1387,1386,1380,1375,1372,1371,1367,1357,1346,1334,1329,1328,1327,1325,1319,1317,1313,1285,1274,1270,1266,1261,1258,1251,1242,1228,1219,1205,1179,1177,1174,1170,1168,1165,1163,1152,1147,1142,1136,1123,1106,1105,1098,1088,1065,1056,1050,1048,1045,1040,1039,1037,1036,1034,1030,1029,1026,1025,1024,1020,1016,1014,1012,1005,1001,941,939,907,906,905,904,901,900,898,896,895,889,885,883,879,878,877,875,858,847,829,811,804,794,772,763,757,755,753,752,747,741,738,733,731,730,728,726,725,724,723,718,716,714,713,712,711,710,709,705,702,699,698,697,696,689,549,548]) ).
thf(3329,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[3328]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP133^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.18 % Computer : n018.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Oct 6 11:20:21 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 69.46/14.13 ..
% 69.46/14.13
% 69.46/14.13 No.of.Axioms: 162
% 69.46/14.13
% 69.46/14.13 Length.of.Defs: 0
% 69.46/14.13
% 69.46/14.13 Contains.Choice.Funs: false
% 69.46/14.13 ........................................................................................
% 69.46/14.13
% 69.46/14.13 ********************************
% 69.46/14.13 * All subproblems solved! *
% 69.46/14.13 ********************************
% 69.46/14.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:162,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:3328,loop_count:0,foatp_calls:1,translation:fof_full)
% 69.46/14.13
% 69.46/14.13 %**** Beginning of derivation protocol ****
% 69.46/14.13 % SZS output start CNFRefutation
% See solution above
% 69.46/14.16
% 69.46/14.16 %**** End of derivation protocol ****
% 69.46/14.16 %**** no. of clauses in derivation: 3230 ****
% 69.46/14.16 %**** clause counter: 3328 ****
% 69.46/14.16
% 69.46/14.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:162,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:3328,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------